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Diffstat (limited to 'Build/source/texk/web2c/mplibdir/decNumber.c')
| -rw-r--r-- | Build/source/texk/web2c/mplibdir/decNumber.c | 8141 |
1 files changed, 8141 insertions, 0 deletions
diff --git a/Build/source/texk/web2c/mplibdir/decNumber.c b/Build/source/texk/web2c/mplibdir/decNumber.c new file mode 100644 index 00000000000..19230b89576 --- /dev/null +++ b/Build/source/texk/web2c/mplibdir/decNumber.c @@ -0,0 +1,8141 @@ +/* ------------------------------------------------------------------ */
+/* Decimal Number arithmetic module */
+/* ------------------------------------------------------------------ */
+/* Copyright (c) IBM Corporation, 2000, 2009. All rights reserved. */
+/* */
+/* This software is made available under the terms of the */
+/* ICU License -- ICU 1.8.1 and later. */
+/* */
+/* The description and User's Guide ("The decNumber C Library") for */
+/* this software is called decNumber.pdf. This document is */
+/* available, together with arithmetic and format specifications, */
+/* testcases, and Web links, on the General Decimal Arithmetic page. */
+/* */
+/* Please send comments, suggestions, and corrections to the author: */
+/* mfc@uk.ibm.com */
+/* Mike Cowlishaw, IBM Fellow */
+/* IBM UK, PO Box 31, Birmingham Road, Warwick CV34 5JL, UK */
+/* ------------------------------------------------------------------ */
+/* This module comprises the routines for arbitrary-precision General */
+/* Decimal Arithmetic as defined in the specification which may be */
+/* found on the General Decimal Arithmetic pages. It implements both */
+/* the full ('extended') arithmetic and the simpler ('subset') */
+/* arithmetic. */
+/* */
+/* Usage notes: */
+/* */
+/* 1. This code is ANSI C89 except: */
+/* */
+/* a) C99 line comments (double forward slash) are used. (Most C */
+/* compilers accept these. If yours does not, a simple script */
+/* can be used to convert them to ANSI C comments.) */
+/* */
+/* b) Types from C99 stdint.h are used. If you do not have this */
+/* header file, see the User's Guide section of the decNumber */
+/* documentation; this lists the necessary definitions. */
+/* */
+/* c) If DECDPUN>4 or DECUSE64=1, the C99 64-bit int64_t and */
+/* uint64_t types may be used. To avoid these, set DECUSE64=0 */
+/* and DECDPUN<=4 (see documentation). */
+/* */
+/* The code also conforms to C99 restrictions; in particular, */
+/* strict aliasing rules are observed. */
+/* */
+/* 2. The decNumber format which this library uses is optimized for */
+/* efficient processing of relatively short numbers; in particular */
+/* it allows the use of fixed sized structures and minimizes copy */
+/* and move operations. It does, however, support arbitrary */
+/* precision (up to 999,999,999 digits) and arbitrary exponent */
+/* range (Emax in the range 0 through 999,999,999 and Emin in the */
+/* range -999,999,999 through 0). Mathematical functions (for */
+/* example decNumberExp) as identified below are restricted more */
+/* tightly: digits, emax, and -emin in the context must be <= */
+/* DEC_MAX_MATH (999999), and their operand(s) must be within */
+/* these bounds. */
+/* */
+/* 3. Logical functions are further restricted; their operands must */
+/* be finite, positive, have an exponent of zero, and all digits */
+/* must be either 0 or 1. The result will only contain digits */
+/* which are 0 or 1 (and will have exponent=0 and a sign of 0). */
+/* */
+/* 4. Operands to operator functions are never modified unless they */
+/* are also specified to be the result number (which is always */
+/* permitted). Other than that case, operands must not overlap. */
+/* */
+/* 5. Error handling: the type of the error is ORed into the status */
+/* flags in the current context (decContext structure). The */
+/* SIGFPE signal is then raised if the corresponding trap-enabler */
+/* flag in the decContext is set (is 1). */
+/* */
+/* It is the responsibility of the caller to clear the status */
+/* flags as required. */
+/* */
+/* The result of any routine which returns a number will always */
+/* be a valid number (which may be a special value, such as an */
+/* Infinity or NaN). */
+/* */
+/* 6. The decNumber format is not an exchangeable concrete */
+/* representation as it comprises fields which may be machine- */
+/* dependent (packed or unpacked, or special length, for example). */
+/* Canonical conversions to and from strings are provided; other */
+/* conversions are available in separate modules. */
+/* */
+/* 7. Normally, input operands are assumed to be valid. Set DECCHECK */
+/* to 1 for extended operand checking (including NULL operands). */
+/* Results are undefined if a badly-formed structure (or a NULL */
+/* pointer to a structure) is provided, though with DECCHECK */
+/* enabled the operator routines are protected against exceptions. */
+/* (Except if the result pointer is NULL, which is unrecoverable.) */
+/* */
+/* However, the routines will never cause exceptions if they are */
+/* given well-formed operands, even if the value of the operands */
+/* is inappropriate for the operation and DECCHECK is not set. */
+/* (Except for SIGFPE, as and where documented.) */
+/* */
+/* 8. Subset arithmetic is available only if DECSUBSET is set to 1. */
+/* ------------------------------------------------------------------ */
+/* Implementation notes for maintenance of this module: */
+/* */
+/* 1. Storage leak protection: Routines which use malloc are not */
+/* permitted to use return for fastpath or error exits (i.e., */
+/* they follow strict structured programming conventions). */
+/* Instead they have a do{}while(0); construct surrounding the */
+/* code which is protected -- break may be used to exit this. */
+/* Other routines can safely use the return statement inline. */
+/* */
+/* Storage leak accounting can be enabled using DECALLOC. */
+/* */
+/* 2. All loops use the for(;;) construct. Any do construct does */
+/* not loop; it is for allocation protection as just described. */
+/* */
+/* 3. Setting status in the context must always be the very last */
+/* action in a routine, as non-0 status may raise a trap and hence */
+/* the call to set status may not return (if the handler uses long */
+/* jump). Therefore all cleanup must be done first. In general, */
+/* to achieve this status is accumulated and is only applied just */
+/* before return by calling decContextSetStatus (via decStatus). */
+/* */
+/* Routines which allocate storage cannot, in general, use the */
+/* 'top level' routines which could cause a non-returning */
+/* transfer of control. The decXxxxOp routines are safe (do not */
+/* call decStatus even if traps are set in the context) and should */
+/* be used instead (they are also a little faster). */
+/* */
+/* 4. Exponent checking is minimized by allowing the exponent to */
+/* grow outside its limits during calculations, provided that */
+/* the decFinalize function is called later. Multiplication and */
+/* division, and intermediate calculations in exponentiation, */
+/* require more careful checks because of the risk of 31-bit */
+/* overflow (the most negative valid exponent is -1999999997, for */
+/* a 999999999-digit number with adjusted exponent of -999999999). */
+/* */
+/* 5. Rounding is deferred until finalization of results, with any */
+/* 'off to the right' data being represented as a single digit */
+/* residue (in the range -1 through 9). This avoids any double- */
+/* rounding when more than one shortening takes place (for */
+/* example, when a result is subnormal). */
+/* */
+/* 6. The digits count is allowed to rise to a multiple of DECDPUN */
+/* during many operations, so whole Units are handled and exact */
+/* accounting of digits is not needed. The correct digits value */
+/* is found by decGetDigits, which accounts for leading zeros. */
+/* This must be called before any rounding if the number of digits */
+/* is not known exactly. */
+/* */
+/* 7. The multiply-by-reciprocal 'trick' is used for partitioning */
+/* numbers up to four digits, using appropriate constants. This */
+/* is not useful for longer numbers because overflow of 32 bits */
+/* would lead to 4 multiplies, which is almost as expensive as */
+/* a divide (unless a floating-point or 64-bit multiply is */
+/* assumed to be available). */
+/* */
+/* 8. Unusual abbreviations that may be used in the commentary: */
+/* lhs -- left hand side (operand, of an operation) */
+/* lsd -- least significant digit (of coefficient) */
+/* lsu -- least significant Unit (of coefficient) */
+/* msd -- most significant digit (of coefficient) */
+/* msi -- most significant item (in an array) */
+/* msu -- most significant Unit (of coefficient) */
+/* rhs -- right hand side (operand, of an operation) */
+/* +ve -- positive */
+/* -ve -- negative */
+/* ** -- raise to the power */
+/* ------------------------------------------------------------------ */
+
+#include <stdlib.h> // for malloc, free, etc.
+#include <stdio.h> // for printf [if needed]
+#include <string.h> // for strcpy
+#include <ctype.h> // for lower
+#include "decNumber.h" // base number library
+#include "decNumberLocal.h" // decNumber local types, etc.
+
+/* Constants */
+// Public lookup table used by the D2U macro
+const uByte d2utable[DECMAXD2U+1]=D2UTABLE;
+
+#define DECVERB 1 // set to 1 for verbose DECCHECK
+#define powers DECPOWERS // old internal name
+
+// Local constants
+#define DIVIDE 0x80 // Divide operators
+#define REMAINDER 0x40 // ..
+#define DIVIDEINT 0x20 // ..
+#define REMNEAR 0x10 // ..
+#define COMPARE 0x01 // Compare operators
+#define COMPMAX 0x02 // ..
+#define COMPMIN 0x03 // ..
+#define COMPTOTAL 0x04 // ..
+#define COMPNAN 0x05 // .. [NaN processing]
+#define COMPSIG 0x06 // .. [signaling COMPARE]
+#define COMPMAXMAG 0x07 // ..
+#define COMPMINMAG 0x08 // ..
+
+#define DEC_sNaN 0x40000000 // local status: sNaN signal
+#define BADINT (Int)0x80000000 // most-negative Int; error indicator
+// Next two indicate an integer >= 10**6, and its parity (bottom bit)
+#define BIGEVEN (Int)0x80000002
+#define BIGODD (Int)0x80000003
+
+static Unit uarrone[1]={1}; // Unit array of 1, used for incrementing
+
+/* Granularity-dependent code */
+#if DECDPUN<=4
+ #define eInt Int // extended integer
+ #define ueInt uInt // unsigned extended integer
+ // Constant multipliers for divide-by-power-of five using reciprocal
+ // multiply, after removing powers of 2 by shifting, and final shift
+ // of 17 [we only need up to **4]
+ static const uInt multies[]={131073, 26215, 5243, 1049, 210};
+ // QUOT10 -- macro to return the quotient of unit u divided by 10**n
+ #define QUOT10(u, n) ((((uInt)(u)>>(n))*multies[n])>>17)
+#else
+ // For DECDPUN>4 non-ANSI-89 64-bit types are needed.
+ #if !DECUSE64
+ #error decNumber.c: DECUSE64 must be 1 when DECDPUN>4
+ #endif
+ #define eInt Long // extended integer
+ #define ueInt uLong // unsigned extended integer
+#endif
+
+/* Local routines */
+static decNumber * decAddOp(decNumber *, const decNumber *, const decNumber *,
+ decContext *, uByte, uInt *);
+static Flag decBiStr(const char *, const char *, const char *);
+static uInt decCheckMath(const decNumber *, decContext *, uInt *);
+static void decApplyRound(decNumber *, decContext *, Int, uInt *);
+static Int decCompare(const decNumber *lhs, const decNumber *rhs, Flag);
+static decNumber * decCompareOp(decNumber *, const decNumber *,
+ const decNumber *, decContext *,
+ Flag, uInt *);
+static void decCopyFit(decNumber *, const decNumber *, decContext *,
+ Int *, uInt *);
+static decNumber * decDecap(decNumber *, Int);
+static decNumber * decDivideOp(decNumber *, const decNumber *,
+ const decNumber *, decContext *, Flag, uInt *);
+static decNumber * decExpOp(decNumber *, const decNumber *,
+ decContext *, uInt *);
+static void decFinalize(decNumber *, decContext *, Int *, uInt *);
+static Int decGetDigits(Unit *, Int);
+static Int decGetInt(const decNumber *);
+static decNumber * decLnOp(decNumber *, const decNumber *,
+ decContext *, uInt *);
+static decNumber * decMultiplyOp(decNumber *, const decNumber *,
+ const decNumber *, decContext *,
+ uInt *);
+static decNumber * decNaNs(decNumber *, const decNumber *,
+ const decNumber *, decContext *, uInt *);
+static decNumber * decQuantizeOp(decNumber *, const decNumber *,
+ const decNumber *, decContext *, Flag,
+ uInt *);
+static void decReverse(Unit *, Unit *);
+static void decSetCoeff(decNumber *, decContext *, const Unit *,
+ Int, Int *, uInt *);
+static void decSetMaxValue(decNumber *, decContext *);
+static void decSetOverflow(decNumber *, decContext *, uInt *);
+static void decSetSubnormal(decNumber *, decContext *, Int *, uInt *);
+static Int decShiftToLeast(Unit *, Int, Int);
+static Int decShiftToMost(Unit *, Int, Int);
+static void decStatus(decNumber *, uInt, decContext *);
+static void decToString(const decNumber *, char[], Flag);
+static decNumber * decTrim(decNumber *, decContext *, Flag, Flag, Int *);
+static Int decUnitAddSub(const Unit *, Int, const Unit *, Int, Int,
+ Unit *, Int);
+static Int decUnitCompare(const Unit *, Int, const Unit *, Int, Int);
+
+#if !DECSUBSET
+/* decFinish == decFinalize when no subset arithmetic needed */
+#define decFinish(a,b,c,d) decFinalize(a,b,c,d)
+#else
+static void decFinish(decNumber *, decContext *, Int *, uInt *);
+static decNumber * decRoundOperand(const decNumber *, decContext *, uInt *);
+#endif
+
+/* Local macros */
+// masked special-values bits
+#define SPECIALARG (rhs->bits & DECSPECIAL)
+#define SPECIALARGS ((lhs->bits | rhs->bits) & DECSPECIAL)
+
+/* Diagnostic macros, etc. */
+#if DECALLOC
+// Handle malloc/free accounting. If enabled, our accountable routines
+// are used; otherwise the code just goes straight to the system malloc
+// and free routines.
+#define malloc(a) decMalloc(a)
+#define free(a) decFree(a)
+#define DECFENCE 0x5a // corruption detector
+// 'Our' malloc and free:
+static void *decMalloc(size_t);
+static void decFree(void *);
+uInt decAllocBytes=0; // count of bytes allocated
+// Note that DECALLOC code only checks for storage buffer overflow.
+// To check for memory leaks, the decAllocBytes variable must be
+// checked to be 0 at appropriate times (e.g., after the test
+// harness completes a set of tests). This checking may be unreliable
+// if the testing is done in a multi-thread environment.
+#endif
+
+#if DECCHECK
+// Optional checking routines. Enabling these means that decNumber
+// and decContext operands to operator routines are checked for
+// correctness. This roughly doubles the execution time of the
+// fastest routines (and adds 600+ bytes), so should not normally be
+// used in 'production'.
+// decCheckInexact is used to check that inexact results have a full
+// complement of digits (where appropriate -- this is not the case
+// for Quantize, for example)
+#define DECUNRESU ((decNumber *)(void *)0xffffffff)
+#define DECUNUSED ((const decNumber *)(void *)0xffffffff)
+#define DECUNCONT ((decContext *)(void *)(0xffffffff))
+static Flag decCheckOperands(decNumber *, const decNumber *,
+ const decNumber *, decContext *);
+static Flag decCheckNumber(const decNumber *);
+static void decCheckInexact(const decNumber *, decContext *);
+#endif
+
+#if DECTRACE || DECCHECK
+// Optional trace/debugging routines (may or may not be used)
+void decNumberShow(const decNumber *); // displays the components of a number
+static void decDumpAr(char, const Unit *, Int);
+#endif
+
+/* ================================================================== */
+/* Conversions */
+/* ================================================================== */
+
+/* ------------------------------------------------------------------ */
+/* from-int32 -- conversion from Int or uInt */
+/* */
+/* dn is the decNumber to receive the integer */
+/* in or uin is the integer to be converted */
+/* returns dn */
+/* */
+/* No error is possible. */
+/* ------------------------------------------------------------------ */
+decNumber * decNumberFromInt32(decNumber *dn, Int in) {
+ uInt unsig;
+ if (in>=0) unsig=in;
+ else { // negative (possibly BADINT)
+ if (in==BADINT) unsig=(uInt)1073741824*2; // special case
+ else unsig=-in; // invert
+ }
+ // in is now positive
+ decNumberFromUInt32(dn, unsig);
+ if (in<0) dn->bits=DECNEG; // sign needed
+ return dn;
+ } // decNumberFromInt32
+
+decNumber * decNumberFromUInt32(decNumber *dn, uInt uin) {
+ Unit *up; // work pointer
+ decNumberZero(dn); // clean
+ if (uin==0) return dn; // [or decGetDigits bad call]
+ for (up=dn->lsu; uin>0; up++) {
+ *up=(Unit)(uin%(DECDPUNMAX+1));
+ uin=uin/(DECDPUNMAX+1);
+ }
+ dn->digits=decGetDigits(dn->lsu, up-dn->lsu);
+ return dn;
+ } // decNumberFromUInt32
+
+/* ------------------------------------------------------------------ */
+/* to-int32 -- conversion to Int or uInt */
+/* */
+/* dn is the decNumber to convert */
+/* set is the context for reporting errors */
+/* returns the converted decNumber, or 0 if Invalid is set */
+/* */
+/* Invalid is set if the decNumber does not have exponent==0 or if */
+/* it is a NaN, Infinite, or out-of-range. */
+/* ------------------------------------------------------------------ */
+Int decNumberToInt32(const decNumber *dn, decContext *set) {
+ #if DECCHECK
+ if (decCheckOperands(DECUNRESU, DECUNUSED, dn, set)) return 0;
+ #endif
+
+ // special or too many digits, or bad exponent
+ if (dn->bits&DECSPECIAL || dn->digits>10 || dn->exponent!=0) ; // bad
+ else { // is a finite integer with 10 or fewer digits
+ Int d; // work
+ const Unit *up; // ..
+ uInt hi=0, lo; // ..
+ up=dn->lsu; // -> lsu
+ lo=*up; // get 1 to 9 digits
+ #if DECDPUN>1 // split to higher
+ hi=lo/10;
+ lo=lo%10;
+ #endif
+ up++;
+ // collect remaining Units, if any, into hi
+ for (d=DECDPUN; d<dn->digits; up++, d+=DECDPUN) hi+=*up*powers[d-1];
+ // now low has the lsd, hi the remainder
+ if (hi>214748364 || (hi==214748364 && lo>7)) { // out of range?
+ // most-negative is a reprieve
+ if (dn->bits&DECNEG && hi==214748364 && lo==8) return 0x80000000;
+ // bad -- drop through
+ }
+ else { // in-range always
+ Int i=X10(hi)+lo;
+ if (dn->bits&DECNEG) return -i;
+ return i;
+ }
+ } // integer
+ decContextSetStatus(set, DEC_Invalid_operation); // [may not return]
+ return 0;
+ } // decNumberToInt32
+
+uInt decNumberToUInt32(const decNumber *dn, decContext *set) {
+ #if DECCHECK
+ if (decCheckOperands(DECUNRESU, DECUNUSED, dn, set)) return 0;
+ #endif
+ // special or too many digits, or bad exponent, or negative (<0)
+ if (dn->bits&DECSPECIAL || dn->digits>10 || dn->exponent!=0
+ || (dn->bits&DECNEG && !ISZERO(dn))); // bad
+ else { // is a finite integer with 10 or fewer digits
+ Int d; // work
+ const Unit *up; // ..
+ uInt hi=0, lo; // ..
+ up=dn->lsu; // -> lsu
+ lo=*up; // get 1 to 9 digits
+ #if DECDPUN>1 // split to higher
+ hi=lo/10;
+ lo=lo%10;
+ #endif
+ up++;
+ // collect remaining Units, if any, into hi
+ for (d=DECDPUN; d<dn->digits; up++, d+=DECDPUN) hi+=*up*powers[d-1];
+
+ // now low has the lsd, hi the remainder
+ if (hi>429496729 || (hi==429496729 && lo>5)) ; // no reprieve possible
+ else return X10(hi)+lo;
+ } // integer
+ decContextSetStatus(set, DEC_Invalid_operation); // [may not return]
+ return 0;
+ } // decNumberToUInt32
+
+/* ------------------------------------------------------------------ */
+/* to-scientific-string -- conversion to numeric string */
+/* to-engineering-string -- conversion to numeric string */
+/* */
+/* decNumberToString(dn, string); */
+/* decNumberToEngString(dn, string); */
+/* */
+/* dn is the decNumber to convert */
+/* string is the string where the result will be laid out */
+/* */
+/* string must be at least dn->digits+14 characters long */
+/* */
+/* No error is possible, and no status can be set. */
+/* ------------------------------------------------------------------ */
+char * decNumberToString(const decNumber *dn, char *string){
+ decToString(dn, string, 0);
+ return string;
+ } // DecNumberToString
+
+char * decNumberToEngString(const decNumber *dn, char *string){
+ decToString(dn, string, 1);
+ return string;
+ } // DecNumberToEngString
+
+/* ------------------------------------------------------------------ */
+/* to-number -- conversion from numeric string */
+/* */
+/* decNumberFromString -- convert string to decNumber */
+/* dn -- the number structure to fill */
+/* chars[] -- the string to convert ('\0' terminated) */
+/* set -- the context used for processing any error, */
+/* determining the maximum precision available */
+/* (set.digits), determining the maximum and minimum */
+/* exponent (set.emax and set.emin), determining if */
+/* extended values are allowed, and checking the */
+/* rounding mode if overflow occurs or rounding is */
+/* needed. */
+/* */
+/* The length of the coefficient and the size of the exponent are */
+/* checked by this routine, so the correct error (Underflow or */
+/* Overflow) can be reported or rounding applied, as necessary. */
+/* */
+/* If bad syntax is detected, the result will be a quiet NaN. */
+/* ------------------------------------------------------------------ */
+decNumber * decNumberFromString(decNumber *dn, const char chars[],
+ decContext *set) {
+ Int exponent=0; // working exponent [assume 0]
+ uByte bits=0; // working flags [assume +ve]
+ Unit *res; // where result will be built
+ Unit resbuff[SD2U(DECBUFFER+9)];// local buffer in case need temporary
+ // [+9 allows for ln() constants]
+ Unit *allocres=NULL; // -> allocated result, iff allocated
+ Int d=0; // count of digits found in decimal part
+ const char *dotchar=NULL; // where dot was found
+ const char *cfirst=chars; // -> first character of decimal part
+ const char *last=NULL; // -> last digit of decimal part
+ const char *c; // work
+ Unit *up; // ..
+ #if DECDPUN>1
+ Int cut, out; // ..
+ #endif
+ Int residue; // rounding residue
+ uInt status=0; // error code
+
+ #if DECCHECK
+ if (decCheckOperands(DECUNRESU, DECUNUSED, DECUNUSED, set))
+ return decNumberZero(dn);
+ #endif
+
+ do { // status & malloc protection
+ for (c=chars;; c++) { // -> input character
+ if (*c>='0' && *c<='9') { // test for Arabic digit
+ last=c;
+ d++; // count of real digits
+ continue; // still in decimal part
+ }
+ if (*c=='.' && dotchar==NULL) { // first '.'
+ dotchar=c; // record offset into decimal part
+ if (c==cfirst) cfirst++; // first digit must follow
+ continue;}
+ if (c==chars) { // first in string...
+ if (*c=='-') { // valid - sign
+ cfirst++;
+ bits=DECNEG;
+ continue;}
+ if (*c=='+') { // valid + sign
+ cfirst++;
+ continue;}
+ }
+ // *c is not a digit, or a valid +, -, or '.'
+ break;
+ } // c
+
+ if (last==NULL) { // no digits yet
+ status=DEC_Conversion_syntax;// assume the worst
+ if (*c=='\0') break; // and no more to come...
+ #if DECSUBSET
+ // if subset then infinities and NaNs are not allowed
+ if (!set->extended) break; // hopeless
+ #endif
+ // Infinities and NaNs are possible, here
+ if (dotchar!=NULL) break; // .. unless had a dot
+ decNumberZero(dn); // be optimistic
+ if (decBiStr(c, "infinity", "INFINITY")
+ || decBiStr(c, "inf", "INF")) {
+ dn->bits=bits | DECINF;
+ status=0; // is OK
+ break; // all done
+ }
+ // a NaN expected
+ // 2003.09.10 NaNs are now permitted to have a sign
+ dn->bits=bits | DECNAN; // assume simple NaN
+ if (*c=='s' || *c=='S') { // looks like an sNaN
+ c++;
+ dn->bits=bits | DECSNAN;
+ }
+ if (*c!='n' && *c!='N') break; // check caseless "NaN"
+ c++;
+ if (*c!='a' && *c!='A') break; // ..
+ c++;
+ if (*c!='n' && *c!='N') break; // ..
+ c++;
+ // now either nothing, or nnnn payload, expected
+ // -> start of integer and skip leading 0s [including plain 0]
+ for (cfirst=c; *cfirst=='0';) cfirst++;
+ if (*cfirst=='\0') { // "NaN" or "sNaN", maybe with all 0s
+ status=0; // it's good
+ break; // ..
+ }
+ // something other than 0s; setup last and d as usual [no dots]
+ for (c=cfirst;; c++, d++) {
+ if (*c<'0' || *c>'9') break; // test for Arabic digit
+ last=c;
+ }
+ if (*c!='\0') break; // not all digits
+ if (d>set->digits-1) {
+ // [NB: payload in a decNumber can be full length unless
+ // clamped, in which case can only be digits-1]
+ if (set->clamp) break;
+ if (d>set->digits) break;
+ } // too many digits?
+ // good; drop through to convert the integer to coefficient
+ status=0; // syntax is OK
+ bits=dn->bits; // for copy-back
+ } // last==NULL
+
+ else if (*c!='\0') { // more to process...
+ // had some digits; exponent is only valid sequence now
+ Flag nege; // 1=negative exponent
+ const char *firstexp; // -> first significant exponent digit
+ status=DEC_Conversion_syntax;// assume the worst
+ if (*c!='e' && *c!='E') break;
+ /* Found 'e' or 'E' -- now process explicit exponent */
+ // 1998.07.11: sign no longer required
+ nege=0;
+ c++; // to (possible) sign
+ if (*c=='-') {nege=1; c++;}
+ else if (*c=='+') c++;
+ if (*c=='\0') break;
+
+ for (; *c=='0' && *(c+1)!='\0';) c++; // strip insignificant zeros
+ firstexp=c; // save exponent digit place
+ for (; ;c++) {
+ if (*c<'0' || *c>'9') break; // not a digit
+ exponent=X10(exponent)+(Int)*c-(Int)'0';
+ } // c
+ // if not now on a '\0', *c must not be a digit
+ if (*c!='\0') break;
+
+ // (this next test must be after the syntax checks)
+ // if it was too long the exponent may have wrapped, so check
+ // carefully and set it to a certain overflow if wrap possible
+ if (c>=firstexp+9+1) {
+ if (c>firstexp+9+1 || *firstexp>'1') exponent=DECNUMMAXE*2;
+ // [up to 1999999999 is OK, for example 1E-1000000998]
+ }
+ if (nege) exponent=-exponent; // was negative
+ status=0; // is OK
+ } // stuff after digits
+
+ // Here when whole string has been inspected; syntax is good
+ // cfirst->first digit (never dot), last->last digit (ditto)
+
+ // strip leading zeros/dot [leave final 0 if all 0's]
+ if (*cfirst=='0') { // [cfirst has stepped over .]
+ for (c=cfirst; c<last; c++, cfirst++) {
+ if (*c=='.') continue; // ignore dots
+ if (*c!='0') break; // non-zero found
+ d--; // 0 stripped
+ } // c
+ #if DECSUBSET
+ // make a rapid exit for easy zeros if !extended
+ if (*cfirst=='0' && !set->extended) {
+ decNumberZero(dn); // clean result
+ break; // [could be return]
+ }
+ #endif
+ } // at least one leading 0
+
+ // Handle decimal point...
+ if (dotchar!=NULL && dotchar<last) // non-trailing '.' found?
+ exponent-=(last-dotchar); // adjust exponent
+ // [we can now ignore the .]
+
+ // OK, the digits string is good. Assemble in the decNumber, or in
+ // a temporary units array if rounding is needed
+ if (d<=set->digits) res=dn->lsu; // fits into supplied decNumber
+ else { // rounding needed
+ Int needbytes=D2U(d)*sizeof(Unit);// bytes needed
+ res=resbuff; // assume use local buffer
+ if (needbytes>(Int)sizeof(resbuff)) { // too big for local
+ allocres=(Unit *)malloc(needbytes);
+ if (allocres==NULL) {status|=DEC_Insufficient_storage; break;}
+ res=allocres;
+ }
+ }
+ // res now -> number lsu, buffer, or allocated storage for Unit array
+
+ // Place the coefficient into the selected Unit array
+ // [this is often 70% of the cost of this function when DECDPUN>1]
+ #if DECDPUN>1
+ out=0; // accumulator
+ up=res+D2U(d)-1; // -> msu
+ cut=d-(up-res)*DECDPUN; // digits in top unit
+ for (c=cfirst;; c++) { // along the digits
+ if (*c=='.') continue; // ignore '.' [don't decrement cut]
+ out=X10(out)+(Int)*c-(Int)'0';
+ if (c==last) break; // done [never get to trailing '.']
+ cut--;
+ if (cut>0) continue; // more for this unit
+ *up=(Unit)out; // write unit
+ up--; // prepare for unit below..
+ cut=DECDPUN; // ..
+ out=0; // ..
+ } // c
+ *up=(Unit)out; // write lsu
+
+ #else
+ // DECDPUN==1
+ up=res; // -> lsu
+ for (c=last; c>=cfirst; c--) { // over each character, from least
+ if (*c=='.') continue; // ignore . [don't step up]
+ *up=(Unit)((Int)*c-(Int)'0');
+ up++;
+ } // c
+ #endif
+
+ dn->bits=bits;
+ dn->exponent=exponent;
+ dn->digits=d;
+
+ // if not in number (too long) shorten into the number
+ if (d>set->digits) {
+ residue=0;
+ decSetCoeff(dn, set, res, d, &residue, &status);
+ // always check for overflow or subnormal and round as needed
+ decFinalize(dn, set, &residue, &status);
+ }
+ else { // no rounding, but may still have overflow or subnormal
+ // [these tests are just for performance; finalize repeats them]
+ if ((dn->exponent-1<set->emin-dn->digits)
+ || (dn->exponent-1>set->emax-set->digits)) {
+ residue=0;
+ decFinalize(dn, set, &residue, &status);
+ }
+ }
+ // decNumberShow(dn);
+ } while(0); // [for break]
+
+ if (allocres!=NULL) free(allocres); // drop any storage used
+ if (status!=0) decStatus(dn, status, set);
+ return dn;
+ } /* decNumberFromString */
+
+/* ================================================================== */
+/* Operators */
+/* ================================================================== */
+
+/* ------------------------------------------------------------------ */
+/* decNumberAbs -- absolute value operator */
+/* */
+/* This computes C = abs(A) */
+/* */
+/* res is C, the result. C may be A */
+/* rhs is A */
+/* set is the context */
+/* */
+/* See also decNumberCopyAbs for a quiet bitwise version of this. */
+/* C must have space for set->digits digits. */
+/* ------------------------------------------------------------------ */
+/* This has the same effect as decNumberPlus unless A is negative, */
+/* in which case it has the same effect as decNumberMinus. */
+/* ------------------------------------------------------------------ */
+decNumber * decNumberAbs(decNumber *res, const decNumber *rhs,
+ decContext *set) {
+ decNumber dzero; // for 0
+ uInt status=0; // accumulator
+
+ #if DECCHECK
+ if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
+ #endif
+
+ decNumberZero(&dzero); // set 0
+ dzero.exponent=rhs->exponent; // [no coefficient expansion]
+ decAddOp(res, &dzero, rhs, set, (uByte)(rhs->bits & DECNEG), &status);
+ if (status!=0) decStatus(res, status, set);
+ #if DECCHECK
+ decCheckInexact(res, set);
+ #endif
+ return res;
+ } // decNumberAbs
+
+/* ------------------------------------------------------------------ */
+/* decNumberAdd -- add two Numbers */
+/* */
+/* This computes C = A + B */
+/* */
+/* res is C, the result. C may be A and/or B (e.g., X=X+X) */
+/* lhs is A */
+/* rhs is B */
+/* set is the context */
+/* */
+/* C must have space for set->digits digits. */
+/* ------------------------------------------------------------------ */
+/* This just calls the routine shared with Subtract */
+decNumber * decNumberAdd(decNumber *res, const decNumber *lhs,
+ const decNumber *rhs, decContext *set) {
+ uInt status=0; // accumulator
+ decAddOp(res, lhs, rhs, set, 0, &status);
+ if (status!=0) decStatus(res, status, set);
+ #if DECCHECK
+ decCheckInexact(res, set);
+ #endif
+ return res;
+ } // decNumberAdd
+
+/* ------------------------------------------------------------------ */
+/* decNumberAnd -- AND two Numbers, digitwise */
+/* */
+/* This computes C = A & B */
+/* */
+/* res is C, the result. C may be A and/or B (e.g., X=X&X) */
+/* lhs is A */
+/* rhs is B */
+/* set is the context (used for result length and error report) */
+/* */
+/* C must have space for set->digits digits. */
+/* */
+/* Logical function restrictions apply (see above); a NaN is */
+/* returned with Invalid_operation if a restriction is violated. */
+/* ------------------------------------------------------------------ */
+decNumber * decNumberAnd(decNumber *res, const decNumber *lhs,
+ const decNumber *rhs, decContext *set) {
+ const Unit *ua, *ub; // -> operands
+ const Unit *msua, *msub; // -> operand msus
+ Unit *uc, *msuc; // -> result and its msu
+ Int msudigs; // digits in res msu
+ #if DECCHECK
+ if (decCheckOperands(res, lhs, rhs, set)) return res;
+ #endif
+
+ if (lhs->exponent!=0 || decNumberIsSpecial(lhs) || decNumberIsNegative(lhs)
+ || rhs->exponent!=0 || decNumberIsSpecial(rhs) || decNumberIsNegative(rhs)) {
+ decStatus(res, DEC_Invalid_operation, set);
+ return res;
+ }
+
+ // operands are valid
+ ua=lhs->lsu; // bottom-up
+ ub=rhs->lsu; // ..
+ uc=res->lsu; // ..
+ msua=ua+D2U(lhs->digits)-1; // -> msu of lhs
+ msub=ub+D2U(rhs->digits)-1; // -> msu of rhs
+ msuc=uc+D2U(set->digits)-1; // -> msu of result
+ msudigs=MSUDIGITS(set->digits); // [faster than remainder]
+ for (; uc<=msuc; ua++, ub++, uc++) { // Unit loop
+ Unit a, b; // extract units
+ if (ua>msua) a=0;
+ else a=*ua;
+ if (ub>msub) b=0;
+ else b=*ub;
+ *uc=0; // can now write back
+ if (a|b) { // maybe 1 bits to examine
+ Int i, j;
+ *uc=0; // can now write back
+ // This loop could be unrolled and/or use BIN2BCD tables
+ for (i=0; i<DECDPUN; i++) {
+ if (a&b&1) *uc=*uc+(Unit)powers[i]; // effect AND
+ j=a%10;
+ a=a/10;
+ j|=b%10;
+ b=b/10;
+ if (j>1) {
+ decStatus(res, DEC_Invalid_operation, set);
+ return res;
+ }
+ if (uc==msuc && i==msudigs-1) break; // just did final digit
+ } // each digit
+ } // both OK
+ } // each unit
+ // [here uc-1 is the msu of the result]
+ res->digits=decGetDigits(res->lsu, uc-res->lsu);
+ res->exponent=0; // integer
+ res->bits=0; // sign=0
+ return res; // [no status to set]
+ } // decNumberAnd
+
+/* ------------------------------------------------------------------ */
+/* decNumberCompare -- compare two Numbers */
+/* */
+/* This computes C = A ? B */
+/* */
+/* res is C, the result. C may be A and/or B (e.g., X=X?X) */
+/* lhs is A */
+/* rhs is B */
+/* set is the context */
+/* */
+/* C must have space for one digit (or NaN). */
+/* ------------------------------------------------------------------ */
+decNumber * decNumberCompare(decNumber *res, const decNumber *lhs,
+ const decNumber *rhs, decContext *set) {
+ uInt status=0; // accumulator
+ decCompareOp(res, lhs, rhs, set, COMPARE, &status);
+ if (status!=0) decStatus(res, status, set);
+ return res;
+ } // decNumberCompare
+
+/* ------------------------------------------------------------------ */
+/* decNumberCompareSignal -- compare, signalling on all NaNs */
+/* */
+/* This computes C = A ? B */
+/* */
+/* res is C, the result. C may be A and/or B (e.g., X=X?X) */
+/* lhs is A */
+/* rhs is B */
+/* set is the context */
+/* */
+/* C must have space for one digit (or NaN). */
+/* ------------------------------------------------------------------ */
+decNumber * decNumberCompareSignal(decNumber *res, const decNumber *lhs,
+ const decNumber *rhs, decContext *set) {
+ uInt status=0; // accumulator
+ decCompareOp(res, lhs, rhs, set, COMPSIG, &status);
+ if (status!=0) decStatus(res, status, set);
+ return res;
+ } // decNumberCompareSignal
+
+/* ------------------------------------------------------------------ */
+/* decNumberCompareTotal -- compare two Numbers, using total ordering */
+/* */
+/* This computes C = A ? B, under total ordering */
+/* */
+/* res is C, the result. C may be A and/or B (e.g., X=X?X) */
+/* lhs is A */
+/* rhs is B */
+/* set is the context */
+/* */
+/* C must have space for one digit; the result will always be one of */
+/* -1, 0, or 1. */
+/* ------------------------------------------------------------------ */
+decNumber * decNumberCompareTotal(decNumber *res, const decNumber *lhs,
+ const decNumber *rhs, decContext *set) {
+ uInt status=0; // accumulator
+ decCompareOp(res, lhs, rhs, set, COMPTOTAL, &status);
+ if (status!=0) decStatus(res, status, set);
+ return res;
+ } // decNumberCompareTotal
+
+/* ------------------------------------------------------------------ */
+/* decNumberCompareTotalMag -- compare, total ordering of magnitudes */
+/* */
+/* This computes C = |A| ? |B|, under total ordering */
+/* */
+/* res is C, the result. C may be A and/or B (e.g., X=X?X) */
+/* lhs is A */
+/* rhs is B */
+/* set is the context */
+/* */
+/* C must have space for one digit; the result will always be one of */
+/* -1, 0, or 1. */
+/* ------------------------------------------------------------------ */
+decNumber * decNumberCompareTotalMag(decNumber *res, const decNumber *lhs,
+ const decNumber *rhs, decContext *set) {
+ uInt status=0; // accumulator
+ uInt needbytes; // for space calculations
+ decNumber bufa[D2N(DECBUFFER+1)];// +1 in case DECBUFFER=0
+ decNumber *allocbufa=NULL; // -> allocated bufa, iff allocated
+ decNumber bufb[D2N(DECBUFFER+1)];
+ decNumber *allocbufb=NULL; // -> allocated bufb, iff allocated
+ decNumber *a, *b; // temporary pointers
+
+ #if DECCHECK
+ if (decCheckOperands(res, lhs, rhs, set)) return res;
+ #endif
+
+ do { // protect allocated storage
+ // if either is negative, take a copy and absolute
+ if (decNumberIsNegative(lhs)) { // lhs<0
+ a=bufa;
+ needbytes=sizeof(decNumber)+(D2U(lhs->digits)-1)*sizeof(Unit);
+ if (needbytes>sizeof(bufa)) { // need malloc space
+ allocbufa=(decNumber *)malloc(needbytes);
+ if (allocbufa==NULL) { // hopeless -- abandon
+ status|=DEC_Insufficient_storage;
+ break;}
+ a=allocbufa; // use the allocated space
+ }
+ decNumberCopy(a, lhs); // copy content
+ a->bits&=~DECNEG; // .. and clear the sign
+ lhs=a; // use copy from here on
+ }
+ if (decNumberIsNegative(rhs)) { // rhs<0
+ b=bufb;
+ needbytes=sizeof(decNumber)+(D2U(rhs->digits)-1)*sizeof(Unit);
+ if (needbytes>sizeof(bufb)) { // need malloc space
+ allocbufb=(decNumber *)malloc(needbytes);
+ if (allocbufb==NULL) { // hopeless -- abandon
+ status|=DEC_Insufficient_storage;
+ break;}
+ b=allocbufb; // use the allocated space
+ }
+ decNumberCopy(b, rhs); // copy content
+ b->bits&=~DECNEG; // .. and clear the sign
+ rhs=b; // use copy from here on
+ }
+ decCompareOp(res, lhs, rhs, set, COMPTOTAL, &status);
+ } while(0); // end protected
+
+ if (allocbufa!=NULL) free(allocbufa); // drop any storage used
+ if (allocbufb!=NULL) free(allocbufb); // ..
+ if (status!=0) decStatus(res, status, set);
+ return res;
+ } // decNumberCompareTotalMag
+
+/* ------------------------------------------------------------------ */
+/* decNumberDivide -- divide one number by another */
+/* */
+/* This computes C = A / B */
+/* */
+/* res is C, the result. C may be A and/or B (e.g., X=X/X) */
+/* lhs is A */
+/* rhs is B */
+/* set is the context */
+/* */
+/* C must have space for set->digits digits. */
+/* ------------------------------------------------------------------ */
+decNumber * decNumberDivide(decNumber *res, const decNumber *lhs,
+ const decNumber *rhs, decContext *set) {
+ uInt status=0; // accumulator
+ decDivideOp(res, lhs, rhs, set, DIVIDE, &status);
+ if (status!=0) decStatus(res, status, set);
+ #if DECCHECK
+ decCheckInexact(res, set);
+ #endif
+ return res;
+ } // decNumberDivide
+
+/* ------------------------------------------------------------------ */
+/* decNumberDivideInteger -- divide and return integer quotient */
+/* */
+/* This computes C = A # B, where # is the integer divide operator */
+/* */
+/* res is C, the result. C may be A and/or B (e.g., X=X#X) */
+/* lhs is A */
+/* rhs is B */
+/* set is the context */
+/* */
+/* C must have space for set->digits digits. */
+/* ------------------------------------------------------------------ */
+decNumber * decNumberDivideInteger(decNumber *res, const decNumber *lhs,
+ const decNumber *rhs, decContext *set) {
+ uInt status=0; // accumulator
+ decDivideOp(res, lhs, rhs, set, DIVIDEINT, &status);
+ if (status!=0) decStatus(res, status, set);
+ return res;
+ } // decNumberDivideInteger
+
+/* ------------------------------------------------------------------ */
+/* decNumberExp -- exponentiation */
+/* */
+/* This computes C = exp(A) */
+/* */
+/* res is C, the result. C may be A */
+/* rhs is A */
+/* set is the context; note that rounding mode has no effect */
+/* */
+/* C must have space for set->digits digits. */
+/* */
+/* Mathematical function restrictions apply (see above); a NaN is */
+/* returned with Invalid_operation if a restriction is violated. */
+/* */
+/* Finite results will always be full precision and Inexact, except */
+/* when A is a zero or -Infinity (giving 1 or 0 respectively). */
+/* */
+/* An Inexact result is rounded using DEC_ROUND_HALF_EVEN; it will */
+/* almost always be correctly rounded, but may be up to 1 ulp in */
+/* error in rare cases. */
+/* ------------------------------------------------------------------ */
+/* This is a wrapper for decExpOp which can handle the slightly wider */
+/* (double) range needed by Ln (which has to be able to calculate */
+/* exp(-a) where a can be the tiniest number (Ntiny). */
+/* ------------------------------------------------------------------ */
+decNumber * decNumberExp(decNumber *res, const decNumber *rhs,
+ decContext *set) {
+ uInt status=0; // accumulator
+ #if DECSUBSET
+ decNumber *allocrhs=NULL; // non-NULL if rounded rhs allocated
+ #endif
+
+ #if DECCHECK
+ if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
+ #endif
+
+ // Check restrictions; these restrictions ensure that if h=8 (see
+ // decExpOp) then the result will either overflow or underflow to 0.
+ // Other math functions restrict the input range, too, for inverses.
+ // If not violated then carry out the operation.
+ if (!decCheckMath(rhs, set, &status)) do { // protect allocation
+ #if DECSUBSET
+ if (!set->extended) {
+ // reduce operand and set lostDigits status, as needed
+ if (rhs->digits>set->digits) {
+ allocrhs=decRoundOperand(rhs, set, &status);
+ if (allocrhs==NULL) break;
+ rhs=allocrhs;
+ }
+ }
+ #endif
+ decExpOp(res, rhs, set, &status);
+ } while(0); // end protected
+
+ #if DECSUBSET
+ if (allocrhs !=NULL) free(allocrhs); // drop any storage used
+ #endif
+ // apply significant status
+ if (status!=0) decStatus(res, status, set);
+ #if DECCHECK
+ decCheckInexact(res, set);
+ #endif
+ return res;
+ } // decNumberExp
+
+/* ------------------------------------------------------------------ */
+/* decNumberFMA -- fused multiply add */
+/* */
+/* This computes D = (A * B) + C with only one rounding */
+/* */
+/* res is D, the result. D may be A or B or C (e.g., X=FMA(X,X,X)) */
+/* lhs is A */
+/* rhs is B */
+/* fhs is C [far hand side] */
+/* set is the context */
+/* */
+/* Mathematical function restrictions apply (see above); a NaN is */
+/* returned with Invalid_operation if a restriction is violated. */
+/* */
+/* C must have space for set->digits digits. */
+/* ------------------------------------------------------------------ */
+decNumber * decNumberFMA(decNumber *res, const decNumber *lhs,
+ const decNumber *rhs, const decNumber *fhs,
+ decContext *set) {
+ uInt status=0; // accumulator
+ decContext dcmul; // context for the multiplication
+ uInt needbytes; // for space calculations
+ decNumber bufa[D2N(DECBUFFER*2+1)];
+ decNumber *allocbufa=NULL; // -> allocated bufa, iff allocated
+ decNumber *acc; // accumulator pointer
+ decNumber dzero; // work
+
+ #if DECCHECK
+ if (decCheckOperands(res, lhs, rhs, set)) return res;
+ if (decCheckOperands(res, fhs, DECUNUSED, set)) return res;
+ #endif
+
+ do { // protect allocated storage
+ #if DECSUBSET
+ if (!set->extended) { // [undefined if subset]
+ status|=DEC_Invalid_operation;
+ break;}
+ #endif
+ // Check math restrictions [these ensure no overflow or underflow]
+ if ((!decNumberIsSpecial(lhs) && decCheckMath(lhs, set, &status))
+ || (!decNumberIsSpecial(rhs) && decCheckMath(rhs, set, &status))
+ || (!decNumberIsSpecial(fhs) && decCheckMath(fhs, set, &status))) break;
+ // set up context for multiply
+ dcmul=*set;
+ dcmul.digits=lhs->digits+rhs->digits; // just enough
+ // [The above may be an over-estimate for subset arithmetic, but that's OK]
+ dcmul.emax=DEC_MAX_EMAX; // effectively unbounded ..
+ dcmul.emin=DEC_MIN_EMIN; // [thanks to Math restrictions]
+ // set up decNumber space to receive the result of the multiply
+ acc=bufa; // may fit
+ needbytes=sizeof(decNumber)+(D2U(dcmul.digits)-1)*sizeof(Unit);
+ if (needbytes>sizeof(bufa)) { // need malloc space
+ allocbufa=(decNumber *)malloc(needbytes);
+ if (allocbufa==NULL) { // hopeless -- abandon
+ status|=DEC_Insufficient_storage;
+ break;}
+ acc=allocbufa; // use the allocated space
+ }
+ // multiply with extended range and necessary precision
+ //printf("emin=%ld\n", dcmul.emin);
+ decMultiplyOp(acc, lhs, rhs, &dcmul, &status);
+ // Only Invalid operation (from sNaN or Inf * 0) is possible in
+ // status; if either is seen than ignore fhs (in case it is
+ // another sNaN) and set acc to NaN unless we had an sNaN
+ // [decMultiplyOp leaves that to caller]
+ // Note sNaN has to go through addOp to shorten payload if
+ // necessary
+ if ((status&DEC_Invalid_operation)!=0) {
+ if (!(status&DEC_sNaN)) { // but be true invalid
+ decNumberZero(res); // acc not yet set
+ res->bits=DECNAN;
+ break;
+ }
+ decNumberZero(&dzero); // make 0 (any non-NaN would do)
+ fhs=&dzero; // use that
+ }
+ #if DECCHECK
+ else { // multiply was OK
+ if (status!=0) printf("Status=%08lx after FMA multiply\n", (LI)status);
+ }
+ #endif
+ // add the third operand and result -> res, and all is done
+ decAddOp(res, acc, fhs, set, 0, &status);
+ } while(0); // end protected
+
+ if (allocbufa!=NULL) free(allocbufa); // drop any storage used
+ if (status!=0) decStatus(res, status, set);
+ #if DECCHECK
+ decCheckInexact(res, set);
+ #endif
+ return res;
+ } // decNumberFMA
+
+/* ------------------------------------------------------------------ */
+/* decNumberInvert -- invert a Number, digitwise */
+/* */
+/* This computes C = ~A */
+/* */
+/* res is C, the result. C may be A (e.g., X=~X) */
+/* rhs is A */
+/* set is the context (used for result length and error report) */
+/* */
+/* C must have space for set->digits digits. */
+/* */
+/* Logical function restrictions apply (see above); a NaN is */
+/* returned with Invalid_operation if a restriction is violated. */
+/* ------------------------------------------------------------------ */
+decNumber * decNumberInvert(decNumber *res, const decNumber *rhs,
+ decContext *set) {
+ const Unit *ua, *msua; // -> operand and its msu
+ Unit *uc, *msuc; // -> result and its msu
+ Int msudigs; // digits in res msu
+ #if DECCHECK
+ if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
+ #endif
+
+ if (rhs->exponent!=0 || decNumberIsSpecial(rhs) || decNumberIsNegative(rhs)) {
+ decStatus(res, DEC_Invalid_operation, set);
+ return res;
+ }
+ // operand is valid
+ ua=rhs->lsu; // bottom-up
+ uc=res->lsu; // ..
+ msua=ua+D2U(rhs->digits)-1; // -> msu of rhs
+ msuc=uc+D2U(set->digits)-1; // -> msu of result
+ msudigs=MSUDIGITS(set->digits); // [faster than remainder]
+ for (; uc<=msuc; ua++, uc++) { // Unit loop
+ Unit a; // extract unit
+ Int i, j; // work
+ if (ua>msua) a=0;
+ else a=*ua;
+ *uc=0; // can now write back
+ // always need to examine all bits in rhs
+ // This loop could be unrolled and/or use BIN2BCD tables
+ for (i=0; i<DECDPUN; i++) {
+ if ((~a)&1) *uc=*uc+(Unit)powers[i]; // effect INVERT
+ j=a%10;
+ a=a/10;
+ if (j>1) {
+ decStatus(res, DEC_Invalid_operation, set);
+ return res;
+ }
+ if (uc==msuc && i==msudigs-1) break; // just did final digit
+ } // each digit
+ } // each unit
+ // [here uc-1 is the msu of the result]
+ res->digits=decGetDigits(res->lsu, uc-res->lsu);
+ res->exponent=0; // integer
+ res->bits=0; // sign=0
+ return res; // [no status to set]
+ } // decNumberInvert
+
+/* ------------------------------------------------------------------ */
+/* decNumberLn -- natural logarithm */
+/* */
+/* This computes C = ln(A) */
+/* */
+/* res is C, the result. C may be A */
+/* rhs is A */
+/* set is the context; note that rounding mode has no effect */
+/* */
+/* C must have space for set->digits digits. */
+/* */
+/* Notable cases: */
+/* A<0 -> Invalid */
+/* A=0 -> -Infinity (Exact) */
+/* A=+Infinity -> +Infinity (Exact) */
+/* A=1 exactly -> 0 (Exact) */
+/* */
+/* Mathematical function restrictions apply (see above); a NaN is */
+/* returned with Invalid_operation if a restriction is violated. */
+/* */
+/* An Inexact result is rounded using DEC_ROUND_HALF_EVEN; it will */
+/* almost always be correctly rounded, but may be up to 1 ulp in */
+/* error in rare cases. */
+/* ------------------------------------------------------------------ */
+/* This is a wrapper for decLnOp which can handle the slightly wider */
+/* (+11) range needed by Ln, Log10, etc. (which may have to be able */
+/* to calculate at p+e+2). */
+/* ------------------------------------------------------------------ */
+decNumber * decNumberLn(decNumber *res, const decNumber *rhs,
+ decContext *set) {
+ uInt status=0; // accumulator
+ #if DECSUBSET
+ decNumber *allocrhs=NULL; // non-NULL if rounded rhs allocated
+ #endif
+
+ #if DECCHECK
+ if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
+ #endif
+
+ // Check restrictions; this is a math function; if not violated
+ // then carry out the operation.
+ if (!decCheckMath(rhs, set, &status)) do { // protect allocation
+ #if DECSUBSET
+ if (!set->extended) {
+ // reduce operand and set lostDigits status, as needed
+ if (rhs->digits>set->digits) {
+ allocrhs=decRoundOperand(rhs, set, &status);
+ if (allocrhs==NULL) break;
+ rhs=allocrhs;
+ }
+ // special check in subset for rhs=0
+ if (ISZERO(rhs)) { // +/- zeros -> error
+ status|=DEC_Invalid_operation;
+ break;}
+ } // extended=0
+ #endif
+ decLnOp(res, rhs, set, &status);
+ } while(0); // end protected
+
+ #if DECSUBSET
+ if (allocrhs !=NULL) free(allocrhs); // drop any storage used
+ #endif
+ // apply significant status
+ if (status!=0) decStatus(res, status, set);
+ #if DECCHECK
+ decCheckInexact(res, set);
+ #endif
+ return res;
+ } // decNumberLn
+
+/* ------------------------------------------------------------------ */
+/* decNumberLogB - get adjusted exponent, by 754 rules */
+/* */
+/* This computes C = adjustedexponent(A) */
+/* */
+/* res is C, the result. C may be A */
+/* rhs is A */
+/* set is the context, used only for digits and status */
+/* */
+/* For an unrounded result, digits may need to be 10 (A might have */
+/* 10**9 digits and an exponent of +999999999, or one digit and an */
+/* exponent of -1999999999). */
+/* */
+/* This returns the adjusted exponent of A after (in theory) padding */
+/* with zeros on the right to set->digits digits while keeping the */
+/* same value. The exponent is not limited by emin/emax. */
+/* */
+/* Notable cases: */
+/* A<0 -> Use |A| */
+/* A=0 -> -Infinity (Division by zero) */
+/* A=Infinite -> +Infinity (Exact) */
+/* A=1 exactly -> 0 (Exact) */
+/* NaNs are propagated as usual */
+/* ------------------------------------------------------------------ */
+decNumber * decNumberLogB(decNumber *res, const decNumber *rhs,
+ decContext *set) {
+ uInt status=0; // accumulator
+
+ #if DECCHECK
+ if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
+ #endif
+
+ // NaNs as usual; Infinities return +Infinity; 0->oops
+ if (decNumberIsNaN(rhs)) decNaNs(res, rhs, NULL, set, &status);
+ else if (decNumberIsInfinite(rhs)) decNumberCopyAbs(res, rhs);
+ else if (decNumberIsZero(rhs)) {
+ decNumberZero(res); // prepare for Infinity
+ res->bits=DECNEG|DECINF; // -Infinity
+ status|=DEC_Division_by_zero; // as per 754
+ }
+ else { // finite non-zero
+ Int ae=rhs->exponent+rhs->digits-1; // adjusted exponent
+ if (set->digits>=10) decNumberFromInt32(res, ae); // lay it out
+ else {
+ decNumber buft[D2N(10)]; // temporary number
+ decNumber *t=buft; // ..
+ decNumberFromInt32(t, ae); // lay it out
+ decNumberPlus(res, t, set); // round as necessary
+ }
+ }
+
+ if (status!=0) decStatus(res, status, set);
+ return res;
+ } // decNumberLogB
+
+/* ------------------------------------------------------------------ */
+/* decNumberLog10 -- logarithm in base 10 */
+/* */
+/* This computes C = log10(A) */
+/* */
+/* res is C, the result. C may be A */
+/* rhs is A */
+/* set is the context; note that rounding mode has no effect */
+/* */
+/* C must have space for set->digits digits. */
+/* */
+/* Notable cases: */
+/* A<0 -> Invalid */
+/* A=0 -> -Infinity (Exact) */
+/* A=+Infinity -> +Infinity (Exact) */
+/* A=10**n (if n is an integer) -> n (Exact) */
+/* */
+/* Mathematical function restrictions apply (see above); a NaN is */
+/* returned with Invalid_operation if a restriction is violated. */
+/* */
+/* An Inexact result is rounded using DEC_ROUND_HALF_EVEN; it will */
+/* almost always be correctly rounded, but may be up to 1 ulp in */
+/* error in rare cases. */
+/* ------------------------------------------------------------------ */
+/* This calculates ln(A)/ln(10) using appropriate precision. For */
+/* ln(A) this is the max(p, rhs->digits + t) + 3, where p is the */
+/* requested digits and t is the number of digits in the exponent */
+/* (maximum 6). For ln(10) it is p + 3; this is often handled by the */
+/* fastpath in decLnOp. The final division is done to the requested */
+/* precision. */
+/* ------------------------------------------------------------------ */
+decNumber * decNumberLog10(decNumber *res, const decNumber *rhs,
+ decContext *set) {
+ uInt status=0, ignore=0; // status accumulators
+ uInt needbytes; // for space calculations
+ Int p; // working precision
+ Int t; // digits in exponent of A
+
+ // buffers for a and b working decimals
+ // (adjustment calculator, same size)
+ decNumber bufa[D2N(DECBUFFER+2)];
+ decNumber *allocbufa=NULL; // -> allocated bufa, iff allocated
+ decNumber *a=bufa; // temporary a
+ decNumber bufb[D2N(DECBUFFER+2)];
+ decNumber *allocbufb=NULL; // -> allocated bufb, iff allocated
+ decNumber *b=bufb; // temporary b
+ decNumber bufw[D2N(10)]; // working 2-10 digit number
+ decNumber *w=bufw; // ..
+ #if DECSUBSET
+ decNumber *allocrhs=NULL; // non-NULL if rounded rhs allocated
+ #endif
+
+ decContext aset; // working context
+
+ #if DECCHECK
+ if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
+ #endif
+
+ // Check restrictions; this is a math function; if not violated
+ // then carry out the operation.
+ if (!decCheckMath(rhs, set, &status)) do { // protect malloc
+ #if DECSUBSET
+ if (!set->extended) {
+ // reduce operand and set lostDigits status, as needed
+ if (rhs->digits>set->digits) {
+ allocrhs=decRoundOperand(rhs, set, &status);
+ if (allocrhs==NULL) break;
+ rhs=allocrhs;
+ }
+ // special check in subset for rhs=0
+ if (ISZERO(rhs)) { // +/- zeros -> error
+ status|=DEC_Invalid_operation;
+ break;}
+ } // extended=0
+ #endif
+
+ decContextDefault(&aset, DEC_INIT_DECIMAL64); // clean context
+
+ // handle exact powers of 10; only check if +ve finite
+ if (!(rhs->bits&(DECNEG|DECSPECIAL)) && !ISZERO(rhs)) {
+ Int residue=0; // (no residue)
+ uInt copystat=0; // clean status
+
+ // round to a single digit...
+ aset.digits=1;
+ decCopyFit(w, rhs, &aset, &residue, ©stat); // copy & shorten
+ // if exact and the digit is 1, rhs is a power of 10
+ if (!(copystat&DEC_Inexact) && w->lsu[0]==1) {
+ // the exponent, conveniently, is the power of 10; making
+ // this the result needs a little care as it might not fit,
+ // so first convert it into the working number, and then move
+ // to res
+ decNumberFromInt32(w, w->exponent);
+ residue=0;
+ decCopyFit(res, w, set, &residue, &status); // copy & round
+ decFinish(res, set, &residue, &status); // cleanup/set flags
+ break;
+ } // not a power of 10
+ } // not a candidate for exact
+
+ // simplify the information-content calculation to use 'total
+ // number of digits in a, including exponent' as compared to the
+ // requested digits, as increasing this will only rarely cost an
+ // iteration in ln(a) anyway
+ t=6; // it can never be >6
+
+ // allocate space when needed...
+ p=(rhs->digits+t>set->digits?rhs->digits+t:set->digits)+3;
+ needbytes=sizeof(decNumber)+(D2U(p)-1)*sizeof(Unit);
+ if (needbytes>sizeof(bufa)) { // need malloc space
+ allocbufa=(decNumber *)malloc(needbytes);
+ if (allocbufa==NULL) { // hopeless -- abandon
+ status|=DEC_Insufficient_storage;
+ break;}
+ a=allocbufa; // use the allocated space
+ }
+ aset.digits=p; // as calculated
+ aset.emax=DEC_MAX_MATH; // usual bounds
+ aset.emin=-DEC_MAX_MATH; // ..
+ aset.clamp=0; // and no concrete format
+ decLnOp(a, rhs, &aset, &status); // a=ln(rhs)
+
+ // skip the division if the result so far is infinite, NaN, or
+ // zero, or there was an error; note NaN from sNaN needs copy
+ if (status&DEC_NaNs && !(status&DEC_sNaN)) break;
+ if (a->bits&DECSPECIAL || ISZERO(a)) {
+ decNumberCopy(res, a); // [will fit]
+ break;}
+
+ // for ln(10) an extra 3 digits of precision are needed
+ p=set->digits+3;
+ needbytes=sizeof(decNumber)+(D2U(p)-1)*sizeof(Unit);
+ if (needbytes>sizeof(bufb)) { // need malloc space
+ allocbufb=(decNumber *)malloc(needbytes);
+ if (allocbufb==NULL) { // hopeless -- abandon
+ status|=DEC_Insufficient_storage;
+ break;}
+ b=allocbufb; // use the allocated space
+ }
+ decNumberZero(w); // set up 10...
+ #if DECDPUN==1
+ w->lsu[1]=1; w->lsu[0]=0; // ..
+ #else
+ w->lsu[0]=10; // ..
+ #endif
+ w->digits=2; // ..
+
+ aset.digits=p;
+ decLnOp(b, w, &aset, &ignore); // b=ln(10)
+
+ aset.digits=set->digits; // for final divide
+ decDivideOp(res, a, b, &aset, DIVIDE, &status); // into result
+ } while(0); // [for break]
+
+ if (allocbufa!=NULL) free(allocbufa); // drop any storage used
+ if (allocbufb!=NULL) free(allocbufb); // ..
+ #if DECSUBSET
+ if (allocrhs !=NULL) free(allocrhs); // ..
+ #endif
+ // apply significant status
+ if (status!=0) decStatus(res, status, set);
+ #if DECCHECK
+ decCheckInexact(res, set);
+ #endif
+ return res;
+ } // decNumberLog10
+
+/* ------------------------------------------------------------------ */
+/* decNumberMax -- compare two Numbers and return the maximum */
+/* */
+/* This computes C = A ? B, returning the maximum by 754 rules */
+/* */
+/* res is C, the result. C may be A and/or B (e.g., X=X?X) */
+/* lhs is A */
+/* rhs is B */
+/* set is the context */
+/* */
+/* C must have space for set->digits digits. */
+/* ------------------------------------------------------------------ */
+decNumber * decNumberMax(decNumber *res, const decNumber *lhs,
+ const decNumber *rhs, decContext *set) {
+ uInt status=0; // accumulator
+ decCompareOp(res, lhs, rhs, set, COMPMAX, &status);
+ if (status!=0) decStatus(res, status, set);
+ #if DECCHECK
+ decCheckInexact(res, set);
+ #endif
+ return res;
+ } // decNumberMax
+
+/* ------------------------------------------------------------------ */
+/* decNumberMaxMag -- compare and return the maximum by magnitude */
+/* */
+/* This computes C = A ? B, returning the maximum by 754 rules */
+/* */
+/* res is C, the result. C may be A and/or B (e.g., X=X?X) */
+/* lhs is A */
+/* rhs is B */
+/* set is the context */
+/* */
+/* C must have space for set->digits digits. */
+/* ------------------------------------------------------------------ */
+decNumber * decNumberMaxMag(decNumber *res, const decNumber *lhs,
+ const decNumber *rhs, decContext *set) {
+ uInt status=0; // accumulator
+ decCompareOp(res, lhs, rhs, set, COMPMAXMAG, &status);
+ if (status!=0) decStatus(res, status, set);
+ #if DECCHECK
+ decCheckInexact(res, set);
+ #endif
+ return res;
+ } // decNumberMaxMag
+
+/* ------------------------------------------------------------------ */
+/* decNumberMin -- compare two Numbers and return the minimum */
+/* */
+/* This computes C = A ? B, returning the minimum by 754 rules */
+/* */
+/* res is C, the result. C may be A and/or B (e.g., X=X?X) */
+/* lhs is A */
+/* rhs is B */
+/* set is the context */
+/* */
+/* C must have space for set->digits digits. */
+/* ------------------------------------------------------------------ */
+decNumber * decNumberMin(decNumber *res, const decNumber *lhs,
+ const decNumber *rhs, decContext *set) {
+ uInt status=0; // accumulator
+ decCompareOp(res, lhs, rhs, set, COMPMIN, &status);
+ if (status!=0) decStatus(res, status, set);
+ #if DECCHECK
+ decCheckInexact(res, set);
+ #endif
+ return res;
+ } // decNumberMin
+
+/* ------------------------------------------------------------------ */
+/* decNumberMinMag -- compare and return the minimum by magnitude */
+/* */
+/* This computes C = A ? B, returning the minimum by 754 rules */
+/* */
+/* res is C, the result. C may be A and/or B (e.g., X=X?X) */
+/* lhs is A */
+/* rhs is B */
+/* set is the context */
+/* */
+/* C must have space for set->digits digits. */
+/* ------------------------------------------------------------------ */
+decNumber * decNumberMinMag(decNumber *res, const decNumber *lhs,
+ const decNumber *rhs, decContext *set) {
+ uInt status=0; // accumulator
+ decCompareOp(res, lhs, rhs, set, COMPMINMAG, &status);
+ if (status!=0) decStatus(res, status, set);
+ #if DECCHECK
+ decCheckInexact(res, set);
+ #endif
+ return res;
+ } // decNumberMinMag
+
+/* ------------------------------------------------------------------ */
+/* decNumberMinus -- prefix minus operator */
+/* */
+/* This computes C = 0 - A */
+/* */
+/* res is C, the result. C may be A */
+/* rhs is A */
+/* set is the context */
+/* */
+/* See also decNumberCopyNegate for a quiet bitwise version of this. */
+/* C must have space for set->digits digits. */
+/* ------------------------------------------------------------------ */
+/* Simply use AddOp for the subtract, which will do the necessary. */
+/* ------------------------------------------------------------------ */
+decNumber * decNumberMinus(decNumber *res, const decNumber *rhs,
+ decContext *set) {
+ decNumber dzero;
+ uInt status=0; // accumulator
+
+ #if DECCHECK
+ if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
+ #endif
+
+ decNumberZero(&dzero); // make 0
+ dzero.exponent=rhs->exponent; // [no coefficient expansion]
+ decAddOp(res, &dzero, rhs, set, DECNEG, &status);
+ if (status!=0) decStatus(res, status, set);
+ #if DECCHECK
+ decCheckInexact(res, set);
+ #endif
+ return res;
+ } // decNumberMinus
+
+/* ------------------------------------------------------------------ */
+/* decNumberNextMinus -- next towards -Infinity */
+/* */
+/* This computes C = A - infinitesimal, rounded towards -Infinity */
+/* */
+/* res is C, the result. C may be A */
+/* rhs is A */
+/* set is the context */
+/* */
+/* This is a generalization of 754 NextDown. */
+/* ------------------------------------------------------------------ */
+decNumber * decNumberNextMinus(decNumber *res, const decNumber *rhs,
+ decContext *set) {
+ decNumber dtiny; // constant
+ decContext workset=*set; // work
+ uInt status=0; // accumulator
+ #if DECCHECK
+ if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
+ #endif
+
+ // +Infinity is the special case
+ if ((rhs->bits&(DECINF|DECNEG))==DECINF) {
+ decSetMaxValue(res, set); // is +ve
+ // there is no status to set
+ return res;
+ }
+ decNumberZero(&dtiny); // start with 0
+ dtiny.lsu[0]=1; // make number that is ..
+ dtiny.exponent=DEC_MIN_EMIN-1; // .. smaller than tiniest
+ workset.round=DEC_ROUND_FLOOR;
+ decAddOp(res, rhs, &dtiny, &workset, DECNEG, &status);
+ status&=DEC_Invalid_operation|DEC_sNaN; // only sNaN Invalid please
+ if (status!=0) decStatus(res, status, set);
+ return res;
+ } // decNumberNextMinus
+
+/* ------------------------------------------------------------------ */
+/* decNumberNextPlus -- next towards +Infinity */
+/* */
+/* This computes C = A + infinitesimal, rounded towards +Infinity */
+/* */
+/* res is C, the result. C may be A */
+/* rhs is A */
+/* set is the context */
+/* */
+/* This is a generalization of 754 NextUp. */
+/* ------------------------------------------------------------------ */
+decNumber * decNumberNextPlus(decNumber *res, const decNumber *rhs,
+ decContext *set) {
+ decNumber dtiny; // constant
+ decContext workset=*set; // work
+ uInt status=0; // accumulator
+ #if DECCHECK
+ if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
+ #endif
+
+ // -Infinity is the special case
+ if ((rhs->bits&(DECINF|DECNEG))==(DECINF|DECNEG)) {
+ decSetMaxValue(res, set);
+ res->bits=DECNEG; // negative
+ // there is no status to set
+ return res;
+ }
+ decNumberZero(&dtiny); // start with 0
+ dtiny.lsu[0]=1; // make number that is ..
+ dtiny.exponent=DEC_MIN_EMIN-1; // .. smaller than tiniest
+ workset.round=DEC_ROUND_CEILING;
+ decAddOp(res, rhs, &dtiny, &workset, 0, &status);
+ status&=DEC_Invalid_operation|DEC_sNaN; // only sNaN Invalid please
+ if (status!=0) decStatus(res, status, set);
+ return res;
+ } // decNumberNextPlus
+
+/* ------------------------------------------------------------------ */
+/* decNumberNextToward -- next towards rhs */
+/* */
+/* This computes C = A +/- infinitesimal, rounded towards */
+/* +/-Infinity in the direction of B, as per 754-1985 nextafter */
+/* modified during revision but dropped from 754-2008. */
+/* */
+/* res is C, the result. C may be A or B. */
+/* lhs is A */
+/* rhs is B */
+/* set is the context */
+/* */
+/* This is a generalization of 754-1985 NextAfter. */
+/* ------------------------------------------------------------------ */
+decNumber * decNumberNextToward(decNumber *res, const decNumber *lhs,
+ const decNumber *rhs, decContext *set) {
+ decNumber dtiny; // constant
+ decContext workset=*set; // work
+ Int result; // ..
+ uInt status=0; // accumulator
+ #if DECCHECK
+ if (decCheckOperands(res, lhs, rhs, set)) return res;
+ #endif
+
+ if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs)) {
+ decNaNs(res, lhs, rhs, set, &status);
+ }
+ else { // Is numeric, so no chance of sNaN Invalid, etc.
+ result=decCompare(lhs, rhs, 0); // sign matters
+ if (result==BADINT) status|=DEC_Insufficient_storage; // rare
+ else { // valid compare
+ if (result==0) decNumberCopySign(res, lhs, rhs); // easy
+ else { // differ: need NextPlus or NextMinus
+ uByte sub; // add or subtract
+ if (result<0) { // lhs<rhs, do nextplus
+ // -Infinity is the special case
+ if ((lhs->bits&(DECINF|DECNEG))==(DECINF|DECNEG)) {
+ decSetMaxValue(res, set);
+ res->bits=DECNEG; // negative
+ return res; // there is no status to set
+ }
+ workset.round=DEC_ROUND_CEILING;
+ sub=0; // add, please
+ } // plus
+ else { // lhs>rhs, do nextminus
+ // +Infinity is the special case
+ if ((lhs->bits&(DECINF|DECNEG))==DECINF) {
+ decSetMaxValue(res, set);
+ return res; // there is no status to set
+ }
+ workset.round=DEC_ROUND_FLOOR;
+ sub=DECNEG; // subtract, please
+ } // minus
+ decNumberZero(&dtiny); // start with 0
+ dtiny.lsu[0]=1; // make number that is ..
+ dtiny.exponent=DEC_MIN_EMIN-1; // .. smaller than tiniest
+ decAddOp(res, lhs, &dtiny, &workset, sub, &status); // + or -
+ // turn off exceptions if the result is a normal number
+ // (including Nmin), otherwise let all status through
+ if (decNumberIsNormal(res, set)) status=0;
+ } // unequal
+ } // compare OK
+ } // numeric
+ if (status!=0) decStatus(res, status, set);
+ return res;
+ } // decNumberNextToward
+
+/* ------------------------------------------------------------------ */
+/* decNumberOr -- OR two Numbers, digitwise */
+/* */
+/* This computes C = A | B */
+/* */
+/* res is C, the result. C may be A and/or B (e.g., X=X|X) */
+/* lhs is A */
+/* rhs is B */
+/* set is the context (used for result length and error report) */
+/* */
+/* C must have space for set->digits digits. */
+/* */
+/* Logical function restrictions apply (see above); a NaN is */
+/* returned with Invalid_operation if a restriction is violated. */
+/* ------------------------------------------------------------------ */
+decNumber * decNumberOr(decNumber *res, const decNumber *lhs,
+ const decNumber *rhs, decContext *set) {
+ const Unit *ua, *ub; // -> operands
+ const Unit *msua, *msub; // -> operand msus
+ Unit *uc, *msuc; // -> result and its msu
+ Int msudigs; // digits in res msu
+ #if DECCHECK
+ if (decCheckOperands(res, lhs, rhs, set)) return res;
+ #endif
+
+ if (lhs->exponent!=0 || decNumberIsSpecial(lhs) || decNumberIsNegative(lhs)
+ || rhs->exponent!=0 || decNumberIsSpecial(rhs) || decNumberIsNegative(rhs)) {
+ decStatus(res, DEC_Invalid_operation, set);
+ return res;
+ }
+ // operands are valid
+ ua=lhs->lsu; // bottom-up
+ ub=rhs->lsu; // ..
+ uc=res->lsu; // ..
+ msua=ua+D2U(lhs->digits)-1; // -> msu of lhs
+ msub=ub+D2U(rhs->digits)-1; // -> msu of rhs
+ msuc=uc+D2U(set->digits)-1; // -> msu of result
+ msudigs=MSUDIGITS(set->digits); // [faster than remainder]
+ for (; uc<=msuc; ua++, ub++, uc++) { // Unit loop
+ Unit a, b; // extract units
+ if (ua>msua) a=0;
+ else a=*ua;
+ if (ub>msub) b=0;
+ else b=*ub;
+ *uc=0; // can now write back
+ if (a|b) { // maybe 1 bits to examine
+ Int i, j;
+ // This loop could be unrolled and/or use BIN2BCD tables
+ for (i=0; i<DECDPUN; i++) {
+ if ((a|b)&1) *uc=*uc+(Unit)powers[i]; // effect OR
+ j=a%10;
+ a=a/10;
+ j|=b%10;
+ b=b/10;
+ if (j>1) {
+ decStatus(res, DEC_Invalid_operation, set);
+ return res;
+ }
+ if (uc==msuc && i==msudigs-1) break; // just did final digit
+ } // each digit
+ } // non-zero
+ } // each unit
+ // [here uc-1 is the msu of the result]
+ res->digits=decGetDigits(res->lsu, uc-res->lsu);
+ res->exponent=0; // integer
+ res->bits=0; // sign=0
+ return res; // [no status to set]
+ } // decNumberOr
+
+/* ------------------------------------------------------------------ */
+/* decNumberPlus -- prefix plus operator */
+/* */
+/* This computes C = 0 + A */
+/* */
+/* res is C, the result. C may be A */
+/* rhs is A */
+/* set is the context */
+/* */
+/* See also decNumberCopy for a quiet bitwise version of this. */
+/* C must have space for set->digits digits. */
+/* ------------------------------------------------------------------ */
+/* This simply uses AddOp; Add will take fast path after preparing A. */
+/* Performance is a concern here, as this routine is often used to */
+/* check operands and apply rounding and overflow/underflow testing. */
+/* ------------------------------------------------------------------ */
+decNumber * decNumberPlus(decNumber *res, const decNumber *rhs,
+ decContext *set) {
+ decNumber dzero;
+ uInt status=0; // accumulator
+ #if DECCHECK
+ if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
+ #endif
+
+ decNumberZero(&dzero); // make 0
+ dzero.exponent=rhs->exponent; // [no coefficient expansion]
+ decAddOp(res, &dzero, rhs, set, 0, &status);
+ if (status!=0) decStatus(res, status, set);
+ #if DECCHECK
+ decCheckInexact(res, set);
+ #endif
+ return res;
+ } // decNumberPlus
+
+/* ------------------------------------------------------------------ */
+/* decNumberMultiply -- multiply two Numbers */
+/* */
+/* This computes C = A x B */
+/* */
+/* res is C, the result. C may be A and/or B (e.g., X=X+X) */
+/* lhs is A */
+/* rhs is B */
+/* set is the context */
+/* */
+/* C must have space for set->digits digits. */
+/* ------------------------------------------------------------------ */
+decNumber * decNumberMultiply(decNumber *res, const decNumber *lhs,
+ const decNumber *rhs, decContext *set) {
+ uInt status=0; // accumulator
+ decMultiplyOp(res, lhs, rhs, set, &status);
+ if (status!=0) decStatus(res, status, set);
+ #if DECCHECK
+ decCheckInexact(res, set);
+ #endif
+ return res;
+ } // decNumberMultiply
+
+/* ------------------------------------------------------------------ */
+/* decNumberPower -- raise a number to a power */
+/* */
+/* This computes C = A ** B */
+/* */
+/* res is C, the result. C may be A and/or B (e.g., X=X**X) */
+/* lhs is A */
+/* rhs is B */
+/* set is the context */
+/* */
+/* C must have space for set->digits digits. */
+/* */
+/* Mathematical function restrictions apply (see above); a NaN is */
+/* returned with Invalid_operation if a restriction is violated. */
+/* */
+/* However, if 1999999997<=B<=999999999 and B is an integer then the */
+/* restrictions on A and the context are relaxed to the usual bounds, */
+/* for compatibility with the earlier (integer power only) version */
+/* of this function. */
+/* */
+/* When B is an integer, the result may be exact, even if rounded. */
+/* */
+/* The final result is rounded according to the context; it will */
+/* almost always be correctly rounded, but may be up to 1 ulp in */
+/* error in rare cases. */
+/* ------------------------------------------------------------------ */
+decNumber * decNumberPower(decNumber *res, const decNumber *lhs,
+ const decNumber *rhs, decContext *set) {
+ #if DECSUBSET
+ decNumber *alloclhs=NULL; // non-NULL if rounded lhs allocated
+ decNumber *allocrhs=NULL; // .., rhs
+ #endif
+ decNumber *allocdac=NULL; // -> allocated acc buffer, iff used
+ decNumber *allocinv=NULL; // -> allocated 1/x buffer, iff used
+ Int reqdigits=set->digits; // requested DIGITS
+ Int n; // rhs in binary
+ Flag rhsint=0; // 1 if rhs is an integer
+ Flag useint=0; // 1 if can use integer calculation
+ Flag isoddint=0; // 1 if rhs is an integer and odd
+ Int i; // work
+ #if DECSUBSET
+ Int dropped; // ..
+ #endif
+ uInt needbytes; // buffer size needed
+ Flag seenbit; // seen a bit while powering
+ Int residue=0; // rounding residue
+ uInt status=0; // accumulators
+ uByte bits=0; // result sign if errors
+ decContext aset; // working context
+ decNumber dnOne; // work value 1...
+ // local accumulator buffer [a decNumber, with digits+elength+1 digits]
+ decNumber dacbuff[D2N(DECBUFFER+9)];
+ decNumber *dac=dacbuff; // -> result accumulator
+ // same again for possible 1/lhs calculation
+ decNumber invbuff[D2N(DECBUFFER+9)];
+
+ #if DECCHECK
+ if (decCheckOperands(res, lhs, rhs, set)) return res;
+ #endif
+
+ do { // protect allocated storage
+ #if DECSUBSET
+ if (!set->extended) { // reduce operands and set status, as needed
+ if (lhs->digits>reqdigits) {
+ alloclhs=decRoundOperand(lhs, set, &status);
+ if (alloclhs==NULL) break;
+ lhs=alloclhs;
+ }
+ if (rhs->digits>reqdigits) {
+ allocrhs=decRoundOperand(rhs, set, &status);
+ if (allocrhs==NULL) break;
+ rhs=allocrhs;
+ }
+ }
+ #endif
+ // [following code does not require input rounding]
+
+ // handle NaNs and rhs Infinity (lhs infinity is harder)
+ if (SPECIALARGS) {
+ if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs)) { // NaNs
+ decNaNs(res, lhs, rhs, set, &status);
+ break;}
+ if (decNumberIsInfinite(rhs)) { // rhs Infinity
+ Flag rhsneg=rhs->bits&DECNEG; // save rhs sign
+ if (decNumberIsNegative(lhs) // lhs<0
+ && !decNumberIsZero(lhs)) // ..
+ status|=DEC_Invalid_operation;
+ else { // lhs >=0
+ decNumberZero(&dnOne); // set up 1
+ dnOne.lsu[0]=1;
+ decNumberCompare(dac, lhs, &dnOne, set); // lhs ? 1
+ decNumberZero(res); // prepare for 0/1/Infinity
+ if (decNumberIsNegative(dac)) { // lhs<1
+ if (rhsneg) res->bits|=DECINF; // +Infinity [else is +0]
+ }
+ else if (dac->lsu[0]==0) { // lhs=1
+ // 1**Infinity is inexact, so return fully-padded 1.0000
+ Int shift=set->digits-1;
+ *res->lsu=1; // was 0, make int 1
+ res->digits=decShiftToMost(res->lsu, 1, shift);
+ res->exponent=-shift; // make 1.0000...
+ status|=DEC_Inexact|DEC_Rounded; // deemed inexact
+ }
+ else { // lhs>1
+ if (!rhsneg) res->bits|=DECINF; // +Infinity [else is +0]
+ }
+ } // lhs>=0
+ break;}
+ // [lhs infinity drops through]
+ } // specials
+
+ // Original rhs may be an integer that fits and is in range
+ n=decGetInt(rhs);
+ if (n!=BADINT) { // it is an integer
+ rhsint=1; // record the fact for 1**n
+ isoddint=(Flag)n&1; // [works even if big]
+ if (n!=BIGEVEN && n!=BIGODD) // can use integer path?
+ useint=1; // looks good
+ }
+
+ if (decNumberIsNegative(lhs) // -x ..
+ && isoddint) bits=DECNEG; // .. to an odd power
+
+ // handle LHS infinity
+ if (decNumberIsInfinite(lhs)) { // [NaNs already handled]
+ uByte rbits=rhs->bits; // save
+ decNumberZero(res); // prepare
+ if (n==0) *res->lsu=1; // [-]Inf**0 => 1
+ else {
+ // -Inf**nonint -> error
+ if (!rhsint && decNumberIsNegative(lhs)) {
+ status|=DEC_Invalid_operation; // -Inf**nonint is error
+ break;}
+ if (!(rbits & DECNEG)) bits|=DECINF; // was not a **-n
+ // [otherwise will be 0 or -0]
+ res->bits=bits;
+ }
+ break;}
+
+ // similarly handle LHS zero
+ if (decNumberIsZero(lhs)) {
+ if (n==0) { // 0**0 => Error
+ #if DECSUBSET
+ if (!set->extended) { // [unless subset]
+ decNumberZero(res);
+ *res->lsu=1; // return 1
+ break;}
+ #endif
+ status|=DEC_Invalid_operation;
+ }
+ else { // 0**x
+ uByte rbits=rhs->bits; // save
+ if (rbits & DECNEG) { // was a 0**(-n)
+ #if DECSUBSET
+ if (!set->extended) { // [bad if subset]
+ status|=DEC_Invalid_operation;
+ break;}
+ #endif
+ bits|=DECINF;
+ }
+ decNumberZero(res); // prepare
+ // [otherwise will be 0 or -0]
+ res->bits=bits;
+ }
+ break;}
+
+ // here both lhs and rhs are finite; rhs==0 is handled in the
+ // integer path. Next handle the non-integer cases
+ if (!useint) { // non-integral rhs
+ // any -ve lhs is bad, as is either operand or context out of
+ // bounds
+ if (decNumberIsNegative(lhs)) {
+ status|=DEC_Invalid_operation;
+ break;}
+ if (decCheckMath(lhs, set, &status)
+ || decCheckMath(rhs, set, &status)) break; // variable status
+
+ decContextDefault(&aset, DEC_INIT_DECIMAL64); // clean context
+ aset.emax=DEC_MAX_MATH; // usual bounds
+ aset.emin=-DEC_MAX_MATH; // ..
+ aset.clamp=0; // and no concrete format
+
+ // calculate the result using exp(ln(lhs)*rhs), which can
+ // all be done into the accumulator, dac. The precision needed
+ // is enough to contain the full information in the lhs (which
+ // is the total digits, including exponent), or the requested
+ // precision, if larger, + 4; 6 is used for the exponent
+ // maximum length, and this is also used when it is shorter
+ // than the requested digits as it greatly reduces the >0.5 ulp
+ // cases at little cost (because Ln doubles digits each
+ // iteration so a few extra digits rarely causes an extra
+ // iteration)
+ aset.digits=MAXI(lhs->digits, set->digits)+6+4;
+ } // non-integer rhs
+
+ else { // rhs is in-range integer
+ if (n==0) { // x**0 = 1
+ // (0**0 was handled above)
+ decNumberZero(res); // result=1
+ *res->lsu=1; // ..
+ break;}
+ // rhs is a non-zero integer
+ if (n<0) n=-n; // use abs(n)
+
+ aset=*set; // clone the context
+ aset.round=DEC_ROUND_HALF_EVEN; // internally use balanced
+ // calculate the working DIGITS
+ aset.digits=reqdigits+(rhs->digits+rhs->exponent)+2;
+ #if DECSUBSET
+ if (!set->extended) aset.digits--; // use classic precision
+ #endif
+ // it's an error if this is more than can be handled
+ if (aset.digits>DECNUMMAXP) {status|=DEC_Invalid_operation; break;}
+ } // integer path
+
+ // aset.digits is the count of digits for the accumulator needed
+ // if accumulator is too long for local storage, then allocate
+ needbytes=sizeof(decNumber)+(D2U(aset.digits)-1)*sizeof(Unit);
+ // [needbytes also used below if 1/lhs needed]
+ if (needbytes>sizeof(dacbuff)) {
+ allocdac=(decNumber *)malloc(needbytes);
+ if (allocdac==NULL) { // hopeless -- abandon
+ status|=DEC_Insufficient_storage;
+ break;}
+ dac=allocdac; // use the allocated space
+ }
+ // here, aset is set up and accumulator is ready for use
+
+ if (!useint) { // non-integral rhs
+ // x ** y; special-case x=1 here as it will otherwise always
+ // reduce to integer 1; decLnOp has a fastpath which detects
+ // the case of x=1
+ decLnOp(dac, lhs, &aset, &status); // dac=ln(lhs)
+ // [no error possible, as lhs 0 already handled]
+ if (ISZERO(dac)) { // x==1, 1.0, etc.
+ // need to return fully-padded 1.0000 etc., but rhsint->1
+ *dac->lsu=1; // was 0, make int 1
+ if (!rhsint) { // add padding
+ Int shift=set->digits-1;
+ dac->digits=decShiftToMost(dac->lsu, 1, shift);
+ dac->exponent=-shift; // make 1.0000...
+ status|=DEC_Inexact|DEC_Rounded; // deemed inexact
+ }
+ }
+ else {
+ decMultiplyOp(dac, dac, rhs, &aset, &status); // dac=dac*rhs
+ decExpOp(dac, dac, &aset, &status); // dac=exp(dac)
+ }
+ // and drop through for final rounding
+ } // non-integer rhs
+
+ else { // carry on with integer
+ decNumberZero(dac); // acc=1
+ *dac->lsu=1; // ..
+
+ // if a negative power the constant 1 is needed, and if not subset
+ // invert the lhs now rather than inverting the result later
+ if (decNumberIsNegative(rhs)) { // was a **-n [hence digits>0]
+ decNumber *inv=invbuff; // asssume use fixed buffer
+ decNumberCopy(&dnOne, dac); // dnOne=1; [needed now or later]
+ #if DECSUBSET
+ if (set->extended) { // need to calculate 1/lhs
+ #endif
+ // divide lhs into 1, putting result in dac [dac=1/dac]
+ decDivideOp(dac, &dnOne, lhs, &aset, DIVIDE, &status);
+ // now locate or allocate space for the inverted lhs
+ if (needbytes>sizeof(invbuff)) {
+ allocinv=(decNumber *)malloc(needbytes);
+ if (allocinv==NULL) { // hopeless -- abandon
+ status|=DEC_Insufficient_storage;
+ break;}
+ inv=allocinv; // use the allocated space
+ }
+ // [inv now points to big-enough buffer or allocated storage]
+ decNumberCopy(inv, dac); // copy the 1/lhs
+ decNumberCopy(dac, &dnOne); // restore acc=1
+ lhs=inv; // .. and go forward with new lhs
+ #if DECSUBSET
+ }
+ #endif
+ }
+
+ // Raise-to-the-power loop...
+ seenbit=0; // set once a 1-bit is encountered
+ for (i=1;;i++){ // for each bit [top bit ignored]
+ // abandon if had overflow or terminal underflow
+ if (status & (DEC_Overflow|DEC_Underflow)) { // interesting?
+ if (status&DEC_Overflow || ISZERO(dac)) break;
+ }
+ // [the following two lines revealed an optimizer bug in a C++
+ // compiler, with symptom: 5**3 -> 25, when n=n+n was used]
+ n=n<<1; // move next bit to testable position
+ if (n<0) { // top bit is set
+ seenbit=1; // OK, significant bit seen
+ decMultiplyOp(dac, dac, lhs, &aset, &status); // dac=dac*x
+ }
+ if (i==31) break; // that was the last bit
+ if (!seenbit) continue; // no need to square 1
+ decMultiplyOp(dac, dac, dac, &aset, &status); // dac=dac*dac [square]
+ } /*i*/ // 32 bits
+
+ // complete internal overflow or underflow processing
+ if (status & (DEC_Overflow|DEC_Underflow)) {
+ #if DECSUBSET
+ // If subset, and power was negative, reverse the kind of -erflow
+ // [1/x not yet done]
+ if (!set->extended && decNumberIsNegative(rhs)) {
+ if (status & DEC_Overflow)
+ status^=DEC_Overflow | DEC_Underflow | DEC_Subnormal;
+ else { // trickier -- Underflow may or may not be set
+ status&=~(DEC_Underflow | DEC_Subnormal); // [one or both]
+ status|=DEC_Overflow;
+ }
+ }
+ #endif
+ dac->bits=(dac->bits & ~DECNEG) | bits; // force correct sign
+ // round subnormals [to set.digits rather than aset.digits]
+ // or set overflow result similarly as required
+ decFinalize(dac, set, &residue, &status);
+ decNumberCopy(res, dac); // copy to result (is now OK length)
+ break;
+ }
+
+ #if DECSUBSET
+ if (!set->extended && // subset math
+ decNumberIsNegative(rhs)) { // was a **-n [hence digits>0]
+ // so divide result into 1 [dac=1/dac]
+ decDivideOp(dac, &dnOne, dac, &aset, DIVIDE, &status);
+ }
+ #endif
+ } // rhs integer path
+
+ // reduce result to the requested length and copy to result
+ decCopyFit(res, dac, set, &residue, &status);
+ decFinish(res, set, &residue, &status); // final cleanup
+ #if DECSUBSET
+ if (!set->extended) decTrim(res, set, 0, 1, &dropped); // trailing zeros
+ #endif
+ } while(0); // end protected
+
+ if (allocdac!=NULL) free(allocdac); // drop any storage used
+ if (allocinv!=NULL) free(allocinv); // ..
+ #if DECSUBSET
+ if (alloclhs!=NULL) free(alloclhs); // ..
+ if (allocrhs!=NULL) free(allocrhs); // ..
+ #endif
+ if (status!=0) decStatus(res, status, set);
+ #if DECCHECK
+ decCheckInexact(res, set);
+ #endif
+ return res;
+ } // decNumberPower
+
+/* ------------------------------------------------------------------ */
+/* decNumberQuantize -- force exponent to requested value */
+/* */
+/* This computes C = op(A, B), where op adjusts the coefficient */
+/* of C (by rounding or shifting) such that the exponent (-scale) */
+/* of C has exponent of B. The numerical value of C will equal A, */
+/* except for the effects of any rounding that occurred. */
+/* */
+/* res is C, the result. C may be A or B */
+/* lhs is A, the number to adjust */
+/* rhs is B, the number with exponent to match */
+/* set is the context */
+/* */
+/* C must have space for set->digits digits. */
+/* */
+/* Unless there is an error or the result is infinite, the exponent */
+/* after the operation is guaranteed to be equal to that of B. */
+/* ------------------------------------------------------------------ */
+decNumber * decNumberQuantize(decNumber *res, const decNumber *lhs,
+ const decNumber *rhs, decContext *set) {
+ uInt status=0; // accumulator
+ decQuantizeOp(res, lhs, rhs, set, 1, &status);
+ if (status!=0) decStatus(res, status, set);
+ return res;
+ } // decNumberQuantize
+
+/* ------------------------------------------------------------------ */
+/* decNumberReduce -- remove trailing zeros */
+/* */
+/* This computes C = 0 + A, and normalizes the result */
+/* */
+/* res is C, the result. C may be A */
+/* rhs is A */
+/* set is the context */
+/* */
+/* C must have space for set->digits digits. */
+/* ------------------------------------------------------------------ */
+// Previously known as Normalize
+decNumber * decNumberNormalize(decNumber *res, const decNumber *rhs,
+ decContext *set) {
+ return decNumberReduce(res, rhs, set);
+ } // decNumberNormalize
+
+decNumber * decNumberReduce(decNumber *res, const decNumber *rhs,
+ decContext *set) {
+ #if DECSUBSET
+ decNumber *allocrhs=NULL; // non-NULL if rounded rhs allocated
+ #endif
+ uInt status=0; // as usual
+ Int residue=0; // as usual
+ Int dropped; // work
+
+ #if DECCHECK
+ if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
+ #endif
+
+ do { // protect allocated storage
+ #if DECSUBSET
+ if (!set->extended) {
+ // reduce operand and set lostDigits status, as needed
+ if (rhs->digits>set->digits) {
+ allocrhs=decRoundOperand(rhs, set, &status);
+ if (allocrhs==NULL) break;
+ rhs=allocrhs;
+ }
+ }
+ #endif
+ // [following code does not require input rounding]
+
+ // Infinities copy through; NaNs need usual treatment
+ if (decNumberIsNaN(rhs)) {
+ decNaNs(res, rhs, NULL, set, &status);
+ break;
+ }
+
+ // reduce result to the requested length and copy to result
+ decCopyFit(res, rhs, set, &residue, &status); // copy & round
+ decFinish(res, set, &residue, &status); // cleanup/set flags
+ decTrim(res, set, 1, 0, &dropped); // normalize in place
+ // [may clamp]
+ } while(0); // end protected
+
+ #if DECSUBSET
+ if (allocrhs !=NULL) free(allocrhs); // ..
+ #endif
+ if (status!=0) decStatus(res, status, set);// then report status
+ return res;
+ } // decNumberReduce
+
+/* ------------------------------------------------------------------ */
+/* decNumberRescale -- force exponent to requested value */
+/* */
+/* This computes C = op(A, B), where op adjusts the coefficient */
+/* of C (by rounding or shifting) such that the exponent (-scale) */
+/* of C has the value B. The numerical value of C will equal A, */
+/* except for the effects of any rounding that occurred. */
+/* */
+/* res is C, the result. C may be A or B */
+/* lhs is A, the number to adjust */
+/* rhs is B, the requested exponent */
+/* set is the context */
+/* */
+/* C must have space for set->digits digits. */
+/* */
+/* Unless there is an error or the result is infinite, the exponent */
+/* after the operation is guaranteed to be equal to B. */
+/* ------------------------------------------------------------------ */
+decNumber * decNumberRescale(decNumber *res, const decNumber *lhs,
+ const decNumber *rhs, decContext *set) {
+ uInt status=0; // accumulator
+ decQuantizeOp(res, lhs, rhs, set, 0, &status);
+ if (status!=0) decStatus(res, status, set);
+ return res;
+ } // decNumberRescale
+
+/* ------------------------------------------------------------------ */
+/* decNumberRemainder -- divide and return remainder */
+/* */
+/* This computes C = A % B */
+/* */
+/* res is C, the result. C may be A and/or B (e.g., X=X%X) */
+/* lhs is A */
+/* rhs is B */
+/* set is the context */
+/* */
+/* C must have space for set->digits digits. */
+/* ------------------------------------------------------------------ */
+decNumber * decNumberRemainder(decNumber *res, const decNumber *lhs,
+ const decNumber *rhs, decContext *set) {
+ uInt status=0; // accumulator
+ decDivideOp(res, lhs, rhs, set, REMAINDER, &status);
+ if (status!=0) decStatus(res, status, set);
+ #if DECCHECK
+ decCheckInexact(res, set);
+ #endif
+ return res;
+ } // decNumberRemainder
+
+/* ------------------------------------------------------------------ */
+/* decNumberRemainderNear -- divide and return remainder from nearest */
+/* */
+/* This computes C = A % B, where % is the IEEE remainder operator */
+/* */
+/* res is C, the result. C may be A and/or B (e.g., X=X%X) */
+/* lhs is A */
+/* rhs is B */
+/* set is the context */
+/* */
+/* C must have space for set->digits digits. */
+/* ------------------------------------------------------------------ */
+decNumber * decNumberRemainderNear(decNumber *res, const decNumber *lhs,
+ const decNumber *rhs, decContext *set) {
+ uInt status=0; // accumulator
+ decDivideOp(res, lhs, rhs, set, REMNEAR, &status);
+ if (status!=0) decStatus(res, status, set);
+ #if DECCHECK
+ decCheckInexact(res, set);
+ #endif
+ return res;
+ } // decNumberRemainderNear
+
+/* ------------------------------------------------------------------ */
+/* decNumberRotate -- rotate the coefficient of a Number left/right */
+/* */
+/* This computes C = A rot B (in base ten and rotating set->digits */
+/* digits). */
+/* */
+/* res is C, the result. C may be A and/or B (e.g., X=XrotX) */
+/* lhs is A */
+/* rhs is B, the number of digits to rotate (-ve to right) */
+/* set is the context */
+/* */
+/* The digits of the coefficient of A are rotated to the left (if B */
+/* is positive) or to the right (if B is negative) without adjusting */
+/* the exponent or the sign of A. If lhs->digits is less than */
+/* set->digits the coefficient is padded with zeros on the left */
+/* before the rotate. Any leading zeros in the result are removed */
+/* as usual. */
+/* */
+/* B must be an integer (q=0) and in the range -set->digits through */
+/* +set->digits. */
+/* C must have space for set->digits digits. */
+/* NaNs are propagated as usual. Infinities are unaffected (but */
+/* B must be valid). No status is set unless B is invalid or an */
+/* operand is an sNaN. */
+/* ------------------------------------------------------------------ */
+decNumber * decNumberRotate(decNumber *res, const decNumber *lhs,
+ const decNumber *rhs, decContext *set) {
+ uInt status=0; // accumulator
+ Int rotate; // rhs as an Int
+
+ #if DECCHECK
+ if (decCheckOperands(res, lhs, rhs, set)) return res;
+ #endif
+
+ // NaNs propagate as normal
+ if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs))
+ decNaNs(res, lhs, rhs, set, &status);
+ // rhs must be an integer
+ else if (decNumberIsInfinite(rhs) || rhs->exponent!=0)
+ status=DEC_Invalid_operation;
+ else { // both numeric, rhs is an integer
+ rotate=decGetInt(rhs); // [cannot fail]
+ if (rotate==BADINT // something bad ..
+ || rotate==BIGODD || rotate==BIGEVEN // .. very big ..
+ || abs(rotate)>set->digits) // .. or out of range
+ status=DEC_Invalid_operation;
+ else { // rhs is OK
+ decNumberCopy(res, lhs);
+ // convert -ve rotate to equivalent positive rotation
+ if (rotate<0) rotate=set->digits+rotate;
+ if (rotate!=0 && rotate!=set->digits // zero or full rotation
+ && !decNumberIsInfinite(res)) { // lhs was infinite
+ // left-rotate to do; 0 < rotate < set->digits
+ uInt units, shift; // work
+ uInt msudigits; // digits in result msu
+ Unit *msu=res->lsu+D2U(res->digits)-1; // current msu
+ Unit *msumax=res->lsu+D2U(set->digits)-1; // rotation msu
+ for (msu++; msu<=msumax; msu++) *msu=0; // ensure high units=0
+ res->digits=set->digits; // now full-length
+ msudigits=MSUDIGITS(res->digits); // actual digits in msu
+
+ // rotation here is done in-place, in three steps
+ // 1. shift all to least up to one unit to unit-align final
+ // lsd [any digits shifted out are rotated to the left,
+ // abutted to the original msd (which may require split)]
+ //
+ // [if there are no whole units left to rotate, the
+ // rotation is now complete]
+ //
+ // 2. shift to least, from below the split point only, so that
+ // the final msd is in the right place in its Unit [any
+ // digits shifted out will fit exactly in the current msu,
+ // left aligned, no split required]
+ //
+ // 3. rotate all the units by reversing left part, right
+ // part, and then whole
+ //
+ // example: rotate right 8 digits (2 units + 2), DECDPUN=3.
+ //
+ // start: 00a bcd efg hij klm npq
+ //
+ // 1a 000 0ab cde fgh|ijk lmn [pq saved]
+ // 1b 00p qab cde fgh|ijk lmn
+ //
+ // 2a 00p qab cde fgh|00i jkl [mn saved]
+ // 2b mnp qab cde fgh|00i jkl
+ //
+ // 3a fgh cde qab mnp|00i jkl
+ // 3b fgh cde qab mnp|jkl 00i
+ // 3c 00i jkl mnp qab cde fgh
+
+ // Step 1: amount to shift is the partial right-rotate count
+ rotate=set->digits-rotate; // make it right-rotate
+ units=rotate/DECDPUN; // whole units to rotate
+ shift=rotate%DECDPUN; // left-over digits count
+ if (shift>0) { // not an exact number of units
+ uInt save=res->lsu[0]%powers[shift]; // save low digit(s)
+ decShiftToLeast(res->lsu, D2U(res->digits), shift);
+ if (shift>msudigits) { // msumax-1 needs >0 digits
+ uInt rem=save%powers[shift-msudigits];// split save
+ *msumax=(Unit)(save/powers[shift-msudigits]); // and insert
+ *(msumax-1)=*(msumax-1)
+ +(Unit)(rem*powers[DECDPUN-(shift-msudigits)]); // ..
+ }
+ else { // all fits in msumax
+ *msumax=*msumax+(Unit)(save*powers[msudigits-shift]); // [maybe *1]
+ }
+ } // digits shift needed
+
+ // If whole units to rotate...
+ if (units>0) { // some to do
+ // Step 2: the units to touch are the whole ones in rotate,
+ // if any, and the shift is DECDPUN-msudigits (which may be
+ // 0, again)
+ shift=DECDPUN-msudigits;
+ if (shift>0) { // not an exact number of units
+ uInt save=res->lsu[0]%powers[shift]; // save low digit(s)
+ decShiftToLeast(res->lsu, units, shift);
+ *msumax=*msumax+(Unit)(save*powers[msudigits]);
+ } // partial shift needed
+
+ // Step 3: rotate the units array using triple reverse
+ // (reversing is easy and fast)
+ decReverse(res->lsu+units, msumax); // left part
+ decReverse(res->lsu, res->lsu+units-1); // right part
+ decReverse(res->lsu, msumax); // whole
+ } // whole units to rotate
+ // the rotation may have left an undetermined number of zeros
+ // on the left, so true length needs to be calculated
+ res->digits=decGetDigits(res->lsu, msumax-res->lsu+1);
+ } // rotate needed
+ } // rhs OK
+ } // numerics
+ if (status!=0) decStatus(res, status, set);
+ return res;
+ } // decNumberRotate
+
+/* ------------------------------------------------------------------ */
+/* decNumberSameQuantum -- test for equal exponents */
+/* */
+/* res is the result number, which will contain either 0 or 1 */
+/* lhs is a number to test */
+/* rhs is the second (usually a pattern) */
+/* */
+/* No errors are possible and no context is needed. */
+/* ------------------------------------------------------------------ */
+decNumber * decNumberSameQuantum(decNumber *res, const decNumber *lhs,
+ const decNumber *rhs) {
+ Unit ret=0; // return value
+
+ #if DECCHECK
+ if (decCheckOperands(res, lhs, rhs, DECUNCONT)) return res;
+ #endif
+
+ if (SPECIALARGS) {
+ if (decNumberIsNaN(lhs) && decNumberIsNaN(rhs)) ret=1;
+ else if (decNumberIsInfinite(lhs) && decNumberIsInfinite(rhs)) ret=1;
+ // [anything else with a special gives 0]
+ }
+ else if (lhs->exponent==rhs->exponent) ret=1;
+
+ decNumberZero(res); // OK to overwrite an operand now
+ *res->lsu=ret;
+ return res;
+ } // decNumberSameQuantum
+
+/* ------------------------------------------------------------------ */
+/* decNumberScaleB -- multiply by a power of 10 */
+/* */
+/* This computes C = A x 10**B where B is an integer (q=0) with */
+/* maximum magnitude 2*(emax+digits) */
+/* */
+/* res is C, the result. C may be A or B */
+/* lhs is A, the number to adjust */
+/* rhs is B, the requested power of ten to use */
+/* set is the context */
+/* */
+/* C must have space for set->digits digits. */
+/* */
+/* The result may underflow or overflow. */
+/* ------------------------------------------------------------------ */
+decNumber * decNumberScaleB(decNumber *res, const decNumber *lhs,
+ const decNumber *rhs, decContext *set) {
+ Int reqexp; // requested exponent change [B]
+ uInt status=0; // accumulator
+ Int residue; // work
+
+ #if DECCHECK
+ if (decCheckOperands(res, lhs, rhs, set)) return res;
+ #endif
+
+ // Handle special values except lhs infinite
+ if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs))
+ decNaNs(res, lhs, rhs, set, &status);
+ // rhs must be an integer
+ else if (decNumberIsInfinite(rhs) || rhs->exponent!=0)
+ status=DEC_Invalid_operation;
+ else {
+ // lhs is a number; rhs is a finite with q==0
+ reqexp=decGetInt(rhs); // [cannot fail]
+ // maximum range is larger than getInt can handle, so this is
+ // more restrictive than the specification
+ if (reqexp==BADINT // something bad ..
+ || reqexp==BIGODD || reqexp==BIGEVEN // it was huge
+ || (abs(reqexp)+1)/2>(set->digits+set->emax)) // .. or out of range
+ status=DEC_Invalid_operation;
+ else { // rhs is OK
+ decNumberCopy(res, lhs); // all done if infinite lhs
+ if (!decNumberIsInfinite(res)) { // prepare to scale
+ Int exp=res->exponent; // save for overflow test
+ res->exponent+=reqexp; // adjust the exponent
+ if (((exp^reqexp)>=0) // same sign ...
+ && ((exp^res->exponent)<0)) { // .. but result had different
+ // the calculation overflowed, so force right treatment
+ if (exp<0) res->exponent=DEC_MIN_EMIN-DEC_MAX_DIGITS;
+ else res->exponent=DEC_MAX_EMAX+1;
+ }
+ residue=0;
+ decFinalize(res, set, &residue, &status); // final check
+ } // finite LHS
+ } // rhs OK
+ } // rhs finite
+ if (status!=0) decStatus(res, status, set);
+ return res;
+ } // decNumberScaleB
+
+/* ------------------------------------------------------------------ */
+/* decNumberShift -- shift the coefficient of a Number left or right */
+/* */
+/* This computes C = A << B or C = A >> -B (in base ten). */
+/* */
+/* res is C, the result. C may be A and/or B (e.g., X=X<<X) */
+/* lhs is A */
+/* rhs is B, the number of digits to shift (-ve to right) */
+/* set is the context */
+/* */
+/* The digits of the coefficient of A are shifted to the left (if B */
+/* is positive) or to the right (if B is negative) without adjusting */
+/* the exponent or the sign of A. */
+/* */
+/* B must be an integer (q=0) and in the range -set->digits through */
+/* +set->digits. */
+/* C must have space for set->digits digits. */
+/* NaNs are propagated as usual. Infinities are unaffected (but */
+/* B must be valid). No status is set unless B is invalid or an */
+/* operand is an sNaN. */
+/* ------------------------------------------------------------------ */
+decNumber * decNumberShift(decNumber *res, const decNumber *lhs,
+ const decNumber *rhs, decContext *set) {
+ uInt status=0; // accumulator
+ Int shift; // rhs as an Int
+
+ #if DECCHECK
+ if (decCheckOperands(res, lhs, rhs, set)) return res;
+ #endif
+
+ // NaNs propagate as normal
+ if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs))
+ decNaNs(res, lhs, rhs, set, &status);
+ // rhs must be an integer
+ else if (decNumberIsInfinite(rhs) || rhs->exponent!=0)
+ status=DEC_Invalid_operation;
+ else { // both numeric, rhs is an integer
+ shift=decGetInt(rhs); // [cannot fail]
+ if (shift==BADINT // something bad ..
+ || shift==BIGODD || shift==BIGEVEN // .. very big ..
+ || abs(shift)>set->digits) // .. or out of range
+ status=DEC_Invalid_operation;
+ else { // rhs is OK
+ decNumberCopy(res, lhs);
+ if (shift!=0 && !decNumberIsInfinite(res)) { // something to do
+ if (shift>0) { // to left
+ if (shift==set->digits) { // removing all
+ *res->lsu=0; // so place 0
+ res->digits=1; // ..
+ }
+ else { //
+ // first remove leading digits if necessary
+ if (res->digits+shift>set->digits) {
+ decDecap(res, res->digits+shift-set->digits);
+ // that updated res->digits; may have gone to 1 (for a
+ // single digit or for zero
+ }
+ if (res->digits>1 || *res->lsu) // if non-zero..
+ res->digits=decShiftToMost(res->lsu, res->digits, shift);
+ } // partial left
+ } // left
+ else { // to right
+ if (-shift>=res->digits) { // discarding all
+ *res->lsu=0; // so place 0
+ res->digits=1; // ..
+ }
+ else {
+ decShiftToLeast(res->lsu, D2U(res->digits), -shift);
+ res->digits-=(-shift);
+ }
+ } // to right
+ } // non-0 non-Inf shift
+ } // rhs OK
+ } // numerics
+ if (status!=0) decStatus(res, status, set);
+ return res;
+ } // decNumberShift
+
+/* ------------------------------------------------------------------ */
+/* decNumberSquareRoot -- square root operator */
+/* */
+/* This computes C = squareroot(A) */
+/* */
+/* res is C, the result. C may be A */
+/* rhs is A */
+/* set is the context; note that rounding mode has no effect */
+/* */
+/* C must have space for set->digits digits. */
+/* ------------------------------------------------------------------ */
+/* This uses the following varying-precision algorithm in: */
+/* */
+/* Properly Rounded Variable Precision Square Root, T. E. Hull and */
+/* A. Abrham, ACM Transactions on Mathematical Software, Vol 11 #3, */
+/* pp229-237, ACM, September 1985. */
+/* */
+/* The square-root is calculated using Newton's method, after which */
+/* a check is made to ensure the result is correctly rounded. */
+/* */
+/* % [Reformatted original Numerical Turing source code follows.] */
+/* function sqrt(x : real) : real */
+/* % sqrt(x) returns the properly rounded approximation to the square */
+/* % root of x, in the precision of the calling environment, or it */
+/* % fails if x < 0. */
+/* % t e hull and a abrham, august, 1984 */
+/* if x <= 0 then */
+/* if x < 0 then */
+/* assert false */
+/* else */
+/* result 0 */
+/* end if */
+/* end if */
+/* var f := setexp(x, 0) % fraction part of x [0.1 <= x < 1] */
+/* var e := getexp(x) % exponent part of x */
+/* var approx : real */
+/* if e mod 2 = 0 then */
+/* approx := .259 + .819 * f % approx to root of f */
+/* else */
+/* f := f/l0 % adjustments */
+/* e := e + 1 % for odd */
+/* approx := .0819 + 2.59 * f % exponent */
+/* end if */
+/* */
+/* var p:= 3 */
+/* const maxp := currentprecision + 2 */
+/* loop */
+/* p := min(2*p - 2, maxp) % p = 4,6,10, . . . , maxp */
+/* precision p */
+/* approx := .5 * (approx + f/approx) */
+/* exit when p = maxp */
+/* end loop */
+/* */
+/* % approx is now within 1 ulp of the properly rounded square root */
+/* % of f; to ensure proper rounding, compare squares of (approx - */
+/* % l/2 ulp) and (approx + l/2 ulp) with f. */
+/* p := currentprecision */
+/* begin */
+/* precision p + 2 */
+/* const approxsubhalf := approx - setexp(.5, -p) */
+/* if mulru(approxsubhalf, approxsubhalf) > f then */
+/* approx := approx - setexp(.l, -p + 1) */
+/* else */
+/* const approxaddhalf := approx + setexp(.5, -p) */
+/* if mulrd(approxaddhalf, approxaddhalf) < f then */
+/* approx := approx + setexp(.l, -p + 1) */
+/* end if */
+/* end if */
+/* end */
+/* result setexp(approx, e div 2) % fix exponent */
+/* end sqrt */
+/* ------------------------------------------------------------------ */
+decNumber * decNumberSquareRoot(decNumber *res, const decNumber *rhs,
+ decContext *set) {
+ decContext workset, approxset; // work contexts
+ decNumber dzero; // used for constant zero
+ Int maxp; // largest working precision
+ Int workp; // working precision
+ Int residue=0; // rounding residue
+ uInt status=0, ignore=0; // status accumulators
+ uInt rstatus; // ..
+ Int exp; // working exponent
+ Int ideal; // ideal (preferred) exponent
+ Int needbytes; // work
+ Int dropped; // ..
+
+ #if DECSUBSET
+ decNumber *allocrhs=NULL; // non-NULL if rounded rhs allocated
+ #endif
+ // buffer for f [needs +1 in case DECBUFFER 0]
+ decNumber buff[D2N(DECBUFFER+1)];
+ // buffer for a [needs +2 to match likely maxp]
+ decNumber bufa[D2N(DECBUFFER+2)];
+ // buffer for temporary, b [must be same size as a]
+ decNumber bufb[D2N(DECBUFFER+2)];
+ decNumber *allocbuff=NULL; // -> allocated buff, iff allocated
+ decNumber *allocbufa=NULL; // -> allocated bufa, iff allocated
+ decNumber *allocbufb=NULL; // -> allocated bufb, iff allocated
+ decNumber *f=buff; // reduced fraction
+ decNumber *a=bufa; // approximation to result
+ decNumber *b=bufb; // intermediate result
+ // buffer for temporary variable, up to 3 digits
+ decNumber buft[D2N(3)];
+ decNumber *t=buft; // up-to-3-digit constant or work
+
+ #if DECCHECK
+ if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
+ #endif
+
+ do { // protect allocated storage
+ #if DECSUBSET
+ if (!set->extended) {
+ // reduce operand and set lostDigits status, as needed
+ if (rhs->digits>set->digits) {
+ allocrhs=decRoundOperand(rhs, set, &status);
+ if (allocrhs==NULL) break;
+ // [Note: 'f' allocation below could reuse this buffer if
+ // used, but as this is rare they are kept separate for clarity.]
+ rhs=allocrhs;
+ }
+ }
+ #endif
+ // [following code does not require input rounding]
+
+ // handle infinities and NaNs
+ if (SPECIALARG) {
+ if (decNumberIsInfinite(rhs)) { // an infinity
+ if (decNumberIsNegative(rhs)) status|=DEC_Invalid_operation;
+ else decNumberCopy(res, rhs); // +Infinity
+ }
+ else decNaNs(res, rhs, NULL, set, &status); // a NaN
+ break;
+ }
+
+ // calculate the ideal (preferred) exponent [floor(exp/2)]
+ // [It would be nicer to write: ideal=rhs->exponent>>1, but this
+ // generates a compiler warning. Generated code is the same.]
+ ideal=(rhs->exponent&~1)/2; // target
+
+ // handle zeros
+ if (ISZERO(rhs)) {
+ decNumberCopy(res, rhs); // could be 0 or -0
+ res->exponent=ideal; // use the ideal [safe]
+ // use decFinish to clamp any out-of-range exponent, etc.
+ decFinish(res, set, &residue, &status);
+ break;
+ }
+
+ // any other -x is an oops
+ if (decNumberIsNegative(rhs)) {
+ status|=DEC_Invalid_operation;
+ break;
+ }
+
+ // space is needed for three working variables
+ // f -- the same precision as the RHS, reduced to 0.01->0.99...
+ // a -- Hull's approximation -- precision, when assigned, is
+ // currentprecision+1 or the input argument precision,
+ // whichever is larger (+2 for use as temporary)
+ // b -- intermediate temporary result (same size as a)
+ // if any is too long for local storage, then allocate
+ workp=MAXI(set->digits+1, rhs->digits); // actual rounding precision
+ workp=MAXI(workp, 7); // at least 7 for low cases
+ maxp=workp+2; // largest working precision
+
+ needbytes=sizeof(decNumber)+(D2U(rhs->digits)-1)*sizeof(Unit);
+ if (needbytes>(Int)sizeof(buff)) {
+ allocbuff=(decNumber *)malloc(needbytes);
+ if (allocbuff==NULL) { // hopeless -- abandon
+ status|=DEC_Insufficient_storage;
+ break;}
+ f=allocbuff; // use the allocated space
+ }
+ // a and b both need to be able to hold a maxp-length number
+ needbytes=sizeof(decNumber)+(D2U(maxp)-1)*sizeof(Unit);
+ if (needbytes>(Int)sizeof(bufa)) { // [same applies to b]
+ allocbufa=(decNumber *)malloc(needbytes);
+ allocbufb=(decNumber *)malloc(needbytes);
+ if (allocbufa==NULL || allocbufb==NULL) { // hopeless
+ status|=DEC_Insufficient_storage;
+ break;}
+ a=allocbufa; // use the allocated spaces
+ b=allocbufb; // ..
+ }
+
+ // copy rhs -> f, save exponent, and reduce so 0.1 <= f < 1
+ decNumberCopy(f, rhs);
+ exp=f->exponent+f->digits; // adjusted to Hull rules
+ f->exponent=-(f->digits); // to range
+
+ // set up working context
+ decContextDefault(&workset, DEC_INIT_DECIMAL64);
+ workset.emax=DEC_MAX_EMAX;
+ workset.emin=DEC_MIN_EMIN;
+
+ // [Until further notice, no error is possible and status bits
+ // (Rounded, etc.) should be ignored, not accumulated.]
+
+ // Calculate initial approximation, and allow for odd exponent
+ workset.digits=workp; // p for initial calculation
+ t->bits=0; t->digits=3;
+ a->bits=0; a->digits=3;
+ if ((exp & 1)==0) { // even exponent
+ // Set t=0.259, a=0.819
+ t->exponent=-3;
+ a->exponent=-3;
+ #if DECDPUN>=3
+ t->lsu[0]=259;
+ a->lsu[0]=819;
+ #elif DECDPUN==2
+ t->lsu[0]=59; t->lsu[1]=2;
+ a->lsu[0]=19; a->lsu[1]=8;
+ #else
+ t->lsu[0]=9; t->lsu[1]=5; t->lsu[2]=2;
+ a->lsu[0]=9; a->lsu[1]=1; a->lsu[2]=8;
+ #endif
+ }
+ else { // odd exponent
+ // Set t=0.0819, a=2.59
+ f->exponent--; // f=f/10
+ exp++; // e=e+1
+ t->exponent=-4;
+ a->exponent=-2;
+ #if DECDPUN>=3
+ t->lsu[0]=819;
+ a->lsu[0]=259;
+ #elif DECDPUN==2
+ t->lsu[0]=19; t->lsu[1]=8;
+ a->lsu[0]=59; a->lsu[1]=2;
+ #else
+ t->lsu[0]=9; t->lsu[1]=1; t->lsu[2]=8;
+ a->lsu[0]=9; a->lsu[1]=5; a->lsu[2]=2;
+ #endif
+ }
+
+ decMultiplyOp(a, a, f, &workset, &ignore); // a=a*f
+ decAddOp(a, a, t, &workset, 0, &ignore); // ..+t
+ // [a is now the initial approximation for sqrt(f), calculated with
+ // currentprecision, which is also a's precision.]
+
+ // the main calculation loop
+ decNumberZero(&dzero); // make 0
+ decNumberZero(t); // set t = 0.5
+ t->lsu[0]=5; // ..
+ t->exponent=-1; // ..
+ workset.digits=3; // initial p
+ for (; workset.digits<maxp;) {
+ // set p to min(2*p - 2, maxp) [hence 3; or: 4, 6, 10, ... , maxp]
+ workset.digits=MINI(workset.digits*2-2, maxp);
+ // a = 0.5 * (a + f/a)
+ // [calculated at p then rounded to currentprecision]
+ decDivideOp(b, f, a, &workset, DIVIDE, &ignore); // b=f/a
+ decAddOp(b, b, a, &workset, 0, &ignore); // b=b+a
+ decMultiplyOp(a, b, t, &workset, &ignore); // a=b*0.5
+ } // loop
+
+ // Here, 0.1 <= a < 1 [Hull], and a has maxp digits
+ // now reduce to length, etc.; this needs to be done with a
+ // having the correct exponent so as to handle subnormals
+ // correctly
+ approxset=*set; // get emin, emax, etc.
+ approxset.round=DEC_ROUND_HALF_EVEN;
+ a->exponent+=exp/2; // set correct exponent
+ rstatus=0; // clear status
+ residue=0; // .. and accumulator
+ decCopyFit(a, a, &approxset, &residue, &rstatus); // reduce (if needed)
+ decFinish(a, &approxset, &residue, &rstatus); // clean and finalize
+
+ // Overflow was possible if the input exponent was out-of-range,
+ // in which case quit
+ if (rstatus&DEC_Overflow) {
+ status=rstatus; // use the status as-is
+ decNumberCopy(res, a); // copy to result
+ break;
+ }
+
+ // Preserve status except Inexact/Rounded
+ status|=(rstatus & ~(DEC_Rounded|DEC_Inexact));
+
+ // Carry out the Hull correction
+ a->exponent-=exp/2; // back to 0.1->1
+
+ // a is now at final precision and within 1 ulp of the properly
+ // rounded square root of f; to ensure proper rounding, compare
+ // squares of (a - l/2 ulp) and (a + l/2 ulp) with f.
+ // Here workset.digits=maxp and t=0.5, and a->digits determines
+ // the ulp
+ workset.digits--; // maxp-1 is OK now
+ t->exponent=-a->digits-1; // make 0.5 ulp
+ decAddOp(b, a, t, &workset, DECNEG, &ignore); // b = a - 0.5 ulp
+ workset.round=DEC_ROUND_UP;
+ decMultiplyOp(b, b, b, &workset, &ignore); // b = mulru(b, b)
+ decCompareOp(b, f, b, &workset, COMPARE, &ignore); // b ? f, reversed
+ if (decNumberIsNegative(b)) { // f < b [i.e., b > f]
+ // this is the more common adjustment, though both are rare
+ t->exponent++; // make 1.0 ulp
+ t->lsu[0]=1; // ..
+ decAddOp(a, a, t, &workset, DECNEG, &ignore); // a = a - 1 ulp
+ // assign to approx [round to length]
+ approxset.emin-=exp/2; // adjust to match a
+ approxset.emax-=exp/2;
+ decAddOp(a, &dzero, a, &approxset, 0, &ignore);
+ }
+ else {
+ decAddOp(b, a, t, &workset, 0, &ignore); // b = a + 0.5 ulp
+ workset.round=DEC_ROUND_DOWN;
+ decMultiplyOp(b, b, b, &workset, &ignore); // b = mulrd(b, b)
+ decCompareOp(b, b, f, &workset, COMPARE, &ignore); // b ? f
+ if (decNumberIsNegative(b)) { // b < f
+ t->exponent++; // make 1.0 ulp
+ t->lsu[0]=1; // ..
+ decAddOp(a, a, t, &workset, 0, &ignore); // a = a + 1 ulp
+ // assign to approx [round to length]
+ approxset.emin-=exp/2; // adjust to match a
+ approxset.emax-=exp/2;
+ decAddOp(a, &dzero, a, &approxset, 0, &ignore);
+ }
+ }
+ // [no errors are possible in the above, and rounding/inexact during
+ // estimation are irrelevant, so status was not accumulated]
+
+ // Here, 0.1 <= a < 1 (still), so adjust back
+ a->exponent+=exp/2; // set correct exponent
+
+ // count droppable zeros [after any subnormal rounding] by
+ // trimming a copy
+ decNumberCopy(b, a);
+ decTrim(b, set, 1, 1, &dropped); // [drops trailing zeros]
+
+ // Set Inexact and Rounded. The answer can only be exact if
+ // it is short enough so that squaring it could fit in workp
+ // digits, so this is the only (relatively rare) condition that
+ // a careful check is needed
+ if (b->digits*2-1 > workp) { // cannot fit
+ status|=DEC_Inexact|DEC_Rounded;
+ }
+ else { // could be exact/unrounded
+ uInt mstatus=0; // local status
+ decMultiplyOp(b, b, b, &workset, &mstatus); // try the multiply
+ if (mstatus&DEC_Overflow) { // result just won't fit
+ status|=DEC_Inexact|DEC_Rounded;
+ }
+ else { // plausible
+ decCompareOp(t, b, rhs, &workset, COMPARE, &mstatus); // b ? rhs
+ if (!ISZERO(t)) status|=DEC_Inexact|DEC_Rounded; // not equal
+ else { // is Exact
+ // here, dropped is the count of trailing zeros in 'a'
+ // use closest exponent to ideal...
+ Int todrop=ideal-a->exponent; // most that can be dropped
+ if (todrop<0) status|=DEC_Rounded; // ideally would add 0s
+ else { // unrounded
+ // there are some to drop, but emax may not allow all
+ Int maxexp=set->emax-set->digits+1;
+ Int maxdrop=maxexp-a->exponent;
+ if (todrop>maxdrop && set->clamp) { // apply clamping
+ todrop=maxdrop;
+ status|=DEC_Clamped;
+ }
+ if (dropped<todrop) { // clamp to those available
+ todrop=dropped;
+ status|=DEC_Clamped;
+ }
+ if (todrop>0) { // have some to drop
+ decShiftToLeast(a->lsu, D2U(a->digits), todrop);
+ a->exponent+=todrop; // maintain numerical value
+ a->digits-=todrop; // new length
+ }
+ }
+ }
+ }
+ }
+
+ // double-check Underflow, as perhaps the result could not have
+ // been subnormal (initial argument too big), or it is now Exact
+ if (status&DEC_Underflow) {
+ Int ae=rhs->exponent+rhs->digits-1; // adjusted exponent
+ // check if truly subnormal
+ #if DECEXTFLAG // DEC_Subnormal too
+ if (ae>=set->emin*2) status&=~(DEC_Subnormal|DEC_Underflow);
+ #else
+ if (ae>=set->emin*2) status&=~DEC_Underflow;
+ #endif
+ // check if truly inexact
+ if (!(status&DEC_Inexact)) status&=~DEC_Underflow;
+ }
+
+ decNumberCopy(res, a); // a is now the result
+ } while(0); // end protected
+
+ if (allocbuff!=NULL) free(allocbuff); // drop any storage used
+ if (allocbufa!=NULL) free(allocbufa); // ..
+ if (allocbufb!=NULL) free(allocbufb); // ..
+ #if DECSUBSET
+ if (allocrhs !=NULL) free(allocrhs); // ..
+ #endif
+ if (status!=0) decStatus(res, status, set);// then report status
+ #if DECCHECK
+ decCheckInexact(res, set);
+ #endif
+ return res;
+ } // decNumberSquareRoot
+
+/* ------------------------------------------------------------------ */
+/* decNumberSubtract -- subtract two Numbers */
+/* */
+/* This computes C = A - B */
+/* */
+/* res is C, the result. C may be A and/or B (e.g., X=X-X) */
+/* lhs is A */
+/* rhs is B */
+/* set is the context */
+/* */
+/* C must have space for set->digits digits. */
+/* ------------------------------------------------------------------ */
+decNumber * decNumberSubtract(decNumber *res, const decNumber *lhs,
+ const decNumber *rhs, decContext *set) {
+ uInt status=0; // accumulator
+
+ decAddOp(res, lhs, rhs, set, DECNEG, &status);
+ if (status!=0) decStatus(res, status, set);
+ #if DECCHECK
+ decCheckInexact(res, set);
+ #endif
+ return res;
+ } // decNumberSubtract
+
+/* ------------------------------------------------------------------ */
+/* decNumberToIntegralExact -- round-to-integral-value with InExact */
+/* decNumberToIntegralValue -- round-to-integral-value */
+/* */
+/* res is the result */
+/* rhs is input number */
+/* set is the context */
+/* */
+/* res must have space for any value of rhs. */
+/* */
+/* This implements the IEEE special operators and therefore treats */
+/* special values as valid. For finite numbers it returns */
+/* rescale(rhs, 0) if rhs->exponent is <0. */
+/* Otherwise the result is rhs (so no error is possible, except for */
+/* sNaN). */
+/* */
+/* The context is used for rounding mode and status after sNaN, but */
+/* the digits setting is ignored. The Exact version will signal */
+/* Inexact if the result differs numerically from rhs; the other */
+/* never signals Inexact. */
+/* ------------------------------------------------------------------ */
+decNumber * decNumberToIntegralExact(decNumber *res, const decNumber *rhs,
+ decContext *set) {
+ decNumber dn;
+ decContext workset; // working context
+ uInt status=0; // accumulator
+
+ #if DECCHECK
+ if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
+ #endif
+
+ // handle infinities and NaNs
+ if (SPECIALARG) {
+ if (decNumberIsInfinite(rhs)) decNumberCopy(res, rhs); // an Infinity
+ else decNaNs(res, rhs, NULL, set, &status); // a NaN
+ }
+ else { // finite
+ // have a finite number; no error possible (res must be big enough)
+ if (rhs->exponent>=0) return decNumberCopy(res, rhs);
+ // that was easy, but if negative exponent there is work to do...
+ workset=*set; // clone rounding, etc.
+ workset.digits=rhs->digits; // no length rounding
+ workset.traps=0; // no traps
+ decNumberZero(&dn); // make a number with exponent 0
+ decNumberQuantize(res, rhs, &dn, &workset);
+ status|=workset.status;
+ }
+ if (status!=0) decStatus(res, status, set);
+ return res;
+ } // decNumberToIntegralExact
+
+decNumber * decNumberToIntegralValue(decNumber *res, const decNumber *rhs,
+ decContext *set) {
+ decContext workset=*set; // working context
+ workset.traps=0; // no traps
+ decNumberToIntegralExact(res, rhs, &workset);
+ // this never affects set, except for sNaNs; NaN will have been set
+ // or propagated already, so no need to call decStatus
+ set->status|=workset.status&DEC_Invalid_operation;
+ return res;
+ } // decNumberToIntegralValue
+
+/* ------------------------------------------------------------------ */
+/* decNumberXor -- XOR two Numbers, digitwise */
+/* */
+/* This computes C = A ^ B */
+/* */
+/* res is C, the result. C may be A and/or B (e.g., X=X^X) */
+/* lhs is A */
+/* rhs is B */
+/* set is the context (used for result length and error report) */
+/* */
+/* C must have space for set->digits digits. */
+/* */
+/* Logical function restrictions apply (see above); a NaN is */
+/* returned with Invalid_operation if a restriction is violated. */
+/* ------------------------------------------------------------------ */
+decNumber * decNumberXor(decNumber *res, const decNumber *lhs,
+ const decNumber *rhs, decContext *set) {
+ const Unit *ua, *ub; // -> operands
+ const Unit *msua, *msub; // -> operand msus
+ Unit *uc, *msuc; // -> result and its msu
+ Int msudigs; // digits in res msu
+ #if DECCHECK
+ if (decCheckOperands(res, lhs, rhs, set)) return res;
+ #endif
+
+ if (lhs->exponent!=0 || decNumberIsSpecial(lhs) || decNumberIsNegative(lhs)
+ || rhs->exponent!=0 || decNumberIsSpecial(rhs) || decNumberIsNegative(rhs)) {
+ decStatus(res, DEC_Invalid_operation, set);
+ return res;
+ }
+ // operands are valid
+ ua=lhs->lsu; // bottom-up
+ ub=rhs->lsu; // ..
+ uc=res->lsu; // ..
+ msua=ua+D2U(lhs->digits)-1; // -> msu of lhs
+ msub=ub+D2U(rhs->digits)-1; // -> msu of rhs
+ msuc=uc+D2U(set->digits)-1; // -> msu of result
+ msudigs=MSUDIGITS(set->digits); // [faster than remainder]
+ for (; uc<=msuc; ua++, ub++, uc++) { // Unit loop
+ Unit a, b; // extract units
+ if (ua>msua) a=0;
+ else a=*ua;
+ if (ub>msub) b=0;
+ else b=*ub;
+ *uc=0; // can now write back
+ if (a|b) { // maybe 1 bits to examine
+ Int i, j;
+ // This loop could be unrolled and/or use BIN2BCD tables
+ for (i=0; i<DECDPUN; i++) {
+ if ((a^b)&1) *uc=*uc+(Unit)powers[i]; // effect XOR
+ j=a%10;
+ a=a/10;
+ j|=b%10;
+ b=b/10;
+ if (j>1) {
+ decStatus(res, DEC_Invalid_operation, set);
+ return res;
+ }
+ if (uc==msuc && i==msudigs-1) break; // just did final digit
+ } // each digit
+ } // non-zero
+ } // each unit
+ // [here uc-1 is the msu of the result]
+ res->digits=decGetDigits(res->lsu, uc-res->lsu);
+ res->exponent=0; // integer
+ res->bits=0; // sign=0
+ return res; // [no status to set]
+ } // decNumberXor
+
+
+/* ================================================================== */
+/* Utility routines */
+/* ================================================================== */
+
+/* ------------------------------------------------------------------ */
+/* decNumberClass -- return the decClass of a decNumber */
+/* dn -- the decNumber to test */
+/* set -- the context to use for Emin */
+/* returns the decClass enum */
+/* ------------------------------------------------------------------ */
+enum decClass decNumberClass(const decNumber *dn, decContext *set) {
+ if (decNumberIsSpecial(dn)) {
+ if (decNumberIsQNaN(dn)) return DEC_CLASS_QNAN;
+ if (decNumberIsSNaN(dn)) return DEC_CLASS_SNAN;
+ // must be an infinity
+ if (decNumberIsNegative(dn)) return DEC_CLASS_NEG_INF;
+ return DEC_CLASS_POS_INF;
+ }
+ // is finite
+ if (decNumberIsNormal(dn, set)) { // most common
+ if (decNumberIsNegative(dn)) return DEC_CLASS_NEG_NORMAL;
+ return DEC_CLASS_POS_NORMAL;
+ }
+ // is subnormal or zero
+ if (decNumberIsZero(dn)) { // most common
+ if (decNumberIsNegative(dn)) return DEC_CLASS_NEG_ZERO;
+ return DEC_CLASS_POS_ZERO;
+ }
+ if (decNumberIsNegative(dn)) return DEC_CLASS_NEG_SUBNORMAL;
+ return DEC_CLASS_POS_SUBNORMAL;
+ } // decNumberClass
+
+/* ------------------------------------------------------------------ */
+/* decNumberClassToString -- convert decClass to a string */
+/* */
+/* eclass is a valid decClass */
+/* returns a constant string describing the class (max 13+1 chars) */
+/* ------------------------------------------------------------------ */
+const char *decNumberClassToString(enum decClass eclass) {
+ if (eclass==DEC_CLASS_POS_NORMAL) return DEC_ClassString_PN;
+ if (eclass==DEC_CLASS_NEG_NORMAL) return DEC_ClassString_NN;
+ if (eclass==DEC_CLASS_POS_ZERO) return DEC_ClassString_PZ;
+ if (eclass==DEC_CLASS_NEG_ZERO) return DEC_ClassString_NZ;
+ if (eclass==DEC_CLASS_POS_SUBNORMAL) return DEC_ClassString_PS;
+ if (eclass==DEC_CLASS_NEG_SUBNORMAL) return DEC_ClassString_NS;
+ if (eclass==DEC_CLASS_POS_INF) return DEC_ClassString_PI;
+ if (eclass==DEC_CLASS_NEG_INF) return DEC_ClassString_NI;
+ if (eclass==DEC_CLASS_QNAN) return DEC_ClassString_QN;
+ if (eclass==DEC_CLASS_SNAN) return DEC_ClassString_SN;
+ return DEC_ClassString_UN; // Unknown
+ } // decNumberClassToString
+
+/* ------------------------------------------------------------------ */
+/* decNumberCopy -- copy a number */
+/* */
+/* dest is the target decNumber */
+/* src is the source decNumber */
+/* returns dest */
+/* */
+/* (dest==src is allowed and is a no-op) */
+/* All fields are updated as required. This is a utility operation, */
+/* so special values are unchanged and no error is possible. */
+/* ------------------------------------------------------------------ */
+decNumber * decNumberCopy(decNumber *dest, const decNumber *src) {
+
+ #if DECCHECK
+ if (src==NULL) return decNumberZero(dest);
+ #endif
+
+ if (dest==src) return dest; // no copy required
+
+ // Use explicit assignments here as structure assignment could copy
+ // more than just the lsu (for small DECDPUN). This would not affect
+ // the value of the results, but could disturb test harness spill
+ // checking.
+ dest->bits=src->bits;
+ dest->exponent=src->exponent;
+ dest->digits=src->digits;
+ dest->lsu[0]=src->lsu[0];
+ if (src->digits>DECDPUN) { // more Units to come
+ const Unit *smsup, *s; // work
+ Unit *d; // ..
+ // memcpy for the remaining Units would be safe as they cannot
+ // overlap. However, this explicit loop is faster in short cases.
+ d=dest->lsu+1; // -> first destination
+ smsup=src->lsu+D2U(src->digits); // -> source msu+1
+ for (s=src->lsu+1; s<smsup; s++, d++) *d=*s;
+ }
+ return dest;
+ } // decNumberCopy
+
+/* ------------------------------------------------------------------ */
+/* decNumberCopyAbs -- quiet absolute value operator */
+/* */
+/* This sets C = abs(A) */
+/* */
+/* res is C, the result. C may be A */
+/* rhs is A */
+/* */
+/* C must have space for set->digits digits. */
+/* No exception or error can occur; this is a quiet bitwise operation.*/
+/* See also decNumberAbs for a checking version of this. */
+/* ------------------------------------------------------------------ */
+decNumber * decNumberCopyAbs(decNumber *res, const decNumber *rhs) {
+ #if DECCHECK
+ if (decCheckOperands(res, DECUNUSED, rhs, DECUNCONT)) return res;
+ #endif
+ decNumberCopy(res, rhs);
+ res->bits&=~DECNEG; // turn off sign
+ return res;
+ } // decNumberCopyAbs
+
+/* ------------------------------------------------------------------ */
+/* decNumberCopyNegate -- quiet negate value operator */
+/* */
+/* This sets C = negate(A) */
+/* */
+/* res is C, the result. C may be A */
+/* rhs is A */
+/* */
+/* C must have space for set->digits digits. */
+/* No exception or error can occur; this is a quiet bitwise operation.*/
+/* See also decNumberMinus for a checking version of this. */
+/* ------------------------------------------------------------------ */
+decNumber * decNumberCopyNegate(decNumber *res, const decNumber *rhs) {
+ #if DECCHECK
+ if (decCheckOperands(res, DECUNUSED, rhs, DECUNCONT)) return res;
+ #endif
+ decNumberCopy(res, rhs);
+ res->bits^=DECNEG; // invert the sign
+ return res;
+ } // decNumberCopyNegate
+
+/* ------------------------------------------------------------------ */
+/* decNumberCopySign -- quiet copy and set sign operator */
+/* */
+/* This sets C = A with the sign of B */
+/* */
+/* res is C, the result. C may be A */
+/* lhs is A */
+/* rhs is B */
+/* */
+/* C must have space for set->digits digits. */
+/* No exception or error can occur; this is a quiet bitwise operation.*/
+/* ------------------------------------------------------------------ */
+decNumber * decNumberCopySign(decNumber *res, const decNumber *lhs,
+ const decNumber *rhs) {
+ uByte sign; // rhs sign
+ #if DECCHECK
+ if (decCheckOperands(res, DECUNUSED, rhs, DECUNCONT)) return res;
+ #endif
+ sign=rhs->bits & DECNEG; // save sign bit
+ decNumberCopy(res, lhs);
+ res->bits&=~DECNEG; // clear the sign
+ res->bits|=sign; // set from rhs
+ return res;
+ } // decNumberCopySign
+
+/* ------------------------------------------------------------------ */
+/* decNumberGetBCD -- get the coefficient in BCD8 */
+/* dn is the source decNumber */
+/* bcd is the uInt array that will receive dn->digits BCD bytes, */
+/* most-significant at offset 0 */
+/* returns bcd */
+/* */
+/* bcd must have at least dn->digits bytes. No error is possible; if */
+/* dn is a NaN or Infinite, digits must be 1 and the coefficient 0. */
+/* ------------------------------------------------------------------ */
+uByte * decNumberGetBCD(const decNumber *dn, uByte *bcd) {
+ uByte *ub=bcd+dn->digits-1; // -> lsd
+ const Unit *up=dn->lsu; // Unit pointer, -> lsu
+
+ #if DECDPUN==1 // trivial simple copy
+ for (; ub>=bcd; ub--, up++) *ub=*up;
+ #else // chopping needed
+ uInt u=*up; // work
+ uInt cut=DECDPUN; // downcounter through unit
+ for (; ub>=bcd; ub--) {
+ *ub=(uByte)(u%10); // [*6554 trick inhibits, here]
+ u=u/10;
+ cut--;
+ if (cut>0) continue; // more in this unit
+ up++;
+ u=*up;
+ cut=DECDPUN;
+ }
+ #endif
+ return bcd;
+ } // decNumberGetBCD
+
+/* ------------------------------------------------------------------ */
+/* decNumberSetBCD -- set (replace) the coefficient from BCD8 */
+/* dn is the target decNumber */
+/* bcd is the uInt array that will source n BCD bytes, most- */
+/* significant at offset 0 */
+/* n is the number of digits in the source BCD array (bcd) */
+/* returns dn */
+/* */
+/* dn must have space for at least n digits. No error is possible; */
+/* if dn is a NaN, or Infinite, or is to become a zero, n must be 1 */
+/* and bcd[0] zero. */
+/* ------------------------------------------------------------------ */
+decNumber * decNumberSetBCD(decNumber *dn, const uByte *bcd, uInt n) {
+ Unit *up=dn->lsu+D2U(dn->digits)-1; // -> msu [target pointer]
+ const uByte *ub=bcd; // -> source msd
+
+ #if DECDPUN==1 // trivial simple copy
+ for (; ub<bcd+n; ub++, up--) *up=*ub;
+ #else // some assembly needed
+ // calculate how many digits in msu, and hence first cut
+ Int cut=MSUDIGITS(n); // [faster than remainder]
+ for (;up>=dn->lsu; up--) { // each Unit from msu
+ *up=0; // will take <=DECDPUN digits
+ for (; cut>0; ub++, cut--) *up=X10(*up)+*ub;
+ cut=DECDPUN; // next Unit has all digits
+ }
+ #endif
+ dn->digits=n; // set digit count
+ return dn;
+ } // decNumberSetBCD
+
+/* ------------------------------------------------------------------ */
+/* decNumberIsNormal -- test normality of a decNumber */
+/* dn is the decNumber to test */
+/* set is the context to use for Emin */
+/* returns 1 if |dn| is finite and >=Nmin, 0 otherwise */
+/* ------------------------------------------------------------------ */
+Int decNumberIsNormal(const decNumber *dn, decContext *set) {
+ Int ae; // adjusted exponent
+ #if DECCHECK
+ if (decCheckOperands(DECUNRESU, DECUNUSED, dn, set)) return 0;
+ #endif
+
+ if (decNumberIsSpecial(dn)) return 0; // not finite
+ if (decNumberIsZero(dn)) return 0; // not non-zero
+
+ ae=dn->exponent+dn->digits-1; // adjusted exponent
+ if (ae<set->emin) return 0; // is subnormal
+ return 1;
+ } // decNumberIsNormal
+
+/* ------------------------------------------------------------------ */
+/* decNumberIsSubnormal -- test subnormality of a decNumber */
+/* dn is the decNumber to test */
+/* set is the context to use for Emin */
+/* returns 1 if |dn| is finite, non-zero, and <Nmin, 0 otherwise */
+/* ------------------------------------------------------------------ */
+Int decNumberIsSubnormal(const decNumber *dn, decContext *set) {
+ Int ae; // adjusted exponent
+ #if DECCHECK
+ if (decCheckOperands(DECUNRESU, DECUNUSED, dn, set)) return 0;
+ #endif
+
+ if (decNumberIsSpecial(dn)) return 0; // not finite
+ if (decNumberIsZero(dn)) return 0; // not non-zero
+
+ ae=dn->exponent+dn->digits-1; // adjusted exponent
+ if (ae<set->emin) return 1; // is subnormal
+ return 0;
+ } // decNumberIsSubnormal
+
+/* ------------------------------------------------------------------ */
+/* decNumberTrim -- remove insignificant zeros */
+/* */
+/* dn is the number to trim */
+/* returns dn */
+/* */
+/* All fields are updated as required. This is a utility operation, */
+/* so special values are unchanged and no error is possible. The */
+/* zeros are removed unconditionally. */
+/* ------------------------------------------------------------------ */
+decNumber * decNumberTrim(decNumber *dn) {
+ Int dropped; // work
+ decContext set; // ..
+ #if DECCHECK
+ if (decCheckOperands(DECUNRESU, DECUNUSED, dn, DECUNCONT)) return dn;
+ #endif
+ decContextDefault(&set, DEC_INIT_BASE); // clamp=0
+ return decTrim(dn, &set, 0, 1, &dropped);
+ } // decNumberTrim
+
+/* ------------------------------------------------------------------ */
+/* decNumberVersion -- return the name and version of this module */
+/* */
+/* No error is possible. */
+/* ------------------------------------------------------------------ */
+const char * decNumberVersion(void) {
+ return DECVERSION;
+ } // decNumberVersion
+
+/* ------------------------------------------------------------------ */
+/* decNumberZero -- set a number to 0 */
+/* */
+/* dn is the number to set, with space for one digit */
+/* returns dn */
+/* */
+/* No error is possible. */
+/* ------------------------------------------------------------------ */
+// Memset is not used as it is much slower in some environments.
+decNumber * decNumberZero(decNumber *dn) {
+
+ #if DECCHECK
+ if (decCheckOperands(dn, DECUNUSED, DECUNUSED, DECUNCONT)) return dn;
+ #endif
+
+ dn->bits=0;
+ dn->exponent=0;
+ dn->digits=1;
+ dn->lsu[0]=0;
+ return dn;
+ } // decNumberZero
+
+/* ================================================================== */
+/* Local routines */
+/* ================================================================== */
+
+/* ------------------------------------------------------------------ */
+/* decToString -- lay out a number into a string */
+/* */
+/* dn is the number to lay out */
+/* string is where to lay out the number */
+/* eng is 1 if Engineering, 0 if Scientific */
+/* */
+/* string must be at least dn->digits+14 characters long */
+/* No error is possible. */
+/* */
+/* Note that this routine can generate a -0 or 0.000. These are */
+/* never generated in subset to-number or arithmetic, but can occur */
+/* in non-subset arithmetic (e.g., -1*0 or 1.234-1.234). */
+/* ------------------------------------------------------------------ */
+// If DECCHECK is enabled the string "?" is returned if a number is
+// invalid.
+static void decToString(const decNumber *dn, char *string, Flag eng) {
+ Int exp=dn->exponent; // local copy
+ Int e; // E-part value
+ Int pre; // digits before the '.'
+ Int cut; // for counting digits in a Unit
+ char *c=string; // work [output pointer]
+ const Unit *up=dn->lsu+D2U(dn->digits)-1; // -> msu [input pointer]
+ uInt u, pow; // work
+
+ #if DECCHECK
+ if (decCheckOperands(DECUNRESU, dn, DECUNUSED, DECUNCONT)) {
+ strcpy(string, "?");
+ return;}
+ #endif
+
+ if (decNumberIsNegative(dn)) { // Negatives get a minus
+ *c='-';
+ c++;
+ }
+ if (dn->bits&DECSPECIAL) { // Is a special value
+ if (decNumberIsInfinite(dn)) {
+ strcpy(c, "Inf");
+ strcpy(c+3, "inity");
+ return;}
+ // a NaN
+ if (dn->bits&DECSNAN) { // signalling NaN
+ *c='s';
+ c++;
+ }
+ strcpy(c, "NaN");
+ c+=3; // step past
+ // if not a clean non-zero coefficient, that's all there is in a
+ // NaN string
+ if (exp!=0 || (*dn->lsu==0 && dn->digits==1)) return;
+ // [drop through to add integer]
+ }
+
+ // calculate how many digits in msu, and hence first cut
+ cut=MSUDIGITS(dn->digits); // [faster than remainder]
+ cut--; // power of ten for digit
+
+ if (exp==0) { // simple integer [common fastpath]
+ for (;up>=dn->lsu; up--) { // each Unit from msu
+ u=*up; // contains DECDPUN digits to lay out
+ for (; cut>=0; c++, cut--) TODIGIT(u, cut, c, pow);
+ cut=DECDPUN-1; // next Unit has all digits
+ }
+ *c='\0'; // terminate the string
+ return;}
+
+ /* non-0 exponent -- assume plain form */
+ pre=dn->digits+exp; // digits before '.'
+ e=0; // no E
+ if ((exp>0) || (pre<-5)) { // need exponential form
+ e=exp+dn->digits-1; // calculate E value
+ pre=1; // assume one digit before '.'
+ if (eng && (e!=0)) { // engineering: may need to adjust
+ Int adj; // adjustment
+ // The C remainder operator is undefined for negative numbers, so
+ // a positive remainder calculation must be used here
+ if (e<0) {
+ adj=(-e)%3;
+ if (adj!=0) adj=3-adj;
+ }
+ else { // e>0
+ adj=e%3;
+ }
+ e=e-adj;
+ // if dealing with zero still produce an exponent which is a
+ // multiple of three, as expected, but there will only be the
+ // one zero before the E, still. Otherwise note the padding.
+ if (!ISZERO(dn)) pre+=adj;
+ else { // is zero
+ if (adj!=0) { // 0.00Esnn needed
+ e=e+3;
+ pre=-(2-adj);
+ }
+ } // zero
+ } // eng
+ } // need exponent
+
+ /* lay out the digits of the coefficient, adding 0s and . as needed */
+ u=*up;
+ if (pre>0) { // xxx.xxx or xx00 (engineering) form
+ Int n=pre;
+ for (; pre>0; pre--, c++, cut--) {
+ if (cut<0) { // need new Unit
+ if (up==dn->lsu) break; // out of input digits (pre>digits)
+ up--;
+ cut=DECDPUN-1;
+ u=*up;
+ }
+ TODIGIT(u, cut, c, pow);
+ }
+ if (n<dn->digits) { // more to come, after '.'
+ *c='.'; c++;
+ for (;; c++, cut--) {
+ if (cut<0) { // need new Unit
+ if (up==dn->lsu) break; // out of input digits
+ up--;
+ cut=DECDPUN-1;
+ u=*up;
+ }
+ TODIGIT(u, cut, c, pow);
+ }
+ }
+ else for (; pre>0; pre--, c++) *c='0'; // 0 padding (for engineering) needed
+ }
+ else { // 0.xxx or 0.000xxx form
+ *c='0'; c++;
+ *c='.'; c++;
+ for (; pre<0; pre++, c++) *c='0'; // add any 0's after '.'
+ for (; ; c++, cut--) {
+ if (cut<0) { // need new Unit
+ if (up==dn->lsu) break; // out of input digits
+ up--;
+ cut=DECDPUN-1;
+ u=*up;
+ }
+ TODIGIT(u, cut, c, pow);
+ }
+ }
+
+ /* Finally add the E-part, if needed. It will never be 0, has a
+ base maximum and minimum of +999999999 through -999999999, but
+ could range down to -1999999998 for anormal numbers */
+ if (e!=0) {
+ Flag had=0; // 1=had non-zero
+ *c='E'; c++;
+ *c='+'; c++; // assume positive
+ u=e; // ..
+ if (e<0) {
+ *(c-1)='-'; // oops, need -
+ u=-e; // uInt, please
+ }
+ // lay out the exponent [_itoa or equivalent is not ANSI C]
+ for (cut=9; cut>=0; cut--) {
+ TODIGIT(u, cut, c, pow);
+ if (*c=='0' && !had) continue; // skip leading zeros
+ had=1; // had non-0
+ c++; // step for next
+ } // cut
+ }
+ *c='\0'; // terminate the string (all paths)
+ return;
+ } // decToString
+
+/* ------------------------------------------------------------------ */
+/* decAddOp -- add/subtract operation */
+/* */
+/* This computes C = A + B */
+/* */
+/* res is C, the result. C may be A and/or B (e.g., X=X+X) */
+/* lhs is A */
+/* rhs is B */
+/* set is the context */
+/* negate is DECNEG if rhs should be negated, or 0 otherwise */
+/* status accumulates status for the caller */
+/* */
+/* C must have space for set->digits digits. */
+/* Inexact in status must be 0 for correct Exact zero sign in result */
+/* ------------------------------------------------------------------ */
+/* If possible, the coefficient is calculated directly into C. */
+/* However, if: */
+/* -- a digits+1 calculation is needed because the numbers are */
+/* unaligned and span more than set->digits digits */
+/* -- a carry to digits+1 digits looks possible */
+/* -- C is the same as A or B, and the result would destructively */
+/* overlap the A or B coefficient */
+/* then the result must be calculated into a temporary buffer. In */
+/* this case a local (stack) buffer is used if possible, and only if */
+/* too long for that does malloc become the final resort. */
+/* */
+/* Misalignment is handled as follows: */
+/* Apad: (AExp>BExp) Swap operands and proceed as for BExp>AExp. */
+/* BPad: Apply the padding by a combination of shifting (whole */
+/* units) and multiplication (part units). */
+/* */
+/* Addition, especially x=x+1, is speed-critical. */
+/* The static buffer is larger than might be expected to allow for */
+/* calls from higher-level funtions (notable exp). */
+/* ------------------------------------------------------------------ */
+static decNumber * decAddOp(decNumber *res, const decNumber *lhs,
+ const decNumber *rhs, decContext *set,
+ uByte negate, uInt *status) {
+ #if DECSUBSET
+ decNumber *alloclhs=NULL; // non-NULL if rounded lhs allocated
+ decNumber *allocrhs=NULL; // .., rhs
+ #endif
+ Int rhsshift; // working shift (in Units)
+ Int maxdigits; // longest logical length
+ Int mult; // multiplier
+ Int residue; // rounding accumulator
+ uByte bits; // result bits
+ Flag diffsign; // non-0 if arguments have different sign
+ Unit *acc; // accumulator for result
+ Unit accbuff[SD2U(DECBUFFER*2+20)]; // local buffer [*2+20 reduces many
+ // allocations when called from
+ // other operations, notable exp]
+ Unit *allocacc=NULL; // -> allocated acc buffer, iff allocated
+ Int reqdigits=set->digits; // local copy; requested DIGITS
+ Int padding; // work
+
+ #if DECCHECK
+ if (decCheckOperands(res, lhs, rhs, set)) return res;
+ #endif
+
+ do { // protect allocated storage
+ #if DECSUBSET
+ if (!set->extended) {
+ // reduce operands and set lostDigits status, as needed
+ if (lhs->digits>reqdigits) {
+ alloclhs=decRoundOperand(lhs, set, status);
+ if (alloclhs==NULL) break;
+ lhs=alloclhs;
+ }
+ if (rhs->digits>reqdigits) {
+ allocrhs=decRoundOperand(rhs, set, status);
+ if (allocrhs==NULL) break;
+ rhs=allocrhs;
+ }
+ }
+ #endif
+ // [following code does not require input rounding]
+
+ // note whether signs differ [used all paths]
+ diffsign=(Flag)((lhs->bits^rhs->bits^negate)&DECNEG);
+
+ // handle infinities and NaNs
+ if (SPECIALARGS) { // a special bit set
+ if (SPECIALARGS & (DECSNAN | DECNAN)) // a NaN
+ decNaNs(res, lhs, rhs, set, status);
+ else { // one or two infinities
+ if (decNumberIsInfinite(lhs)) { // LHS is infinity
+ // two infinities with different signs is invalid
+ if (decNumberIsInfinite(rhs) && diffsign) {
+ *status|=DEC_Invalid_operation;
+ break;
+ }
+ bits=lhs->bits & DECNEG; // get sign from LHS
+ }
+ else bits=(rhs->bits^negate) & DECNEG;// RHS must be Infinity
+ bits|=DECINF;
+ decNumberZero(res);
+ res->bits=bits; // set +/- infinity
+ } // an infinity
+ break;
+ }
+
+ // Quick exit for add 0s; return the non-0, modified as need be
+ if (ISZERO(lhs)) {
+ Int adjust; // work
+ Int lexp=lhs->exponent; // save in case LHS==RES
+ bits=lhs->bits; // ..
+ residue=0; // clear accumulator
+ decCopyFit(res, rhs, set, &residue, status); // copy (as needed)
+ res->bits^=negate; // flip if rhs was negated
+ #if DECSUBSET
+ if (set->extended) { // exponents on zeros count
+ #endif
+ // exponent will be the lower of the two
+ adjust=lexp-res->exponent; // adjustment needed [if -ve]
+ if (ISZERO(res)) { // both 0: special IEEE 754 rules
+ if (adjust<0) res->exponent=lexp; // set exponent
+ // 0-0 gives +0 unless rounding to -infinity, and -0-0 gives -0
+ if (diffsign) {
+ if (set->round!=DEC_ROUND_FLOOR) res->bits=0;
+ else res->bits=DECNEG; // preserve 0 sign
+ }
+ }
+ else { // non-0 res
+ if (adjust<0) { // 0-padding needed
+ if ((res->digits-adjust)>set->digits) {
+ adjust=res->digits-set->digits; // to fit exactly
+ *status|=DEC_Rounded; // [but exact]
+ }
+ res->digits=decShiftToMost(res->lsu, res->digits, -adjust);
+ res->exponent+=adjust; // set the exponent.
+ }
+ } // non-0 res
+ #if DECSUBSET
+ } // extended
+ #endif
+ decFinish(res, set, &residue, status); // clean and finalize
+ break;}
+
+ if (ISZERO(rhs)) { // [lhs is non-zero]
+ Int adjust; // work
+ Int rexp=rhs->exponent; // save in case RHS==RES
+ bits=rhs->bits; // be clean
+ residue=0; // clear accumulator
+ decCopyFit(res, lhs, set, &residue, status); // copy (as needed)
+ #if DECSUBSET
+ if (set->extended) { // exponents on zeros count
+ #endif
+ // exponent will be the lower of the two
+ // [0-0 case handled above]
+ adjust=rexp-res->exponent; // adjustment needed [if -ve]
+ if (adjust<0) { // 0-padding needed
+ if ((res->digits-adjust)>set->digits) {
+ adjust=res->digits-set->digits; // to fit exactly
+ *status|=DEC_Rounded; // [but exact]
+ }
+ res->digits=decShiftToMost(res->lsu, res->digits, -adjust);
+ res->exponent+=adjust; // set the exponent.
+ }
+ #if DECSUBSET
+ } // extended
+ #endif
+ decFinish(res, set, &residue, status); // clean and finalize
+ break;}
+
+ // [NB: both fastpath and mainpath code below assume these cases
+ // (notably 0-0) have already been handled]
+
+ // calculate the padding needed to align the operands
+ padding=rhs->exponent-lhs->exponent;
+
+ // Fastpath cases where the numbers are aligned and normal, the RHS
+ // is all in one unit, no operand rounding is needed, and no carry,
+ // lengthening, or borrow is needed
+ if (padding==0
+ && rhs->digits<=DECDPUN
+ && rhs->exponent>=set->emin // [some normals drop through]
+ && rhs->exponent<=set->emax-set->digits+1 // [could clamp]
+ && rhs->digits<=reqdigits
+ && lhs->digits<=reqdigits) {
+ Int partial=*lhs->lsu;
+ if (!diffsign) { // adding
+ partial+=*rhs->lsu;
+ if ((partial<=DECDPUNMAX) // result fits in unit
+ && (lhs->digits>=DECDPUN || // .. and no digits-count change
+ partial<(Int)powers[lhs->digits])) { // ..
+ if (res!=lhs) decNumberCopy(res, lhs); // not in place
+ *res->lsu=(Unit)partial; // [copy could have overwritten RHS]
+ break;
+ }
+ // else drop out for careful add
+ }
+ else { // signs differ
+ partial-=*rhs->lsu;
+ if (partial>0) { // no borrow needed, and non-0 result
+ if (res!=lhs) decNumberCopy(res, lhs); // not in place
+ *res->lsu=(Unit)partial;
+ // this could have reduced digits [but result>0]
+ res->digits=decGetDigits(res->lsu, D2U(res->digits));
+ break;
+ }
+ // else drop out for careful subtract
+ }
+ }
+
+ // Now align (pad) the lhs or rhs so they can be added or
+ // subtracted, as necessary. If one number is much larger than
+ // the other (that is, if in plain form there is a least one
+ // digit between the lowest digit of one and the highest of the
+ // other) padding with up to DIGITS-1 trailing zeros may be
+ // needed; then apply rounding (as exotic rounding modes may be
+ // affected by the residue).
+ rhsshift=0; // rhs shift to left (padding) in Units
+ bits=lhs->bits; // assume sign is that of LHS
+ mult=1; // likely multiplier
+
+ // [if padding==0 the operands are aligned; no padding is needed]
+ if (padding!=0) {
+ // some padding needed; always pad the RHS, as any required
+ // padding can then be effected by a simple combination of
+ // shifts and a multiply
+ Flag swapped=0;
+ if (padding<0) { // LHS needs the padding
+ const decNumber *t;
+ padding=-padding; // will be +ve
+ bits=(uByte)(rhs->bits^negate); // assumed sign is now that of RHS
+ t=lhs; lhs=rhs; rhs=t;
+ swapped=1;
+ }
+
+ // If, after pad, rhs would be longer than lhs by digits+1 or
+ // more then lhs cannot affect the answer, except as a residue,
+ // so only need to pad up to a length of DIGITS+1.
+ if (rhs->digits+padding > lhs->digits+reqdigits+1) {
+ // The RHS is sufficient
+ // for residue use the relative sign indication...
+ Int shift=reqdigits-rhs->digits; // left shift needed
+ residue=1; // residue for rounding
+ if (diffsign) residue=-residue; // signs differ
+ // copy, shortening if necessary
+ decCopyFit(res, rhs, set, &residue, status);
+ // if it was already shorter, then need to pad with zeros
+ if (shift>0) {
+ res->digits=decShiftToMost(res->lsu, res->digits, shift);
+ res->exponent-=shift; // adjust the exponent.
+ }
+ // flip the result sign if unswapped and rhs was negated
+ if (!swapped) res->bits^=negate;
+ decFinish(res, set, &residue, status); // done
+ break;}
+
+ // LHS digits may affect result
+ rhsshift=D2U(padding+1)-1; // this much by Unit shift ..
+ mult=powers[padding-(rhsshift*DECDPUN)]; // .. this by multiplication
+ } // padding needed
+
+ if (diffsign) mult=-mult; // signs differ
+
+ // determine the longer operand
+ maxdigits=rhs->digits+padding; // virtual length of RHS
+ if (lhs->digits>maxdigits) maxdigits=lhs->digits;
+
+ // Decide on the result buffer to use; if possible place directly
+ // into result.
+ acc=res->lsu; // assume add direct to result
+ // If destructive overlap, or the number is too long, or a carry or
+ // borrow to DIGITS+1 might be possible, a buffer must be used.
+ // [Might be worth more sophisticated tests when maxdigits==reqdigits]
+ if ((maxdigits>=reqdigits) // is, or could be, too large
+ || (res==rhs && rhsshift>0)) { // destructive overlap
+ // buffer needed, choose it; units for maxdigits digits will be
+ // needed, +1 Unit for carry or borrow
+ Int need=D2U(maxdigits)+1;
+ acc=accbuff; // assume use local buffer
+ if (need*sizeof(Unit)>sizeof(accbuff)) {
+ // printf("malloc add %ld %ld\n", need, sizeof(accbuff));
+ allocacc=(Unit *)malloc(need*sizeof(Unit));
+ if (allocacc==NULL) { // hopeless -- abandon
+ *status|=DEC_Insufficient_storage;
+ break;}
+ acc=allocacc;
+ }
+ }
+
+ res->bits=(uByte)(bits&DECNEG); // it's now safe to overwrite..
+ res->exponent=lhs->exponent; // .. operands (even if aliased)
+
+ #if DECTRACE
+ decDumpAr('A', lhs->lsu, D2U(lhs->digits));
+ decDumpAr('B', rhs->lsu, D2U(rhs->digits));
+ printf(" :h: %ld %ld\n", rhsshift, mult);
+ #endif
+
+ // add [A+B*m] or subtract [A+B*(-m)]
+ res->digits=decUnitAddSub(lhs->lsu, D2U(lhs->digits),
+ rhs->lsu, D2U(rhs->digits),
+ rhsshift, acc, mult)
+ *DECDPUN; // [units -> digits]
+ if (res->digits<0) { // borrowed...
+ res->digits=-res->digits;
+ res->bits^=DECNEG; // flip the sign
+ }
+ #if DECTRACE
+ decDumpAr('+', acc, D2U(res->digits));
+ #endif
+
+ // If a buffer was used the result must be copied back, possibly
+ // shortening. (If no buffer was used then the result must have
+ // fit, so can't need rounding and residue must be 0.)
+ residue=0; // clear accumulator
+ if (acc!=res->lsu) {
+ #if DECSUBSET
+ if (set->extended) { // round from first significant digit
+ #endif
+ // remove leading zeros that were added due to rounding up to
+ // integral Units -- before the test for rounding.
+ if (res->digits>reqdigits)
+ res->digits=decGetDigits(acc, D2U(res->digits));
+ decSetCoeff(res, set, acc, res->digits, &residue, status);
+ #if DECSUBSET
+ }
+ else { // subset arithmetic rounds from original significant digit
+ // May have an underestimate. This only occurs when both
+ // numbers fit in DECDPUN digits and are padding with a
+ // negative multiple (-10, -100...) and the top digit(s) become
+ // 0. (This only matters when using X3.274 rules where the
+ // leading zero could be included in the rounding.)
+ if (res->digits<maxdigits) {
+ *(acc+D2U(res->digits))=0; // ensure leading 0 is there
+ res->digits=maxdigits;
+ }
+ else {
+ // remove leading zeros that added due to rounding up to
+ // integral Units (but only those in excess of the original
+ // maxdigits length, unless extended) before test for rounding.
+ if (res->digits>reqdigits) {
+ res->digits=decGetDigits(acc, D2U(res->digits));
+ if (res->digits<maxdigits) res->digits=maxdigits;
+ }
+ }
+ decSetCoeff(res, set, acc, res->digits, &residue, status);
+ // Now apply rounding if needed before removing leading zeros.
+ // This is safe because subnormals are not a possibility
+ if (residue!=0) {
+ decApplyRound(res, set, residue, status);
+ residue=0; // did what needed to be done
+ }
+ } // subset
+ #endif
+ } // used buffer
+
+ // strip leading zeros [these were left on in case of subset subtract]
+ res->digits=decGetDigits(res->lsu, D2U(res->digits));
+
+ // apply checks and rounding
+ decFinish(res, set, &residue, status);
+
+ // "When the sum of two operands with opposite signs is exactly
+ // zero, the sign of that sum shall be '+' in all rounding modes
+ // except round toward -Infinity, in which mode that sign shall be
+ // '-'." [Subset zeros also never have '-', set by decFinish.]
+ if (ISZERO(res) && diffsign
+ #if DECSUBSET
+ && set->extended
+ #endif
+ && (*status&DEC_Inexact)==0) {
+ if (set->round==DEC_ROUND_FLOOR) res->bits|=DECNEG; // sign -
+ else res->bits&=~DECNEG; // sign +
+ }
+ } while(0); // end protected
+
+ if (allocacc!=NULL) free(allocacc); // drop any storage used
+ #if DECSUBSET
+ if (allocrhs!=NULL) free(allocrhs); // ..
+ if (alloclhs!=NULL) free(alloclhs); // ..
+ #endif
+ return res;
+ } // decAddOp
+
+/* ------------------------------------------------------------------ */
+/* decDivideOp -- division operation */
+/* */
+/* This routine performs the calculations for all four division */
+/* operators (divide, divideInteger, remainder, remainderNear). */
+/* */
+/* C=A op B */
+/* */
+/* res is C, the result. C may be A and/or B (e.g., X=X/X) */
+/* lhs is A */
+/* rhs is B */
+/* set is the context */
+/* op is DIVIDE, DIVIDEINT, REMAINDER, or REMNEAR respectively. */
+/* status is the usual accumulator */
+/* */
+/* C must have space for set->digits digits. */
+/* */
+/* ------------------------------------------------------------------ */
+/* The underlying algorithm of this routine is the same as in the */
+/* 1981 S/370 implementation, that is, non-restoring long division */
+/* with bi-unit (rather than bi-digit) estimation for each unit */
+/* multiplier. In this pseudocode overview, complications for the */
+/* Remainder operators and division residues for exact rounding are */
+/* omitted for clarity. */
+/* */
+/* Prepare operands and handle special values */
+/* Test for x/0 and then 0/x */
+/* Exp =Exp1 - Exp2 */
+/* Exp =Exp +len(var1) -len(var2) */
+/* Sign=Sign1 * Sign2 */
+/* Pad accumulator (Var1) to double-length with 0's (pad1) */
+/* Pad Var2 to same length as Var1 */
+/* msu2pair/plus=1st 2 or 1 units of var2, +1 to allow for round */
+/* have=0 */
+/* Do until (have=digits+1 OR residue=0) */
+/* if exp<0 then if integer divide/residue then leave */
+/* this_unit=0 */
+/* Do forever */
+/* compare numbers */
+/* if <0 then leave inner_loop */
+/* if =0 then (* quick exit without subtract *) do */
+/* this_unit=this_unit+1; output this_unit */
+/* leave outer_loop; end */
+/* Compare lengths of numbers (mantissae): */
+/* If same then tops2=msu2pair -- {units 1&2 of var2} */
+/* else tops2=msu2plus -- {0, unit 1 of var2} */
+/* tops1=first_unit_of_Var1*10**DECDPUN +second_unit_of_var1 */
+/* mult=tops1/tops2 -- Good and safe guess at divisor */
+/* if mult=0 then mult=1 */
+/* this_unit=this_unit+mult */
+/* subtract */
+/* end inner_loop */
+/* if have\=0 | this_unit\=0 then do */
+/* output this_unit */
+/* have=have+1; end */
+/* var2=var2/10 */
+/* exp=exp-1 */
+/* end outer_loop */
+/* exp=exp+1 -- set the proper exponent */
+/* if have=0 then generate answer=0 */
+/* Return (Result is defined by Var1) */
+/* */
+/* ------------------------------------------------------------------ */
+/* Two working buffers are needed during the division; one (digits+ */
+/* 1) to accumulate the result, and the other (up to 2*digits+1) for */
+/* long subtractions. These are acc and var1 respectively. */
+/* var1 is a copy of the lhs coefficient, var2 is the rhs coefficient.*/
+/* The static buffers may be larger than might be expected to allow */
+/* for calls from higher-level funtions (notable exp). */
+/* ------------------------------------------------------------------ */
+static decNumber * decDivideOp(decNumber *res,
+ const decNumber *lhs, const decNumber *rhs,
+ decContext *set, Flag op, uInt *status) {
+ #if DECSUBSET
+ decNumber *alloclhs=NULL; // non-NULL if rounded lhs allocated
+ decNumber *allocrhs=NULL; // .., rhs
+ #endif
+ Unit accbuff[SD2U(DECBUFFER+DECDPUN+10)]; // local buffer
+ Unit *acc=accbuff; // -> accumulator array for result
+ Unit *allocacc=NULL; // -> allocated buffer, iff allocated
+ Unit *accnext; // -> where next digit will go
+ Int acclength; // length of acc needed [Units]
+ Int accunits; // count of units accumulated
+ Int accdigits; // count of digits accumulated
+
+ Unit varbuff[SD2U(DECBUFFER*2+DECDPUN)]; // buffer for var1
+ Unit *var1=varbuff; // -> var1 array for long subtraction
+ Unit *varalloc=NULL; // -> allocated buffer, iff used
+ Unit *msu1; // -> msu of var1
+
+ const Unit *var2; // -> var2 array
+ const Unit *msu2; // -> msu of var2
+ Int msu2plus; // msu2 plus one [does not vary]
+ eInt msu2pair; // msu2 pair plus one [does not vary]
+
+ Int var1units, var2units; // actual lengths
+ Int var2ulen; // logical length (units)
+ Int var1initpad=0; // var1 initial padding (digits)
+ Int maxdigits; // longest LHS or required acc length
+ Int mult; // multiplier for subtraction
+ Unit thisunit; // current unit being accumulated
+ Int residue; // for rounding
+ Int reqdigits=set->digits; // requested DIGITS
+ Int exponent; // working exponent
+ Int maxexponent=0; // DIVIDE maximum exponent if unrounded
+ uByte bits; // working sign
+ Unit *target; // work
+ const Unit *source; // ..
+ uInt const *pow; // ..
+ Int shift, cut; // ..
+ #if DECSUBSET
+ Int dropped; // work
+ #endif
+
+ #if DECCHECK
+ if (decCheckOperands(res, lhs, rhs, set)) return res;
+ #endif
+
+ do { // protect allocated storage
+ #if DECSUBSET
+ if (!set->extended) {
+ // reduce operands and set lostDigits status, as needed
+ if (lhs->digits>reqdigits) {
+ alloclhs=decRoundOperand(lhs, set, status);
+ if (alloclhs==NULL) break;
+ lhs=alloclhs;
+ }
+ if (rhs->digits>reqdigits) {
+ allocrhs=decRoundOperand(rhs, set, status);
+ if (allocrhs==NULL) break;
+ rhs=allocrhs;
+ }
+ }
+ #endif
+ // [following code does not require input rounding]
+
+ bits=(lhs->bits^rhs->bits)&DECNEG; // assumed sign for divisions
+
+ // handle infinities and NaNs
+ if (SPECIALARGS) { // a special bit set
+ if (SPECIALARGS & (DECSNAN | DECNAN)) { // one or two NaNs
+ decNaNs(res, lhs, rhs, set, status);
+ break;
+ }
+ // one or two infinities
+ if (decNumberIsInfinite(lhs)) { // LHS (dividend) is infinite
+ if (decNumberIsInfinite(rhs) || // two infinities are invalid ..
+ op & (REMAINDER | REMNEAR)) { // as is remainder of infinity
+ *status|=DEC_Invalid_operation;
+ break;
+ }
+ // [Note that infinity/0 raises no exceptions]
+ decNumberZero(res);
+ res->bits=bits|DECINF; // set +/- infinity
+ break;
+ }
+ else { // RHS (divisor) is infinite
+ residue=0;
+ if (op&(REMAINDER|REMNEAR)) {
+ // result is [finished clone of] lhs
+ decCopyFit(res, lhs, set, &residue, status);
+ }
+ else { // a division
+ decNumberZero(res);
+ res->bits=bits; // set +/- zero
+ // for DIVIDEINT the exponent is always 0. For DIVIDE, result
+ // is a 0 with infinitely negative exponent, clamped to minimum
+ if (op&DIVIDE) {
+ res->exponent=set->emin-set->digits+1;
+ *status|=DEC_Clamped;
+ }
+ }
+ decFinish(res, set, &residue, status);
+ break;
+ }
+ }
+
+ // handle 0 rhs (x/0)
+ if (ISZERO(rhs)) { // x/0 is always exceptional
+ if (ISZERO(lhs)) {
+ decNumberZero(res); // [after lhs test]
+ *status|=DEC_Division_undefined;// 0/0 will become NaN
+ }
+ else {
+ decNumberZero(res);
+ if (op&(REMAINDER|REMNEAR)) *status|=DEC_Invalid_operation;
+ else {
+ *status|=DEC_Division_by_zero; // x/0
+ res->bits=bits|DECINF; // .. is +/- Infinity
+ }
+ }
+ break;}
+
+ // handle 0 lhs (0/x)
+ if (ISZERO(lhs)) { // 0/x [x!=0]
+ #if DECSUBSET
+ if (!set->extended) decNumberZero(res);
+ else {
+ #endif
+ if (op&DIVIDE) {
+ residue=0;
+ exponent=lhs->exponent-rhs->exponent; // ideal exponent
+ decNumberCopy(res, lhs); // [zeros always fit]
+ res->bits=bits; // sign as computed
+ res->exponent=exponent; // exponent, too
+ decFinalize(res, set, &residue, status); // check exponent
+ }
+ else if (op&DIVIDEINT) {
+ decNumberZero(res); // integer 0
+ res->bits=bits; // sign as computed
+ }
+ else { // a remainder
+ exponent=rhs->exponent; // [save in case overwrite]
+ decNumberCopy(res, lhs); // [zeros always fit]
+ if (exponent<res->exponent) res->exponent=exponent; // use lower
+ }
+ #if DECSUBSET
+ }
+ #endif
+ break;}
+
+ // Precalculate exponent. This starts off adjusted (and hence fits
+ // in 31 bits) and becomes the usual unadjusted exponent as the
+ // division proceeds. The order of evaluation is important, here,
+ // to avoid wrap.
+ exponent=(lhs->exponent+lhs->digits)-(rhs->exponent+rhs->digits);
+
+ // If the working exponent is -ve, then some quick exits are
+ // possible because the quotient is known to be <1
+ // [for REMNEAR, it needs to be < -1, as -0.5 could need work]
+ if (exponent<0 && !(op==DIVIDE)) {
+ if (op&DIVIDEINT) {
+ decNumberZero(res); // integer part is 0
+ #if DECSUBSET
+ if (set->extended)
+ #endif
+ res->bits=bits; // set +/- zero
+ break;}
+ // fastpath remainders so long as the lhs has the smaller
+ // (or equal) exponent
+ if (lhs->exponent<=rhs->exponent) {
+ if (op&REMAINDER || exponent<-1) {
+ // It is REMAINDER or safe REMNEAR; result is [finished
+ // clone of] lhs (r = x - 0*y)
+ residue=0;
+ decCopyFit(res, lhs, set, &residue, status);
+ decFinish(res, set, &residue, status);
+ break;
+ }
+ // [unsafe REMNEAR drops through]
+ }
+ } // fastpaths
+
+ /* Long (slow) division is needed; roll up the sleeves... */
+
+ // The accumulator will hold the quotient of the division.
+ // If it needs to be too long for stack storage, then allocate.
+ acclength=D2U(reqdigits+DECDPUN); // in Units
+ if (acclength*sizeof(Unit)>sizeof(accbuff)) {
+ // printf("malloc dvacc %ld units\n", acclength);
+ allocacc=(Unit *)malloc(acclength*sizeof(Unit));
+ if (allocacc==NULL) { // hopeless -- abandon
+ *status|=DEC_Insufficient_storage;
+ break;}
+ acc=allocacc; // use the allocated space
+ }
+
+ // var1 is the padded LHS ready for subtractions.
+ // If it needs to be too long for stack storage, then allocate.
+ // The maximum units needed for var1 (long subtraction) is:
+ // Enough for
+ // (rhs->digits+reqdigits-1) -- to allow full slide to right
+ // or (lhs->digits) -- to allow for long lhs
+ // whichever is larger
+ // +1 -- for rounding of slide to right
+ // +1 -- for leading 0s
+ // +1 -- for pre-adjust if a remainder or DIVIDEINT
+ // [Note: unused units do not participate in decUnitAddSub data]
+ maxdigits=rhs->digits+reqdigits-1;
+ if (lhs->digits>maxdigits) maxdigits=lhs->digits;
+ var1units=D2U(maxdigits)+2;
+ // allocate a guard unit above msu1 for REMAINDERNEAR
+ if (!(op&DIVIDE)) var1units++;
+ if ((var1units+1)*sizeof(Unit)>sizeof(varbuff)) {
+ // printf("malloc dvvar %ld units\n", var1units+1);
+ varalloc=(Unit *)malloc((var1units+1)*sizeof(Unit));
+ if (varalloc==NULL) { // hopeless -- abandon
+ *status|=DEC_Insufficient_storage;
+ break;}
+ var1=varalloc; // use the allocated space
+ }
+
+ // Extend the lhs and rhs to full long subtraction length. The lhs
+ // is truly extended into the var1 buffer, with 0 padding, so a
+ // subtract in place is always possible. The rhs (var2) has
+ // virtual padding (implemented by decUnitAddSub).
+ // One guard unit was allocated above msu1 for rem=rem+rem in
+ // REMAINDERNEAR.
+ msu1=var1+var1units-1; // msu of var1
+ source=lhs->lsu+D2U(lhs->digits)-1; // msu of input array
+ for (target=msu1; source>=lhs->lsu; source--, target--) *target=*source;
+ for (; target>=var1; target--) *target=0;
+
+ // rhs (var2) is left-aligned with var1 at the start
+ var2ulen=var1units; // rhs logical length (units)
+ var2units=D2U(rhs->digits); // rhs actual length (units)
+ var2=rhs->lsu; // -> rhs array
+ msu2=var2+var2units-1; // -> msu of var2 [never changes]
+ // now set up the variables which will be used for estimating the
+ // multiplication factor. If these variables are not exact, add
+ // 1 to make sure that the multiplier is never overestimated.
+ msu2plus=*msu2; // it's value ..
+ if (var2units>1) msu2plus++; // .. +1 if any more
+ msu2pair=(eInt)*msu2*(DECDPUNMAX+1);// top two pair ..
+ if (var2units>1) { // .. [else treat 2nd as 0]
+ msu2pair+=*(msu2-1); // ..
+ if (var2units>2) msu2pair++; // .. +1 if any more
+ }
+
+ // The calculation is working in units, which may have leading zeros,
+ // but the exponent was calculated on the assumption that they are
+ // both left-aligned. Adjust the exponent to compensate: add the
+ // number of leading zeros in var1 msu and subtract those in var2 msu.
+ // [This is actually done by counting the digits and negating, as
+ // lead1=DECDPUN-digits1, and similarly for lead2.]
+ for (pow=&powers[1]; *msu1>=*pow; pow++) exponent--;
+ for (pow=&powers[1]; *msu2>=*pow; pow++) exponent++;
+
+ // Now, if doing an integer divide or remainder, ensure that
+ // the result will be Unit-aligned. To do this, shift the var1
+ // accumulator towards least if need be. (It's much easier to
+ // do this now than to reassemble the residue afterwards, if
+ // doing a remainder.) Also ensure the exponent is not negative.
+ if (!(op&DIVIDE)) {
+ Unit *u; // work
+ // save the initial 'false' padding of var1, in digits
+ var1initpad=(var1units-D2U(lhs->digits))*DECDPUN;
+ // Determine the shift to do.
+ if (exponent<0) cut=-exponent;
+ else cut=DECDPUN-exponent%DECDPUN;
+ decShiftToLeast(var1, var1units, cut);
+ exponent+=cut; // maintain numerical value
+ var1initpad-=cut; // .. and reduce padding
+ // clean any most-significant units which were just emptied
+ for (u=msu1; cut>=DECDPUN; cut-=DECDPUN, u--) *u=0;
+ } // align
+ else { // is DIVIDE
+ maxexponent=lhs->exponent-rhs->exponent; // save
+ // optimization: if the first iteration will just produce 0,
+ // preadjust to skip it [valid for DIVIDE only]
+ if (*msu1<*msu2) {
+ var2ulen--; // shift down
+ exponent-=DECDPUN; // update the exponent
+ }
+ }
+
+ // ---- start the long-division loops ------------------------------
+ accunits=0; // no units accumulated yet
+ accdigits=0; // .. or digits
+ accnext=acc+acclength-1; // -> msu of acc [NB: allows digits+1]
+ for (;;) { // outer forever loop
+ thisunit=0; // current unit assumed 0
+ // find the next unit
+ for (;;) { // inner forever loop
+ // strip leading zero units [from either pre-adjust or from
+ // subtract last time around]. Leave at least one unit.
+ for (; *msu1==0 && msu1>var1; msu1--) var1units--;
+
+ if (var1units<var2ulen) break; // var1 too low for subtract
+ if (var1units==var2ulen) { // unit-by-unit compare needed
+ // compare the two numbers, from msu
+ const Unit *pv1, *pv2;
+ Unit v2; // units to compare
+ pv2=msu2; // -> msu
+ for (pv1=msu1; ; pv1--, pv2--) {
+ // v1=*pv1 -- always OK
+ v2=0; // assume in padding
+ if (pv2>=var2) v2=*pv2; // in range
+ if (*pv1!=v2) break; // no longer the same
+ if (pv1==var1) break; // done; leave pv1 as is
+ }
+ // here when all inspected or a difference seen
+ if (*pv1<v2) break; // var1 too low to subtract
+ if (*pv1==v2) { // var1 == var2
+ // reach here if var1 and var2 are identical; subtraction
+ // would increase digit by one, and the residue will be 0 so
+ // the calculation is done; leave the loop with residue=0.
+ thisunit++; // as though subtracted
+ *var1=0; // set var1 to 0
+ var1units=1; // ..
+ break; // from inner
+ } // var1 == var2
+ // *pv1>v2. Prepare for real subtraction; the lengths are equal
+ // Estimate the multiplier (there's always a msu1-1)...
+ // Bring in two units of var2 to provide a good estimate.
+ mult=(Int)(((eInt)*msu1*(DECDPUNMAX+1)+*(msu1-1))/msu2pair);
+ } // lengths the same
+ else { // var1units > var2ulen, so subtraction is safe
+ // The var2 msu is one unit towards the lsu of the var1 msu,
+ // so only one unit for var2 can be used.
+ mult=(Int)(((eInt)*msu1*(DECDPUNMAX+1)+*(msu1-1))/msu2plus);
+ }
+ if (mult==0) mult=1; // must always be at least 1
+ // subtraction needed; var1 is > var2
+ thisunit=(Unit)(thisunit+mult); // accumulate
+ // subtract var1-var2, into var1; only the overlap needs
+ // processing, as this is an in-place calculation
+ shift=var2ulen-var2units;
+ #if DECTRACE
+ decDumpAr('1', &var1[shift], var1units-shift);
+ decDumpAr('2', var2, var2units);
+ printf("m=%ld\n", -mult);
+ #endif
+ decUnitAddSub(&var1[shift], var1units-shift,
+ var2, var2units, 0,
+ &var1[shift], -mult);
+ #if DECTRACE
+ decDumpAr('#', &var1[shift], var1units-shift);
+ #endif
+ // var1 now probably has leading zeros; these are removed at the
+ // top of the inner loop.
+ } // inner loop
+
+ // The next unit has been calculated in full; unless it's a
+ // leading zero, add to acc
+ if (accunits!=0 || thisunit!=0) { // is first or non-zero
+ *accnext=thisunit; // store in accumulator
+ // account exactly for the new digits
+ if (accunits==0) {
+ accdigits++; // at least one
+ for (pow=&powers[1]; thisunit>=*pow; pow++) accdigits++;
+ }
+ else accdigits+=DECDPUN;
+ accunits++; // update count
+ accnext--; // ready for next
+ if (accdigits>reqdigits) break; // have enough digits
+ }
+
+ // if the residue is zero, the operation is done (unless divide
+ // or divideInteger and still not enough digits yet)
+ if (*var1==0 && var1units==1) { // residue is 0
+ if (op&(REMAINDER|REMNEAR)) break;
+ if ((op&DIVIDE) && (exponent<=maxexponent)) break;
+ // [drop through if divideInteger]
+ }
+ // also done enough if calculating remainder or integer
+ // divide and just did the last ('units') unit
+ if (exponent==0 && !(op&DIVIDE)) break;
+
+ // to get here, var1 is less than var2, so divide var2 by the per-
+ // Unit power of ten and go for the next digit
+ var2ulen--; // shift down
+ exponent-=DECDPUN; // update the exponent
+ } // outer loop
+
+ // ---- division is complete ---------------------------------------
+ // here: acc has at least reqdigits+1 of good results (or fewer
+ // if early stop), starting at accnext+1 (its lsu)
+ // var1 has any residue at the stopping point
+ // accunits is the number of digits collected in acc
+ if (accunits==0) { // acc is 0
+ accunits=1; // show have a unit ..
+ accdigits=1; // ..
+ *accnext=0; // .. whose value is 0
+ }
+ else accnext++; // back to last placed
+ // accnext now -> lowest unit of result
+
+ residue=0; // assume no residue
+ if (op&DIVIDE) {
+ // record the presence of any residue, for rounding
+ if (*var1!=0 || var1units>1) residue=1;
+ else { // no residue
+ // Had an exact division; clean up spurious trailing 0s.
+ // There will be at most DECDPUN-1, from the final multiply,
+ // and then only if the result is non-0 (and even) and the
+ // exponent is 'loose'.
+ #if DECDPUN>1
+ Unit lsu=*accnext;
+ if (!(lsu&0x01) && (lsu!=0)) {
+ // count the trailing zeros
+ Int drop=0;
+ for (;; drop++) { // [will terminate because lsu!=0]
+ if (exponent>=maxexponent) break; // don't chop real 0s
+ #if DECDPUN<=4
+ if ((lsu-QUOT10(lsu, drop+1)
+ *powers[drop+1])!=0) break; // found non-0 digit
+ #else
+ if (lsu%powers[drop+1]!=0) break; // found non-0 digit
+ #endif
+ exponent++;
+ }
+ if (drop>0) {
+ accunits=decShiftToLeast(accnext, accunits, drop);
+ accdigits=decGetDigits(accnext, accunits);
+ accunits=D2U(accdigits);
+ // [exponent was adjusted in the loop]
+ }
+ } // neither odd nor 0
+ #endif
+ } // exact divide
+ } // divide
+ else /* op!=DIVIDE */ {
+ // check for coefficient overflow
+ if (accdigits+exponent>reqdigits) {
+ *status|=DEC_Division_impossible;
+ break;
+ }
+ if (op & (REMAINDER|REMNEAR)) {
+ // [Here, the exponent will be 0, because var1 was adjusted
+ // appropriately.]
+ Int postshift; // work
+ Flag wasodd=0; // integer was odd
+ Unit *quotlsu; // for save
+ Int quotdigits; // ..
+
+ bits=lhs->bits; // remainder sign is always as lhs
+
+ // Fastpath when residue is truly 0 is worthwhile [and
+ // simplifies the code below]
+ if (*var1==0 && var1units==1) { // residue is 0
+ Int exp=lhs->exponent; // save min(exponents)
+ if (rhs->exponent<exp) exp=rhs->exponent;
+ decNumberZero(res); // 0 coefficient
+ #if DECSUBSET
+ if (set->extended)
+ #endif
+ res->exponent=exp; // .. with proper exponent
+ res->bits=(uByte)(bits&DECNEG); // [cleaned]
+ decFinish(res, set, &residue, status); // might clamp
+ break;
+ }
+ // note if the quotient was odd
+ if (*accnext & 0x01) wasodd=1; // acc is odd
+ quotlsu=accnext; // save in case need to reinspect
+ quotdigits=accdigits; // ..
+
+ // treat the residue, in var1, as the value to return, via acc
+ // calculate the unused zero digits. This is the smaller of:
+ // var1 initial padding (saved above)
+ // var2 residual padding, which happens to be given by:
+ postshift=var1initpad+exponent-lhs->exponent+rhs->exponent;
+ // [the 'exponent' term accounts for the shifts during divide]
+ if (var1initpad<postshift) postshift=var1initpad;
+
+ // shift var1 the requested amount, and adjust its digits
+ var1units=decShiftToLeast(var1, var1units, postshift);
+ accnext=var1;
+ accdigits=decGetDigits(var1, var1units);
+ accunits=D2U(accdigits);
+
+ exponent=lhs->exponent; // exponent is smaller of lhs & rhs
+ if (rhs->exponent<exponent) exponent=rhs->exponent;
+
+ // Now correct the result if doing remainderNear; if it
+ // (looking just at coefficients) is > rhs/2, or == rhs/2 and
+ // the integer was odd then the result should be rem-rhs.
+ if (op&REMNEAR) {
+ Int compare, tarunits; // work
+ Unit *up; // ..
+ // calculate remainder*2 into the var1 buffer (which has
+ // 'headroom' of an extra unit and hence enough space)
+ // [a dedicated 'double' loop would be faster, here]
+ tarunits=decUnitAddSub(accnext, accunits, accnext, accunits,
+ 0, accnext, 1);
+ // decDumpAr('r', accnext, tarunits);
+
+ // Here, accnext (var1) holds tarunits Units with twice the
+ // remainder's coefficient, which must now be compared to the
+ // RHS. The remainder's exponent may be smaller than the RHS's.
+ compare=decUnitCompare(accnext, tarunits, rhs->lsu, D2U(rhs->digits),
+ rhs->exponent-exponent);
+ if (compare==BADINT) { // deep trouble
+ *status|=DEC_Insufficient_storage;
+ break;}
+
+ // now restore the remainder by dividing by two; the lsu
+ // is known to be even.
+ for (up=accnext; up<accnext+tarunits; up++) {
+ Int half; // half to add to lower unit
+ half=*up & 0x01;
+ *up/=2; // [shift]
+ if (!half) continue;
+ *(up-1)+=(DECDPUNMAX+1)/2;
+ }
+ // [accunits still describes the original remainder length]
+
+ if (compare>0 || (compare==0 && wasodd)) { // adjustment needed
+ Int exp, expunits, exprem; // work
+ // This is effectively causing round-up of the quotient,
+ // so if it was the rare case where it was full and all
+ // nines, it would overflow and hence division-impossible
+ // should be raised
+ Flag allnines=0; // 1 if quotient all nines
+ if (quotdigits==reqdigits) { // could be borderline
+ for (up=quotlsu; ; up++) {
+ if (quotdigits>DECDPUN) {
+ if (*up!=DECDPUNMAX) break;// non-nines
+ }
+ else { // this is the last Unit
+ if (*up==powers[quotdigits]-1) allnines=1;
+ break;
+ }
+ quotdigits-=DECDPUN; // checked those digits
+ } // up
+ } // borderline check
+ if (allnines) {
+ *status|=DEC_Division_impossible;
+ break;}
+
+ // rem-rhs is needed; the sign will invert. Again, var1
+ // can safely be used for the working Units array.
+ exp=rhs->exponent-exponent; // RHS padding needed
+ // Calculate units and remainder from exponent.
+ expunits=exp/DECDPUN;
+ exprem=exp%DECDPUN;
+ // subtract [A+B*(-m)]; the result will always be negative
+ accunits=-decUnitAddSub(accnext, accunits,
+ rhs->lsu, D2U(rhs->digits),
+ expunits, accnext, -(Int)powers[exprem]);
+ accdigits=decGetDigits(accnext, accunits); // count digits exactly
+ accunits=D2U(accdigits); // and recalculate the units for copy
+ // [exponent is as for original remainder]
+ bits^=DECNEG; // flip the sign
+ }
+ } // REMNEAR
+ } // REMAINDER or REMNEAR
+ } // not DIVIDE
+
+ // Set exponent and bits
+ res->exponent=exponent;
+ res->bits=(uByte)(bits&DECNEG); // [cleaned]
+
+ // Now the coefficient.
+ decSetCoeff(res, set, accnext, accdigits, &residue, status);
+
+ decFinish(res, set, &residue, status); // final cleanup
+
+ #if DECSUBSET
+ // If a divide then strip trailing zeros if subset [after round]
+ if (!set->extended && (op==DIVIDE)) decTrim(res, set, 0, 1, &dropped);
+ #endif
+ } while(0); // end protected
+
+ if (varalloc!=NULL) free(varalloc); // drop any storage used
+ if (allocacc!=NULL) free(allocacc); // ..
+ #if DECSUBSET
+ if (allocrhs!=NULL) free(allocrhs); // ..
+ if (alloclhs!=NULL) free(alloclhs); // ..
+ #endif
+ return res;
+ } // decDivideOp
+
+/* ------------------------------------------------------------------ */
+/* decMultiplyOp -- multiplication operation */
+/* */
+/* This routine performs the multiplication C=A x B. */
+/* */
+/* res is C, the result. C may be A and/or B (e.g., X=X*X) */
+/* lhs is A */
+/* rhs is B */
+/* set is the context */
+/* status is the usual accumulator */
+/* */
+/* C must have space for set->digits digits. */
+/* */
+/* ------------------------------------------------------------------ */
+/* 'Classic' multiplication is used rather than Karatsuba, as the */
+/* latter would give only a minor improvement for the short numbers */
+/* expected to be handled most (and uses much more memory). */
+/* */
+/* There are two major paths here: the general-purpose ('old code') */
+/* path which handles all DECDPUN values, and a fastpath version */
+/* which is used if 64-bit ints are available, DECDPUN<=4, and more */
+/* than two calls to decUnitAddSub would be made. */
+/* */
+/* The fastpath version lumps units together into 8-digit or 9-digit */
+/* chunks, and also uses a lazy carry strategy to minimise expensive */
+/* 64-bit divisions. The chunks are then broken apart again into */
+/* units for continuing processing. Despite this overhead, the */
+/* fastpath can speed up some 16-digit operations by 10x (and much */
+/* more for higher-precision calculations). */
+/* */
+/* A buffer always has to be used for the accumulator; in the */
+/* fastpath, buffers are also always needed for the chunked copies of */
+/* of the operand coefficients. */
+/* Static buffers are larger than needed just for multiply, to allow */
+/* for calls from other operations (notably exp). */
+/* ------------------------------------------------------------------ */
+#define FASTMUL (DECUSE64 && DECDPUN<5)
+static decNumber * decMultiplyOp(decNumber *res, const decNumber *lhs,
+ const decNumber *rhs, decContext *set,
+ uInt *status) {
+ Int accunits; // Units of accumulator in use
+ Int exponent; // work
+ Int residue=0; // rounding residue
+ uByte bits; // result sign
+ Unit *acc; // -> accumulator Unit array
+ Int needbytes; // size calculator
+ void *allocacc=NULL; // -> allocated accumulator, iff allocated
+ Unit accbuff[SD2U(DECBUFFER*4+1)]; // buffer (+1 for DECBUFFER==0,
+ // *4 for calls from other operations)
+ const Unit *mer, *mermsup; // work
+ Int madlength; // Units in multiplicand
+ Int shift; // Units to shift multiplicand by
+
+ #if FASTMUL
+ // if DECDPUN is 1 or 3 work in base 10**9, otherwise
+ // (DECDPUN is 2 or 4) then work in base 10**8
+ #if DECDPUN & 1 // odd
+ #define FASTBASE 1000000000 // base
+ #define FASTDIGS 9 // digits in base
+ #define FASTLAZY 18 // carry resolution point [1->18]
+ #else
+ #define FASTBASE 100000000
+ #define FASTDIGS 8
+ #define FASTLAZY 1844 // carry resolution point [1->1844]
+ #endif
+ // three buffers are used, two for chunked copies of the operands
+ // (base 10**8 or base 10**9) and one base 2**64 accumulator with
+ // lazy carry evaluation
+ uInt zlhibuff[(DECBUFFER*2+1)/8+1]; // buffer (+1 for DECBUFFER==0)
+ uInt *zlhi=zlhibuff; // -> lhs array
+ uInt *alloclhi=NULL; // -> allocated buffer, iff allocated
+ uInt zrhibuff[(DECBUFFER*2+1)/8+1]; // buffer (+1 for DECBUFFER==0)
+ uInt *zrhi=zrhibuff; // -> rhs array
+ uInt *allocrhi=NULL; // -> allocated buffer, iff allocated
+ uLong zaccbuff[(DECBUFFER*2+1)/4+2]; // buffer (+1 for DECBUFFER==0)
+ // [allocacc is shared for both paths, as only one will run]
+ uLong *zacc=zaccbuff; // -> accumulator array for exact result
+ #if DECDPUN==1
+ Int zoff; // accumulator offset
+ #endif
+ uInt *lip, *rip; // item pointers
+ uInt *lmsi, *rmsi; // most significant items
+ Int ilhs, irhs, iacc; // item counts in the arrays
+ Int lazy; // lazy carry counter
+ uLong lcarry; // uLong carry
+ uInt carry; // carry (NB not uLong)
+ Int count; // work
+ const Unit *cup; // ..
+ Unit *up; // ..
+ uLong *lp; // ..
+ Int p; // ..
+ #endif
+
+ #if DECSUBSET
+ decNumber *alloclhs=NULL; // -> allocated buffer, iff allocated
+ decNumber *allocrhs=NULL; // -> allocated buffer, iff allocated
+ #endif
+
+ #if DECCHECK
+ if (decCheckOperands(res, lhs, rhs, set)) return res;
+ #endif
+
+ // precalculate result sign
+ bits=(uByte)((lhs->bits^rhs->bits)&DECNEG);
+
+ // handle infinities and NaNs
+ if (SPECIALARGS) { // a special bit set
+ if (SPECIALARGS & (DECSNAN | DECNAN)) { // one or two NaNs
+ decNaNs(res, lhs, rhs, set, status);
+ return res;}
+ // one or two infinities; Infinity * 0 is invalid
+ if (((lhs->bits & DECINF)==0 && ISZERO(lhs))
+ ||((rhs->bits & DECINF)==0 && ISZERO(rhs))) {
+ *status|=DEC_Invalid_operation;
+ return res;}
+ decNumberZero(res);
+ res->bits=bits|DECINF; // infinity
+ return res;}
+
+ // For best speed, as in DMSRCN [the original Rexx numerics
+ // module], use the shorter number as the multiplier (rhs) and
+ // the longer as the multiplicand (lhs) to minimise the number of
+ // adds (partial products)
+ if (lhs->digits<rhs->digits) { // swap...
+ const decNumber *hold=lhs;
+ lhs=rhs;
+ rhs=hold;
+ }
+
+ do { // protect allocated storage
+ #if DECSUBSET
+ if (!set->extended) {
+ // reduce operands and set lostDigits status, as needed
+ if (lhs->digits>set->digits) {
+ alloclhs=decRoundOperand(lhs, set, status);
+ if (alloclhs==NULL) break;
+ lhs=alloclhs;
+ }
+ if (rhs->digits>set->digits) {
+ allocrhs=decRoundOperand(rhs, set, status);
+ if (allocrhs==NULL) break;
+ rhs=allocrhs;
+ }
+ }
+ #endif
+ // [following code does not require input rounding]
+
+ #if FASTMUL // fastpath can be used
+ // use the fast path if there are enough digits in the shorter
+ // operand to make the setup and takedown worthwhile
+ #define NEEDTWO (DECDPUN*2) // within two decUnitAddSub calls
+ if (rhs->digits>NEEDTWO) { // use fastpath...
+ // calculate the number of elements in each array
+ ilhs=(lhs->digits+FASTDIGS-1)/FASTDIGS; // [ceiling]
+ irhs=(rhs->digits+FASTDIGS-1)/FASTDIGS; // ..
+ iacc=ilhs+irhs;
+
+ // allocate buffers if required, as usual
+ needbytes=ilhs*sizeof(uInt);
+ if (needbytes>(Int)sizeof(zlhibuff)) {
+ alloclhi=(uInt *)malloc(needbytes);
+ zlhi=alloclhi;}
+ needbytes=irhs*sizeof(uInt);
+ if (needbytes>(Int)sizeof(zrhibuff)) {
+ allocrhi=(uInt *)malloc(needbytes);
+ zrhi=allocrhi;}
+
+ // Allocating the accumulator space needs a special case when
+ // DECDPUN=1 because when converting the accumulator to Units
+ // after the multiplication each 8-byte item becomes 9 1-byte
+ // units. Therefore iacc extra bytes are needed at the front
+ // (rounded up to a multiple of 8 bytes), and the uLong
+ // accumulator starts offset the appropriate number of units
+ // to the right to avoid overwrite during the unchunking.
+ needbytes=iacc*sizeof(uLong);
+ #if DECDPUN==1
+ zoff=(iacc+7)/8; // items to offset by
+ needbytes+=zoff*8;
+ #endif
+ if (needbytes>(Int)sizeof(zaccbuff)) {
+ allocacc=(uLong *)malloc(needbytes);
+ zacc=(uLong *)allocacc;}
+ if (zlhi==NULL||zrhi==NULL||zacc==NULL) {
+ *status|=DEC_Insufficient_storage;
+ break;}
+
+ acc=(Unit *)zacc; // -> target Unit array
+ #if DECDPUN==1
+ zacc+=zoff; // start uLong accumulator to right
+ #endif
+
+ // assemble the chunked copies of the left and right sides
+ for (count=lhs->digits, cup=lhs->lsu, lip=zlhi; count>0; lip++)
+ for (p=0, *lip=0; p<FASTDIGS && count>0;
+ p+=DECDPUN, cup++, count-=DECDPUN)
+ *lip+=*cup*powers[p];
+ lmsi=lip-1; // save -> msi
+ for (count=rhs->digits, cup=rhs->lsu, rip=zrhi; count>0; rip++)
+ for (p=0, *rip=0; p<FASTDIGS && count>0;
+ p+=DECDPUN, cup++, count-=DECDPUN)
+ *rip+=*cup*powers[p];
+ rmsi=rip-1; // save -> msi
+
+ // zero the accumulator
+ for (lp=zacc; lp<zacc+iacc; lp++) *lp=0;
+
+ /* Start the multiplication */
+ // Resolving carries can dominate the cost of accumulating the
+ // partial products, so this is only done when necessary.
+ // Each uLong item in the accumulator can hold values up to
+ // 2**64-1, and each partial product can be as large as
+ // (10**FASTDIGS-1)**2. When FASTDIGS=9, this can be added to
+ // itself 18.4 times in a uLong without overflowing, so during
+ // the main calculation resolution is carried out every 18th
+ // add -- every 162 digits. Similarly, when FASTDIGS=8, the
+ // partial products can be added to themselves 1844.6 times in
+ // a uLong without overflowing, so intermediate carry
+ // resolution occurs only every 14752 digits. Hence for common
+ // short numbers usually only the one final carry resolution
+ // occurs.
+ // (The count is set via FASTLAZY to simplify experiments to
+ // measure the value of this approach: a 35% improvement on a
+ // [34x34] multiply.)
+ lazy=FASTLAZY; // carry delay count
+ for (rip=zrhi; rip<=rmsi; rip++) { // over each item in rhs
+ lp=zacc+(rip-zrhi); // where to add the lhs
+ for (lip=zlhi; lip<=lmsi; lip++, lp++) { // over each item in lhs
+ *lp+=(uLong)(*lip)*(*rip); // [this should in-line]
+ } // lip loop
+ lazy--;
+ if (lazy>0 && rip!=rmsi) continue;
+ lazy=FASTLAZY; // reset delay count
+ // spin up the accumulator resolving overflows
+ for (lp=zacc; lp<zacc+iacc; lp++) {
+ if (*lp<FASTBASE) continue; // it fits
+ lcarry=*lp/FASTBASE; // top part [slow divide]
+ // lcarry can exceed 2**32-1, so check again; this check
+ // and occasional extra divide (slow) is well worth it, as
+ // it allows FASTLAZY to be increased to 18 rather than 4
+ // in the FASTDIGS=9 case
+ if (lcarry<FASTBASE) carry=(uInt)lcarry; // [usual]
+ else { // two-place carry [fairly rare]
+ uInt carry2=(uInt)(lcarry/FASTBASE); // top top part
+ *(lp+2)+=carry2; // add to item+2
+ *lp-=((uLong)FASTBASE*FASTBASE*carry2); // [slow]
+ carry=(uInt)(lcarry-((uLong)FASTBASE*carry2)); // [inline]
+ }
+ *(lp+1)+=carry; // add to item above [inline]
+ *lp-=((uLong)FASTBASE*carry); // [inline]
+ } // carry resolution
+ } // rip loop
+
+ // The multiplication is complete; time to convert back into
+ // units. This can be done in-place in the accumulator and in
+ // 32-bit operations, because carries were resolved after the
+ // final add. This needs N-1 divides and multiplies for
+ // each item in the accumulator (which will become up to N
+ // units, where 2<=N<=9).
+ for (lp=zacc, up=acc; lp<zacc+iacc; lp++) {
+ uInt item=(uInt)*lp; // decapitate to uInt
+ for (p=0; p<FASTDIGS-DECDPUN; p+=DECDPUN, up++) {
+ uInt part=item/(DECDPUNMAX+1);
+ *up=(Unit)(item-(part*(DECDPUNMAX+1)));
+ item=part;
+ } // p
+ *up=(Unit)item; up++; // [final needs no division]
+ } // lp
+ accunits=up-acc; // count of units
+ }
+ else { // here to use units directly, without chunking ['old code']
+ #endif
+
+ // if accumulator will be too long for local storage, then allocate
+ acc=accbuff; // -> assume buffer for accumulator
+ needbytes=(D2U(lhs->digits)+D2U(rhs->digits))*sizeof(Unit);
+ if (needbytes>(Int)sizeof(accbuff)) {
+ allocacc=(Unit *)malloc(needbytes);
+ if (allocacc==NULL) {*status|=DEC_Insufficient_storage; break;}
+ acc=(Unit *)allocacc; // use the allocated space
+ }
+
+ /* Now the main long multiplication loop */
+ // Unlike the equivalent in the IBM Java implementation, there
+ // is no advantage in calculating from msu to lsu. So, do it
+ // by the book, as it were.
+ // Each iteration calculates ACC=ACC+MULTAND*MULT
+ accunits=1; // accumulator starts at '0'
+ *acc=0; // .. (lsu=0)
+ shift=0; // no multiplicand shift at first
+ madlength=D2U(lhs->digits); // this won't change
+ mermsup=rhs->lsu+D2U(rhs->digits); // -> msu+1 of multiplier
+
+ for (mer=rhs->lsu; mer<mermsup; mer++) {
+ // Here, *mer is the next Unit in the multiplier to use
+ // If non-zero [optimization] add it...
+ if (*mer!=0) accunits=decUnitAddSub(&acc[shift], accunits-shift,
+ lhs->lsu, madlength, 0,
+ &acc[shift], *mer)
+ + shift;
+ else { // extend acc with a 0; it will be used shortly
+ *(acc+accunits)=0; // [this avoids length of <=0 later]
+ accunits++;
+ }
+ // multiply multiplicand by 10**DECDPUN for next Unit to left
+ shift++; // add this for 'logical length'
+ } // n
+ #if FASTMUL
+ } // unchunked units
+ #endif
+ // common end-path
+ #if DECTRACE
+ decDumpAr('*', acc, accunits); // Show exact result
+ #endif
+
+ // acc now contains the exact result of the multiplication,
+ // possibly with a leading zero unit; build the decNumber from
+ // it, noting if any residue
+ res->bits=bits; // set sign
+ res->digits=decGetDigits(acc, accunits); // count digits exactly
+
+ // There can be a 31-bit wrap in calculating the exponent.
+ // This can only happen if both input exponents are negative and
+ // both their magnitudes are large. If there was a wrap, set a
+ // safe very negative exponent, from which decFinalize() will
+ // raise a hard underflow shortly.
+ exponent=lhs->exponent+rhs->exponent; // calculate exponent
+ if (lhs->exponent<0 && rhs->exponent<0 && exponent>0)
+ exponent=-2*DECNUMMAXE; // force underflow
+ res->exponent=exponent; // OK to overwrite now
+
+
+ // Set the coefficient. If any rounding, residue records
+ decSetCoeff(res, set, acc, res->digits, &residue, status);
+ decFinish(res, set, &residue, status); // final cleanup
+ } while(0); // end protected
+
+ if (allocacc!=NULL) free(allocacc); // drop any storage used
+ #if DECSUBSET
+ if (allocrhs!=NULL) free(allocrhs); // ..
+ if (alloclhs!=NULL) free(alloclhs); // ..
+ #endif
+ #if FASTMUL
+ if (allocrhi!=NULL) free(allocrhi); // ..
+ if (alloclhi!=NULL) free(alloclhi); // ..
+ #endif
+ return res;
+ } // decMultiplyOp
+
+/* ------------------------------------------------------------------ */
+/* decExpOp -- effect exponentiation */
+/* */
+/* This computes C = exp(A) */
+/* */
+/* res is C, the result. C may be A */
+/* rhs is A */
+/* set is the context; note that rounding mode has no effect */
+/* */
+/* C must have space for set->digits digits. status is updated but */
+/* not set. */
+/* */
+/* Restrictions: */
+/* */
+/* digits, emax, and -emin in the context must be less than */
+/* 2*DEC_MAX_MATH (1999998), and the rhs must be within these */
+/* bounds or a zero. This is an internal routine, so these */
+/* restrictions are contractual and not enforced. */
+/* */
+/* A finite result is rounded using DEC_ROUND_HALF_EVEN; it will */
+/* almost always be correctly rounded, but may be up to 1 ulp in */
+/* error in rare cases. */
+/* */
+/* Finite results will always be full precision and Inexact, except */
+/* when A is a zero or -Infinity (giving 1 or 0 respectively). */
+/* ------------------------------------------------------------------ */
+/* This approach used here is similar to the algorithm described in */
+/* */
+/* Variable Precision Exponential Function, T. E. Hull and */
+/* A. Abrham, ACM Transactions on Mathematical Software, Vol 12 #2, */
+/* pp79-91, ACM, June 1986. */
+/* */
+/* with the main difference being that the iterations in the series */
+/* evaluation are terminated dynamically (which does not require the */
+/* extra variable-precision variables which are expensive in this */
+/* context). */
+/* */
+/* The error analysis in Hull & Abrham's paper applies except for the */
+/* round-off error accumulation during the series evaluation. This */
+/* code does not precalculate the number of iterations and so cannot */
+/* use Horner's scheme. Instead, the accumulation is done at double- */
+/* precision, which ensures that the additions of the terms are exact */
+/* and do not accumulate round-off (and any round-off errors in the */
+/* terms themselves move 'to the right' faster than they can */
+/* accumulate). This code also extends the calculation by allowing, */
+/* in the spirit of other decNumber operators, the input to be more */
+/* precise than the result (the precision used is based on the more */
+/* precise of the input or requested result). */
+/* */
+/* Implementation notes: */
+/* */
+/* 1. This is separated out as decExpOp so it can be called from */
+/* other Mathematical functions (notably Ln) with a wider range */
+/* than normal. In particular, it can handle the slightly wider */
+/* (double) range needed by Ln (which has to be able to calculate */
+/* exp(-x) where x can be the tiniest number (Ntiny). */
+/* */
+/* 2. Normalizing x to be <=0.1 (instead of <=1) reduces loop */
+/* iterations by appoximately a third with additional (although */
+/* diminishing) returns as the range is reduced to even smaller */
+/* fractions. However, h (the power of 10 used to correct the */
+/* result at the end, see below) must be kept <=8 as otherwise */
+/* the final result cannot be computed. Hence the leverage is a */
+/* sliding value (8-h), where potentially the range is reduced */
+/* more for smaller values. */
+/* */
+/* The leverage that can be applied in this way is severely */
+/* limited by the cost of the raise-to-the power at the end, */
+/* which dominates when the number of iterations is small (less */
+/* than ten) or when rhs is short. As an example, the adjustment */
+/* x**10,000,000 needs 31 multiplications, all but one full-width. */
+/* */
+/* 3. The restrictions (especially precision) could be raised with */
+/* care, but the full decNumber range seems very hard within the */
+/* 32-bit limits. */
+/* */
+/* 4. The working precisions for the static buffers are twice the */
+/* obvious size to allow for calls from decNumberPower. */
+/* ------------------------------------------------------------------ */
+decNumber * decExpOp(decNumber *res, const decNumber *rhs,
+ decContext *set, uInt *status) {
+ uInt ignore=0; // working status
+ Int h; // adjusted exponent for 0.xxxx
+ Int p; // working precision
+ Int residue; // rounding residue
+ uInt needbytes; // for space calculations
+ const decNumber *x=rhs; // (may point to safe copy later)
+ decContext aset, tset, dset; // working contexts
+ Int comp; // work
+
+ // the argument is often copied to normalize it, so (unusually) it
+ // is treated like other buffers, using DECBUFFER, +1 in case
+ // DECBUFFER is 0
+ decNumber bufr[D2N(DECBUFFER*2+1)];
+ decNumber *allocrhs=NULL; // non-NULL if rhs buffer allocated
+
+ // the working precision will be no more than set->digits+8+1
+ // so for on-stack buffers DECBUFFER+9 is used, +1 in case DECBUFFER
+ // is 0 (and twice that for the accumulator)
+
+ // buffer for t, term (working precision plus)
+ decNumber buft[D2N(DECBUFFER*2+9+1)];
+ decNumber *allocbuft=NULL; // -> allocated buft, iff allocated
+ decNumber *t=buft; // term
+ // buffer for a, accumulator (working precision * 2), at least 9
+ decNumber bufa[D2N(DECBUFFER*4+18+1)];
+ decNumber *allocbufa=NULL; // -> allocated bufa, iff allocated
+ decNumber *a=bufa; // accumulator
+ // decNumber for the divisor term; this needs at most 9 digits
+ // and so can be fixed size [16 so can use standard context]
+ decNumber bufd[D2N(16)];
+ decNumber *d=bufd; // divisor
+ decNumber numone; // constant 1
+
+ #if DECCHECK
+ Int iterations=0; // for later sanity check
+ if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
+ #endif
+
+ do { // protect allocated storage
+ if (SPECIALARG) { // handle infinities and NaNs
+ if (decNumberIsInfinite(rhs)) { // an infinity
+ if (decNumberIsNegative(rhs)) // -Infinity -> +0
+ decNumberZero(res);
+ else decNumberCopy(res, rhs); // +Infinity -> self
+ }
+ else decNaNs(res, rhs, NULL, set, status); // a NaN
+ break;}
+
+ if (ISZERO(rhs)) { // zeros -> exact 1
+ decNumberZero(res); // make clean 1
+ *res->lsu=1; // ..
+ break;} // [no status to set]
+
+ // e**x when 0 < x < 0.66 is < 1+3x/2, hence can fast-path
+ // positive and negative tiny cases which will result in inexact
+ // 1. This also allows the later add-accumulate to always be
+ // exact (because its length will never be more than twice the
+ // working precision).
+ // The comparator (tiny) needs just one digit, so use the
+ // decNumber d for it (reused as the divisor, etc., below); its
+ // exponent is such that if x is positive it will have
+ // set->digits-1 zeros between the decimal point and the digit,
+ // which is 4, and if x is negative one more zero there as the
+ // more precise result will be of the form 0.9999999 rather than
+ // 1.0000001. Hence, tiny will be 0.0000004 if digits=7 and x>0
+ // or 0.00000004 if digits=7 and x<0. If RHS not larger than
+ // this then the result will be 1.000000
+ decNumberZero(d); // clean
+ *d->lsu=4; // set 4 ..
+ d->exponent=-set->digits; // * 10**(-d)
+ if (decNumberIsNegative(rhs)) d->exponent--; // negative case
+ comp=decCompare(d, rhs, 1); // signless compare
+ if (comp==BADINT) {
+ *status|=DEC_Insufficient_storage;
+ break;}
+ if (comp>=0) { // rhs < d
+ Int shift=set->digits-1;
+ decNumberZero(res); // set 1
+ *res->lsu=1; // ..
+ res->digits=decShiftToMost(res->lsu, 1, shift);
+ res->exponent=-shift; // make 1.0000...
+ *status|=DEC_Inexact | DEC_Rounded; // .. inexactly
+ break;} // tiny
+
+ // set up the context to be used for calculating a, as this is
+ // used on both paths below
+ decContextDefault(&aset, DEC_INIT_DECIMAL64);
+ // accumulator bounds are as requested (could underflow)
+ aset.emax=set->emax; // usual bounds
+ aset.emin=set->emin; // ..
+ aset.clamp=0; // and no concrete format
+
+ // calculate the adjusted (Hull & Abrham) exponent (where the
+ // decimal point is just to the left of the coefficient msd)
+ h=rhs->exponent+rhs->digits;
+ // if h>8 then 10**h cannot be calculated safely; however, when
+ // h=8 then exp(|rhs|) will be at least exp(1E+7) which is at
+ // least 6.59E+4342944, so (due to the restriction on Emax/Emin)
+ // overflow (or underflow to 0) is guaranteed -- so this case can
+ // be handled by simply forcing the appropriate excess
+ if (h>8) { // overflow/underflow
+ // set up here so Power call below will over or underflow to
+ // zero; set accumulator to either 2 or 0.02
+ // [stack buffer for a is always big enough for this]
+ decNumberZero(a);
+ *a->lsu=2; // not 1 but < exp(1)
+ if (decNumberIsNegative(rhs)) a->exponent=-2; // make 0.02
+ h=8; // clamp so 10**h computable
+ p=9; // set a working precision
+ }
+ else { // h<=8
+ Int maxlever=(rhs->digits>8?1:0);
+ // [could/should increase this for precisions >40 or so, too]
+
+ // if h is 8, cannot normalize to a lower upper limit because
+ // the final result will not be computable (see notes above),
+ // but leverage can be applied whenever h is less than 8.
+ // Apply as much as possible, up to a MAXLEVER digits, which
+ // sets the tradeoff against the cost of the later a**(10**h).
+ // As h is increased, the working precision below also
+ // increases to compensate for the "constant digits at the
+ // front" effect.
+ Int lever=MINI(8-h, maxlever); // leverage attainable
+ Int use=-rhs->digits-lever; // exponent to use for RHS
+ h+=lever; // apply leverage selected
+ if (h<0) { // clamp
+ use+=h; // [may end up subnormal]
+ h=0;
+ }
+ // Take a copy of RHS if it needs normalization (true whenever x>=1)
+ if (rhs->exponent!=use) {
+ decNumber *newrhs=bufr; // assume will fit on stack
+ needbytes=sizeof(decNumber)+(D2U(rhs->digits)-1)*sizeof(Unit);
+ if (needbytes>sizeof(bufr)) { // need malloc space
+ allocrhs=(decNumber *)malloc(needbytes);
+ if (allocrhs==NULL) { // hopeless -- abandon
+ *status|=DEC_Insufficient_storage;
+ break;}
+ newrhs=allocrhs; // use the allocated space
+ }
+ decNumberCopy(newrhs, rhs); // copy to safe space
+ newrhs->exponent=use; // normalize; now <1
+ x=newrhs; // ready for use
+ // decNumberShow(x);
+ }
+
+ // Now use the usual power series to evaluate exp(x). The
+ // series starts as 1 + x + x^2/2 ... so prime ready for the
+ // third term by setting the term variable t=x, the accumulator
+ // a=1, and the divisor d=2.
+
+ // First determine the working precision. From Hull & Abrham
+ // this is set->digits+h+2. However, if x is 'over-precise' we
+ // need to allow for all its digits to potentially participate
+ // (consider an x where all the excess digits are 9s) so in
+ // this case use x->digits+h+2
+ p=MAXI(x->digits, set->digits)+h+2; // [h<=8]
+
+ // a and t are variable precision, and depend on p, so space
+ // must be allocated for them if necessary
+
+ // the accumulator needs to be able to hold 2p digits so that
+ // the additions on the second and subsequent iterations are
+ // sufficiently exact.
+ needbytes=sizeof(decNumber)+(D2U(p*2)-1)*sizeof(Unit);
+ if (needbytes>sizeof(bufa)) { // need malloc space
+ allocbufa=(decNumber *)malloc(needbytes);
+ if (allocbufa==NULL) { // hopeless -- abandon
+ *status|=DEC_Insufficient_storage;
+ break;}
+ a=allocbufa; // use the allocated space
+ }
+ // the term needs to be able to hold p digits (which is
+ // guaranteed to be larger than x->digits, so the initial copy
+ // is safe); it may also be used for the raise-to-power
+ // calculation below, which needs an extra two digits
+ needbytes=sizeof(decNumber)+(D2U(p+2)-1)*sizeof(Unit);
+ if (needbytes>sizeof(buft)) { // need malloc space
+ allocbuft=(decNumber *)malloc(needbytes);
+ if (allocbuft==NULL) { // hopeless -- abandon
+ *status|=DEC_Insufficient_storage;
+ break;}
+ t=allocbuft; // use the allocated space
+ }
+
+ decNumberCopy(t, x); // term=x
+ decNumberZero(a); *a->lsu=1; // accumulator=1
+ decNumberZero(d); *d->lsu=2; // divisor=2
+ decNumberZero(&numone); *numone.lsu=1; // constant 1 for increment
+
+ // set up the contexts for calculating a, t, and d
+ decContextDefault(&tset, DEC_INIT_DECIMAL64);
+ dset=tset;
+ // accumulator bounds are set above, set precision now
+ aset.digits=p*2; // double
+ // term bounds avoid any underflow or overflow
+ tset.digits=p;
+ tset.emin=DEC_MIN_EMIN; // [emax is plenty]
+ // [dset.digits=16, etc., are sufficient]
+
+ // finally ready to roll
+ for (;;) {
+ #if DECCHECK
+ iterations++;
+ #endif
+ // only the status from the accumulation is interesting
+ // [but it should remain unchanged after first add]
+ decAddOp(a, a, t, &aset, 0, status); // a=a+t
+ decMultiplyOp(t, t, x, &tset, &ignore); // t=t*x
+ decDivideOp(t, t, d, &tset, DIVIDE, &ignore); // t=t/d
+ // the iteration ends when the term cannot affect the result,
+ // if rounded to p digits, which is when its value is smaller
+ // than the accumulator by p+1 digits. There must also be
+ // full precision in a.
+ if (((a->digits+a->exponent)>=(t->digits+t->exponent+p+1))
+ && (a->digits>=p)) break;
+ decAddOp(d, d, &numone, &dset, 0, &ignore); // d=d+1
+ } // iterate
+
+ #if DECCHECK
+ // just a sanity check; comment out test to show always
+ if (iterations>p+3)
+ printf("Exp iterations=%ld, status=%08lx, p=%ld, d=%ld\n",
+ (LI)iterations, (LI)*status, (LI)p, (LI)x->digits);
+ #endif
+ } // h<=8
+
+ // apply postconditioning: a=a**(10**h) -- this is calculated
+ // at a slightly higher precision than Hull & Abrham suggest
+ if (h>0) {
+ Int seenbit=0; // set once a 1-bit is seen
+ Int i; // counter
+ Int n=powers[h]; // always positive
+ aset.digits=p+2; // sufficient precision
+ // avoid the overhead and many extra digits of decNumberPower
+ // as all that is needed is the short 'multipliers' loop; here
+ // accumulate the answer into t
+ decNumberZero(t); *t->lsu=1; // acc=1
+ for (i=1;;i++){ // for each bit [top bit ignored]
+ // abandon if have had overflow or terminal underflow
+ if (*status & (DEC_Overflow|DEC_Underflow)) { // interesting?
+ if (*status&DEC_Overflow || ISZERO(t)) break;}
+ n=n<<1; // move next bit to testable position
+ if (n<0) { // top bit is set
+ seenbit=1; // OK, have a significant bit
+ decMultiplyOp(t, t, a, &aset, status); // acc=acc*x
+ }
+ if (i==31) break; // that was the last bit
+ if (!seenbit) continue; // no need to square 1
+ decMultiplyOp(t, t, t, &aset, status); // acc=acc*acc [square]
+ } /*i*/ // 32 bits
+ // decNumberShow(t);
+ a=t; // and carry on using t instead of a
+ }
+
+ // Copy and round the result to res
+ residue=1; // indicate dirt to right ..
+ if (ISZERO(a)) residue=0; // .. unless underflowed to 0
+ aset.digits=set->digits; // [use default rounding]
+ decCopyFit(res, a, &aset, &residue, status); // copy & shorten
+ decFinish(res, set, &residue, status); // cleanup/set flags
+ } while(0); // end protected
+
+ if (allocrhs !=NULL) free(allocrhs); // drop any storage used
+ if (allocbufa!=NULL) free(allocbufa); // ..
+ if (allocbuft!=NULL) free(allocbuft); // ..
+ // [status is handled by caller]
+ return res;
+ } // decExpOp
+
+/* ------------------------------------------------------------------ */
+/* Initial-estimate natural logarithm table */
+/* */
+/* LNnn -- 90-entry 16-bit table for values from .10 through .99. */
+/* The result is a 4-digit encode of the coefficient (c=the */
+/* top 14 bits encoding 0-9999) and a 2-digit encode of the */
+/* exponent (e=the bottom 2 bits encoding 0-3) */
+/* */
+/* The resulting value is given by: */
+/* */
+/* v = -c * 10**(-e-3) */
+/* */
+/* where e and c are extracted from entry k = LNnn[x-10] */
+/* where x is truncated (NB) into the range 10 through 99, */
+/* and then c = k>>2 and e = k&3. */
+/* ------------------------------------------------------------------ */
+const uShort LNnn[90]={9016, 8652, 8316, 8008, 7724, 7456, 7208,
+ 6972, 6748, 6540, 6340, 6148, 5968, 5792, 5628, 5464, 5312,
+ 5164, 5020, 4884, 4748, 4620, 4496, 4376, 4256, 4144, 4032,
+ 39233, 38181, 37157, 36157, 35181, 34229, 33297, 32389, 31501, 30629,
+ 29777, 28945, 28129, 27329, 26545, 25777, 25021, 24281, 23553, 22837,
+ 22137, 21445, 20769, 20101, 19445, 18801, 18165, 17541, 16925, 16321,
+ 15721, 15133, 14553, 13985, 13421, 12865, 12317, 11777, 11241, 10717,
+ 10197, 9685, 9177, 8677, 8185, 7697, 7213, 6737, 6269, 5801,
+ 5341, 4889, 4437, 39930, 35534, 31186, 26886, 22630, 18418, 14254,
+ 10130, 6046, 20055};
+
+/* ------------------------------------------------------------------ */
+/* decLnOp -- effect natural logarithm */
+/* */
+/* This computes C = ln(A) */
+/* */
+/* res is C, the result. C may be A */
+/* rhs is A */
+/* set is the context; note that rounding mode has no effect */
+/* */
+/* C must have space for set->digits digits. */
+/* */
+/* Notable cases: */
+/* A<0 -> Invalid */
+/* A=0 -> -Infinity (Exact) */
+/* A=+Infinity -> +Infinity (Exact) */
+/* A=1 exactly -> 0 (Exact) */
+/* */
+/* Restrictions (as for Exp): */
+/* */
+/* digits, emax, and -emin in the context must be less than */
+/* DEC_MAX_MATH+11 (1000010), and the rhs must be within these */
+/* bounds or a zero. This is an internal routine, so these */
+/* restrictions are contractual and not enforced. */
+/* */
+/* A finite result is rounded using DEC_ROUND_HALF_EVEN; it will */
+/* almost always be correctly rounded, but may be up to 1 ulp in */
+/* error in rare cases. */
+/* ------------------------------------------------------------------ */
+/* The result is calculated using Newton's method, with each */
+/* iteration calculating a' = a + x * exp(-a) - 1. See, for example, */
+/* Epperson 1989. */
+/* */
+/* The iteration ends when the adjustment x*exp(-a)-1 is tiny enough. */
+/* This has to be calculated at the sum of the precision of x and the */
+/* working precision. */
+/* */
+/* Implementation notes: */
+/* */
+/* 1. This is separated out as decLnOp so it can be called from */
+/* other Mathematical functions (e.g., Log 10) with a wider range */
+/* than normal. In particular, it can handle the slightly wider */
+/* (+9+2) range needed by a power function. */
+/* */
+/* 2. The speed of this function is about 10x slower than exp, as */
+/* it typically needs 4-6 iterations for short numbers, and the */
+/* extra precision needed adds a squaring effect, twice. */
+/* */
+/* 3. Fastpaths are included for ln(10) and ln(2), up to length 40, */
+/* as these are common requests. ln(10) is used by log10(x). */
+/* */
+/* 4. An iteration might be saved by widening the LNnn table, and */
+/* would certainly save at least one if it were made ten times */
+/* bigger, too (for truncated fractions 0.100 through 0.999). */
+/* However, for most practical evaluations, at least four or five */
+/* iterations will be neede -- so this would only speed up by */
+/* 20-25% and that probably does not justify increasing the table */
+/* size. */
+/* */
+/* 5. The static buffers are larger than might be expected to allow */
+/* for calls from decNumberPower. */
+/* ------------------------------------------------------------------ */
+decNumber * decLnOp(decNumber *res, const decNumber *rhs,
+ decContext *set, uInt *status) {
+ uInt ignore=0; // working status accumulator
+ uInt needbytes; // for space calculations
+ Int residue; // rounding residue
+ Int r; // rhs=f*10**r [see below]
+ Int p; // working precision
+ Int pp; // precision for iteration
+ Int t; // work
+
+ // buffers for a (accumulator, typically precision+2) and b
+ // (adjustment calculator, same size)
+ decNumber bufa[D2N(DECBUFFER+12)];
+ decNumber *allocbufa=NULL; // -> allocated bufa, iff allocated
+ decNumber *a=bufa; // accumulator/work
+ decNumber bufb[D2N(DECBUFFER*2+2)];
+ decNumber *allocbufb=NULL; // -> allocated bufa, iff allocated
+ decNumber *b=bufb; // adjustment/work
+
+ decNumber numone; // constant 1
+ decNumber cmp; // work
+ decContext aset, bset; // working contexts
+
+ #if DECCHECK
+ Int iterations=0; // for later sanity check
+ if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
+ #endif
+
+ do { // protect allocated storage
+ if (SPECIALARG) { // handle infinities and NaNs
+ if (decNumberIsInfinite(rhs)) { // an infinity
+ if (decNumberIsNegative(rhs)) // -Infinity -> error
+ *status|=DEC_Invalid_operation;
+ else decNumberCopy(res, rhs); // +Infinity -> self
+ }
+ else decNaNs(res, rhs, NULL, set, status); // a NaN
+ break;}
+
+ if (ISZERO(rhs)) { // +/- zeros -> -Infinity
+ decNumberZero(res); // make clean
+ res->bits=DECINF|DECNEG; // set - infinity
+ break;} // [no status to set]
+
+ // Non-zero negatives are bad...
+ if (decNumberIsNegative(rhs)) { // -x -> error
+ *status|=DEC_Invalid_operation;
+ break;}
+
+ // Here, rhs is positive, finite, and in range
+
+ // lookaside fastpath code for ln(2) and ln(10) at common lengths
+ if (rhs->exponent==0 && set->digits<=40) {
+ #if DECDPUN==1
+ if (rhs->lsu[0]==0 && rhs->lsu[1]==1 && rhs->digits==2) { // ln(10)
+ #else
+ if (rhs->lsu[0]==10 && rhs->digits==2) { // ln(10)
+ #endif
+ aset=*set; aset.round=DEC_ROUND_HALF_EVEN;
+ #define LN10 "2.302585092994045684017991454684364207601"
+ decNumberFromString(res, LN10, &aset);
+ *status|=(DEC_Inexact | DEC_Rounded); // is inexact
+ break;}
+ if (rhs->lsu[0]==2 && rhs->digits==1) { // ln(2)
+ aset=*set; aset.round=DEC_ROUND_HALF_EVEN;
+ #define LN2 "0.6931471805599453094172321214581765680755"
+ decNumberFromString(res, LN2, &aset);
+ *status|=(DEC_Inexact | DEC_Rounded);
+ break;}
+ } // integer and short
+
+ // Determine the working precision. This is normally the
+ // requested precision + 2, with a minimum of 9. However, if
+ // the rhs is 'over-precise' then allow for all its digits to
+ // potentially participate (consider an rhs where all the excess
+ // digits are 9s) so in this case use rhs->digits+2.
+ p=MAXI(rhs->digits, MAXI(set->digits, 7))+2;
+
+ // Allocate space for the accumulator and the high-precision
+ // adjustment calculator, if necessary. The accumulator must
+ // be able to hold p digits, and the adjustment up to
+ // rhs->digits+p digits. They are also made big enough for 16
+ // digits so that they can be used for calculating the initial
+ // estimate.
+ needbytes=sizeof(decNumber)+(D2U(MAXI(p,16))-1)*sizeof(Unit);
+ if (needbytes>sizeof(bufa)) { // need malloc space
+ allocbufa=(decNumber *)malloc(needbytes);
+ if (allocbufa==NULL) { // hopeless -- abandon
+ *status|=DEC_Insufficient_storage;
+ break;}
+ a=allocbufa; // use the allocated space
+ }
+ pp=p+rhs->digits;
+ needbytes=sizeof(decNumber)+(D2U(MAXI(pp,16))-1)*sizeof(Unit);
+ if (needbytes>sizeof(bufb)) { // need malloc space
+ allocbufb=(decNumber *)malloc(needbytes);
+ if (allocbufb==NULL) { // hopeless -- abandon
+ *status|=DEC_Insufficient_storage;
+ break;}
+ b=allocbufb; // use the allocated space
+ }
+
+ // Prepare an initial estimate in acc. Calculate this by
+ // considering the coefficient of x to be a normalized fraction,
+ // f, with the decimal point at far left and multiplied by
+ // 10**r. Then, rhs=f*10**r and 0.1<=f<1, and
+ // ln(x) = ln(f) + ln(10)*r
+ // Get the initial estimate for ln(f) from a small lookup
+ // table (see above) indexed by the first two digits of f,
+ // truncated.
+
+ decContextDefault(&aset, DEC_INIT_DECIMAL64); // 16-digit extended
+ r=rhs->exponent+rhs->digits; // 'normalised' exponent
+ decNumberFromInt32(a, r); // a=r
+ decNumberFromInt32(b, 2302585); // b=ln(10) (2.302585)
+ b->exponent=-6; // ..
+ decMultiplyOp(a, a, b, &aset, &ignore); // a=a*b
+ // now get top two digits of rhs into b by simple truncate and
+ // force to integer
+ residue=0; // (no residue)
+ aset.digits=2; aset.round=DEC_ROUND_DOWN;
+ decCopyFit(b, rhs, &aset, &residue, &ignore); // copy & shorten
+ b->exponent=0; // make integer
+ t=decGetInt(b); // [cannot fail]
+ if (t<10) t=X10(t); // adjust single-digit b
+ t=LNnn[t-10]; // look up ln(b)
+ decNumberFromInt32(b, t>>2); // b=ln(b) coefficient
+ b->exponent=-(t&3)-3; // set exponent
+ b->bits=DECNEG; // ln(0.10)->ln(0.99) always -ve
+ aset.digits=16; aset.round=DEC_ROUND_HALF_EVEN; // restore
+ decAddOp(a, a, b, &aset, 0, &ignore); // acc=a+b
+ // the initial estimate is now in a, with up to 4 digits correct.
+ // When rhs is at or near Nmax the estimate will be low, so we
+ // will approach it from below, avoiding overflow when calling exp.
+
+ decNumberZero(&numone); *numone.lsu=1; // constant 1 for adjustment
+
+ // accumulator bounds are as requested (could underflow, but
+ // cannot overflow)
+ aset.emax=set->emax;
+ aset.emin=set->emin;
+ aset.clamp=0; // no concrete format
+ // set up a context to be used for the multiply and subtract
+ bset=aset;
+ bset.emax=DEC_MAX_MATH*2; // use double bounds for the
+ bset.emin=-DEC_MAX_MATH*2; // adjustment calculation
+ // [see decExpOp call below]
+ // for each iteration double the number of digits to calculate,
+ // up to a maximum of p
+ pp=9; // initial precision
+ // [initially 9 as then the sequence starts 7+2, 16+2, and
+ // 34+2, which is ideal for standard-sized numbers]
+ aset.digits=pp; // working context
+ bset.digits=pp+rhs->digits; // wider context
+ for (;;) { // iterate
+ #if DECCHECK
+ iterations++;
+ if (iterations>24) break; // consider 9 * 2**24
+ #endif
+ // calculate the adjustment (exp(-a)*x-1) into b. This is a
+ // catastrophic subtraction but it really is the difference
+ // from 1 that is of interest.
+ // Use the internal entry point to Exp as it allows the double
+ // range for calculating exp(-a) when a is the tiniest subnormal.
+ a->bits^=DECNEG; // make -a
+ decExpOp(b, a, &bset, &ignore); // b=exp(-a)
+ a->bits^=DECNEG; // restore sign of a
+ // now multiply by rhs and subtract 1, at the wider precision
+ decMultiplyOp(b, b, rhs, &bset, &ignore); // b=b*rhs
+ decAddOp(b, b, &numone, &bset, DECNEG, &ignore); // b=b-1
+
+ // the iteration ends when the adjustment cannot affect the
+ // result by >=0.5 ulp (at the requested digits), which
+ // is when its value is smaller than the accumulator by
+ // set->digits+1 digits (or it is zero) -- this is a looser
+ // requirement than for Exp because all that happens to the
+ // accumulator after this is the final rounding (but note that
+ // there must also be full precision in a, or a=0).
+
+ if (decNumberIsZero(b) ||
+ (a->digits+a->exponent)>=(b->digits+b->exponent+set->digits+1)) {
+ if (a->digits==p) break;
+ if (decNumberIsZero(a)) {
+ decCompareOp(&cmp, rhs, &numone, &aset, COMPARE, &ignore); // rhs=1 ?
+ if (cmp.lsu[0]==0) a->exponent=0; // yes, exact 0
+ else *status|=(DEC_Inexact | DEC_Rounded); // no, inexact
+ break;
+ }
+ // force padding if adjustment has gone to 0 before full length
+ if (decNumberIsZero(b)) b->exponent=a->exponent-p;
+ }
+
+ // not done yet ...
+ decAddOp(a, a, b, &aset, 0, &ignore); // a=a+b for next estimate
+ if (pp==p) continue; // precision is at maximum
+ // lengthen the next calculation
+ pp=pp*2; // double precision
+ if (pp>p) pp=p; // clamp to maximum
+ aset.digits=pp; // working context
+ bset.digits=pp+rhs->digits; // wider context
+ } // Newton's iteration
+
+ #if DECCHECK
+ // just a sanity check; remove the test to show always
+ if (iterations>24)
+ printf("Ln iterations=%ld, status=%08lx, p=%ld, d=%ld\n",
+ (LI)iterations, (LI)*status, (LI)p, (LI)rhs->digits);
+ #endif
+
+ // Copy and round the result to res
+ residue=1; // indicate dirt to right
+ if (ISZERO(a)) residue=0; // .. unless underflowed to 0
+ aset.digits=set->digits; // [use default rounding]
+ decCopyFit(res, a, &aset, &residue, status); // copy & shorten
+ decFinish(res, set, &residue, status); // cleanup/set flags
+ } while(0); // end protected
+
+ if (allocbufa!=NULL) free(allocbufa); // drop any storage used
+ if (allocbufb!=NULL) free(allocbufb); // ..
+ // [status is handled by caller]
+ return res;
+ } // decLnOp
+
+/* ------------------------------------------------------------------ */
+/* decQuantizeOp -- force exponent to requested value */
+/* */
+/* This computes C = op(A, B), where op adjusts the coefficient */
+/* of C (by rounding or shifting) such that the exponent (-scale) */
+/* of C has the value B or matches the exponent of B. */
+/* The numerical value of C will equal A, except for the effects of */
+/* any rounding that occurred. */
+/* */
+/* res is C, the result. C may be A or B */
+/* lhs is A, the number to adjust */
+/* rhs is B, the requested exponent */
+/* set is the context */
+/* quant is 1 for quantize or 0 for rescale */
+/* status is the status accumulator (this can be called without */
+/* risk of control loss) */
+/* */
+/* C must have space for set->digits digits. */
+/* */
+/* Unless there is an error or the result is infinite, the exponent */
+/* after the operation is guaranteed to be that requested. */
+/* ------------------------------------------------------------------ */
+static decNumber * decQuantizeOp(decNumber *res, const decNumber *lhs,
+ const decNumber *rhs, decContext *set,
+ Flag quant, uInt *status) {
+ #if DECSUBSET
+ decNumber *alloclhs=NULL; // non-NULL if rounded lhs allocated
+ decNumber *allocrhs=NULL; // .., rhs
+ #endif
+ const decNumber *inrhs=rhs; // save original rhs
+ Int reqdigits=set->digits; // requested DIGITS
+ Int reqexp; // requested exponent [-scale]
+ Int residue=0; // rounding residue
+ Int etiny=set->emin-(reqdigits-1);
+
+ #if DECCHECK
+ if (decCheckOperands(res, lhs, rhs, set)) return res;
+ #endif
+
+ do { // protect allocated storage
+ #if DECSUBSET
+ if (!set->extended) {
+ // reduce operands and set lostDigits status, as needed
+ if (lhs->digits>reqdigits) {
+ alloclhs=decRoundOperand(lhs, set, status);
+ if (alloclhs==NULL) break;
+ lhs=alloclhs;
+ }
+ if (rhs->digits>reqdigits) { // [this only checks lostDigits]
+ allocrhs=decRoundOperand(rhs, set, status);
+ if (allocrhs==NULL) break;
+ rhs=allocrhs;
+ }
+ }
+ #endif
+ // [following code does not require input rounding]
+
+ // Handle special values
+ if (SPECIALARGS) {
+ // NaNs get usual processing
+ if (SPECIALARGS & (DECSNAN | DECNAN))
+ decNaNs(res, lhs, rhs, set, status);
+ // one infinity but not both is bad
+ else if ((lhs->bits ^ rhs->bits) & DECINF)
+ *status|=DEC_Invalid_operation;
+ // both infinity: return lhs
+ else decNumberCopy(res, lhs); // [nop if in place]
+ break;
+ }
+
+ // set requested exponent
+ if (quant) reqexp=inrhs->exponent; // quantize -- match exponents
+ else { // rescale -- use value of rhs
+ // Original rhs must be an integer that fits and is in range,
+ // which could be from -1999999997 to +999999999, thanks to
+ // subnormals
+ reqexp=decGetInt(inrhs); // [cannot fail]
+ }
+
+ #if DECSUBSET
+ if (!set->extended) etiny=set->emin; // no subnormals
+ #endif
+
+ if (reqexp==BADINT // bad (rescale only) or ..
+ || reqexp==BIGODD || reqexp==BIGEVEN // very big (ditto) or ..
+ || (reqexp<etiny) // < lowest
+ || (reqexp>set->emax)) { // > emax
+ *status|=DEC_Invalid_operation;
+ break;}
+
+ // the RHS has been processed, so it can be overwritten now if necessary
+ if (ISZERO(lhs)) { // zero coefficient unchanged
+ decNumberCopy(res, lhs); // [nop if in place]
+ res->exponent=reqexp; // .. just set exponent
+ #if DECSUBSET
+ if (!set->extended) res->bits=0; // subset specification; no -0
+ #endif
+ }
+ else { // non-zero lhs
+ Int adjust=reqexp-lhs->exponent; // digit adjustment needed
+ // if adjusted coefficient will definitely not fit, give up now
+ if ((lhs->digits-adjust)>reqdigits) {
+ *status|=DEC_Invalid_operation;
+ break;
+ }
+
+ if (adjust>0) { // increasing exponent
+ // this will decrease the length of the coefficient by adjust
+ // digits, and must round as it does so
+ decContext workset; // work
+ workset=*set; // clone rounding, etc.
+ workset.digits=lhs->digits-adjust; // set requested length
+ // [note that the latter can be <1, here]
+ decCopyFit(res, lhs, &workset, &residue, status); // fit to result
+ decApplyRound(res, &workset, residue, status); // .. and round
+ residue=0; // [used]
+ // If just rounded a 999s case, exponent will be off by one;
+ // adjust back (after checking space), if so.
+ if (res->exponent>reqexp) {
+ // re-check needed, e.g., for quantize(0.9999, 0.001) under
+ // set->digits==3
+ if (res->digits==reqdigits) { // cannot shift by 1
+ *status&=~(DEC_Inexact | DEC_Rounded); // [clean these]
+ *status|=DEC_Invalid_operation;
+ break;
+ }
+ res->digits=decShiftToMost(res->lsu, res->digits, 1); // shift
+ res->exponent--; // (re)adjust the exponent.
+ }
+ #if DECSUBSET
+ if (ISZERO(res) && !set->extended) res->bits=0; // subset; no -0
+ #endif
+ } // increase
+ else /* adjust<=0 */ { // decreasing or = exponent
+ // this will increase the length of the coefficient by -adjust
+ // digits, by adding zero or more trailing zeros; this is
+ // already checked for fit, above
+ decNumberCopy(res, lhs); // [it will fit]
+ // if padding needed (adjust<0), add it now...
+ if (adjust<0) {
+ res->digits=decShiftToMost(res->lsu, res->digits, -adjust);
+ res->exponent+=adjust; // adjust the exponent
+ }
+ } // decrease
+ } // non-zero
+
+ // Check for overflow [do not use Finalize in this case, as an
+ // overflow here is a "don't fit" situation]
+ if (res->exponent>set->emax-res->digits+1) { // too big
+ *status|=DEC_Invalid_operation;
+ break;
+ }
+ else {
+ decFinalize(res, set, &residue, status); // set subnormal flags
+ *status&=~DEC_Underflow; // suppress Underflow [as per 754]
+ }
+ } while(0); // end protected
+
+ #if DECSUBSET
+ if (allocrhs!=NULL) free(allocrhs); // drop any storage used
+ if (alloclhs!=NULL) free(alloclhs); // ..
+ #endif
+ return res;
+ } // decQuantizeOp
+
+/* ------------------------------------------------------------------ */
+/* decCompareOp -- compare, min, or max two Numbers */
+/* */
+/* This computes C = A ? B and carries out one of four operations: */
+/* COMPARE -- returns the signum (as a number) giving the */
+/* result of a comparison unless one or both */
+/* operands is a NaN (in which case a NaN results) */
+/* COMPSIG -- as COMPARE except that a quiet NaN raises */
+/* Invalid operation. */
+/* COMPMAX -- returns the larger of the operands, using the */
+/* 754 maxnum operation */
+/* COMPMAXMAG -- ditto, comparing absolute values */
+/* COMPMIN -- the 754 minnum operation */
+/* COMPMINMAG -- ditto, comparing absolute values */
+/* COMTOTAL -- returns the signum (as a number) giving the */
+/* result of a comparison using 754 total ordering */
+/* */
+/* res is C, the result. C may be A and/or B (e.g., X=X?X) */
+/* lhs is A */
+/* rhs is B */
+/* set is the context */
+/* op is the operation flag */
+/* status is the usual accumulator */
+/* */
+/* C must have space for one digit for COMPARE or set->digits for */
+/* COMPMAX, COMPMIN, COMPMAXMAG, or COMPMINMAG. */
+/* ------------------------------------------------------------------ */
+/* The emphasis here is on speed for common cases, and avoiding */
+/* coefficient comparison if possible. */
+/* ------------------------------------------------------------------ */
+decNumber * decCompareOp(decNumber *res, const decNumber *lhs,
+ const decNumber *rhs, decContext *set,
+ Flag op, uInt *status) {
+ #if DECSUBSET
+ decNumber *alloclhs=NULL; // non-NULL if rounded lhs allocated
+ decNumber *allocrhs=NULL; // .., rhs
+ #endif
+ Int result=0; // default result value
+ uByte merged; // work
+
+ #if DECCHECK
+ if (decCheckOperands(res, lhs, rhs, set)) return res;
+ #endif
+
+ do { // protect allocated storage
+ #if DECSUBSET
+ if (!set->extended) {
+ // reduce operands and set lostDigits status, as needed
+ if (lhs->digits>set->digits) {
+ alloclhs=decRoundOperand(lhs, set, status);
+ if (alloclhs==NULL) {result=BADINT; break;}
+ lhs=alloclhs;
+ }
+ if (rhs->digits>set->digits) {
+ allocrhs=decRoundOperand(rhs, set, status);
+ if (allocrhs==NULL) {result=BADINT; break;}
+ rhs=allocrhs;
+ }
+ }
+ #endif
+ // [following code does not require input rounding]
+
+ // If total ordering then handle differing signs 'up front'
+ if (op==COMPTOTAL) { // total ordering
+ if (decNumberIsNegative(lhs) & !decNumberIsNegative(rhs)) {
+ result=-1;
+ break;
+ }
+ if (!decNumberIsNegative(lhs) & decNumberIsNegative(rhs)) {
+ result=+1;
+ break;
+ }
+ }
+
+ // handle NaNs specially; let infinities drop through
+ // This assumes sNaN (even just one) leads to NaN.
+ merged=(lhs->bits | rhs->bits) & (DECSNAN | DECNAN);
+ if (merged) { // a NaN bit set
+ if (op==COMPARE); // result will be NaN
+ else if (op==COMPSIG) // treat qNaN as sNaN
+ *status|=DEC_Invalid_operation | DEC_sNaN;
+ else if (op==COMPTOTAL) { // total ordering, always finite
+ // signs are known to be the same; compute the ordering here
+ // as if the signs are both positive, then invert for negatives
+ if (!decNumberIsNaN(lhs)) result=-1;
+ else if (!decNumberIsNaN(rhs)) result=+1;
+ // here if both NaNs
+ else if (decNumberIsSNaN(lhs) && decNumberIsQNaN(rhs)) result=-1;
+ else if (decNumberIsQNaN(lhs) && decNumberIsSNaN(rhs)) result=+1;
+ else { // both NaN or both sNaN
+ // now it just depends on the payload
+ result=decUnitCompare(lhs->lsu, D2U(lhs->digits),
+ rhs->lsu, D2U(rhs->digits), 0);
+ // [Error not possible, as these are 'aligned']
+ } // both same NaNs
+ if (decNumberIsNegative(lhs)) result=-result;
+ break;
+ } // total order
+
+ else if (merged & DECSNAN); // sNaN -> qNaN
+ else { // here if MIN or MAX and one or two quiet NaNs
+ // min or max -- 754 rules ignore single NaN
+ if (!decNumberIsNaN(lhs) || !decNumberIsNaN(rhs)) {
+ // just one NaN; force choice to be the non-NaN operand
+ op=COMPMAX;
+ if (lhs->bits & DECNAN) result=-1; // pick rhs
+ else result=+1; // pick lhs
+ break;
+ }
+ } // max or min
+ op=COMPNAN; // use special path
+ decNaNs(res, lhs, rhs, set, status); // propagate NaN
+ break;
+ }
+ // have numbers
+ if (op==COMPMAXMAG || op==COMPMINMAG) result=decCompare(lhs, rhs, 1);
+ else result=decCompare(lhs, rhs, 0); // sign matters
+ } while(0); // end protected
+
+ if (result==BADINT) *status|=DEC_Insufficient_storage; // rare
+ else {
+ if (op==COMPARE || op==COMPSIG ||op==COMPTOTAL) { // returning signum
+ if (op==COMPTOTAL && result==0) {
+ // operands are numerically equal or same NaN (and same sign,
+ // tested first); if identical, leave result 0
+ if (lhs->exponent!=rhs->exponent) {
+ if (lhs->exponent<rhs->exponent) result=-1;
+ else result=+1;
+ if (decNumberIsNegative(lhs)) result=-result;
+ } // lexp!=rexp
+ } // total-order by exponent
+ decNumberZero(res); // [always a valid result]
+ if (result!=0) { // must be -1 or +1
+ *res->lsu=1;
+ if (result<0) res->bits=DECNEG;
+ }
+ }
+ else if (op==COMPNAN); // special, drop through
+ else { // MAX or MIN, non-NaN result
+ Int residue=0; // rounding accumulator
+ // choose the operand for the result
+ const decNumber *choice;
+ if (result==0) { // operands are numerically equal
+ // choose according to sign then exponent (see 754)
+ uByte slhs=(lhs->bits & DECNEG);
+ uByte srhs=(rhs->bits & DECNEG);
+ #if DECSUBSET
+ if (!set->extended) { // subset: force left-hand
+ op=COMPMAX;
+ result=+1;
+ }
+ else
+ #endif
+ if (slhs!=srhs) { // signs differ
+ if (slhs) result=-1; // rhs is max
+ else result=+1; // lhs is max
+ }
+ else if (slhs && srhs) { // both negative
+ if (lhs->exponent<rhs->exponent) result=+1;
+ else result=-1;
+ // [if equal, use lhs, technically identical]
+ }
+ else { // both positive
+ if (lhs->exponent>rhs->exponent) result=+1;
+ else result=-1;
+ // [ditto]
+ }
+ } // numerically equal
+ // here result will be non-0; reverse if looking for MIN
+ if (op==COMPMIN || op==COMPMINMAG) result=-result;
+ choice=(result>0 ? lhs : rhs); // choose
+ // copy chosen to result, rounding if need be
+ decCopyFit(res, choice, set, &residue, status);
+ decFinish(res, set, &residue, status);
+ }
+ }
+ #if DECSUBSET
+ if (allocrhs!=NULL) free(allocrhs); // free any storage used
+ if (alloclhs!=NULL) free(alloclhs); // ..
+ #endif
+ return res;
+ } // decCompareOp
+
+/* ------------------------------------------------------------------ */
+/* decCompare -- compare two decNumbers by numerical value */
+/* */
+/* This routine compares A ? B without altering them. */
+/* */
+/* Arg1 is A, a decNumber which is not a NaN */
+/* Arg2 is B, a decNumber which is not a NaN */
+/* Arg3 is 1 for a sign-independent compare, 0 otherwise */
+/* */
+/* returns -1, 0, or 1 for A<B, A==B, or A>B, or BADINT if failure */
+/* (the only possible failure is an allocation error) */
+/* ------------------------------------------------------------------ */
+static Int decCompare(const decNumber *lhs, const decNumber *rhs,
+ Flag abs) {
+ Int result; // result value
+ Int sigr; // rhs signum
+ Int compare; // work
+
+ result=1; // assume signum(lhs)
+ if (ISZERO(lhs)) result=0;
+ if (abs) {
+ if (ISZERO(rhs)) return result; // LHS wins or both 0
+ // RHS is non-zero
+ if (result==0) return -1; // LHS is 0; RHS wins
+ // [here, both non-zero, result=1]
+ }
+ else { // signs matter
+ if (result && decNumberIsNegative(lhs)) result=-1;
+ sigr=1; // compute signum(rhs)
+ if (ISZERO(rhs)) sigr=0;
+ else if (decNumberIsNegative(rhs)) sigr=-1;
+ if (result > sigr) return +1; // L > R, return 1
+ if (result < sigr) return -1; // L < R, return -1
+ if (result==0) return 0; // both 0
+ }
+
+ // signums are the same; both are non-zero
+ if ((lhs->bits | rhs->bits) & DECINF) { // one or more infinities
+ if (decNumberIsInfinite(rhs)) {
+ if (decNumberIsInfinite(lhs)) result=0;// both infinite
+ else result=-result; // only rhs infinite
+ }
+ return result;
+ }
+ // must compare the coefficients, allowing for exponents
+ if (lhs->exponent>rhs->exponent) { // LHS exponent larger
+ // swap sides, and sign
+ const decNumber *temp=lhs;
+ lhs=rhs;
+ rhs=temp;
+ result=-result;
+ }
+ compare=decUnitCompare(lhs->lsu, D2U(lhs->digits),
+ rhs->lsu, D2U(rhs->digits),
+ rhs->exponent-lhs->exponent);
+ if (compare!=BADINT) compare*=result; // comparison succeeded
+ return compare;
+ } // decCompare
+
+/* ------------------------------------------------------------------ */
+/* decUnitCompare -- compare two >=0 integers in Unit arrays */
+/* */
+/* This routine compares A ? B*10**E where A and B are unit arrays */
+/* A is a plain integer */
+/* B has an exponent of E (which must be non-negative) */
+/* */
+/* Arg1 is A first Unit (lsu) */
+/* Arg2 is A length in Units */
+/* Arg3 is B first Unit (lsu) */
+/* Arg4 is B length in Units */
+/* Arg5 is E (0 if the units are aligned) */
+/* */
+/* returns -1, 0, or 1 for A<B, A==B, or A>B, or BADINT if failure */
+/* (the only possible failure is an allocation error, which can */
+/* only occur if E!=0) */
+/* ------------------------------------------------------------------ */
+static Int decUnitCompare(const Unit *a, Int alength,
+ const Unit *b, Int blength, Int exp) {
+ Unit *acc; // accumulator for result
+ Unit accbuff[SD2U(DECBUFFER*2+1)]; // local buffer
+ Unit *allocacc=NULL; // -> allocated acc buffer, iff allocated
+ Int accunits, need; // units in use or needed for acc
+ const Unit *l, *r, *u; // work
+ Int expunits, exprem, result; // ..
+
+ if (exp==0) { // aligned; fastpath
+ if (alength>blength) return 1;
+ if (alength<blength) return -1;
+ // same number of units in both -- need unit-by-unit compare
+ l=a+alength-1;
+ r=b+alength-1;
+ for (;l>=a; l--, r--) {
+ if (*l>*r) return 1;
+ if (*l<*r) return -1;
+ }
+ return 0; // all units match
+ } // aligned
+
+ // Unaligned. If one is >1 unit longer than the other, padded
+ // approximately, then can return easily
+ if (alength>blength+(Int)D2U(exp)) return 1;
+ if (alength+1<blength+(Int)D2U(exp)) return -1;
+
+ // Need to do a real subtract. For this, a result buffer is needed
+ // even though only the sign is of interest. Its length needs
+ // to be the larger of alength and padded blength, +2
+ need=blength+D2U(exp); // maximum real length of B
+ if (need<alength) need=alength;
+ need+=2;
+ acc=accbuff; // assume use local buffer
+ if (need*sizeof(Unit)>sizeof(accbuff)) {
+ allocacc=(Unit *)malloc(need*sizeof(Unit));
+ if (allocacc==NULL) return BADINT; // hopeless -- abandon
+ acc=allocacc;
+ }
+ // Calculate units and remainder from exponent.
+ expunits=exp/DECDPUN;
+ exprem=exp%DECDPUN;
+ // subtract [A+B*(-m)]
+ accunits=decUnitAddSub(a, alength, b, blength, expunits, acc,
+ -(Int)powers[exprem]);
+ // [UnitAddSub result may have leading zeros, even on zero]
+ if (accunits<0) result=-1; // negative result
+ else { // non-negative result
+ // check units of the result before freeing any storage
+ for (u=acc; u<acc+accunits-1 && *u==0;) u++;
+ result=(*u==0 ? 0 : +1);
+ }
+ // clean up and return the result
+ if (allocacc!=NULL) free(allocacc); // drop any storage used
+ return result;
+ } // decUnitCompare
+
+/* ------------------------------------------------------------------ */
+/* decUnitAddSub -- add or subtract two >=0 integers in Unit arrays */
+/* */
+/* This routine performs the calculation: */
+/* */
+/* C=A+(B*M) */
+/* */
+/* Where M is in the range -DECDPUNMAX through +DECDPUNMAX. */
+/* */
+/* A may be shorter or longer than B. */
+/* */
+/* Leading zeros are not removed after a calculation. The result is */
+/* either the same length as the longer of A and B (adding any */
+/* shift), or one Unit longer than that (if a Unit carry occurred). */
+/* */
+/* A and B content are not altered unless C is also A or B. */
+/* C may be the same array as A or B, but only if no zero padding is */
+/* requested (that is, C may be B only if bshift==0). */
+/* C is filled from the lsu; only those units necessary to complete */
+/* the calculation are referenced. */
+/* */
+/* Arg1 is A first Unit (lsu) */
+/* Arg2 is A length in Units */
+/* Arg3 is B first Unit (lsu) */
+/* Arg4 is B length in Units */
+/* Arg5 is B shift in Units (>=0; pads with 0 units if positive) */
+/* Arg6 is C first Unit (lsu) */
+/* Arg7 is M, the multiplier */
+/* */
+/* returns the count of Units written to C, which will be non-zero */
+/* and negated if the result is negative. That is, the sign of the */
+/* returned Int is the sign of the result (positive for zero) and */
+/* the absolute value of the Int is the count of Units. */
+/* */
+/* It is the caller's responsibility to make sure that C size is */
+/* safe, allowing space if necessary for a one-Unit carry. */
+/* */
+/* This routine is severely performance-critical; *any* change here */
+/* must be measured (timed) to assure no performance degradation. */
+/* In particular, trickery here tends to be counter-productive, as */
+/* increased complexity of code hurts register optimizations on */
+/* register-poor architectures. Avoiding divisions is nearly */
+/* always a Good Idea, however. */
+/* */
+/* Special thanks to Rick McGuire (IBM Cambridge, MA) and Dave Clark */
+/* (IBM Warwick, UK) for some of the ideas used in this routine. */
+/* ------------------------------------------------------------------ */
+static Int decUnitAddSub(const Unit *a, Int alength,
+ const Unit *b, Int blength, Int bshift,
+ Unit *c, Int m) {
+ const Unit *alsu=a; // A lsu [need to remember it]
+ Unit *clsu=c; // C ditto
+ Unit *minC; // low water mark for C
+ Unit *maxC; // high water mark for C
+ eInt carry=0; // carry integer (could be Long)
+ Int add; // work
+ #if DECDPUN<=4 // myriadal, millenary, etc.
+ Int est; // estimated quotient
+ #endif
+
+ #if DECTRACE
+ if (alength<1 || blength<1)
+ printf("decUnitAddSub: alen blen m %ld %ld [%ld]\n", alength, blength, m);
+ #endif
+
+ maxC=c+alength; // A is usually the longer
+ minC=c+blength; // .. and B the shorter
+ if (bshift!=0) { // B is shifted; low As copy across
+ minC+=bshift;
+ // if in place [common], skip copy unless there's a gap [rare]
+ if (a==c && bshift<=alength) {
+ c+=bshift;
+ a+=bshift;
+ }
+ else for (; c<clsu+bshift; a++, c++) { // copy needed
+ if (a<alsu+alength) *c=*a;
+ else *c=0;
+ }
+ }
+ if (minC>maxC) { // swap
+ Unit *hold=minC;
+ minC=maxC;
+ maxC=hold;
+ }
+
+ // For speed, do the addition as two loops; the first where both A
+ // and B contribute, and the second (if necessary) where only one or
+ // other of the numbers contribute.
+ // Carry handling is the same (i.e., duplicated) in each case.
+ for (; c<minC; c++) {
+ carry+=*a;
+ a++;
+ carry+=((eInt)*b)*m; // [special-casing m=1/-1
+ b++; // here is not a win]
+ // here carry is new Unit of digits; it could be +ve or -ve
+ if ((ueInt)carry<=DECDPUNMAX) { // fastpath 0-DECDPUNMAX
+ *c=(Unit)carry;
+ carry=0;
+ continue;
+ }
+ #if DECDPUN==4 // use divide-by-multiply
+ if (carry>=0) {
+ est=(((ueInt)carry>>11)*53687)>>18;
+ *c=(Unit)(carry-est*(DECDPUNMAX+1)); // remainder
+ carry=est; // likely quotient [89%]
+ if (*c<DECDPUNMAX+1) continue; // estimate was correct
+ carry++;
+ *c-=DECDPUNMAX+1;
+ continue;
+ }
+ // negative case
+ carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); // make positive
+ est=(((ueInt)carry>>11)*53687)>>18;
+ *c=(Unit)(carry-est*(DECDPUNMAX+1));
+ carry=est-(DECDPUNMAX+1); // correctly negative
+ if (*c<DECDPUNMAX+1) continue; // was OK
+ carry++;
+ *c-=DECDPUNMAX+1;
+ #elif DECDPUN==3
+ if (carry>=0) {
+ est=(((ueInt)carry>>3)*16777)>>21;
+ *c=(Unit)(carry-est*(DECDPUNMAX+1)); // remainder
+ carry=est; // likely quotient [99%]
+ if (*c<DECDPUNMAX+1) continue; // estimate was correct
+ carry++;
+ *c-=DECDPUNMAX+1;
+ continue;
+ }
+ // negative case
+ carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); // make positive
+ est=(((ueInt)carry>>3)*16777)>>21;
+ *c=(Unit)(carry-est*(DECDPUNMAX+1));
+ carry=est-(DECDPUNMAX+1); // correctly negative
+ if (*c<DECDPUNMAX+1) continue; // was OK
+ carry++;
+ *c-=DECDPUNMAX+1;
+ #elif DECDPUN<=2
+ // Can use QUOT10 as carry <= 4 digits
+ if (carry>=0) {
+ est=QUOT10(carry, DECDPUN);
+ *c=(Unit)(carry-est*(DECDPUNMAX+1)); // remainder
+ carry=est; // quotient
+ continue;
+ }
+ // negative case
+ carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); // make positive
+ est=QUOT10(carry, DECDPUN);
+ *c=(Unit)(carry-est*(DECDPUNMAX+1));
+ carry=est-(DECDPUNMAX+1); // correctly negative
+ #else
+ // remainder operator is undefined if negative, so must test
+ if ((ueInt)carry<(DECDPUNMAX+1)*2) { // fastpath carry +1
+ *c=(Unit)(carry-(DECDPUNMAX+1)); // [helps additions]
+ carry=1;
+ continue;
+ }
+ if (carry>=0) {
+ *c=(Unit)(carry%(DECDPUNMAX+1));
+ carry=carry/(DECDPUNMAX+1);
+ continue;
+ }
+ // negative case
+ carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); // make positive
+ *c=(Unit)(carry%(DECDPUNMAX+1));
+ carry=carry/(DECDPUNMAX+1)-(DECDPUNMAX+1);
+ #endif
+ } // c
+
+ // now may have one or other to complete
+ // [pretest to avoid loop setup/shutdown]
+ if (c<maxC) for (; c<maxC; c++) {
+ if (a<alsu+alength) { // still in A
+ carry+=*a;
+ a++;
+ }
+ else { // inside B
+ carry+=((eInt)*b)*m;
+ b++;
+ }
+ // here carry is new Unit of digits; it could be +ve or -ve and
+ // magnitude up to DECDPUNMAX squared
+ if ((ueInt)carry<=DECDPUNMAX) { // fastpath 0-DECDPUNMAX
+ *c=(Unit)carry;
+ carry=0;
+ continue;
+ }
+ // result for this unit is negative or >DECDPUNMAX
+ #if DECDPUN==4 // use divide-by-multiply
+ if (carry>=0) {
+ est=(((ueInt)carry>>11)*53687)>>18;
+ *c=(Unit)(carry-est*(DECDPUNMAX+1)); // remainder
+ carry=est; // likely quotient [79.7%]
+ if (*c<DECDPUNMAX+1) continue; // estimate was correct
+ carry++;
+ *c-=DECDPUNMAX+1;
+ continue;
+ }
+ // negative case
+ carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); // make positive
+ est=(((ueInt)carry>>11)*53687)>>18;
+ *c=(Unit)(carry-est*(DECDPUNMAX+1));
+ carry=est-(DECDPUNMAX+1); // correctly negative
+ if (*c<DECDPUNMAX+1) continue; // was OK
+ carry++;
+ *c-=DECDPUNMAX+1;
+ #elif DECDPUN==3
+ if (carry>=0) {
+ est=(((ueInt)carry>>3)*16777)>>21;
+ *c=(Unit)(carry-est*(DECDPUNMAX+1)); // remainder
+ carry=est; // likely quotient [99%]
+ if (*c<DECDPUNMAX+1) continue; // estimate was correct
+ carry++;
+ *c-=DECDPUNMAX+1;
+ continue;
+ }
+ // negative case
+ carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); // make positive
+ est=(((ueInt)carry>>3)*16777)>>21;
+ *c=(Unit)(carry-est*(DECDPUNMAX+1));
+ carry=est-(DECDPUNMAX+1); // correctly negative
+ if (*c<DECDPUNMAX+1) continue; // was OK
+ carry++;
+ *c-=DECDPUNMAX+1;
+ #elif DECDPUN<=2
+ if (carry>=0) {
+ est=QUOT10(carry, DECDPUN);
+ *c=(Unit)(carry-est*(DECDPUNMAX+1)); // remainder
+ carry=est; // quotient
+ continue;
+ }
+ // negative case
+ carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); // make positive
+ est=QUOT10(carry, DECDPUN);
+ *c=(Unit)(carry-est*(DECDPUNMAX+1));
+ carry=est-(DECDPUNMAX+1); // correctly negative
+ #else
+ if ((ueInt)carry<(DECDPUNMAX+1)*2){ // fastpath carry 1
+ *c=(Unit)(carry-(DECDPUNMAX+1));
+ carry=1;
+ continue;
+ }
+ // remainder operator is undefined if negative, so must test
+ if (carry>=0) {
+ *c=(Unit)(carry%(DECDPUNMAX+1));
+ carry=carry/(DECDPUNMAX+1);
+ continue;
+ }
+ // negative case
+ carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); // make positive
+ *c=(Unit)(carry%(DECDPUNMAX+1));
+ carry=carry/(DECDPUNMAX+1)-(DECDPUNMAX+1);
+ #endif
+ } // c
+
+ // OK, all A and B processed; might still have carry or borrow
+ // return number of Units in the result, negated if a borrow
+ if (carry==0) return c-clsu; // no carry, so no more to do
+ if (carry>0) { // positive carry
+ *c=(Unit)carry; // place as new unit
+ c++; // ..
+ return c-clsu;
+ }
+ // -ve carry: it's a borrow; complement needed
+ add=1; // temporary carry...
+ for (c=clsu; c<maxC; c++) {
+ add=DECDPUNMAX+add-*c;
+ if (add<=DECDPUNMAX) {
+ *c=(Unit)add;
+ add=0;
+ }
+ else {
+ *c=0;
+ add=1;
+ }
+ }
+ // add an extra unit iff it would be non-zero
+ #if DECTRACE
+ printf("UAS borrow: add %ld, carry %ld\n", add, carry);
+ #endif
+ if ((add-carry-1)!=0) {
+ *c=(Unit)(add-carry-1);
+ c++; // interesting, include it
+ }
+ return clsu-c; // -ve result indicates borrowed
+ } // decUnitAddSub
+
+/* ------------------------------------------------------------------ */
+/* decTrim -- trim trailing zeros or normalize */
+/* */
+/* dn is the number to trim or normalize */
+/* set is the context to use to check for clamp */
+/* all is 1 to remove all trailing zeros, 0 for just fraction ones */
+/* noclamp is 1 to unconditional (unclamped) trim */
+/* dropped returns the number of discarded trailing zeros */
+/* returns dn */
+/* */
+/* If clamp is set in the context then the number of zeros trimmed */
+/* may be limited if the exponent is high. */
+/* All fields are updated as required. This is a utility operation, */
+/* so special values are unchanged and no error is possible. */
+/* ------------------------------------------------------------------ */
+static decNumber * decTrim(decNumber *dn, decContext *set, Flag all,
+ Flag noclamp, Int *dropped) {
+ Int d, exp; // work
+ uInt cut; // ..
+ Unit *up; // -> current Unit
+
+ #if DECCHECK
+ if (decCheckOperands(dn, DECUNUSED, DECUNUSED, DECUNCONT)) return dn;
+ #endif
+
+ *dropped=0; // assume no zeros dropped
+ if ((dn->bits & DECSPECIAL) // fast exit if special ..
+ || (*dn->lsu & 0x01)) return dn; // .. or odd
+ if (ISZERO(dn)) { // .. or 0
+ dn->exponent=0; // (sign is preserved)
+ return dn;
+ }
+
+ // have a finite number which is even
+ exp=dn->exponent;
+ cut=1; // digit (1-DECDPUN) in Unit
+ up=dn->lsu; // -> current Unit
+ for (d=0; d<dn->digits-1; d++) { // [don't strip the final digit]
+ // slice by powers
+ #if DECDPUN<=4
+ uInt quot=QUOT10(*up, cut);
+ if ((*up-quot*powers[cut])!=0) break; // found non-0 digit
+ #else
+ if (*up%powers[cut]!=0) break; // found non-0 digit
+ #endif
+ // have a trailing 0
+ if (!all) { // trimming
+ // [if exp>0 then all trailing 0s are significant for trim]
+ if (exp<=0) { // if digit might be significant
+ if (exp==0) break; // then quit
+ exp++; // next digit might be significant
+ }
+ }
+ cut++; // next power
+ if (cut>DECDPUN) { // need new Unit
+ up++;
+ cut=1;
+ }
+ } // d
+ if (d==0) return dn; // none to drop
+
+ // may need to limit drop if clamping
+ if (set->clamp && !noclamp) {
+ Int maxd=set->emax-set->digits+1-dn->exponent;
+ if (maxd<=0) return dn; // nothing possible
+ if (d>maxd) d=maxd;
+ }
+
+ // effect the drop
+ decShiftToLeast(dn->lsu, D2U(dn->digits), d);
+ dn->exponent+=d; // maintain numerical value
+ dn->digits-=d; // new length
+ *dropped=d; // report the count
+ return dn;
+ } // decTrim
+
+/* ------------------------------------------------------------------ */
+/* decReverse -- reverse a Unit array in place */
+/* */
+/* ulo is the start of the array */
+/* uhi is the end of the array (highest Unit to include) */
+/* */
+/* The units ulo through uhi are reversed in place (if the number */
+/* of units is odd, the middle one is untouched). Note that the */
+/* digit(s) in each unit are unaffected. */
+/* ------------------------------------------------------------------ */
+static void decReverse(Unit *ulo, Unit *uhi) {
+ Unit temp;
+ for (; ulo<uhi; ulo++, uhi--) {
+ temp=*ulo;
+ *ulo=*uhi;
+ *uhi=temp;
+ }
+ return;
+ } // decReverse
+
+/* ------------------------------------------------------------------ */
+/* decShiftToMost -- shift digits in array towards most significant */
+/* */
+/* uar is the array */
+/* digits is the count of digits in use in the array */
+/* shift is the number of zeros to pad with (least significant); */
+/* it must be zero or positive */
+/* */
+/* returns the new length of the integer in the array, in digits */
+/* */
+/* No overflow is permitted (that is, the uar array must be known to */
+/* be large enough to hold the result, after shifting). */
+/* ------------------------------------------------------------------ */
+static Int decShiftToMost(Unit *uar, Int digits, Int shift) {
+ Unit *target, *source, *first; // work
+ Int cut; // odd 0's to add
+ uInt next; // work
+
+ if (shift==0) return digits; // [fastpath] nothing to do
+ if ((digits+shift)<=DECDPUN) { // [fastpath] single-unit case
+ *uar=(Unit)(*uar*powers[shift]);
+ return digits+shift;
+ }
+
+ next=0; // all paths
+ source=uar+D2U(digits)-1; // where msu comes from
+ target=source+D2U(shift); // where upper part of first cut goes
+ cut=DECDPUN-MSUDIGITS(shift); // where to slice
+ if (cut==0) { // unit-boundary case
+ for (; source>=uar; source--, target--) *target=*source;
+ }
+ else {
+ first=uar+D2U(digits+shift)-1; // where msu of source will end up
+ for (; source>=uar; source--, target--) {
+ // split the source Unit and accumulate remainder for next
+ #if DECDPUN<=4
+ uInt quot=QUOT10(*source, cut);
+ uInt rem=*source-quot*powers[cut];
+ next+=quot;
+ #else
+ uInt rem=*source%powers[cut];
+ next+=*source/powers[cut];
+ #endif
+ if (target<=first) *target=(Unit)next; // write to target iff valid
+ next=rem*powers[DECDPUN-cut]; // save remainder for next Unit
+ }
+ } // shift-move
+
+ // propagate any partial unit to one below and clear the rest
+ for (; target>=uar; target--) {
+ *target=(Unit)next;
+ next=0;
+ }
+ return digits+shift;
+ } // decShiftToMost
+
+/* ------------------------------------------------------------------ */
+/* decShiftToLeast -- shift digits in array towards least significant */
+/* */
+/* uar is the array */
+/* units is length of the array, in units */
+/* shift is the number of digits to remove from the lsu end; it */
+/* must be zero or positive and <= than units*DECDPUN. */
+/* */
+/* returns the new length of the integer in the array, in units */
+/* */
+/* Removed digits are discarded (lost). Units not required to hold */
+/* the final result are unchanged. */
+/* ------------------------------------------------------------------ */
+static Int decShiftToLeast(Unit *uar, Int units, Int shift) {
+ Unit *target, *up; // work
+ Int cut, count; // work
+ Int quot, rem; // for division
+
+ if (shift==0) return units; // [fastpath] nothing to do
+ if (shift==units*DECDPUN) { // [fastpath] little to do
+ *uar=0; // all digits cleared gives zero
+ return 1; // leaves just the one
+ }
+
+ target=uar; // both paths
+ cut=MSUDIGITS(shift);
+ if (cut==DECDPUN) { // unit-boundary case; easy
+ up=uar+D2U(shift);
+ for (; up<uar+units; target++, up++) *target=*up;
+ return target-uar;
+ }
+
+ // messier
+ up=uar+D2U(shift-cut); // source; correct to whole Units
+ count=units*DECDPUN-shift; // the maximum new length
+ #if DECDPUN<=4
+ quot=QUOT10(*up, cut);
+ #else
+ quot=*up/powers[cut];
+ #endif
+ for (; ; target++) {
+ *target=(Unit)quot;
+ count-=(DECDPUN-cut);
+ if (count<=0) break;
+ up++;
+ quot=*up;
+ #if DECDPUN<=4
+ quot=QUOT10(quot, cut);
+ rem=*up-quot*powers[cut];
+ #else
+ rem=quot%powers[cut];
+ quot=quot/powers[cut];
+ #endif
+ *target=(Unit)(*target+rem*powers[DECDPUN-cut]);
+ count-=cut;
+ if (count<=0) break;
+ }
+ return target-uar+1;
+ } // decShiftToLeast
+
+#if DECSUBSET
+/* ------------------------------------------------------------------ */
+/* decRoundOperand -- round an operand [used for subset only] */
+/* */
+/* dn is the number to round (dn->digits is > set->digits) */
+/* set is the relevant context */
+/* status is the status accumulator */
+/* */
+/* returns an allocated decNumber with the rounded result. */
+/* */
+/* lostDigits and other status may be set by this. */
+/* */
+/* Since the input is an operand, it must not be modified. */
+/* Instead, return an allocated decNumber, rounded as required. */
+/* It is the caller's responsibility to free the allocated storage. */
+/* */
+/* If no storage is available then the result cannot be used, so NULL */
+/* is returned. */
+/* ------------------------------------------------------------------ */
+static decNumber *decRoundOperand(const decNumber *dn, decContext *set,
+ uInt *status) {
+ decNumber *res; // result structure
+ uInt newstatus=0; // status from round
+ Int residue=0; // rounding accumulator
+
+ // Allocate storage for the returned decNumber, big enough for the
+ // length specified by the context
+ res=(decNumber *)malloc(sizeof(decNumber)
+ +(D2U(set->digits)-1)*sizeof(Unit));
+ if (res==NULL) {
+ *status|=DEC_Insufficient_storage;
+ return NULL;
+ }
+ decCopyFit(res, dn, set, &residue, &newstatus);
+ decApplyRound(res, set, residue, &newstatus);
+
+ // If that set Inexact then "lost digits" is raised...
+ if (newstatus & DEC_Inexact) newstatus|=DEC_Lost_digits;
+ *status|=newstatus;
+ return res;
+ } // decRoundOperand
+#endif
+
+/* ------------------------------------------------------------------ */
+/* decCopyFit -- copy a number, truncating the coefficient if needed */
+/* */
+/* dest is the target decNumber */
+/* src is the source decNumber */
+/* set is the context [used for length (digits) and rounding mode] */
+/* residue is the residue accumulator */
+/* status contains the current status to be updated */
+/* */
+/* (dest==src is allowed and will be a no-op if fits) */
+/* All fields are updated as required. */
+/* ------------------------------------------------------------------ */
+static void decCopyFit(decNumber *dest, const decNumber *src,
+ decContext *set, Int *residue, uInt *status) {
+ dest->bits=src->bits;
+ dest->exponent=src->exponent;
+ decSetCoeff(dest, set, src->lsu, src->digits, residue, status);
+ } // decCopyFit
+
+/* ------------------------------------------------------------------ */
+/* decSetCoeff -- set the coefficient of a number */
+/* */
+/* dn is the number whose coefficient array is to be set. */
+/* It must have space for set->digits digits */
+/* set is the context [for size] */
+/* lsu -> lsu of the source coefficient [may be dn->lsu] */
+/* len is digits in the source coefficient [may be dn->digits] */
+/* residue is the residue accumulator. This has values as in */
+/* decApplyRound, and will be unchanged unless the */
+/* target size is less than len. In this case, the */
+/* coefficient is truncated and the residue is updated to */
+/* reflect the previous residue and the dropped digits. */
+/* status is the status accumulator, as usual */
+/* */
+/* The coefficient may already be in the number, or it can be an */
+/* external intermediate array. If it is in the number, lsu must == */
+/* dn->lsu and len must == dn->digits. */
+/* */
+/* Note that the coefficient length (len) may be < set->digits, and */
+/* in this case this merely copies the coefficient (or is a no-op */
+/* if dn->lsu==lsu). */
+/* */
+/* Note also that (only internally, from decQuantizeOp and */
+/* decSetSubnormal) the value of set->digits may be less than one, */
+/* indicating a round to left. This routine handles that case */
+/* correctly; caller ensures space. */
+/* */
+/* dn->digits, dn->lsu (and as required), and dn->exponent are */
+/* updated as necessary. dn->bits (sign) is unchanged. */
+/* */
+/* DEC_Rounded status is set if any digits are discarded. */
+/* DEC_Inexact status is set if any non-zero digits are discarded, or */
+/* incoming residue was non-0 (implies rounded) */
+/* ------------------------------------------------------------------ */
+// mapping array: maps 0-9 to canonical residues, so that a residue
+// can be adjusted in the range [-1, +1] and achieve correct rounding
+// 0 1 2 3 4 5 6 7 8 9
+static const uByte resmap[10]={0, 3, 3, 3, 3, 5, 7, 7, 7, 7};
+static void decSetCoeff(decNumber *dn, decContext *set, const Unit *lsu,
+ Int len, Int *residue, uInt *status) {
+ Int discard; // number of digits to discard
+ uInt cut; // cut point in Unit
+ const Unit *up; // work
+ Unit *target; // ..
+ Int count; // ..
+ #if DECDPUN<=4
+ uInt temp; // ..
+ #endif
+
+ discard=len-set->digits; // digits to discard
+ if (discard<=0) { // no digits are being discarded
+ if (dn->lsu!=lsu) { // copy needed
+ // copy the coefficient array to the result number; no shift needed
+ count=len; // avoids D2U
+ up=lsu;
+ for (target=dn->lsu; count>0; target++, up++, count-=DECDPUN)
+ *target=*up;
+ dn->digits=len; // set the new length
+ }
+ // dn->exponent and residue are unchanged, record any inexactitude
+ if (*residue!=0) *status|=(DEC_Inexact | DEC_Rounded);
+ return;
+ }
+
+ // some digits must be discarded ...
+ dn->exponent+=discard; // maintain numerical value
+ *status|=DEC_Rounded; // accumulate Rounded status
+ if (*residue>1) *residue=1; // previous residue now to right, so reduce
+
+ if (discard>len) { // everything, +1, is being discarded
+ // guard digit is 0
+ // residue is all the number [NB could be all 0s]
+ if (*residue<=0) { // not already positive
+ count=len; // avoids D2U
+ for (up=lsu; count>0; up++, count-=DECDPUN) if (*up!=0) { // found non-0
+ *residue=1;
+ break; // no need to check any others
+ }
+ }
+ if (*residue!=0) *status|=DEC_Inexact; // record inexactitude
+ *dn->lsu=0; // coefficient will now be 0
+ dn->digits=1; // ..
+ return;
+ } // total discard
+
+ // partial discard [most common case]
+ // here, at least the first (most significant) discarded digit exists
+
+ // spin up the number, noting residue during the spin, until get to
+ // the Unit with the first discarded digit. When reach it, extract
+ // it and remember its position
+ count=0;
+ for (up=lsu;; up++) {
+ count+=DECDPUN;
+ if (count>=discard) break; // full ones all checked
+ if (*up!=0) *residue=1;
+ } // up
+
+ // here up -> Unit with first discarded digit
+ cut=discard-(count-DECDPUN)-1;
+ if (cut==DECDPUN-1) { // unit-boundary case (fast)
+ Unit half=(Unit)powers[DECDPUN]>>1;
+ // set residue directly
+ if (*up>=half) {
+ if (*up>half) *residue=7;
+ else *residue+=5; // add sticky bit
+ }
+ else { // <half
+ if (*up!=0) *residue=3; // [else is 0, leave as sticky bit]
+ }
+ if (set->digits<=0) { // special for Quantize/Subnormal :-(
+ *dn->lsu=0; // .. result is 0
+ dn->digits=1; // ..
+ }
+ else { // shift to least
+ count=set->digits; // now digits to end up with
+ dn->digits=count; // set the new length
+ up++; // move to next
+ // on unit boundary, so shift-down copy loop is simple
+ for (target=dn->lsu; count>0; target++, up++, count-=DECDPUN)
+ *target=*up;
+ }
+ } // unit-boundary case
+
+ else { // discard digit is in low digit(s), and not top digit
+ uInt discard1; // first discarded digit
+ uInt quot, rem; // for divisions
+ if (cut==0) quot=*up; // is at bottom of unit
+ else /* cut>0 */ { // it's not at bottom of unit
+ #if DECDPUN<=4
+ quot=QUOT10(*up, cut);
+ rem=*up-quot*powers[cut];
+ #else
+ rem=*up%powers[cut];
+ quot=*up/powers[cut];
+ #endif
+ if (rem!=0) *residue=1;
+ }
+ // discard digit is now at bottom of quot
+ #if DECDPUN<=4
+ temp=(quot*6554)>>16; // fast /10
+ // Vowels algorithm here not a win (9 instructions)
+ discard1=quot-X10(temp);
+ quot=temp;
+ #else
+ discard1=quot%10;
+ quot=quot/10;
+ #endif
+ // here, discard1 is the guard digit, and residue is everything
+ // else [use mapping array to accumulate residue safely]
+ *residue+=resmap[discard1];
+ cut++; // update cut
+ // here: up -> Unit of the array with bottom digit
+ // cut is the division point for each Unit
+ // quot holds the uncut high-order digits for the current unit
+ if (set->digits<=0) { // special for Quantize/Subnormal :-(
+ *dn->lsu=0; // .. result is 0
+ dn->digits=1; // ..
+ }
+ else { // shift to least needed
+ count=set->digits; // now digits to end up with
+ dn->digits=count; // set the new length
+ // shift-copy the coefficient array to the result number
+ for (target=dn->lsu; ; target++) {
+ *target=(Unit)quot;
+ count-=(DECDPUN-cut);
+ if (count<=0) break;
+ up++;
+ quot=*up;
+ #if DECDPUN<=4
+ quot=QUOT10(quot, cut);
+ rem=*up-quot*powers[cut];
+ #else
+ rem=quot%powers[cut];
+ quot=quot/powers[cut];
+ #endif
+ *target=(Unit)(*target+rem*powers[DECDPUN-cut]);
+ count-=cut;
+ if (count<=0) break;
+ } // shift-copy loop
+ } // shift to least
+ } // not unit boundary
+
+ if (*residue!=0) *status|=DEC_Inexact; // record inexactitude
+ return;
+ } // decSetCoeff
+
+/* ------------------------------------------------------------------ */
+/* decApplyRound -- apply pending rounding to a number */
+/* */
+/* dn is the number, with space for set->digits digits */
+/* set is the context [for size and rounding mode] */
+/* residue indicates pending rounding, being any accumulated */
+/* guard and sticky information. It may be: */
+/* 6-9: rounding digit is >5 */
+/* 5: rounding digit is exactly half-way */
+/* 1-4: rounding digit is <5 and >0 */
+/* 0: the coefficient is exact */
+/* -1: as 1, but the hidden digits are subtractive, that */
+/* is, of the opposite sign to dn. In this case the */
+/* coefficient must be non-0. This case occurs when */
+/* subtracting a small number (which can be reduced to */
+/* a sticky bit); see decAddOp. */
+/* status is the status accumulator, as usual */
+/* */
+/* This routine applies rounding while keeping the length of the */
+/* coefficient constant. The exponent and status are unchanged */
+/* except if: */
+/* */
+/* -- the coefficient was increased and is all nines (in which */
+/* case Overflow could occur, and is handled directly here so */
+/* the caller does not need to re-test for overflow) */
+/* */
+/* -- the coefficient was decreased and becomes all nines (in which */
+/* case Underflow could occur, and is also handled directly). */
+/* */
+/* All fields in dn are updated as required. */
+/* */
+/* ------------------------------------------------------------------ */
+static void decApplyRound(decNumber *dn, decContext *set, Int residue,
+ uInt *status) {
+ Int bump; // 1 if coefficient needs to be incremented
+ // -1 if coefficient needs to be decremented
+
+ if (residue==0) return; // nothing to apply
+
+ bump=0; // assume a smooth ride
+
+ // now decide whether, and how, to round, depending on mode
+ switch (set->round) {
+ case DEC_ROUND_05UP: { // round zero or five up (for reround)
+ // This is the same as DEC_ROUND_DOWN unless there is a
+ // positive residue and the lsd of dn is 0 or 5, in which case
+ // it is bumped; when residue is <0, the number is therefore
+ // bumped down unless the final digit was 1 or 6 (in which
+ // case it is bumped down and then up -- a no-op)
+ Int lsd5=*dn->lsu%5; // get lsd and quintate
+ if (residue<0 && lsd5!=1) bump=-1;
+ else if (residue>0 && lsd5==0) bump=1;
+ // [bump==1 could be applied directly; use common path for clarity]
+ break;} // r-05
+
+ case DEC_ROUND_DOWN: {
+ // no change, except if negative residue
+ if (residue<0) bump=-1;
+ break;} // r-d
+
+ case DEC_ROUND_HALF_DOWN: {
+ if (residue>5) bump=1;
+ break;} // r-h-d
+
+ case DEC_ROUND_HALF_EVEN: {
+ if (residue>5) bump=1; // >0.5 goes up
+ else if (residue==5) { // exactly 0.5000...
+ // 0.5 goes up iff [new] lsd is odd
+ if (*dn->lsu & 0x01) bump=1;
+ }
+ break;} // r-h-e
+
+ case DEC_ROUND_HALF_UP: {
+ if (residue>=5) bump=1;
+ break;} // r-h-u
+
+ case DEC_ROUND_UP: {
+ if (residue>0) bump=1;
+ break;} // r-u
+
+ case DEC_ROUND_CEILING: {
+ // same as _UP for positive numbers, and as _DOWN for negatives
+ // [negative residue cannot occur on 0]
+ if (decNumberIsNegative(dn)) {
+ if (residue<0) bump=-1;
+ }
+ else {
+ if (residue>0) bump=1;
+ }
+ break;} // r-c
+
+ case DEC_ROUND_FLOOR: {
+ // same as _UP for negative numbers, and as _DOWN for positive
+ // [negative residue cannot occur on 0]
+ if (!decNumberIsNegative(dn)) {
+ if (residue<0) bump=-1;
+ }
+ else {
+ if (residue>0) bump=1;
+ }
+ break;} // r-f
+
+ default: { // e.g., DEC_ROUND_MAX
+ *status|=DEC_Invalid_context;
+ #if DECTRACE || (DECCHECK && DECVERB)
+ printf("Unknown rounding mode: %d\n", set->round);
+ #endif
+ break;}
+ } // switch
+
+ // now bump the number, up or down, if need be
+ if (bump==0) return; // no action required
+
+ // Simply use decUnitAddSub unless bumping up and the number is
+ // all nines. In this special case set to 100... explicitly
+ // and adjust the exponent by one (as otherwise could overflow
+ // the array)
+ // Similarly handle all-nines result if bumping down.
+ if (bump>0) {
+ Unit *up; // work
+ uInt count=dn->digits; // digits to be checked
+ for (up=dn->lsu; ; up++) {
+ if (count<=DECDPUN) {
+ // this is the last Unit (the msu)
+ if (*up!=powers[count]-1) break; // not still 9s
+ // here if it, too, is all nines
+ *up=(Unit)powers[count-1]; // here 999 -> 100 etc.
+ for (up=up-1; up>=dn->lsu; up--) *up=0; // others all to 0
+ dn->exponent++; // and bump exponent
+ // [which, very rarely, could cause Overflow...]
+ if ((dn->exponent+dn->digits)>set->emax+1) {
+ decSetOverflow(dn, set, status);
+ }
+ return; // done
+ }
+ // a full unit to check, with more to come
+ if (*up!=DECDPUNMAX) break; // not still 9s
+ count-=DECDPUN;
+ } // up
+ } // bump>0
+ else { // -1
+ // here checking for a pre-bump of 1000... (leading 1, all
+ // other digits zero)
+ Unit *up, *sup; // work
+ uInt count=dn->digits; // digits to be checked
+ for (up=dn->lsu; ; up++) {
+ if (count<=DECDPUN) {
+ // this is the last Unit (the msu)
+ if (*up!=powers[count-1]) break; // not 100..
+ // here if have the 1000... case
+ sup=up; // save msu pointer
+ *up=(Unit)powers[count]-1; // here 100 in msu -> 999
+ // others all to all-nines, too
+ for (up=up-1; up>=dn->lsu; up--) *up=(Unit)powers[DECDPUN]-1;
+ dn->exponent--; // and bump exponent
+
+ // iff the number was at the subnormal boundary (exponent=etiny)
+ // then the exponent is now out of range, so it will in fact get
+ // clamped to etiny and the final 9 dropped.
+ // printf(">> emin=%d exp=%d sdig=%d\n", set->emin,
+ // dn->exponent, set->digits);
+ if (dn->exponent+1==set->emin-set->digits+1) {
+ if (count==1 && dn->digits==1) *sup=0; // here 9 -> 0[.9]
+ else {
+ *sup=(Unit)powers[count-1]-1; // here 999.. in msu -> 99..
+ dn->digits--;
+ }
+ dn->exponent++;
+ *status|=DEC_Underflow | DEC_Subnormal | DEC_Inexact | DEC_Rounded;
+ }
+ return; // done
+ }
+
+ // a full unit to check, with more to come
+ if (*up!=0) break; // not still 0s
+ count-=DECDPUN;
+ } // up
+
+ } // bump<0
+
+ // Actual bump needed. Do it.
+ decUnitAddSub(dn->lsu, D2U(dn->digits), uarrone, 1, 0, dn->lsu, bump);
+ } // decApplyRound
+
+#if DECSUBSET
+/* ------------------------------------------------------------------ */
+/* decFinish -- finish processing a number */
+/* */
+/* dn is the number */
+/* set is the context */
+/* residue is the rounding accumulator (as in decApplyRound) */
+/* status is the accumulator */
+/* */
+/* This finishes off the current number by: */
+/* 1. If not extended: */
+/* a. Converting a zero result to clean '0' */
+/* b. Reducing positive exponents to 0, if would fit in digits */
+/* 2. Checking for overflow and subnormals (always) */
+/* Note this is just Finalize when no subset arithmetic. */
+/* All fields are updated as required. */
+/* ------------------------------------------------------------------ */
+static void decFinish(decNumber *dn, decContext *set, Int *residue,
+ uInt *status) {
+ if (!set->extended) {
+ if ISZERO(dn) { // value is zero
+ dn->exponent=0; // clean exponent ..
+ dn->bits=0; // .. and sign
+ return; // no error possible
+ }
+ if (dn->exponent>=0) { // non-negative exponent
+ // >0; reduce to integer if possible
+ if (set->digits >= (dn->exponent+dn->digits)) {
+ dn->digits=decShiftToMost(dn->lsu, dn->digits, dn->exponent);
+ dn->exponent=0;
+ }
+ }
+ } // !extended
+
+ decFinalize(dn, set, residue, status);
+ } // decFinish
+#endif
+
+/* ------------------------------------------------------------------ */
+/* decFinalize -- final check, clamp, and round of a number */
+/* */
+/* dn is the number */
+/* set is the context */
+/* residue is the rounding accumulator (as in decApplyRound) */
+/* status is the status accumulator */
+/* */
+/* This finishes off the current number by checking for subnormal */
+/* results, applying any pending rounding, checking for overflow, */
+/* and applying any clamping. */
+/* Underflow and overflow conditions are raised as appropriate. */
+/* All fields are updated as required. */
+/* ------------------------------------------------------------------ */
+static void decFinalize(decNumber *dn, decContext *set, Int *residue,
+ uInt *status) {
+ Int shift; // shift needed if clamping
+ Int tinyexp=set->emin-dn->digits+1; // precalculate subnormal boundary
+
+ // Must be careful, here, when checking the exponent as the
+ // adjusted exponent could overflow 31 bits [because it may already
+ // be up to twice the expected].
+
+ // First test for subnormal. This must be done before any final
+ // round as the result could be rounded to Nmin or 0.
+ if (dn->exponent<=tinyexp) { // prefilter
+ Int comp;
+ decNumber nmin;
+ // A very nasty case here is dn == Nmin and residue<0
+ if (dn->exponent<tinyexp) {
+ // Go handle subnormals; this will apply round if needed.
+ decSetSubnormal(dn, set, residue, status);
+ return;
+ }
+ // Equals case: only subnormal if dn=Nmin and negative residue
+ decNumberZero(&nmin);
+ nmin.lsu[0]=1;
+ nmin.exponent=set->emin;
+ comp=decCompare(dn, &nmin, 1); // (signless compare)
+ if (comp==BADINT) { // oops
+ *status|=DEC_Insufficient_storage; // abandon...
+ return;
+ }
+ if (*residue<0 && comp==0) { // neg residue and dn==Nmin
+ decApplyRound(dn, set, *residue, status); // might force down
+ decSetSubnormal(dn, set, residue, status);
+ return;
+ }
+ }
+
+ // now apply any pending round (this could raise overflow).
+ if (*residue!=0) decApplyRound(dn, set, *residue, status);
+
+ // Check for overflow [redundant in the 'rare' case] or clamp
+ if (dn->exponent<=set->emax-set->digits+1) return; // neither needed
+
+
+ // here when might have an overflow or clamp to do
+ if (dn->exponent>set->emax-dn->digits+1) { // too big
+ decSetOverflow(dn, set, status);
+ return;
+ }
+ // here when the result is normal but in clamp range
+ if (!set->clamp) return;
+
+ // here when need to apply the IEEE exponent clamp (fold-down)
+ shift=dn->exponent-(set->emax-set->digits+1);
+
+ // shift coefficient (if non-zero)
+ if (!ISZERO(dn)) {
+ dn->digits=decShiftToMost(dn->lsu, dn->digits, shift);
+ }
+ dn->exponent-=shift; // adjust the exponent to match
+ *status|=DEC_Clamped; // and record the dirty deed
+ return;
+ } // decFinalize
+
+/* ------------------------------------------------------------------ */
+/* decSetOverflow -- set number to proper overflow value */
+/* */
+/* dn is the number (used for sign [only] and result) */
+/* set is the context [used for the rounding mode, etc.] */
+/* status contains the current status to be updated */
+/* */
+/* This sets the sign of a number and sets its value to either */
+/* Infinity or the maximum finite value, depending on the sign of */
+/* dn and the rounding mode, following IEEE 754 rules. */
+/* ------------------------------------------------------------------ */
+static void decSetOverflow(decNumber *dn, decContext *set, uInt *status) {
+ Flag needmax=0; // result is maximum finite value
+ uByte sign=dn->bits&DECNEG; // clean and save sign bit
+
+ if (ISZERO(dn)) { // zero does not overflow magnitude
+ Int emax=set->emax; // limit value
+ if (set->clamp) emax-=set->digits-1; // lower if clamping
+ if (dn->exponent>emax) { // clamp required
+ dn->exponent=emax;
+ *status|=DEC_Clamped;
+ }
+ return;
+ }
+
+ decNumberZero(dn);
+ switch (set->round) {
+ case DEC_ROUND_DOWN: {
+ needmax=1; // never Infinity
+ break;} // r-d
+ case DEC_ROUND_05UP: {
+ needmax=1; // never Infinity
+ break;} // r-05
+ case DEC_ROUND_CEILING: {
+ if (sign) needmax=1; // Infinity if non-negative
+ break;} // r-c
+ case DEC_ROUND_FLOOR: {
+ if (!sign) needmax=1; // Infinity if negative
+ break;} // r-f
+ default: break; // Infinity in all other cases
+ }
+ if (needmax) {
+ decSetMaxValue(dn, set);
+ dn->bits=sign; // set sign
+ }
+ else dn->bits=sign|DECINF; // Value is +/-Infinity
+ *status|=DEC_Overflow | DEC_Inexact | DEC_Rounded;
+ } // decSetOverflow
+
+/* ------------------------------------------------------------------ */
+/* decSetMaxValue -- set number to +Nmax (maximum normal value) */
+/* */
+/* dn is the number to set */
+/* set is the context [used for digits and emax] */
+/* */
+/* This sets the number to the maximum positive value. */
+/* ------------------------------------------------------------------ */
+static void decSetMaxValue(decNumber *dn, decContext *set) {
+ Unit *up; // work
+ Int count=set->digits; // nines to add
+ dn->digits=count;
+ // fill in all nines to set maximum value
+ for (up=dn->lsu; ; up++) {
+ if (count>DECDPUN) *up=DECDPUNMAX; // unit full o'nines
+ else { // this is the msu
+ *up=(Unit)(powers[count]-1);
+ break;
+ }
+ count-=DECDPUN; // filled those digits
+ } // up
+ dn->bits=0; // + sign
+ dn->exponent=set->emax-set->digits+1;
+ } // decSetMaxValue
+
+/* ------------------------------------------------------------------ */
+/* decSetSubnormal -- process value whose exponent is <Emin */
+/* */
+/* dn is the number (used as input as well as output; it may have */
+/* an allowed subnormal value, which may need to be rounded) */
+/* set is the context [used for the rounding mode] */
+/* residue is any pending residue */
+/* status contains the current status to be updated */
+/* */
+/* If subset mode, set result to zero and set Underflow flags. */
+/* */
+/* Value may be zero with a low exponent; this does not set Subnormal */
+/* but the exponent will be clamped to Etiny. */
+/* */
+/* Otherwise ensure exponent is not out of range, and round as */
+/* necessary. Underflow is set if the result is Inexact. */
+/* ------------------------------------------------------------------ */
+static void decSetSubnormal(decNumber *dn, decContext *set, Int *residue,
+ uInt *status) {
+ decContext workset; // work
+ Int etiny, adjust; // ..
+
+ #if DECSUBSET
+ // simple set to zero and 'hard underflow' for subset
+ if (!set->extended) {
+ decNumberZero(dn);
+ // always full overflow
+ *status|=DEC_Underflow | DEC_Subnormal | DEC_Inexact | DEC_Rounded;
+ return;
+ }
+ #endif
+
+ // Full arithmetic -- allow subnormals, rounded to minimum exponent
+ // (Etiny) if needed
+ etiny=set->emin-(set->digits-1); // smallest allowed exponent
+
+ if ISZERO(dn) { // value is zero
+ // residue can never be non-zero here
+ #if DECCHECK
+ if (*residue!=0) {
+ printf("++ Subnormal 0 residue %ld\n", (LI)*residue);
+ *status|=DEC_Invalid_operation;
+ }
+ #endif
+ if (dn->exponent<etiny) { // clamp required
+ dn->exponent=etiny;
+ *status|=DEC_Clamped;
+ }
+ return;
+ }
+
+ *status|=DEC_Subnormal; // have a non-zero subnormal
+ adjust=etiny-dn->exponent; // calculate digits to remove
+ if (adjust<=0) { // not out of range; unrounded
+ // residue can never be non-zero here, except in the Nmin-residue
+ // case (which is a subnormal result), so can take fast-path here
+ // it may already be inexact (from setting the coefficient)
+ if (*status&DEC_Inexact) *status|=DEC_Underflow;
+ return;
+ }
+
+ // adjust>0, so need to rescale the result so exponent becomes Etiny
+ // [this code is similar to that in rescale]
+ workset=*set; // clone rounding, etc.
+ workset.digits=dn->digits-adjust; // set requested length
+ workset.emin-=adjust; // and adjust emin to match
+ // [note that the latter can be <1, here, similar to Rescale case]
+ decSetCoeff(dn, &workset, dn->lsu, dn->digits, residue, status);
+ decApplyRound(dn, &workset, *residue, status);
+
+ // Use 754 default rule: Underflow is set iff Inexact
+ // [independent of whether trapped]
+ if (*status&DEC_Inexact) *status|=DEC_Underflow;
+
+ // if rounded up a 999s case, exponent will be off by one; adjust
+ // back if so [it will fit, because it was shortened earlier]
+ if (dn->exponent>etiny) {
+ dn->digits=decShiftToMost(dn->lsu, dn->digits, 1);
+ dn->exponent--; // (re)adjust the exponent.
+ }
+
+ // if rounded to zero, it is by definition clamped...
+ if (ISZERO(dn)) *status|=DEC_Clamped;
+ } // decSetSubnormal
+
+/* ------------------------------------------------------------------ */
+/* decCheckMath - check entry conditions for a math function */
+/* */
+/* This checks the context and the operand */
+/* */
+/* rhs is the operand to check */
+/* set is the context to check */
+/* status is unchanged if both are good */
+/* */
+/* returns non-zero if status is changed, 0 otherwise */
+/* */
+/* Restrictions enforced: */
+/* */
+/* digits, emax, and -emin in the context must be less than */
+/* DEC_MAX_MATH (999999), and A must be within these bounds if */
+/* non-zero. Invalid_operation is set in the status if a */
+/* restriction is violated. */
+/* ------------------------------------------------------------------ */
+static uInt decCheckMath(const decNumber *rhs, decContext *set,
+ uInt *status) {
+ uInt save=*status; // record
+ if (set->digits>DEC_MAX_MATH
+ || set->emax>DEC_MAX_MATH
+ || -set->emin>DEC_MAX_MATH) *status|=DEC_Invalid_context;
+ else if ((rhs->digits>DEC_MAX_MATH
+ || rhs->exponent+rhs->digits>DEC_MAX_MATH+1
+ || rhs->exponent+rhs->digits<2*(1-DEC_MAX_MATH))
+ && !ISZERO(rhs)) *status|=DEC_Invalid_operation;
+ return (*status!=save);
+ } // decCheckMath
+
+/* ------------------------------------------------------------------ */
+/* decGetInt -- get integer from a number */
+/* */
+/* dn is the number [which will not be altered] */
+/* */
+/* returns one of: */
+/* BADINT if there is a non-zero fraction */
+/* the converted integer */
+/* BIGEVEN if the integer is even and magnitude > 2*10**9 */
+/* BIGODD if the integer is odd and magnitude > 2*10**9 */
+/* */
+/* This checks and gets a whole number from the input decNumber. */
+/* The sign can be determined from dn by the caller when BIGEVEN or */
+/* BIGODD is returned. */
+/* ------------------------------------------------------------------ */
+static Int decGetInt(const decNumber *dn) {
+ Int theInt; // result accumulator
+ const Unit *up; // work
+ Int got; // digits (real or not) processed
+ Int ilength=dn->digits+dn->exponent; // integral length
+ Flag neg=decNumberIsNegative(dn); // 1 if -ve
+
+ // The number must be an integer that fits in 10 digits
+ // Assert, here, that 10 is enough for any rescale Etiny
+ #if DEC_MAX_EMAX > 999999999
+ #error GetInt may need updating [for Emax]
+ #endif
+ #if DEC_MIN_EMIN < -999999999
+ #error GetInt may need updating [for Emin]
+ #endif
+ if (ISZERO(dn)) return 0; // zeros are OK, with any exponent
+
+ up=dn->lsu; // ready for lsu
+ theInt=0; // ready to accumulate
+ if (dn->exponent>=0) { // relatively easy
+ // no fractional part [usual]; allow for positive exponent
+ got=dn->exponent;
+ }
+ else { // -ve exponent; some fractional part to check and discard
+ Int count=-dn->exponent; // digits to discard
+ // spin up whole units until reach the Unit with the unit digit
+ for (; count>=DECDPUN; up++) {
+ if (*up!=0) return BADINT; // non-zero Unit to discard
+ count-=DECDPUN;
+ }
+ if (count==0) got=0; // [a multiple of DECDPUN]
+ else { // [not multiple of DECDPUN]
+ Int rem; // work
+ // slice off fraction digits and check for non-zero
+ #if DECDPUN<=4
+ theInt=QUOT10(*up, count);
+ rem=*up-theInt*powers[count];
+ #else
+ rem=*up%powers[count]; // slice off discards
+ theInt=*up/powers[count];
+ #endif
+ if (rem!=0) return BADINT; // non-zero fraction
+ // it looks good
+ got=DECDPUN-count; // number of digits so far
+ up++; // ready for next
+ }
+ }
+ // now it's known there's no fractional part
+
+ // tricky code now, to accumulate up to 9.3 digits
+ if (got==0) {theInt=*up; got+=DECDPUN; up++;} // ensure lsu is there
+
+ if (ilength<11) {
+ Int save=theInt;
+ // collect any remaining unit(s)
+ for (; got<ilength; up++) {
+ theInt+=*up*powers[got];
+ got+=DECDPUN;
+ }
+ if (ilength==10) { // need to check for wrap
+ if (theInt/(Int)powers[got-DECDPUN]!=(Int)*(up-1)) ilength=11;
+ // [that test also disallows the BADINT result case]
+ else if (neg && theInt>1999999997) ilength=11;
+ else if (!neg && theInt>999999999) ilength=11;
+ if (ilength==11) theInt=save; // restore correct low bit
+ }
+ }
+
+ if (ilength>10) { // too big
+ if (theInt&1) return BIGODD; // bottom bit 1
+ return BIGEVEN; // bottom bit 0
+ }
+
+ if (neg) theInt=-theInt; // apply sign
+ return theInt;
+ } // decGetInt
+
+/* ------------------------------------------------------------------ */
+/* decDecap -- decapitate the coefficient of a number */
+/* */
+/* dn is the number to be decapitated */
+/* drop is the number of digits to be removed from the left of dn; */
+/* this must be <= dn->digits (if equal, the coefficient is */
+/* set to 0) */
+/* */
+/* Returns dn; dn->digits will be <= the initial digits less drop */
+/* (after removing drop digits there may be leading zero digits */
+/* which will also be removed). Only dn->lsu and dn->digits change. */
+/* ------------------------------------------------------------------ */
+static decNumber *decDecap(decNumber *dn, Int drop) {
+ Unit *msu; // -> target cut point
+ Int cut; // work
+ if (drop>=dn->digits) { // losing the whole thing
+ #if DECCHECK
+ if (drop>dn->digits)
+ printf("decDecap called with drop>digits [%ld>%ld]\n",
+ (LI)drop, (LI)dn->digits);
+ #endif
+ dn->lsu[0]=0;
+ dn->digits=1;
+ return dn;
+ }
+ msu=dn->lsu+D2U(dn->digits-drop)-1; // -> likely msu
+ cut=MSUDIGITS(dn->digits-drop); // digits to be in use in msu
+ if (cut!=DECDPUN) *msu%=powers[cut]; // clear left digits
+ // that may have left leading zero digits, so do a proper count...
+ dn->digits=decGetDigits(dn->lsu, msu-dn->lsu+1);
+ return dn;
+ } // decDecap
+
+/* ------------------------------------------------------------------ */
+/* decBiStr -- compare string with pairwise options */
+/* */
+/* targ is the string to compare */
+/* str1 is one of the strings to compare against (length may be 0) */
+/* str2 is the other; it must be the same length as str1 */
+/* */
+/* returns 1 if strings compare equal, (that is, it is the same */
+/* length as str1 and str2, and each character of targ is in either */
+/* str1 or str2 in the corresponding position), or 0 otherwise */
+/* */
+/* This is used for generic caseless compare, including the awkward */
+/* case of the Turkish dotted and dotless Is. Use as (for example): */
+/* if (decBiStr(test, "mike", "MIKE")) ... */
+/* ------------------------------------------------------------------ */
+static Flag decBiStr(const char *targ, const char *str1, const char *str2) {
+ for (;;targ++, str1++, str2++) {
+ if (*targ!=*str1 && *targ!=*str2) return 0;
+ // *targ has a match in one (or both, if terminator)
+ if (*targ=='\0') break;
+ } // forever
+ return 1;
+ } // decBiStr
+
+/* ------------------------------------------------------------------ */
+/* decNaNs -- handle NaN operand or operands */
+/* */
+/* res is the result number */
+/* lhs is the first operand */
+/* rhs is the second operand, or NULL if none */
+/* context is used to limit payload length */
+/* status contains the current status */
+/* returns res in case convenient */
+/* */
+/* Called when one or both operands is a NaN, and propagates the */
+/* appropriate result to res. When an sNaN is found, it is changed */
+/* to a qNaN and Invalid operation is set. */
+/* ------------------------------------------------------------------ */
+static decNumber * decNaNs(decNumber *res, const decNumber *lhs,
+ const decNumber *rhs, decContext *set,
+ uInt *status) {
+ // This decision tree ends up with LHS being the source pointer,
+ // and status updated if need be
+ if (lhs->bits & DECSNAN)
+ *status|=DEC_Invalid_operation | DEC_sNaN;
+ else if (rhs==NULL);
+ else if (rhs->bits & DECSNAN) {
+ lhs=rhs;
+ *status|=DEC_Invalid_operation | DEC_sNaN;
+ }
+ else if (lhs->bits & DECNAN);
+ else lhs=rhs;
+
+ // propagate the payload
+ if (lhs->digits<=set->digits) decNumberCopy(res, lhs); // easy
+ else { // too long
+ const Unit *ul;
+ Unit *ur, *uresp1;
+ // copy safe number of units, then decapitate
+ res->bits=lhs->bits; // need sign etc.
+ uresp1=res->lsu+D2U(set->digits);
+ for (ur=res->lsu, ul=lhs->lsu; ur<uresp1; ur++, ul++) *ur=*ul;
+ res->digits=D2U(set->digits)*DECDPUN;
+ // maybe still too long
+ if (res->digits>set->digits) decDecap(res, res->digits-set->digits);
+ }
+
+ res->bits&=~DECSNAN; // convert any sNaN to NaN, while
+ res->bits|=DECNAN; // .. preserving sign
+ res->exponent=0; // clean exponent
+ // [coefficient was copied/decapitated]
+ return res;
+ } // decNaNs
+
+/* ------------------------------------------------------------------ */
+/* decStatus -- apply non-zero status */
+/* */
+/* dn is the number to set if error */
+/* status contains the current status (not yet in context) */
+/* set is the context */
+/* */
+/* If the status is an error status, the number is set to a NaN, */
+/* unless the error was an overflow, divide-by-zero, or underflow, */
+/* in which case the number will have already been set. */
+/* */
+/* The context status is then updated with the new status. Note that */
+/* this may raise a signal, so control may never return from this */
+/* routine (hence resources must be recovered before it is called). */
+/* ------------------------------------------------------------------ */
+static void decStatus(decNumber *dn, uInt status, decContext *set) {
+ if (status & DEC_NaNs) { // error status -> NaN
+ // if cause was an sNaN, clear and propagate [NaN is already set up]
+ if (status & DEC_sNaN) status&=~DEC_sNaN;
+ else {
+ decNumberZero(dn); // other error: clean throughout
+ dn->bits=DECNAN; // and make a quiet NaN
+ }
+ }
+ decContextSetStatus(set, status); // [may not return]
+ return;
+ } // decStatus
+
+/* ------------------------------------------------------------------ */
+/* decGetDigits -- count digits in a Units array */
+/* */
+/* uar is the Unit array holding the number (this is often an */
+/* accumulator of some sort) */
+/* len is the length of the array in units [>=1] */
+/* */
+/* returns the number of (significant) digits in the array */
+/* */
+/* All leading zeros are excluded, except the last if the array has */
+/* only zero Units. */
+/* ------------------------------------------------------------------ */
+// This may be called twice during some operations.
+static Int decGetDigits(Unit *uar, Int len) {
+ Unit *up=uar+(len-1); // -> msu
+ Int digits=(len-1)*DECDPUN+1; // possible digits excluding msu
+ #if DECDPUN>4
+ uInt const *pow; // work
+ #endif
+ // (at least 1 in final msu)
+ #if DECCHECK
+ if (len<1) printf("decGetDigits called with len<1 [%ld]\n", (LI)len);
+ #endif
+
+ for (; up>=uar; up--) {
+ if (*up==0) { // unit is all 0s
+ if (digits==1) break; // a zero has one digit
+ digits-=DECDPUN; // adjust for 0 unit
+ continue;}
+ // found the first (most significant) non-zero Unit
+ #if DECDPUN>1 // not done yet
+ if (*up<10) break; // is 1-9
+ digits++;
+ #if DECDPUN>2 // not done yet
+ if (*up<100) break; // is 10-99
+ digits++;
+ #if DECDPUN>3 // not done yet
+ if (*up<1000) break; // is 100-999
+ digits++;
+ #if DECDPUN>4 // count the rest ...
+ for (pow=&powers[4]; *up>=*pow; pow++) digits++;
+ #endif
+ #endif
+ #endif
+ #endif
+ break;
+ } // up
+ return digits;
+ } // decGetDigits
+
+#if DECTRACE | DECCHECK
+/* ------------------------------------------------------------------ */
+/* decNumberShow -- display a number [debug aid] */
+/* dn is the number to show */
+/* */
+/* Shows: sign, exponent, coefficient (msu first), digits */
+/* or: sign, special-value */
+/* ------------------------------------------------------------------ */
+// this is public so other modules can use it
+void decNumberShow(const decNumber *dn) {
+ const Unit *up; // work
+ uInt u, d; // ..
+ Int cut; // ..
+ char isign='+'; // main sign
+ if (dn==NULL) {
+ printf("NULL\n");
+ return;}
+ if (decNumberIsNegative(dn)) isign='-';
+ printf(" >> %c ", isign);
+ if (dn->bits&DECSPECIAL) { // Is a special value
+ if (decNumberIsInfinite(dn)) printf("Infinity");
+ else { // a NaN
+ if (dn->bits&DECSNAN) printf("sNaN"); // signalling NaN
+ else printf("NaN");
+ }
+ // if coefficient and exponent are 0, no more to do
+ if (dn->exponent==0 && dn->digits==1 && *dn->lsu==0) {
+ printf("\n");
+ return;}
+ // drop through to report other information
+ printf(" ");
+ }
+
+ // now carefully display the coefficient
+ up=dn->lsu+D2U(dn->digits)-1; // msu
+ printf("%ld", (LI)*up);
+ for (up=up-1; up>=dn->lsu; up--) {
+ u=*up;
+ printf(":");
+ for (cut=DECDPUN-1; cut>=0; cut--) {
+ d=u/powers[cut];
+ u-=d*powers[cut];
+ printf("%ld", (LI)d);
+ } // cut
+ } // up
+ if (dn->exponent!=0) {
+ char esign='+';
+ if (dn->exponent<0) esign='-';
+ printf(" E%c%ld", esign, (LI)abs(dn->exponent));
+ }
+ printf(" [%ld]\n", (LI)dn->digits);
+ } // decNumberShow
+#endif
+
+#if DECTRACE || DECCHECK
+/* ------------------------------------------------------------------ */
+/* decDumpAr -- display a unit array [debug/check aid] */
+/* name is a single-character tag name */
+/* ar is the array to display */
+/* len is the length of the array in Units */
+/* ------------------------------------------------------------------ */
+static void decDumpAr(char name, const Unit *ar, Int len) {
+ Int i;
+ const char *spec;
+ #if DECDPUN==9
+ spec="%09d ";
+ #elif DECDPUN==8
+ spec="%08d ";
+ #elif DECDPUN==7
+ spec="%07d ";
+ #elif DECDPUN==6
+ spec="%06d ";
+ #elif DECDPUN==5
+ spec="%05d ";
+ #elif DECDPUN==4
+ spec="%04d ";
+ #elif DECDPUN==3
+ spec="%03d ";
+ #elif DECDPUN==2
+ spec="%02d ";
+ #else
+ spec="%d ";
+ #endif
+ printf(" :%c: ", name);
+ for (i=len-1; i>=0; i--) {
+ if (i==len-1) printf("%ld ", (LI)ar[i]);
+ else printf(spec, ar[i]);
+ }
+ printf("\n");
+ return;}
+#endif
+
+#if DECCHECK
+/* ------------------------------------------------------------------ */
+/* decCheckOperands -- check operand(s) to a routine */
+/* res is the result structure (not checked; it will be set to */
+/* quiet NaN if error found (and it is not NULL)) */
+/* lhs is the first operand (may be DECUNRESU) */
+/* rhs is the second (may be DECUNUSED) */
+/* set is the context (may be DECUNCONT) */
+/* returns 0 if both operands, and the context are clean, or 1 */
+/* otherwise (in which case the context will show an error, */
+/* unless NULL). Note that res is not cleaned; caller should */
+/* handle this so res=NULL case is safe. */
+/* The caller is expected to abandon immediately if 1 is returned. */
+/* ------------------------------------------------------------------ */
+static Flag decCheckOperands(decNumber *res, const decNumber *lhs,
+ const decNumber *rhs, decContext *set) {
+ Flag bad=0;
+ if (set==NULL) { // oops; hopeless
+ #if DECTRACE || DECVERB
+ printf("Reference to context is NULL.\n");
+ #endif
+ bad=1;
+ return 1;}
+ else if (set!=DECUNCONT
+ && (set->digits<1 || set->round>=DEC_ROUND_MAX)) {
+ bad=1;
+ #if DECTRACE || DECVERB
+ printf("Bad context [digits=%ld round=%ld].\n",
+ (LI)set->digits, (LI)set->round);
+ #endif
+ }
+ else {
+ if (res==NULL) {
+ bad=1;
+ #if DECTRACE
+ // this one not DECVERB as standard tests include NULL
+ printf("Reference to result is NULL.\n");
+ #endif
+ }
+ if (!bad && lhs!=DECUNUSED) bad=(decCheckNumber(lhs));
+ if (!bad && rhs!=DECUNUSED) bad=(decCheckNumber(rhs));
+ }
+ if (bad) {
+ if (set!=DECUNCONT) decContextSetStatus(set, DEC_Invalid_operation);
+ if (res!=DECUNRESU && res!=NULL) {
+ decNumberZero(res);
+ res->bits=DECNAN; // qNaN
+ }
+ }
+ return bad;
+ } // decCheckOperands
+
+/* ------------------------------------------------------------------ */
+/* decCheckNumber -- check a number */
+/* dn is the number to check */
+/* returns 0 if the number is clean, or 1 otherwise */
+/* */
+/* The number is considered valid if it could be a result from some */
+/* operation in some valid context. */
+/* ------------------------------------------------------------------ */
+static Flag decCheckNumber(const decNumber *dn) {
+ const Unit *up; // work
+ uInt maxuint; // ..
+ Int ae, d, digits; // ..
+ Int emin, emax; // ..
+
+ if (dn==NULL) { // hopeless
+ #if DECTRACE
+ // this one not DECVERB as standard tests include NULL
+ printf("Reference to decNumber is NULL.\n");
+ #endif
+ return 1;}
+
+ // check special values
+ if (dn->bits & DECSPECIAL) {
+ if (dn->exponent!=0) {
+ #if DECTRACE || DECVERB
+ printf("Exponent %ld (not 0) for a special value [%02x].\n",
+ (LI)dn->exponent, dn->bits);
+ #endif
+ return 1;}
+
+ // 2003.09.08: NaNs may now have coefficients, so next tests Inf only
+ if (decNumberIsInfinite(dn)) {
+ if (dn->digits!=1) {
+ #if DECTRACE || DECVERB
+ printf("Digits %ld (not 1) for an infinity.\n", (LI)dn->digits);
+ #endif
+ return 1;}
+ if (*dn->lsu!=0) {
+ #if DECTRACE || DECVERB
+ printf("LSU %ld (not 0) for an infinity.\n", (LI)*dn->lsu);
+ #endif
+ decDumpAr('I', dn->lsu, D2U(dn->digits));
+ return 1;}
+ } // Inf
+ // 2002.12.26: negative NaNs can now appear through proposed IEEE
+ // concrete formats (decimal64, etc.).
+ return 0;
+ }
+
+ // check the coefficient
+ if (dn->digits<1 || dn->digits>DECNUMMAXP) {
+ #if DECTRACE || DECVERB
+ printf("Digits %ld in number.\n", (LI)dn->digits);
+ #endif
+ return 1;}
+
+ d=dn->digits;
+
+ for (up=dn->lsu; d>0; up++) {
+ if (d>DECDPUN) maxuint=DECDPUNMAX;
+ else { // reached the msu
+ maxuint=powers[d]-1;
+ if (dn->digits>1 && *up<powers[d-1]) {
+ #if DECTRACE || DECVERB
+ printf("Leading 0 in number.\n");
+ decNumberShow(dn);
+ #endif
+ return 1;}
+ }
+ if (*up>maxuint) {
+ #if DECTRACE || DECVERB
+ printf("Bad Unit [%08lx] in %ld-digit number at offset %ld [maxuint %ld].\n",
+ (LI)*up, (LI)dn->digits, (LI)(up-dn->lsu), (LI)maxuint);
+ #endif
+ return 1;}
+ d-=DECDPUN;
+ }
+
+ // check the exponent. Note that input operands can have exponents
+ // which are out of the set->emin/set->emax and set->digits range
+ // (just as they can have more digits than set->digits).
+ ae=dn->exponent+dn->digits-1; // adjusted exponent
+ emax=DECNUMMAXE;
+ emin=DECNUMMINE;
+ digits=DECNUMMAXP;
+ if (ae<emin-(digits-1)) {
+ #if DECTRACE || DECVERB
+ printf("Adjusted exponent underflow [%ld].\n", (LI)ae);
+ decNumberShow(dn);
+ #endif
+ return 1;}
+ if (ae>+emax) {
+ #if DECTRACE || DECVERB
+ printf("Adjusted exponent overflow [%ld].\n", (LI)ae);
+ decNumberShow(dn);
+ #endif
+ return 1;}
+
+ return 0; // it's OK
+ } // decCheckNumber
+
+/* ------------------------------------------------------------------ */
+/* decCheckInexact -- check a normal finite inexact result has digits */
+/* dn is the number to check */
+/* set is the context (for status and precision) */
+/* sets Invalid operation, etc., if some digits are missing */
+/* [this check is not made for DECSUBSET compilation or when */
+/* subnormal is not set] */
+/* ------------------------------------------------------------------ */
+static void decCheckInexact(const decNumber *dn, decContext *set) {
+ #if !DECSUBSET && DECEXTFLAG
+ if ((set->status & (DEC_Inexact|DEC_Subnormal))==DEC_Inexact
+ && (set->digits!=dn->digits) && !(dn->bits & DECSPECIAL)) {
+ #if DECTRACE || DECVERB
+ printf("Insufficient digits [%ld] on normal Inexact result.\n",
+ (LI)dn->digits);
+ decNumberShow(dn);
+ #endif
+ decContextSetStatus(set, DEC_Invalid_operation);
+ }
+ #else
+ // next is a noop for quiet compiler
+ if (dn!=NULL && dn->digits==0) set->status|=DEC_Invalid_operation;
+ #endif
+ return;
+ } // decCheckInexact
+#endif
+
+#if DECALLOC
+#undef malloc
+#undef free
+/* ------------------------------------------------------------------ */
+/* decMalloc -- accountable allocation routine */
+/* n is the number of bytes to allocate */
+/* */
+/* Semantics is the same as the stdlib malloc routine, but bytes */
+/* allocated are accounted for globally, and corruption fences are */
+/* added before and after the 'actual' storage. */
+/* ------------------------------------------------------------------ */
+/* This routine allocates storage with an extra twelve bytes; 8 are */
+/* at the start and hold: */
+/* 0-3 the original length requested */
+/* 4-7 buffer corruption detection fence (DECFENCE, x4) */
+/* The 4 bytes at the end also hold a corruption fence (DECFENCE, x4) */
+/* ------------------------------------------------------------------ */
+static void *decMalloc(size_t n) {
+ uInt size=n+12; // true size
+ void *alloc; // -> allocated storage
+ uByte *b, *b0; // work
+ uInt uiwork; // for macros
+
+ alloc=malloc(size); // -> allocated storage
+ if (alloc==NULL) return NULL; // out of strorage
+ b0=(uByte *)alloc; // as bytes
+ decAllocBytes+=n; // account for storage
+ UBFROMUI(alloc, n); // save n
+ // printf(" alloc ++ dAB: %ld (%ld)\n", (LI)decAllocBytes, (LI)n);
+ for (b=b0+4; b<b0+8; b++) *b=DECFENCE;
+ for (b=b0+n+8; b<b0+n+12; b++) *b=DECFENCE;
+ return b0+8; // -> play area
+ } // decMalloc
+
+/* ------------------------------------------------------------------ */
+/* decFree -- accountable free routine */
+/* alloc is the storage to free */
+/* */
+/* Semantics is the same as the stdlib malloc routine, except that */
+/* the global storage accounting is updated and the fences are */
+/* checked to ensure that no routine has written 'out of bounds'. */
+/* ------------------------------------------------------------------ */
+/* This routine first checks that the fences have not been corrupted. */
+/* It then frees the storage using the 'truw' storage address (that */
+/* is, offset by 8). */
+/* ------------------------------------------------------------------ */
+static void decFree(void *alloc) {
+ uInt n; // original length
+ uByte *b, *b0; // work
+ uInt uiwork; // for macros
+
+ if (alloc==NULL) return; // allowed; it's a nop
+ b0=(uByte *)alloc; // as bytes
+ b0-=8; // -> true start of storage
+ n=UBTOUI(b0); // lift length
+ for (b=b0+4; b<b0+8; b++) if (*b!=DECFENCE)
+ printf("=== Corrupt byte [%02x] at offset %d from %ld ===\n", *b,
+ b-b0-8, (LI)b0);
+ for (b=b0+n+8; b<b0+n+12; b++) if (*b!=DECFENCE)
+ printf("=== Corrupt byte [%02x] at offset +%d from %ld, n=%ld ===\n", *b,
+ b-b0-8, (LI)b0, (LI)n);
+ free(b0); // drop the storage
+ decAllocBytes-=n; // account for storage
+ // printf(" free -- dAB: %d (%d)\n", decAllocBytes, -n);
+ } // decFree
+#define malloc(a) decMalloc(a)
+#define free(a) decFree(a)
+#endif
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