/* ------------------------------------------------------------------ */ /* 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 // for malloc, free, etc. #include // for printf [if needed] #include // for strcpy #include // 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; ddigits; 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; ddigits; 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; cextended) { decNumberZero(dn); // clean result break; // [could be return] } #endif } // at least one leading 0 // Handle decimal point... if (dotchar!=NULL && dotchardigits) 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-1emin-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; i1) { 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; i1) { 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) { // lhsbits&(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; i1) { 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<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.digitsexponent+=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 (dropped0) { // 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; i1) { 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; sdigits 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=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 (aeemin) 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 exponent+dn->digits-1; // adjusted exponent if (aeemin) 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 (ndigits) { // 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->digitsdigits))=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->digitsdigits=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 (exponentexponent) 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 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 (*pv1v2. 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->exponentexponent; 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 (var1initpadexponent; // exponent is smaller of lhs & rhs if (rhs->exponentexponent; // 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; up0 || (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->digitsdigits) { // 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; p0; 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; p0; p+=DECDPUN, cup++, count-=DECDPUN) *rip+=*cup*powers[p]; rmsi=rip-1; // save -> msi // zero the accumulator for (lp=zacc; lp0 && rip!=rmsi) continue; lazy=FASTLAZY; // reset delay count // spin up the accumulator resolving overflows for (lp=zacc; lp 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; merlsu, 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 .. || (reqexpset->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->exponentexponent) 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->exponentexponent) 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 AB, 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 AB, 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=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+1sizeof(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=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 (; cmaxC) { // 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=0) { est=(((ueInt)carry>>11)*53687)>>18; *c=(Unit)(carry-est*(DECDPUNMAX+1)); // remainder carry=est; // likely quotient [89%] if (*c>11)*53687)>>18; *c=(Unit)(carry-est*(DECDPUNMAX+1)); carry=est-(DECDPUNMAX+1); // correctly negative if (*c=0) { est=(((ueInt)carry>>3)*16777)>>21; *c=(Unit)(carry-est*(DECDPUNMAX+1)); // remainder carry=est; // likely quotient [99%] if (*c>3)*16777)>>21; *c=(Unit)(carry-est*(DECDPUNMAX+1)); carry=est-(DECDPUNMAX+1); // correctly negative if (*c=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 (cDECDPUNMAX #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>11)*53687)>>18; *c=(Unit)(carry-est*(DECDPUNMAX+1)); carry=est-(DECDPUNMAX+1); // correctly negative if (*c=0) { est=(((ueInt)carry>>3)*16777)>>21; *c=(Unit)(carry-est*(DECDPUNMAX+1)); // remainder carry=est; // likely quotient [99%] if (*c>3)*16777)>>21; *c=(Unit)(carry-est*(DECDPUNMAX+1)); carry=est-(DECDPUNMAX+1); // correctly negative if (*c=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 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; ddigits-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=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 (; updigits 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 { // 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->exponentemin; 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 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->exponentexponent=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 (; got1999999997) 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; urdigits=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 && *upmaxuint) { #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+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 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