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author | Karl Berry <karl@freefriends.org> | 2006-01-17 21:41:51 +0000 |
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committer | Karl Berry <karl@freefriends.org> | 2006-01-17 21:41:51 +0000 |
commit | 487ca4806cc046076293cf6cc5fbba0db282bac7 (patch) | |
tree | 847b412ab5158dd7bdd7ed7e5a4cc3fbca94be32 /Build/source/texk/ps2pkm/arith.c | |
parent | a3d3111bfe26b8e5f5bc6049dfb2a4ca2edc7881 (diff) |
texk 1
git-svn-id: svn://tug.org/texlive/trunk@1485 c570f23f-e606-0410-a88d-b1316a301751
Diffstat (limited to 'Build/source/texk/ps2pkm/arith.c')
-rw-r--r-- | Build/source/texk/ps2pkm/arith.c | 419 |
1 files changed, 419 insertions, 0 deletions
diff --git a/Build/source/texk/ps2pkm/arith.c b/Build/source/texk/ps2pkm/arith.c new file mode 100644 index 00000000000..ef74f42b770 --- /dev/null +++ b/Build/source/texk/ps2pkm/arith.c @@ -0,0 +1,419 @@ +/* $XConsortium: arith.c,v 1.2 91/10/10 11:14:06 rws Exp $ */ +/* Copyright International Business Machines, Corp. 1991 + * All Rights Reserved + * Copyright Lexmark International, Inc. 1991 + * All Rights Reserved + * + * License to use, copy, modify, and distribute this software and its + * documentation for any purpose and without fee is hereby granted, + * provided that the above copyright notice appear in all copies and that + * both that copyright notice and this permission notice appear in + * supporting documentation, and that the name of IBM or Lexmark not be + * used in advertising or publicity pertaining to distribution of the + * software without specific, written prior permission. + * + * IBM AND LEXMARK PROVIDE THIS SOFTWARE "AS IS", WITHOUT ANY WARRANTIES OF + * ANY KIND, EITHER EXPRESS OR IMPLIED, INCLUDING, BUT NOT LIMITED TO ANY + * IMPLIED WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE, + * AND NONINFRINGEMENT OF THIRD PARTY RIGHTS. THE ENTIRE RISK AS TO THE + * QUALITY AND PERFORMANCE OF THE SOFTWARE, INCLUDING ANY DUTY TO SUPPORT + * OR MAINTAIN, BELONGS TO THE LICENSEE. SHOULD ANY PORTION OF THE + * SOFTWARE PROVE DEFECTIVE, THE LICENSEE (NOT IBM OR LEXMARK) ASSUMES THE + * ENTIRE COST OF ALL SERVICING, REPAIR AND CORRECTION. IN NO EVENT SHALL + * IBM OR LEXMARK BE LIABLE FOR ANY SPECIAL, INDIRECT OR CONSEQUENTIAL + * DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR + * PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS + * ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE OF + * THIS SOFTWARE. + */ + /* ARITH CWEB V0006 ******** */ +/* +:h1.ARITH Module - Portable Module for Multiple Precision Fixed Point Arithmetic + +This module provides division and multiplication of 64-bit fixed point +numbers. (To be more precise, the module works on numbers that take +two 'longs' to store. That is almost always equivalent to saying 64-bit +numbers.) + +Note: it is frequently easy and desirable to recode these functions in +assembly language for the particular processor being used, because +assembly language, unlike C, will have 64-bit multiply products and +64-bit dividends. This module is offered as a portable version. + +&author. Jeffrey B. Lotspiech (lotspiech@almaden.ibm.com) and Sten F. Andler + + +:h3.Include Files + +The included files are: +*/ + +#include "types.h" +#include "objects.h" +#include "spaces.h" +#include "arith.h" + +/* +:h3. +*/ +/*SHARED LINE(S) ORIGINATED HERE*/ +/* +Reference for all algorithms: Donald E. Knuth, "The Art of Computer +Programming, Volume 2, Semi-Numerical Algorithms," Addison-Wesley Co., +Massachusetts, 1969, pp. 229-279. + +Knuth talks about a 'digit' being an arbitrary sized unit and a number +being a sequence of digits. We'll take a digit to be a 'short'. +The following assumption must be valid for these algorithms to work: +:ol. +:li.A 'long' is two 'short's. +:eol. +The following code is INDEPENDENT of: +:ol. +:li.The actual size of a short. +:li.Whether shorts and longs are stored most significant byte +first or least significant byte first. +:eol. + +SHORTSIZE is the number of bits in a short; LONGSIZE is the number of +bits in a long; MAXSHORT is the maximum unsigned short: +*/ +/*SHARED LINE(S) ORIGINATED HERE*/ +/* +ASSEMBLE concatenates two shorts to form a long: +*/ +#define ASSEMBLE(hi,lo) ((((ULONG)hi)<<SHORTSIZE)+(lo)) +/* +HIGHDIGIT extracts the most significant short from a long; LOWDIGIT +extracts the least significant short from a long: +*/ +#define HIGHDIGIT(u) ((u)>>SHORTSIZE) +#define LOWDIGIT(u) ((u)&MAXSHORT) + +/* +SIGNBITON tests the high order bit of a long 'w': +*/ +#define SIGNBITON(w) (((LONG)w)<0) + +/*SHARED LINE(S) ORIGINATED HERE*/ + +/* +:h2.Double Long Arithmetic + +:h3.DLmult() - Multiply Two Longs to Yield a Double Long + +The two multiplicands must be positive. +*/ + +void DLmult(product, u, v) + register doublelong *product; + register ULONG u; + register ULONG v; +{ + register ULONG u1, u2; /* the digits of u */ + register ULONG v1, v2; /* the digits of v */ + register unsigned int w1, w2, w3, w4; /* the digits of w */ + register ULONG t; /* temporary variable */ +/* printf("DLmult(? ?, %x, %x)\n", u, v); */ + u1 = HIGHDIGIT(u); + u2 = LOWDIGIT(u); + v1 = HIGHDIGIT(v); + v2 = LOWDIGIT(v); + + if (v2 == 0) w4 = w3 = w2 = 0; + else + { + t = u2 * v2; + w4 = LOWDIGIT(t); + t = u1 * v2 + HIGHDIGIT(t); + w3 = LOWDIGIT(t); + w2 = HIGHDIGIT(t); + } + + if (v1 == 0) w1 = 0; + else + { + t = u2 * v1 + w3; + w3 = LOWDIGIT(t); + t = u1 * v1 + w2 + HIGHDIGIT(t); + w2 = LOWDIGIT(t); + w1 = HIGHDIGIT(t); + } + + product->high = ASSEMBLE(w1, w2); + product->low = ASSEMBLE(w3, w4); +} + +/* +:h2.DLdiv() - Divide Two Longs by One Long, Yielding Two Longs + +Both the dividend and the divisor must be positive. +*/ + +void DLdiv(quotient, divisor) + doublelong *quotient; /* also where dividend is, originally */ + ULONG divisor; +{ + register ULONG u1u2 = quotient->high; + register ULONG u3u4 = quotient->low; + register LONG u3; /* single digit of dividend */ + register int v1,v2; /* divisor in registers */ + register LONG t; /* signed copy of u1u2 */ + register int qhat; /* guess at the quotient digit */ + register ULONG q3q4; /* low two digits of quotient */ + register int shift; /* holds the shift value for normalizing */ + register int j; /* loop variable */ + +/* printf("DLdiv(%x %x, %x)\n", quotient->high, quotient->low, divisor); */ + /* + * Knuth's algorithm works if the dividend is smaller than the + * divisor. We can get to that state quickly: + */ + if (u1u2 >= divisor) { + quotient->high = u1u2 / divisor; + u1u2 %= divisor; + } + else + quotient->high = 0; + + if (divisor <= MAXSHORT) { + + /* + * This is the case where the divisor is contained in one + * 'short'. It is worthwhile making this fast: + */ + u1u2 = ASSEMBLE(u1u2, HIGHDIGIT(u3u4)); + q3q4 = u1u2 / divisor; + u1u2 %= divisor; + u1u2 = ASSEMBLE(u1u2, LOWDIGIT(u3u4)); + quotient->low = ASSEMBLE(q3q4, u1u2 / divisor); + return; + } + + + /* + * At this point the divisor is a true 'long' so we must use + * Knuth's algorithm. + * + * Step D1: Normalize divisor and dividend (this makes our 'qhat' + * guesses more accurate): + */ + for (shift=0; !SIGNBITON(divisor); shift++, divisor <<= 1) { ; } + shift--; + divisor >>= 1; + + if ((u1u2 >> (LONGSIZE - shift)) != 0 && shift != 0) + t1_abort("DLdiv: dividend too large"); + u1u2 = (u1u2 << shift) + ((shift == 0) ? 0 : u3u4 >> (LONGSIZE - shift)); + u3u4 <<= shift; + + /* + * Step D2: Begin Loop through digits, dividing u1,u2,u3 by v1,v2, + * then shifting U left by 1 digit: + */ + v1 = HIGHDIGIT(divisor); + v2 = LOWDIGIT(divisor); + q3q4 = 0; + u3 = HIGHDIGIT(u3u4); + + for (j=0; j < 2; j++) { + + /* + * Step D3: make a guess (qhat) at the next quotient denominator: + */ + qhat = (HIGHDIGIT(u1u2) == v1) ? MAXSHORT : u1u2 / v1; + /* + * At this point Knuth would have us further refine our + * guess, since we know qhat is too big if + * + * v2 * qhat > ASSEMBLE(u1u2 % v, u3) + * + * That would make sense if u1u2 % v was easy to find, as it + * would be in assembly language. I ignore this step, and + * repeat step D6 if qhat is too big. + */ + + /* + * Step D4: Multiply v1,v2 times qhat and subtract it from + * u1,u2,u3: + */ + u3 -= qhat * v2; + /* + * The high digit of u3 now contains the "borrow" for the + * rest of the substraction from u1,u2. + * Sometimes we can lose the sign bit with the above. + * If so, we have to force the high digit negative: + */ + t = HIGHDIGIT(u3); + if (t > 0) + t |= -1 << SHORTSIZE; + t += u1u2 - qhat * v1; +/* printf("..>divide step qhat=%x t=%x u3=%x u1u2=%x v1=%x v2=%x\n", + qhat, t, u3, u1u2, v1, v2); */ + while (t < 0) { /* Test is Step D5. */ + + /* + * D6: Oops, qhat was too big. Add back in v1,v2 and + * decrease qhat by 1: + */ + u3 = LOWDIGIT(u3) + v2; + t += HIGHDIGIT(u3) + v1; + qhat--; +/* printf("..>>qhat correction t=%x u3=%x qhat=%x\n", t, u3, qhat); */ + } + /* + * Step D7: shift U left one digit and loop: + */ + u1u2 = t; + if (HIGHDIGIT(u1u2) != 0) + t1_abort("divide algorithm error"); + u1u2 = ASSEMBLE(u1u2, LOWDIGIT(u3)); + u3 = LOWDIGIT(u3u4); + q3q4 = ASSEMBLE(q3q4, qhat); + } + quotient->low = q3q4; +/* printf("DLdiv returns %x %x\n", quotient->high, quotient->low); */ + return; +} + +/* +:h3.DLadd() - Add Two Double Longs + +In this case, the doublelongs may be signed. The algorithm takes the +piecewise sum of the high and low longs, with the possibility that the +high should be incremented if there is a carry out of the low. How to +tell if there is a carry? Alex Harbury suggested that if the sum of +the lows is less than the max of the lows, there must have been a +carry. Conversely, if there was a carry, the sum of the lows must be +less than the max of the lows. So, the test is "if and only if". +*/ + +void DLadd(u, v) + doublelong *u; /* u = u + v */ + doublelong *v; +{ + register ULONG lowmax = MAX(u->low, v->low); + +/* printf("DLadd(%x %x, %x %x)\n", u->high, u->low, v->high, v->low); */ + u->high += v->high; + u->low += v->low; + if (lowmax > u->low) + u->high++; +} +/* +:h3.DLsub() - Subtract Two Double Longs + +Testing for a borrow is even easier. If the v.low is greater than +u.low, there must be a borrow. +*/ + +void DLsub(u, v) + doublelong *u; /* u = u - v */ + doublelong *v; +{ +/* printf("DLsub(%x %x, %x %x)\n", u->high, u->low, v->high, v->low);*/ + u->high -= v->high; + if (v->low > u->low) + u->high--; + u->low -= v->low; +} +/* +:h3.DLrightshift() - Macro to Shift Double Long Right by N +*/ + +/*SHARED LINE(S) ORIGINATED HERE*/ + +/* +:h2.Fractional Pel Arithmetic +*/ +/* +:h3.FPmult() - Multiply Two Fractional Pel Values + +This funtion first calculates w = u * v to "doublelong" precision. +It then shifts w right by FRACTBITS bits, and checks that no +overflow will occur when the resulting value is passed back as +a fractpel. +*/ + +fractpel FPmult(u, v) + register fractpel u,v; +{ + doublelong w; + register int negative = FALSE; /* sign flag */ + + if ((u == 0) || (v == 0)) return (0); + + + if (u < 0) {u = -u; negative = TRUE;} + if (v < 0) {v = -v; negative = !negative;} + + if (u == TOFRACTPEL(1)) return ((negative) ? -v : v); + if (v == TOFRACTPEL(1)) return ((negative) ? -u : u); + + DLmult(&w, u, v); + DLrightshift(w, FRACTBITS); + if (w.high != 0 || SIGNBITON(w.low)) { + IfTrace2(TRUE,"FPmult: overflow, %dlx%dl\n", u, v); + w.low = TOFRACTPEL(MAXSHORT); + } + + return ((negative) ? -w.low : w.low); +} + +/* +:h3.FPdiv() - Divide Two Fractional Pel Values + +These values may be signed. The function returns the quotient. +*/ + +fractpel FPdiv(dividend, divisor) + register fractpel dividend; + register fractpel divisor; +{ + doublelong w; /* result will be built here */ + int negative = FALSE; /* flag for sign bit */ + + if (dividend < 0) { + dividend = -dividend; + negative = TRUE; + } + if (divisor < 0) { + divisor = -divisor; + negative = !negative; + } + w.low = dividend << FRACTBITS; + w.high = dividend >> (LONGSIZE - FRACTBITS); + DLdiv(&w, divisor); + if (w.high != 0 || SIGNBITON(w.low)) { + IfTrace2(TRUE,"FPdiv: overflow, %dl/%dl\n", dividend, divisor); + w.low = TOFRACTPEL(MAXSHORT); + } + return( (negative) ? -w.low : w.low); +} + +/* +:h3.FPstarslash() - Multiply then Divide + +Borrowing a chapter from the language Forth, it is useful to define +an operator that first multiplies by one constant then divides by +another, keeping the intermediate result in extended precision. +*/ + +fractpel FPstarslash(a, b, c) + register fractpel a,b,c; /* result = a * b / c */ +{ + doublelong w; /* result will be built here */ + int negative = FALSE; + + if (a < 0) { a = -a; negative = TRUE; } + if (b < 0) { b = -b; negative = !negative; } + if (c < 0) { c = -c; negative = !negative; } + + DLmult(&w, a, b); + DLdiv(&w, c); + if (w.high != 0 || SIGNBITON(w.low)) { + IfTrace3(TRUE,"FPstarslash: overflow, %dl*%dl/%dl\n", a, b, c); + w.low = TOFRACTPEL(MAXSHORT); + } + return((negative) ? -w.low : w.low); +} |