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Diffstat (limited to 'libjava/java/lang/mprec.c')
-rw-r--r-- | libjava/java/lang/mprec.c | 958 |
1 files changed, 958 insertions, 0 deletions
diff --git a/libjava/java/lang/mprec.c b/libjava/java/lang/mprec.c new file mode 100644 index 00000000000..12dd5d2617a --- /dev/null +++ b/libjava/java/lang/mprec.c @@ -0,0 +1,958 @@ +/**************************************************************** + * + * The author of this software is David M. Gay. + * + * Copyright (c) 1991 by AT&T. + * + * Permission to use, copy, modify, and distribute this software for any + * purpose without fee is hereby granted, provided that this entire notice + * is included in all copies of any software which is or includes a copy + * or modification of this software and in all copies of the supporting + * documentation for such software. + * + * THIS SOFTWARE IS BEING PROVIDED "AS IS", WITHOUT ANY EXPRESS OR IMPLIED + * WARRANTY. IN PARTICULAR, NEITHER THE AUTHOR NOR AT&T MAKES ANY + * REPRESENTATION OR WARRANTY OF ANY KIND CONCERNING THE MERCHANTABILITY + * OF THIS SOFTWARE OR ITS FITNESS FOR ANY PARTICULAR PURPOSE. + * + ***************************************************************/ + +/* Please send bug reports to + David M. Gay + AT&T Bell Laboratories, Room 2C-463 + 600 Mountain Avenue + Murray Hill, NJ 07974-2070 + U.S.A. + dmg@research.att.com or research!dmg + */ + +/* strtod for IEEE-, VAX-, and IBM-arithmetic machines. + * + * This strtod returns a nearest machine number to the input decimal + * string (or sets errno to ERANGE). With IEEE arithmetic, ties are + * broken by the IEEE round-even rule. Otherwise ties are broken by + * biased rounding (add half and chop). + * + * Inspired loosely by William D. Clinger's paper "How to Read Floating + * Point Numbers Accurately" [Proc. ACM SIGPLAN '90, pp. 92-101]. + * + * Modifications: + * + * 1. We only require IEEE, IBM, or VAX double-precision + * arithmetic (not IEEE double-extended). + * 2. We get by with floating-point arithmetic in a case that + * Clinger missed -- when we're computing d * 10^n + * for a small integer d and the integer n is not too + * much larger than 22 (the maximum integer k for which + * we can represent 10^k exactly), we may be able to + * compute (d*10^k) * 10^(e-k) with just one roundoff. + * 3. Rather than a bit-at-a-time adjustment of the binary + * result in the hard case, we use floating-point + * arithmetic to determine the adjustment to within + * one bit; only in really hard cases do we need to + * compute a second residual. + * 4. Because of 3., we don't need a large table of powers of 10 + * for ten-to-e (just some small tables, e.g. of 10^k + * for 0 <= k <= 22). + */ + +/* + * #define IEEE_8087 for IEEE-arithmetic machines where the least + * significant byte has the lowest address. + * #define IEEE_MC68k for IEEE-arithmetic machines where the most + * significant byte has the lowest address. + * #define Sudden_Underflow for IEEE-format machines without gradual + * underflow (i.e., that flush to zero on underflow). + * #define IBM for IBM mainframe-style floating-point arithmetic. + * #define VAX for VAX-style floating-point arithmetic. + * #define Unsigned_Shifts if >> does treats its left operand as unsigned. + * #define No_leftright to omit left-right logic in fast floating-point + * computation of dtoa. + * #define Check_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3. + * #define RND_PRODQUOT to use rnd_prod and rnd_quot (assembly routines + * that use extended-precision instructions to compute rounded + * products and quotients) with IBM. + * #define ROUND_BIASED for IEEE-format with biased rounding. + * #define Inaccurate_Divide for IEEE-format with correctly rounded + * products but inaccurate quotients, e.g., for Intel i860. + * #define Just_16 to store 16 bits per 32-bit long when doing high-precision + * integer arithmetic. Whether this speeds things up or slows things + * down depends on the machine and the number being converted. + */ + +#include <stdlib.h> +#include <string.h> +#include <java-assert.h> +#include "mprec.h" + +/* reent.c knows this value */ +#define _Kmax 15 +#include <stdio.h> + +_Jv_Bigint * +_DEFUN (Balloc, (ptr, k), struct _Jv_reent *ptr _AND int k) +{ + _Jv_Bigint *rv = NULL; + + int i = 0; + int j = 1; + + JvAssert ((1 << k) < MAX_BIGNUM_WDS); + + while ((ptr->_allocation_map & j) && i < MAX_BIGNUMS) + i++, j <<= 1; + + JvAssert (i < MAX_BIGNUMS); + + if (i >= MAX_BIGNUMS) + return NULL; + + ptr->_allocation_map |= j; + rv = &ptr->_freelist[i]; + + rv->_k = k; + rv->_maxwds = 32; + + return rv; +} + + +void +_DEFUN (Bfree, (ptr, v), struct _Jv_reent *ptr _AND _Jv_Bigint * v) +{ + long i; + + i = v - ptr->_freelist; + + JvAssert (i >= 0 && i < MAX_BIGNUMS); + + if (i >= 0 && i < MAX_BIGNUMS) + ptr->_allocation_map &= ~ (1 << i); +} + + +_Jv_Bigint * +_DEFUN (multadd, (ptr, b, m, a), + struct _Jv_reent *ptr _AND + _Jv_Bigint * b _AND + int m _AND + int a) +{ + int i, wds; + unsigned long *x, y; +#ifdef Pack_32 + unsigned long xi, z; +#endif + _Jv_Bigint *b1; + + wds = b->_wds; + x = b->_x; + i = 0; + do + { +#ifdef Pack_32 + xi = *x; + y = (xi & 0xffff) * m + a; + z = (xi >> 16) * m + (y >> 16); + a = (int) (z >> 16); + *x++ = (z << 16) + (y & 0xffff); +#else + y = *x * m + a; + a = (int) (y >> 16); + *x++ = y & 0xffff; +#endif + } + while (++i < wds); + if (a) + { + if (wds >= b->_maxwds) + { + b1 = Balloc (ptr, b->_k + 1); + Bcopy (b1, b); + Bfree (ptr, b); + b = b1; + } + b->_x[wds++] = a; + b->_wds = wds; + } + return b; +} + +_Jv_Bigint * +_DEFUN (s2b, (ptr, s, nd0, nd, y9), + struct _Jv_reent * ptr _AND + _CONST char *s _AND + int nd0 _AND + int nd _AND + unsigned long y9) +{ + _Jv_Bigint *b; + int i, k; + long x, y; + + x = (nd + 8) / 9; + for (k = 0, y = 1; x > y; y <<= 1, k++); +#ifdef Pack_32 + b = Balloc (ptr, k); + b->_x[0] = y9; + b->_wds = 1; +#else + b = Balloc (ptr, k + 1); + b->_x[0] = y9 & 0xffff; + b->_wds = (b->_x[1] = y9 >> 16) ? 2 : 1; +#endif + + i = 9; + if (9 < nd0) + { + s += 9; + do + b = multadd (ptr, b, 10, *s++ - '0'); + while (++i < nd0); + s++; + } + else + s += 10; + for (; i < nd; i++) + b = multadd (ptr, b, 10, *s++ - '0'); + return b; +} + +int +_DEFUN (hi0bits, + (x), register unsigned long x) +{ + register int k = 0; + + if (!(x & 0xffff0000)) + { + k = 16; + x <<= 16; + } + if (!(x & 0xff000000)) + { + k += 8; + x <<= 8; + } + if (!(x & 0xf0000000)) + { + k += 4; + x <<= 4; + } + if (!(x & 0xc0000000)) + { + k += 2; + x <<= 2; + } + if (!(x & 0x80000000)) + { + k++; + if (!(x & 0x40000000)) + return 32; + } + return k; +} + +int +_DEFUN (lo0bits, (y), unsigned long *y) +{ + register int k; + register unsigned long x = *y; + + if (x & 7) + { + if (x & 1) + return 0; + if (x & 2) + { + *y = x >> 1; + return 1; + } + *y = x >> 2; + return 2; + } + k = 0; + if (!(x & 0xffff)) + { + k = 16; + x >>= 16; + } + if (!(x & 0xff)) + { + k += 8; + x >>= 8; + } + if (!(x & 0xf)) + { + k += 4; + x >>= 4; + } + if (!(x & 0x3)) + { + k += 2; + x >>= 2; + } + if (!(x & 1)) + { + k++; + x >>= 1; + if (!x & 1) + return 32; + } + *y = x; + return k; +} + +_Jv_Bigint * +_DEFUN (i2b, (ptr, i), struct _Jv_reent * ptr _AND int i) +{ + _Jv_Bigint *b; + + b = Balloc (ptr, 1); + b->_x[0] = i; + b->_wds = 1; + return b; +} + +_Jv_Bigint * +_DEFUN (mult, (ptr, a, b), struct _Jv_reent * ptr _AND _Jv_Bigint * a _AND _Jv_Bigint * b) +{ + _Jv_Bigint *c; + int k, wa, wb, wc; + unsigned long carry, y, z; + unsigned long *x, *xa, *xae, *xb, *xbe, *xc, *xc0; +#ifdef Pack_32 + unsigned long z2; +#endif + + if (a->_wds < b->_wds) + { + c = a; + a = b; + b = c; + } + k = a->_k; + wa = a->_wds; + wb = b->_wds; + wc = wa + wb; + if (wc > a->_maxwds) + k++; + c = Balloc (ptr, k); + for (x = c->_x, xa = x + wc; x < xa; x++) + *x = 0; + xa = a->_x; + xae = xa + wa; + xb = b->_x; + xbe = xb + wb; + xc0 = c->_x; +#ifdef Pack_32 + for (; xb < xbe; xb++, xc0++) + { + if ((y = *xb & 0xffff)) + { + x = xa; + xc = xc0; + carry = 0; + do + { + z = (*x & 0xffff) * y + (*xc & 0xffff) + carry; + carry = z >> 16; + z2 = (*x++ >> 16) * y + (*xc >> 16) + carry; + carry = z2 >> 16; + Storeinc (xc, z2, z); + } + while (x < xae); + *xc = carry; + } + if ((y = *xb >> 16)) + { + x = xa; + xc = xc0; + carry = 0; + z2 = *xc; + do + { + z = (*x & 0xffff) * y + (*xc >> 16) + carry; + carry = z >> 16; + Storeinc (xc, z, z2); + z2 = (*x++ >> 16) * y + (*xc & 0xffff) + carry; + carry = z2 >> 16; + } + while (x < xae); + *xc = z2; + } + } +#else + for (; xb < xbe; xc0++) + { + if (y = *xb++) + { + x = xa; + xc = xc0; + carry = 0; + do + { + z = *x++ * y + *xc + carry; + carry = z >> 16; + *xc++ = z & 0xffff; + } + while (x < xae); + *xc = carry; + } + } +#endif + for (xc0 = c->_x, xc = xc0 + wc; wc > 0 && !*--xc; --wc); + c->_wds = wc; + return c; +} + +_Jv_Bigint * +_DEFUN (pow5mult, + (ptr, b, k), struct _Jv_reent * ptr _AND _Jv_Bigint * b _AND int k) +{ + _Jv_Bigint *b1, *p5, *p51; + int i; + static _CONST int p05[3] = {5, 25, 125}; + + if ((i = k & 3)) + b = multadd (ptr, b, p05[i - 1], 0); + + if (!(k >>= 2)) + return b; + if (!(p5 = ptr->_p5s)) + { + /* first time */ + p5 = ptr->_p5s = i2b (ptr, 625); + p5->_next = 0; + } + for (;;) + { + if (k & 1) + { + b1 = mult (ptr, b, p5); + Bfree (ptr, b); + b = b1; + } + if (!(k >>= 1)) + break; + if (!(p51 = p5->_next)) + { + p51 = p5->_next = mult (ptr, p5, p5); + p51->_next = 0; + } + p5 = p51; + } + return b; +} + +_Jv_Bigint * +_DEFUN (lshift, (ptr, b, k), struct _Jv_reent * ptr _AND _Jv_Bigint * b _AND int k) +{ + int i, k1, n, n1; + _Jv_Bigint *b1; + unsigned long *x, *x1, *xe, z; + +#ifdef Pack_32 + n = k >> 5; +#else + n = k >> 4; +#endif + k1 = b->_k; + n1 = n + b->_wds + 1; + for (i = b->_maxwds; n1 > i; i <<= 1) + k1++; + b1 = Balloc (ptr, k1); + x1 = b1->_x; + for (i = 0; i < n; i++) + *x1++ = 0; + x = b->_x; + xe = x + b->_wds; +#ifdef Pack_32 + if (k &= 0x1f) + { + k1 = 32 - k; + z = 0; + do + { + *x1++ = *x << k | z; + z = *x++ >> k1; + } + while (x < xe); + if ((*x1 = z)) + ++n1; + } +#else + if (k &= 0xf) + { + k1 = 16 - k; + z = 0; + do + { + *x1++ = *x << k & 0xffff | z; + z = *x++ >> k1; + } + while (x < xe); + if (*x1 = z) + ++n1; + } +#endif + else + do + *x1++ = *x++; + while (x < xe); + b1->_wds = n1 - 1; + Bfree (ptr, b); + return b1; +} + +int +_DEFUN (cmp, (a, b), _Jv_Bigint * a _AND _Jv_Bigint * b) +{ + unsigned long *xa, *xa0, *xb, *xb0; + int i, j; + + i = a->_wds; + j = b->_wds; +#ifdef DEBUG + if (i > 1 && !a->_x[i - 1]) + Bug ("cmp called with a->_x[a->_wds-1] == 0"); + if (j > 1 && !b->_x[j - 1]) + Bug ("cmp called with b->_x[b->_wds-1] == 0"); +#endif + if (i -= j) + return i; + xa0 = a->_x; + xa = xa0 + j; + xb0 = b->_x; + xb = xb0 + j; + for (;;) + { + if (*--xa != *--xb) + return *xa < *xb ? -1 : 1; + if (xa <= xa0) + break; + } + return 0; +} + +_Jv_Bigint * +_DEFUN (diff, (ptr, a, b), struct _Jv_reent * ptr _AND + _Jv_Bigint * a _AND _Jv_Bigint * b) +{ + _Jv_Bigint *c; + int i, wa, wb; + long borrow, y; /* We need signed shifts here. */ + unsigned long *xa, *xae, *xb, *xbe, *xc; +#ifdef Pack_32 + long z; +#endif + + i = cmp (a, b); + if (!i) + { + c = Balloc (ptr, 0); + c->_wds = 1; + c->_x[0] = 0; + return c; + } + if (i < 0) + { + c = a; + a = b; + b = c; + i = 1; + } + else + i = 0; + c = Balloc (ptr, a->_k); + c->_sign = i; + wa = a->_wds; + xa = a->_x; + xae = xa + wa; + wb = b->_wds; + xb = b->_x; + xbe = xb + wb; + xc = c->_x; + borrow = 0; +#ifdef Pack_32 + do + { + y = (*xa & 0xffff) - (*xb & 0xffff) + borrow; + borrow = y >> 16; + Sign_Extend (borrow, y); + z = (*xa++ >> 16) - (*xb++ >> 16) + borrow; + borrow = z >> 16; + Sign_Extend (borrow, z); + Storeinc (xc, z, y); + } + while (xb < xbe); + while (xa < xae) + { + y = (*xa & 0xffff) + borrow; + borrow = y >> 16; + Sign_Extend (borrow, y); + z = (*xa++ >> 16) + borrow; + borrow = z >> 16; + Sign_Extend (borrow, z); + Storeinc (xc, z, y); + } +#else + do + { + y = *xa++ - *xb++ + borrow; + borrow = y >> 16; + Sign_Extend (borrow, y); + *xc++ = y & 0xffff; + } + while (xb < xbe); + while (xa < xae) + { + y = *xa++ + borrow; + borrow = y >> 16; + Sign_Extend (borrow, y); + *xc++ = y & 0xffff; + } +#endif + while (!*--xc) + wa--; + c->_wds = wa; + return c; +} + +double +_DEFUN (ulp, (_x), double _x) +{ + union double_union x, a; + register long L; + + x.d = _x; + + L = (word0 (x) & Exp_mask) - (P - 1) * Exp_msk1; +#ifndef Sudden_Underflow + if (L > 0) + { +#endif +#ifdef IBM + L |= Exp_msk1 >> 4; +#endif + word0 (a) = L; +#ifndef _DOUBLE_IS_32BITS + word1 (a) = 0; +#endif + +#ifndef Sudden_Underflow + } + else + { + L = -L >> Exp_shift; + if (L < Exp_shift) + { + word0 (a) = 0x80000 >> L; +#ifndef _DOUBLE_IS_32BITS + word1 (a) = 0; +#endif + } + else + { + word0 (a) = 0; + L -= Exp_shift; +#ifndef _DOUBLE_IS_32BITS + word1 (a) = L >= 31 ? 1 : 1 << (31 - L); +#endif + } + } +#endif + return a.d; +} + +double +_DEFUN (b2d, (a, e), + _Jv_Bigint * a _AND int *e) +{ + unsigned long *xa, *xa0, w, y, z; + int k; + union double_union d; +#ifdef VAX + unsigned long d0, d1; +#else +#define d0 word0(d) +#define d1 word1(d) +#endif + + xa0 = a->_x; + xa = xa0 + a->_wds; + y = *--xa; +#ifdef DEBUG + if (!y) + Bug ("zero y in b2d"); +#endif + k = hi0bits (y); + *e = 32 - k; +#ifdef Pack_32 + if (k < Ebits) + { + d0 = Exp_1 | y >> (Ebits - k); + w = xa > xa0 ? *--xa : 0; +#ifndef _DOUBLE_IS_32BITS + d1 = y << (32 - Ebits + k) | w >> (Ebits - k); +#endif + goto ret_d; + } + z = xa > xa0 ? *--xa : 0; + if (k -= Ebits) + { + d0 = Exp_1 | y << k | z >> (32 - k); + y = xa > xa0 ? *--xa : 0; +#ifndef _DOUBLE_IS_32BITS + d1 = z << k | y >> (32 - k); +#endif + } + else + { + d0 = Exp_1 | y; +#ifndef _DOUBLE_IS_32BITS + d1 = z; +#endif + } +#else + if (k < Ebits + 16) + { + z = xa > xa0 ? *--xa : 0; + d0 = Exp_1 | y << k - Ebits | z >> Ebits + 16 - k; + w = xa > xa0 ? *--xa : 0; + y = xa > xa0 ? *--xa : 0; + d1 = z << k + 16 - Ebits | w << k - Ebits | y >> 16 + Ebits - k; + goto ret_d; + } + z = xa > xa0 ? *--xa : 0; + w = xa > xa0 ? *--xa : 0; + k -= Ebits + 16; + d0 = Exp_1 | y << k + 16 | z << k | w >> 16 - k; + y = xa > xa0 ? *--xa : 0; + d1 = w << k + 16 | y << k; +#endif +ret_d: +#ifdef VAX + word0 (d) = d0 >> 16 | d0 << 16; + word1 (d) = d1 >> 16 | d1 << 16; +#else +#undef d0 +#undef d1 +#endif + return d.d; +} + +_Jv_Bigint * +_DEFUN (d2b, + (ptr, _d, e, bits), + struct _Jv_reent * ptr _AND + double _d _AND + int *e _AND + int *bits) + +{ + union double_union d; + _Jv_Bigint *b; + int de, i, k; + unsigned long *x, y, z; +#ifdef VAX + unsigned long d0, d1; + d.d = _d; + d0 = word0 (d) >> 16 | word0 (d) << 16; + d1 = word1 (d) >> 16 | word1 (d) << 16; +#else +#define d0 word0(d) +#define d1 word1(d) + d.d = _d; +#endif + +#ifdef Pack_32 + b = Balloc (ptr, 1); +#else + b = Balloc (ptr, 2); +#endif + x = b->_x; + + z = d0 & Frac_mask; + d0 &= 0x7fffffff; /* clear sign bit, which we ignore */ +#ifdef Sudden_Underflow + de = (int) (d0 >> Exp_shift); +#ifndef IBM + z |= Exp_msk11; +#endif +#else + if ((de = (int) (d0 >> Exp_shift))) + z |= Exp_msk1; +#endif +#ifdef Pack_32 +#ifndef _DOUBLE_IS_32BITS + if ((y = d1)) + { + if ((k = lo0bits (&y))) + { + x[0] = y | z << (32 - k); + z >>= k; + } + else + x[0] = y; + i = b->_wds = (x[1] = z) ? 2 : 1; + } + else +#endif + { +#ifdef DEBUG + if (!z) + Bug ("Zero passed to d2b"); +#endif + k = lo0bits (&z); + x[0] = z; + i = b->_wds = 1; +#ifndef _DOUBLE_IS_32BITS + k += 32; +#endif + } +#else + if (y = d1) + { + if (k = lo0bits (&y)) + if (k >= 16) + { + x[0] = y | z << 32 - k & 0xffff; + x[1] = z >> k - 16 & 0xffff; + x[2] = z >> k; + i = 2; + } + else + { + x[0] = y & 0xffff; + x[1] = y >> 16 | z << 16 - k & 0xffff; + x[2] = z >> k & 0xffff; + x[3] = z >> k + 16; + i = 3; + } + else + { + x[0] = y & 0xffff; + x[1] = y >> 16; + x[2] = z & 0xffff; + x[3] = z >> 16; + i = 3; + } + } + else + { +#ifdef DEBUG + if (!z) + Bug ("Zero passed to d2b"); +#endif + k = lo0bits (&z); + if (k >= 16) + { + x[0] = z; + i = 0; + } + else + { + x[0] = z & 0xffff; + x[1] = z >> 16; + i = 1; + } + k += 32; + } + while (!x[i]) + --i; + b->_wds = i + 1; +#endif +#ifndef Sudden_Underflow + if (de) + { +#endif +#ifdef IBM + *e = (de - Bias - (P - 1) << 2) + k; + *bits = 4 * P + 8 - k - hi0bits (word0 (d) & Frac_mask); +#else + *e = de - Bias - (P - 1) + k; + *bits = P - k; +#endif +#ifndef Sudden_Underflow + } + else + { + *e = de - Bias - (P - 1) + 1 + k; +#ifdef Pack_32 + *bits = 32 * i - hi0bits (x[i - 1]); +#else + *bits = (i + 2) * 16 - hi0bits (x[i]); +#endif + } +#endif + return b; +} +#undef d0 +#undef d1 + +double +_DEFUN (ratio, (a, b), _Jv_Bigint * a _AND _Jv_Bigint * b) + +{ + union double_union da, db; + int k, ka, kb; + + da.d = b2d (a, &ka); + db.d = b2d (b, &kb); +#ifdef Pack_32 + k = ka - kb + 32 * (a->_wds - b->_wds); +#else + k = ka - kb + 16 * (a->_wds - b->_wds); +#endif +#ifdef IBM + if (k > 0) + { + word0 (da) += (k >> 2) * Exp_msk1; + if (k &= 3) + da.d *= 1 << k; + } + else + { + k = -k; + word0 (db) += (k >> 2) * Exp_msk1; + if (k &= 3) + db.d *= 1 << k; + } +#else + if (k > 0) + word0 (da) += k * Exp_msk1; + else + { + k = -k; + word0 (db) += k * Exp_msk1; + } +#endif + return da.d / db.d; +} + + +_CONST double + tens[] = +{ + 1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9, + 1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19, + 1e20, 1e21, 1e22, 1e23, 1e24 + +}; + +#if !defined(_DOUBLE_IS_32BITS) && !defined(__v800) +_CONST double bigtens[] = +{1e16, 1e32, 1e64, 1e128, 1e256}; + +_CONST double tinytens[] = +{1e-16, 1e-32, 1e-64, 1e-128, 1e-256}; +#else +_CONST double bigtens[] = +{1e16, 1e32}; + +_CONST double tinytens[] = +{1e-16, 1e-32}; +#endif + + |