/* Copyright (C) 1993, 1994 Free Software Foundation This file is part of the GNU IO Library. This library is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2, or (at your option) any later version. This library is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this library; see the file COPYING. If not, write to the Free Software Foundation, 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. As a special exception, if you link this library with files compiled with a GNU compiler to produce an executable, this does not cause the resulting executable to be covered by the GNU General Public License. This exception does not however invalidate any other reasons why the executable file might be covered by the GNU General Public License. */ #include #ifdef _IO_USE_DTOA /**************************************************************** * * 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. * ***************************************************************/ /* Some cleaning up by Per Bothner, bothner@cygnus.com, 1992, 1993. Re-written to not need static variables (except result, result_k, HIWORD, LOWORD). */ /* Note that the checking of _DOUBLE_IS_32BITS is for use with the cross targets that employ the newlib ieeefp.h header. -- brendan */ /* 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 KR_headers for old-style C function headers. */ #ifdef DEBUG #include #define Bug(x) {fprintf(stderr, "%s\n", x); exit(1);} #endif #ifdef __STDC__ #include #include #include #define CONST const #else #define CONST #define KR_headers /* In this case, we assume IEEE floats. */ #define FLT_ROUNDS 1 #define FLT_RADIX 2 #define DBL_MANT_DIG 53 #define DBL_DIG 15 #define DBL_MAX_10_EXP 308 #define DBL_MAX_EXP 1024 #endif #include #ifndef __MATH_H__ #include #endif #ifdef Unsigned_Shifts #define Sign_Extend(a,b) if (b < 0) a |= 0xffff0000; #else #define Sign_Extend(a,b) /*no-op*/ #endif #if defined(__i386__) || defined(__i860__) || defined(clipper) #define IEEE_8087 #endif #if defined(MIPSEL) || defined(__alpha__) #define IEEE_8087 #endif #if defined(__sparc__) || defined(sparc) || defined(MIPSEB) #define IEEE_MC68k #endif #if defined(IEEE_8087) + defined(IEEE_MC68k) + defined(VAX) + defined(IBM) != 1 #ifndef _DOUBLE_IS_32BITS #if FLT_RADIX==16 #define IBM #else #if DBL_MANT_DIG==56 #define VAX #else #if DBL_MANT_DIG==53 && DBL_MAX_10_EXP==308 #define IEEE_Unknown #else Exactly one of IEEE_8087, IEEE_MC68k, VAX, or IBM should be defined. #endif #endif #endif #endif /* !_DOUBLE_IS_32BITS */ #endif typedef _G_uint32_t unsigned32; union doubleword { double d; unsigned32 u[2]; }; #ifdef IEEE_8087 #define HIWORD 1 #define LOWORD 0 #define TEST_ENDIANNESS /* nothing */ #else #if defined(IEEE_MC68k) #define HIWORD 0 #define LOWORD 1 #define TEST_ENDIANNESS /* nothing */ #else static int HIWORD = -1, LOWORD; static void test_endianness() { union doubleword dw; dw.d = 10; if (dw.u[0] != 0) /* big-endian */ HIWORD=0, LOWORD=1; else HIWORD=1, LOWORD=0; } #define TEST_ENDIANNESS if (HIWORD<0) test_endianness(); #endif #endif #if 0 union doubleword _temp; #endif #if defined(__GNUC__) && !defined(_DOUBLE_IS_32BITS) #define word0(x) ({ union doubleword _du; _du.d = (x); _du.u[HIWORD]; }) #define word1(x) ({ union doubleword _du; _du.d = (x); _du.u[LOWORD]; }) #define setword0(D,W) \ ({ union doubleword _du; _du.d = (D); _du.u[HIWORD]=(W); (D)=_du.d; }) #define setword1(D,W) \ ({ union doubleword _du; _du.d = (D); _du.u[LOWORD]=(W); (D)=_du.d; }) #define setwords(D,W0,W1) ({ union doubleword _du; \ _du.u[HIWORD]=(W0); _du.u[LOWORD]=(W1); (D)=_du.d; }) #define addword0(D,W) \ ({ union doubleword _du; _du.d = (D); _du.u[HIWORD]+=(W); (D)=_du.d; }) #else #define word0(x) ((unsigned32 *)&x)[HIWORD] #ifndef _DOUBLE_IS_32BITS #define word1(x) ((unsigned32 *)&x)[LOWORD] #else #define word1(x) 0 #endif #define setword0(D,W) word0(D) = (W) #ifndef _DOUBLE_IS_32BITS #define setword1(D,W) word1(D) = (W) #define setwords(D,W0,W1) (setword0(D,W0),setword1(D,W1)) #else #define setword1(D,W) #define setwords(D,W0,W1) (setword0(D,W0)) #endif #define addword0(D,X) (word0(D) += (X)) #endif /* The following definition of Storeinc is appropriate for MIPS processors. */ #if defined(IEEE_8087) + defined(VAX) #define Storeinc(a,b,c) (((unsigned short *)a)[1] = (unsigned short)b, \ ((unsigned short *)a)[0] = (unsigned short)c, a++) #else #if defined(IEEE_MC68k) #define Storeinc(a,b,c) (((unsigned short *)a)[0] = (unsigned short)b, \ ((unsigned short *)a)[1] = (unsigned short)c, a++) #else #define Storeinc(a,b,c) (*a++ = b << 16 | c & 0xffff) #endif #endif /* #define P DBL_MANT_DIG */ /* Ten_pmax = floor(P*log(2)/log(5)) */ /* Bletch = (highest power of 2 < DBL_MAX_10_EXP) / 16 */ /* Quick_max = floor((P-1)*log(FLT_RADIX)/log(10) - 1) */ /* Int_max = floor(P*log(FLT_RADIX)/log(10) - 1) */ #if defined(IEEE_8087) + defined(IEEE_MC68k) + defined(IEEE_Unknown) #define Exp_shift 20 #define Exp_shift1 20 #define Exp_msk1 0x100000 #define Exp_msk11 0x100000 #define Exp_mask 0x7ff00000 #define P 53 #define Bias 1023 #define IEEE_Arith #define Emin (-1022) #define Exp_1 0x3ff00000 #define Exp_11 0x3ff00000 #define Ebits 11 #define Frac_mask 0xfffff #define Frac_mask1 0xfffff #define Ten_pmax 22 #define Bletch 0x10 #define Bndry_mask 0xfffff #define Bndry_mask1 0xfffff #define LSB 1 #define Sign_bit 0x80000000 #define Log2P 1 #define Tiny0 0 #define Tiny1 1 #define Quick_max 14 #define Int_max 14 #define Infinite(x) (word0(x) == 0x7ff00000) /* sufficient test for here */ #else #undef Sudden_Underflow #define Sudden_Underflow #ifdef IBM #define Exp_shift 24 #define Exp_shift1 24 #define Exp_msk1 0x1000000 #define Exp_msk11 0x1000000 #define Exp_mask 0x7f000000 #define P 14 #define Bias 65 #define Exp_1 0x41000000 #define Exp_11 0x41000000 #define Ebits 8 /* exponent has 7 bits, but 8 is the right value in b2d */ #define Frac_mask 0xffffff #define Frac_mask1 0xffffff #define Bletch 4 #define Ten_pmax 22 #define Bndry_mask 0xefffff #define Bndry_mask1 0xffffff #define LSB 1 #define Sign_bit 0x80000000 #define Log2P 4 #define Tiny0 0x100000 #define Tiny1 0 #define Quick_max 14 #define Int_max 15 #else /* VAX */ #define Exp_shift 23 #define Exp_shift1 7 #define Exp_msk1 0x80 #define Exp_msk11 0x800000 #define Exp_mask 0x7f80 #define P 56 #define Bias 129 #define Exp_1 0x40800000 #define Exp_11 0x4080 #define Ebits 8 #define Frac_mask 0x7fffff #define Frac_mask1 0xffff007f #define Ten_pmax 24 #define Bletch 2 #define Bndry_mask 0xffff007f #define Bndry_mask1 0xffff007f #define LSB 0x10000 #define Sign_bit 0x8000 #define Log2P 1 #define Tiny0 0x80 #define Tiny1 0 #define Quick_max 15 #define Int_max 15 #endif #endif #ifndef IEEE_Arith #define ROUND_BIASED #endif #ifdef RND_PRODQUOT #define rounded_product(a,b) a = rnd_prod(a, b) #define rounded_quotient(a,b) a = rnd_quot(a, b) extern double rnd_prod(double, double), rnd_quot(double, double); #else #define rounded_product(a,b) a *= b #define rounded_quotient(a,b) a /= b #endif #define Big0 (Frac_mask1 | Exp_msk1*(DBL_MAX_EXP+Bias-1)) #define Big1 0xffffffff #define Kmax 15 /* (1<on_stack = 1; v->k = BIGINT_MINIMUM_K; v->maxwds = 1 << BIGINT_MINIMUM_K; v->sign = v->wds = 0; return v; } /* Allocate a Bigint with '1<k = k; rv->maxwds = x; rv->sign = rv->wds = 0; rv->on_stack = 0; return rv; } static void Bfree #ifdef KR_headers (v) Bigint *v; #else (Bigint *v) #endif { if (v && !v->on_stack) free (v); } static void Bcopy #ifdef KR_headers (x, y) Bigint *x, *y; #else (Bigint *x, Bigint *y) #endif { register unsigned32 *xp, *yp; register int i = y->wds; x->sign = y->sign; x->wds = i; for (xp = x->x, yp = y->x; --i >= 0; ) *xp++ = *yp++; } /* Make sure b has room for at least 1<k >= k) return b; else { Bigint *rv = Balloc (k); Bcopy(rv, b); Bfree(b); return rv; } } /* Return b*m+a. b is modified. Assumption: 0xFFFF*m+a fits in 32 bits. */ static Bigint * multadd #ifdef KR_headers (b, m, a) Bigint *b; int m, a; #else (Bigint *b, int m, int a) #endif { int i, wds; unsigned32 *x, y; unsigned32 xi, z; wds = b->wds; x = b->x; i = 0; do { xi = *x; y = (xi & 0xffff) * m + a; z = (xi >> 16) * m + (y >> 16); a = (int)(z >> 16); *x++ = (z << 16) + (y & 0xffff); } while(++i < wds); if (a) { if (wds >= b->maxwds) b = Brealloc(b, b->k+1); b->x[wds++] = a; b->wds = wds; } return b; } static Bigint * s2b #ifdef KR_headers (result, s, nd0, nd, y9) Bigint *result; CONST char *s; int nd0, nd; unsigned32 y9; #else (Bigint *result, CONST char *s, int nd0, int nd, unsigned32 y9) #endif { int i, k; _G_int32_t x, y; x = (nd + 8) / 9; for(k = 0, y = 1; x > y; y <<= 1, k++) ; result = Brealloc(result, k); result->x[0] = y9; result->wds = 1; i = 9; if (9 < nd0) { s += 9; do result = multadd(result, 10, *s++ - '0'); while (++i < nd0); s++; } else s += 10; for(; i < nd; i++) result = multadd(result, 10, *s++ - '0'); return result; } static int hi0bits #ifdef KR_headers (x) register unsigned32 x; #else (register unsigned32 x) #endif { 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; } static int lo0bits #ifdef KR_headers (y) unsigned32 *y; #else (unsigned32 *y) #endif { register int k; register unsigned32 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; } static Bigint * i2b #ifdef KR_headers (result, i) Bigint *result; int i; #else (Bigint* result, int i) #endif { result = Brealloc(result, 1); result->x[0] = i; result->wds = 1; return result; } /* Do: c = a * b. */ static Bigint * mult #ifdef KR_headers (c, a, b) Bigint *a, *b, *c; #else (Bigint *c, Bigint *a, Bigint *b) #endif { int k, wa, wb, wc; unsigned32 carry, y, z; unsigned32 *x, *xa, *xae, *xb, *xbe, *xc, *xc0; unsigned32 z2; if (a->wds < b->wds) { Bigint *tmp = a; a = b; b = tmp; } k = a->k; wa = a->wds; wb = b->wds; wc = wa + wb; if (wc > a->maxwds) k++; c = Brealloc(c, 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; 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; } } for(xc0 = c->x, xc = xc0 + wc; wc > 0 && !*--xc; --wc) ; c->wds = wc; return c; } /* Returns b*(5**k). b is modified. */ /* Re-written by Per Bothner to not need a static list. */ static Bigint * pow5mult #ifdef KR_headers (b, k) Bigint *b; int k; #else (Bigint *b, int k) #endif { static int p05[6] = { 5, 25, 125, 625, 3125, 15625 }; for (; k > 6; k -= 6) b = multadd(b, 15625, 0); /* b *= 5**6 */ if (k == 0) return b; else return multadd(b, p05[k-1], 0); } /* Re-written by Per Bothner so shift can be in place. */ static Bigint * lshift #ifdef KR_headers (b, k) Bigint *b; int k; #else (Bigint *b, int k) #endif { int i; unsigned32 *x, *x1, *xe; int old_wds = b->wds; int n = k >> 5; int k1 = b->k; int n1 = n + old_wds + 1; if (k == 0) return b; for(i = b->maxwds; n1 > i; i <<= 1) k1++; b = Brealloc(b, k1); xe = b->x; /* Source limit */ x = xe + old_wds; /* Source pointer */ x1 = x + n; /* Destination pointer */ if (k &= 0x1f) { int k1 = 32 - k; unsigned32 z = *--x; if ((*x1 = (z >> k1)) != 0) { ++n1; } while (x > xe) { unsigned32 w = *--x; *--x1 = (z << k) | (w >> k1); z = w; } *--x1 = z << k; } else do { *--x1 = *--x; } while(x > xe); while (x1 > xe) *--x1 = 0; b->wds = n1 - 1; return b; } static int cmp #ifdef KR_headers (a, b) Bigint *a, *b; #else (Bigint *a, Bigint *b) #endif { unsigned32 *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; } /* Do: c = a-b. */ static Bigint * diff #ifdef KR_headers (c, a, b) Bigint *c, *a, *b; #else (Bigint *c, Bigint *a, Bigint *b) #endif { int i, wa, wb; _G_int32_t borrow, y; /* We need signed shifts here. */ unsigned32 *xa, *xae, *xb, *xbe, *xc; _G_int32_t z; i = cmp(a,b); if (!i) { c = Brealloc(c, 0); c->wds = 1; c->x[0] = 0; return c; } if (i < 0) { Bigint *tmp = a; a = b; b = tmp; i = 1; } else i = 0; c = Brealloc(c, 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; 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); } while(!*--xc) wa--; c->wds = wa; return c; } static double ulp #ifdef KR_headers (x) double x; #else (double x) #endif { register _G_int32_t L; double a; L = (word0(x) & Exp_mask) - (P-1)*Exp_msk1; #ifndef Sudden_Underflow if (L > 0) { #endif #ifdef IBM L |= Exp_msk1 >> 4; #endif setwords(a, L, 0); #ifndef Sudden_Underflow } else { L = -L >> Exp_shift; if (L < Exp_shift) setwords(a, 0x80000 >> L, 0); else { L -= Exp_shift; setwords(a, 0, L >= 31 ? 1 : 1 << (31 - L)); } } #endif return a; } static double b2d #ifdef KR_headers (a, e) Bigint *a; int *e; #else (Bigint *a, int *e) #endif { unsigned32 *xa, *xa0, w, y, z; int k; double d; unsigned32 d0, d1; 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; 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 } ret_d: #ifdef VAX setwords(d, d0 >> 16 | d0 << 16, d1 >> 16 | d1 << 16); #else setwords (d, d0, d1); #endif return d; } static Bigint * d2b #ifdef KR_headers (result, d, e, bits) Bigint *result; double d; _G_int32_t *e, *bits; #else (Bigint *result, double d, _G_int32_t *e, _G_int32_t *bits) #endif { int de, i, k; unsigned32 *x, y, z; unsigned32 d0, d1; #ifdef VAX d0 = word0(d) >> 16 | word0(d) << 16; d1 = word1(d) >> 16 | word1(d) << 16; #else d0 = word0(d); d1 = word1(d); #endif result = Brealloc(result, 1); x = result->x; z = d0 & Frac_mask; d0 &= 0x7fffffff; /* clear sign bit, which we ignore */ de = (int)(d0 >> Exp_shift); /* The exponent part of d. */ /* Put back the suppressed high-order bit, if normalized. */ #ifndef IBM #ifndef Sudden_Underflow if (de) #endif z |= Exp_msk11; #endif #ifndef _DOUBLE_IS_32BITS if ((y = d1)) { if ((k = lo0bits(&y))) { x[0] = y | z << (32 - k); z >>= k; } else x[0] = y; i = result->wds = (x[1] = z) ? 2 : 1; } else { #endif /* !_DOUBLE_IS_32BITS */ #ifdef DEBUG if (!z) Bug("Zero passed to d2b"); #endif k = lo0bits(&z); x[0] = z; i = result->wds = 1; #ifndef _DOUBLE_IS_32BITS k += 32; } #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; *bits = 32*i - hi0bits(x[i-1]); } #endif return result; } static double ratio #ifdef KR_headers (a, b) Bigint *a, *b; #else (Bigint *a, Bigint *b) #endif { double da, db; int k, ka, kb; da = b2d(a, &ka); db = b2d(b, &kb); k = ka - kb + 32*(a->wds - b->wds); #ifdef IBM if (k > 0) { addword0(da, (k >> 2)*Exp_msk1); if (k &= 3) da *= 1 << k; } else { k = -k; addword0(db,(k >> 2)*Exp_msk1); if (k &= 3) db *= 1 << k; } #else if (k > 0) addword0(da, k*Exp_msk1); else { k = -k; addword0(db, k*Exp_msk1); } #endif return da / db; } static 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 #ifdef VAX , 1e23, 1e24 #endif }; #ifdef IEEE_Arith static CONST double bigtens[] = { 1e16, 1e32, 1e64, 1e128, 1e256 }; static CONST double tinytens[] = { 1e-16, 1e-32, 1e-64, 1e-128, 1e-256 }; #define n_bigtens 5 #else #ifdef IBM static CONST double bigtens[] = { 1e16, 1e32, 1e64 }; static CONST double tinytens[] = { 1e-16, 1e-32, 1e-64 }; #define n_bigtens 3 #else /* Also used for the case when !_DOUBLE_IS_32BITS. */ static CONST double bigtens[] = { 1e16, 1e32 }; static CONST double tinytens[] = { 1e-16, 1e-32 }; #define n_bigtens 2 #endif #endif double _IO_strtod #ifdef KR_headers (s00, se) CONST char *s00; char **se; #else (CONST char *s00, char **se) #endif { _G_int32_t bb2, bb5, bbe, bd2, bd5, bbbits, bs2, c, dsign, e, e1, esign, i, j, k, nd, nd0, nf, nz, nz0, sign; CONST char *s, *s0, *s1; double aadj, aadj1, adj, rv, rv0; _G_int32_t L; unsigned32 y, z; Bigint _bb, _b_avail, _bd, _bd0, _bs, _delta; Bigint *bb = Binit(&_bb); Bigint *bd = Binit(&_bd); Bigint *bd0 = Binit(&_bd0); Bigint *bs = Binit(&_bs); Bigint *b_avail = Binit(&_b_avail); Bigint *delta = Binit(&_delta); TEST_ENDIANNESS; sign = nz0 = nz = 0; rv = 0.; (void)&rv; /* Force rv into the stack */ for(s = s00;;s++) switch(*s) { case '-': sign = 1; /* no break */ case '+': if (*++s) goto break2; /* no break */ case 0: /* "+" and "-" should be reported as an error? */ sign = 0; s = s00; goto ret; case '\t': case '\n': case '\v': case '\f': case '\r': case ' ': continue; default: goto break2; } break2: if (*s == '0') { nz0 = 1; while(*++s == '0') ; if (!*s) goto ret; } s0 = s; y = z = 0; for(nd = nf = 0; (c = *s) >= '0' && c <= '9'; nd++, s++) if (nd < 9) y = 10*y + c - '0'; else if (nd < 16) z = 10*z + c - '0'; nd0 = nd; if (c == '.') { c = *++s; if (!nd) { for(; c == '0'; c = *++s) nz++; if (c > '0' && c <= '9') { s0 = s; nf += nz; nz = 0; goto have_dig; } goto dig_done; } for(; c >= '0' && c <= '9'; c = *++s) { have_dig: nz++; if (c -= '0') { nf += nz; for(i = 1; i < nz; i++) if (nd++ < 9) y *= 10; else if (nd <= DBL_DIG + 1) z *= 10; if (nd++ < 9) y = 10*y + c; else if (nd <= DBL_DIG + 1) z = 10*z + c; nz = 0; } } } dig_done: e = 0; if (c == 'e' || c == 'E') { if (!nd && !nz && !nz0) { s = s00; goto ret; } s00 = s; esign = 0; switch(c = *++s) { case '-': esign = 1; case '+': c = *++s; } if (c >= '0' && c <= '9') { while(c == '0') c = *++s; if (c > '0' && c <= '9') { e = c - '0'; s1 = s; while((c = *++s) >= '0' && c <= '9') e = 10*e + c - '0'; if (s - s1 > 8) /* Avoid confusion from exponents * so large that e might overflow. */ e = 9999999; if (esign) e = -e; } else e = 0; } else s = s00; } if (!nd) { if (!nz && !nz0) s = s00; goto ret; } e1 = e -= nf; /* Now we have nd0 digits, starting at s0, followed by a * decimal point, followed by nd-nd0 digits. The number we're * after is the integer represented by those digits times * 10**e */ if (!nd0) nd0 = nd; k = nd < DBL_DIG + 1 ? nd : DBL_DIG + 1; rv = y; if (k > 9) rv = tens[k - 9] * rv + z; if (nd <= DBL_DIG #ifndef RND_PRODQUOT && FLT_ROUNDS == 1 #endif ) { if (!e) goto ret; if (e > 0) { if (e <= Ten_pmax) { #ifdef VAX goto vax_ovfl_check; #else /* rv = */ rounded_product(rv, tens[e]); goto ret; #endif } i = DBL_DIG - nd; if (e <= Ten_pmax + i) { /* A fancier test would sometimes let us do * this for larger i values. */ e -= i; rv *= tens[i]; #ifdef VAX /* VAX exponent range is so narrow we must * worry about overflow here... */ vax_ovfl_check: addword0(rv, - P*Exp_msk1); /* rv = */ rounded_product(rv, tens[e]); if ((word0(rv) & Exp_mask) > Exp_msk1*(DBL_MAX_EXP+Bias-1-P)) goto ovfl; addword0(rv, P*Exp_msk1); #else /* rv = */ rounded_product(rv, tens[e]); #endif goto ret; } } #ifndef Inaccurate_Divide else if (e >= -Ten_pmax) { /* rv = */ rounded_quotient(rv, tens[-e]); goto ret; } #endif } e1 += nd - k; /* Get starting approximation = rv * 10**e1 */ if (e1 > 0) { if ((i = e1 & 15)) rv *= tens[i]; if (e1 &= ~15) { if (e1 > DBL_MAX_10_EXP) { ovfl: errno = ERANGE; #if defined(sun) && !defined(__svr4__) /* SunOS defines HUGE_VAL as __infinity(), which is in libm. */ #undef HUGE_VAL #endif #ifndef HUGE_VAL #define HUGE_VAL 1.7976931348623157E+308 #endif rv = HUGE_VAL; goto ret; } if (e1 >>= 4) { for(j = 0; e1 > 1; j++, e1 >>= 1) if (e1 & 1) rv *= bigtens[j]; /* The last multiplication could overflow. */ addword0(rv, -P*Exp_msk1); rv *= bigtens[j]; if ((z = word0(rv) & Exp_mask) > Exp_msk1*(DBL_MAX_EXP+Bias-P)) goto ovfl; if (z > Exp_msk1*(DBL_MAX_EXP+Bias-1-P)) { /* set to largest number */ /* (Can't trust DBL_MAX) */ setwords(rv, Big0, Big1); } else addword0(rv, P*Exp_msk1); } } } else if (e1 < 0) { e1 = -e1; if ((i = e1 & 15)) rv /= tens[i]; if (e1 &= ~15) { e1 >>= 4; for(j = 0; e1 > 1; j++, e1 >>= 1) if (e1 & 1) rv *= tinytens[j]; /* The last multiplication could underflow. */ rv0 = rv; rv *= tinytens[j]; if (!rv) { rv = 2.*rv0; rv *= tinytens[j]; if (!rv) { undfl: rv = 0.; errno = ERANGE; goto ret; } setwords(rv, Tiny0, Tiny1); /* The refinement below will clean * this approximation up. */ } } } /* Now the hard part -- adjusting rv to the correct value.*/ /* Put digits into bd: true value = bd * 10^e */ bd0 = s2b(bd0, s0, nd0, nd, y); bd = Brealloc(bd, bd0->k); for(;;) { Bcopy(bd, bd0); bb = d2b(bb, rv, &bbe, &bbbits); /* rv = bb * 2^bbe */ bs = i2b(bs, 1); if (e >= 0) { bb2 = bb5 = 0; bd2 = bd5 = e; } else { bb2 = bb5 = -e; bd2 = bd5 = 0; } if (bbe >= 0) bb2 += bbe; else bd2 -= bbe; bs2 = bb2; #ifdef Sudden_Underflow #ifdef IBM j = 1 + 4*P - 3 - bbbits + ((bbe + bbbits - 1) & 3); #else j = P + 1 - bbbits; #endif #else i = bbe + bbbits - 1; /* logb(rv) */ if (i < Emin) /* denormal */ j = bbe + (P-Emin); else j = P + 1 - bbbits; #endif bb2 += j; bd2 += j; i = bb2 < bd2 ? bb2 : bd2; if (i > bs2) i = bs2; if (i > 0) { bb2 -= i; bd2 -= i; bs2 -= i; } if (bb5 > 0) { Bigint *b_tmp; bs = pow5mult(bs, bb5); b_tmp = mult(b_avail, bs, bb); b_avail = bb; bb = b_tmp; } if (bb2 > 0) bb = lshift(bb, bb2); if (bd5 > 0) bd = pow5mult(bd, bd5); if (bd2 > 0) bd = lshift(bd, bd2); if (bs2 > 0) bs = lshift(bs, bs2); delta = diff(delta, bb, bd); dsign = delta->sign; delta->sign = 0; i = cmp(delta, bs); if (i < 0) { /* Error is less than half an ulp -- check for * special case of mantissa a power of two. */ if (dsign || word1(rv) || word0(rv) & Bndry_mask) break; delta = lshift(delta,Log2P); if (cmp(delta, bs) > 0) goto drop_down; break; } if (i == 0) { /* exactly half-way between */ if (dsign) { if ((word0(rv) & Bndry_mask1) == Bndry_mask1 && word1(rv) == 0xffffffff) { /*boundary case -- increment exponent*/ setword0(rv, (word0(rv) & Exp_mask) + Exp_msk1); #ifdef IBM setword0 (rv, word0(rv) | (Exp_msk1 >> 4)); #endif setword1(rv, 0); break; } } else if (!(word0(rv) & Bndry_mask) && !word1(rv)) { drop_down: /* boundary case -- decrement exponent */ #ifdef Sudden_Underflow L = word0(rv) & Exp_mask; #ifdef IBM if (L < Exp_msk1) #else if (L <= Exp_msk1) #endif goto undfl; L -= Exp_msk1; #else L = (word0(rv) & Exp_mask) - Exp_msk1; #endif setwords(rv, L | Bndry_mask1, 0xffffffff); #ifdef IBM continue; #else break; #endif } #ifndef ROUND_BIASED if (!(word1(rv) & LSB)) break; #endif if (dsign) rv += ulp(rv); #ifndef ROUND_BIASED else { rv -= ulp(rv); #ifndef Sudden_Underflow if (!rv) goto undfl; #endif } #endif break; } if ((aadj = ratio(delta, bs)) <= 2.) { if (dsign) aadj = aadj1 = 1.; else if (word1(rv) || word0(rv) & Bndry_mask) { #ifndef Sudden_Underflow if (word1(rv) == Tiny1 && !word0(rv)) goto undfl; #endif aadj = 1.; aadj1 = -1.; } else { /* special case -- power of FLT_RADIX to be */ /* rounded down... */ if (aadj < 2./FLT_RADIX) aadj = 1./FLT_RADIX; else aadj *= 0.5; aadj1 = -aadj; } } else { aadj *= 0.5; aadj1 = dsign ? aadj : -aadj; #ifdef Check_FLT_ROUNDS switch(FLT_ROUNDS) { case 2: /* towards +infinity */ aadj1 -= 0.5; break; case 0: /* towards 0 */ case 3: /* towards -infinity */ aadj1 += 0.5; } #else if (FLT_ROUNDS == 0) aadj1 += 0.5; #endif } y = word0(rv) & Exp_mask; /* Check for overflow */ if (y == Exp_msk1*(DBL_MAX_EXP+Bias-1)) { rv0 = rv; addword0(rv, - P*Exp_msk1); adj = aadj1 * ulp(rv); rv += adj; if ((word0(rv) & Exp_mask) >= Exp_msk1*(DBL_MAX_EXP+Bias-P)) { if (word0(rv0) == Big0 && word1(rv0) == Big1) goto ovfl; setwords(rv, Big0, Big1); continue; } else addword0(rv, P*Exp_msk1); } else { #ifdef Sudden_Underflow if ((word0(rv) & Exp_mask) <= P*Exp_msk1) { rv0 = rv; addword0(rv, P*Exp_msk1); adj = aadj1 * ulp(rv); rv += adj; #ifdef IBM if ((word0(rv) & Exp_mask) < P*Exp_msk1) #else if ((word0(rv) & Exp_mask) <= P*Exp_msk1) #endif { if (word0(rv0) == Tiny0 && word1(rv0) == Tiny1) goto undfl; setwords(rv, Tiny0, Tiny1); continue; } else addword0(rv, -P*Exp_msk1); } else { adj = aadj1 * ulp(rv); rv += adj; } #else /* Compute adj so that the IEEE rounding rules will * correctly round rv + adj in some half-way cases. * If rv * ulp(rv) is denormalized (i.e., * y <= (P-1)*Exp_msk1), we must adjust aadj to avoid * trouble from bits lost to denormalization; * example: 1.2e-307 . */ if (y <= (P-1)*Exp_msk1 && aadj >= 1.) { aadj1 = (double)(int)(aadj + 0.5); if (!dsign) aadj1 = -aadj1; } adj = aadj1 * ulp(rv); rv += adj; #endif } z = word0(rv) & Exp_mask; if (y == z) { /* Can we stop now? */ L = (_G_int32_t)aadj; aadj -= L; /* The tolerances below are conservative. */ if (dsign || word1(rv) || word0(rv) & Bndry_mask) { if (aadj < .4999999 || aadj > .5000001) break; } else if (aadj < .4999999/FLT_RADIX) break; } } Bfree(bb); Bfree(bd); Bfree(bs); Bfree(bd0); Bfree(delta); Bfree(b_avail); ret: if (se) *se = (char *)s; return sign ? -rv : rv; } static int quorem #ifdef KR_headers (b, S) Bigint *b, *S; #else (Bigint *b, Bigint *S) #endif { int n; _G_int32_t borrow, y; unsigned32 carry, q, ys; unsigned32 *bx, *bxe, *sx, *sxe; _G_int32_t z; unsigned32 si, zs; n = S->wds; #ifdef DEBUG /*debug*/ if (b->wds > n) /*debug*/ Bug("oversize b in quorem"); #endif if (b->wds < n) return 0; sx = S->x; sxe = sx + --n; bx = b->x; bxe = bx + n; q = *bxe / (*sxe + 1); /* ensure q <= true quotient */ #ifdef DEBUG /*debug*/ if (q > 9) /*debug*/ Bug("oversized quotient in quorem"); #endif if (q) { borrow = 0; carry = 0; do { si = *sx++; ys = (si & 0xffff) * q + carry; zs = (si >> 16) * q + (ys >> 16); carry = zs >> 16; y = (*bx & 0xffff) - (ys & 0xffff) + borrow; borrow = y >> 16; Sign_Extend(borrow, y); z = (*bx >> 16) - (zs & 0xffff) + borrow; borrow = z >> 16; Sign_Extend(borrow, z); Storeinc(bx, z, y); } while(sx <= sxe); if (!*bxe) { bx = b->x; while(--bxe > bx && !*bxe) --n; b->wds = n; } } if (cmp(b, S) >= 0) { q++; borrow = 0; carry = 0; bx = b->x; sx = S->x; do { si = *sx++; ys = (si & 0xffff) + carry; zs = (si >> 16) + (ys >> 16); carry = zs >> 16; y = (*bx & 0xffff) - (ys & 0xffff) + borrow; borrow = y >> 16; Sign_Extend(borrow, y); z = (*bx >> 16) - (zs & 0xffff) + borrow; borrow = z >> 16; Sign_Extend(borrow, z); Storeinc(bx, z, y); } while(sx <= sxe); bx = b->x; bxe = bx + n; if (!*bxe) { while(--bxe > bx && !*bxe) --n; b->wds = n; } } return q; } /* dtoa for IEEE arithmetic (dmg): convert double to ASCII string. * * Inspired by "How to Print Floating-Point Numbers Accurately" by * Guy L. Steele, Jr. and Jon L. White [Proc. ACM SIGPLAN '90, pp. 92-101]. * * Modifications: * 1. Rather than iterating, we use a simple numeric overestimate * to determine k = floor(log10(d)). We scale relevant * quantities using O(log2(k)) rather than O(k) multiplications. * 2. For some modes > 2 (corresponding to ecvt and fcvt), we don't * try to generate digits strictly left to right. Instead, we * compute with fewer bits and propagate the carry if necessary * when rounding the final digit up. This is often faster. * 3. Under the assumption that input will be rounded nearest, * mode 0 renders 1e23 as 1e23 rather than 9.999999999999999e22. * That is, we allow equality in stopping tests when the * round-nearest rule will give the same floating-point value * as would satisfaction of the stopping test with strict * inequality. * 4. We remove common factors of powers of 2 from relevant * quantities. * 5. When converting floating-point integers less than 1e16, * we use floating-point arithmetic rather than resorting * to multiple-precision integers. * 6. When asked to produce fewer than 15 digits, we first try * to get by with floating-point arithmetic; we resort to * multiple-precision integer arithmetic only if we cannot * guarantee that the floating-point calculation has given * the correctly rounded result. For k requested digits and * "uniformly" distributed input, the probability is * something like 10^(k-15) that we must resort to the long * calculation. */ char * _IO_dtoa #ifdef KR_headers (d, mode, ndigits, decpt, sign, rve) double d; int mode, ndigits, *decpt, *sign; char **rve; #else (double d, int mode, int ndigits, int *decpt, int *sign, char **rve) #endif { /* Arguments ndigits, decpt, sign are similar to those of ecvt and fcvt; trailing zeros are suppressed from the returned string. If not null, *rve is set to point to the end of the return value. If d is +-Infinity or NaN, then *decpt is set to 9999. mode: 0 ==> shortest string that yields d when read in and rounded to nearest. 1 ==> like 0, but with Steele & White stopping rule; e.g. with IEEE P754 arithmetic , mode 0 gives 1e23 whereas mode 1 gives 9.999999999999999e22. 2 ==> max(1,ndigits) significant digits. This gives a return value similar to that of ecvt, except that trailing zeros are suppressed. 3 ==> through ndigits past the decimal point. This gives a return value similar to that from fcvt, except that trailing zeros are suppressed, and ndigits can be negative. 4-9 should give the same return values as 2-3, i.e., 4 <= mode <= 9 ==> same return as mode 2 + (mode & 1). These modes are mainly for debugging; often they run slower but sometimes faster than modes 2-3. 4,5,8,9 ==> left-to-right digit generation. 6-9 ==> don't try fast floating-point estimate (if applicable). Values of mode other than 0-9 are treated as mode 0. Sufficient space is allocated to the return value to hold the suppressed trailing zeros. */ _G_int32_t bbits, b2, b5, be, dig, i, ieps, ilim, ilim0, ilim1, j, j1, k, k0, k_check, leftright, m2, m5, s2, s5, spec_case, try_quick; _G_int32_t L; #ifndef Sudden_Underflow int denorm; #endif Bigint _b_avail, _b, _mhi, _mlo, _S; Bigint *b_avail = Binit(&_b_avail); Bigint *b = Binit(&_b); Bigint *S = Binit(&_S); /* mhi and mlo are only set and used if leftright. */ Bigint *mhi = NULL, *mlo = NULL; double d2, ds, eps; char *s, *s0; static Bigint *result = NULL; static int result_k; TEST_ENDIANNESS; if (result) { /* result is contains a string, so its fields (interpreted as a Bigint have been trashed. Restore them. This is a really ugly interface - result should not be static, since that is not thread-safe. FIXME. */ result->k = result_k; result->maxwds = 1 << result_k; result->on_stack = 0; } if (word0(d) & Sign_bit) { /* set sign for everything, including 0's and NaNs */ *sign = 1; setword0(d, word0(d) & ~Sign_bit); /* clear sign bit */ } else *sign = 0; #if defined(IEEE_Arith) + defined(VAX) #ifdef IEEE_Arith if ((word0(d) & Exp_mask) == Exp_mask) #else if (word0(d) == 0x8000) #endif { /* Infinity or NaN */ *decpt = 9999; #ifdef IEEE_Arith if (!word1(d) && !(word0(d) & 0xfffff)) { s = "Infinity"; if (rve) *rve = s + 8; } else #endif { s = "NaN"; if (rve) *rve = s +3; } return s; } #endif #ifdef IBM d += 0; /* normalize */ #endif if (!d) { *decpt = 1; s = "0"; if (rve) *rve = s + 1; return s; } b = d2b(b, d, &be, &bbits); i = (int)(word0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1)); #ifndef Sudden_Underflow if (i) { #endif d2 = d; setword0(d2, (word0(d2) & Frac_mask1) | Exp_11); #ifdef IBM if (j = 11 - hi0bits(word0(d2) & Frac_mask)) d2 /= 1 << j; #endif i -= Bias; #ifdef IBM i <<= 2; i += j; #endif #ifndef Sudden_Underflow denorm = 0; } else { /* d is denormalized */ unsigned32 x; i = bbits + be + (Bias + (P-1) - 1); x = i > 32 ? word0(d) << (64 - i) | word1(d) >> (i - 32) : word1(d) << (32 - i); d2 = x; addword0(d2, - 31*Exp_msk1); /* adjust exponent */ i -= (Bias + (P-1) - 1) + 1; denorm = 1; } #endif /* Now i is the unbiased base-2 exponent. */ /* log(x) ~=~ log(1.5) + (x-1.5)/1.5 * log10(x) = log(x) / log(10) * ~=~ log(1.5)/log(10) + (x-1.5)/(1.5*log(10)) * log10(d) = i*log(2)/log(10) + log10(d2) * * This suggests computing an approximation k to log10(d) by * * k = i*0.301029995663981 * + ( (d2-1.5)*0.289529654602168 + 0.176091259055681 ); * * We want k to be too large rather than too small. * The error in the first-order Taylor series approximation * is in our favor, so we just round up the constant enough * to compensate for any error in the multiplication of * (i) by 0.301029995663981; since |i| <= 1077, * and 1077 * 0.30103 * 2^-52 ~=~ 7.2e-14, * adding 1e-13 to the constant term more than suffices. * Hence we adjust the constant term to 0.1760912590558. * (We could get a more accurate k by invoking log10, * but this is probably not worthwhile.) */ ds = (d2-1.5)*0.289529654602168 + 0.1760912590558 + i*0.301029995663981; k = (int)ds; if (ds < 0. && ds != k) k--; /* want k = floor(ds) */ k_check = 1; if (k >= 0 && k <= Ten_pmax) { if (d < tens[k]) k--; k_check = 0; } j = bbits - i - 1; if (j >= 0) { b2 = 0; s2 = j; } else { b2 = -j; s2 = 0; } if (k >= 0) { b5 = 0; s5 = k; s2 += k; } else { b2 -= k; b5 = -k; s5 = 0; } if (mode < 0 || mode > 9) mode = 0; try_quick = 1; if (mode > 5) { mode -= 4; try_quick = 0; } leftright = 1; switch(mode) { case 0: case 1: ilim = ilim1 = -1; i = 18; ndigits = 0; break; case 2: leftright = 0; /* no break */ case 4: if (ndigits <= 0) ndigits = 1; ilim = ilim1 = i = ndigits; break; case 3: leftright = 0; /* no break */ case 5: i = ndigits + k + 1; ilim = i; ilim1 = i - 1; if (i <= 0) i = 1; } /* i is now an upper bound of the number of digits to generate. */ j = sizeof(unsigned32) * (1< result->k) { Bfree (result); result = Balloc(result_k); } s = s0 = (char *)result; if (ilim >= 0 && ilim <= Quick_max && try_quick) { /* Try to get by with floating-point arithmetic. */ i = 0; d2 = d; k0 = k; ilim0 = ilim; ieps = 2; /* conservative */ if (k > 0) { ds = tens[k&0xf]; j = k >> 4; if (j & Bletch) { /* prevent overflows */ j &= Bletch - 1; d /= bigtens[n_bigtens-1]; ieps++; } for(; j; j >>= 1, i++) if (j & 1) { ieps++; ds *= bigtens[i]; } d /= ds; } else if ((j1 = -k)) { d *= tens[j1 & 0xf]; for(j = j1 >> 4; j; j >>= 1, i++) if (j & 1) { ieps++; d *= bigtens[i]; } } if (k_check && d < 1. && ilim > 0) { if (ilim1 <= 0) goto fast_failed; ilim = ilim1; k--; d *= 10.; ieps++; } eps = ieps*d + 7.; addword0(eps, - (P-1)*Exp_msk1); if (ilim == 0) { d -= 5.; if (d > eps) goto one_digit; if (d < -eps) goto no_digits; goto fast_failed; } #ifndef No_leftright if (leftright) { /* Use Steele & White method of only * generating digits needed. */ eps = 0.5/tens[ilim-1] - eps; for(i = 0;;) { L = (_G_int32_t)d; d -= L; *s++ = '0' + (int)L; if (d < eps) goto ret1; if (1. - d < eps) goto bump_up; if (++i >= ilim) break; eps *= 10.; d *= 10.; } } else { #endif /* Generate ilim digits, then fix them up. */ eps *= tens[ilim-1]; for(i = 1;; i++, d *= 10.) { L = (_G_int32_t)d; d -= L; *s++ = '0' + (int)L; if (i == ilim) { if (d > 0.5 + eps) goto bump_up; else if (d < 0.5 - eps) { while(*--s == '0'); s++; goto ret1; } break; } } #ifndef No_leftright } #endif fast_failed: s = s0; d = d2; k = k0; ilim = ilim0; } /* Do we have a "small" integer? */ if (be >= 0 && k <= Int_max) { /* Yes. */ ds = tens[k]; if (ndigits < 0 && ilim <= 0) { if (ilim < 0 || d <= 5*ds) goto no_digits; goto one_digit; } for(i = 1;; i++) { L = (_G_int32_t)(d / ds); d -= L*ds; #ifdef Check_FLT_ROUNDS /* If FLT_ROUNDS == 2, L will usually be high by 1 */ if (d < 0) { L--; d += ds; } #endif *s++ = '0' + (int)L; if (i == ilim) { d += d; if (d > ds || (d == ds && L & 1)) { bump_up: while(*--s == '9') if (s == s0) { k++; *s = '0'; break; } ++*s++; } break; } if (!(d *= 10.)) break; } goto ret1; } m2 = b2; m5 = b5; if (leftright) { if (mode < 2) { i = #ifndef Sudden_Underflow denorm ? be + (Bias + (P-1) - 1 + 1) : #endif #ifdef IBM 1 + 4*P - 3 - bbits + ((bbits + be - 1) & 3); #else 1 + P - bbits; #endif } else { j = ilim - 1; if (m5 >= j) m5 -= j; else { s5 += j -= m5; b5 += j; m5 = 0; } if ((i = ilim) < 0) { m2 -= i; i = 0; } } b2 += i; s2 += i; mhi = i2b(Binit(&_mhi), 1); } if (m2 > 0 && s2 > 0) { i = m2 < s2 ? m2 : s2; b2 -= i; m2 -= i; s2 -= i; } if (b5 > 0) { if (leftright) { if (m5 > 0) { Bigint *b_tmp; mhi = pow5mult(mhi, m5); b_tmp = mult(b_avail, mhi, b); b_avail = b; b = b_tmp; } if ((j = b5 - m5)) b = pow5mult(b, j); } else b = pow5mult(b, b5); } S = i2b(S, 1); if (s5 > 0) S = pow5mult(S, s5); /* Check for special case that d is a normalized power of 2. */ if (mode < 2) { if (!word1(d) && !(word0(d) & Bndry_mask) #ifndef Sudden_Underflow && word0(d) & Exp_mask #endif ) { /* The special case */ b2 += Log2P; s2 += Log2P; spec_case = 1; } else spec_case = 0; } /* Arrange for convenient computation of quotients: * shift left if necessary so divisor has 4 leading 0 bits. * * Perhaps we should just compute leading 28 bits of S once * and for all and pass them and a shift to quorem, so it * can do shifts and ors to compute the numerator for q. */ if ((i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0x1f)) i = 32 - i; if (i > 4) { i -= 4; b2 += i; m2 += i; s2 += i; } else if (i < 4) { i += 28; b2 += i; m2 += i; s2 += i; } if (b2 > 0) b = lshift(b, b2); if (s2 > 0) S = lshift(S, s2); if (k_check) { if (cmp(b,S) < 0) { k--; b = multadd(b, 10, 0); /* we botched the k estimate */ if (leftright) mhi = multadd(mhi, 10, 0); ilim = ilim1; } } if (ilim <= 0 && mode > 2) { if (ilim < 0 || cmp(b,S = multadd(S,5,0)) <= 0) { /* no digits, fcvt style */ no_digits: k = -1 - ndigits; goto ret; } one_digit: *s++ = '1'; k++; goto ret; } if (leftright) { if (m2 > 0) mhi = lshift(mhi, m2); /* Compute mlo -- check for special case * that d is a normalized power of 2. */ if (spec_case) { mlo = Brealloc(Binit(&_mlo), mhi->k); Bcopy(mlo, mhi); mhi = lshift(mhi, Log2P); } else mlo = mhi; for(i = 1;;i++) { dig = quorem(b,S) + '0'; /* Do we yet have the shortest decimal string * that will round to d? */ j = cmp(b, mlo); b_avail = diff(b_avail, S, mhi); /* b_avail = S - mi */ j1 = b_avail->sign ? 1 : cmp(b, b_avail); #ifndef ROUND_BIASED if (j1 == 0 && !mode && !(word1(d) & 1)) { if (dig == '9') goto round_9_up; if (j > 0) dig++; *s++ = dig; goto ret; } #endif if (j < 0 || (j == 0 && !mode #ifndef ROUND_BIASED && !(word1(d) & 1) #endif )) { if (j1 > 0) { b = lshift(b, 1); j1 = cmp(b, S); if ((j1 > 0 || (j1 == 0 && dig & 1)) && dig++ == '9') goto round_9_up; } *s++ = dig; goto ret; } if (j1 > 0) { if (dig == '9') { /* possible if i == 1 */ round_9_up: *s++ = '9'; goto roundoff; } *s++ = dig + 1; goto ret; } *s++ = dig; if (i == ilim) break; b = multadd(b, 10, 0); if (mlo == mhi) mlo = mhi = multadd(mhi, 10, 0); else { mlo = multadd(mlo, 10, 0); mhi = multadd(mhi, 10, 0); } } } else for(i = 1;; i++) { *s++ = dig = quorem(b,S) + '0'; if (i >= ilim) break; b = multadd(b, 10, 0); } /* Round off last digit */ b = lshift(b, 1); j = cmp(b, S); if (j > 0 || (j == 0 && dig & 1)) { roundoff: while(*--s == '9') if (s == s0) { k++; *s++ = '1'; goto ret; } ++*s++; } else { while(*--s == '0'); s++; } ret: Bfree(b_avail); Bfree(S); if (mhi) { if (mlo && mlo != mhi) Bfree(mlo); Bfree(mhi); } ret1: Bfree(b); *s = 0; *decpt = k + 1; if (rve) *rve = s; return s0; } #endif /* _IO_USE_DTOA */