| /* |
| 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 <libioP.h> |
| #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 <stdio.h> |
| #define Bug(x) {fprintf(stderr, "%s\n", x); exit(1);} |
| #endif |
| |
| #ifdef __STDC__ |
| #include <stdlib.h> |
| #include <string.h> |
| #include <float.h> |
| #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 <errno.h> |
| #ifndef __MATH_H__ |
| #include <math.h> |
| #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<<BIGINT_MINIMUM_K) is the minimum number of words to allocate |
| in a Bigint. dtoa usually manages with 1<<2, and has not been |
| known to need more than 1<<3. */ |
| |
| #define BIGINT_MINIMUM_K 3 |
| |
| struct Bigint { |
| struct Bigint *next; |
| int k; /* Parameter given to Balloc(k) */ |
| int maxwds; /* Allocated space: equals 1<<k. */ |
| short on_stack; /* 1 if stack-allocated. */ |
| short sign; /* 0 if value is positive or zero; 1 if negative. */ |
| int wds; /* Current length. */ |
| unsigned32 x[1<<BIGINT_MINIMUM_K]; /* Actually: x[maxwds] */ |
| }; |
| |
| #define BIGINT_HEADER_SIZE \ |
| (sizeof(Bigint) - (1<<BIGINT_MINIMUM_K) * sizeof(unsigned32)) |
| |
| typedef struct Bigint Bigint; |
| |
| /* Initialize a stack-allocated Bigint. */ |
| |
| static Bigint * |
| Binit |
| #ifdef KR_headers |
| (v) Bigint *v; |
| #else |
| (Bigint *v) |
| #endif |
| { |
| v->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' big digits. */ |
| |
| static Bigint * |
| Balloc |
| #ifdef KR_headers |
| (k) int k; |
| #else |
| (int k) |
| #endif |
| { |
| int x; |
| Bigint *rv; |
| |
| if (k < BIGINT_MINIMUM_K) |
| k = BIGINT_MINIMUM_K; |
| |
| x = 1 << k; |
| rv = (Bigint *) |
| malloc(BIGINT_HEADER_SIZE + x * sizeof(unsigned32)); |
| rv->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 big digits. */ |
| |
| static Bigint * |
| Brealloc |
| #ifdef KR_headers |
| (b, k) Bigint *b; int k; |
| #else |
| (Bigint * b, int k) |
| #endif |
| { |
| if (b == NULL) |
| return Balloc(k); |
| if (b->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<<BIGINT_MINIMUM_K); |
| /* The test is <= so as to allow room for the final '\0'. */ |
| for(result_k = BIGINT_MINIMUM_K; BIGINT_HEADER_SIZE + j <= i; |
| j <<= 1) result_k++; |
| if (!result || result_k > 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 */ |