diff options
Diffstat (limited to 'libc/stdlib/strtod.c')
-rw-r--r-- | libc/stdlib/strtod.c | 2590 |
1 files changed, 2590 insertions, 0 deletions
diff --git a/libc/stdlib/strtod.c b/libc/stdlib/strtod.c new file mode 100644 index 0000000..7fb7112 --- /dev/null +++ b/libc/stdlib/strtod.c @@ -0,0 +1,2590 @@ +/* $NetBSD: strtod.c,v 1.45.2.1 2005/04/19 13:35:54 tron Exp $ */ + +/**************************************************************** + * + * The author of this software is David M. Gay. + * + * Copyright (c) 1991 by AT&T. + * + * Permission to use, copy, modify, and distribute this software for any + * purpose without fee is hereby granted, provided that this entire notice + * is included in all copies of any software which is or includes a copy + * or modification of this software and in all copies of the supporting + * documentation for such software. + * + * THIS SOFTWARE IS BEING PROVIDED "AS IS", WITHOUT ANY EXPRESS OR IMPLIED + * WARRANTY. IN PARTICULAR, NEITHER THE AUTHOR NOR AT&T MAKES ANY + * REPRESENTATION OR WARRANTY OF ANY KIND CONCERNING THE MERCHANTABILITY + * OF THIS SOFTWARE OR ITS FITNESS FOR ANY PARTICULAR PURPOSE. + * + ***************************************************************/ + +/* Please send bug reports to + David M. Gay + AT&T Bell Laboratories, Room 2C-463 + 600 Mountain Avenue + Murray Hill, NJ 07974-2070 + U.S.A. + dmg@research.att.com or research!dmg + */ + +/* strtod for IEEE-, VAX-, and IBM-arithmetic machines. + * + * This strtod returns a nearest machine number to the input decimal + * string (or sets errno to ERANGE). With IEEE arithmetic, ties are + * broken by the IEEE round-even rule. Otherwise ties are broken by + * biased rounding (add half and chop). + * + * Inspired loosely by William D. Clinger's paper "How to Read Floating + * Point Numbers Accurately" [Proc. ACM SIGPLAN '90, pp. 92-101]. + * + * Modifications: + * + * 1. We only require IEEE, IBM, or VAX double-precision + * arithmetic (not IEEE double-extended). + * 2. We get by with floating-point arithmetic in a case that + * Clinger missed -- when we're computing d * 10^n + * for a small integer d and the integer n is not too + * much larger than 22 (the maximum integer k for which + * we can represent 10^k exactly), we may be able to + * compute (d*10^k) * 10^(e-k) with just one roundoff. + * 3. Rather than a bit-at-a-time adjustment of the binary + * result in the hard case, we use floating-point + * arithmetic to determine the adjustment to within + * one bit; only in really hard cases do we need to + * compute a second residual. + * 4. Because of 3., we don't need a large table of powers of 10 + * for ten-to-e (just some small tables, e.g. of 10^k + * for 0 <= k <= 22). + */ + +/* + * #define IEEE_LITTLE_ENDIAN for IEEE-arithmetic machines where the least + * significant byte has the lowest address. + * #define IEEE_BIG_ENDIAN for IEEE-arithmetic machines where the most + * significant byte has the lowest address. + * #define Long int on machines with 32-bit ints and 64-bit longs. + * #define Sudden_Underflow for IEEE-format machines without gradual + * underflow (i.e., that flush to zero on underflow). + * #define IBM for IBM mainframe-style floating-point arithmetic. + * #define VAX for VAX-style floating-point arithmetic. + * #define Unsigned_Shifts if >> does treats its left operand as unsigned. + * #define No_leftright to omit left-right logic in fast floating-point + * computation of dtoa. + * #define Check_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3. + * #define RND_PRODQUOT to use rnd_prod and rnd_quot (assembly routines + * that use extended-precision instructions to compute rounded + * products and quotients) with IBM. + * #define ROUND_BIASED for IEEE-format with biased rounding. + * #define Inaccurate_Divide for IEEE-format with correctly rounded + * products but inaccurate quotients, e.g., for Intel i860. + * #define Just_16 to store 16 bits per 32-bit Long when doing high-precision + * integer arithmetic. Whether this speeds things up or slows things + * down depends on the machine and the number being converted. + * #define KR_headers for old-style C function headers. + * #define Bad_float_h if your system lacks a float.h or if it does not + * define some or all of DBL_DIG, DBL_MAX_10_EXP, DBL_MAX_EXP, + * FLT_RADIX, FLT_ROUNDS, and DBL_MAX. + * #define MALLOC your_malloc, where your_malloc(n) acts like malloc(n) + * if memory is available and otherwise does something you deem + * appropriate. If MALLOC is undefined, malloc will be invoked + * directly -- and assumed always to succeed. + */ + +#ifdef ANDROID_CHANGES +#include <pthread.h> +#define mutex_lock(x) pthread_mutex_lock(x) +#define mutex_unlock(x) pthread_mutex_unlock(x) +#endif + +#include <sys/cdefs.h> +#if defined(LIBC_SCCS) && !defined(lint) +__RCSID("$NetBSD: strtod.c,v 1.45.2.1 2005/04/19 13:35:54 tron Exp $"); +#endif /* LIBC_SCCS and not lint */ + +#define Unsigned_Shifts +#if defined(__m68k__) || defined(__sparc__) || defined(__i386__) || \ + defined(__mips__) || defined(__ns32k__) || defined(__alpha__) || \ + defined(__powerpc__) || defined(__sh__) || defined(__x86_64__) || \ + defined(__hppa__) || \ + (defined(__arm__) && defined(__VFP_FP__)) +#include <endian.h> +#if BYTE_ORDER == BIG_ENDIAN +#define IEEE_BIG_ENDIAN +#else +#define IEEE_LITTLE_ENDIAN +#endif +#endif + +#if defined(__arm__) && !defined(__VFP_FP__) +/* + * Although the CPU is little endian the FP has different + * byte and word endianness. The byte order is still little endian + * but the word order is big endian. + */ +#define IEEE_BIG_ENDIAN +#endif + +#ifdef __vax__ +#define VAX +#endif + +#if defined(__hppa__) || defined(__mips__) || defined(__sh__) +#define NAN_WORD0 0x7ff40000 +#else +#define NAN_WORD0 0x7ff80000 +#endif +#define NAN_WORD1 0 + +#define Long int32_t +#define ULong u_int32_t + +#ifdef DEBUG +#include "stdio.h" +#define Bug(x) {fprintf(stderr, "%s\n", x); exit(1);} +#endif + +#ifdef __cplusplus +#include "malloc.h" +#include "memory.h" +#else +#ifndef KR_headers +#include "stdlib.h" +#include "string.h" +#ifndef ANDROID_CHANGES +#include "locale.h" +#endif /* ANDROID_CHANGES */ +#else +#include "malloc.h" +#include "memory.h" +#endif +#endif +#ifndef ANDROID_CHANGES +#include "extern.h" +#include "reentrant.h" +#endif /* ANDROID_CHANGES */ + +#ifdef MALLOC +#ifdef KR_headers +extern char *MALLOC(); +#else +extern void *MALLOC(size_t); +#endif +#else +#define MALLOC malloc +#endif + +#include "ctype.h" +#include "errno.h" +#include "float.h" + +#ifndef __MATH_H__ +#include "math.h" +#endif + +#ifdef __cplusplus +extern "C" { +#endif + +#ifndef CONST +#ifdef KR_headers +#define CONST /* blank */ +#else +#define CONST const +#endif +#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(IEEE_LITTLE_ENDIAN) + defined(IEEE_BIG_ENDIAN) + defined(VAX) + \ + defined(IBM) != 1 +Exactly one of IEEE_LITTLE_ENDIAN IEEE_BIG_ENDIAN, VAX, or +IBM should be defined. +#endif + +typedef union { + double d; + ULong ul[2]; +} _double; +#define value(x) ((x).d) +#ifdef IEEE_LITTLE_ENDIAN +#define word0(x) ((x).ul[1]) +#define word1(x) ((x).ul[0]) +#else +#define word0(x) ((x).ul[0]) +#define word1(x) ((x).ul[1]) +#endif + +/* The following definition of Storeinc is appropriate for MIPS processors. + * An alternative that might be better on some machines is + * #define Storeinc(a,b,c) (*a++ = b << 16 | c & 0xffff) + */ +#if defined(IEEE_LITTLE_ENDIAN) + defined(VAX) + defined(__arm__) +#define Storeinc(a,b,c) \ + (((u_short *)(void *)a)[1] = \ + (u_short)b, ((u_short *)(void *)a)[0] = (u_short)c, a++) +#else +#define Storeinc(a,b,c) \ + (((u_short *)(void *)a)[0] = \ + (u_short)b, ((u_short *)(void *)a)[1] = (u_short)c, a++) +#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_LITTLE_ENDIAN) + defined(IEEE_BIG_ENDIAN) +#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) +#ifdef KR_headers +extern double rnd_prod(), rnd_quot(); +#else +extern double rnd_prod(double, double), rnd_quot(double, double); +#endif +#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 + +#ifndef Just_16 +/* When Pack_32 is not defined, we store 16 bits per 32-bit Long. + * This makes some inner loops simpler and sometimes saves work + * during multiplications, but it often seems to make things slightly + * slower. Hence the default is now to store 32 bits per Long. + */ +#ifndef Pack_32 +#define Pack_32 +#endif +#endif + +#define Kmax 15 + +#ifdef __cplusplus +extern "C" double strtod(const char *s00, char **se); +extern "C" char *__dtoa(double d, int mode, int ndigits, + int *decpt, int *sign, char **rve); +#endif + + struct +Bigint { + struct Bigint *next; + int k, maxwds, sign, wds; + ULong x[1]; + }; + + typedef struct Bigint Bigint; + + static Bigint *freelist[Kmax+1]; + +#ifdef ANDROID_CHANGES + static pthread_mutex_t freelist_mutex = PTHREAD_MUTEX_INITIALIZER; +#else +#ifdef _REENTRANT + static mutex_t freelist_mutex = MUTEX_INITIALIZER; +#endif +#endif + + static Bigint * +Balloc +#ifdef KR_headers + (k) int k; +#else + (int k) +#endif +{ + int x; + Bigint *rv; + + mutex_lock(&freelist_mutex); + + if ((rv = freelist[k]) != NULL) { + freelist[k] = rv->next; + } + else { + x = 1 << k; + rv = (Bigint *)MALLOC(sizeof(Bigint) + (x-1)*sizeof(Long)); + rv->k = k; + rv->maxwds = x; + } + rv->sign = rv->wds = 0; + + mutex_unlock(&freelist_mutex); + + return rv; + } + + static void +Bfree +#ifdef KR_headers + (v) Bigint *v; +#else + (Bigint *v) +#endif +{ + if (v) { + mutex_lock(&freelist_mutex); + + v->next = freelist[v->k]; + freelist[v->k] = v; + + mutex_unlock(&freelist_mutex); + } + } + +#define Bcopy(x,y) memcpy(&x->sign, &y->sign, \ + y->wds*sizeof(Long) + 2*sizeof(int)) + + static Bigint * +multadd +#ifdef KR_headers + (b, m, a) Bigint *b; int m, a; +#else + (Bigint *b, int m, int a) /* multiply by m and add a */ +#endif +{ + int i, wds; + ULong *x, y; +#ifdef Pack_32 + ULong xi, z; +#endif + Bigint *b1; + + wds = b->wds; + x = b->x; + i = 0; + do { +#ifdef Pack_32 + xi = *x; + y = (xi & 0xffff) * m + a; + z = (xi >> 16) * m + (y >> 16); + a = (int)(z >> 16); + *x++ = (z << 16) + (y & 0xffff); +#else + y = *x * m + a; + a = (int)(y >> 16); + *x++ = y & 0xffff; +#endif + } + while(++i < wds); + if (a) { + if (wds >= b->maxwds) { + b1 = Balloc(b->k+1); + Bcopy(b1, b); + Bfree(b); + b = b1; + } + b->x[wds++] = a; + b->wds = wds; + } + return b; + } + + static Bigint * +s2b +#ifdef KR_headers + (s, nd0, nd, y9) CONST char *s; int nd0, nd; ULong y9; +#else + (CONST char *s, int nd0, int nd, ULong y9) +#endif +{ + Bigint *b; + int i, k; + Long x, y; + + x = (nd + 8) / 9; + for(k = 0, y = 1; x > y; y <<= 1, k++) ; +#ifdef Pack_32 + b = Balloc(k); + b->x[0] = y9; + b->wds = 1; +#else + b = Balloc(k+1); + b->x[0] = y9 & 0xffff; + b->wds = (b->x[1] = y9 >> 16) ? 2 : 1; +#endif + + i = 9; + if (9 < nd0) { + s += 9; + do b = multadd(b, 10, *s++ - '0'); + while(++i < nd0); + s++; + } + else + s += 10; + for(; i < nd; i++) + b = multadd(b, 10, *s++ - '0'); + return b; + } + + static int +hi0bits +#ifdef KR_headers + (x) ULong x; +#else + (ULong x) +#endif +{ + 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) ULong *y; +#else + (ULong *y) +#endif +{ + int k; + ULong 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 + (i) int i; +#else + (int i) +#endif +{ + Bigint *b; + + b = Balloc(1); + b->x[0] = i; + b->wds = 1; + return b; + } + + static Bigint * +mult +#ifdef KR_headers + (a, b) Bigint *a, *b; +#else + (Bigint *a, Bigint *b) +#endif +{ + Bigint *c; + int k, wa, wb, wc; + ULong carry, y, z; + ULong *x, *xa, *xae, *xb, *xbe, *xc, *xc0; +#ifdef Pack_32 + ULong z2; +#endif + + if (a->wds < b->wds) { + c = a; + a = b; + b = c; + } + k = a->k; + wa = a->wds; + wb = b->wds; + wc = wa + wb; + if (wc > a->maxwds) + k++; + c = Balloc(k); + for(x = c->x, xa = x + wc; x < xa; x++) + *x = 0; + xa = a->x; + xae = xa + wa; + xb = b->x; + xbe = xb + wb; + xc0 = c->x; +#ifdef Pack_32 + for(; xb < xbe; xb++, xc0++) { + if ((y = *xb & 0xffff) != 0) { + 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) != 0) { + x = xa; + xc = xc0; + carry = 0; + z2 = *xc; + do { + z = (*x & 0xffff) * y + (*xc >> 16) + carry; + carry = z >> 16; + Storeinc(xc, z, z2); + z2 = (*x++ >> 16) * y + (*xc & 0xffff) + carry; + carry = z2 >> 16; + } + while(x < xae); + *xc = z2; + } + } +#else + for(; xb < xbe; xc0++) { + if (y = *xb++) { + x = xa; + xc = xc0; + carry = 0; + do { + z = *x++ * y + *xc + carry; + carry = z >> 16; + *xc++ = z & 0xffff; + } + while(x < xae); + *xc = carry; + } + } +#endif + for(xc0 = c->x, xc = xc0 + wc; wc > 0 && !*--xc; --wc) ; + c->wds = wc; + return c; + } + + static Bigint *p5s; + + static Bigint * +pow5mult +#ifdef KR_headers + (b, k) Bigint *b; int k; +#else + (Bigint *b, int k) +#endif +{ + Bigint *b1, *p5, *p51; + int i; + static const int p05[3] = { 5, 25, 125 }; + + if ((i = k & 3) != 0) + b = multadd(b, p05[i-1], 0); + + if (!(k = (unsigned int) k >> 2)) + return b; + if (!(p5 = p5s)) { + /* first time */ + p5 = p5s = i2b(625); + p5->next = 0; + } + for(;;) { + if (k & 1) { + b1 = mult(b, p5); + Bfree(b); + b = b1; + } + if (!(k = (unsigned int) k >> 1)) + break; + if (!(p51 = p5->next)) { + p51 = p5->next = mult(p5,p5); + p51->next = 0; + } + p5 = p51; + } + return b; + } + + static Bigint * +lshift +#ifdef KR_headers + (b, k) Bigint *b; int k; +#else + (Bigint *b, int k) +#endif +{ + int i, k1, n, n1; + Bigint *b1; + ULong *x, *x1, *xe, z; + +#ifdef Pack_32 + n = (unsigned int)k >> 5; +#else + n = (unsigned int)k >> 4; +#endif + k1 = b->k; + n1 = n + b->wds + 1; + for(i = b->maxwds; n1 > i; i <<= 1) + k1++; + b1 = Balloc(k1); + x1 = b1->x; + for(i = 0; i < n; i++) + *x1++ = 0; + x = b->x; + xe = x + b->wds; +#ifdef Pack_32 + if (k &= 0x1f) { + k1 = 32 - k; + z = 0; + do { + *x1++ = *x << k | z; + z = *x++ >> k1; + } + while(x < xe); + if ((*x1 = z) != 0) + ++n1; + } +#else + if (k &= 0xf) { + k1 = 16 - k; + z = 0; + do { + *x1++ = *x << k & 0xffff | z; + z = *x++ >> k1; + } + while(x < xe); + if (*x1 = z) + ++n1; + } +#endif + else do + *x1++ = *x++; + while(x < xe); + b1->wds = n1 - 1; + Bfree(b); + return b1; + } + + static int +cmp +#ifdef KR_headers + (a, b) Bigint *a, *b; +#else + (Bigint *a, Bigint *b) +#endif +{ + ULong *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; + } + + static Bigint * +diff +#ifdef KR_headers + (a, b) Bigint *a, *b; +#else + (Bigint *a, Bigint *b) +#endif +{ + Bigint *c; + int i, wa, wb; + Long borrow, y; /* We need signed shifts here. */ + ULong *xa, *xae, *xb, *xbe, *xc; +#ifdef Pack_32 + Long z; +#endif + + i = cmp(a,b); + if (!i) { + c = Balloc(0); + c->wds = 1; + c->x[0] = 0; + return c; + } + if (i < 0) { + c = a; + a = b; + b = c; + i = 1; + } + else + i = 0; + c = Balloc(a->k); + c->sign = i; + wa = a->wds; + xa = a->x; + xae = xa + wa; + wb = b->wds; + xb = b->x; + xbe = xb + wb; + xc = c->x; + borrow = 0; +#ifdef Pack_32 + do { + y = (*xa & 0xffff) - (*xb & 0xffff) + borrow; + borrow = (ULong)y >> 16; + Sign_Extend(borrow, y); + z = (*xa++ >> 16) - (*xb++ >> 16) + borrow; + borrow = (ULong)z >> 16; + Sign_Extend(borrow, z); + Storeinc(xc, z, y); + } + while(xb < xbe); + while(xa < xae) { + y = (*xa & 0xffff) + borrow; + borrow = (ULong)y >> 16; + Sign_Extend(borrow, y); + z = (*xa++ >> 16) + borrow; + borrow = (ULong)z >> 16; + Sign_Extend(borrow, z); + Storeinc(xc, z, y); + } +#else + do { + y = *xa++ - *xb++ + borrow; + borrow = y >> 16; + Sign_Extend(borrow, y); + *xc++ = y & 0xffff; + } + while(xb < xbe); + while(xa < xae) { + y = *xa++ + borrow; + borrow = y >> 16; + Sign_Extend(borrow, y); + *xc++ = y & 0xffff; + } +#endif + while(!*--xc) + wa--; + c->wds = wa; + return c; + } + + static double +ulp +#ifdef KR_headers + (_x) double _x; +#else + (double _x) +#endif +{ + _double x; + Long L; + _double a; + + value(x) = _x; + L = (word0(x) & Exp_mask) - (P-1)*Exp_msk1; +#ifndef Sudden_Underflow + if (L > 0) { +#endif +#ifdef IBM + L |= Exp_msk1 >> 4; +#endif + word0(a) = L; + word1(a) = 0; +#ifndef Sudden_Underflow + } + else { + L = (ULong)-L >> Exp_shift; + if (L < Exp_shift) { + word0(a) = 0x80000 >> L; + word1(a) = 0; + } + else { + word0(a) = 0; + L -= Exp_shift; + word1(a) = L >= 31 ? 1 : 1 << (31 - L); + } + } +#endif + return value(a); + } + + static double +b2d +#ifdef KR_headers + (a, e) Bigint *a; int *e; +#else + (Bigint *a, int *e) +#endif +{ + ULong *xa, *xa0, w, y, z; + int k; + _double d; +#ifdef VAX + ULong d0, d1; +#else +#define d0 word0(d) +#define d1 word1(d) +#endif + + xa0 = a->x; + xa = xa0 + a->wds; + y = *--xa; +#ifdef DEBUG + if (!y) Bug("zero y in b2d"); +#endif + k = hi0bits(y); + *e = 32 - k; +#ifdef Pack_32 + if (k < Ebits) { + d0 = Exp_1 | y >> (Ebits - k); + w = xa > xa0 ? *--xa : 0; + d1 = y << ((32-Ebits) + k) | w >> (Ebits - k); + goto ret_d; + } + z = xa > xa0 ? *--xa : 0; + if (k -= Ebits) { + d0 = Exp_1 | y << k | z >> (32 - k); + y = xa > xa0 ? *--xa : 0; + d1 = z << k | y >> (32 - k); + } + else { + d0 = Exp_1 | y; + d1 = z; + } +#else + if (k < Ebits + 16) { + z = xa > xa0 ? *--xa : 0; + d0 = Exp_1 | y << k - Ebits | z >> Ebits + 16 - k; + w = xa > xa0 ? *--xa : 0; + y = xa > xa0 ? *--xa : 0; + d1 = z << k + 16 - Ebits | w << k - Ebits | y >> 16 + Ebits - k; + goto ret_d; + } + z = xa > xa0 ? *--xa : 0; + w = xa > xa0 ? *--xa : 0; + k -= Ebits + 16; + d0 = Exp_1 | y << k + 16 | z << k | w >> 16 - k; + y = xa > xa0 ? *--xa : 0; + d1 = w << k + 16 | y << k; +#endif + ret_d: +#ifdef VAX + word0(d) = d0 >> 16 | d0 << 16; + word1(d) = d1 >> 16 | d1 << 16; +#else +#undef d0 +#undef d1 +#endif + return value(d); + } + + static Bigint * +d2b +#ifdef KR_headers + (_d, e, bits) double d; int *e, *bits; +#else + (double _d, int *e, int *bits) +#endif +{ + Bigint *b; + int de, i, k; + ULong *x, y, z; + _double d; +#ifdef VAX + ULong d0, d1; +#endif + + value(d) = _d; +#ifdef VAX + d0 = word0(d) >> 16 | word0(d) << 16; + d1 = word1(d) >> 16 | word1(d) << 16; +#else +#define d0 word0(d) +#define d1 word1(d) +#endif + +#ifdef Pack_32 + b = Balloc(1); +#else + b = Balloc(2); +#endif + x = b->x; + + z = d0 & Frac_mask; + d0 &= 0x7fffffff; /* clear sign bit, which we ignore */ +#ifdef Sudden_Underflow + de = (int)(d0 >> Exp_shift); +#ifndef IBM + z |= Exp_msk11; +#endif +#else + if ((de = (int)(d0 >> Exp_shift)) != 0) + z |= Exp_msk1; +#endif +#ifdef Pack_32 + if ((y = d1) != 0) { + if ((k = lo0bits(&y)) != 0) { + x[0] = y | z << (32 - k); + z >>= k; + } + else + x[0] = y; + i = b->wds = (x[1] = z) ? 2 : 1; + } + else { +#ifdef DEBUG + if (!z) + Bug("Zero passed to d2b"); +#endif + k = lo0bits(&z); + x[0] = z; + i = b->wds = 1; + k += 32; + } +#else + if (y = d1) { + if (k = lo0bits(&y)) + if (k >= 16) { + x[0] = y | z << 32 - k & 0xffff; + x[1] = z >> k - 16 & 0xffff; + x[2] = z >> k; + i = 2; + } + else { + x[0] = y & 0xffff; + x[1] = y >> 16 | z << 16 - k & 0xffff; + x[2] = z >> k & 0xffff; + x[3] = z >> k+16; + i = 3; + } + else { + x[0] = y & 0xffff; + x[1] = y >> 16; + x[2] = z & 0xffff; + x[3] = z >> 16; + i = 3; + } + } + else { +#ifdef DEBUG + if (!z) + Bug("Zero passed to d2b"); +#endif + k = lo0bits(&z); + if (k >= 16) { + x[0] = z; + i = 0; + } + else { + x[0] = z & 0xffff; + x[1] = z >> 16; + i = 1; + } + k += 32; + } + while(!x[i]) + --i; + b->wds = i + 1; +#endif +#ifndef Sudden_Underflow + if (de) { +#endif +#ifdef IBM + *e = (de - Bias - (P-1) << 2) + k; + *bits = 4*P + 8 - k - hi0bits(word0(d) & Frac_mask); +#else + *e = de - Bias - (P-1) + k; + *bits = P - k; +#endif +#ifndef Sudden_Underflow + } + else { + *e = de - Bias - (P-1) + 1 + k; +#ifdef Pack_32 + *bits = 32*i - hi0bits(x[i-1]); +#else + *bits = (i+2)*16 - hi0bits(x[i]); +#endif + } +#endif + return b; + } +#undef d0 +#undef d1 + + static double +ratio +#ifdef KR_headers + (a, b) Bigint *a, *b; +#else + (Bigint *a, Bigint *b) +#endif +{ + _double da, db; + int k, ka, kb; + + value(da) = b2d(a, &ka); + value(db) = b2d(b, &kb); +#ifdef Pack_32 + k = ka - kb + 32*(a->wds - b->wds); +#else + k = ka - kb + 16*(a->wds - b->wds); +#endif +#ifdef IBM + if (k > 0) { + word0(da) += (k >> 2)*Exp_msk1; + if (k &= 3) + da *= 1 << k; + } + else { + k = -k; + word0(db) += (k >> 2)*Exp_msk1; + if (k &= 3) + db *= 1 << k; + } +#else + if (k > 0) + word0(da) += k*Exp_msk1; + else { + k = -k; + word0(db) += k*Exp_msk1; + } +#endif + return value(da) / value(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 +static CONST double bigtens[] = { 1e16, 1e32 }; +static CONST double tinytens[] = { 1e-16, 1e-32 }; +#define n_bigtens 2 +#endif +#endif + + double +strtod +#ifdef KR_headers + (s00, se) CONST char *s00; char **se; +#else + (CONST char *s00, char **se) +#endif +{ + int 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; + _double rv, rv0; + Long L; + ULong y, z; + Bigint *bb1, *bd0; + Bigint *bb = NULL, *bd = NULL, *bs = NULL, *delta = NULL;/* pacify gcc */ + +#ifdef ANDROID_CHANGES + CONST char decimal_point = '.'; +#else /* ANDROID_CHANGES */ +#ifndef KR_headers + CONST char decimal_point = localeconv()->decimal_point[0]; +#else + CONST char decimal_point = '.'; +#endif + +#endif /* ANDROID_CHANGES */ + + sign = nz0 = nz = 0; + value(rv) = 0.; + + + for(s = s00; isspace((unsigned char) *s); s++) + ; + + if (*s == '-') { + sign = 1; + s++; + } else if (*s == '+') { + s++; + } + + if (*s == '\0') { + s = s00; + goto ret; + } + + /* "INF" or "INFINITY" */ + if (tolower((unsigned char)*s) == 'i' && strncasecmp(s, "inf", 3) == 0) { + if (strncasecmp(s + 3, "inity", 5) == 0) + s += 8; + else + s += 3; + + value(rv) = HUGE_VAL; + goto ret; + } + +#ifdef IEEE_Arith + /* "NAN" or "NAN(n-char-sequence-opt)" */ + if (tolower((unsigned char)*s) == 'n' && strncasecmp(s, "nan", 3) == 0) { + /* Build a quiet NaN. */ + word0(rv) = NAN_WORD0; + word1(rv) = NAN_WORD1; + s+= 3; + + /* Don't interpret (n-char-sequence-opt), for now. */ + if (*s == '(') { + s0 = s; + for (s++; *s != ')' && *s != '\0'; s++) + ; + if (*s == ')') + s++; /* Skip over closing paren ... */ + else + s = s0; /* ... otherwise go back. */ + } + + goto ret; + } +#endif + + 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 == decimal_point) { + 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; + /* FALLTHROUGH */ + case '+': + c = *++s; + } + if (c >= '0' && c <= '9') { + while(c == '0') + c = *++s; + if (c > '0' && c <= '9') { + L = c - '0'; + s1 = s; + while((c = *++s) >= '0' && c <= '9') + L = 10*L + c - '0'; + if (s - s1 > 8 || L > 19999) + /* Avoid confusion from exponents + * so large that e might overflow. + */ + e = 19999; /* safe for 16 bit ints */ + else + e = (int)L; + 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; + value(rv) = y; + if (k > 9) + value(rv) = tens[k - 9] * value(rv) + z; + bd0 = 0; + 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 + /* value(rv) = */ rounded_product(value(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; + value(rv) *= tens[i]; +#ifdef VAX + /* VAX exponent range is so narrow we must + * worry about overflow here... + */ + vax_ovfl_check: + word0(rv) -= P*Exp_msk1; + /* value(rv) = */ rounded_product(value(rv), + tens[e]); + if ((word0(rv) & Exp_mask) + > Exp_msk1*(DBL_MAX_EXP+Bias-1-P)) + goto ovfl; + word0(rv) += P*Exp_msk1; +#else + /* value(rv) = */ rounded_product(value(rv), + tens[e]); +#endif + goto ret; + } + } +#ifndef Inaccurate_Divide + else if (e >= -Ten_pmax) { + /* value(rv) = */ rounded_quotient(value(rv), + tens[-e]); + goto ret; + } +#endif + } + e1 += nd - k; + + /* Get starting approximation = rv * 10**e1 */ + + if (e1 > 0) { + if ((i = e1 & 15) != 0) + value(rv) *= tens[i]; + if (e1 &= ~15) { + if (e1 > DBL_MAX_10_EXP) { + ovfl: + errno = ERANGE; + value(rv) = HUGE_VAL; + if (bd0) + goto retfree; + goto ret; + } + if ((e1 = (unsigned int)e1 >> 4) != 0) { + for(j = 0; e1 > 1; j++, + e1 = (unsigned int)e1 >> 1) + if (e1 & 1) + value(rv) *= bigtens[j]; + /* The last multiplication could overflow. */ + word0(rv) -= P*Exp_msk1; + value(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) */ + word0(rv) = Big0; + word1(rv) = Big1; + } + else + word0(rv) += P*Exp_msk1; + } + + } + } + else if (e1 < 0) { + e1 = -e1; + if ((i = e1 & 15) != 0) + value(rv) /= tens[i]; + if (e1 &= ~15) { + e1 = (unsigned int)e1 >> 4; + if (e1 >= 1 << n_bigtens) + goto undfl; + for(j = 0; e1 > 1; j++, + e1 = (unsigned int)e1 >> 1) + if (e1 & 1) + value(rv) *= tinytens[j]; + /* The last multiplication could underflow. */ + value(rv0) = value(rv); + value(rv) *= tinytens[j]; + if (!value(rv)) { + value(rv) = 2.*value(rv0); + value(rv) *= tinytens[j]; + if (!value(rv)) { + undfl: + value(rv) = 0.; + errno = ERANGE; + if (bd0) + goto retfree; + goto ret; + } + word0(rv) = Tiny0; + word1(rv) = 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(s0, nd0, nd, y); + + for(;;) { + bd = Balloc(bd0->k); + Bcopy(bd, bd0); + bb = d2b(value(rv), &bbe, &bbbits); /* rv = bb * 2^bbe */ + bs = i2b(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) { + bs = pow5mult(bs, bb5); + bb1 = mult(bs, bb); + Bfree(bb); + bb = bb1; + } + 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(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*/ + word0(rv) = (word0(rv) & Exp_mask) + + Exp_msk1 +#ifdef IBM + | Exp_msk1 >> 4 +#endif + ; + word1(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 + word0(rv) = L | Bndry_mask1; + word1(rv) = 0xffffffff; +#ifdef IBM + goto cont; +#else + break; +#endif + } +#ifndef ROUND_BIASED + if (!(word1(rv) & LSB)) + break; +#endif + if (dsign) + value(rv) += ulp(value(rv)); +#ifndef ROUND_BIASED + else { + value(rv) -= ulp(value(rv)); +#ifndef Sudden_Underflow + if (!value(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)) { + value(rv0) = value(rv); + word0(rv) -= P*Exp_msk1; + adj = aadj1 * ulp(value(rv)); + value(rv) += adj; + if ((word0(rv) & Exp_mask) >= + Exp_msk1*(DBL_MAX_EXP+Bias-P)) { + if (word0(rv0) == Big0 && word1(rv0) == Big1) + goto ovfl; + word0(rv) = Big0; + word1(rv) = Big1; + goto cont; + } + else + word0(rv) += P*Exp_msk1; + } + else { +#ifdef Sudden_Underflow + if ((word0(rv) & Exp_mask) <= P*Exp_msk1) { + value(rv0) = value(rv); + word0(rv) += P*Exp_msk1; + adj = aadj1 * ulp(value(rv)); + value(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; + word0(rv) = Tiny0; + word1(rv) = Tiny1; + goto cont; + } + else + word0(rv) -= P*Exp_msk1; + } + else { + adj = aadj1 * ulp(value(rv)); + value(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(value(rv)); + value(rv) += adj; +#endif + } + z = word0(rv) & Exp_mask; + if (y == z) { + /* Can we stop now? */ + L = 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; + } + cont: + Bfree(bb); + Bfree(bd); + Bfree(bs); + Bfree(delta); + } + retfree: + Bfree(bb); + Bfree(bd); + Bfree(bs); + Bfree(bd0); + Bfree(delta); + ret: + if (se) + /* LINTED interface specification */ + *se = (char *)s; + return sign ? -value(rv) : value(rv); + } + + static int +quorem +#ifdef KR_headers + (b, S) Bigint *b, *S; +#else + (Bigint *b, Bigint *S) +#endif +{ + int n; + Long borrow, y; + ULong carry, q, ys; + ULong *bx, *bxe, *sx, *sxe; +#ifdef Pack_32 + Long z; + ULong si, zs; +#endif + + 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 { +#ifdef Pack_32 + si = *sx++; + ys = (si & 0xffff) * q + carry; + zs = (si >> 16) * q + (ys >> 16); + carry = zs >> 16; + y = (*bx & 0xffff) - (ys & 0xffff) + borrow; + borrow = (ULong)y >> 16; + Sign_Extend(borrow, y); + z = (*bx >> 16) - (zs & 0xffff) + borrow; + borrow = (ULong)z >> 16; + Sign_Extend(borrow, z); + Storeinc(bx, z, y); +#else + ys = *sx++ * q + carry; + carry = ys >> 16; + y = *bx - (ys & 0xffff) + borrow; + borrow = y >> 16; + Sign_Extend(borrow, y); + *bx++ = y & 0xffff; +#endif + } + 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 { +#ifdef Pack_32 + si = *sx++; + ys = (si & 0xffff) + carry; + zs = (si >> 16) + (ys >> 16); + carry = zs >> 16; + y = (*bx & 0xffff) - (ys & 0xffff) + borrow; + borrow = (ULong)y >> 16; + Sign_Extend(borrow, y); + z = (*bx >> 16) - (zs & 0xffff) + borrow; + borrow = (ULong)z >> 16; + Sign_Extend(borrow, z); + Storeinc(bx, z, y); +#else + ys = *sx++ + carry; + carry = ys >> 16; + y = *bx - (ys & 0xffff) + borrow; + borrow = y >> 16; + Sign_Extend(borrow, y); + *bx++ = y & 0xffff; +#endif + } + while(sx <= sxe); + bx = b->x; + bxe = bx + n; + if (!*bxe) { + while(--bxe > bx && !*bxe) + --n; + b->wds = n; + } + } + return q; + } + +/* freedtoa(s) must be used to free values s returned by dtoa + * when MULTIPLE_THREADS is #defined. It should be used in all cases, + * but for consistency with earlier versions of dtoa, it is optional + * when MULTIPLE_THREADS is not defined. + */ + +void +#ifdef KR_headers +freedtoa(s) char *s; +#else +freedtoa(char *s) +#endif +{ + free(s); +} + + + +/* 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 * +__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. + */ + + int bbits, b2, b5, be, dig, i, ieps, ilim0, + j, jj1, k, k0, k_check, leftright, m2, m5, s2, s5, + try_quick; + int ilim = 0, ilim1 = 0, spec_case = 0; /* pacify gcc */ + Long L; +#ifndef Sudden_Underflow + int denorm; + ULong x; +#endif + Bigint *b, *b1, *delta, *mhi, *S; + Bigint *mlo = NULL; /* pacify gcc */ + double ds; + char *s, *s0; + Bigint *result = NULL; + int result_k = 0; + _double d, d2, eps; + + value(d) = _d; + + if (word0(d) & Sign_bit) { + /* set sign for everything, including 0's and NaNs */ + *sign = 1; + 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; + s = +#ifdef IEEE_Arith + !word1(d) && !(word0(d) & 0xfffff) ? "Infinity" : +#endif + "NaN"; + result = Balloc(strlen(s)+1); + s0 = (char *)(void *)result; + strcpy(s0, s); + if (rve) + *rve = +#ifdef IEEE_Arith + s0[3] ? s0 + 8 : +#endif + s0 + 3; + return s0; + } +#endif +#ifdef IBM + value(d) += 0; /* normalize */ +#endif + if (!value(d)) { + *decpt = 1; + result = Balloc(2); + s0 = (char *)(void *)result; + strcpy(s0, "0"); + if (rve) + *rve = s0 + 1; + return s0; + } + + b = d2b(value(d), &be, &bbits); +#ifdef Sudden_Underflow + i = (int)(word0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1)); +#else + if ((i = (int)(word0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1))) != 0) { +#endif + value(d2) = value(d); + word0(d2) &= Frac_mask1; + word0(d2) |= Exp_11; +#ifdef IBM + if (j = 11 - hi0bits(word0(d2) & Frac_mask)) + value(d2) /= 1 << j; +#endif + + /* 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-Bias)*log(2)/log(10) + log10(d2) + * + * This suggests computing an approximation k to log10(d) by + * + * k = (i - Bias)*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 - Bias) by 0.301029995663981; since |i - Bias| <= 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.) + */ + + i -= Bias; +#ifdef IBM + i <<= 2; + i += j; +#endif +#ifndef Sudden_Underflow + denorm = 0; + } + else { + /* d is denormalized */ + + i = bbits + be + (Bias + (P-1) - 1); + x = i > 32 ? word0(d) << (64 - i) | word1(d) >> (i - 32) + : word1(d) << (32 - i); + value(d2) = x; + word0(d2) -= 31*Exp_msk1; /* adjust exponent */ + i -= (Bias + (P-1) - 1) + 1; + denorm = 1; + } +#endif + ds = (value(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 (value(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; + /* FALLTHROUGH */ + case 4: + if (ndigits <= 0) + ndigits = 1; + ilim = ilim1 = i = ndigits; + break; + case 3: + leftright = 0; + /* FALLTHROUGH */ + case 5: + i = ndigits + k + 1; + ilim = i; + ilim1 = i - 1; + if (i <= 0) + i = 1; + } + j = sizeof(ULong); + for(result_k = 0; (int)(sizeof(Bigint) - sizeof(ULong)) + j <= i; + j <<= 1) result_k++; + // this is really a ugly hack, the code uses Balloc + // instead of malloc, but casts the result into a char* + // it seems the only reason to do that is due to the + // complicated way the block size need to be computed + // buuurk.... + result = Balloc(result_k); + s = s0 = (char *)(void *)result; + + if (ilim >= 0 && ilim <= Quick_max && try_quick) { + + /* Try to get by with floating-point arithmetic. */ + + i = 0; + value(d2) = value(d); + k0 = k; + ilim0 = ilim; + ieps = 2; /* conservative */ + if (k > 0) { + ds = tens[k&0xf]; + j = (unsigned int)k >> 4; + if (j & Bletch) { + /* prevent overflows */ + j &= Bletch - 1; + value(d) /= bigtens[n_bigtens-1]; + ieps++; + } + for(; j; j = (unsigned int)j >> 1, i++) + if (j & 1) { + ieps++; + ds *= bigtens[i]; + } + value(d) /= ds; + } + else if ((jj1 = -k) != 0) { + value(d) *= tens[jj1 & 0xf]; + for(j = (unsigned int)jj1 >> 4; j; + j = (unsigned int)j >> 1, i++) + if (j & 1) { + ieps++; + value(d) *= bigtens[i]; + } + } + if (k_check && value(d) < 1. && ilim > 0) { + if (ilim1 <= 0) + goto fast_failed; + ilim = ilim1; + k--; + value(d) *= 10.; + ieps++; + } + value(eps) = ieps*value(d) + 7.; + word0(eps) -= (P-1)*Exp_msk1; + if (ilim == 0) { + S = mhi = 0; + value(d) -= 5.; + if (value(d) > value(eps)) + goto one_digit; + if (value(d) < -value(eps)) + goto no_digits; + goto fast_failed; + } +#ifndef No_leftright + if (leftright) { + /* Use Steele & White method of only + * generating digits needed. + */ + value(eps) = 0.5/tens[ilim-1] - value(eps); + for(i = 0;;) { + L = value(d); + value(d) -= L; + *s++ = '0' + (int)L; + if (value(d) < value(eps)) + goto ret1; + if (1. - value(d) < value(eps)) + goto bump_up; + if (++i >= ilim) + break; + value(eps) *= 10.; + value(d) *= 10.; + } + } + else { +#endif + /* Generate ilim digits, then fix them up. */ + value(eps) *= tens[ilim-1]; + for(i = 1;; i++, value(d) *= 10.) { + L = value(d); + value(d) -= L; + *s++ = '0' + (int)L; + if (i == ilim) { + if (value(d) > 0.5 + value(eps)) + goto bump_up; + else if (value(d) < 0.5 - value(eps)) { + while(*--s == '0'); + s++; + goto ret1; + } + break; + } + } +#ifndef No_leftright + } +#endif + fast_failed: + s = s0; + value(d) = value(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) { + S = mhi = 0; + if (ilim < 0 || value(d) <= 5*ds) + goto no_digits; + goto one_digit; + } + for(i = 1;; i++) { + L = value(d) / ds; + value(d) -= L*ds; +#ifdef Check_FLT_ROUNDS + /* If FLT_ROUNDS == 2, L will usually be high by 1 */ + if (value(d) < 0) { + L--; + value(d) += ds; + } +#endif + *s++ = '0' + (int)L; + if (i == ilim) { + value(d) += value(d); + if (value(d) > ds || (value(d) == ds && L & 1)) { + bump_up: + while(*--s == '9') + if (s == s0) { + k++; + *s = '0'; + break; + } + ++*s++; + } + break; + } + if (!(value(d) *= 10.)) + break; + } + goto ret1; + } + + m2 = b2; + m5 = b5; + mhi = mlo = 0; + 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(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) { + mhi = pow5mult(mhi, m5); + b1 = mult(mhi, b); + Bfree(b); + b = b1; + } + if ((j = b5 - m5) != 0) + b = pow5mult(b, j); + } + else + b = pow5mult(b, b5); + } + S = i2b(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. + */ +#ifdef Pack_32 + if ((i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0x1f) != 0) + i = 32 - i; +#else + if (i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0xf) + i = 16 - i; +#endif + 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. + */ + + mlo = mhi; + if (spec_case) { + mhi = Balloc(mhi->k); + Bcopy(mhi, mlo); + mhi = lshift(mhi, Log2P); + } + + 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); + delta = diff(S, mhi); + jj1 = delta->sign ? 1 : cmp(b, delta); + Bfree(delta); +#ifndef ROUND_BIASED + if (jj1 == 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 (jj1 > 0) { + b = lshift(b, 1); + jj1 = cmp(b, S); + if ((jj1 > 0 || (jj1 == 0 && dig & 1)) + && dig++ == '9') + goto round_9_up; + } + *s++ = dig; + goto ret; + } + if (jj1 > 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(S); + if (mhi) { + if (mlo && mlo != mhi) + Bfree(mlo); + Bfree(mhi); + } + ret1: + Bfree(b); + if (s == s0) { /* don't return empty string */ + *s++ = '0'; + k = 0; + } + *s = 0; + *decpt = k + 1; + if (rve) + *rve = s; + return s0; + } +#ifdef __cplusplus +} +#endif |