From 867338c36ea8094b6c45ed3e081315c654fd3617 Mon Sep 17 00:00:00 2001 From: nobu Date: Thu, 7 Feb 2019 08:53:11 +0000 Subject: Split dtoa.c git-svn-id: svn+ssh://ci.ruby-lang.org/ruby/trunk@67022 b2dd03c8-39d4-4d8f-98ff-823fe69b080e --- util.c | 3423 +--------------------------------------------------------------- 1 file changed, 7 insertions(+), 3416 deletions(-) (limited to 'util.c') diff --git a/util.c b/util.c index 7c83b50b8b..aa8e7ef3f2 100644 --- a/util.c +++ b/util.c @@ -581,3276 +581,6 @@ ruby_getcwd(void) return buf; } -/**************************************************************** - * - * The author of this software is David M. Gay. - * - * Copyright (c) 1991, 2000, 2001 by Lucent Technologies. - * - * 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 LUCENT 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 (dmg at acm dot org, - * with " at " changed at "@" and " dot " changed to "."). */ - -/* On a machine with IEEE extended-precision registers, it is - * necessary to specify double-precision (53-bit) rounding precision - * before invoking strtod or dtoa. If the machine uses (the equivalent - * of) Intel 80x87 arithmetic, the call - * _control87(PC_53, MCW_PC); - * does this with many compilers. Whether this or another call is - * appropriate depends on the compiler; for this to work, it may be - * necessary to #include "float.h" or another system-dependent header - * file. - */ - -/* 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 IBM for IBM mainframe-style floating-point arithmetic. - * #define VAX for VAX-style floating-point arithmetic (D_floating). - * #define No_leftright to omit left-right logic in fast floating-point - * computation of dtoa. - * #define Honor_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3 - * and strtod and dtoa should round accordingly. - * #define Check_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3 - * and Honor_FLT_ROUNDS is not #defined. - * #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 NO_LONG_LONG on machines that do not have a "long long" - * integer type (of >= 64 bits). On such machines, you can - * #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. If long long is available and the name is - * something other than "long long", #define Llong to be the name, - * and if "unsigned Llong" does not work as an unsigned version of - * Llong, #define #ULLong to be the corresponding unsigned type. - * #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. - * #define Omit_Private_Memory to omit logic (added Jan. 1998) for making - * memory allocations from a private pool of memory when possible. - * When used, the private pool is PRIVATE_MEM bytes long: 2304 bytes, - * unless #defined to be a different length. This default length - * suffices to get rid of MALLOC calls except for unusual cases, - * such as decimal-to-binary conversion of a very long string of - * digits. The longest string dtoa can return is about 751 bytes - * long. For conversions by strtod of strings of 800 digits and - * all dtoa conversions in single-threaded executions with 8-byte - * pointers, PRIVATE_MEM >= 7400 appears to suffice; with 4-byte - * pointers, PRIVATE_MEM >= 7112 appears adequate. - * #define INFNAN_CHECK on IEEE systems to cause strtod to check for - * Infinity and NaN (case insensitively). On some systems (e.g., - * some HP systems), it may be necessary to #define NAN_WORD0 - * appropriately -- to the most significant word of a quiet NaN. - * (On HP Series 700/800 machines, -DNAN_WORD0=0x7ff40000 works.) - * When INFNAN_CHECK is #defined and No_Hex_NaN is not #defined, - * strtod also accepts (case insensitively) strings of the form - * NaN(x), where x is a string of hexadecimal digits and spaces; - * if there is only one string of hexadecimal digits, it is taken - * for the 52 fraction bits of the resulting NaN; if there are two - * or more strings of hex digits, the first is for the high 20 bits, - * the second and subsequent for the low 32 bits, with intervening - * white space ignored; but if this results in none of the 52 - * fraction bits being on (an IEEE Infinity symbol), then NAN_WORD0 - * and NAN_WORD1 are used instead. - * #define MULTIPLE_THREADS if the system offers preemptively scheduled - * multiple threads. In this case, you must provide (or suitably - * #define) two locks, acquired by ACQUIRE_DTOA_LOCK(n) and freed - * by FREE_DTOA_LOCK(n) for n = 0 or 1. (The second lock, accessed - * in pow5mult, ensures lazy evaluation of only one copy of high - * powers of 5; omitting this lock would introduce a small - * probability of wasting memory, but would otherwise be harmless.) - * You must also invoke freedtoa(s) to free the value s returned by - * dtoa. You may do so whether or not MULTIPLE_THREADS is #defined. - * #define NO_IEEE_Scale to disable new (Feb. 1997) logic in strtod that - * avoids underflows on inputs whose result does not underflow. - * If you #define NO_IEEE_Scale on a machine that uses IEEE-format - * floating-point numbers and flushes underflows to zero rather - * than implementing gradual underflow, then you must also #define - * Sudden_Underflow. - * #define YES_ALIAS to permit aliasing certain double values with - * arrays of ULongs. This leads to slightly better code with - * some compilers and was always used prior to 19990916, but it - * is not strictly legal and can cause trouble with aggressively - * optimizing compilers (e.g., gcc 2.95.1 under -O2). - * #define USE_LOCALE to use the current locale's decimal_point value. - * #define SET_INEXACT if IEEE arithmetic is being used and extra - * computation should be done to set the inexact flag when the - * result is inexact and avoid setting inexact when the result - * is exact. In this case, dtoa.c must be compiled in - * an environment, perhaps provided by #include "dtoa.c" in a - * suitable wrapper, that defines two functions, - * int get_inexact(void); - * void clear_inexact(void); - * such that get_inexact() returns a nonzero value if the - * inexact bit is already set, and clear_inexact() sets the - * inexact bit to 0. When SET_INEXACT is #defined, strtod - * also does extra computations to set the underflow and overflow - * flags when appropriate (i.e., when the result is tiny and - * inexact or when it is a numeric value rounded to +-infinity). - * #define NO_ERRNO if strtod should not assign errno = ERANGE when - * the result overflows to +-Infinity or underflows to 0. - */ - -#ifdef WORDS_BIGENDIAN -#define IEEE_BIG_ENDIAN -#else -#define IEEE_LITTLE_ENDIAN -#endif - -#ifdef __vax__ -#define VAX -#undef IEEE_BIG_ENDIAN -#undef IEEE_LITTLE_ENDIAN -#endif - -#if defined(__arm__) && !defined(__VFP_FP__) -#define IEEE_BIG_ENDIAN -#undef IEEE_LITTLE_ENDIAN -#endif - -#undef Long -#undef ULong - -#if SIZEOF_INT == 4 -#define Long int -#define ULong unsigned int -#elif SIZEOF_LONG == 4 -#define Long long int -#define ULong unsigned long int -#endif - -#if HAVE_LONG_LONG -#define Llong LONG_LONG -#else -#define NO_LONG_LONG -#endif - -#ifdef DEBUG -#include "stdio.h" -#define Bug(x) {fprintf(stderr, "%s\n", (x)); exit(EXIT_FAILURE);} -#endif - -#include "stdlib.h" -#include "string.h" - -#ifdef USE_LOCALE -#include "locale.h" -#endif - -#ifdef MALLOC -extern void *MALLOC(size_t); -#else -#define MALLOC xmalloc -#endif -#ifdef FREE -extern void FREE(void*); -#else -#define FREE xfree -#endif - -#ifndef Omit_Private_Memory -#ifndef PRIVATE_MEM -#define PRIVATE_MEM 2304 -#endif -#define PRIVATE_mem ((PRIVATE_MEM+sizeof(double)-1)/sizeof(double)) -static double private_mem[PRIVATE_mem], *pmem_next = private_mem; -#endif - -#undef IEEE_Arith -#undef Avoid_Underflow -#ifdef IEEE_BIG_ENDIAN -#define IEEE_Arith -#endif -#ifdef IEEE_LITTLE_ENDIAN -#define IEEE_Arith -#endif - -#ifdef Bad_float_h - -#ifdef IEEE_Arith -#define DBL_DIG 15 -#define DBL_MAX_10_EXP 308 -#define DBL_MAX_EXP 1024 -#define FLT_RADIX 2 -#endif /*IEEE_Arith*/ - -#ifdef IBM -#define DBL_DIG 16 -#define DBL_MAX_10_EXP 75 -#define DBL_MAX_EXP 63 -#define FLT_RADIX 16 -#define DBL_MAX 7.2370055773322621e+75 -#endif - -#ifdef VAX -#define DBL_DIG 16 -#define DBL_MAX_10_EXP 38 -#define DBL_MAX_EXP 127 -#define FLT_RADIX 2 -#define DBL_MAX 1.7014118346046923e+38 -#endif - -#ifndef LONG_MAX -#define LONG_MAX 2147483647 -#endif - -#else /* ifndef Bad_float_h */ -#include "float.h" -#endif /* Bad_float_h */ - -#ifndef __MATH_H__ -#include "math.h" -#endif - -#ifdef __cplusplus -extern "C" { -#if 0 -} /* satisfy cc-mode */ -#endif -#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 L[2]; } U; - -#ifdef YES_ALIAS -typedef double double_u; -# define dval(x) (x) -# ifdef IEEE_LITTLE_ENDIAN -# define word0(x) (((ULong *)&(x))[1]) -# define word1(x) (((ULong *)&(x))[0]) -# else -# define word0(x) (((ULong *)&(x))[0]) -# define word1(x) (((ULong *)&(x))[1]) -# endif -#else -typedef U double_u; -# ifdef IEEE_LITTLE_ENDIAN -# define word0(x) ((x).L[1]) -# define word1(x) ((x).L[0]) -# else -# define word0(x) ((x).L[0]) -# define word1(x) ((x).L[1]) -# endif -# define dval(x) ((x).d) -#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) (((unsigned short *)(a))[1] = (unsigned short)(b), \ -((unsigned short *)(a))[0] = (unsigned short)(c), (a)++) -#else -#define Storeinc(a,b,c) (((unsigned short *)(a))[0] = (unsigned short)(b), \ -((unsigned short *)(a))[1] = (unsigned 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) */ - -#ifdef IEEE_Arith -#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 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 -#ifndef NO_IEEE_Scale -#define Avoid_Underflow -#ifdef Flush_Denorm /* debugging option */ -#undef Sudden_Underflow -#endif -#endif - -#ifndef Flt_Rounds -#ifdef FLT_ROUNDS -#define Flt_Rounds FLT_ROUNDS -#else -#define Flt_Rounds 1 -#endif -#endif /*Flt_Rounds*/ - -#ifdef Honor_FLT_ROUNDS -#define Rounding rounding -#undef Check_FLT_ROUNDS -#define Check_FLT_ROUNDS -#else -#define Rounding Flt_Rounds -#endif - -#else /* ifndef IEEE_Arith */ -#undef Check_FLT_ROUNDS -#undef Honor_FLT_ROUNDS -#undef SET_INEXACT -#undef Sudden_Underflow -#define Sudden_Underflow -#ifdef IBM -#undef Flt_Rounds -#define Flt_Rounds 0 -#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 */ -#undef Flt_Rounds -#define Flt_Rounds 1 -#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 /* IBM, VAX */ -#endif /* IEEE_Arith */ - -#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 - -#ifndef Pack_32 -#define Pack_32 -#endif - -#define FFFFFFFF 0xffffffffUL - -#ifdef NO_LONG_LONG -#undef ULLong -#ifdef Just_16 -#undef Pack_32 -/* 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. - */ -#endif -#else /* long long available */ -#ifndef Llong -#define Llong long long -#endif -#ifndef ULLong -#define ULLong unsigned Llong -#endif -#endif /* NO_LONG_LONG */ - -#define MULTIPLE_THREADS 1 - -#ifndef MULTIPLE_THREADS -#define ACQUIRE_DTOA_LOCK(n) /*nothing*/ -#define FREE_DTOA_LOCK(n) /*nothing*/ -#else -#define ACQUIRE_DTOA_LOCK(n) /*unused right now*/ -#define FREE_DTOA_LOCK(n) /*unused right now*/ -#endif - -#define Kmax 15 - -struct Bigint { - struct Bigint *next; - int k, maxwds, sign, wds; - ULong x[1]; -}; - -typedef struct Bigint Bigint; - -static Bigint *freelist[Kmax+1]; - -static Bigint * -Balloc(int k) -{ - int x; - Bigint *rv; -#ifndef Omit_Private_Memory - size_t len; -#endif - - ACQUIRE_DTOA_LOCK(0); - if (k <= Kmax && (rv = freelist[k]) != 0) { - freelist[k] = rv->next; - } - else { - x = 1 << k; -#ifdef Omit_Private_Memory - rv = (Bigint *)MALLOC(sizeof(Bigint) + (x-1)*sizeof(ULong)); -#else - len = (sizeof(Bigint) + (x-1)*sizeof(ULong) + sizeof(double) - 1) - /sizeof(double); - if (k <= Kmax && pmem_next - private_mem + len <= PRIVATE_mem) { - rv = (Bigint*)pmem_next; - pmem_next += len; - } - else - rv = (Bigint*)MALLOC(len*sizeof(double)); -#endif - rv->k = k; - rv->maxwds = x; - } - FREE_DTOA_LOCK(0); - rv->sign = rv->wds = 0; - return rv; -} - -static void -Bfree(Bigint *v) -{ - if (v) { - if (v->k > Kmax) { - FREE(v); - return; - } - ACQUIRE_DTOA_LOCK(0); - v->next = freelist[v->k]; - freelist[v->k] = v; - FREE_DTOA_LOCK(0); - } -} - -#define Bcopy(x,y) memcpy((char *)&(x)->sign, (char *)&(y)->sign, \ -(y)->wds*sizeof(Long) + 2*sizeof(int)) - -static Bigint * -multadd(Bigint *b, int m, int a) /* multiply by m and add a */ -{ - int i, wds; - ULong *x; -#ifdef ULLong - ULLong carry, y; -#else - ULong carry, y; -#ifdef Pack_32 - ULong xi, z; -#endif -#endif - Bigint *b1; - - wds = b->wds; - x = b->x; - i = 0; - carry = a; - do { -#ifdef ULLong - y = *x * (ULLong)m + carry; - carry = y >> 32; - *x++ = (ULong)(y & FFFFFFFF); -#else -#ifdef Pack_32 - xi = *x; - y = (xi & 0xffff) * m + carry; - z = (xi >> 16) * m + (y >> 16); - carry = z >> 16; - *x++ = (z << 16) + (y & 0xffff); -#else - y = *x * m + carry; - carry = y >> 16; - *x++ = y & 0xffff; -#endif -#endif - } while (++i < wds); - if (carry) { - if (wds >= b->maxwds) { - b1 = Balloc(b->k+1); - Bcopy(b1, b); - Bfree(b); - b = b1; - } - b->x[wds++] = (ULong)carry; - b->wds = wds; - } - return b; -} - -static Bigint * -s2b(const char *s, int nd0, int nd, ULong y9) -{ - 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(register ULong x) -{ - register int k = 0; - - if (!(x & 0xffff0000)) { - k = 16; - x <<= 16; - } - if (!(x & 0xff000000)) { - k += 8; - x <<= 8; - } - if (!(x & 0xf0000000)) { - k += 4; - x <<= 4; - } - if (!(x & 0xc0000000)) { - k += 2; - x <<= 2; - } - if (!(x & 0x80000000)) { - k++; - if (!(x & 0x40000000)) - return 32; - } - return k; -} - -static int -lo0bits(ULong *y) -{ - register int k; - register 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) - return 32; - } - *y = x; - return k; -} - -static Bigint * -i2b(int i) -{ - Bigint *b; - - b = Balloc(1); - b->x[0] = i; - b->wds = 1; - return b; -} - -static Bigint * -mult(Bigint *a, Bigint *b) -{ - Bigint *c; - int k, wa, wb, wc; - ULong *x, *xa, *xae, *xb, *xbe, *xc, *xc0; - ULong y; -#ifdef ULLong - ULLong carry, z; -#else - ULong carry, z; -#ifdef Pack_32 - ULong z2; -#endif -#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 ULLong - for (; xb < xbe; xc0++) { - if ((y = *xb++) != 0) { - x = xa; - xc = xc0; - carry = 0; - do { - z = *x++ * (ULLong)y + *xc + carry; - carry = z >> 32; - *xc++ = (ULong)(z & FFFFFFFF); - } while (x < xae); - *xc = (ULong)carry; - } - } -#else -#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 = (ULong)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 = (ULong)carry; - } - } -#endif -#endif - for (xc0 = c->x, xc = xc0 + wc; wc > 0 && !*--xc; --wc) ; - c->wds = wc; - return c; -} - -static Bigint *p5s; - -static Bigint * -pow5mult(Bigint *b, int k) -{ - Bigint *b1, *p5, *p51; - int i; - static int p05[3] = { 5, 25, 125 }; - - if ((i = k & 3) != 0) - b = multadd(b, p05[i-1], 0); - - if (!(k >>= 2)) - return b; - if (!(p5 = p5s)) { - /* first time */ -#ifdef MULTIPLE_THREADS - ACQUIRE_DTOA_LOCK(1); - if (!(p5 = p5s)) { - p5 = p5s = i2b(625); - p5->next = 0; - } - FREE_DTOA_LOCK(1); -#else - p5 = p5s = i2b(625); - p5->next = 0; -#endif - } - for (;;) { - if (k & 1) { - b1 = mult(b, p5); - Bfree(b); - b = b1; - } - if (!(k >>= 1)) - break; - if (!(p51 = p5->next)) { -#ifdef MULTIPLE_THREADS - ACQUIRE_DTOA_LOCK(1); - if (!(p51 = p5->next)) { - p51 = p5->next = mult(p5,p5); - p51->next = 0; - } - FREE_DTOA_LOCK(1); -#else - p51 = p5->next = mult(p5,p5); - p51->next = 0; -#endif - } - p5 = p51; - } - return b; -} - -static Bigint * -lshift(Bigint *b, int k) -{ - int i, k1, n, n1; - Bigint *b1; - ULong *x, *x1, *xe, z; - -#ifdef Pack_32 - n = k >> 5; -#else - n = k >> 4; -#endif - k1 = b->k; - n1 = n + b->wds + 1; - for (i = b->maxwds; n1 > i; i <<= 1) - k1++; - b1 = Balloc(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(Bigint *a, Bigint *b) -{ - 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; -} - -NO_SANITIZE("unsigned-integer-overflow", static Bigint * diff(Bigint *a, Bigint *b)); -static Bigint * -diff(Bigint *a, Bigint *b) -{ - Bigint *c; - int i, wa, wb; - ULong *xa, *xae, *xb, *xbe, *xc; -#ifdef ULLong - ULLong borrow, y; -#else - ULong borrow, y; -#ifdef Pack_32 - ULong z; -#endif -#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 ULLong - do { - y = (ULLong)*xa++ - *xb++ - borrow; - borrow = y >> 32 & (ULong)1; - *xc++ = (ULong)(y & FFFFFFFF); - } while (xb < xbe); - while (xa < xae) { - y = *xa++ - borrow; - borrow = y >> 32 & (ULong)1; - *xc++ = (ULong)(y & FFFFFFFF); - } -#else -#ifdef Pack_32 - do { - y = (*xa & 0xffff) - (*xb & 0xffff) - borrow; - borrow = (y & 0x10000) >> 16; - z = (*xa++ >> 16) - (*xb++ >> 16) - borrow; - borrow = (z & 0x10000) >> 16; - Storeinc(xc, z, y); - } while (xb < xbe); - while (xa < xae) { - y = (*xa & 0xffff) - borrow; - borrow = (y & 0x10000) >> 16; - z = (*xa++ >> 16) - borrow; - borrow = (z & 0x10000) >> 16; - Storeinc(xc, z, y); - } -#else - do { - y = *xa++ - *xb++ - borrow; - borrow = (y & 0x10000) >> 16; - *xc++ = y & 0xffff; - } while (xb < xbe); - while (xa < xae) { - y = *xa++ - borrow; - borrow = (y & 0x10000) >> 16; - *xc++ = y & 0xffff; - } -#endif -#endif - while (!*--xc) - wa--; - c->wds = wa; - return c; -} - -static double -ulp(double x_) -{ - register Long L; - double_u x, a; - dval(x) = x_; - - L = (word0(x) & Exp_mask) - (P-1)*Exp_msk1; -#ifndef Avoid_Underflow -#ifndef Sudden_Underflow - if (L > 0) { -#endif -#endif -#ifdef IBM - L |= Exp_msk1 >> 4; -#endif - word0(a) = L; - word1(a) = 0; -#ifndef Avoid_Underflow -#ifndef Sudden_Underflow - } - else { - L = -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 -#endif - return dval(a); -} - -static double -b2d(Bigint *a, int *e) -{ - ULong *xa, *xa0, w, y, z; - int k; - double_u 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 dval(d); -} - -static Bigint * -d2b(double d_, int *e, int *bits) -{ - double_u d; - Bigint *b; - int de, k; - ULong *x, y, z; -#ifndef Sudden_Underflow - int i; -#endif -#ifdef VAX - ULong d0, d1; -#endif - dval(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; -#ifndef Sudden_Underflow - i = -#endif - b->wds = (x[1] = z) ? 2 : 1; - } - else { -#ifdef DEBUG - if (!z) - Bug("Zero passed to d2b"); -#endif - k = lo0bits(&z); - x[0] = z; -#ifndef Sudden_Underflow - i = -#endif - 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(Bigint *a, Bigint *b) -{ - double_u da, db; - int k, ka, kb; - - dval(da) = b2d(a, &ka); - dval(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) - dval(da) *= 1 << k; - } - else { - k = -k; - word0(db) += (k >> 2)*Exp_msk1; - if (k &= 3) - dval(db) *= 1 << k; - } -#else - if (k > 0) - word0(da) += k*Exp_msk1; - else { - k = -k; - word0(db) += k*Exp_msk1; - } -#endif - return dval(da) / dval(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 -}; - -static const double -#ifdef IEEE_Arith -bigtens[] = { 1e16, 1e32, 1e64, 1e128, 1e256 }; -static const double tinytens[] = { 1e-16, 1e-32, 1e-64, 1e-128, -#ifdef Avoid_Underflow - 9007199254740992.*9007199254740992.e-256 - /* = 2^106 * 1e-53 */ -#else - 1e-256 -#endif -}; -/* The factor of 2^53 in tinytens[4] helps us avoid setting the underflow */ -/* flag unnecessarily. It leads to a song and dance at the end of strtod. */ -#define Scale_Bit 0x10 -#define n_bigtens 5 -#else -#ifdef IBM -bigtens[] = { 1e16, 1e32, 1e64 }; -static const double tinytens[] = { 1e-16, 1e-32, 1e-64 }; -#define n_bigtens 3 -#else -bigtens[] = { 1e16, 1e32 }; -static const double tinytens[] = { 1e-16, 1e-32 }; -#define n_bigtens 2 -#endif -#endif - -#ifndef IEEE_Arith -#undef INFNAN_CHECK -#endif - -#ifdef INFNAN_CHECK - -#ifndef NAN_WORD0 -#define NAN_WORD0 0x7ff80000 -#endif - -#ifndef NAN_WORD1 -#define NAN_WORD1 0 -#endif - -static int -match(const char **sp, char *t) -{ - int c, d; - const char *s = *sp; - - while (d = *t++) { - if ((c = *++s) >= 'A' && c <= 'Z') - c += 'a' - 'A'; - if (c != d) - return 0; - } - *sp = s + 1; - return 1; -} - -#ifndef No_Hex_NaN -static void -hexnan(double *rvp, const char **sp) -{ - ULong c, x[2]; - const char *s; - int havedig, udx0, xshift; - - x[0] = x[1] = 0; - havedig = xshift = 0; - udx0 = 1; - s = *sp; - while (c = *(const unsigned char*)++s) { - if (c >= '0' && c <= '9') - c -= '0'; - else if (c >= 'a' && c <= 'f') - c += 10 - 'a'; - else if (c >= 'A' && c <= 'F') - c += 10 - 'A'; - else if (c <= ' ') { - if (udx0 && havedig) { - udx0 = 0; - xshift = 1; - } - continue; - } - else if (/*(*/ c == ')' && havedig) { - *sp = s + 1; - break; - } - else - return; /* invalid form: don't change *sp */ - havedig = 1; - if (xshift) { - xshift = 0; - x[0] = x[1]; - x[1] = 0; - } - if (udx0) - x[0] = (x[0] << 4) | (x[1] >> 28); - x[1] = (x[1] << 4) | c; - } - if ((x[0] &= 0xfffff) || x[1]) { - word0(*rvp) = Exp_mask | x[0]; - word1(*rvp) = x[1]; - } -} -#endif /*No_Hex_NaN*/ -#endif /* INFNAN_CHECK */ - -NO_SANITIZE("unsigned-integer-overflow", double ruby_strtod(const char *s00, char **se)); -double -ruby_strtod(const char *s00, char **se) -{ -#ifdef Avoid_Underflow - int scale; -#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, adj; - double_u aadj1, rv, rv0; - Long L; - ULong y, z; - Bigint *bb, *bb1, *bd, *bd0, *bs, *delta; -#ifdef SET_INEXACT - int inexact, oldinexact; -#endif -#ifdef Honor_FLT_ROUNDS - int rounding; -#endif -#ifdef USE_LOCALE - const char *s2; -#endif - - errno = 0; - sign = nz0 = nz = 0; - dval(rv) = 0.; - for (s = s00;;s++) - switch (*s) { - case '-': - sign = 1; - /* no break */ - case '+': - if (*++s) - goto break2; - /* no break */ - case 0: - goto ret0; - case '\t': - case '\n': - case '\v': - case '\f': - case '\r': - case ' ': - continue; - default: - goto break2; - } -break2: - if (*s == '0') { - if (s[1] == 'x' || s[1] == 'X') { - s0 = ++s; - adj = 0; - aadj = 1.0; - nd0 = -4; - - if (!*++s || !(s1 = strchr(hexdigit, *s))) goto ret0; - if (*s == '0') { - while (*++s == '0'); - s1 = strchr(hexdigit, *s); - } - if (s1 != NULL) { - do { - adj += aadj * ((s1 - hexdigit) & 15); - nd0 += 4; - aadj /= 16; - } while (*++s && (s1 = strchr(hexdigit, *s))); - } - - if (*s == '.') { - dsign = 1; - if (!*++s || !(s1 = strchr(hexdigit, *s))) goto ret0; - if (nd0 < 0) { - while (*s == '0') { - s++; - nd0 -= 4; - } - } - for (; *s && (s1 = strchr(hexdigit, *s)); ++s) { - adj += aadj * ((s1 - hexdigit) & 15); - if ((aadj /= 16) == 0.0) { - while (strchr(hexdigit, *++s)); - break; - } - } - } - else { - dsign = 0; - } - - if (*s == 'P' || *s == 'p') { - dsign = 0x2C - *++s; /* +: 2B, -: 2D */ - if (abs(dsign) == 1) s++; - else dsign = 1; - - nd = 0; - c = *s; - if (c < '0' || '9' < c) goto ret0; - do { - nd *= 10; - nd += c; - nd -= '0'; - c = *++s; - /* Float("0x0."+("0"*267)+"1fp2095") */ - if (nd + dsign * nd0 > 2095) { - while ('0' <= c && c <= '9') c = *++s; - break; - } - } while ('0' <= c && c <= '9'); - nd0 += nd * dsign; - } - else { - if (dsign) goto ret0; - } - dval(rv) = ldexp(adj, nd0); - goto ret; - } - 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 < DBL_DIG + 2) - z = 10*z + c - '0'; - nd0 = nd; -#ifdef USE_LOCALE - s1 = localeconv()->decimal_point; - if (c == *s1) { - c = '.'; - if (*++s1) { - s2 = s; - for (;;) { - if (*++s2 != *s1) { - c = 0; - break; - } - if (!*++s1) { - s = s2; - break; - } - } - } - } -#endif - if (c == '.') { - if (!ISDIGIT(s[1])) - goto dig_done; - 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 (nd > DBL_DIG * 4) { - continue; - } - if (c -= '0') { - nf += nz; - for (i = 1; i < nz; i++) - if (nd++ < 9) - y *= 10; - else if (nd <= DBL_DIG + 2) - z *= 10; - if (nd++ < 9) - y = 10*y + c; - else if (nd <= DBL_DIG + 2) - z = 10*z + c; - nz = 0; - } - } - } -dig_done: - e = 0; - if (c == 'e' || c == 'E') { - if (!nd && !nz && !nz0) { - goto ret0; - } - 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') { - 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) { -#ifdef INFNAN_CHECK - /* Check for Nan and Infinity */ - switch (c) { - case 'i': - case 'I': - if (match(&s,"nf")) { - --s; - if (!match(&s,"inity")) - ++s; - word0(rv) = 0x7ff00000; - word1(rv) = 0; - goto ret; - } - break; - case 'n': - case 'N': - if (match(&s, "an")) { - word0(rv) = NAN_WORD0; - word1(rv) = NAN_WORD1; -#ifndef No_Hex_NaN - if (*s == '(') /*)*/ - hexnan(&rv, &s); -#endif - goto ret; - } - } -#endif /* INFNAN_CHECK */ -ret0: - s = s00; - sign = 0; - } - 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 + 2 ? nd : DBL_DIG + 2; - dval(rv) = y; - if (k > 9) { -#ifdef SET_INEXACT - if (k > DBL_DIG) - oldinexact = get_inexact(); -#endif - dval(rv) = tens[k - 9] * dval(rv) + z; - } - bd0 = bb = bd = bs = delta = 0; - if (nd <= DBL_DIG -#ifndef RND_PRODQUOT -#ifndef Honor_FLT_ROUNDS - && Flt_Rounds == 1 -#endif -#endif - ) { - if (!e) - goto ret; - if (e > 0) { - if (e <= Ten_pmax) { -#ifdef VAX - goto vax_ovfl_check; -#else -#ifdef Honor_FLT_ROUNDS - /* round correctly FLT_ROUNDS = 2 or 3 */ - if (sign) { - dval(rv) = -dval(rv); - sign = 0; - } -#endif - /* rv = */ rounded_product(dval(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. - */ -#ifdef Honor_FLT_ROUNDS - /* round correctly FLT_ROUNDS = 2 or 3 */ - if (sign) { - dval(rv) = -dval(rv); - sign = 0; - } -#endif - e -= i; - dval(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; - /* rv = */ rounded_product(dval(rv), tens[e]); - if ((word0(rv) & Exp_mask) - > Exp_msk1*(DBL_MAX_EXP+Bias-1-P)) - goto ovfl; - word0(rv) += P*Exp_msk1; -#else - /* rv = */ rounded_product(dval(rv), tens[e]); -#endif - goto ret; - } - } -#ifndef Inaccurate_Divide - else if (e >= -Ten_pmax) { -#ifdef Honor_FLT_ROUNDS - /* round correctly FLT_ROUNDS = 2 or 3 */ - if (sign) { - dval(rv) = -dval(rv); - sign = 0; - } -#endif - /* rv = */ rounded_quotient(dval(rv), tens[-e]); - goto ret; - } -#endif - } - e1 += nd - k; - -#ifdef IEEE_Arith -#ifdef SET_INEXACT - inexact = 1; - if (k <= DBL_DIG) - oldinexact = get_inexact(); -#endif -#ifdef Avoid_Underflow - scale = 0; -#endif -#ifdef Honor_FLT_ROUNDS - if ((rounding = Flt_Rounds) >= 2) { - if (sign) - rounding = rounding == 2 ? 0 : 2; - else - if (rounding != 2) - rounding = 0; - } -#endif -#endif /*IEEE_Arith*/ - - /* Get starting approximation = rv * 10**e1 */ - - if (e1 > 0) { - if ((i = e1 & 15) != 0) - dval(rv) *= tens[i]; - if (e1 &= ~15) { - if (e1 > DBL_MAX_10_EXP) { -ovfl: -#ifndef NO_ERRNO - errno = ERANGE; -#endif - /* Can't trust HUGE_VAL */ -#ifdef IEEE_Arith -#ifdef Honor_FLT_ROUNDS - switch (rounding) { - case 0: /* toward 0 */ - case 3: /* toward -infinity */ - word0(rv) = Big0; - word1(rv) = Big1; - break; - default: - word0(rv) = Exp_mask; - word1(rv) = 0; - } -#else /*Honor_FLT_ROUNDS*/ - word0(rv) = Exp_mask; - word1(rv) = 0; -#endif /*Honor_FLT_ROUNDS*/ -#ifdef SET_INEXACT - /* set overflow bit */ - dval(rv0) = 1e300; - dval(rv0) *= dval(rv0); -#endif -#else /*IEEE_Arith*/ - word0(rv) = Big0; - word1(rv) = Big1; -#endif /*IEEE_Arith*/ - if (bd0) - goto retfree; - goto ret; - } - e1 >>= 4; - for (j = 0; e1 > 1; j++, e1 >>= 1) - if (e1 & 1) - dval(rv) *= bigtens[j]; - /* The last multiplication could overflow. */ - word0(rv) -= P*Exp_msk1; - dval(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) - dval(rv) /= tens[i]; - if (e1 >>= 4) { - if (e1 >= 1 << n_bigtens) - goto undfl; -#ifdef Avoid_Underflow - if (e1 & Scale_Bit) - scale = 2*P; - for (j = 0; e1 > 0; j++, e1 >>= 1) - if (e1 & 1) - dval(rv) *= tinytens[j]; - if (scale && (j = 2*P + 1 - ((word0(rv) & Exp_mask) - >> Exp_shift)) > 0) { - /* scaled rv is denormal; zap j low bits */ - if (j >= 32) { - word1(rv) = 0; - if (j >= 53) - word0(rv) = (P+2)*Exp_msk1; - else - word0(rv) &= 0xffffffff << (j-32); - } - else - word1(rv) &= 0xffffffff << j; - } -#else - for (j = 0; e1 > 1; j++, e1 >>= 1) - if (e1 & 1) - dval(rv) *= tinytens[j]; - /* The last multiplication could underflow. */ - dval(rv0) = dval(rv); - dval(rv) *= tinytens[j]; - if (!dval(rv)) { - dval(rv) = 2.*dval(rv0); - dval(rv) *= tinytens[j]; -#endif - if (!dval(rv)) { -undfl: - dval(rv) = 0.; -#ifndef NO_ERRNO - errno = ERANGE; -#endif - if (bd0) - goto retfree; - goto ret; - } -#ifndef Avoid_Underflow - word0(rv) = Tiny0; - word1(rv) = Tiny1; - /* The refinement below will clean - * this approximation up. - */ - } -#endif - } - } - - /* 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(dval(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 Honor_FLT_ROUNDS - if (rounding != 1) - bs2++; -#endif -#ifdef Avoid_Underflow - j = bbe - scale; - i = j + bbbits - 1; /* logb(rv) */ - if (i < Emin) /* denormal */ - j += P - Emin; - else - j = P + 1 - bbbits; -#else /*Avoid_Underflow*/ -#ifdef Sudden_Underflow -#ifdef IBM - j = 1 + 4*P - 3 - bbbits + ((bbe + bbbits - 1) & 3); -#else - j = P + 1 - bbbits; -#endif -#else /*Sudden_Underflow*/ - j = bbe; - i = j + bbbits - 1; /* logb(rv) */ - if (i < Emin) /* denormal */ - j += P - Emin; - else - j = P + 1 - bbbits; -#endif /*Sudden_Underflow*/ -#endif /*Avoid_Underflow*/ - bb2 += j; - bd2 += j; -#ifdef Avoid_Underflow - bd2 += scale; -#endif - 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); -#ifdef Honor_FLT_ROUNDS - if (rounding != 1) { - if (i < 0) { - /* Error is less than an ulp */ - if (!delta->x[0] && delta->wds <= 1) { - /* exact */ -#ifdef SET_INEXACT - inexact = 0; -#endif - break; - } - if (rounding) { - if (dsign) { - adj = 1.; - goto apply_adj; - } - } - else if (!dsign) { - adj = -1.; - if (!word1(rv) - && !(word0(rv) & Frac_mask)) { - y = word0(rv) & Exp_mask; -#ifdef Avoid_Underflow - if (!scale || y > 2*P*Exp_msk1) -#else - if (y) -#endif - { - delta = lshift(delta,Log2P); - if (cmp(delta, bs) <= 0) - adj = -0.5; - } - } -apply_adj: -#ifdef Avoid_Underflow - if (scale && (y = word0(rv) & Exp_mask) - <= 2*P*Exp_msk1) - word0(adj) += (2*P+1)*Exp_msk1 - y; -#else -#ifdef Sudden_Underflow - if ((word0(rv) & Exp_mask) <= - P*Exp_msk1) { - word0(rv) += P*Exp_msk1; - dval(rv) += adj*ulp(dval(rv)); - word0(rv) -= P*Exp_msk1; - } - else -#endif /*Sudden_Underflow*/ -#endif /*Avoid_Underflow*/ - dval(rv) += adj*ulp(dval(rv)); - } - break; - } - adj = ratio(delta, bs); - if (adj < 1.) - adj = 1.; - if (adj <= 0x7ffffffe) { - /* adj = rounding ? ceil(adj) : floor(adj); */ - y = adj; - if (y != adj) { - if (!((rounding>>1) ^ dsign)) - y++; - adj = y; - } - } -#ifdef Avoid_Underflow - if (scale && (y = word0(rv) & Exp_mask) <= 2*P*Exp_msk1) - word0(adj) += (2*P+1)*Exp_msk1 - y; -#else -#ifdef Sudden_Underflow - if ((word0(rv) & Exp_mask) <= P*Exp_msk1) { - word0(rv) += P*Exp_msk1; - adj *= ulp(dval(rv)); - if (dsign) - dval(rv) += adj; - else - dval(rv) -= adj; - word0(rv) -= P*Exp_msk1; - goto cont; - } -#endif /*Sudden_Underflow*/ -#endif /*Avoid_Underflow*/ - adj *= ulp(dval(rv)); - if (dsign) - dval(rv) += adj; - else - dval(rv) -= adj; - goto cont; - } -#endif /*Honor_FLT_ROUNDS*/ - - 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 -#ifdef IEEE_Arith -#ifdef Avoid_Underflow - || (word0(rv) & Exp_mask) <= (2*P+1)*Exp_msk1 -#else - || (word0(rv) & Exp_mask) <= Exp_msk1 -#endif -#endif - ) { -#ifdef SET_INEXACT - if (!delta->x[0] && delta->wds <= 1) - inexact = 0; -#endif - break; - } - if (!delta->x[0] && delta->wds <= 1) { - /* exact result */ -#ifdef SET_INEXACT - inexact = 0; -#endif - 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) == ( -#ifdef Avoid_Underflow - (scale && (y = word0(rv) & Exp_mask) <= 2*P*Exp_msk1) - ? (0xffffffff & (0xffffffff << (2*P+1-(y>>Exp_shift)))) : -#endif - 0xffffffff)) { - /*boundary case -- increment exponent*/ - word0(rv) = (word0(rv) & Exp_mask) - + Exp_msk1 -#ifdef IBM - | Exp_msk1 >> 4 -#endif - ; - word1(rv) = 0; -#ifdef Avoid_Underflow - dsign = 0; -#endif - 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 -#ifdef Avoid_Underflow - if (L <= (scale ? (2*P+1)*Exp_msk1 : Exp_msk1)) -#else - if (L <= Exp_msk1) -#endif /*Avoid_Underflow*/ -#endif /*IBM*/ - goto undfl; - L -= Exp_msk1; -#else /*Sudden_Underflow}{*/ -#ifdef Avoid_Underflow - if (scale) { - L = word0(rv) & Exp_mask; - if (L <= (2*P+1)*Exp_msk1) { - if (L > (P+2)*Exp_msk1) - /* round even ==> */ - /* accept rv */ - break; - /* rv = smallest denormal */ - goto undfl; - } - } -#endif /*Avoid_Underflow*/ - L = (word0(rv) & Exp_mask) - Exp_msk1; -#endif /*Sudden_Underflow}}*/ - 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) - dval(rv) += ulp(dval(rv)); -#ifndef ROUND_BIASED - else { - dval(rv) -= ulp(dval(rv)); -#ifndef Sudden_Underflow - if (!dval(rv)) - goto undfl; -#endif - } -#ifdef Avoid_Underflow - dsign = 1 - dsign; -#endif -#endif - break; - } - if ((aadj = ratio(delta, bs)) <= 2.) { - if (dsign) - aadj = dval(aadj1) = 1.; - else if (word1(rv) || word0(rv) & Bndry_mask) { -#ifndef Sudden_Underflow - if (word1(rv) == Tiny1 && !word0(rv)) - goto undfl; -#endif - aadj = 1.; - dval(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; - dval(aadj1) = -aadj; - } - } - else { - aadj *= 0.5; - dval(aadj1) = dsign ? aadj : -aadj; -#ifdef Check_FLT_ROUNDS - switch (Rounding) { - case 2: /* towards +infinity */ - dval(aadj1) -= 0.5; - break; - case 0: /* towards 0 */ - case 3: /* towards -infinity */ - dval(aadj1) += 0.5; - } -#else - if (Flt_Rounds == 0) - dval(aadj1) += 0.5; -#endif /*Check_FLT_ROUNDS*/ - } - y = word0(rv) & Exp_mask; - - /* Check for overflow */ - - if (y == Exp_msk1*(DBL_MAX_EXP+Bias-1)) { - dval(rv0) = dval(rv); - word0(rv) -= P*Exp_msk1; - adj = dval(aadj1) * ulp(dval(rv)); - dval(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 Avoid_Underflow - if (scale && y <= 2*P*Exp_msk1) { - if (aadj <= 0x7fffffff) { - if ((z = (int)aadj) <= 0) - z = 1; - aadj = z; - dval(aadj1) = dsign ? aadj : -aadj; - } - word0(aadj1) += (2*P+1)*Exp_msk1 - y; - } - adj = dval(aadj1) * ulp(dval(rv)); - dval(rv) += adj; -#else -#ifdef Sudden_Underflow - if ((word0(rv) & Exp_mask) <= P*Exp_msk1) { - dval(rv0) = dval(rv); - word0(rv) += P*Exp_msk1; - adj = dval(aadj1) * ulp(dval(rv)); - dval(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 = dval(aadj1) * ulp(dval(rv)); - dval(rv) += adj; - } -#else /*Sudden_Underflow*/ - /* 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.) { - dval(aadj1) = (double)(int)(aadj + 0.5); - if (!dsign) - dval(aadj1) = -dval(aadj1); - } - adj = dval(aadj1) * ulp(dval(rv)); - dval(rv) += adj; -#endif /*Sudden_Underflow*/ -#endif /*Avoid_Underflow*/ - } - z = word0(rv) & Exp_mask; -#ifndef SET_INEXACT -#ifdef Avoid_Underflow - if (!scale) -#endif - if (y == z) { - /* Can we stop now? */ - L = (Long)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; - } -#endif -cont: - Bfree(bb); - Bfree(bd); - Bfree(bs); - Bfree(delta); - } -#ifdef SET_INEXACT - if (inexact) { - if (!oldinexact) { - word0(rv0) = Exp_1 + (70 << Exp_shift); - word1(rv0) = 0; - dval(rv0) += 1.; - } - } - else if (!oldinexact) - clear_inexact(); -#endif -#ifdef Avoid_Underflow - if (scale) { - word0(rv0) = Exp_1 - 2*P*Exp_msk1; - word1(rv0) = 0; - dval(rv) *= dval(rv0); -#ifndef NO_ERRNO - /* try to avoid the bug of testing an 8087 register value */ - if (word0(rv) == 0 && word1(rv) == 0) - errno = ERANGE; -#endif - } -#endif /* Avoid_Underflow */ -#ifdef SET_INEXACT - if (inexact && !(word0(rv) & Exp_mask)) { - /* set underflow bit */ - dval(rv0) = 1e-300; - dval(rv0) *= dval(rv0); - } -#endif -retfree: - Bfree(bb); - Bfree(bd); - Bfree(bs); - Bfree(bd0); - Bfree(delta); -ret: - if (se) - *se = (char *)s; - return sign ? -dval(rv) : dval(rv); -} - -NO_SANITIZE("unsigned-integer-overflow", static int quorem(Bigint *b, Bigint *S)); -static int -quorem(Bigint *b, Bigint *S) -{ - int n; - ULong *bx, *bxe, q, *sx, *sxe; -#ifdef ULLong - ULLong borrow, carry, y, ys; -#else - ULong borrow, carry, y, ys; -#ifdef Pack_32 - ULong si, z, zs; -#endif -#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 ULLong - ys = *sx++ * (ULLong)q + carry; - carry = ys >> 32; - y = *bx - (ys & FFFFFFFF) - borrow; - borrow = y >> 32 & (ULong)1; - *bx++ = (ULong)(y & FFFFFFFF); -#else -#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 = (y & 0x10000) >> 16; - z = (*bx >> 16) - (zs & 0xffff) - borrow; - borrow = (z & 0x10000) >> 16; - Storeinc(bx, z, y); -#else - ys = *sx++ * q + carry; - carry = ys >> 16; - y = *bx - (ys & 0xffff) - borrow; - borrow = (y & 0x10000) >> 16; - *bx++ = y & 0xffff; -#endif -#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 ULLong - ys = *sx++ + carry; - carry = ys >> 32; - y = *bx - (ys & FFFFFFFF) - borrow; - borrow = y >> 32 & (ULong)1; - *bx++ = (ULong)(y & FFFFFFFF); -#else -#ifdef Pack_32 - si = *sx++; - ys = (si & 0xffff) + carry; - zs = (si >> 16) + (ys >> 16); - carry = zs >> 16; - y = (*bx & 0xffff) - (ys & 0xffff) - borrow; - borrow = (y & 0x10000) >> 16; - z = (*bx >> 16) - (zs & 0xffff) - borrow; - borrow = (z & 0x10000) >> 16; - Storeinc(bx, z, y); -#else - ys = *sx++ + carry; - carry = ys >> 16; - y = *bx - (ys & 0xffff) - borrow; - borrow = (y & 0x10000) >> 16; - *bx++ = y & 0xffff; -#endif -#endif - } while (sx <= sxe); - bx = b->x; - bxe = bx + n; - if (!*bxe) { - while (--bxe > bx && !*bxe) - --n; - b->wds = n; - } - } - return q; -} - -#ifndef MULTIPLE_THREADS -static char *dtoa_result; -#endif - -#ifndef MULTIPLE_THREADS -static char * -rv_alloc(int i) -{ - return dtoa_result = xmalloc(i); -} -#else -#define rv_alloc(i) xmalloc(i) -#endif - -static char * -nrv_alloc(const char *s, char **rve, size_t n) -{ - char *rv, *t; - - t = rv = rv_alloc(n); - while ((*t = *s++) != 0) t++; - if (rve) - *rve = t; - return rv; -} - -#define rv_strdup(s, rve) nrv_alloc((s), (rve), strlen(s)+1) - -#ifndef MULTIPLE_THREADS -/* 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. - */ - -static void -freedtoa(char *s) -{ - xfree(s); -} -#endif - -static const char INFSTR[] = "Infinity"; -static const char NANSTR[] = "NaN"; -static const char ZEROSTR[] = "0"; - -/* 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. 112-126]. - * - * 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 * -ruby_dtoa(double d_, int mode, int ndigits, int *decpt, int *sign, char **rve) -{ - /* 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. - 4,5 ==> similar to 2 and 3, respectively, but (in - round-nearest mode) with the tests of mode 0 to - possibly return a shorter string that rounds to d. - With IEEE arithmetic and compilation with - -DHonor_FLT_ROUNDS, modes 4 and 5 behave the same - as modes 2 and 3 when FLT_ROUNDS != 1. - 6-9 ==> Debugging modes similar to mode - 4: 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, ilim, ilim0, ilim1, - j, j1, k, k0, k_check, leftright, m2, m5, s2, s5, - spec_case, try_quick, half = 0; - Long L; -#ifndef Sudden_Underflow - int denorm; - ULong x; -#endif - Bigint *b, *b1, *delta, *mlo = 0, *mhi = 0, *S; - double ds; - double_u d, d2, eps; - char *s, *s0; -#ifdef Honor_FLT_ROUNDS - int rounding; -#endif -#ifdef SET_INEXACT - int inexact, oldinexact; -#endif - - dval(d) = d_; - -#ifndef MULTIPLE_THREADS - if (dtoa_result) { - freedtoa(dtoa_result); - dtoa_result = 0; - } -#endif - - 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; -#ifdef IEEE_Arith - if (!word1(d) && !(word0(d) & 0xfffff)) - return rv_strdup(INFSTR, rve); -#endif - return rv_strdup(NANSTR, rve); - } -#endif -#ifdef IBM - dval(d) += 0; /* normalize */ -#endif - if (!dval(d)) { - *decpt = 1; - return rv_strdup(ZEROSTR, rve); - } - -#ifdef SET_INEXACT - try_quick = oldinexact = get_inexact(); - inexact = 1; -#endif -#ifdef Honor_FLT_ROUNDS - if ((rounding = Flt_Rounds) >= 2) { - if (*sign) - rounding = rounding == 2 ? 0 : 2; - else - if (rounding != 2) - rounding = 0; - } -#endif - - b = d2b(dval(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 - dval(d2) = dval(d); - word0(d2) &= Frac_mask1; - word0(d2) |= Exp_11; -#ifdef IBM - if (j = 11 - hi0bits(word0(d2) & Frac_mask)) - dval(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); - dval(d2) = x; - word0(d2) -= 31*Exp_msk1; /* adjust exponent */ - i -= (Bias + (P-1) - 1) + 1; - denorm = 1; - } -#endif - ds = (dval(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 (dval(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; - -#ifndef SET_INEXACT -#ifdef Check_FLT_ROUNDS - try_quick = Rounding == 1; -#else - try_quick = 1; -#endif -#endif /*SET_INEXACT*/ - - if (mode > 5) { - mode -= 4; - try_quick = 0; - } - leftright = 1; - ilim = ilim1 = -1; - switch (mode) { - case 0: - case 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; - } - s = s0 = rv_alloc(i+1); - -#ifdef Honor_FLT_ROUNDS - if (mode > 1 && rounding != 1) - leftright = 0; -#endif - - if (ilim >= 0 && ilim <= Quick_max && try_quick) { - - /* Try to get by with floating-point arithmetic. */ - - i = 0; - dval(d2) = dval(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; - dval(d) /= bigtens[n_bigtens-1]; - ieps++; - } - for (; j; j >>= 1, i++) - if (j & 1) { - ieps++; - ds *= bigtens[i]; - } - dval(d) /= ds; - } - else if ((j1 = -k) != 0) { - dval(d) *= tens[j1 & 0xf]; - for (j = j1 >> 4; j; j >>= 1, i++) - if (j & 1) { - ieps++; - dval(d) *= bigtens[i]; - } - } - if (k_check && dval(d) < 1. && ilim > 0) { - if (ilim1 <= 0) - goto fast_failed; - ilim = ilim1; - k--; - dval(d) *= 10.; - ieps++; - } - dval(eps) = ieps*dval(d) + 7.; - word0(eps) -= (P-1)*Exp_msk1; - if (ilim == 0) { - S = mhi = 0; - dval(d) -= 5.; - if (dval(d) > dval(eps)) - goto one_digit; - if (dval(d) < -dval(eps)) - goto no_digits; - goto fast_failed; - } -#ifndef No_leftright - if (leftright) { - /* Use Steele & White method of only - * generating digits needed. - */ - dval(eps) = 0.5/tens[ilim-1] - dval(eps); - for (i = 0;;) { - L = (int)dval(d); - dval(d) -= L; - *s++ = '0' + (int)L; - if (dval(d) < dval(eps)) - goto ret1; - if (1. - dval(d) < dval(eps)) - goto bump_up; - if (++i >= ilim) - break; - dval(eps) *= 10.; - dval(d) *= 10.; - } - } - else { -#endif - /* Generate ilim digits, then fix them up. */ - dval(eps) *= tens[ilim-1]; - for (i = 1;; i++, dval(d) *= 10.) { - L = (Long)(dval(d)); - if (!(dval(d) -= L)) - ilim = i; - *s++ = '0' + (int)L; - if (i == ilim) { - if (dval(d) > 0.5 + dval(eps)) - goto bump_up; - else if (dval(d) < 0.5 - dval(eps)) { - while (*--s == '0') ; - s++; - goto ret1; - } - half = 1; - if ((*(s-1) - '0') & 1) { - goto bump_up; - } - break; - } - } -#ifndef No_leftright - } -#endif -fast_failed: - s = s0; - dval(d) = dval(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 || dval(d) <= 5*ds) - goto no_digits; - goto one_digit; - } - for (i = 1;; i++, dval(d) *= 10.) { - L = (Long)(dval(d) / ds); - dval(d) -= L*ds; -#ifdef Check_FLT_ROUNDS - /* If FLT_ROUNDS == 2, L will usually be high by 1 */ - if (dval(d) < 0) { - L--; - dval(d) += ds; - } -#endif - *s++ = '0' + (int)L; - if (!dval(d)) { -#ifdef SET_INEXACT - inexact = 0; -#endif - break; - } - if (i == ilim) { -#ifdef Honor_FLT_ROUNDS - if (mode > 1) - switch (rounding) { - case 0: goto ret1; - case 2: goto bump_up; - } -#endif - dval(d) += dval(d); - if (dval(d) > ds || (dval(d) == ds && (L & 1))) { -bump_up: - while (*--s == '9') - if (s == s0) { - k++; - *s = '0'; - break; - } - ++*s++; - } - break; - } - } - goto ret1; - } - - m2 = b2; - m5 = b5; - if (leftright) { - 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 - 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. */ - - spec_case = 0; - if ((mode < 2 || leftright) -#ifdef Honor_FLT_ROUNDS - && rounding == 1 -#endif - ) { - if (!word1(d) && !(word0(d) & Bndry_mask) -#ifndef Sudden_Underflow - && word0(d) & (Exp_mask & ~Exp_msk1) -#endif - ) { - /* The special case */ - b2 += Log2P; - s2 += Log2P; - spec_case = 1; - } - } - - /* 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) != 0) - 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 == 3 || mode == 5)) { - 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); - j1 = delta->sign ? 1 : cmp(b, delta); - Bfree(delta); -#ifndef ROUND_BIASED - if (j1 == 0 && mode != 1 && !(word1(d) & 1) -#ifdef Honor_FLT_ROUNDS - && rounding >= 1 -#endif - ) { - if (dig == '9') - goto round_9_up; - if (j > 0) - dig++; -#ifdef SET_INEXACT - else if (!b->x[0] && b->wds <= 1) - inexact = 0; -#endif - *s++ = dig; - goto ret; - } -#endif - if (j < 0 || (j == 0 && mode != 1 -#ifndef ROUND_BIASED - && !(word1(d) & 1) -#endif - )) { - if (!b->x[0] && b->wds <= 1) { -#ifdef SET_INEXACT - inexact = 0; -#endif - goto accept_dig; - } -#ifdef Honor_FLT_ROUNDS - if (mode > 1) - switch (rounding) { - case 0: goto accept_dig; - case 2: goto keep_dig; - } -#endif /*Honor_FLT_ROUNDS*/ - if (j1 > 0) { - b = lshift(b, 1); - j1 = cmp(b, S); - if ((j1 > 0 || (j1 == 0 && (dig & 1))) && dig++ == '9') - goto round_9_up; - } -accept_dig: - *s++ = dig; - goto ret; - } - if (j1 > 0) { -#ifdef Honor_FLT_ROUNDS - if (!rounding) - goto accept_dig; -#endif - if (dig == '9') { /* possible if i == 1 */ -round_9_up: - *s++ = '9'; - goto roundoff; - } - *s++ = dig + 1; - goto ret; - } -#ifdef Honor_FLT_ROUNDS -keep_dig: -#endif - *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 (!b->x[0] && b->wds <= 1) { -#ifdef SET_INEXACT - inexact = 0; -#endif - goto ret; - } - if (i >= ilim) - break; - b = multadd(b, 10, 0); - } - - /* Round off last digit */ - -#ifdef Honor_FLT_ROUNDS - switch (rounding) { - case 0: goto trimzeros; - case 2: goto roundoff; - } -#endif - 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; - } - if (!half || (*s - '0') & 1) - ++*s; - } - else { - while (*--s == '0') ; - } - s++; -ret: - Bfree(S); - if (mhi) { - if (mlo && mlo != mhi) - Bfree(mlo); - Bfree(mhi); - } -ret1: -#ifdef SET_INEXACT - if (inexact) { - if (!oldinexact) { - word0(d) = Exp_1 + (70 << Exp_shift); - word1(d) = 0; - dval(d) += 1.; - } - } - else if (!oldinexact) - clear_inexact(); -#endif - Bfree(b); - *s = 0; - *decpt = k + 1; - if (rve) - *rve = s; - return s0; -} - void ruby_each_words(const char *str, void (*func)(const char*, int, void*), void *arg) { @@ -3868,149 +598,10 @@ ruby_each_words(const char *str, void (*func)(const char*, int, void*), void *ar } } -/*- - * Copyright (c) 2004-2008 David Schultz - * All rights reserved. - * - * Redistribution and use in source and binary forms, with or without - * modification, are permitted provided that the following conditions - * are met: - * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. - * 2. Redistributions in binary form must reproduce the above copyright - * notice, this list of conditions and the following disclaimer in the - * documentation and/or other materials provided with the distribution. - * - * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND - * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE - * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE - * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE - * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL - * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS - * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) - * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT - * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY - * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF - * SUCH DAMAGE. - */ - -#define DBL_MANH_SIZE 20 -#define DBL_MANL_SIZE 32 -#define DBL_ADJ (DBL_MAX_EXP - 2) -#define SIGFIGS ((DBL_MANT_DIG + 3) / 4 + 1) -#define dexp_get(u) ((int)(word0(u) >> Exp_shift) & ~Exp_msk1) -#define dexp_set(u,v) (word0(u) = (((int)(word0(u)) & ~Exp_mask) | ((v) << Exp_shift))) -#define dmanh_get(u) ((uint32_t)(word0(u) & Frac_mask)) -#define dmanl_get(u) ((uint32_t)word1(u)) - - -/* - * This procedure converts a double-precision number in IEEE format - * into a string of hexadecimal digits and an exponent of 2. Its - * behavior is bug-for-bug compatible with dtoa() in mode 2, with the - * following exceptions: - * - * - An ndigits < 0 causes it to use as many digits as necessary to - * represent the number exactly. - * - The additional xdigs argument should point to either the string - * "0123456789ABCDEF" or the string "0123456789abcdef", depending on - * which case is desired. - * - This routine does not repeat dtoa's mistake of setting decpt - * to 9999 in the case of an infinity or NaN. INT_MAX is used - * for this purpose instead. - * - * Note that the C99 standard does not specify what the leading digit - * should be for non-zero numbers. For instance, 0x1.3p3 is the same - * as 0x2.6p2 is the same as 0x4.cp3. This implementation always makes - * the leading digit a 1. This ensures that the exponent printed is the - * actual base-2 exponent, i.e., ilogb(d). - * - * Inputs: d, xdigs, ndigits - * Outputs: decpt, sign, rve - */ -char * -ruby_hdtoa(double d, const char *xdigs, int ndigits, int *decpt, int *sign, - char **rve) -{ - U u; - char *s, *s0; - int bufsize; - uint32_t manh, manl; - - u.d = d; - if (word0(u) & Sign_bit) { - /* set sign for everything, including 0's and NaNs */ - *sign = 1; - word0(u) &= ~Sign_bit; /* clear sign bit */ - } - else - *sign = 0; - - if (isinf(d)) { /* FP_INFINITE */ - *decpt = INT_MAX; - return rv_strdup(INFSTR, rve); - } - else if (isnan(d)) { /* FP_NAN */ - *decpt = INT_MAX; - return rv_strdup(NANSTR, rve); - } - else if (d == 0.0) { /* FP_ZERO */ - *decpt = 1; - return rv_strdup(ZEROSTR, rve); - } - else if (dexp_get(u)) { /* FP_NORMAL */ - *decpt = dexp_get(u) - DBL_ADJ; - } - else { /* FP_SUBNORMAL */ - u.d *= 5.363123171977039e+154 /* 0x1p514 */; - *decpt = dexp_get(u) - (514 + DBL_ADJ); - } - - if (ndigits == 0) /* dtoa() compatibility */ - ndigits = 1; - - /* - * If ndigits < 0, we are expected to auto-size, so we allocate - * enough space for all the digits. - */ - bufsize = (ndigits > 0) ? ndigits : SIGFIGS; - s0 = rv_alloc(bufsize+1); - - /* Round to the desired number of digits. */ - if (SIGFIGS > ndigits && ndigits > 0) { - float redux = 1.0f; - int offset = 4 * ndigits + DBL_MAX_EXP - 4 - DBL_MANT_DIG; - dexp_set(u, offset); - u.d += redux; - u.d -= redux; - *decpt += dexp_get(u) - offset; - } - - manh = dmanh_get(u); - manl = dmanl_get(u); - *s0 = '1'; - for (s = s0 + 1; s < s0 + bufsize; s++) { - *s = xdigs[(manh >> (DBL_MANH_SIZE - 4)) & 0xf]; - manh = (manh << 4) | (manl >> (DBL_MANL_SIZE - 4)); - manl <<= 4; - } - - /* If ndigits < 0, we are expected to auto-size the precision. */ - if (ndigits < 0) { - for (ndigits = SIGFIGS; s0[ndigits - 1] == '0'; ndigits--) - ; - } - - s = s0 + ndigits; - *s = '\0'; - if (rve != NULL) - *rve = s; - return (s0); -} - -#ifdef __cplusplus -#if 0 -{ /* satisfy cc-mode */ -#endif -} -#endif +#undef strtod +#define strtod ruby_strtod +#undef dtoa +#define dtoa ruby_dtoa +#undef hdtoa +#define hdtoa ruby_hdtoa +#include "missing/dtoa.c" -- cgit v1.2.1