diff options
author | shyouhei <shyouhei@b2dd03c8-39d4-4d8f-98ff-823fe69b080e> | 2008-06-15 13:47:02 +0000 |
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committer | shyouhei <shyouhei@b2dd03c8-39d4-4d8f-98ff-823fe69b080e> | 2008-06-15 13:47:02 +0000 |
commit | 8bc157cbb09bc07347379617915304a7f1c18e77 (patch) | |
tree | 1fb57694dfac495efc19bafede3c6b6dfab19a89 /util.c | |
parent | 79a77c8619b92c73cde17810d8ccc76163f2487f (diff) |
merge revision(s) 16342:
* util.c (ruby_strtod): backported from 1.9. a patch from Satoshi
Nakagawa <psychs at limechat.net> in [ruby-dev:34625].
fixed: [ruby-dev:34623]
git-svn-id: svn+ssh://ci.ruby-lang.org/ruby/branches/ruby_1_8_6@17282 b2dd03c8-39d4-4d8f-98ff-823fe69b080e
Diffstat (limited to 'util.c')
-rw-r--r-- | util.c | 3411 |
1 files changed, 3158 insertions, 253 deletions
@@ -668,288 +668,3193 @@ ruby_getcwd() return buf; } -/* copyright notice for strtod implementation -- + +/**************************************************************** + * + * The author of this software is David M. Gay. + * + * Copyright (c) 1991, 2000, 2001 by Lucent Technologies. * - * Copyright (c) 1988-1993 The Regents of the University of California. - * Copyright (c) 1994 Sun Microsystems, Inc. + * 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. * - * Permission to use, copy, modify, and distribute this - * software and its documentation for any purpose and without - * fee is hereby granted, provided that the above copyright - * notice appear in all copies. The University of California - * makes no representations about the suitability of this - * software for any purpose. It is provided "as is" without - * express or implied warranty. + * 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. */ -#define MDMINEXPT DBL_MIN_10_EXP -#define MDMAXEXPT DBL_MAX_10_EXP - -static const -double powersOf10[] = { /* Table giving binary powers of 10. Entry */ - 10.0, /* is 10^2^i. Used to convert decimal */ - 100.0, /* exponents into floating-point numbers. */ - 1.0e4, - 1.0e8, - 1.0e16, - 1.0e32, - 1.0e64, - 1.0e128, - 1.0e256 -}; - -/* - *---------------------------------------------------------------------- - * - * strtod -- +/* strtod for IEEE-, VAX-, and IBM-arithmetic machines. * - * This procedure converts a floating-point number from an ASCII - * decimal representation to internal double-precision format. + * 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). * - * Results: - * The return value is the double-precision floating-point - * representation of the characters in string. If endPtr isn't - * NULL, then *endPtr is filled in with the address of the - * next character after the last one that was part of the - * floating-point number. + * Inspired loosely by William D. Clinger's paper "How to Read Floating + * Point Numbers Accurately" [Proc. ACM SIGPLAN '90, pp. 92-101]. * - * Side effects: - * None. + * 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). */ -double -ruby_strtod(string, endPtr) - const char *string; /* A decimal ASCII floating-point number, - * optionally preceded by white space. - * Must have form "-I.FE-X", where I is the - * integer part of the mantissa, F is the - * fractional part of the mantissa, and X - * is the exponent. Either of the signs - * may be "+", "-", or omitted. Either I - * or F may be omitted, but both cannot be - * ommitted at once. The decimal - * point isn't necessary unless F is present. - * The "E" may actually be an "e". E and X - * may both be omitted (but not just one). - */ - char **endPtr; /* If non-NULL, store terminating character's - * address here. */ -{ - int sign, expSign = Qfalse; - double fraction = 0.0, dblExp; - const double *d; - register const char *p; - register int c; - int exp = 0; /* Exponent read from "EX" field. */ - int fracExp = 0; /* Exponent that derives from the fractional - * part. Under normal circumstatnces, it is - * the negative of the number of digits in F. - * However, if I is very long, the last digits - * of I get dropped (otherwise a long I with a - * large negative exponent could cause an - * unnecessary overflow on I alone). In this - * case, fracExp is incremented one for each - * dropped digit. */ - int mantSize = 0; /* Number of digits in mantissa. */ - int hasPoint = Qfalse; /* Decimal point exists. */ - int hasDigit = Qfalse; /* I or F exists. */ - const char *pMant; /* Temporarily holds location of mantissa - * in string. */ - const char *pExp; /* Temporarily holds location of exponent - * in string. */ +/* + * #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. + */ - /* - * Strip off leading blanks and check for a sign. - */ +#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 +#endif + +#ifdef DEBUG +#include "stdio.h" +#define Bug(x) {fprintf(stderr, "%s\n", x); exit(1);} +#endif + +#include "stdlib.h" +#include "string.h" + +#ifdef USE_LOCALE +#include "locale.h" +#endif + +#ifdef MALLOC +extern void *MALLOC(size_t); +#else +#define MALLOC malloc +#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 + +#include "errno.h" + +#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" { +#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 +#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 +#ifdef IEEE_LITTLE_ENDIAN +#define word0(x) ((U*)&x)->L[1] +#define word1(x) ((U*)&x)->L[0] +#else +#define word0(x) ((U*)&x)->L[0] +#define word1(x) ((U*)&x)->L[1] +#endif +#define dval(x) ((U*)&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 - errno = 0; - p = string; - while (ISSPACE(*p)) p++; - if (*p == '-') { - sign = Qtrue; - p++; +#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 */ + +#ifndef MULTIPLE_THREADS +#define ACQUIRE_DTOA_LOCK(n) /*nothing*/ +#define FREE_DTOA_LOCK(n) /*nothing*/ +#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 + unsigned int len; +#endif + + ACQUIRE_DTOA_LOCK(0); + if ((rv = freelist[k]) != 0) { + freelist[k] = rv->next; } else { - if (*p == '+') p++; - sign = Qfalse; + 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 (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; +} - fraction = 0.; - exp = 0; +static void +Bfree(Bigint *v) +{ + if (v) { + ACQUIRE_DTOA_LOCK(0); + v->next = freelist[v->k]; + freelist[v->k] = v; + FREE_DTOA_LOCK(0); + } +} - /* - * Count the number of digits in the mantissa - * and also locate the decimal point. - */ +#define Bcopy(x,y) memcpy((char *)&x->sign, (char *)&y->sign, \ +y->wds*sizeof(Long) + 2*sizeof(int)) - for ( ; (c = *p) != '\0'; p++) { - if (!ISDIGIT(c)) { - if (c != '.' || hasPoint || !ISDIGIT(p[1])) { - break; - } - hasPoint = Qtrue; - } - else { - if (hasPoint) { /* already in fractional part */ - fracExp--; - } - if (mantSize) { /* already in mantissa */ - mantSize++; - } - else if (c != '0') { /* have entered mantissa */ - mantSize++; - pMant = p; - } - hasDigit = Qtrue; - } +static Bigint * +multadd(Bigint *b, int m, int a) /* multiply by m and add a */ +{ + int i, wds; +#ifdef ULLong + ULong *x; + ULLong carry, y; +#else + ULong carry, *x, 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++ = 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++] = carry; + b->wds = wds; } + return b; +} - /* - * Now suck up the digits in the mantissa. Use two integers to - * collect 9 digits each (this is faster than using floating-point). - * If the mantissa has more than 18 digits, ignore the extras, since - * they can't affect the value anyway. - */ - - pExp = p; - if (mantSize) { - p = pMant; +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++ = z & FFFFFFFF; + } while (x < xae); + *xc = carry; + } + } +#else +#ifdef Pack_32 + for (; xb < xbe; xb++, xc0++) { + if (y = *xb & 0xffff) { + x = xa; + xc = xc0; + carry = 0; + do { + z = (*x & 0xffff) * y + (*xc & 0xffff) + carry; + carry = z >> 16; + z2 = (*x++ >> 16) * y + (*xc >> 16) + carry; + carry = z2 >> 16; + Storeinc(xc, z2, z); + } while (x < xae); + *xc = carry; + } + if (y = *xb >> 16) { + x = xa; + xc = xc0; + carry = 0; + z2 = *xc; + do { + z = (*x & 0xffff) * y + (*xc >> 16) + carry; + carry = z >> 16; + Storeinc(xc, z, z2); + z2 = (*x++ >> 16) * y + (*xc & 0xffff) + carry; + carry = z2 >> 16; + } while (x < xae); + *xc = z2; + } + } +#else + for (; xb < xbe; xc0++) { + if (y = *xb++) { + x = xa; + xc = xc0; + carry = 0; + do { + z = *x++ * y + *xc + carry; + carry = z >> 16; + *xc++ = z & 0xffff; + } while (x < xae); + *xc = carry; + } + } +#endif +#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; } - if (mantSize > 18) { - fracExp += (mantSize - 18); - mantSize = 18; + 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; } - if (!hasDigit) { - fraction = 0.0; - p = string; +#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; +} + +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++ = y & FFFFFFFF; + } while (xb < xbe); + while (xa < xae) { + y = *xa++ - borrow; + borrow = y >> 32 & (ULong)1; + *xc++ = 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 a; + + 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 { - double frac1, frac2; - frac1 = 0; - for ( ; mantSize > 9; mantSize -= 1) { - c = *p; - p += 1; - if (c == '.') { - c = *p; - p += 1; - } - frac1 = 10*frac1 + (c - '0'); - } - frac2 = 0; - for (; mantSize > 0; mantSize -= 1) { - c = *p; - p += 1; - if (c == '.') { - c = *p; - p += 1; - } - frac2 = 10*frac2 + (c - '0'); - } + 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); +} - /* - * Skim off the exponent. - */ - - p = pExp; - if ((*p == 'E') || (*p == 'e')) { - p++; - if (*p == '-') { - expSign = Qtrue; - p++; - } - else { - if (*p == '+') { - p++; - } - expSign = Qfalse; - } - if (ISDIGIT(*p)) { - do { - exp = exp * 10 + (*p++ - '0'); - } - while (ISDIGIT(*p)); - } - else { - p = pExp; - } - } - if (expSign) { - exp = fracExp - exp; - } - else { - exp = fracExp + exp; - } +static double +b2d(Bigint *a, int *e) +{ + 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 - /* - * Generate a floating-point number that represents the exponent. - * Do this by processing the exponent one bit at a time to combine - * many powers of 2 of 10. Then combine the exponent with the - * fraction. - */ - - if (exp >= MDMAXEXPT) { - errno = ERANGE; - fraction = HUGE_VAL; - goto ret; - } - else if (exp < MDMINEXPT) { - errno = ERANGE; - fraction = 0.0; - goto ret; - } - fracExp = exp; - exp += 9; - if (exp < 0) { - expSign = Qtrue; - exp = -exp; - } - else { - expSign = Qfalse; - } - dblExp = 1.0; - for (d = powersOf10; exp != 0; exp >>= 1, d += 1) { - if (exp & 01) { - dblExp *= *d; - } - } - if (expSign) { - frac1 /= dblExp; - } - else { - frac1 *= dblExp; - } - exp = fracExp; - if (exp < 0) { - expSign = Qtrue; - exp = -exp; - } - else { - expSign = Qfalse; - } - dblExp = 1.0; - for (d = powersOf10; exp != 0; exp >>= 1, d += 1) { - if (exp & 01) { - dblExp *= *d; - } - } - if (expSign) { - frac2 /= dblExp; - } - else { - frac2 *= dblExp; - } - fraction = frac1 + frac2; + 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) +{ + Bigint *b; + int de, k; + ULong *x, y, z; +#ifndef Sudden_Underflow + int i; +#endif +#ifdef VAX + ULong d0, d1; + 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 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 */ + +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, aadj1, adj, 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 + + 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') { + 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; +#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 == '.') { + 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) { + 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 + 1 ? nd : DBL_DIG + 1; + 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 = 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) { + rv = -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) { + rv = -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) { + rv = -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 = 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 (Rounding) { + 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 /*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 = 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 = aadj) <= 0) + z = 1; + aadj = z; + aadj1 = dsign ? aadj : -aadj; + } + word0(aadj1) += (2*P+1)*Exp_msk1 - y; + } + adj = 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 = 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 = 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.) { + aadj1 = (double)(int)(aadj + 0.5); + if (!dsign) + aadj1 = -aadj1; + } + adj = 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); +} + +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++ = 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++ = 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 + +static char * +rv_alloc(int i) +{ + int j, k, *r; + + j = sizeof(ULong); + for (k = 0; + sizeof(Bigint) - sizeof(ULong) - sizeof(int) + j <= i; + j <<= 1) + k++; + r = (int*)Balloc(k); + *r = k; + return +#ifndef MULTIPLE_THREADS + dtoa_result = +#endif + (char *)(r+1); +} + +static char * +nrv_alloc(char *s, char **rve, int n) +{ + char *rv, *t; + + t = rv = rv_alloc(n); + while ((*t = *s++) != 0) t++; + if (rve) + *rve = t; + return rv; +} + +/* 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 +freedtoa(char *s) +{ + Bigint *b = (Bigint *)((int *)s - 1); + b->maxwds = 1 << (b->k = *(int*)b); + Bfree(b); +#ifndef MULTIPLE_THREADS + if (s == dtoa_result) + dtoa_result = 0; +#endif +} + +/* 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 * +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; + Long L; +#ifndef Sudden_Underflow + int denorm; + ULong x; +#endif + Bigint *b, *b1, *delta, *mlo, *mhi, *S; + double d2, ds, eps; + char *s, *s0; +#ifdef Honor_FLT_ROUNDS + int rounding; +#endif +#ifdef SET_INEXACT + int inexact, oldinexact; +#endif - ret: - if (endPtr != NULL) { - *endPtr = (char *)p; +#ifndef MULTIPLE_THREADS + if (dtoa_result) { + freedtoa(dtoa_result); + dtoa_result = 0; } - if (sign) { - return -fraction; +#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 nrv_alloc("Infinity", rve, 8); +#endif + return nrv_alloc("NaN", rve, 3); + } +#endif +#ifdef IBM + dval(d) += 0; /* normalize */ +#endif + if (!dval(d)) { + *decpt = 1; + return nrv_alloc("0", rve, 1); } - return fraction; + +#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); + +#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 = 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; + } + 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; + mhi = mlo = 0; + 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; + } + ++*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) +{ + const char *end; + int len; + + if (!str) return; + for (; *str; str = end) { + while (ISSPACE(*str) || *str == ',') str++; + if (!*str) break; + end = str; + while (*end && !ISSPACE(*end) && *end != ',') end++; + len = end - str; + (*func)(str, len, arg); + } +} + +#ifdef __cplusplus +} +#endif |