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dtoa.cpp /**************************************************************** * * 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 Bell Laboratories, Room 2C-463 600 Mountain Avenue Murray Hill, NJ 07974-0636 U.S.A. dmg@bell-labs.com */ /* 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_8087 for IEEE-arithmetic machines where the least * significant byte has the lowest address. * #define IEEE_MC68k for IEEE-arithmetic machines where the most * significant byte has the lowest address. * #define 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. */ // Put this before anything else that may import a definition of CONST. CONST from grammar.cpp conflicts with this. #ifdef KDE_USE_FINAL #undef CONST #endif #include <config.h> #include "stdlib.h" #ifdef WORDS_BIGENDIAN #define IEEE_MC68k #else #define IEEE_8087 #endif #define INFNAN_CHECK #include "dtoa.h" #ifndef Long #define Long int #endif #ifndef ULong typedef unsigned Long ULong; #endif #ifdef DEBUG #include "stdio.h" #define Bug(x) {fprintf(stderr, "%s\n", x); exit(1);} #endif #include "string.h" #ifdef USE_LOCALE #include "locale.h" #endif #ifdef MALLOC #ifdef KR_headers extern char *MALLOC(); #else extern void *MALLOC(size_t); #endif #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_MC68k #define IEEE_Arith #endif #ifdef IEEE_8087 #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 #else /* ifndef Bad_float_h */ #include "float.h" #endif /* Bad_float_h */ #ifndef __MATH_H__ #include "math.h" #endif #ifdef __cplusplus extern "C" { #endif #ifndef CONST #ifdef KR_headers #define CONST /* blank */ #else #define CONST const #endif #endif #if defined(IEEE_8087) + defined(IEEE_MC68k) + defined(VAX) + defined(IBM) != 1 Exactly one of IEEE_8087, IEEE_MC68k, VAX, or IBM should be defined. #endif typedef union { double d; ULong L[2]; } U; #ifdef YES_ALIAS #define dval(x) x #ifdef IEEE_8087 #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_8087 #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_8087) + defined(VAX) #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) #ifdef KR_headers extern double rnd_prod(), rnd_quot(); #else extern double rnd_prod(double, double), rnd_quot(double, double); #endif #else #define rounded_product(a,b) a *= b #define rounded_quotient(a,b) a /= b #endif #define Big0 (Frac_mask1 | Exp_msk1*(DBL_MAX_EXP+Bias-1)) #define Big1 0xffffffff #ifndef Pack_32 #define Pack_32 #endif #ifdef KR_headers #define FFFFFFFF ((((unsigned long)0xffff)<<16)|(unsigned long)0xffff) #else #define FFFFFFFF 0xffffffffUL #endif #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 #ifdef KR_headers (k) int k; #else (int k) #endif { int x; Bigint *rv; #ifndef Omit_Private_Memory unsigned int len; #endif ACQUIRE_DTOA_LOCK(0); if ((rv = freelist[k])) { 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 (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 #ifdef KR_headers (v) Bigint *v; #else (Bigint *v) #endif { if (v) { 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 #ifdef KR_headers (b, m, a) Bigint *b; int m, a; #else (Bigint *b, int m, int a) /* multiply by m and add a */ #endif { int i, wds; #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; } static Bigint * s2b #ifdef KR_headers (s, nd0, nd, y9) CONST char *s; int nd0, nd; ULong y9; #else (CONST char *s, int nd0, int nd, ULong y9) #endif { Bigint *b; int i, k; Long x, y; x = (nd + 8) / 9; for(k = 0, y = 1; x > y; y <<= 1, k++) ; #ifdef Pack_32 b = Balloc(k); b->x[0] = y9; b->wds = 1; #else b = Balloc(k+1); b->x[0] = y9 & 0xffff; b->wds = (b->x[1] = y9 >> 16) ? 2 : 1; #endif i = 9; if (9 < nd0) { s += 9; do b = multadd(b, 10, *s++ - '0'); while(++i < nd0); s++; } else s += 10; for(; i < nd; i++) b = multadd(b, 10, *s++ - '0'); return b; } static int hi0bits #ifdef KR_headers (x) register ULong x; #else (register ULong x) #endif { register int k = 0; if (!(x & 0xffff0000)) { k = 16; x <<= 16; } if (!(x & 0xff000000)) { k += 8; x <<= 8; } if (!(x & 0xf0000000)) { k += 4; x <<= 4; } if (!(x & 0xc0000000)) { k += 2; x <<= 2; } if (!(x & 0x80000000)) { k++; if (!(x & 0x40000000)) return 32; } return k; } static int lo0bits #ifdef KR_headers (y) ULong *y; #else (ULong *y) #endif { 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 & 1) return 32; } *y = x; return k; } static Bigint * i2b #ifdef KR_headers (i) int i; #else (int i) #endif { Bigint *b; b = Balloc(1); b->x[0] = i; b->wds = 1; return b; } static Bigint * mult #ifdef KR_headers (a, b) Bigint *a, *b; #else (Bigint *a, Bigint *b) #endif { Bigint *c; int k, wa, wb, wc; ULong *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++)) { 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 #ifdef KR_headers (b, k) Bigint *b; int k; #else (Bigint *b, int k) #endif { Bigint *b1, *p5, *p51; int i; static int p05[3] = { 5, 25, 125 }; if ((i = k & 3)) 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 #ifdef KR_headers (b, k) Bigint *b; int k; #else (Bigint *b, int k) #endif { int i, k1, n, n1; Bigint *b1; ULong *x, *x1, *xe, z; #ifdef Pack_32 n = 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)) ++n1; } #else if (k &= 0xf) { k1 = 16 - k; z = 0; do { *x1++ = *x << k & 0xffff | z; z = *x++ >> k1; } while(x < xe); if (*x1 = z) ++n1; } #endif else do *x1++ = *x++; while(x < xe); b1->wds = n1 - 1; Bfree(b); return b1; } static int cmp #ifdef KR_headers (a, b) Bigint *a, *b; #else (Bigint *a, Bigint *b) #endif { ULong *xa, *xa0, *xb, *xb0; int i, j; i = a->wds; j = b->wds; #ifdef DEBUG if (i > 1 && !a->x[i-1]) Bug("cmp called with a->x[a->wds-1] == 0"); if (j > 1 && !b->x[j-1]) Bug("cmp called with b->x[b->wds-1] == 0"); #endif if (i -= j) return i; xa0 = a->x; xa = xa0 + j; xb0 = b->x; xb = xb0 + j; for(;;) { if (*--xa != *--xb) return *xa < *xb ? -1 : 1; if (xa <= xa0) break; } return 0; } static Bigint * diff #ifdef KR_headers (a, b) Bigint *a, *b; #else (Bigint *a, Bigint *b) #endif { Bigint *c; int i, wa, wb; 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 #ifdef KR_headers (x) double x; #else (double x) #endif { 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 { 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 #ifdef KR_headers (a, e) Bigint *a; int *e; #else (Bigint *a, int *e) #endif { ULong *xa, *xa0, w, y, z; int k; double d; #ifdef VAX ULong d0, d1; #else #define d0 word0(d) #define d1 word1(d) #endif xa0 = a->x; xa = xa0 + a->wds; y = *--xa; #ifdef DEBUG if (!y) Bug("zero y in b2d"); #endif k = hi0bits(y); *e = 32 - k; #ifdef Pack_32 if (k < Ebits) { d0 = Exp_1 | y >> Ebits - k; w = xa > xa0 ? *--xa : 0; d1 = y << (32-Ebits) + k | w >> Ebits - k; goto ret_d; } z = xa > xa0 ? *--xa : 0; if (k -= Ebits) { d0 = Exp_1 | y << k | z >> 32 - k; y = xa > xa0 ? *--xa : 0; d1 = z << k | y >> 32 - k; } else { d0 = Exp_1 | y; d1 = z; } #else if (k < Ebits + 16) { z = xa > xa0 ? *--xa : 0; d0 = Exp_1 | y << k - Ebits | z >> Ebits + 16 - k; w = xa > xa0 ? *--xa : 0; y = xa > xa0 ? *--xa : 0; d1 = z << k + 16 - Ebits | w << k - Ebits | y >> 16 + Ebits - k; goto ret_d; } z = xa > xa0 ? *--xa : 0; w = xa > xa0 ? *--xa : 0; k -= Ebits + 16; d0 = Exp_1 | y << k + 16 | z << k | w >> 16 - k; y = xa > xa0 ? *--xa : 0; d1 = w << k + 16 | y << k; #endif ret_d: #ifdef VAX word0(d) = d0 >> 16 | d0 << 16; word1(d) = d1 >> 16 | d1 << 16; #else #undef d0 #undef d1 #endif return dval(d); } static Bigint * d2b #ifdef KR_headers (d, e, bits) double d; int *e, *bits; #else (double d, int *e, int *bits) #endif { Bigint *b; int de, 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))) z |= Exp_msk1; #endif #ifdef Pack_32 if ((y = d1)) { if ((k = lo0bits(&y))) { 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 #ifdef KR_headers (a, b) Bigint *a, *b; #else (Bigint *a, Bigint *b) #endif { 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 #ifdef KR_headers (sp, t) char **sp, *t; #else (CONST char **sp, CONST char *t) #endif { 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 #ifdef KR_headers (rvp, sp) double *rvp; CONST char **sp; #else (double *rvp, CONST char **sp) #endif { 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 kjs_strtod #ifdef KR_headers (s00, se) CONST char *s00; char **se; #else (CONST char *s00, char **se) #endif { #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 = NULL, *bb1 = NULL, *bd = NULL, *bd0 = NULL, *bs = NULL, *delta = NULL; #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':