| /* -*- Mode: C; tab-width: 8; indent-tabs-mode: t; c-basic-offset: 8 -*- */ |
| /**************************************************************** |
| * |
| * The author of this software is David M. Gay. |
| * |
| * Copyright (c) 1991, 2000, 2001 by Lucent Technologies. |
| * |
| * Permission to use, copy, modify, and distribute this software for any |
| * purpose without fee is hereby granted, provided that this entire notice |
| * is included in all copies of any software which is or includes a copy |
| * or modification of this software and in all copies of the supporting |
| * documentation for such software. |
| * |
| * THIS SOFTWARE IS BEING PROVIDED "AS IS", WITHOUT ANY EXPRESS OR IMPLIED |
| * WARRANTY. IN PARTICULAR, NEITHER THE AUTHOR NOR LUCENT MAKES ANY |
| * REPRESENTATION OR WARRANTY OF ANY KIND CONCERNING THE MERCHANTABILITY |
| * OF THIS SOFTWARE OR ITS FITNESS FOR ANY PARTICULAR PURPOSE. |
| * |
| ***************************************************************/ |
| |
| /* Please send bug reports to David M. Gay (dmg at acm dot org, |
| * with " at " changed at "@" and " dot " changed to "."). */ |
| |
| /* On a machine with IEEE extended-precision registers, it is |
| * necessary to specify double-precision (53-bit) rounding precision |
| * before invoking strtod or dtoa. If the machine uses (the equivalent |
| * of) Intel 80x87 arithmetic, the call |
| * _control87(PC_53, MCW_PC); |
| * does this with many compilers. Whether this or another call is |
| * appropriate depends on the compiler; for this to work, it may be |
| * necessary to #include "float.h" or another system-dependent header |
| * file. |
| */ |
| |
| /* strtod for IEEE-, VAX-, and IBM-arithmetic machines. |
| * |
| * This strtod returns a nearest machine number to the input decimal |
| * string (or sets errno to ERANGE). With IEEE arithmetic, ties are |
| * broken by the IEEE round-even rule. Otherwise ties are broken by |
| * biased rounding (add half and chop). |
| * |
| * Inspired loosely by William D. Clinger's paper "How to Read Floating |
| * Point Numbers Accurately" [Proc. ACM SIGPLAN '90, pp. 92-101]. |
| * |
| * Modifications: |
| * |
| * 1. We only require IEEE, IBM, or VAX double-precision |
| * arithmetic (not IEEE double-extended). |
| * 2. We get by with floating-point arithmetic in a case that |
| * Clinger missed -- when we're computing d * 10^n |
| * for a small integer d and the integer n is not too |
| * much larger than 22 (the maximum integer k for which |
| * we can represent 10^k exactly), we may be able to |
| * compute (d*10^k) * 10^(e-k) with just one roundoff. |
| * 3. Rather than a bit-at-a-time adjustment of the binary |
| * result in the hard case, we use floating-point |
| * arithmetic to determine the adjustment to within |
| * one bit; only in really hard cases do we need to |
| * compute a second residual. |
| * 4. Because of 3., we don't need a large table of powers of 10 |
| * for ten-to-e (just some small tables, e.g. of 10^k |
| * for 0 <= k <= 22). |
| */ |
| |
| /* |
| * #define IEEE_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. Similarly, if you |
| * want something other than the system's free() to be called to |
| * recycle memory acquired from MALLOC, #define FREE to be the |
| * name of the alternate routine. (Unless you #define |
| * NO_GLOBAL_STATE and call destroydtoa, FREE or free is only |
| * called in pathological cases, e.g., in a dtoa call after a dtoa |
| * return in mode 3 with thousands of digits requested.) |
| * #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 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 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. |
| * #define NO_GLOBAL_STATE to avoid defining any non-const global or |
| * static variables. Instead the necessary state is stored in an |
| * opaque struct, DtoaState, a pointer to which must be passed to |
| * every entry point. Two new functions are added to the API: |
| * DtoaState *newdtoa(void); |
| * void destroydtoa(DtoaState *); |
| */ |
| |
| #ifndef Long |
| #define Long long |
| #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 "stdlib.h" |
| #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 FREE |
| #define FREE free |
| #endif |
| |
| #ifndef Omit_Private_Memory |
| #ifndef PRIVATE_MEM |
| #define PRIVATE_MEM 2304 |
| #endif |
| #define PRIVATE_mem ((PRIVATE_MEM+sizeof(double)-1)/sizeof(double)) |
| #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 |
| |
| #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 |
| |
| #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; |
| |
| #define dval(x) ((x).d) |
| #ifdef IEEE_8087 |
| #define word0(x) ((x).L[1]) |
| #define word1(x) ((x).L[0]) |
| #else |
| #define word0(x) ((x).L[0]) |
| #define word1(x) ((x).L[1]) |
| #endif |
| |
| /* 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 7 |
| |
| struct |
| Bigint { |
| struct Bigint *next; |
| int k, maxwds, sign, wds; |
| ULong x[1]; |
| }; |
| |
| typedef struct Bigint Bigint; |
| |
| #ifdef NO_GLOBAL_STATE |
| #ifdef MULTIPLE_THREADS |
| #error "cannot have both NO_GLOBAL_STATE and MULTIPLE_THREADS" |
| #endif |
| struct |
| DtoaState { |
| #define DECLARE_GLOBAL_STATE /* nothing */ |
| #else |
| #define DECLARE_GLOBAL_STATE static |
| #endif |
| |
| DECLARE_GLOBAL_STATE Bigint *freelist[Kmax+1]; |
| DECLARE_GLOBAL_STATE Bigint *p5s; |
| #ifndef Omit_Private_Memory |
| DECLARE_GLOBAL_STATE double private_mem[PRIVATE_mem]; |
| DECLARE_GLOBAL_STATE double *pmem_next |
| #ifndef NO_GLOBAL_STATE |
| = private_mem |
| #endif |
| ; |
| #endif |
| #ifdef NO_GLOBAL_STATE |
| }; |
| typedef struct DtoaState DtoaState; |
| #ifdef KR_headers |
| #define STATE_PARAM state, |
| #define STATE_PARAM_DECL DtoaState *state; |
| #else |
| #define STATE_PARAM DtoaState *state, |
| #endif |
| #define PASS_STATE state, |
| #define GET_STATE(field) (state->field) |
| |
| static DtoaState * |
| newdtoa(void) |
| { |
| DtoaState *state = (DtoaState *) MALLOC(sizeof(DtoaState)); |
| if (state) { |
| memset(state, 0, sizeof(DtoaState)); |
| #ifndef Omit_Private_Memory |
| state->pmem_next = state->private_mem; |
| #endif |
| } |
| return state; |
| } |
| |
| static void |
| destroydtoa |
| #ifdef KR_headers |
| (state) STATE_PARAM_DECL |
| #else |
| (DtoaState *state) |
| #endif |
| { |
| int i; |
| Bigint *v, *next; |
| |
| for (i = 0; i <= Kmax; i++) { |
| for (v = GET_STATE(freelist)[i]; v; v = next) { |
| next = v->next; |
| #ifndef Omit_Private_Memory |
| if ((double*)v < GET_STATE(private_mem) || |
| (double*)v >= GET_STATE(private_mem) + PRIVATE_mem) |
| #endif |
| FREE((void*)v); |
| } |
| } |
| FREE((void *)state); |
| } |
| |
| #else |
| #define STATE_PARAM /* nothing */ |
| #define STATE_PARAM_DECL /* nothing */ |
| #define PASS_STATE /* nothing */ |
| #define GET_STATE(name) name |
| #endif |
| |
| static Bigint * |
| Balloc |
| #ifdef KR_headers |
| (STATE_PARAM k) STATE_PARAM_DECL int k; |
| #else |
| (STATE_PARAM int k) |
| #endif |
| { |
| int x; |
| Bigint *rv; |
| #ifndef Omit_Private_Memory |
| size_t len; |
| #endif |
| |
| ACQUIRE_DTOA_LOCK(0); |
| /* The k > Kmax case does not need ACQUIRE_DTOA_LOCK(0), */ |
| /* but this case seems very unlikely. */ |
| if (k <= Kmax && (rv = GET_STATE(freelist)[k])) |
| GET_STATE(freelist)[k] = rv->next; |
| else { |
| x = 1 << k; |
| #ifdef Omit_Private_Memory |
| rv = (Bigint *)MALLOC(sizeof(Bigint) + (x-1)*sizeof(ULong)); |
| #else |
| len = (sizeof(Bigint) + (x-1)*sizeof(ULong) + sizeof(double) - 1) |
| /sizeof(double); |
| if (k <= Kmax && GET_STATE(pmem_next) - GET_STATE(private_mem) + len <= PRIVATE_mem) { |
| rv = (Bigint*)GET_STATE(pmem_next); |
| GET_STATE(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 |
| (STATE_PARAM v) STATE_PARAM_DECL Bigint *v; |
| #else |
| (STATE_PARAM Bigint *v) |
| #endif |
| { |
| if (v) { |
| if (v->k > Kmax) |
| FREE((void*)v); |
| else { |
| ACQUIRE_DTOA_LOCK(0); |
| v->next = GET_STATE(freelist)[v->k]; |
| GET_STATE(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 |
| (STATE_PARAM b, m, a) STATE_PARAM_DECL Bigint *b; int m, a; |
| #else |
| (STATE_PARAM 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++ = (ULong) y & FFFFFFFF; |
| #else |
| #ifdef Pack_32 |
| xi = *x; |
| y = (xi & 0xffff) * m + carry; |
| z = (xi >> 16) * m + (y >> 16); |
| carry = z >> 16; |
| *x++ = (z << 16) + (y & 0xffff); |
| #else |
| y = *x * m + carry; |
| carry = y >> 16; |
| *x++ = y & 0xffff; |
| #endif |
| #endif |
| } |
| while(++i < wds); |
| if (carry) { |
| if (wds >= b->maxwds) { |
| b1 = Balloc(PASS_STATE b->k+1); |
| Bcopy(b1, b); |
| Bfree(PASS_STATE b); |
| b = b1; |
| } |
| b->x[wds++] = (ULong) carry; |
| b->wds = wds; |
| } |
| return b; |
| } |
| |
| static Bigint * |
| s2b |
| #ifdef KR_headers |
| (STATE_PARAM s, nd0, nd, y9) STATE_PARAM_DECL CONST char *s; int nd0, nd; ULong y9; |
| #else |
| (STATE_PARAM 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(PASS_STATE k); |
| b->x[0] = y9; |
| b->wds = 1; |
| #else |
| b = Balloc(PASS_STATE 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(PASS_STATE b, 10, *s++ - '0'); |
| while(++i < nd0); |
| s++; |
| } |
| else |
| s += 10; |
| for(; i < nd; i++) |
| b = multadd(PASS_STATE 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) |
| return 32; |
| } |
| *y = x; |
| return k; |
| } |
| |
| static Bigint * |
| i2b |
| #ifdef KR_headers |
| (STATE_PARAM i) STATE_PARAM_DECL int i; |
| #else |
| (STATE_PARAM int i) |
| #endif |
| { |
| Bigint *b; |
| |
| b = Balloc(PASS_STATE 1); |
| b->x[0] = i; |
| b->wds = 1; |
| return b; |
| } |
| |
| static Bigint * |
| mult |
| #ifdef KR_headers |
| (STATE_PARAM a, b) STATE_PARAM_DECL Bigint *a, *b; |
| #else |
| (STATE_PARAM 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(PASS_STATE 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++ = (ULong) z & FFFFFFFF; |
| } |
| while(x < xae); |
| *xc = (ULong) 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 * |
| pow5mult |
| #ifdef KR_headers |
| (STATE_PARAM b, k) STATE_PARAM_DECL Bigint *b; int k; |
| #else |
| (STATE_PARAM Bigint *b, int k) |
| #endif |
| { |
| Bigint *b1, *p5, *p51; |
| int i; |
| static CONST int p05[3] = { 5, 25, 125 }; |
| |
| if ((i = k & 3)) |
| b = multadd(PASS_STATE b, p05[i-1], 0); |
| |
| if (!(k >>= 2)) |
| return b; |
| if (!(p5 = GET_STATE(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 = GET_STATE(p5s) = i2b(PASS_STATE 625); |
| p5->next = 0; |
| #endif |
| } |
| for(;;) { |
| if (k & 1) { |
| b1 = mult(PASS_STATE b, p5); |
| Bfree(PASS_STATE 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(PASS_STATE p5,p5); |
| p51->next = 0; |
| #endif |
| } |
| p5 = p51; |
| } |
| return b; |
| } |
| |
| static Bigint * |
| lshift |
| #ifdef KR_headers |
| (STATE_PARAM b, k) STATE_PARAM_DECL Bigint *b; int k; |
| #else |
| (STATE_PARAM 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(PASS_STATE 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(PASS_STATE 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 |
| (STATE_PARAM a, b) STATE_PARAM_DECL Bigint *a, *b; |
| #else |
| (STATE_PARAM 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(PASS_STATE 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(PASS_STATE a->k); |
| c->sign = i; |
| wa = a->wds; |
| xa = a->x; |
| xae = xa + wa; |
| wb = b->wds; |
| xb = b->x; |
| xbe = xb + wb; |
| xc = c->x; |
| borrow = 0; |
| #ifdef ULLong |
| do { |
| y = (ULLong)*xa++ - *xb++ - borrow; |
| borrow = y >> 32 & (ULong)1; |
| *xc++ = (ULong) y & FFFFFFFF; |
| } |
| while(xb < xbe); |
| while(xa < xae) { |
| y = *xa++ - borrow; |
| borrow = y >> 32 & (ULong)1; |
| *xc++ = (ULong) y & FFFFFFFF; |
| } |
| #else |
| #ifdef Pack_32 |
| do { |
| y = (*xa & 0xffff) - (*xb & 0xffff) - borrow; |
| borrow = (y & 0x10000) >> 16; |
| z = (*xa++ >> 16) - (*xb++ >> 16) - borrow; |
| borrow = (z & 0x10000) >> 16; |
| Storeinc(xc, z, y); |
| } |
| while(xb < xbe); |
| while(xa < xae) { |
| y = (*xa & 0xffff) - borrow; |
| borrow = (y & 0x10000) >> 16; |
| z = (*xa++ >> 16) - borrow; |
| borrow = (z & 0x10000) >> 16; |
| Storeinc(xc, z, y); |
| } |
| #else |
| do { |
| y = *xa++ - *xb++ - borrow; |
| borrow = (y & 0x10000) >> 16; |
| *xc++ = y & 0xffff; |
| } |
| while(xb < xbe); |
| while(xa < xae) { |
| y = *xa++ - borrow; |
| borrow = (y & 0x10000) >> 16; |
| *xc++ = y & 0xffff; |
| } |
| #endif |
| #endif |
| while(!*--xc) |
| wa--; |
| c->wds = wa; |
| return c; |
| } |
| |
| static double |
| ulp |
| #ifdef KR_headers |
| (x) U x; |
| #else |
| (U x) |
| #endif |
| { |
| register Long L; |
| U 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; |
| U d; |
| #ifdef VAX |
| ULong d0, d1; |
| #else |
| #define d0 word0(d) |
| #define d1 word1(d) |
| #endif |
| |
| xa0 = a->x; |
| xa = xa0 + a->wds; |
| y = *--xa; |
| #ifdef DEBUG |
| if (!y) Bug("zero y in b2d"); |
| #endif |
| k = hi0bits(y); |
| *e = 32 - k; |
| #ifdef Pack_32 |
| if (k < Ebits) { |
| d0 = Exp_1 | y >> (Ebits - k); |
| w = xa > xa0 ? *--xa : 0; |
| d1 = y << ((32-Ebits) + k) | w >> (Ebits - k); |
| goto ret_d; |
| } |
| z = xa > xa0 ? *--xa : 0; |
| if (k -= Ebits) { |
| d0 = Exp_1 | y << k | z >> (32 - k); |
| y = xa > xa0 ? *--xa : 0; |
| d1 = z << k | y >> (32 - k); |
| } |
| else { |
| d0 = Exp_1 | y; |
| d1 = z; |
| } |
| #else |
| if (k < Ebits + 16) { |
| z = xa > xa0 ? *--xa : 0; |
| d0 = Exp_1 | y << k - Ebits | z >> Ebits + 16 - k; |
| w = xa > xa0 ? *--xa : 0; |
| y = xa > xa0 ? *--xa : 0; |
| d1 = z << k + 16 - Ebits | w << k - Ebits | y >> 16 + Ebits - k; |
| goto ret_d; |
| } |
| z = xa > xa0 ? *--xa : 0; |
| w = xa > xa0 ? *--xa : 0; |
| k -= Ebits + 16; |
| d0 = Exp_1 | y << k + 16 | z << k | w >> 16 - k; |
| y = xa > xa0 ? *--xa : 0; |
| d1 = w << k + 16 | y << k; |
| #endif |
| ret_d: |
| #ifdef VAX |
| word0(d) = d0 >> 16 | d0 << 16; |
| word1(d) = d1 >> 16 | d1 << 16; |
| #else |
| #undef d0 |
| #undef d1 |
| #endif |
| return dval(d); |
| } |
| |
| static Bigint * |
| d2b |
| #ifdef KR_headers |
| (STATE_PARAM d, e, bits) STATE_PARAM_DECL U d; int *e, *bits; |
| #else |
| (STATE_PARAM U 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(PASS_STATE 1); |
| #else |
| b = Balloc(PASS_STATE 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 { |
| 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 |
| { |
| U da, db; |
| int k, ka, kb; |
| |
| dval(da) = b2d(a, &ka); |
| dval(db) = b2d(b, &kb); |
| #ifdef Pack_32 |
| k = ka - kb + 32*(a->wds - b->wds); |
| #else |
| k = ka - kb + 16*(a->wds - b->wds); |
| #endif |
| #ifdef IBM |
| if (k > 0) { |
| word0(da) += (k >> 2)*Exp_msk1; |
| if (k &= 3) |
| dval(da) *= 1 << k; |
| } |
| else { |
| k = -k; |
| word0(db) += (k >> 2)*Exp_msk1; |
| if (k &= 3) |
| dval(db) *= 1 << k; |
| } |
| #else |
| if (k > 0) |
| word0(da) += k*Exp_msk1; |
| else { |
| k = -k; |
| word0(db) += k*Exp_msk1; |
| } |
| #endif |
| return dval(da) / dval(db); |
| } |
| |
| static CONST double |
| tens[] = { |
| 1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9, |
| 1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19, |
| 1e20, 1e21, 1e22 |
| #ifdef VAX |
| , 1e23, 1e24 |
| #endif |
| }; |
| |
| static CONST double |
| #ifdef IEEE_Arith |
| bigtens[] = { 1e16, 1e32, 1e64, 1e128, 1e256 }; |
| static CONST double tinytens[] = { 1e-16, 1e-32, 1e-64, 1e-128, |
| #ifdef Avoid_Underflow |
| 9007199254740992.*9007199254740992.e-256 |
| /* = 2^106 * 1e-53 */ |
| #else |
| 1e-256 |
| #endif |
| }; |
| /* The factor of 2^53 in tinytens[4] helps us avoid setting the underflow */ |
| /* flag unnecessarily. It leads to a song and dance at the end of strtod. */ |
| #define Scale_Bit 0x10 |
| #define n_bigtens 5 |
| #else |
| #ifdef IBM |
| bigtens[] = { 1e16, 1e32, 1e64 }; |
| static CONST double tinytens[] = { 1e-16, 1e-32, 1e-64 }; |
| #define n_bigtens 3 |
| #else |
| bigtens[] = { 1e16, 1e32 }; |
| static CONST double tinytens[] = { 1e-16, 1e-32 }; |
| #define n_bigtens 2 |
| #endif |
| #endif |
| |
| static double |
| _strtod |
| #ifdef KR_headers |
| (STATE_PARAM s00, se) STATE_PARAM_DECL CONST char *s00; char **se; |
| #else |
| (STATE_PARAM 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, adj; |
| U aadj1, rv, rv0; |
| Long L; |
| ULong y, z; |
| Bigint *bb, *bb1, *bd, *bd0, *bs, *delta; |
| #ifdef SET_INEXACT |
| int inexact, oldinexact; |
| #endif |
| #ifdef Honor_FLT_ROUNDS |
| int rounding; |
| #endif |
| #ifdef USE_LOCALE |
| CONST char *s2; |
| #endif |
| |
| #ifdef __GNUC__ |
| delta = bb = bd = bs = 0; |
| #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) { |
| 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)) |
| 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)) |
| 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(PASS_STATE s0, nd0, nd, y); |
| |
| for(;;) { |
| bd = Balloc(PASS_STATE bd0->k); |
| Bcopy(bd, bd0); |
| bb = d2b(PASS_STATE rv, &bbe, &bbbits); /* rv = bb * 2^bbe */ |
| bs = i2b(PASS_STATE 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(PASS_STATE bs, bb5); |
| bb1 = mult(PASS_STATE bs, bb); |
| Bfree(PASS_STATE bb); |
| bb = bb1; |
| } |
| if (bb2 > 0) |
| bb = lshift(PASS_STATE bb, bb2); |
| if (bd5 > 0) |
| bd = pow5mult(PASS_STATE bd, bd5); |
| if (bd2 > 0) |
| bd = lshift(PASS_STATE bd, bd2); |
| if (bs2 > 0) |
| bs = lshift(PASS_STATE bs, bs2); |
| delta = diff(PASS_STATE 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(PASS_STATE 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(rv); |
| word0(rv) -= P*Exp_msk1; |
| } |
| else |
| #endif /*Sudden_Underflow*/ |
| #endif /*Avoid_Underflow*/ |
| dval(rv) += adj*ulp(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(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(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(PASS_STATE 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(rv); |
| #ifndef ROUND_BIASED |
| else { |
| dval(rv) -= ulp(rv); |
| #ifndef Sudden_Underflow |
| if (!dval(rv)) |
| goto undfl; |
| #endif |
| } |
| #ifdef Avoid_Underflow |
| dsign = 1 - dsign; |
| #endif |
| #endif |
| break; |
| } |
| if ((aadj = ratio(delta, bs)) <= 2.) { |
| if (dsign) |
| aadj = dval(aadj1) = 1.; |
| else if (word1(rv) || word0(rv) & Bndry_mask) { |
| #ifndef Sudden_Underflow |
| if (word1(rv) == Tiny1 && !word0(rv)) |
| goto undfl; |
| #endif |
| aadj = 1.; |
| dval(aadj1) = -1.; |
| } |
| else { |
| /* special case -- power of FLT_RADIX to be */ |
| /* rounded down... */ |
| |
| if (aadj < 2./FLT_RADIX) |
| aadj = 1./FLT_RADIX; |
| else |
| aadj *= 0.5; |
| dval(aadj1) = -aadj; |
| } |
| } |
| else { |
| aadj *= 0.5; |
| dval(aadj1) = dsign ? aadj : -aadj; |
| #ifdef Check_FLT_ROUNDS |
| switch(Rounding) { |
| case 2: /* towards +infinity */ |
| dval(aadj1) -= 0.5; |
| break; |
| case 0: /* towards 0 */ |
| case 3: /* towards -infinity */ |
| dval(aadj1) += 0.5; |
| } |
| #else |
| if (Flt_Rounds == 0) |
| dval(aadj1) += 0.5; |
| #endif /*Check_FLT_ROUNDS*/ |
| } |
| y = word0(rv) & Exp_mask; |
| |
| /* Check for overflow */ |
| |
| if (y == Exp_msk1*(DBL_MAX_EXP+Bias-1)) { |
| dval(rv0) = dval(rv); |
| word0(rv) -= P*Exp_msk1; |
| adj = dval(aadj1) * ulp(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 = (ULong) aadj) <= 0) |
| z = 1; |
| aadj = z; |
| dval(aadj1) = dsign ? aadj : -aadj; |
| } |
| word0(aadj1) += (2*P+1)*Exp_msk1 - y; |
| } |
| adj = dval(aadj1) * ulp(rv); |
| dval(rv) += adj; |
| #else |
| #ifdef Sudden_Underflow |
| if ((word0(rv) & Exp_mask) <= P*Exp_msk1) { |
| dval(rv0) = dval(rv); |
| word0(rv) += P*Exp_msk1; |
| adj = dval(aadj1) * ulp(rv); |
| dval(rv) += adj; |
| #ifdef IBM |
| if ((word0(rv) & Exp_mask) < P*Exp_msk1) |
| #else |
| if ((word0(rv) & Exp_mask) <= P*Exp_msk1) |
| #endif |
| { |
| if (word0(rv0) == Tiny0 |
| && word1(rv0) == Tiny1) |
| goto undfl; |
| word0(rv) = Tiny0; |
| word1(rv) = Tiny1; |
| goto cont; |
| } |
| else |
| word0(rv) -= P*Exp_msk1; |
| } |
| else { |
| adj = dval(aadj1) * ulp(rv); |
| dval(rv) += adj; |
| } |
| #else /*Sudden_Underflow*/ |
| /* Compute adj so that the IEEE rounding rules will |
| * correctly round rv + adj in some half-way cases. |
| * If rv * ulp(rv) is denormalized (i.e., |
| * y <= (P-1)*Exp_msk1), we must adjust aadj to avoid |
| * trouble from bits lost to denormalization; |
| * example: 1.2e-307 . |
| */ |
| if (y <= (P-1)*Exp_msk1 && aadj > 1.) { |
| dval(aadj1) = (double)(int)(aadj + 0.5); |
| if (!dsign) |
| dval(aadj1) = -dval(aadj1); |
| } |
| adj = dval(aadj1) * ulp(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(PASS_STATE bb); |
| Bfree(PASS_STATE bd); |
| Bfree(PASS_STATE bs); |
| Bfree(PASS_STATE 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(PASS_STATE bb); |
| Bfree(PASS_STATE bd); |
| Bfree(PASS_STATE bs); |
| Bfree(PASS_STATE bd0); |
| Bfree(PASS_STATE delta); |
| ret: |
| if (se) |
| *se = (char *)s; |
| return sign ? -dval(rv) : dval(rv); |
| } |
| |
| static int |
| quorem |
| #ifdef KR_headers |
| (b, S) Bigint *b, *S; |
| #else |
| (Bigint *b, Bigint *S) |
| #endif |
| { |
| int n; |
| ULong *bx, *bxe, q, *sx, *sxe; |
| #ifdef ULLong |
| ULLong borrow, carry, y, ys; |
| #else |
| ULong borrow, carry, y, ys; |
| #ifdef Pack_32 |
| ULong si, z, zs; |
| #endif |
| #endif |
| |
| n = S->wds; |
| #ifdef DEBUG |
| /*debug*/ if (b->wds > n) |
| /*debug*/ Bug("oversize b in quorem"); |
| #endif |
| if (b->wds < n) |
| return 0; |
| sx = S->x; |
| sxe = sx + --n; |
| bx = b->x; |
| bxe = bx + n; |
| q = *bxe / (*sxe + 1); /* ensure q <= true quotient */ |
| #ifdef DEBUG |
| /*debug*/ if (q > 9) |
| /*debug*/ Bug("oversized quotient in quorem"); |
| #endif |
| if (q) { |
| borrow = 0; |
| carry = 0; |
| do { |
| #ifdef ULLong |
| ys = *sx++ * (ULLong)q + carry; |
| carry = ys >> 32; |
| y = *bx - (ys & FFFFFFFF) - borrow; |
| borrow = y >> 32 & (ULong)1; |
| *bx++ = (ULong) y & FFFFFFFF; |
| #else |
| #ifdef Pack_32 |
| si = *sx++; |
| ys = (si & 0xffff) * q + carry; |
| zs = (si >> 16) * q + (ys >> 16); |
| carry = zs >> 16; |
| y = (*bx & 0xffff) - (ys & 0xffff) - borrow; |
| borrow = (y & 0x10000) >> 16; |
| z = (*bx >> 16) - (zs & 0xffff) - borrow; |
| borrow = (z & 0x10000) >> 16; |
| Storeinc(bx, z, y); |
| #else |
| ys = *sx++ * q + carry; |
| carry = ys >> 16; |
| y = *bx - (ys & 0xffff) - borrow; |
| borrow = (y & 0x10000) >> 16; |
| *bx++ = y & 0xffff; |
| #endif |
| #endif |
| } |
| while(sx <= sxe); |
| if (!*bxe) { |
| bx = b->x; |
| while(--bxe > bx && !*bxe) |
| --n; |
| b->wds = n; |
| } |
| } |
| if (cmp(b, S) >= 0) { |
| q++; |
| borrow = 0; |
| carry = 0; |
| bx = b->x; |
| sx = S->x; |
| do { |
| #ifdef ULLong |
| ys = *sx++ + carry; |
| carry = ys >> 32; |
| y = *bx - (ys & FFFFFFFF) - borrow; |
| borrow = y >> 32 & (ULong)1; |
| *bx++ = (ULong) y & FFFFFFFF; |
| #else |
| #ifdef Pack_32 |
| si = *sx++; |
| ys = (si & 0xffff) + carry; |
| zs = (si >> 16) + (ys >> 16); |
| carry = zs >> 16; |
| y = (*bx & 0xffff) - (ys & 0xffff) - borrow; |
| borrow = (y & 0x10000) >> 16; |
| z = (*bx >> 16) - (zs & 0xffff) - borrow; |
| borrow = (z & 0x10000) >> 16; |
| Storeinc(bx, z, y); |
| #else |
| ys = *sx++ + carry; |
| carry = ys >> 16; |
| y = *bx - (ys & 0xffff) - borrow; |
| borrow = (y & 0x10000) >> 16; |
| *bx++ = y & 0xffff; |
| #endif |
| #endif |
| } |
| while(sx <= sxe); |
| bx = b->x; |
| bxe = bx + n; |
| if (!*bxe) { |
| while(--bxe > bx && !*bxe) |
| --n; |
| b->wds = n; |
| } |
| } |
| return q; |
| } |
| |
| #if !defined(MULTIPLE_THREADS) && !defined(NO_GLOBAL_STATE) |
| #define USE_DTOA_RESULT 1 |
| static char *dtoa_result; |
| #endif |
| |
| static char * |
| #ifdef KR_headers |
| rv_alloc(STATE_PARAM i) STATE_PARAM_DECL int i; |
| #else |
| rv_alloc(STATE_PARAM int i) |
| #endif |
| { |
| int j, k, *r; |
| |
| j = sizeof(ULong); |
| for(k = 0; |
| sizeof(Bigint) - sizeof(ULong) - sizeof(int) + j <= (unsigned) i; |
| j <<= 1) |
| k++; |
| r = (int*)Balloc(PASS_STATE k); |
| *r = k; |
| return |
| #ifdef USE_DTOA_RESULT |
| dtoa_result = |
| #endif |
| (char *)(r+1); |
| } |
| |
| static char * |
| #ifdef KR_headers |
| nrv_alloc(STATE_PARAM s, rve, n) STATE_PARAM_DECL char *s, **rve; int n; |
| #else |
| nrv_alloc(STATE_PARAM CONST char *s, char **rve, int n) |
| #endif |
| { |
| char *rv, *t; |
| |
| t = rv = rv_alloc(PASS_STATE n); |
| while((*t = *s++)) 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. |
| */ |
| |
| static void |
| #ifdef KR_headers |
| freedtoa(STATE_PARAM s) STATE_PARAM_DECL char *s; |
| #else |
| freedtoa(STATE_PARAM char *s) |
| #endif |
| { |
| Bigint *b = (Bigint *)((int *)s - 1); |
| b->maxwds = 1 << (b->k = *(int*)b); |
| Bfree(PASS_STATE b); |
| #ifdef USE_DTOA_RESULT |
| 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. |
| */ |
| |
| static char * |
| dtoa |
| #ifdef KR_headers |
| (STATE_PARAM d, mode, ndigits, decpt, sign, rve) |
| STATE_PARAM_DECL U d; int mode, ndigits, *decpt, *sign; char **rve; |
| #else |
| (STATE_PARAM U d, int mode, int ndigits, int *decpt, int *sign, char **rve) |
| #endif |
| { |
| /* Arguments ndigits, decpt, sign are similar to those |
| of ecvt and fcvt; trailing zeros are suppressed from |
| the returned string. If not null, *rve is set to point |
| to the end of the return value. If d is +-Infinity or NaN, |
| then *decpt is set to 9999. |
| |
| mode: |
| 0 ==> shortest string that yields d when read in |
| and rounded to nearest. |
| 1 ==> like 0, but with Steele & White stopping rule; |
| e.g. with IEEE P754 arithmetic , mode 0 gives |
| 1e23 whereas mode 1 gives 9.999999999999999e22. |
| 2 ==> max(1,ndigits) significant digits. This gives a |
| return value similar to that of ecvt, except |
| that trailing zeros are suppressed. |
| 3 ==> through ndigits past the decimal point. This |
| gives a return value similar to that from fcvt, |
| except that trailing zeros are suppressed, and |
| ndigits can be negative. |
| 4,5 ==> 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; |
| U d2, eps; |
| double ds; |
| char *s, *s0; |
| #ifdef Honor_FLT_ROUNDS |
| int rounding; |
| #endif |
| #ifdef SET_INEXACT |
| int inexact, oldinexact; |
| #endif |
| |
| #ifdef __GNUC__ |
| ilim = ilim1 = 0; |
| mlo = NULL; |
| #endif |
| |
| #ifdef USE_DTOA_RESULT |
| if (dtoa_result) { |
| freedtoa(PASS_STATE dtoa_result); |
| dtoa_result = 0; |
| } |
| #endif |
| |
| if (word0(d) & Sign_bit) { |
| /* set sign for everything, including 0's and NaNs */ |
| *sign = 1; |
| word0(d) &= ~Sign_bit; /* clear sign bit */ |
| } |
| else |
| *sign = 0; |
| |
| #if defined(IEEE_Arith) + defined(VAX) |
| #ifdef IEEE_Arith |
| if ((word0(d) & Exp_mask) == Exp_mask) |
| #else |
| if (word0(d) == 0x8000) |
| #endif |
| { |
| /* Infinity or NaN */ |
| *decpt = 9999; |
| #ifdef IEEE_Arith |
| if (!word1(d) && !(word0(d) & 0xfffff)) |
| return nrv_alloc(PASS_STATE "Infinity", rve, 8); |
| #endif |
| return nrv_alloc(PASS_STATE "NaN", rve, 3); |
| } |
| #endif |
| #ifdef IBM |
| dval(d) += 0; /* normalize */ |
| #endif |
| if (!dval(d)) { |
| *decpt = 1; |
| return nrv_alloc(PASS_STATE "0", rve, 1); |
| } |
| |
| #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(PASS_STATE 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)))) { |
| #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; |
| switch(mode) { |
| case 0: |
| case 1: |
| ilim = ilim1 = -1; |
| i = 18; |
| ndigits = 0; |
| break; |
| case 2: |
| leftright = 0; |
| /* no break */ |
| case 4: |
| if (ndigits <= 0) |
| ndigits = 1; |
| ilim = ilim1 = i = ndigits; |
| break; |
| case 3: |
| leftright = 0; |
| /* no break */ |
| case 5: |
| i = ndigits + k + 1; |
| ilim = i; |
| ilim1 = i - 1; |
| if (i <= 0) |
| i = 1; |
| } |
| s = s0 = rv_alloc(PASS_STATE 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)) { |
| 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 = (ULong) 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(PASS_STATE 1); |
| } |
| if (m2 > 0 && s2 > 0) { |
|