| /* $NetBSD: strtod.c,v 1.45.2.1 2005/04/19 13:35:54 tron Exp $ */ |
| |
| /**************************************************************** |
| * |
| * The author of this software is David M. Gay. |
| * |
| * Copyright (c) 1991 by AT&T. |
| * |
| * Permission to use, copy, modify, and distribute this software for any |
| * purpose without fee is hereby granted, provided that this entire notice |
| * is included in all copies of any software which is or includes a copy |
| * or modification of this software and in all copies of the supporting |
| * documentation for such software. |
| * |
| * THIS SOFTWARE IS BEING PROVIDED "AS IS", WITHOUT ANY EXPRESS OR IMPLIED |
| * WARRANTY. IN PARTICULAR, NEITHER THE AUTHOR NOR AT&T MAKES ANY |
| * REPRESENTATION OR WARRANTY OF ANY KIND CONCERNING THE MERCHANTABILITY |
| * OF THIS SOFTWARE OR ITS FITNESS FOR ANY PARTICULAR PURPOSE. |
| * |
| ***************************************************************/ |
| |
| /* Please send bug reports to |
| David M. Gay |
| AT&T Bell Laboratories, Room 2C-463 |
| 600 Mountain Avenue |
| Murray Hill, NJ 07974-2070 |
| U.S.A. |
| dmg@research.att.com or research!dmg |
| */ |
| |
| /* strtod for IEEE-, VAX-, and IBM-arithmetic machines. |
| * |
| * This strtod returns a nearest machine number to the input decimal |
| * string (or sets errno to ERANGE). With IEEE arithmetic, ties are |
| * broken by the IEEE round-even rule. Otherwise ties are broken by |
| * biased rounding (add half and chop). |
| * |
| * Inspired loosely by William D. Clinger's paper "How to Read Floating |
| * Point Numbers Accurately" [Proc. ACM SIGPLAN '90, pp. 92-101]. |
| * |
| * Modifications: |
| * |
| * 1. We only require IEEE, IBM, or VAX double-precision |
| * arithmetic (not IEEE double-extended). |
| * 2. We get by with floating-point arithmetic in a case that |
| * Clinger missed -- when we're computing d * 10^n |
| * for a small integer d and the integer n is not too |
| * much larger than 22 (the maximum integer k for which |
| * we can represent 10^k exactly), we may be able to |
| * compute (d*10^k) * 10^(e-k) with just one roundoff. |
| * 3. Rather than a bit-at-a-time adjustment of the binary |
| * result in the hard case, we use floating-point |
| * arithmetic to determine the adjustment to within |
| * one bit; only in really hard cases do we need to |
| * compute a second residual. |
| * 4. Because of 3., we don't need a large table of powers of 10 |
| * for ten-to-e (just some small tables, e.g. of 10^k |
| * for 0 <= k <= 22). |
| */ |
| |
| /* |
| * #define IEEE_LITTLE_ENDIAN for IEEE-arithmetic machines where the least |
| * significant byte has the lowest address. |
| * #define IEEE_BIG_ENDIAN for IEEE-arithmetic machines where the most |
| * significant byte has the lowest address. |
| * #define Long int on machines with 32-bit ints and 64-bit longs. |
| * #define Sudden_Underflow for IEEE-format machines without gradual |
| * underflow (i.e., that flush to zero on underflow). |
| * #define IBM for IBM mainframe-style floating-point arithmetic. |
| * #define VAX for VAX-style floating-point arithmetic. |
| * #define Unsigned_Shifts if >> does treats its left operand as unsigned. |
| * #define No_leftright to omit left-right logic in fast floating-point |
| * computation of dtoa. |
| * #define Check_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3. |
| * #define RND_PRODQUOT to use rnd_prod and rnd_quot (assembly routines |
| * that use extended-precision instructions to compute rounded |
| * products and quotients) with IBM. |
| * #define ROUND_BIASED for IEEE-format with biased rounding. |
| * #define Inaccurate_Divide for IEEE-format with correctly rounded |
| * products but inaccurate quotients, e.g., for Intel i860. |
| * #define Just_16 to store 16 bits per 32-bit Long when doing high-precision |
| * integer arithmetic. Whether this speeds things up or slows things |
| * down depends on the machine and the number being converted. |
| * #define KR_headers for old-style C function headers. |
| * #define Bad_float_h if your system lacks a float.h or if it does not |
| * define some or all of DBL_DIG, DBL_MAX_10_EXP, DBL_MAX_EXP, |
| * FLT_RADIX, FLT_ROUNDS, and DBL_MAX. |
| * #define MALLOC your_malloc, where your_malloc(n) acts like malloc(n) |
| * if memory is available and otherwise does something you deem |
| * appropriate. If MALLOC is undefined, malloc will be invoked |
| * directly -- and assumed always to succeed. |
| */ |
| |
| #define ANDROID_CHANGES |
| |
| #ifdef ANDROID_CHANGES |
| /* Needs to be above math.h include below */ |
| #include "fpmath.h" |
| |
| #include <pthread.h> |
| #define mutex_lock(x) pthread_mutex_lock(x) |
| #define mutex_unlock(x) pthread_mutex_unlock(x) |
| #endif |
| |
| #include <sys/cdefs.h> |
| #if defined(LIBC_SCCS) && !defined(lint) |
| __RCSID("$NetBSD: strtod.c,v 1.45.2.1 2005/04/19 13:35:54 tron Exp $"); |
| #endif /* LIBC_SCCS and not lint */ |
| |
| #define Unsigned_Shifts |
| #if defined(__m68k__) || defined(__sparc__) || defined(__i386__) || \ |
| defined(__mips__) || defined(__ns32k__) || defined(__alpha__) || \ |
| defined(__powerpc__) || defined(__sh__) || defined(__x86_64__) || \ |
| defined(__hppa__) || \ |
| defined(__arm__) || defined(__aarch64__) |
| #include <endian.h> |
| #if BYTE_ORDER == BIG_ENDIAN |
| #define IEEE_BIG_ENDIAN |
| #else |
| #define IEEE_LITTLE_ENDIAN |
| #endif |
| #endif |
| |
| #ifdef __vax__ |
| #define VAX |
| #endif |
| |
| #if defined(__hppa__) || defined(__mips__) || defined(__sh__) |
| #define NAN_WORD0 0x7ff40000 |
| #else |
| #define NAN_WORD0 0x7ff80000 |
| #endif |
| #define NAN_WORD1 0 |
| |
| #define Long int32_t |
| #define ULong u_int32_t |
| |
| #ifdef DEBUG |
| #include "stdio.h" |
| #define Bug(x) {fprintf(stderr, "%s\n", x); exit(1);} |
| #define BugPrintf(x, v) {fprintf(stderr, x, v); exit(1);} |
| #endif |
| |
| #ifdef __cplusplus |
| #include "malloc.h" |
| #include "memory.h" |
| #else |
| #ifndef KR_headers |
| #include "stdlib.h" |
| #include "string.h" |
| #ifndef ANDROID_CHANGES |
| #include "locale.h" |
| #endif /* ANDROID_CHANGES */ |
| #else |
| #include "malloc.h" |
| #include "memory.h" |
| #endif |
| #endif |
| #ifndef ANDROID_CHANGES |
| #include "extern.h" |
| #include "reentrant.h" |
| #endif /* ANDROID_CHANGES */ |
| |
| #ifdef MALLOC |
| #ifdef KR_headers |
| extern char *MALLOC(); |
| #else |
| extern void *MALLOC(size_t); |
| #endif |
| #else |
| #define MALLOC malloc |
| #endif |
| |
| #include "ctype.h" |
| #include "errno.h" |
| #include "float.h" |
| |
| #ifndef __MATH_H__ |
| #include "math.h" |
| #endif |
| |
| #ifdef __cplusplus |
| extern "C" { |
| #endif |
| |
| #ifndef CONST |
| #ifdef KR_headers |
| #define CONST /* blank */ |
| #else |
| #define CONST const |
| #endif |
| #endif |
| |
| #ifdef Unsigned_Shifts |
| #define Sign_Extend(a,b) if (b < 0) a |= 0xffff0000; |
| #else |
| #define Sign_Extend(a,b) /*no-op*/ |
| #endif |
| |
| #if defined(IEEE_LITTLE_ENDIAN) + defined(IEEE_BIG_ENDIAN) + defined(VAX) + \ |
| defined(IBM) != 1 |
| Exactly one of IEEE_LITTLE_ENDIAN IEEE_BIG_ENDIAN, VAX, or |
| IBM should be defined. |
| #endif |
| |
| typedef union { |
| double d; |
| ULong ul[2]; |
| } _double; |
| #define value(x) ((x).d) |
| #ifdef IEEE_LITTLE_ENDIAN |
| #define word0(x) ((x).ul[1]) |
| #define word1(x) ((x).ul[0]) |
| #else |
| #define word0(x) ((x).ul[0]) |
| #define word1(x) ((x).ul[1]) |
| #endif |
| |
| /* The following definition of Storeinc is appropriate for MIPS processors. |
| * An alternative that might be better on some machines is |
| * #define Storeinc(a,b,c) (*a++ = b << 16 | c & 0xffff) |
| */ |
| #if defined(IEEE_LITTLE_ENDIAN) + defined(VAX) + defined(__arm__) |
| #define Storeinc(a,b,c) \ |
| (((u_short *)(void *)a)[1] = \ |
| (u_short)b, ((u_short *)(void *)a)[0] = (u_short)c, a++) |
| #else |
| #define Storeinc(a,b,c) \ |
| (((u_short *)(void *)a)[0] = \ |
| (u_short)b, ((u_short *)(void *)a)[1] = (u_short)c, a++) |
| #endif |
| |
| /* #define P DBL_MANT_DIG */ |
| /* Ten_pmax = floor(P*log(2)/log(5)) */ |
| /* Bletch = (highest power of 2 < DBL_MAX_10_EXP) / 16 */ |
| /* Quick_max = floor((P-1)*log(FLT_RADIX)/log(10) - 1) */ |
| /* Int_max = floor(P*log(FLT_RADIX)/log(10) - 1) */ |
| |
| #if defined(IEEE_LITTLE_ENDIAN) + defined(IEEE_BIG_ENDIAN) |
| #define Exp_shift 20 |
| #define Exp_shift1 20 |
| #define Exp_msk1 0x100000 |
| #define Exp_msk11 0x100000 |
| #define Exp_mask 0x7ff00000 |
| #define P 53 |
| #define Bias 1023 |
| #define IEEE_Arith |
| #define Emin (-1022) |
| #define Exp_1 0x3ff00000 |
| #define Exp_11 0x3ff00000 |
| #define Ebits 11 |
| #define Frac_mask 0xfffff |
| #define Frac_mask1 0xfffff |
| #define Ten_pmax 22 |
| #define Bletch 0x10 |
| #define Bndry_mask 0xfffff |
| #define Bndry_mask1 0xfffff |
| #define LSB 1 |
| #define Sign_bit 0x80000000 |
| #define Log2P 1 |
| #define Tiny0 0 |
| #define Tiny1 1 |
| #define Quick_max 14 |
| #define Int_max 14 |
| #define Infinite(x) (word0(x) == 0x7ff00000) /* sufficient test for here */ |
| #else |
| #undef Sudden_Underflow |
| #define Sudden_Underflow |
| #ifdef IBM |
| #define Exp_shift 24 |
| #define Exp_shift1 24 |
| #define Exp_msk1 0x1000000 |
| #define Exp_msk11 0x1000000 |
| #define Exp_mask 0x7f000000 |
| #define P 14 |
| #define Bias 65 |
| #define Exp_1 0x41000000 |
| #define Exp_11 0x41000000 |
| #define Ebits 8 /* exponent has 7 bits, but 8 is the right value in b2d */ |
| #define Frac_mask 0xffffff |
| #define Frac_mask1 0xffffff |
| #define Bletch 4 |
| #define Ten_pmax 22 |
| #define Bndry_mask 0xefffff |
| #define Bndry_mask1 0xffffff |
| #define LSB 1 |
| #define Sign_bit 0x80000000 |
| #define Log2P 4 |
| #define Tiny0 0x100000 |
| #define Tiny1 0 |
| #define Quick_max 14 |
| #define Int_max 15 |
| #else /* VAX */ |
| #define Exp_shift 23 |
| #define Exp_shift1 7 |
| #define Exp_msk1 0x80 |
| #define Exp_msk11 0x800000 |
| #define Exp_mask 0x7f80 |
| #define P 56 |
| #define Bias 129 |
| #define Exp_1 0x40800000 |
| #define Exp_11 0x4080 |
| #define Ebits 8 |
| #define Frac_mask 0x7fffff |
| #define Frac_mask1 0xffff007f |
| #define Ten_pmax 24 |
| #define Bletch 2 |
| #define Bndry_mask 0xffff007f |
| #define Bndry_mask1 0xffff007f |
| #define LSB 0x10000 |
| #define Sign_bit 0x8000 |
| #define Log2P 1 |
| #define Tiny0 0x80 |
| #define Tiny1 0 |
| #define Quick_max 15 |
| #define Int_max 15 |
| #endif |
| #endif |
| |
| #ifndef IEEE_Arith |
| #define ROUND_BIASED |
| #endif |
| |
| #ifdef RND_PRODQUOT |
| #define rounded_product(a,b) a = rnd_prod(a, b) |
| #define rounded_quotient(a,b) a = rnd_quot(a, b) |
| #ifdef KR_headers |
| extern double rnd_prod(), rnd_quot(); |
| #else |
| extern double rnd_prod(double, double), rnd_quot(double, double); |
| #endif |
| #else |
| #define rounded_product(a,b) a *= b |
| #define rounded_quotient(a,b) a /= b |
| #endif |
| |
| #define Big0 (Frac_mask1 | Exp_msk1*(DBL_MAX_EXP+Bias-1)) |
| #define Big1 0xffffffff |
| |
| #ifndef Just_16 |
| /* When Pack_32 is not defined, we store 16 bits per 32-bit Long. |
| * This makes some inner loops simpler and sometimes saves work |
| * during multiplications, but it often seems to make things slightly |
| * slower. Hence the default is now to store 32 bits per Long. |
| */ |
| #ifndef Pack_32 |
| #define Pack_32 |
| #endif |
| #endif |
| |
| #define Kmax 15 |
| |
| #ifdef Pack_32 |
| #define ULbits 32 |
| #define kshift 5 |
| #define kmask 31 |
| #define ALL_ON 0xffffffff |
| #else |
| #define ULbits 16 |
| #define kshift 4 |
| #define kmask 15 |
| #define ALL_ON 0xffff |
| #endif |
| |
| #define Kmax 15 |
| |
| enum { /* return values from strtodg */ |
| STRTOG_Zero = 0, |
| STRTOG_Normal = 1, |
| STRTOG_Denormal = 2, |
| STRTOG_Infinite = 3, |
| STRTOG_NaN = 4, |
| STRTOG_NaNbits = 5, |
| STRTOG_NoNumber = 6, |
| STRTOG_Retmask = 7, |
| |
| /* The following may be or-ed into one of the above values. */ |
| |
| STRTOG_Neg = 0x08, /* does not affect STRTOG_Inexlo or STRTOG_Inexhi */ |
| STRTOG_Inexlo = 0x10, /* returned result rounded toward zero */ |
| STRTOG_Inexhi = 0x20, /* returned result rounded away from zero */ |
| STRTOG_Inexact = 0x30, |
| STRTOG_Underflow= 0x40, |
| STRTOG_Overflow = 0x80 |
| }; |
| |
| typedef struct |
| FPI { |
| int nbits; |
| int emin; |
| int emax; |
| int rounding; |
| int sudden_underflow; |
| } FPI; |
| |
| enum { /* FPI.rounding values: same as FLT_ROUNDS */ |
| FPI_Round_zero = 0, |
| FPI_Round_near = 1, |
| FPI_Round_up = 2, |
| FPI_Round_down = 3 |
| }; |
| |
| #undef SI |
| #ifdef Sudden_Underflow |
| #define SI 1 |
| #else |
| #define SI 0 |
| #endif |
| |
| #ifdef __cplusplus |
| extern "C" double strtod(const char *s00, char **se); |
| extern "C" char *__dtoa(double d, int mode, int ndigits, |
| int *decpt, int *sign, char **rve); |
| #endif |
| |
| struct |
| Bigint { |
| struct Bigint *next; |
| int k, maxwds, sign, wds; |
| ULong x[1]; |
| }; |
| |
| typedef struct Bigint Bigint; |
| |
| CONST unsigned char hexdig[256] = { |
| 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, |
| 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, |
| 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, |
| 0x10, 0x11, 0x12, 0x13, 0x14, 0x15, 0x16, 0x17, 0x18, 0x19, 0, 0, 0, 0, 0, 0, |
| 0, 0x1a, 0x1b, 0x1c, 0x1d, 0x1e, 0x1f, 0, 0, 0, 0, 0, 0, 0, 0, 0, |
| 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, |
| 0, 0x1a, 0x1b, 0x1c, 0x1d, 0x1e, 0x1f, 0, 0, 0, 0, 0, 0, 0, 0, 0, |
| 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, |
| 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, |
| 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, |
| 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, |
| 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, |
| 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, |
| 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, |
| 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, |
| 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, |
| }; |
| |
| static int |
| gethex(CONST char **, CONST FPI *, Long *, Bigint **, int, locale_t); |
| |
| |
| static Bigint *freelist[Kmax+1]; |
| |
| #ifdef ANDROID_CHANGES |
| static pthread_mutex_t freelist_mutex = PTHREAD_MUTEX_INITIALIZER; |
| #else |
| #ifdef _REENTRANT |
| static mutex_t freelist_mutex = MUTEX_INITIALIZER; |
| #endif |
| #endif |
| |
| /* Special value used to indicate an invalid Bigint value, |
| * e.g. when a memory allocation fails. The idea is that we |
| * want to avoid introducing NULL checks everytime a bigint |
| * computation is performed. Also the NULL value can also be |
| * already used to indicate "value not initialized yet" and |
| * returning NULL might alter the execution code path in |
| * case of OOM. |
| */ |
| #define BIGINT_INVALID ((Bigint *)&bigint_invalid_value) |
| |
| static const Bigint bigint_invalid_value; |
| |
| |
| static void |
| copybits(ULong *c, int n, Bigint *b) |
| { |
| ULong *ce, *x, *xe; |
| #ifdef Pack_16 |
| int nw, nw1; |
| #endif |
| |
| ce = c + ((n-1) >> kshift) + 1; |
| x = b->x; |
| #ifdef Pack_32 |
| xe = x + b->wds; |
| while(x < xe) |
| *c++ = *x++; |
| #else |
| nw = b->wds; |
| nw1 = nw & 1; |
| for(xe = x + (nw - nw1); x < xe; x += 2) |
| Storeinc(c, x[1], x[0]); |
| if (nw1) |
| *c++ = *x; |
| #endif |
| while(c < ce) |
| *c++ = 0; |
| } |
| |
| ULong |
| any_on(Bigint *b, int k) |
| { |
| int n, nwds; |
| ULong *x, *x0, x1, x2; |
| |
| x = b->x; |
| nwds = b->wds; |
| n = k >> kshift; |
| if (n > nwds) |
| n = nwds; |
| else if (n < nwds && (k &= kmask)) { |
| x1 = x2 = x[n]; |
| x1 >>= k; |
| x1 <<= k; |
| if (x1 != x2) |
| return 1; |
| } |
| x0 = x; |
| x += n; |
| while(x > x0) |
| if (*--x) |
| return 1; |
| return 0; |
| } |
| |
| void |
| rshift(Bigint *b, int k) |
| { |
| ULong *x, *x1, *xe, y; |
| int n; |
| |
| x = x1 = b->x; |
| n = k >> kshift; |
| if (n < b->wds) { |
| xe = x + b->wds; |
| x += n; |
| if (k &= kmask) { |
| n = ULbits - k; |
| y = *x++ >> k; |
| while(x < xe) { |
| *x1++ = (y | (*x << n)) & ALL_ON; |
| y = *x++ >> k; |
| } |
| if ((*x1 = y) !=0) |
| x1++; |
| } |
| else |
| while(x < xe) |
| *x1++ = *x++; |
| } |
| if ((b->wds = x1 - b->x) == 0) |
| b->x[0] = 0; |
| } |
| |
| |
| typedef union { double d; ULong L[2]; } U; |
| |
| static void |
| ULtod(ULong *L, ULong *bits, Long exp, int k) |
| { |
| # define _0 1 |
| # define _1 0 |
| |
| switch(k & STRTOG_Retmask) { |
| case STRTOG_NoNumber: |
| case STRTOG_Zero: |
| L[0] = L[1] = 0; |
| break; |
| |
| case STRTOG_Denormal: |
| L[_1] = bits[0]; |
| L[_0] = bits[1]; |
| break; |
| |
| case STRTOG_Normal: |
| case STRTOG_NaNbits: |
| L[_1] = bits[0]; |
| L[_0] = (bits[1] & ~0x100000) | ((exp + 0x3ff + 52) << 20); |
| break; |
| |
| case STRTOG_Infinite: |
| L[_0] = 0x7ff00000; |
| L[_1] = 0; |
| break; |
| |
| #define d_QNAN0 0x7ff80000 |
| #define d_QNAN1 0x0 |
| case STRTOG_NaN: |
| L[0] = d_QNAN0; |
| L[1] = d_QNAN1; |
| } |
| if (k & STRTOG_Neg) |
| L[_0] |= 0x80000000L; |
| } |
| |
| |
| |
| /* Return BIGINT_INVALID on allocation failure. |
| * |
| * Most of the code here depends on the fact that this function |
| * never returns NULL. |
| */ |
| static Bigint * |
| Balloc |
| #ifdef KR_headers |
| (k) int k; |
| #else |
| (int k) |
| #endif |
| { |
| int x; |
| Bigint *rv; |
| |
| mutex_lock(&freelist_mutex); |
| |
| if ((rv = freelist[k]) != NULL) { |
| freelist[k] = rv->next; |
| } |
| else { |
| x = 1 << k; |
| rv = (Bigint *)MALLOC(sizeof(Bigint) + (x-1)*sizeof(Long)); |
| if (rv == NULL) { |
| rv = BIGINT_INVALID; |
| goto EXIT; |
| } |
| rv->k = k; |
| rv->maxwds = x; |
| } |
| rv->sign = rv->wds = 0; |
| EXIT: |
| mutex_unlock(&freelist_mutex); |
| |
| return rv; |
| } |
| |
| static void |
| Bfree |
| #ifdef KR_headers |
| (v) Bigint *v; |
| #else |
| (Bigint *v) |
| #endif |
| { |
| if (v && v != BIGINT_INVALID) { |
| mutex_lock(&freelist_mutex); |
| |
| v->next = freelist[v->k]; |
| freelist[v->k] = v; |
| |
| mutex_unlock(&freelist_mutex); |
| } |
| } |
| |
| #define Bcopy_valid(x,y) memcpy(&(x)->sign, &(y)->sign, \ |
| (y)->wds*sizeof(Long) + 2*sizeof(int)) |
| |
| #define Bcopy(x,y) Bcopy_ptr(&(x),(y)) |
| |
| static void |
| Bcopy_ptr(Bigint **px, Bigint *y) |
| { |
| if (*px == BIGINT_INVALID) |
| return; /* no space to store copy */ |
| if (y == BIGINT_INVALID) { |
| Bfree(*px); /* invalid input */ |
| *px = BIGINT_INVALID; |
| } else { |
| Bcopy_valid(*px,y); |
| } |
| } |
| |
| static Bigint * |
| multadd |
| #ifdef KR_headers |
| (b, m, a) Bigint *b; int m, a; |
| #else |
| (Bigint *b, int m, int a) /* multiply by m and add a */ |
| #endif |
| { |
| int i, wds; |
| ULong *x, y; |
| #ifdef Pack_32 |
| ULong xi, z; |
| #endif |
| Bigint *b1; |
| |
| if (b == BIGINT_INVALID) |
| return b; |
| |
| wds = b->wds; |
| x = b->x; |
| i = 0; |
| do { |
| #ifdef Pack_32 |
| xi = *x; |
| y = (xi & 0xffff) * m + a; |
| z = (xi >> 16) * m + (y >> 16); |
| a = (int)(z >> 16); |
| *x++ = (z << 16) + (y & 0xffff); |
| #else |
| y = *x * m + a; |
| a = (int)(y >> 16); |
| *x++ = y & 0xffff; |
| #endif |
| } |
| while(++i < wds); |
| if (a) { |
| if (wds >= b->maxwds) { |
| b1 = Balloc(b->k+1); |
| if (b1 == BIGINT_INVALID) { |
| Bfree(b); |
| return b1; |
| } |
| Bcopy_valid(b1, b); |
| Bfree(b); |
| b = b1; |
| } |
| b->x[wds++] = a; |
| b->wds = wds; |
| } |
| return b; |
| } |
| |
| Bigint * |
| increment(Bigint *b) |
| { |
| ULong *x, *xe; |
| Bigint *b1; |
| #ifdef Pack_16 |
| ULong carry = 1, y; |
| #endif |
| |
| x = b->x; |
| xe = x + b->wds; |
| #ifdef Pack_32 |
| do { |
| if (*x < (ULong)0xffffffffL) { |
| ++*x; |
| return b; |
| } |
| *x++ = 0; |
| } while(x < xe); |
| #else |
| do { |
| y = *x + carry; |
| carry = y >> 16; |
| *x++ = y & 0xffff; |
| if (!carry) |
| return b; |
| } while(x < xe); |
| if (carry) |
| #endif |
| { |
| if (b->wds >= b->maxwds) { |
| b1 = Balloc(b->k+1); |
| Bcopy(b1,b); |
| Bfree(b); |
| b = b1; |
| } |
| b->x[b->wds++] = 1; |
| } |
| 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); |
| if (b == BIGINT_INVALID) |
| return b; |
| b->x[0] = y9; |
| b->wds = 1; |
| #else |
| b = Balloc(k+1); |
| if (b == BIGINT_INVALID) |
| return b; |
| |
| b->x[0] = y9 & 0xffff; |
| b->wds = (b->x[1] = y9 >> 16) ? 2 : 1; |
| #endif |
| |
| i = 9; |
| if (9 < nd0) { |
| s += 9; |
| do b = multadd(b, 10, *s++ - '0'); |
| while(++i < nd0); |
| s++; |
| } |
| else |
| s += 10; |
| for(; i < nd; i++) |
| b = multadd(b, 10, *s++ - '0'); |
| return b; |
| } |
| |
| static int |
| hi0bits |
| #ifdef KR_headers |
| (x) ULong x; |
| #else |
| (ULong x) |
| #endif |
| { |
| int k = 0; |
| |
| if (!(x & 0xffff0000)) { |
| k = 16; |
| x <<= 16; |
| } |
| if (!(x & 0xff000000)) { |
| k += 8; |
| x <<= 8; |
| } |
| if (!(x & 0xf0000000)) { |
| k += 4; |
| x <<= 4; |
| } |
| if (!(x & 0xc0000000)) { |
| k += 2; |
| x <<= 2; |
| } |
| if (!(x & 0x80000000)) { |
| k++; |
| if (!(x & 0x40000000)) |
| return 32; |
| } |
| return k; |
| } |
| |
| static int |
| lo0bits |
| #ifdef KR_headers |
| (y) ULong *y; |
| #else |
| (ULong *y) |
| #endif |
| { |
| int k; |
| ULong x = *y; |
| |
| if (x & 7) { |
| if (x & 1) |
| return 0; |
| if (x & 2) { |
| *y = x >> 1; |
| return 1; |
| } |
| *y = x >> 2; |
| return 2; |
| } |
| k = 0; |
| if (!(x & 0xffff)) { |
| k = 16; |
| x >>= 16; |
| } |
| if (!(x & 0xff)) { |
| k += 8; |
| x >>= 8; |
| } |
| if (!(x & 0xf)) { |
| k += 4; |
| x >>= 4; |
| } |
| if (!(x & 0x3)) { |
| k += 2; |
| x >>= 2; |
| } |
| if (!(x & 1)) { |
| k++; |
| x >>= 1; |
| if (!x & 1) |
| return 32; |
| } |
| *y = x; |
| return k; |
| } |
| |
| static Bigint * |
| i2b |
| #ifdef KR_headers |
| (i) int i; |
| #else |
| (int i) |
| #endif |
| { |
| Bigint *b; |
| |
| b = Balloc(1); |
| if (b != BIGINT_INVALID) { |
| b->x[0] = i; |
| b->wds = 1; |
| } |
| return b; |
| } |
| |
| static Bigint * |
| mult |
| #ifdef KR_headers |
| (a, b) Bigint *a, *b; |
| #else |
| (Bigint *a, Bigint *b) |
| #endif |
| { |
| Bigint *c; |
| int k, wa, wb, wc; |
| ULong carry, y, z; |
| ULong *x, *xa, *xae, *xb, *xbe, *xc, *xc0; |
| #ifdef Pack_32 |
| ULong z2; |
| #endif |
| |
| if (a == BIGINT_INVALID || b == BIGINT_INVALID) |
| return BIGINT_INVALID; |
| |
| 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); |
| if (c == BIGINT_INVALID) |
| return c; |
| for(x = c->x, xa = x + wc; x < xa; x++) |
| *x = 0; |
| xa = a->x; |
| xae = xa + wa; |
| xb = b->x; |
| xbe = xb + wb; |
| xc0 = c->x; |
| #ifdef Pack_32 |
| for(; xb < xbe; xb++, xc0++) { |
| if ((y = *xb & 0xffff) != 0) { |
| x = xa; |
| xc = xc0; |
| carry = 0; |
| do { |
| z = (*x & 0xffff) * y + (*xc & 0xffff) + carry; |
| carry = z >> 16; |
| z2 = (*x++ >> 16) * y + (*xc >> 16) + carry; |
| carry = z2 >> 16; |
| Storeinc(xc, z2, z); |
| } |
| while(x < xae); |
| *xc = carry; |
| } |
| if ((y = *xb >> 16) != 0) { |
| x = xa; |
| xc = xc0; |
| carry = 0; |
| z2 = *xc; |
| do { |
| z = (*x & 0xffff) * y + (*xc >> 16) + carry; |
| carry = z >> 16; |
| Storeinc(xc, z, z2); |
| z2 = (*x++ >> 16) * y + (*xc & 0xffff) + carry; |
| carry = z2 >> 16; |
| } |
| while(x < xae); |
| *xc = z2; |
| } |
| } |
| #else |
| for(; xb < xbe; xc0++) { |
| if (y = *xb++) { |
| x = xa; |
| xc = xc0; |
| carry = 0; |
| do { |
| z = *x++ * y + *xc + carry; |
| carry = z >> 16; |
| *xc++ = z & 0xffff; |
| } |
| while(x < xae); |
| *xc = carry; |
| } |
| } |
| #endif |
| for(xc0 = c->x, xc = xc0 + wc; wc > 0 && !*--xc; --wc) ; |
| c->wds = wc; |
| return c; |
| } |
| |
| static Bigint *p5s; |
| static pthread_mutex_t p5s_mutex = PTHREAD_MUTEX_INITIALIZER; |
| |
| static Bigint * |
| pow5mult |
| #ifdef KR_headers |
| (b, k) Bigint *b; int k; |
| #else |
| (Bigint *b, int k) |
| #endif |
| { |
| Bigint *b1, *p5, *p51; |
| int i; |
| static const int p05[3] = { 5, 25, 125 }; |
| |
| if (b == BIGINT_INVALID) |
| return b; |
| |
| if ((i = k & 3) != 0) |
| b = multadd(b, p05[i-1], 0); |
| |
| if (!(k = (unsigned int) k >> 2)) |
| return b; |
| mutex_lock(&p5s_mutex); |
| if (!(p5 = p5s)) { |
| /* first time */ |
| p5 = i2b(625); |
| if (p5 == BIGINT_INVALID) { |
| Bfree(b); |
| mutex_unlock(&p5s_mutex); |
| return p5; |
| } |
| p5s = p5; |
| p5->next = 0; |
| } |
| for(;;) { |
| if (k & 1) { |
| b1 = mult(b, p5); |
| Bfree(b); |
| b = b1; |
| } |
| if (!(k = (unsigned int) k >> 1)) |
| break; |
| if (!(p51 = p5->next)) { |
| p51 = mult(p5,p5); |
| if (p51 == BIGINT_INVALID) { |
| Bfree(b); |
| mutex_unlock(&p5s_mutex); |
| return p51; |
| } |
| p5->next = p51; |
| p51->next = 0; |
| } |
| p5 = p51; |
| } |
| mutex_unlock(&p5s_mutex); |
| 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; |
| |
| if (b == BIGINT_INVALID) |
| return b; |
| |
| #ifdef Pack_32 |
| n = (unsigned int)k >> 5; |
| #else |
| n = (unsigned int)k >> 4; |
| #endif |
| k1 = b->k; |
| n1 = n + b->wds + 1; |
| for(i = b->maxwds; n1 > i; i <<= 1) |
| k1++; |
| b1 = Balloc(k1); |
| if (b1 == BIGINT_INVALID) { |
| Bfree(b); |
| return b1; |
| } |
| x1 = b1->x; |
| for(i = 0; i < n; i++) |
| *x1++ = 0; |
| x = b->x; |
| xe = x + b->wds; |
| #ifdef Pack_32 |
| if (k &= 0x1f) { |
| k1 = 32 - k; |
| z = 0; |
| do { |
| *x1++ = *x << k | z; |
| z = *x++ >> k1; |
| } |
| while(x < xe); |
| if ((*x1 = z) != 0) |
| ++n1; |
| } |
| #else |
| if (k &= 0xf) { |
| k1 = 16 - k; |
| z = 0; |
| do { |
| *x1++ = *x << k & 0xffff | z; |
| z = *x++ >> k1; |
| } |
| while(x < xe); |
| if (*x1 = z) |
| ++n1; |
| } |
| #endif |
| else do |
| *x1++ = *x++; |
| while(x < xe); |
| b1->wds = n1 - 1; |
| Bfree(b); |
| return b1; |
| } |
| |
| static int |
| cmp |
| #ifdef KR_headers |
| (a, b) Bigint *a, *b; |
| #else |
| (Bigint *a, Bigint *b) |
| #endif |
| { |
| ULong *xa, *xa0, *xb, *xb0; |
| int i, j; |
| |
| if (a == BIGINT_INVALID || b == BIGINT_INVALID) |
| #ifdef DEBUG |
| Bug("cmp called with a or b invalid"); |
| #else |
| return 0; /* equal - the best we can do right now */ |
| #endif |
| |
| i = a->wds; |
| j = b->wds; |
| #ifdef DEBUG |
| if (i > 1 && !a->x[i-1]) |
| Bug("cmp called with a->x[a->wds-1] == 0"); |
| if (j > 1 && !b->x[j-1]) |
| Bug("cmp called with b->x[b->wds-1] == 0"); |
| #endif |
| if (i -= j) |
| return i; |
| xa0 = a->x; |
| xa = xa0 + j; |
| xb0 = b->x; |
| xb = xb0 + j; |
| for(;;) { |
| if (*--xa != *--xb) |
| return *xa < *xb ? -1 : 1; |
| if (xa <= xa0) |
| break; |
| } |
| return 0; |
| } |
| |
| static Bigint * |
| diff |
| #ifdef KR_headers |
| (a, b) Bigint *a, *b; |
| #else |
| (Bigint *a, Bigint *b) |
| #endif |
| { |
| Bigint *c; |
| int i, wa, wb; |
| Long borrow, y; /* We need signed shifts here. */ |
| ULong *xa, *xae, *xb, *xbe, *xc; |
| #ifdef Pack_32 |
| Long z; |
| #endif |
| |
| if (a == BIGINT_INVALID || b == BIGINT_INVALID) |
| return BIGINT_INVALID; |
| |
| i = cmp(a,b); |
| if (!i) { |
| c = Balloc(0); |
| if (c != BIGINT_INVALID) { |
| 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); |
| if (c == BIGINT_INVALID) |
| return c; |
| c->sign = i; |
| wa = a->wds; |
| xa = a->x; |
| xae = xa + wa; |
| wb = b->wds; |
| xb = b->x; |
| xbe = xb + wb; |
| xc = c->x; |
| borrow = 0; |
| #ifdef Pack_32 |
| do { |
| y = (*xa & 0xffff) - (*xb & 0xffff) + borrow; |
| borrow = (ULong)y >> 16; |
| Sign_Extend(borrow, y); |
| z = (*xa++ >> 16) - (*xb++ >> 16) + borrow; |
| borrow = (ULong)z >> 16; |
| Sign_Extend(borrow, z); |
| Storeinc(xc, z, y); |
| } |
| while(xb < xbe); |
| while(xa < xae) { |
| y = (*xa & 0xffff) + borrow; |
| borrow = (ULong)y >> 16; |
| Sign_Extend(borrow, y); |
| z = (*xa++ >> 16) + borrow; |
| borrow = (ULong)z >> 16; |
| Sign_Extend(borrow, z); |
| Storeinc(xc, z, y); |
| } |
| #else |
| do { |
| y = *xa++ - *xb++ + borrow; |
| borrow = y >> 16; |
| Sign_Extend(borrow, y); |
| *xc++ = y & 0xffff; |
| } |
| while(xb < xbe); |
| while(xa < xae) { |
| y = *xa++ + borrow; |
| borrow = y >> 16; |
| Sign_Extend(borrow, y); |
| *xc++ = y & 0xffff; |
| } |
| #endif |
| while(!*--xc) |
| wa--; |
| c->wds = wa; |
| return c; |
| } |
| |
| static double |
| ulp |
| #ifdef KR_headers |
| (_x) double _x; |
| #else |
| (double _x) |
| #endif |
| { |
| _double x; |
| Long L; |
| _double a; |
| |
| value(x) = _x; |
| L = (word0(x) & Exp_mask) - (P-1)*Exp_msk1; |
| #ifndef Sudden_Underflow |
| if (L > 0) { |
| #endif |
| #ifdef IBM |
| L |= Exp_msk1 >> 4; |
| #endif |
| word0(a) = L; |
| word1(a) = 0; |
| #ifndef Sudden_Underflow |
| } |
| else { |
| L = (ULong)-L >> Exp_shift; |
| if (L < Exp_shift) { |
| word0(a) = 0x80000 >> L; |
| word1(a) = 0; |
| } |
| else { |
| word0(a) = 0; |
| L -= Exp_shift; |
| word1(a) = L >= 31 ? 1 : 1 << (31 - L); |
| } |
| } |
| #endif |
| return value(a); |
| } |
| |
| static double |
| b2d |
| #ifdef KR_headers |
| (a, e) Bigint *a; int *e; |
| #else |
| (Bigint *a, int *e) |
| #endif |
| { |
| ULong *xa, *xa0, w, y, z; |
| int k; |
| _double d; |
| #ifdef VAX |
| ULong d0, d1; |
| #else |
| #define d0 word0(d) |
| #define d1 word1(d) |
| #endif |
| |
| if (a == BIGINT_INVALID) |
| return NAN; |
| |
| xa0 = a->x; |
| xa = xa0 + a->wds; |
| y = *--xa; |
| #ifdef DEBUG |
| if (!y) Bug("zero y in b2d"); |
| #endif |
| k = hi0bits(y); |
| *e = 32 - k; |
| #ifdef Pack_32 |
| if (k < Ebits) { |
| d0 = Exp_1 | y >> (Ebits - k); |
| w = xa > xa0 ? *--xa : 0; |
| d1 = y << ((32-Ebits) + k) | w >> (Ebits - k); |
| goto ret_d; |
| } |
| z = xa > xa0 ? *--xa : 0; |
| if (k -= Ebits) { |
| d0 = Exp_1 | y << k | z >> (32 - k); |
| y = xa > xa0 ? *--xa : 0; |
| d1 = z << k | y >> (32 - k); |
| } |
| else { |
| d0 = Exp_1 | y; |
| d1 = z; |
| } |
| #else |
| if (k < Ebits + 16) { |
| z = xa > xa0 ? *--xa : 0; |
| d0 = Exp_1 | y << k - Ebits | z >> Ebits + 16 - k; |
| w = xa > xa0 ? *--xa : 0; |
| y = xa > xa0 ? *--xa : 0; |
| d1 = z << k + 16 - Ebits | w << k - Ebits | y >> 16 + Ebits - k; |
| goto ret_d; |
| } |
| z = xa > xa0 ? *--xa : 0; |
| w = xa > xa0 ? *--xa : 0; |
| k -= Ebits + 16; |
| d0 = Exp_1 | y << k + 16 | z << k | w >> 16 - k; |
| y = xa > xa0 ? *--xa : 0; |
| d1 = w << k + 16 | y << k; |
| #endif |
| ret_d: |
| #ifdef VAX |
| word0(d) = d0 >> 16 | d0 << 16; |
| word1(d) = d1 >> 16 | d1 << 16; |
| #else |
| #undef d0 |
| #undef d1 |
| #endif |
| return value(d); |
| } |
| |
| static Bigint * |
| d2b |
| #ifdef KR_headers |
| (_d, e, bits) double d; int *e, *bits; |
| #else |
| (double _d, int *e, int *bits) |
| #endif |
| { |
| Bigint *b; |
| int de, i, k; |
| ULong *x, y, z; |
| _double d; |
| #ifdef VAX |
| ULong d0, d1; |
| #endif |
| |
| value(d) = _d; |
| #ifdef VAX |
| d0 = word0(d) >> 16 | word0(d) << 16; |
| d1 = word1(d) >> 16 | word1(d) << 16; |
| #else |
| #define d0 word0(d) |
| #define d1 word1(d) |
| #endif |
| |
| #ifdef Pack_32 |
| b = Balloc(1); |
| #else |
| b = Balloc(2); |
| #endif |
| if (b == BIGINT_INVALID) |
| return b; |
| x = b->x; |
| |
| z = d0 & Frac_mask; |
| d0 &= 0x7fffffff; /* clear sign bit, which we ignore */ |
| #ifdef Sudden_Underflow |
| de = (int)(d0 >> Exp_shift); |
| #ifndef IBM |
| z |= Exp_msk11; |
| #endif |
| #else |
| if ((de = (int)(d0 >> Exp_shift)) != 0) |
| z |= Exp_msk1; |
| #endif |
| #ifdef Pack_32 |
| if ((y = d1) != 0) { |
| if ((k = lo0bits(&y)) != 0) { |
| x[0] = y | z << (32 - k); |
| z >>= k; |
| } |
| else |
| x[0] = y; |
| i = b->wds = (x[1] = z) ? 2 : 1; |
| } |
| else { |
| #ifdef DEBUG |
| if (!z) |
| Bug("Zero passed to d2b"); |
| #endif |
| k = lo0bits(&z); |
| x[0] = z; |
| i = b->wds = 1; |
| k += 32; |
| } |
| #else |
| if (y = d1) { |
| if (k = lo0bits(&y)) |
| if (k >= 16) { |
| x[0] = y | z << 32 - k & 0xffff; |
| x[1] = z >> k - 16 & 0xffff; |
| x[2] = z >> k; |
| i = 2; |
| } |
| else { |
| x[0] = y & 0xffff; |
| x[1] = y >> 16 | z << 16 - k & 0xffff; |
| x[2] = z >> k & 0xffff; |
| x[3] = z >> k+16; |
| i = 3; |
| } |
| else { |
| x[0] = y & 0xffff; |
| x[1] = y >> 16; |
| x[2] = z & 0xffff; |
| x[3] = z >> 16; |
| i = 3; |
| } |
| } |
| else { |
| #ifdef DEBUG |
| if (!z) |
| Bug("Zero passed to d2b"); |
| #endif |
| k = lo0bits(&z); |
| if (k >= 16) { |
| x[0] = z; |
| i = 0; |
| } |
| else { |
| x[0] = z & 0xffff; |
| x[1] = z >> 16; |
| i = 1; |
| } |
| k += 32; |
| } |
| while(!x[i]) |
| --i; |
| b->wds = i + 1; |
| #endif |
| #ifndef Sudden_Underflow |
| if (de) { |
| #endif |
| #ifdef IBM |
| *e = (de - Bias - (P-1) << 2) + k; |
| *bits = 4*P + 8 - k - hi0bits(word0(d) & Frac_mask); |
| #else |
| *e = de - Bias - (P-1) + k; |
| *bits = P - k; |
| #endif |
| #ifndef Sudden_Underflow |
| } |
| else { |
| *e = de - Bias - (P-1) + 1 + k; |
| #ifdef Pack_32 |
| *bits = 32*i - hi0bits(x[i-1]); |
| #else |
| *bits = (i+2)*16 - hi0bits(x[i]); |
| #endif |
| } |
| #endif |
| return b; |
| } |
| #undef d0 |
| #undef d1 |
| |
| static double |
| ratio |
| #ifdef KR_headers |
| (a, b) Bigint *a, *b; |
| #else |
| (Bigint *a, Bigint *b) |
| #endif |
| { |
| _double da, db; |
| int k, ka, kb; |
| |
| if (a == BIGINT_INVALID || b == BIGINT_INVALID) |
| return NAN; /* for lack of better value ? */ |
| |
| value(da) = b2d(a, &ka); |
| value(db) = b2d(b, &kb); |
| #ifdef Pack_32 |
| k = ka - kb + 32*(a->wds - b->wds); |
| #else |
| k = ka - kb + 16*(a->wds - b->wds); |
| #endif |
| #ifdef IBM |
| if (k > 0) { |
| word0(da) += (k >> 2)*Exp_msk1; |
| if (k &= 3) |
| da *= 1 << k; |
| } |
| else { |
| k = -k; |
| word0(db) += (k >> 2)*Exp_msk1; |
| if (k &= 3) |
| db *= 1 << k; |
| } |
| #else |
| if (k > 0) |
| word0(da) += k*Exp_msk1; |
| else { |
| k = -k; |
| word0(db) += k*Exp_msk1; |
| } |
| #endif |
| return value(da) / value(db); |
| } |
| |
| static CONST double |
| tens[] = { |
| 1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9, |
| 1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19, |
| 1e20, 1e21, 1e22 |
| #ifdef VAX |
| , 1e23, 1e24 |
| #endif |
| }; |
| |
| #ifdef IEEE_Arith |
| static CONST double bigtens[] = { 1e16, 1e32, 1e64, 1e128, 1e256 }; |
| static CONST double tinytens[] = { 1e-16, 1e-32, 1e-64, 1e-128, 1e-256 }; |
| #define n_bigtens 5 |
| #else |
| #ifdef IBM |
| static CONST double bigtens[] = { 1e16, 1e32, 1e64 }; |
| static CONST double tinytens[] = { 1e-16, 1e-32, 1e-64 }; |
| #define n_bigtens 3 |
| #else |
| static CONST double bigtens[] = { 1e16, 1e32 }; |
| static CONST double tinytens[] = { 1e-16, 1e-32 }; |
| #define n_bigtens 2 |
| #endif |
| #endif |
| |
| double |
| strtod |
| #ifdef KR_headers |
| (s00, se) CONST char *s00; char **se; |
| #else |
| (CONST char *s00, char **se) |
| #endif |
| { |
| int bb2, bb5, bbe, bd2, bd5, bbbits, bs2, c, dsign, |
| e, e1, esign, i, j, k, nd, nd0, nf, nz, nz0, sign; |
| CONST char *s, *s0, *s1; |
| double aadj, aadj1, adj; |
| _double rv, rv0; |
| Long L; |
| ULong y, z; |
| Bigint *bb1, *bd0; |
| Bigint *bb = NULL, *bd = NULL, *bs = NULL, *delta = NULL;/* pacify gcc */ |
| |
| #ifdef ANDROID_CHANGES |
| CONST char decimal_point = '.'; |
| #else /* ANDROID_CHANGES */ |
| #ifndef KR_headers |
| CONST char decimal_point = localeconv()->decimal_point[0]; |
| #else |
| CONST char decimal_point = '.'; |
| #endif |
| |
| #endif /* ANDROID_CHANGES */ |
| |
| sign = nz0 = nz = 0; |
| value(rv) = 0.; |
| |
| |
| for(s = s00; isspace((unsigned char) *s); s++) |
| ; |
| |
| if (*s == '-') { |
| sign = 1; |
| s++; |
| } else if (*s == '+') { |
| s++; |
| } |
| |
| if (*s == '\0') { |
| s = s00; |
| goto ret; |
| } |
| |
| /* "INF" or "INFINITY" */ |
| if (tolower((unsigned char)*s) == 'i' && strncasecmp(s, "inf", 3) == 0) { |
| if (strncasecmp(s + 3, "inity", 5) == 0) |
| s += 8; |
| else |
| s += 3; |
| |
| value(rv) = HUGE_VAL; |
| goto ret; |
| } |
| |
| #ifdef IEEE_Arith |
| /* "NAN" or "NAN(n-char-sequence-opt)" */ |
| if (tolower((unsigned char)*s) == 'n' && strncasecmp(s, "nan", 3) == 0) { |
| /* Build a quiet NaN. */ |
| word0(rv) = NAN_WORD0; |
| word1(rv) = NAN_WORD1; |
| s+= 3; |
| |
| /* Don't interpret (n-char-sequence-opt), for now. */ |
| if (*s == '(') { |
| s0 = s; |
| for (s++; *s != ')' && *s != '\0'; s++) |
| ; |
| if (*s == ')') |
| s++; /* Skip over closing paren ... */ |
| else |
| s = s0; /* ... otherwise go back. */ |
| } |
| |
| goto ret; |
| } |
| #endif |
| |
| if (*s == '0') { |
| #ifndef NO_HEX_FP /*{*/ |
| { |
| static CONST FPI fpi = { 53, 1-1023-53+1, 2046-1023-53+1, 1, SI }; |
| Long exp; |
| ULong bits[2]; |
| switch(s[1]) { |
| case 'x': |
| case 'X': |
| { |
| #ifdef Honor_FLT_ROUNDS |
| FPI fpi1 = fpi; |
| fpi1.rounding = Rounding; |
| #else |
| #define fpi1 fpi |
| #endif |
| switch((i = gethex(&s, &fpi1, &exp, &bb, sign, 0)) & STRTOG_Retmask) { |
| case STRTOG_NoNumber: |
| s = s00; |
| sign = 0; |
| case STRTOG_Zero: |
| break; |
| default: |
| if (bb) { |
| copybits(bits, fpi.nbits, bb); |
| Bfree(bb); |
| } |
| ULtod(((U*)&rv)->L, bits, exp, i); |
| }} |
| goto ret; |
| } |
| } |
| #endif /*}*/ |
| nz0 = 1; |
| while(*++s == '0') ; |
| if (!*s) |
| goto ret; |
| } |
| s0 = s; |
| y = z = 0; |
| for(nd = nf = 0; (c = *s) >= '0' && c <= '9'; nd++, s++) |
| if (nd < 9) |
| y = 10*y + c - '0'; |
| else if (nd < 16) |
| z = 10*z + c - '0'; |
| nd0 = nd; |
| if (c == decimal_point) { |
| c = *++s; |
| if (!nd) { |
| for(; c == '0'; c = *++s) |
| nz++; |
| if (c > '0' && c <= '9') { |
| s0 = s; |
| nf += nz; |
| nz = 0; |
| goto have_dig; |
| } |
| goto dig_done; |
| } |
| for(; c >= '0' && c <= '9'; c = *++s) { |
| have_dig: |
| nz++; |
| if (c -= '0') { |
| nf += nz; |
| for(i = 1; i < nz; i++) |
| if (nd++ < 9) |
| y *= 10; |
| else if (nd <= DBL_DIG + 1) |
| z *= 10; |
| if (nd++ < 9) |
| y = 10*y + c; |
| else if (nd <= DBL_DIG + 1) |
| z = 10*z + c; |
| nz = 0; |
| } |
| } |
| } |
| dig_done: |
| e = 0; |
| if (c == 'e' || c == 'E') { |
| if (!nd && !nz && !nz0) { |
| s = s00; |
| goto ret; |
| } |
| s00 = s; |
| esign = 0; |
| switch(c = *++s) { |
| case '-': |
| esign = 1; |
| /* FALLTHROUGH */ |
| case '+': |
| c = *++s; |
| } |
| if (c >= '0' && c <= '9') { |
| while(c == '0') |
| c = *++s; |
| if (c > '0' && c <= '9') { |
| L = c - '0'; |
| s1 = s; |
| while((c = *++s) >= '0' && c <= '9') |
| L = 10*L + c - '0'; |
| if (s - s1 > 8 || L > 19999) |
| /* Avoid confusion from exponents |
| * so large that e might overflow. |
| */ |
| e = 19999; /* safe for 16 bit ints */ |
| else |
| e = (int)L; |
| if (esign) |
| e = -e; |
| } |
| else |
| e = 0; |
| } |
| else |
| s = s00; |
| } |
| if (!nd) { |
| if (!nz && !nz0) |
| s = s00; |
| goto ret; |
| } |
| e1 = e -= nf; |
| |
| /* Now we have nd0 digits, starting at s0, followed by a |
| * decimal point, followed by nd-nd0 digits. The number we're |
| * after is the integer represented by those digits times |
| * 10**e */ |
| |
| if (!nd0) |
| nd0 = nd; |
| k = nd < DBL_DIG + 1 ? nd : DBL_DIG + 1; |
| value(rv) = y; |
| if (k > 9) |
| value(rv) = tens[k - 9] * value(rv) + z; |
| bd0 = 0; |
| if (nd <= DBL_DIG |
| #ifndef RND_PRODQUOT |
| && FLT_ROUNDS == 1 |
| #endif |
| ) { |
| if (!e) |
| goto ret; |
| if (e > 0) { |
| if (e <= Ten_pmax) { |
| #ifdef VAX |
| goto vax_ovfl_check; |
| #else |
| /* value(rv) = */ rounded_product(value(rv), |
| tens[e]); |
| goto ret; |
| #endif |
| } |
| i = DBL_DIG - nd; |
| if (e <= Ten_pmax + i) { |
| /* A fancier test would sometimes let us do |
| * this for larger i values. |
| */ |
| e -= i; |
| value(rv) *= tens[i]; |
| #ifdef VAX |
| /* VAX exponent range is so narrow we must |
| * worry about overflow here... |
| */ |
| vax_ovfl_check: |
| word0(rv) -= P*Exp_msk1; |
| /* value(rv) = */ rounded_product(value(rv), |
| tens[e]); |
| if ((word0(rv) & Exp_mask) |
| > Exp_msk1*(DBL_MAX_EXP+Bias-1-P)) |
| goto ovfl; |
| word0(rv) += P*Exp_msk1; |
| #else |
| /* value(rv) = */ rounded_product(value(rv), |
| tens[e]); |
| #endif |
| goto ret; |
| } |
| } |
| #ifndef Inaccurate_Divide |
| else if (e >= -Ten_pmax) { |
| /* value(rv) = */ rounded_quotient(value(rv), |
| tens[-e]); |
| goto ret; |
| } |
| #endif |
| } |
| e1 += nd - k; |
| |
| /* Get starting approximation = rv * 10**e1 */ |
| |
| if (e1 > 0) { |
| if ((i = e1 & 15) != 0) |
| value(rv) *= tens[i]; |
| if (e1 &= ~15) { |
| if (e1 > DBL_MAX_10_EXP) { |
| ovfl: |
| errno = ERANGE; |
| value(rv) = HUGE_VAL; |
| if (bd0) |
| goto retfree; |
| goto ret; |
| } |
| if ((e1 = (unsigned int)e1 >> 4) != 0) { |
| for(j = 0; e1 > 1; j++, |
| e1 = (unsigned int)e1 >> 1) |
| if (e1 & 1) |
| value(rv) *= bigtens[j]; |
| /* The last multiplication could overflow. */ |
| word0(rv) -= P*Exp_msk1; |
| value(rv) *= bigtens[j]; |
| if ((z = word0(rv) & Exp_mask) |
| > Exp_msk1*(DBL_MAX_EXP+Bias-P)) |
| goto ovfl; |
| if (z > Exp_msk1*(DBL_MAX_EXP+Bias-1-P)) { |
| /* set to largest number */ |
| /* (Can't trust DBL_MAX) */ |
| word0(rv) = Big0; |
| word1(rv) = Big1; |
| } |
| else |
| word0(rv) += P*Exp_msk1; |
| } |
| } |
| } |
| else if (e1 < 0) { |
| e1 = -e1; |
| if ((i = e1 & 15) != 0) |
| value(rv) /= tens[i]; |
| if (e1 &= ~15) { |
| e1 = (unsigned int)e1 >> 4; |
| if (e1 >= 1 << n_bigtens) |
| goto undfl; |
| for(j = 0; e1 > 1; j++, |
| e1 = (unsigned int)e1 >> 1) |
| if (e1 & 1) |
| value(rv) *= tinytens[j]; |
| /* The last multiplication could underflow. */ |
| value(rv0) = value(rv); |
| value(rv) *= tinytens[j]; |
| if (!value(rv)) { |
| value(rv) = 2.*value(rv0); |
| value(rv) *= tinytens[j]; |
| if (!value(rv)) { |
| undfl: |
| value(rv) = 0.; |
| errno = ERANGE; |
| if (bd0) |
| goto retfree; |
| goto ret; |
| } |
| word0(rv) = Tiny0; |
| word1(rv) = Tiny1; |
| /* The refinement below will clean |
| * this approximation up. |
| */ |
| } |
| } |
| } |
| |
| /* Now the hard part -- adjusting rv to the correct value.*/ |
| |
| /* Put digits into bd: true value = bd * 10^e */ |
| |
| bd0 = s2b(s0, nd0, nd, y); |
| |
| for(;;) { |
| bd = Balloc(bd0->k); |
| Bcopy(bd, bd0); |
| bb = d2b(value(rv), &bbe, &bbbits); /* rv = bb * 2^bbe */ |
| bs = i2b(1); |
| |
| if (e >= 0) { |
| bb2 = bb5 = 0; |
| bd2 = bd5 = e; |
| } |
| else { |
| bb2 = bb5 = -e; |
| bd2 = bd5 = 0; |
| } |
| if (bbe >= 0) |
| bb2 += bbe; |
| else |
| bd2 -= bbe; |
| bs2 = bb2; |
| #ifdef Sudden_Underflow |
| #ifdef IBM |
| j = 1 + 4*P - 3 - bbbits + ((bbe + bbbits - 1) & 3); |
| #else |
| j = P + 1 - bbbits; |
| #endif |
| #else |
| i = bbe + bbbits - 1; /* logb(rv) */ |
| if (i < Emin) /* denormal */ |
| j = bbe + (P-Emin); |
| else |
| j = P + 1 - bbbits; |
| #endif |
| bb2 += j; |
| bd2 += j; |
| i = bb2 < bd2 ? bb2 : bd2; |
| if (i > bs2) |
| i = bs2; |
| if (i > 0) { |
| bb2 -= i; |
| bd2 -= i; |
| bs2 -= i; |
| } |
| if (bb5 > 0) { |
| bs = pow5mult(bs, bb5); |
| bb1 = mult(bs, bb); |
| Bfree(bb); |
| bb = bb1; |
| } |
| if (bb2 > 0) |
| bb = lshift(bb, bb2); |
| if (bd5 > 0) |
| bd = pow5mult(bd, bd5); |
| if (bd2 > 0) |
| bd = lshift(bd, bd2); |
| if (bs2 > 0) |
| bs = lshift(bs, bs2); |
| delta = diff(bb, bd); |
| dsign = delta->sign; |
| delta->sign = 0; |
| i = cmp(delta, bs); |
| if (i < 0) { |
| /* Error is less than half an ulp -- check for |
| * special case of mantissa a power of two. |
| */ |
| if (dsign || word1(rv) || word0(rv) & Bndry_mask) |
| break; |
| delta = lshift(delta,Log2P); |
| if (cmp(delta, bs) > 0) |
| goto drop_down; |
| break; |
| } |
| if (i == 0) { |
| /* exactly half-way between */ |
| if (dsign) { |
| if ((word0(rv) & Bndry_mask1) == Bndry_mask1 |
| && word1(rv) == 0xffffffff) { |
| /*boundary case -- increment exponent*/ |
| word0(rv) = (word0(rv) & Exp_mask) |
| + Exp_msk1 |
| #ifdef IBM |
| | Exp_msk1 >> 4 |
| #endif |
| ; |
| word1(rv) = 0; |
| break; |
| } |
| } |
| else if (!(word0(rv) & Bndry_mask) && !word1(rv)) { |
| drop_down: |
| /* boundary case -- decrement exponent */ |
| #ifdef Sudden_Underflow |
| L = word0(rv) & Exp_mask; |
| #ifdef IBM |
| if (L < Exp_msk1) |
| #else |
| if (L <= Exp_msk1) |
| #endif |
| goto undfl; |
| L -= Exp_msk1; |
| #else |
| L = (word0(rv) & Exp_mask) - Exp_msk1; |
| #endif |
| word0(rv) = L | Bndry_mask1; |
| word1(rv) = 0xffffffff; |
| #ifdef IBM |
| goto cont; |
| #else |
| break; |
| #endif |
| } |
| #ifndef ROUND_BIASED |
| if (!(word1(rv) & LSB)) |
| break; |
| #endif |
| if (dsign) |
| value(rv) += ulp(value(rv)); |
| #ifndef ROUND_BIASED |
| else { |
| value(rv) -= ulp(value(rv)); |
| #ifndef Sudden_Underflow |
| if (!value(rv)) |
| goto undfl; |
| #endif |
| } |
| #endif |
| break; |
| } |
| if ((aadj = ratio(delta, bs)) <= 2.) { |
| if (dsign) |
| aadj = aadj1 = 1.; |
| else if (word1(rv) || word0(rv) & Bndry_mask) { |
| #ifndef Sudden_Underflow |
| if (word1(rv) == Tiny1 && !word0(rv)) |
| goto undfl; |
| #endif |
| aadj = 1.; |
| aadj1 = -1.; |
| } |
| else { |
| /* special case -- power of FLT_RADIX to be */ |
| /* rounded down... */ |
| |
| if (aadj < 2./FLT_RADIX) |
| aadj = 1./FLT_RADIX; |
| else |
| aadj *= 0.5; |
| aadj1 = -aadj; |
| } |
| } |
| else { |
| aadj *= 0.5; |
| aadj1 = dsign ? aadj : -aadj; |
| #ifdef Check_FLT_ROUNDS |
| switch(FLT_ROUNDS) { |
| case 2: /* towards +infinity */ |
| aadj1 -= 0.5; |
| break; |
| case 0: /* towards 0 */ |
| case 3: /* towards -infinity */ |
| aadj1 += 0.5; |
| } |
| #else |
| if (FLT_ROUNDS == 0) |
| aadj1 += 0.5; |
| #endif |
| } |
| y = word0(rv) & Exp_mask; |
| |
| /* Check for overflow */ |
| |
| if (y == Exp_msk1*(DBL_MAX_EXP+Bias-1)) { |
| value(rv0) = value(rv); |
| word0(rv) -= P*Exp_msk1; |
| adj = aadj1 * ulp(value(rv)); |
| value(rv) += adj; |
| if ((word0(rv) & Exp_mask) >= |
| Exp_msk1*(DBL_MAX_EXP+Bias-P)) { |
| if (word0(rv0) == Big0 && word1(rv0) == Big1) |
| goto ovfl; |
| word0(rv) = Big0; |
| word1(rv) = Big1; |
| goto cont; |
| } |
| else |
| word0(rv) += P*Exp_msk1; |
| } |
| else { |
| #ifdef Sudden_Underflow |
| if ((word0(rv) & Exp_mask) <= P*Exp_msk1) { |
| value(rv0) = value(rv); |
| word0(rv) += P*Exp_msk1; |
| adj = aadj1 * ulp(value(rv)); |
| value(rv) += adj; |
| #ifdef IBM |
| if ((word0(rv) & Exp_mask) < P*Exp_msk1) |
| #else |
| if ((word0(rv) & Exp_mask) <= P*Exp_msk1) |
| #endif |
| { |
| if (word0(rv0) == Tiny0 |
| && word1(rv0) == Tiny1) |
| goto undfl; |
| word0(rv) = Tiny0; |
| word1(rv) = Tiny1; |
| goto cont; |
| } |
| else |
| word0(rv) -= P*Exp_msk1; |
| } |
| else { |
| adj = aadj1 * ulp(value(rv)); |
| value(rv) += adj; |
| } |
| #else |
| /* Compute adj so that the IEEE rounding rules will |
| * correctly round rv + adj in some half-way cases. |
| * If rv * ulp(rv) is denormalized (i.e., |
| * y <= (P-1)*Exp_msk1), we must adjust aadj to avoid |
| * trouble from bits lost to denormalization; |
| * example: 1.2e-307 . |
| */ |
| if (y <= (P-1)*Exp_msk1 && aadj >= 1.) { |
| aadj1 = (double)(int)(aadj + 0.5); |
| if (!dsign) |
| aadj1 = -aadj1; |
| } |
| adj = aadj1 * ulp(value(rv)); |
| value(rv) += adj; |
| #endif |
| } |
| z = word0(rv) & Exp_mask; |
| if (y == z) { |
| /* Can we stop now? */ |
| L = aadj; |
| aadj -= L; |
| /* The tolerances below are conservative. */ |
| if (dsign || word1(rv) || word0(rv) & Bndry_mask) { |
| if (aadj < .4999999 || aadj > .5000001) |
| break; |
| } |
| else if (aadj < .4999999/FLT_RADIX) |
| break; |
| } |
| cont: |
| Bfree(bb); |
| Bfree(bd); |
| Bfree(bs); |
| Bfree(delta); |
| } |
| retfree: |
| Bfree(bb); |
| Bfree(bd); |
| Bfree(bs); |
| Bfree(bd0); |
| Bfree(delta); |
| ret: |
| if (se) |
| /* LINTED interface specification */ |
| *se = (char *)s; |
| return sign ? -value(rv) : value(rv); |
| } |
| |
| static int |
| quorem |
| #ifdef KR_headers |
| (b, S) Bigint *b, *S; |
| #else |
| (Bigint *b, Bigint *S) |
| #endif |
| { |
| int n; |
| Long borrow, y; |
| ULong carry, q, ys; |
| ULong *bx, *bxe, *sx, *sxe; |
| #ifdef Pack_32 |
| Long z; |
| ULong si, zs; |
| #endif |
| |
| if (b == BIGINT_INVALID || S == BIGINT_INVALID) |
| return 0; |
| |
| n = S->wds; |
| #ifdef DEBUG |
| /*debug*/ if (b->wds > n) |
| /*debug*/ Bug("oversize b in quorem"); |
| #endif |
| if (b->wds < n) |
| return 0; |
| sx = S->x; |
| sxe = sx + --n; |
| bx = b->x; |
| bxe = bx + n; |
| q = *bxe / (*sxe + 1); /* ensure q <= true quotient */ |
| #ifdef DEBUG |
| /*debug*/ if (q > 9) |
| /*debug*/ Bug("oversized quotient in quorem"); |
| #endif |
| if (q) { |
| borrow = 0; |
| carry = 0; |
| do { |
| #ifdef Pack_32 |
| si = *sx++; |
| ys = (si & 0xffff) * q + carry; |
| zs = (si >> 16) * q + (ys >> 16); |
| carry = zs >> 16; |
| y = (*bx & 0xffff) - (ys & 0xffff) + borrow; |
| borrow = (ULong)y >> 16; |
| Sign_Extend(borrow, y); |
| z = (*bx >> 16) - (zs & 0xffff) + borrow; |
| borrow = (ULong)z >> 16; |
| Sign_Extend(borrow, z); |
| Storeinc(bx, z, y); |
| #else |
| ys = *sx++ * q + carry; |
| carry = ys >> 16; |
| y = *bx - (ys & 0xffff) + borrow; |
| borrow = y >> 16; |
| Sign_Extend(borrow, y); |
| *bx++ = y & 0xffff; |
| #endif |
| } |
| while(sx <= sxe); |
| if (!*bxe) { |
| bx = b->x; |
| while(--bxe > bx && !*bxe) |
| --n; |
| b->wds = n; |
| } |
| } |
| if (cmp(b, S) >= 0) { |
| q++; |
| borrow = 0; |
| carry = 0; |
| bx = b->x; |
| sx = S->x; |
| do { |
| #ifdef Pack_32 |
| si = *sx++; |
| ys = (si & 0xffff) + carry; |
| zs = (si >> 16) + (ys >> 16); |
| carry = zs >> 16; |
| y = (*bx & 0xffff) - (ys & 0xffff) + borrow; |
| borrow = (ULong)y >> 16; |
| Sign_Extend(borrow, y); |
| z = (*bx >> 16) - (zs & 0xffff) + borrow; |
| borrow = (ULong)z >> 16; |
| Sign_Extend(borrow, z); |
| Storeinc(bx, z, y); |
| #else |
| ys = *sx++ + carry; |
| carry = ys >> 16; |
| y = *bx - (ys & 0xffff) + borrow; |
| borrow = y >> 16; |
| Sign_Extend(borrow, y); |
| *bx++ = y & 0xffff; |
| #endif |
| } |
| while(sx <= sxe); |
| bx = b->x; |
| bxe = bx + n; |
| if (!*bxe) { |
| while(--bxe > bx && !*bxe) |
| --n; |
| b->wds = n; |
| } |
| } |
| return q; |
| } |
| |
| /* freedtoa(s) must be used to free values s returned by dtoa |
| * when MULTIPLE_THREADS is #defined. It should be used in all cases, |
| * but for consistency with earlier versions of dtoa, it is optional |
| * when MULTIPLE_THREADS is not defined. |
| */ |
| |
| void |
| #ifdef KR_headers |
| freedtoa(s) char *s; |
| #else |
| freedtoa(char *s) |
| #endif |
| { |
| free(s); |
| } |
| |
| |
| |
| /* dtoa for IEEE arithmetic (dmg): convert double to ASCII string. |
| * |
| * Inspired by "How to Print Floating-Point Numbers Accurately" by |
| * Guy L. Steele, Jr. and Jon L. White [Proc. ACM SIGPLAN '90, pp. 92-101]. |
| * |
| * Modifications: |
| * 1. Rather than iterating, we use a simple numeric overestimate |
| * to determine k = floor(log10(d)). We scale relevant |
| * quantities using O(log2(k)) rather than O(k) multiplications. |
| * 2. For some modes > 2 (corresponding to ecvt and fcvt), we don't |
| * try to generate digits strictly left to right. Instead, we |
| * compute with fewer bits and propagate the carry if necessary |
| * when rounding the final digit up. This is often faster. |
| * 3. Under the assumption that input will be rounded nearest, |
| * mode 0 renders 1e23 as 1e23 rather than 9.999999999999999e22. |
| * That is, we allow equality in stopping tests when the |
| * round-nearest rule will give the same floating-point value |
| * as would satisfaction of the stopping test with strict |
| * inequality. |
| * 4. We remove common factors of powers of 2 from relevant |
| * quantities. |
| * 5. When converting floating-point integers less than 1e16, |
| * we use floating-point arithmetic rather than resorting |
| * to multiple-precision integers. |
| * 6. When asked to produce fewer than 15 digits, we first try |
| * to get by with floating-point arithmetic; we resort to |
| * multiple-precision integer arithmetic only if we cannot |
| * guarantee that the floating-point calculation has given |
| * the correctly rounded result. For k requested digits and |
| * "uniformly" distributed input, the probability is |
| * something like 10^(k-15) that we must resort to the Long |
| * calculation. |
| */ |
| |
| __LIBC_HIDDEN__ char * |
| __dtoa |
| #ifdef KR_headers |
| (_d, mode, ndigits, decpt, sign, rve) |
| double _d; int mode, ndigits, *decpt, *sign; char **rve; |
| #else |
| (double _d, int mode, int ndigits, int *decpt, int *sign, char **rve) |
| #endif |
| { |
| /* Arguments ndigits, decpt, sign are similar to those |
| of ecvt and fcvt; trailing zeros are suppressed from |
| the returned string. If not null, *rve is set to point |
| to the end of the return value. If d is +-Infinity or NaN, |
| then *decpt is set to 9999. |
| |
| mode: |
| 0 ==> shortest string that yields d when read in |
| and rounded to nearest. |
| 1 ==> like 0, but with Steele & White stopping rule; |
| e.g. with IEEE P754 arithmetic , mode 0 gives |
| 1e23 whereas mode 1 gives 9.999999999999999e22. |
| 2 ==> max(1,ndigits) significant digits. This gives a |
| return value similar to that of ecvt, except |
| that trailing zeros are suppressed. |
| 3 ==> through ndigits past the decimal point. This |
| gives a return value similar to that from fcvt, |
| except that trailing zeros are suppressed, and |
| ndigits can be negative. |
| 4-9 should give the same return values as 2-3, i.e., |
| 4 <= mode <= 9 ==> same return as mode |
| 2 + (mode & 1). These modes are mainly for |
| debugging; often they run slower but sometimes |
| faster than modes 2-3. |
| 4,5,8,9 ==> left-to-right digit generation. |
| 6-9 ==> don't try fast floating-point estimate |
| (if applicable). |
| |
| Values of mode other than 0-9 are treated as mode 0. |
| |
| Sufficient space is allocated to the return value |
| to hold the suppressed trailing zeros. |
| */ |
| |
| int bbits, b2, b5, be, dig, i, ieps, ilim0, |
| j, jj1, k, k0, k_check, leftright, m2, m5, s2, s5, |
| try_quick; |
| int ilim = 0, ilim1 = 0, spec_case = 0; /* pacify gcc */ |
| Long L; |
| #ifndef Sudden_Underflow |
| int denorm; |
| ULong x; |
| #endif |
| Bigint *b, *b1, *delta, *mhi, *S; |
| Bigint *mlo = NULL; /* pacify gcc */ |
| double ds; |
| char *s, *s0; |
| Bigint *result = NULL; |
| int result_k = 0; |
| _double d, d2, eps; |
| |
| value(d) = _d; |
| |
| if (word0(d) & Sign_bit) { |
| /* set sign for everything, including 0's and NaNs */ |
| *sign = 1; |
| word0(d) &= ~Sign_bit; /* clear sign bit */ |
| } |
| else |
| *sign = 0; |
| |
| #if defined(IEEE_Arith) + defined(VAX) |
| #ifdef IEEE_Arith |
| if ((word0(d) & Exp_mask) == Exp_mask) |
| #else |
| if (word0(d) == 0x8000) |
| #endif |
| { |
| /* Infinity or NaN */ |
| *decpt = 9999; |
| s = |
| #ifdef IEEE_Arith |
| !word1(d) && !(word0(d) & 0xfffff) ? "Infinity" : |
| #endif |
| "NaN"; |
| result = Balloc(strlen(s)+1); |
| if (result == BIGINT_INVALID) |
| return NULL; |
| s0 = (char *)(void *)result; |
| strcpy(s0, s); |
| if (rve) |
| *rve = |
| #ifdef IEEE_Arith |
| s0[3] ? s0 + 8 : |
| #endif |
| s0 + 3; |
| return s0; |
| } |
| #endif |
| #ifdef IBM |
| value(d) += 0; /* normalize */ |
| #endif |
| if (!value(d)) { |
| *decpt = 1; |
| result = Balloc(2); |
| if (result == BIGINT_INVALID) |
| return NULL; |
| s0 = (char *)(void *)result; |
| strcpy(s0, "0"); |
| if (rve) |
| *rve = s0 + 1; |
| return s0; |
| } |
| |
| b = d2b(value(d), &be, &bbits); |
| #ifdef Sudden_Underflow |
| i = (int)(word0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1)); |
| #else |
| if ((i = (int)(word0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1))) != 0) { |
| #endif |
| value(d2) = value(d); |
| word0(d2) &= Frac_mask1; |
| word0(d2) |= Exp_11; |
| #ifdef IBM |
| if (j = 11 - hi0bits(word0(d2) & Frac_mask)) |
| value(d2) /= 1 << j; |
| #endif |
| |
| /* log(x) ~=~ log(1.5) + (x-1.5)/1.5 |
| * log10(x) = log(x) / log(10) |
| * ~=~ log(1.5)/log(10) + (x-1.5)/(1.5*log(10)) |
| * log10(d) = (i-Bias)*log(2)/log(10) + log10(d2) |
| * |
| * This suggests computing an approximation k to log10(d) by |
| * |
| * k = (i - Bias)*0.301029995663981 |
| * + ( (d2-1.5)*0.289529654602168 + 0.176091259055681 ); |
| * |
| * We want k to be too large rather than too small. |
| * The error in the first-order Taylor series approximation |
| * is in our favor, so we just round up the constant enough |
| * to compensate for any error in the multiplication of |
| * (i - Bias) by 0.301029995663981; since |i - Bias| <= 1077, |
| * and 1077 * 0.30103 * 2^-52 ~=~ 7.2e-14, |
| * adding 1e-13 to the constant term more than suffices. |
| * Hence we adjust the constant term to 0.1760912590558. |
| * (We could get a more accurate k by invoking log10, |
| * but this is probably not worthwhile.) |
| */ |
| |
| i -= Bias; |
| #ifdef IBM |
| i <<= 2; |
| i += j; |
| #endif |
| #ifndef Sudden_Underflow |
| denorm = 0; |
| } |
| else { |
| /* d is denormalized */ |
| |
| i = bbits + be + (Bias + (P-1) - 1); |
| x = i > 32 ? word0(d) << (64 - i) | word1(d) >> (i - 32) |
| : word1(d) << (32 - i); |
| value(d2) = x; |
| word0(d2) -= 31*Exp_msk1; /* adjust exponent */ |
| i -= (Bias + (P-1) - 1) + 1; |
| denorm = 1; |
| } |
| #endif |
| ds = (value(d2)-1.5)*0.289529654602168 + 0.1760912590558 + |
| i*0.301029995663981; |
| k = (int)ds; |
| if (ds < 0. && ds != k) |
| k--; /* want k = floor(ds) */ |
| k_check = 1; |
| if (k >= 0 && k <= Ten_pmax) { |
| if (value(d) < tens[k]) |
| k--; |
| k_check = 0; |
| } |
| j = bbits - i - 1; |
| if (j >= 0) { |
| b2 = 0; |
| s2 = j; |
| } |
| else { |
| b2 = -j; |
| s2 = 0; |
| } |
| if (k >= 0) { |
| b5 = 0; |
| s5 = k; |
| s2 += k; |
| } |
| else { |
| b2 -= k; |
| b5 = -k; |
| s5 = 0; |
| } |
| if (mode < 0 || mode > 9) |
| mode = 0; |
| try_quick = 1; |
| if (mode > 5) { |
| mode -= 4; |
| try_quick = 0; |
| } |
| leftright = 1; |
| switch(mode) { |
| case 0: |
| case 1: |
| ilim = ilim1 = -1; |
| i = 18; |
| ndigits = 0; |
| break; |
| case 2: |
| leftright = 0; |
| /* FALLTHROUGH */ |
| case 4: |
| if (ndigits <= 0) |
| ndigits = 1; |
| ilim = ilim1 = i = ndigits; |
| break; |
| case 3: |
| leftright = 0; |
| /* FALLTHROUGH */ |
| case 5: |
| i = ndigits + k + 1; |
| ilim = i; |
| ilim1 = i - 1; |
| if (i <= 0) |
| i = 1; |
| } |
| j = sizeof(ULong); |
| for(result_k = 0; (int)(sizeof(Bigint) - sizeof(ULong)) + j <= i; |
| j <<= 1) result_k++; |
| // this is really a ugly hack, the code uses Balloc |
| // instead of malloc, but casts the result into a char* |
| // it seems the only reason to do that is due to the |
| // complicated way the block size need to be computed |
| // buuurk.... |
| result = Balloc(result_k); |
| if (result == BIGINT_INVALID) { |
| Bfree(b); |
| return NULL; |
| } |
| s = s0 = (char *)(void *)result; |
| |
| if (ilim >= 0 && ilim <= Quick_max && try_quick) { |
| |
| /* Try to get by with floating-point arithmetic. */ |
| |
| i = 0; |
| value(d2) = value(d); |
| k0 = k; |
| ilim0 = ilim; |
| ieps = 2; /* conservative */ |
| if (k > 0) { |
| ds = tens[k&0xf]; |
| j = (unsigned int)k >> 4; |
| if (j & Bletch) { |
| /* prevent overflows */ |
| j &= Bletch - 1; |
| value(d) /= bigtens[n_bigtens-1]; |
| ieps++; |
| } |
| for(; j; j = (unsigned int)j >> 1, i++) |
| if (j & 1) { |
| ieps++; |
| ds *= bigtens[i]; |
| } |
| value(d) /= ds; |
| } |
| else if ((jj1 = -k) != 0) { |
| value(d) *= tens[jj1 & 0xf]; |
| for(j = (unsigned int)jj1 >> 4; j; |
| j = (unsigned int)j >> 1, i++) |
| if (j & 1) { |
| ieps++; |
| value(d) *= bigtens[i]; |
| } |
| } |
| if (k_check && value(d) < 1. && ilim > 0) { |
| if (ilim1 <= 0) |
| goto fast_failed; |
| ilim = ilim1; |
| k--; |
| value(d) *= 10.; |
| ieps++; |
| } |
| value(eps) = ieps*value(d) + 7.; |
| word0(eps) -= (P-1)*Exp_msk1; |
| if (ilim == 0) { |
| S = mhi = 0; |
| value(d) -= 5.; |
| if (value(d) > value(eps)) |
| goto one_digit; |
| if (value(d) < -value(eps)) |
| goto no_digits; |
| goto fast_failed; |
| } |
| #ifndef No_leftright |
| if (leftright) { |
| /* Use Steele & White method of only |
| * generating digits needed. |
| */ |
| value(eps) = 0.5/tens[ilim-1] - value(eps); |
| for(i = 0;;) { |
| L = value(d); |
| value(d) -= L; |
| *s++ = '0' + (int)L; |
| if (value(d) < value(eps)) |
| goto ret1; |
| if (1. - value(d) < value(eps)) |
| goto bump_up; |
| if (++i >= ilim) |
| break; |
| value(eps) *= 10.; |
| value(d) *= 10.; |
| } |
| } |
| else { |
| #endif |
| /* Generate ilim digits, then fix them up. */ |
| value(eps) *= tens[ilim-1]; |
| for(i = 1;; i++, value(d) *= 10.) { |
| L = value(d); |
| value(d) -= L; |
| *s++ = '0' + (int)L; |
| if (i == ilim) { |
| if (value(d) > 0.5 + value(eps)) |
| goto bump_up; |
| else if (value(d) < 0.5 - value(eps)) { |
| while(*--s == '0'); |
| s++; |
| goto ret1; |
| } |
| break; |
| } |
| } |
| #ifndef No_leftright |
| } |
| #endif |
| fast_failed: |
| s = s0; |
| value(d) = value(d2); |
| k = k0; |
| ilim = ilim0; |
| } |
| |
| /* Do we have a "small" integer? */ |
| |
| if (be >= 0 && k <= Int_max) { |
| /* Yes. */ |
| ds = tens[k]; |
| if (ndigits < 0 && ilim <= 0) { |
| S = mhi = 0; |
| if (ilim < 0 || value(d) <= 5*ds) |
| goto no_digits; |
| goto one_digit; |
| } |
| for(i = 1;; i++) { |
| L = value(d) / ds; |
| value(d) -= L*ds; |
| #ifdef Check_FLT_ROUNDS |
| /* If FLT_ROUNDS == 2, L will usually be high by 1 */ |
| if (value(d) < 0) { |
| L--; |
| value(d) += ds; |
| } |
| #endif |
| *s++ = '0' + (int)L; |
| if (i == ilim) { |
| value(d) += value(d); |
| if (value(d) > ds || (value(d) == ds && L & 1)) { |
| bump_up: |
| while(*--s == '9') |
| if (s == s0) { |
| k++; |
| *s = '0'; |
| break; |
| } |
| ++*s++; |
| } |
| break; |
| } |
| if (!(value(d) *= 10.)) |
| break; |
| } |
| goto ret1; |
| } |
| |
| m2 = b2; |
| m5 = b5; |
| mhi = mlo = 0; |
| if (leftright) { |
| if (mode < 2) { |
| i = |
| #ifndef Sudden_Underflow |
| denorm ? be + (Bias + (P-1) - 1 + 1) : |
| #endif |
| #ifdef IBM |
| 1 + 4*P - 3 - bbits + ((bbits + be - 1) & 3); |
| #else |
| 1 + P - bbits; |
| #endif |
| } |
| else { |
| j = ilim - 1; |
| if (m5 >= j) |
| m5 -= j; |
| else { |
| s5 += j -= m5; |
| b5 += j; |
| m5 = 0; |
| } |
| if ((i = ilim) < 0) { |
| m2 -= i; |
| i = 0; |
| } |
| } |
| b2 += i; |
| s2 += i; |
| mhi = i2b(1); |
| } |
| if (m2 > 0 && s2 > 0) { |
| i = m2 < s2 ? m2 : s2; |
| b2 -= i; |
| m2 -= i; |
| s2 -= i; |
| } |
| if (b5 > 0) { |
| if (leftright) { |
| if (m5 > 0) { |
| mhi = pow5mult(mhi, m5); |
| b1 = mult(mhi, b); |
| Bfree(b); |
| b = b1; |
| } |
| if ((j = b5 - m5) != 0) |
| b = pow5mult(b, j); |
| } |
| else |
| b = pow5mult(b, b5); |
| } |
| S = i2b(1); |
| if (s5 > 0) |
| S = pow5mult(S, s5); |
| |
| /* Check for special case that d is a normalized power of 2. */ |
| |
| if (mode < 2) { |
| if (!word1(d) && !(word0(d) & Bndry_mask) |
| #ifndef Sudden_Underflow |
| && word0(d) & Exp_mask |
| #endif |
| ) { |
| /* The special case */ |
| b2 += Log2P; |
| s2 += Log2P; |
| spec_case = 1; |
| } |
| else |
| spec_case = 0; |
| } |
| |
| /* Arrange for convenient computation of quotients: |
| * shift left if necessary so divisor has 4 leading 0 bits. |
| * |
| * Perhaps we should just compute leading 28 bits of S once |
| * and for all and pass them and a shift to quorem, so it |
| * can do shifts and ors to compute the numerator for q. |
| */ |
| if (S == BIGINT_INVALID) { |
| i = 0; |
| } else { |
| #ifdef Pack_32 |
| if ((i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0x1f) != 0) |
| i = 32 - i; |
| #else |
| if (i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0xf) |
| i = 16 - i; |
| #endif |
| } |
| |
| if (i > 4) { |
| i -= 4; |
| b2 += i; |
| m2 += i; |
| s2 += i; |
| } |
| else if (i < 4) { |
| i += 28; |
| b2 += i; |
| m2 += i; |
| s2 += i; |
| } |
| if (b2 > 0) |
| b = lshift(b, b2); |
| if (s2 > 0) |
| S = lshift(S, s2); |
| if (k_check) { |
| if (cmp(b,S) < 0) { |
| k--; |
| b = multadd(b, 10, 0); /* we botched the k estimate */ |
| if (leftright) |
| mhi = multadd(mhi, 10, 0); |
| ilim = ilim1; |
| } |
| } |
| if (ilim <= 0 && mode > 2) { |
| if (ilim < 0 || cmp(b,S = multadd(S,5,0)) <= 0) { |
| /* no digits, fcvt style */ |
| no_digits: |
| k = -1 - ndigits; |
| goto ret; |
| } |
| one_digit: |
| *s++ = '1'; |
| k++; |
| goto ret; |
| } |
| if (leftright) { |
| if (m2 > 0) |
| mhi = lshift(mhi, m2); |
| |
| /* Compute mlo -- check for special case |
| * that d is a normalized power of 2. |
| */ |
| |
| mlo = mhi; |
| if (spec_case) { |
| mhi = Balloc(mhi->k); |
| Bcopy(mhi, mlo); |
| mhi = lshift(mhi, Log2P); |
| } |
| |
| for(i = 1;;i++) { |
| dig = quorem(b,S) + '0'; |
| /* Do we yet have the shortest decimal string |
| * that will round to d? |
| */ |
| j = cmp(b, mlo); |
| delta = diff(S, mhi); |
| jj1 = delta->sign ? 1 : cmp(b, delta); |
| Bfree(delta); |
| #ifndef ROUND_BIASED |
| if (jj1 == 0 && !mode && !(word1(d) & 1)) { |
| if (dig == '9') |
| goto round_9_up; |
| if (j > 0) |
| dig++; |
| *s++ = dig; |
| goto ret; |
| } |
| #endif |
| if (j < 0 || (j == 0 && !mode |
| #ifndef ROUND_BIASED |
| && !(word1(d) & 1) |
| #endif |
| )) { |
| if (jj1 > 0) { |
| b = lshift(b, 1); |
| jj1 = cmp(b, S); |
| if ((jj1 > 0 || (jj1 == 0 && dig & 1)) |
| && dig++ == '9') |
| goto round_9_up; |
| } |
| *s++ = dig; |
| goto ret; |
| } |
| if (jj1 > 0) { |
| if (dig == '9') { /* possible if i == 1 */ |
| round_9_up: |
| *s++ = '9'; |
| goto roundoff; |
| } |
| *s++ = dig + 1; |
| goto ret; |
| } |
| *s++ = dig; |
| if (i == ilim) |
| break; |
| b = multadd(b, 10, 0); |
| if (mlo == mhi) |
| mlo = mhi = multadd(mhi, 10, 0); |
| else { |
| mlo = multadd(mlo, 10, 0); |
| mhi = multadd(mhi, 10, 0); |
| } |
| } |
| } |
| else |
| for(i = 1;; i++) { |
| *s++ = dig = quorem(b,S) + '0'; |
| if (i >= ilim) |
| break; |
| b = multadd(b, 10, 0); |
| } |
| |
| /* Round off last digit */ |
| |
| b = lshift(b, 1); |
| j = cmp(b, S); |
| if (j > 0 || (j == 0 && dig & 1)) { |
| roundoff: |
| while(*--s == '9') |
| if (s == s0) { |
| k++; |
| *s++ = '1'; |
| goto ret; |
| } |
| ++*s++; |
| } |
| else { |
| while(*--s == '0'); |
| s++; |
| } |
| ret: |
| Bfree(S); |
| if (mhi) { |
| if (mlo && mlo != mhi) |
| Bfree(mlo); |
| Bfree(mhi); |
| } |
| ret1: |
| Bfree(b); |
| if (s == s0) { /* don't return empty string */ |
| *s++ = '0'; |
| k = 0; |
| } |
| *s = 0; |
| *decpt = k + 1; |
| if (rve) |
| *rve = s; |
| return s0; |
| } |
| |
| #include <limits.h> |
| |
| char * |
| rv_alloc(int i) |
| { |
| int j, k, *r; |
| |
| j = sizeof(ULong); |
| for(k = 0; |
| sizeof(Bigint) - sizeof(ULong) - sizeof(int) + j <= i; |
| j <<= 1) |
| k++; |
| r = (int*)Balloc(k); |
| *r = k; |
| return (char *)(r+1); |
| } |
| |
| char * |
| nrv_alloc(char *s, char **rve, int n) |
| { |
| char *rv, *t; |
| |
| t = rv = rv_alloc(n); |
| while((*t = *s++) !=0) |
| t++; |
| if (rve) |
| *rve = t; |
| return rv; |
| } |
| |
| |
| /* Strings values used by dtoa() */ |
| #define INFSTR "Infinity" |
| #define NANSTR "NaN" |
| |
| #define DBL_ADJ (DBL_MAX_EXP - 2 + ((DBL_MANT_DIG - 1) % 4)) |
| #define LDBL_ADJ (LDBL_MAX_EXP - 2 + ((LDBL_MANT_DIG - 1) % 4)) |
| |
| /* |
| * Round up the given digit string. If the digit string is fff...f, |
| * this procedure sets it to 100...0 and returns 1 to indicate that |
| * the exponent needs to be bumped. Otherwise, 0 is returned. |
| */ |
| static int |
| roundup(char *s0, int ndigits) |
| { |
| char *s; |
| |
| for (s = s0 + ndigits - 1; *s == 0xf; s--) { |
| if (s == s0) { |
| *s = 1; |
| return (1); |
| } |
| *s = 0; |
| } |
| ++*s; |
| return (0); |
| } |
| |
| /* |
| * Round the given digit string to ndigits digits according to the |
| * current rounding mode. Note that this could produce a string whose |
| * value is not representable in the corresponding floating-point |
| * type. The exponent pointed to by decpt is adjusted if necessary. |
| */ |
| static void |
| dorounding(char *s0, int ndigits, int sign, int *decpt) |
| { |
| int adjust = 0; /* do we need to adjust the exponent? */ |
| |
| switch (FLT_ROUNDS) { |
| case 0: /* toward zero */ |
| default: /* implementation-defined */ |
| break; |
| case 1: /* to nearest, halfway rounds to even */ |
| if ((s0[ndigits] > 8) || |
| (s0[ndigits] == 8 && s0[ndigits + 1] & 1)) |
| adjust = roundup(s0, ndigits); |
| break; |
| case 2: /* toward +inf */ |
| if (sign == 0) |
| adjust = roundup(s0, ndigits); |
| break; |
| case 3: /* toward -inf */ |
| if (sign != 0) |
| adjust = roundup(s0, ndigits); |
| break; |
| } |
| |
| if (adjust) |
| *decpt += 4; |
| } |
| |
| /* |
| * This procedure converts a double-precision number in IEEE format |
| * into a string of hexadecimal digits and an exponent of 2. Its |
| * behavior is bug-for-bug compatible with dtoa() in mode 2, with the |
| * following exceptions: |
| * |
| * - An ndigits < 0 causes it to use as many digits as necessary to |
| * represent the number exactly. |
| * - The additional xdigs argument should point to either the string |
| * "0123456789ABCDEF" or the string "0123456789abcdef", depending on |
| * which case is desired. |
| * - This routine does not repeat dtoa's mistake of setting decpt |
| * to 9999 in the case of an infinity or NaN. INT_MAX is used |
| * for this purpose instead. |
| * |
| * Note that the C99 standard does not specify what the leading digit |
| * should be for non-zero numbers. For instance, 0x1.3p3 is the same |
| * as 0x2.6p2 is the same as 0x4.cp3. This implementation chooses the |
| * first digit so that subsequent digits are aligned on nibble |
| * boundaries (before rounding). |
| * |
| * Inputs: d, xdigs, ndigits |
| * Outputs: decpt, sign, rve |
| */ |
| char * |
| __hdtoa(double d, const char *xdigs, int ndigits, int *decpt, int *sign, |
| char **rve) |
| { |
| static const int sigfigs = (DBL_MANT_DIG + 3) / 4; |
| union IEEEd2bits u; |
| char *s, *s0; |
| int bufsize, f; |
| |
| u.d = d; |
| *sign = u.bits.sign; |
| |
| switch (f = fpclassify(d)) { |
| case FP_NORMAL: |
| *decpt = u.bits.exp - DBL_ADJ; |
| break; |
| case FP_ZERO: |
| return_zero: |
| *decpt = 1; |
| return (nrv_alloc("0", rve, 1)); |
| case FP_SUBNORMAL: |
| /* |
| * For processors that treat subnormals as zero, comparison |
| * with zero will be equal, so we jump to the FP_ZERO case. |
| */ |
| if(u.d == 0.0) goto return_zero; |
| u.d *= 0x1p514; |
| *decpt = u.bits.exp - (514 + DBL_ADJ); |
| break; |
| case FP_INFINITE: |
| *decpt = INT_MAX; |
| return (nrv_alloc(INFSTR, rve, sizeof(INFSTR) - 1)); |
| case FP_NAN: |
| *decpt = INT_MAX; |
| return (nrv_alloc(NANSTR, rve, sizeof(NANSTR) - 1)); |
| default: |
| #ifdef DEBUG |
| BugPrintf("fpclassify returned %d\n", f); |
| #endif |
| return 0; // FIXME?? |
| } |
| |
| /* FP_NORMAL or FP_SUBNORMAL */ |
| |
| if (ndigits == 0) /* dtoa() compatibility */ |
| ndigits = 1; |
| |
| /* |
| * For simplicity, we generate all the digits even if the |
| * caller has requested fewer. |
| */ |
| bufsize = (sigfigs > ndigits) ? sigfigs : ndigits; |
| s0 = rv_alloc(bufsize); |
| |
| /* |
| * We work from right to left, first adding any requested zero |
| * padding, then the least significant portion of the |
| * mantissa, followed by the most significant. The buffer is |
| * filled with the byte values 0x0 through 0xf, which are |
| * converted to xdigs[0x0] through xdigs[0xf] after the |
| * rounding phase. |
| */ |
| for (s = s0 + bufsize - 1; s > s0 + sigfigs - 1; s--) |
| *s = 0; |
| for (; s > s0 + sigfigs - (DBL_MANL_SIZE / 4) - 1 && s > s0; s--) { |
| *s = u.bits.manl & 0xf; |
| u.bits.manl >>= 4; |
| } |
| for (; s > s0; s--) { |
| *s = u.bits.manh & 0xf; |
| u.bits.manh >>= 4; |
| } |
| |
| /* |
| * At this point, we have snarfed all the bits in the |
| * mantissa, with the possible exception of the highest-order |
| * (partial) nibble, which is dealt with by the next |
| * statement. We also tack on the implicit normalization bit. |
| */ |
| *s = u.bits.manh | (1U << ((DBL_MANT_DIG - 1) % 4)); |
| |
| /* If ndigits < 0, we are expected to auto-size the precision. */ |
| if (ndigits < 0) { |
| for (ndigits = sigfigs; s0[ndigits - 1] == 0; ndigits--) |
| ; |
| } |
| |
| if (sigfigs > ndigits && s0[ndigits] != 0) |
| dorounding(s0, ndigits, u.bits.sign, decpt); |
| |
| s = s0 + ndigits; |
| if (rve != NULL) |
| *rve = s; |
| *s-- = '\0'; |
| for (; s >= s0; s--) |
| *s = xdigs[(unsigned int)*s]; |
| |
| return (s0); |
| } |
| |
| #ifndef NO_HEX_FP /*{*/ |
| |
| static int |
| gethex( CONST char **sp, CONST FPI *fpi, Long *exp, Bigint **bp, int sign, locale_t loc) |
| { |
| Bigint *b; |
| CONST unsigned char *decpt, *s0, *s, *s1; |
| unsigned char *strunc; |
| int big, esign, havedig, irv, j, k, n, n0, nbits, up, zret; |
| ULong L, lostbits, *x; |
| Long e, e1; |
| #ifdef USE_LOCALE |
| int i; |
| NORMALIZE_LOCALE(loc); |
| #ifdef NO_LOCALE_CACHE |
| const unsigned char *decimalpoint = (unsigned char*)localeconv_l(loc)->decimal_point; |
| #else |
| const unsigned char *decimalpoint; |
| static unsigned char *decimalpoint_cache; |
| if (!(s0 = decimalpoint_cache)) { |
| s0 = (unsigned char*)localeconv_l(loc)->decimal_point; |
| if ((decimalpoint_cache = (char*)MALLOC(strlen(s0) + 1))) { |
| strcpy(decimalpoint_cache, s0); |
| s0 = decimalpoint_cache; |
| } |
| } |
| decimalpoint = s0; |
| #endif |
| #endif |
| |
| #ifndef ANDROID_CHANGES |
| if (!hexdig['0']) |
| hexdig_init_D2A(); |
| #endif |
| |
| *bp = 0; |
| havedig = 0; |
| s0 = *(CONST unsigned char **)sp + 2; |
| while(s0[havedig] == '0') |
| havedig++; |
| s0 += havedig; |
| s = s0; |
| decpt = 0; |
| zret = 0; |
| e = 0; |
| if (hexdig[*s]) |
| havedig++; |
| else { |
| zret = 1; |
| #ifdef USE_LOCALE |
| for(i = 0; decimalpoint[i]; ++i) { |
| if (s[i] != decimalpoint[i]) |
| goto pcheck; |
| } |
| decpt = s += i; |
| #else |
| if (*s != '.') |
| goto pcheck; |
| decpt = ++s; |
| #endif |
| if (!hexdig[*s]) |
| goto pcheck; |
| while(*s == '0') |
| s++; |
| if (hexdig[*s]) |
| zret = 0; |
| havedig = 1; |
| s0 = s; |
| } |
| while(hexdig[*s]) |
| s++; |
| #ifdef USE_LOCALE |
| if (*s == *decimalpoint && !decpt) { |
| for(i = 1; decimalpoint[i]; ++i) { |
| if (s[i] != decimalpoint[i]) |
| goto pcheck; |
| } |
| decpt = s += i; |
| #else |
| if (*s == '.' && !decpt) { |
| decpt = ++s; |
| #endif |
| while(hexdig[*s]) |
| s++; |
| }/*}*/ |
| if (decpt) |
| e = -(((Long)(s-decpt)) << 2); |
| pcheck: |
| s1 = s; |
| big = esign = 0; |
| switch(*s) { |
| case 'p': |
| case 'P': |
| switch(*++s) { |
| case '-': |
| esign = 1; |
| /* no break */ |
| case '+': |
| s++; |
| } |
| if ((n = hexdig[*s]) == 0 || n > 0x19) { |
| s = s1; |
| break; |
| } |
| e1 = n - 0x10; |
| while((n = hexdig[*++s]) !=0 && n <= 0x19) { |
| if (e1 & 0xf8000000) |
| big = 1; |
| e1 = 10*e1 + n - 0x10; |
| } |
| if (esign) |
| e1 = -e1; |
| e += e1; |
| } |
| *sp = (char*)s; |
| if (!havedig) |
| *sp = (char*)s0 - 1; |
| if (zret) |
| return STRTOG_Zero; |
| if (big) { |
| if (esign) { |
| switch(fpi->rounding) { |
| case FPI_Round_up: |
| if (sign) |
| break; |
| goto ret_tiny; |
| case FPI_Round_down: |
| if (!sign) |
| break; |
| goto ret_tiny; |
| } |
| goto retz; |
| ret_tiny: |
| b = Balloc(0); |
| b->wds = 1; |
| b->x[0] = 1; |
| goto dret; |
| } |
| switch(fpi->rounding) { |
| case FPI_Round_near: |
| goto ovfl1; |
| case FPI_Round_up: |
| if (!sign) |
| goto ovfl1; |
| goto ret_big; |
| case FPI_Round_down: |
| if (sign) |
| goto ovfl1; |
| goto ret_big; |
| } |
| ret_big: |
| nbits = fpi->nbits; |
| n0 = n = nbits >> kshift; |
| if (nbits & kmask) |
| ++n; |
| for(j = n, k = 0; j >>= 1; ++k); |
| *bp = b = Balloc(k); |
| b->wds = n; |
| for(j = 0; j < n0; ++j) |
| b->x[j] = ALL_ON; |
| if (n > n0) |
| b->x[j] = ULbits >> (ULbits - (nbits & kmask)); |
| *exp = fpi->emin; |
| return STRTOG_Normal | STRTOG_Inexlo; |
| } |
| /* |
| * Truncate the hex string if it is longer than the precision needed, |
| * to avoid denial-of-service issues with very large strings. Use |
| * additional digits to insure precision. Scan to-be-truncated digits |
| * and replace with either '1' or '0' to ensure proper rounding. |
| */ |
| { |
| int maxdigits = ((fpi->nbits + 3) >> 2) + 2; |
| size_t nd = s1 - s0; |
| #ifdef USE_LOCALE |
| int dplen = strlen((const char *)decimalpoint); |
| #else |
| int dplen = 1; |
| #endif |
| |
| if (decpt && s0 < decpt) |
| nd -= dplen; |
| if (nd > maxdigits && (strunc = alloca(maxdigits + dplen + 2)) != NULL) { |
| ssize_t nd0 = decpt ? decpt - s0 - dplen : nd; |
| unsigned char *tp = strunc + maxdigits; |
| int found = 0; |
| if ((nd0 -= maxdigits) >= 0 || s0 >= decpt) |
| memcpy(strunc, s0, maxdigits); |
| else { |
| memcpy(strunc, s0, maxdigits + dplen); |
| tp += dplen; |
| } |
| s0 += maxdigits; |
| e += (nd - (maxdigits + 1)) << 2; |
| if (nd0 > 0) { |
| while(nd0-- > 0) |
| if (*s0++ != '0') { |
| found++; |
| break; |
| } |
| s0 += dplen; |
| } |
| if (!found && decpt) { |
| while(s0 < s1) |
| if(*s0++ != '0') { |
| found++; |
| break; |
| } |
| } |
| *tp++ = found ? '1' : '0'; |
| *tp = 0; |
| s0 = strunc; |
| s1 = tp; |
| } |
| } |
| |
| n = s1 - s0 - 1; |
| for(k = 0; n > (1 << (kshift-2)) - 1; n >>= 1) |
| k++; |
| b = Balloc(k); |
| x = b->x; |
| n = 0; |
| L = 0; |
| #ifdef USE_LOCALE |
| for(i = 0; decimalpoint[i+1]; ++i); |
| #endif |
| while(s1 > s0) { |
| #ifdef USE_LOCALE |
| if (*--s1 == decimalpoint[i]) { |
| s1 -= i; |
| continue; |
| } |
| #else |
| if (*--s1 == '.') |
| continue; |
| #endif |
| if (n == ULbits) { |
| *x++ = L; |
| L = 0; |
| n = 0; |
| } |
| L |= (hexdig[*s1] & 0x0f) << n; |
| n += 4; |
| } |
| *x++ = L; |
| b->wds = n = x - b->x; |
| n = ULbits*n - hi0bits(L); |
| nbits = fpi->nbits; |
| lostbits = 0; |
| x = b->x; |
| if (n > nbits) { |
| n -= nbits; |
| if (any_on(b,n)) { |
| lostbits = 1; |
| k = n - 1; |
| if (x[k>>kshift] & 1 << (k & kmask)) { |
| lostbits = 2; |
| if (k > 0 && any_on(b,k)) |
| lostbits = 3; |
| } |
| } |
| rshift(b, n); |
| e += n; |
| } |
| else if (n < nbits) { |
| n = nbits - n; |
| b = lshift(b, n); |
| e -= n; |
| x = b->x; |
| } |
| if (e > fpi->emax) { |
| ovfl: |
| Bfree(b); |
| ovfl1: |
| #ifndef NO_ERRNO |
| errno = ERANGE; |
| #endif |
| return STRTOG_Infinite | STRTOG_Overflow | STRTOG_Inexhi; |
| } |
| irv = STRTOG_Normal; |
| if (e < fpi->emin) { |
| irv = STRTOG_Denormal; |
| n = fpi->emin - e; |
| if (n >= nbits) { |
| switch (fpi->rounding) { |
| case FPI_Round_near: |
| if (n == nbits && (n < 2 || any_on(b,n-1))) |
| goto one_bit; |
| break; |
| case FPI_Round_up: |
| if (!sign) |
| goto one_bit; |
| break; |
| case FPI_Round_down: |
| if (sign) { |
| one_bit: |
| x[0] = b->wds = 1; |
| dret: |
| *bp = b; |
| *exp = fpi->emin; |
| #ifndef NO_ERRNO |
| errno = ERANGE; |
| #endif |
| return STRTOG_Denormal | STRTOG_Inexhi |
| | STRTOG_Underflow; |
| } |
| } |
| Bfree(b); |
| retz: |
| #ifndef NO_ERRNO |
| errno = ERANGE; |
| #endif |
| return STRTOG_Zero | STRTOG_Inexlo | STRTOG_Underflow; |
| } |
| k = n - 1; |
| if (lostbits) |
| lostbits = 1; |
| else if (k > 0) |
| lostbits = any_on(b,k); |
| if (x[k>>kshift] & 1 << (k & kmask)) |
| lostbits |= 2; |
| nbits -= n; |
| rshift(b,n); |
| e = fpi->emin; |
| } |
| if (lostbits) { |
| up = 0; |
| switch(fpi->rounding) { |
| case FPI_Round_zero: |
| break; |
| case FPI_Round_near: |
| if (lostbits & 2 |
| && (lostbits | x[0]) & 1) |
| up = 1; |
| break; |
| case FPI_Round_up: |
| up = 1 - sign; |
| break; |
| case FPI_Round_down: |
| up = sign; |
| } |
| if (up) { |
| k = b->wds; |
| b = increment(b); |
| x = b->x; |
| if (irv == STRTOG_Denormal) { |
| if (nbits == fpi->nbits - 1 |
| && x[nbits >> kshift] & 1 << (nbits & kmask)) |
| irv = STRTOG_Normal; |
| } |
| else if (b->wds > k |
| || ((n = nbits & kmask) !=0 |
| && hi0bits(x[k-1]) < 32-n)) { |
| rshift(b,1); |
| if (++e > fpi->emax) |
| goto ovfl; |
| } |
| irv |= STRTOG_Inexhi; |
| } |
| else |
| irv |= STRTOG_Inexlo; |
| } |
| *bp = b; |
| *exp = e; |
| return irv; |
| } |
| |
| #endif /*}*/ |
| |
| #ifdef __cplusplus |
| } |
| #endif |