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Diffstat (limited to 'media/sphinxbase/src/libsphinxbase/util/dtoa.c')
| -rw-r--r-- | media/sphinxbase/src/libsphinxbase/util/dtoa.c | 2979 |
1 files changed, 0 insertions, 2979 deletions
diff --git a/media/sphinxbase/src/libsphinxbase/util/dtoa.c b/media/sphinxbase/src/libsphinxbase/util/dtoa.c deleted file mode 100644 index 4673ae003..000000000 --- a/media/sphinxbase/src/libsphinxbase/util/dtoa.c +++ /dev/null @@ -1,2979 +0,0 @@ -/**************************************************************** - * - * 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. - * - ***************************************************************/ - -/**************************************************************** - * This is dtoa.c by David M. Gay, downloaded from - * http://www.netlib.org/fp/dtoa.c on April 15, 2009 and modified for - * inclusion into the Python core by Mark E. T. Dickinson and Eric V. Smith. - * It was taken from Python distribution then and imported into sphinxbase. - * Python version is preferred due to cleanups, though original - * version at netlib is still maintained. - * - * Please remember to check http://www.netlib.org/fp regularly for bugfixes and updates. - * - * The major modifications from Gay's original code are as follows: - * - * 0. The original code has been specialized to Sphinxbase's needs by removing - * many of the #ifdef'd sections. In particular, code to support VAX and - * IBM floating-point formats, hex NaNs, hex floats, locale-aware - * treatment of the decimal point, and setting of the inexact flag have - * been removed. - * - * 1. We use cdk_calloc and ckd_free in place of malloc and free. - * - * 2. The public functions strtod, dtoa and freedtoa all now have - * a sb_ prefix. - * - * 3. Instead of assuming that malloc always succeeds, we thread - * malloc failures through the code. The functions - * - * Balloc, multadd, s2b, i2b, mult, pow5mult, lshift, diff, d2b - * - * of return type *Bigint all return NULL to indicate a malloc failure. - * Similarly, rv_alloc and nrv_alloc (return type char *) return NULL on - * failure. bigcomp now has return type int (it used to be void) and - * returns -1 on failure and 0 otherwise. sb_dtoa returns NULL - * on failure. sb_strtod indicates failure due to malloc failure - * by returning -1.0, setting errno=ENOMEM and *se to s00. - * - * 4. The static variable dtoa_result has been removed. Callers of - * sb_dtoa are expected to call sb_freedtoa to free the memory allocated - * by sb_dtoa. - * - * 5. The code has been reformatted to better fit with C style. - * - * 6. A bug in the memory allocation has been fixed: to avoid FREEing memory - * that hasn't been MALLOC'ed, private_mem should only be used when k <= - * Kmax. - * - * 7. sb_strtod has been modified so that it doesn't accept strings with - * leading whitespace. - * - ***************************************************************/ - -/* Please send bug reports for the original dtoa.c code 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). - */ - -/* Linking of sphinxbase's #defines to Gay's #defines starts here. */ - -#ifdef HAVE_CONFIG_H -#include "config.h" -#endif - -#include <errno.h> -#include <string.h> -#include <assert.h> -#include <stdio.h> - -#include <sphinxbase/ckd_alloc.h> -#include <sphinxbase/prim_type.h> - -#ifdef WORDS_BIGENDIAN -#define IEEE_MC68k -#else -#define IEEE_8087 -#endif - -#define Long int32 /* ZOMG */ -#define ULong uint32 /* WTF */ -#ifdef HAVE_LONG_LONG -#define ULLong uint64 -#endif - -#define MALLOC ckd_malloc -#define FREE ckd_free - -#define DBL_DIG 15 -#define DBL_MAX_10_EXP 308 -#define DBL_MAX_EXP 1024 -#define FLT_RADIX 2 - -/* maximum permitted exponent value for strtod; exponents larger than - MAX_ABS_EXP in absolute value get truncated to +-MAX_ABS_EXP. MAX_ABS_EXP - should fit into an int. */ -#ifndef MAX_ABS_EXP -#define MAX_ABS_EXP 1100000000U -#endif -/* Bound on length of pieces of input strings in sb_strtod; specifically, - this is used to bound the total number of digits ignoring leading zeros and - the number of digits that follow the decimal point. Ideally, MAX_DIGITS - should satisfy MAX_DIGITS + 400 < MAX_ABS_EXP; that ensures that the - exponent clipping in sb_strtod can't affect the value of the output. */ -#ifndef MAX_DIGITS -#define MAX_DIGITS 1000000000U -#endif - -/* End sphinxbase #define linking */ - -#ifdef DEBUG -#define Bug(x) {fprintf(stderr, "%s\n", x); exit(1);} -#endif - -#ifndef PRIVATE_MEM -#define PRIVATE_MEM 2304 -#endif -#define PRIVATE_mem ((PRIVATE_MEM+sizeof(double)-1)/sizeof(double)) -static double private_mem[PRIVATE_mem], *pmem_next = private_mem; - -#ifdef __cplusplus -extern "C" { -#endif - -typedef union { double d; ULong L[2]; } U; - -#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 -#define dval(x) (x)->d - -#ifndef STRTOD_DIGLIM -#define STRTOD_DIGLIM 40 -#endif - -/* maximum permitted exponent value for strtod; exponents larger than - MAX_ABS_EXP in absolute value get truncated to +-MAX_ABS_EXP. MAX_ABS_EXP - should fit into an int. */ -#ifndef MAX_ABS_EXP -#define MAX_ABS_EXP 1100000000U -#endif -/* Bound on length of pieces of input strings in sb_strtod; specifically, - this is used to bound the total number of digits ignoring leading zeros and - the number of digits that follow the decimal point. Ideally, MAX_DIGITS - should satisfy MAX_DIGITS + 400 < MAX_ABS_EXP; that ensures that the - exponent clipping in sb_strtod can't affect the value of the output. */ -#ifndef MAX_DIGITS -#define MAX_DIGITS 1000000000U -#endif - -/* Guard against trying to use the above values on unusual platforms with ints - * of width less than 32 bits. */ -#if MAX_ABS_EXP > 0x7fffffff -#error "MAX_ABS_EXP should fit in an int" -#endif -#if MAX_DIGITS > 0x7fffffff -#error "MAX_DIGITS should fit in an int" -#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) -#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) */ - -#define Exp_shift 20 -#define Exp_shift1 20 -#define Exp_msk1 0x100000 -#define Exp_msk11 0x100000 -#define Exp_mask 0x7ff00000 -#define P 53 -#define Nbits 53 -#define Bias 1023 -#define Emax 1023 -#define Emin (-1022) -#define Etiny (-1074) /* smallest denormal is 2**Etiny */ -#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 Sign_bit 0x80000000 -#define Log2P 1 -#define Tiny0 0 -#define Tiny1 1 -#define Quick_max 14 -#define Int_max 14 - -#ifndef Flt_Rounds -#ifdef FLT_ROUNDS -#define Flt_Rounds FLT_ROUNDS -#else -#define Flt_Rounds 1 -#endif -#endif /*Flt_Rounds*/ - -#define Rounding Flt_Rounds - -#define Big0 (Frac_mask1 | Exp_msk1*(DBL_MAX_EXP+Bias-1)) -#define Big1 0xffffffff - -/* Standard NaN used by sb_stdnan. */ - -#define NAN_WORD0 0x7ff80000 -#define NAN_WORD1 0 - -/* Bits of the representation of positive infinity. */ - -#define POSINF_WORD0 0x7ff00000 -#define POSINF_WORD1 0 - -/* struct BCinfo is used to pass information from sb_strtod to bigcomp */ - -typedef struct BCinfo BCinfo; -struct -BCinfo { - int e0, nd, nd0, scale; -}; - -#define FFFFFFFF 0xffffffffUL - -#define Kmax 7 - -/* struct Bigint is used to represent arbitrary-precision integers. These - integers are stored in sign-magnitude format, with the magnitude stored as - an array of base 2**32 digits. Bigints are always normalized: if x is a - Bigint then x->wds >= 1, and either x->wds == 1 or x[wds-1] is nonzero. - - The Bigint fields are as follows: - - - next is a header used by Balloc and Bfree to keep track of lists - of freed Bigints; it's also used for the linked list of - powers of 5 of the form 5**2**i used by pow5mult. - - k indicates which pool this Bigint was allocated from - - maxwds is the maximum number of words space was allocated for - (usually maxwds == 2**k) - - sign is 1 for negative Bigints, 0 for positive. The sign is unused - (ignored on inputs, set to 0 on outputs) in almost all operations - involving Bigints: a notable exception is the diff function, which - ignores signs on inputs but sets the sign of the output correctly. - - wds is the actual number of significant words - - x contains the vector of words (digits) for this Bigint, from least - significant (x[0]) to most significant (x[wds-1]). -*/ - -struct -Bigint { - struct Bigint *next; - int k, maxwds, sign, wds; - ULong x[1]; -}; - -typedef struct Bigint Bigint; - -#ifndef Py_USING_MEMORY_DEBUGGER - -/* Memory management: memory is allocated from, and returned to, Kmax+1 pools - of memory, where pool k (0 <= k <= Kmax) is for Bigints b with b->maxwds == - 1 << k. These pools are maintained as linked lists, with freelist[k] - pointing to the head of the list for pool k. - - On allocation, if there's no free slot in the appropriate pool, MALLOC is - called to get more memory. This memory is not returned to the system until - Python quits. There's also a private memory pool that's allocated from - in preference to using MALLOC. - - For Bigints with more than (1 << Kmax) digits (which implies at least 1233 - decimal digits), memory is directly allocated using MALLOC, and freed using - FREE. - - XXX: it would be easy to bypass this memory-management system and - translate each call to Balloc into a call to PyMem_Malloc, and each - Bfree to PyMem_Free. Investigate whether this has any significant - performance on impact. */ - -static Bigint *freelist[Kmax+1]; - -/* Allocate space for a Bigint with up to 1<<k digits */ - -static Bigint * -Balloc(int k) -{ - int x; - Bigint *rv; - unsigned int len; - - if (k <= Kmax && (rv = freelist[k])) - freelist[k] = rv->next; - else { - x = 1 << k; - len = (sizeof(Bigint) + (x-1)*sizeof(ULong) + sizeof(double) - 1) - /sizeof(double); - if (k <= Kmax && pmem_next - private_mem + len <= PRIVATE_mem) { - rv = (Bigint*)pmem_next; - pmem_next += len; - } - else { - rv = (Bigint*)MALLOC(len*sizeof(double)); - if (rv == NULL) - return NULL; - } - rv->k = k; - rv->maxwds = x; - } - rv->sign = rv->wds = 0; - return rv; -} - -/* Free a Bigint allocated with Balloc */ - -static void -Bfree(Bigint *v) -{ - if (v) { - if (v->k > Kmax) - FREE((void*)v); - else { - v->next = freelist[v->k]; - freelist[v->k] = v; - } - } -} - -#else - -/* Alternative versions of Balloc and Bfree that use PyMem_Malloc and - PyMem_Free directly in place of the custom memory allocation scheme above. - These are provided for the benefit of memory debugging tools like - Valgrind. */ - -/* Allocate space for a Bigint with up to 1<<k digits */ - -static Bigint * -Balloc(int k) -{ - int x; - Bigint *rv; - unsigned int len; - - x = 1 << k; - len = (sizeof(Bigint) + (x-1)*sizeof(ULong) + sizeof(double) - 1) - /sizeof(double); - - rv = (Bigint*)MALLOC(len*sizeof(double)); - if (rv == NULL) - return NULL; - - rv->k = k; - rv->maxwds = x; - rv->sign = rv->wds = 0; - return rv; -} - -/* Free a Bigint allocated with Balloc */ - -static void -Bfree(Bigint *v) -{ - if (v) { - FREE((void*)v); - } -} - -#endif /* Py_USING_MEMORY_DEBUGGER */ - -#define Bcopy(x,y) memcpy((char *)&x->sign, (char *)&y->sign, \ - y->wds*sizeof(Long) + 2*sizeof(int)) - -/* Multiply a Bigint b by m and add a. Either modifies b in place and returns - a pointer to the modified b, or Bfrees b and returns a pointer to a copy. - On failure, return NULL. In this case, b will have been already freed. */ - -static Bigint * -multadd(Bigint *b, int m, int a) /* multiply by m and add a */ -{ - int i, wds; -#ifdef ULLong - ULong *x; - ULLong carry, y; -#else - ULong carry, *x, y; - ULong xi, z; -#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 - xi = *x; - y = (xi & 0xffff) * m + carry; - z = (xi >> 16) * m + (y >> 16); - carry = z >> 16; - *x++ = (z << 16) + (y & 0xffff); -#endif - } - while(++i < wds); - if (carry) { - if (wds >= b->maxwds) { - b1 = Balloc(b->k+1); - if (b1 == NULL){ - Bfree(b); - return NULL; - } - Bcopy(b1, b); - Bfree(b); - b = b1; - } - b->x[wds++] = (ULong)carry; - b->wds = wds; - } - return b; -} - -/* convert a string s containing nd decimal digits (possibly containing a - decimal separator at position nd0, which is ignored) to a Bigint. This - function carries on where the parsing code in sb_strtod leaves off: on - entry, y9 contains the result of converting the first 9 digits. Returns - NULL on failure. */ - -static Bigint * -s2b(const char *s, int nd0, int nd, ULong y9) -{ - Bigint *b; - int i, k; - Long x, y; - - x = (nd + 8) / 9; - for(k = 0, y = 1; x > y; y <<= 1, k++) ; - b = Balloc(k); - if (b == NULL) - return NULL; - b->x[0] = y9; - b->wds = 1; - - if (nd <= 9) - return b; - - s += 9; - for (i = 9; i < nd0; i++) { - b = multadd(b, 10, *s++ - '0'); - if (b == NULL) - return NULL; - } - s++; - for(; i < nd; i++) { - b = multadd(b, 10, *s++ - '0'); - if (b == NULL) - return NULL; - } - return b; -} - -/* count leading 0 bits in the 32-bit integer x. */ - -static int -hi0bits(ULong x) -{ - 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; -} - -/* count trailing 0 bits in the 32-bit integer y, and shift y right by that - number of bits. */ - -static int -lo0bits(ULong *y) -{ - 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) - return 32; - } - *y = x; - return k; -} - -/* convert a small nonnegative integer to a Bigint */ - -static Bigint * -i2b(int i) -{ - Bigint *b; - - b = Balloc(1); - if (b == NULL) - return NULL; - b->x[0] = i; - b->wds = 1; - return b; -} - -/* multiply two Bigints. Returns a new Bigint, or NULL on failure. Ignores - the signs of a and b. */ - -static Bigint * -mult(Bigint *a, Bigint *b) -{ - Bigint *c; - int k, wa, wb, wc; - ULong *x, *xa, *xae, *xb, *xbe, *xc, *xc0; - ULong y; -#ifdef ULLong - ULLong carry, z; -#else - ULong carry, z; - ULong z2; -#endif - - if ((!a->x[0] && a->wds == 1) || (!b->x[0] && b->wds == 1)) { - c = Balloc(0); - if (c == NULL) - return NULL; - c->wds = 1; - c->x[0] = 0; - return c; - } - - 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 == NULL) - return NULL; - 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 - 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; - } - } -#endif - for(xc0 = c->x, xc = xc0 + wc; wc > 0 && !*--xc; --wc) ; - c->wds = wc; - return c; -} - -#ifndef Py_USING_MEMORY_DEBUGGER - -/* p5s is a linked list of powers of 5 of the form 5**(2**i), i >= 2 */ - -static Bigint *p5s; - -/* multiply the Bigint b by 5**k. Returns a pointer to the result, or NULL on - failure; if the returned pointer is distinct from b then the original - Bigint b will have been Bfree'd. Ignores the sign of b. */ - -static Bigint * -pow5mult(Bigint *b, int k) -{ - Bigint *b1, *p5, *p51; - int i; - static int p05[3] = { 5, 25, 125 }; - - if ((i = k & 3)) { - b = multadd(b, p05[i-1], 0); - if (b == NULL) - return NULL; - } - - if (!(k >>= 2)) - return b; - p5 = p5s; - if (!p5) { - /* first time */ - p5 = i2b(625); - if (p5 == NULL) { - Bfree(b); - return NULL; - } - p5s = p5; - p5->next = 0; - } - for(;;) { - if (k & 1) { - b1 = mult(b, p5); - Bfree(b); - b = b1; - if (b == NULL) - return NULL; - } - if (!(k >>= 1)) - break; - p51 = p5->next; - if (!p51) { - p51 = mult(p5,p5); - if (p51 == NULL) { - Bfree(b); - return NULL; - } - p51->next = 0; - p5->next = p51; - } - p5 = p51; - } - return b; -} - -#else - -/* Version of pow5mult that doesn't cache powers of 5. Provided for - the benefit of memory debugging tools like Valgrind. */ - -static Bigint * -pow5mult(Bigint *b, int k) -{ - Bigint *b1, *p5, *p51; - int i; - static int p05[3] = { 5, 25, 125 }; - - if ((i = k & 3)) { - b = multadd(b, p05[i-1], 0); - if (b == NULL) - return NULL; - } - - if (!(k >>= 2)) - return b; - p5 = i2b(625); - if (p5 == NULL) { - Bfree(b); - return NULL; - } - - for(;;) { - if (k & 1) { - b1 = mult(b, p5); - Bfree(b); - b = b1; - if (b == NULL) { - Bfree(p5); - return NULL; - } - } - if (!(k >>= 1)) - break; - p51 = mult(p5, p5); - Bfree(p5); - p5 = p51; - if (p5 == NULL) { - Bfree(b); - return NULL; - } - } - Bfree(p5); - return b; -} - -#endif /* Py_USING_MEMORY_DEBUGGER */ - -/* shift a Bigint b left by k bits. Return a pointer to the shifted result, - or NULL on failure. If the returned pointer is distinct from b then the - original b will have been Bfree'd. Ignores the sign of b. */ - -static Bigint * -lshift(Bigint *b, int k) -{ - int i, k1, n, n1; - Bigint *b1; - ULong *x, *x1, *xe, z; - - if (!k || (!b->x[0] && b->wds == 1)) - return b; - - n = k >> 5; - k1 = b->k; - n1 = n + b->wds + 1; - for(i = b->maxwds; n1 > i; i <<= 1) - k1++; - b1 = Balloc(k1); - if (b1 == NULL) { - Bfree(b); - return NULL; - } - x1 = b1->x; - for(i = 0; i < n; i++) - *x1++ = 0; - x = b->x; - xe = x + b->wds; - if (k &= 0x1f) { - k1 = 32 - k; - z = 0; - do { - *x1++ = *x << k | z; - z = *x++ >> k1; - } - while(x < xe); - if ((*x1 = z)) - ++n1; - } - else do - *x1++ = *x++; - while(x < xe); - b1->wds = n1 - 1; - Bfree(b); - return b1; -} - -/* Do a three-way compare of a and b, returning -1 if a < b, 0 if a == b and - 1 if a > b. Ignores signs of a and b. */ - -static int -cmp(Bigint *a, Bigint *b) -{ - ULong *xa, *xa0, *xb, *xb0; - int i, j; - - i = a->wds; - j = b->wds; -#ifdef DEBUG - if (i > 1 && !a->x[i-1]) - Bug("cmp called with a->x[a->wds-1] == 0"); - if (j > 1 && !b->x[j-1]) - Bug("cmp called with b->x[b->wds-1] == 0"); -#endif - if (i -= j) - return i; - xa0 = a->x; - xa = xa0 + j; - xb0 = b->x; - xb = xb0 + j; - for(;;) { - if (*--xa != *--xb) - return *xa < *xb ? -1 : 1; - if (xa <= xa0) - break; - } - return 0; -} - -/* Take the difference of Bigints a and b, returning a new Bigint. Returns - NULL on failure. The signs of a and b are ignored, but the sign of the - result is set appropriately. */ - -static Bigint * -diff(Bigint *a, Bigint *b) -{ - Bigint *c; - int i, wa, wb; - ULong *xa, *xae, *xb, *xbe, *xc; -#ifdef ULLong - ULLong borrow, y; -#else - ULong borrow, y; - ULong z; -#endif - - i = cmp(a,b); - if (!i) { - c = Balloc(0); - if (c == NULL) - return NULL; - 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 == NULL) - return NULL; - 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 - 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); - } -#endif - while(!*--xc) - wa--; - c->wds = wa; - return c; -} - -/* Given a positive normal double x, return the difference between x and the - next double up. Doesn't give correct results for subnormals. */ - -static double -ulp(U *x) -{ - Long L; - U u; - - L = (word0(x) & Exp_mask) - (P-1)*Exp_msk1; - word0(&u) = L; - word1(&u) = 0; - return dval(&u); -} - -/* Convert a Bigint to a double plus an exponent */ - -static double -b2d(Bigint *a, int *e) -{ - ULong *xa, *xa0, w, y, z; - int k; - U d; - - 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; - if (k < Ebits) { - word0(&d) = Exp_1 | y >> (Ebits - k); - w = xa > xa0 ? *--xa : 0; - word1(&d) = y << ((32-Ebits) + k) | w >> (Ebits - k); - goto ret_d; - } - z = xa > xa0 ? *--xa : 0; - if (k -= Ebits) { - word0(&d) = Exp_1 | y << k | z >> (32 - k); - y = xa > xa0 ? *--xa : 0; - word1(&d) = z << k | y >> (32 - k); - } - else { - word0(&d) = Exp_1 | y; - word1(&d) = z; - } - ret_d: - return dval(&d); -} - -/* Convert a scaled double to a Bigint plus an exponent. Similar to d2b, - except that it accepts the scale parameter used in sb_strtod (which - should be either 0 or 2*P), and the normalization for the return value is - different (see below). On input, d should be finite and nonnegative, and d - / 2**scale should be exactly representable as an IEEE 754 double. - - Returns a Bigint b and an integer e such that - - dval(d) / 2**scale = b * 2**e. - - Unlike d2b, b is not necessarily odd: b and e are normalized so - that either 2**(P-1) <= b < 2**P and e >= Etiny, or b < 2**P - and e == Etiny. This applies equally to an input of 0.0: in that - case the return values are b = 0 and e = Etiny. - - The above normalization ensures that for all possible inputs d, - 2**e gives ulp(d/2**scale). - - Returns NULL on failure. -*/ - -static Bigint * -sd2b(U *d, int scale, int *e) -{ - Bigint *b; - - b = Balloc(1); - if (b == NULL) - return NULL; - - /* First construct b and e assuming that scale == 0. */ - b->wds = 2; - b->x[0] = word1(d); - b->x[1] = word0(d) & Frac_mask; - *e = Etiny - 1 + (int)((word0(d) & Exp_mask) >> Exp_shift); - if (*e < Etiny) - *e = Etiny; - else - b->x[1] |= Exp_msk1; - - /* Now adjust for scale, provided that b != 0. */ - if (scale && (b->x[0] || b->x[1])) { - *e -= scale; - if (*e < Etiny) { - scale = Etiny - *e; - *e = Etiny; - /* We can't shift more than P-1 bits without shifting out a 1. */ - assert(0 < scale && scale <= P - 1); - if (scale >= 32) { - /* The bits shifted out should all be zero. */ - assert(b->x[0] == 0); - b->x[0] = b->x[1]; - b->x[1] = 0; - scale -= 32; - } - if (scale) { - /* The bits shifted out should all be zero. */ - assert(b->x[0] << (32 - scale) == 0); - b->x[0] = (b->x[0] >> scale) | (b->x[1] << (32 - scale)); - b->x[1] >>= scale; - } - } - } - /* Ensure b is normalized. */ - if (!b->x[1]) - b->wds = 1; - - return b; -} - -/* Convert a double to a Bigint plus an exponent. Return NULL on failure. - - Given a finite nonzero double d, return an odd Bigint b and exponent *e - such that fabs(d) = b * 2**e. On return, *bbits gives the number of - significant bits of b; that is, 2**(*bbits-1) <= b < 2**(*bbits). - - If d is zero, then b == 0, *e == -1010, *bbits = 0. - */ - -static Bigint * -d2b(U *d, int *e, int *bits) -{ - Bigint *b; - int de, k; - ULong *x, y, z; - int i; - - b = Balloc(1); - if (b == NULL) - return NULL; - x = b->x; - - z = word0(d) & Frac_mask; - word0(d) &= 0x7fffffff; /* clear sign bit, which we ignore */ - if ((de = (int)(word0(d) >> Exp_shift))) - z |= Exp_msk1; - if ((y = word1(d))) { - if ((k = lo0bits(&y))) { - x[0] = y | z << (32 - k); - z >>= k; - } - else - x[0] = y; - i = - b->wds = (x[1] = z) ? 2 : 1; - } - else { - k = lo0bits(&z); - x[0] = z; - i = - b->wds = 1; - k += 32; - } - if (de) { - *e = de - Bias - (P-1) + k; - *bits = P - k; - } - else { - *e = de - Bias - (P-1) + 1 + k; - *bits = 32*i - hi0bits(x[i-1]); - } - return b; -} - -/* Compute the ratio of two Bigints, as a double. The result may have an - error of up to 2.5 ulps. */ - -static double -ratio(Bigint *a, Bigint *b) -{ - U da, db; - int k, ka, kb; - - dval(&da) = b2d(a, &ka); - dval(&db) = b2d(b, &kb); - k = ka - kb + 32*(a->wds - b->wds); - if (k > 0) - word0(&da) += k*Exp_msk1; - else { - k = -k; - word0(&db) += k*Exp_msk1; - } - 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 -}; - -static const double -bigtens[] = { 1e16, 1e32, 1e64, 1e128, 1e256 }; -static const double tinytens[] = { 1e-16, 1e-32, 1e-64, 1e-128, - 9007199254740992.*9007199254740992.e-256 - /* = 2^106 * 1e-256 */ -}; -/* 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 - -#define ULbits 32 -#define kshift 5 -#define kmask 31 - - -static int -dshift(Bigint *b, int p2) -{ - int rv = hi0bits(b->x[b->wds-1]) - 4; - if (p2 > 0) - rv -= p2; - return rv & kmask; -} - -/* special case of Bigint division. The quotient is always in the range 0 <= - quotient < 10, and on entry the divisor S is normalized so that its top 4 - bits (28--31) are zero and bit 27 is set. */ - -static int -quorem(Bigint *b, Bigint *S) -{ - int n; - ULong *bx, *bxe, q, *sx, *sxe; -#ifdef ULLong - ULLong borrow, carry, y, ys; -#else - ULong borrow, carry, y, ys; - ULong si, z, zs; -#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 - 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); -#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 - 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); -#endif - } - while(sx <= sxe); - bx = b->x; - bxe = bx + n; - if (!*bxe) { - while(--bxe > bx && !*bxe) - --n; - b->wds = n; - } - } - return q; -} - -/* sulp(x) is a version of ulp(x) that takes bc.scale into account. - - Assuming that x is finite and nonnegative (positive zero is fine - here) and x / 2^bc.scale is exactly representable as a double, - sulp(x) is equivalent to 2^bc.scale * ulp(x / 2^bc.scale). */ - -static double -sulp(U *x, BCinfo *bc) -{ - U u; - - if (bc->scale && 2*P + 1 > (int)((word0(x) & Exp_mask) >> Exp_shift)) { - /* rv/2^bc->scale is subnormal */ - word0(&u) = (P+2)*Exp_msk1; - word1(&u) = 0; - return u.d; - } - else { - assert(word0(x) || word1(x)); /* x != 0.0 */ - return ulp(x); - } -} - -/* The bigcomp function handles some hard cases for strtod, for inputs - with more than STRTOD_DIGLIM digits. It's called once an initial - estimate for the double corresponding to the input string has - already been obtained by the code in sb_strtod. - - The bigcomp function is only called after sb_strtod has found a - double value rv such that either rv or rv + 1ulp represents the - correctly rounded value corresponding to the original string. It - determines which of these two values is the correct one by - computing the decimal digits of rv + 0.5ulp and comparing them with - the corresponding digits of s0. - - In the following, write dv for the absolute value of the number represented - by the input string. - - Inputs: - - s0 points to the first significant digit of the input string. - - rv is a (possibly scaled) estimate for the closest double value to the - value represented by the original input to sb_strtod. If - bc->scale is nonzero, then rv/2^(bc->scale) is the approximation to - the input value. - - bc is a struct containing information gathered during the parsing and - estimation steps of sb_strtod. Description of fields follows: - - bc->e0 gives the exponent of the input value, such that dv = (integer - given by the bd->nd digits of s0) * 10**e0 - - bc->nd gives the total number of significant digits of s0. It will - be at least 1. - - bc->nd0 gives the number of significant digits of s0 before the - decimal separator. If there's no decimal separator, bc->nd0 == - bc->nd. - - bc->scale is the value used to scale rv to avoid doing arithmetic with - subnormal values. It's either 0 or 2*P (=106). - - Outputs: - - On successful exit, rv/2^(bc->scale) is the closest double to dv. - - Returns 0 on success, -1 on failure (e.g., due to a failed malloc call). */ - -static int -bigcomp(U *rv, const char *s0, BCinfo *bc) -{ - Bigint *b, *d; - int b2, d2, dd, i, nd, nd0, odd, p2, p5; - - nd = bc->nd; - nd0 = bc->nd0; - p5 = nd + bc->e0; - b = sd2b(rv, bc->scale, &p2); - if (b == NULL) - return -1; - - /* record whether the lsb of rv/2^(bc->scale) is odd: in the exact halfway - case, this is used for round to even. */ - odd = b->x[0] & 1; - - /* left shift b by 1 bit and or a 1 into the least significant bit; - this gives us b * 2**p2 = rv/2^(bc->scale) + 0.5 ulp. */ - b = lshift(b, 1); - if (b == NULL) - return -1; - b->x[0] |= 1; - p2--; - - p2 -= p5; - d = i2b(1); - if (d == NULL) { - Bfree(b); - return -1; - } - /* Arrange for convenient computation of quotients: - * shift left if necessary so divisor has 4 leading 0 bits. - */ - if (p5 > 0) { - d = pow5mult(d, p5); - if (d == NULL) { - Bfree(b); - return -1; - } - } - else if (p5 < 0) { - b = pow5mult(b, -p5); - if (b == NULL) { - Bfree(d); - return -1; - } - } - if (p2 > 0) { - b2 = p2; - d2 = 0; - } - else { - b2 = 0; - d2 = -p2; - } - i = dshift(d, d2); - if ((b2 += i) > 0) { - b = lshift(b, b2); - if (b == NULL) { - Bfree(d); - return -1; - } - } - if ((d2 += i) > 0) { - d = lshift(d, d2); - if (d == NULL) { - Bfree(b); - return -1; - } - } - - /* Compare s0 with b/d: set dd to -1, 0, or 1 according as s0 < b/d, s0 == - * b/d, or s0 > b/d. Here the digits of s0 are thought of as representing - * a number in the range [0.1, 1). */ - if (cmp(b, d) >= 0) - /* b/d >= 1 */ - dd = -1; - else { - i = 0; - for(;;) { - b = multadd(b, 10, 0); - if (b == NULL) { - Bfree(d); - return -1; - } - dd = s0[i < nd0 ? i : i+1] - '0' - quorem(b, d); - i++; - - if (dd) - break; - if (!b->x[0] && b->wds == 1) { - /* b/d == 0 */ - dd = i < nd; - break; - } - if (!(i < nd)) { - /* b/d != 0, but digits of s0 exhausted */ - dd = -1; - break; - } - } - } - Bfree(b); - Bfree(d); - if (dd > 0 || (dd == 0 && odd)) - dval(rv) += sulp(rv, bc); - return 0; -} - -/* Return a 'standard' NaN value. - - There are exactly two quiet NaNs that don't arise by 'quieting' signaling - NaNs (see IEEE 754-2008, section 6.2.1). If sign == 0, return the one whose - sign bit is cleared. Otherwise, return the one whose sign bit is set. -*/ - -double -sb_stdnan(int sign) -{ - U rv; - word0(&rv) = NAN_WORD0; - word1(&rv) = NAN_WORD1; - if (sign) - word0(&rv) |= Sign_bit; - return dval(&rv); -} - -/* Return positive or negative infinity, according to the given sign (0 for - * positive infinity, 1 for negative infinity). */ - -double -sb_infinity(int sign) -{ - U rv; - word0(&rv) = POSINF_WORD0; - word1(&rv) = POSINF_WORD1; - return sign ? -dval(&rv) : dval(&rv); -} - -double -sb_strtod(const char *s00, char **se) -{ - int bb2, bb5, bbe, bd2, bd5, bs2, c, dsign, e, e1, error; - int esign, i, j, k, lz, nd, nd0, odd, sign; - const char *s, *s0, *s1; - double aadj, aadj1; - U aadj2, adj, rv, rv0; - ULong y, z, abs_exp; - Long L; - BCinfo bc; - Bigint *bb, *bb1, *bd, *bd0, *bs, *delta; - size_t ndigits, fraclen; - - dval(&rv) = 0.; - - /* Start parsing. */ - c = *(s = s00); - - /* Parse optional sign, if present. */ - sign = 0; - switch (c) { - case '-': - sign = 1; - /* no break */ - case '+': - c = *++s; - } - - /* Skip leading zeros: lz is true iff there were leading zeros. */ - s1 = s; - while (c == '0') - c = *++s; - lz = s != s1; - - /* Point s0 at the first nonzero digit (if any). fraclen will be the - number of digits between the decimal point and the end of the - digit string. ndigits will be the total number of digits ignoring - leading zeros. */ - s0 = s1 = s; - while ('0' <= c && c <= '9') - c = *++s; - ndigits = s - s1; - fraclen = 0; - - /* Parse decimal point and following digits. */ - if (c == '.') { - c = *++s; - if (!ndigits) { - s1 = s; - while (c == '0') - c = *++s; - lz = lz || s != s1; - fraclen += (s - s1); - s0 = s; - } - s1 = s; - while ('0' <= c && c <= '9') - c = *++s; - ndigits += s - s1; - fraclen += s - s1; - } - - /* Now lz is true if and only if there were leading zero digits, and - ndigits gives the total number of digits ignoring leading zeros. A - valid input must have at least one digit. */ - if (!ndigits && !lz) { - if (se) - *se = (char *)s00; - goto parse_error; - } - - /* Range check ndigits and fraclen to make sure that they, and values - computed with them, can safely fit in an int. */ - if (ndigits > MAX_DIGITS || fraclen > MAX_DIGITS) { - if (se) - *se = (char *)s00; - goto parse_error; - } - nd = (int)ndigits; - nd0 = (int)ndigits - (int)fraclen; - - /* Parse exponent. */ - e = 0; - if (c == 'e' || c == 'E') { - s00 = s; - c = *++s; - - /* Exponent sign. */ - esign = 0; - switch (c) { - case '-': - esign = 1; - /* no break */ - case '+': - c = *++s; - } - - /* Skip zeros. lz is true iff there are leading zeros. */ - s1 = s; - while (c == '0') - c = *++s; - lz = s != s1; - - /* Get absolute value of the exponent. */ - s1 = s; - abs_exp = 0; - while ('0' <= c && c <= '9') { - abs_exp = 10*abs_exp + (c - '0'); - c = *++s; - } - - /* abs_exp will be correct modulo 2**32. But 10**9 < 2**32, so if - there are at most 9 significant exponent digits then overflow is - impossible. */ - if (s - s1 > 9 || abs_exp > MAX_ABS_EXP) - e = (int)MAX_ABS_EXP; - else - e = (int)abs_exp; - if (esign) - e = -e; - - /* A valid exponent must have at least one digit. */ - if (s == s1 && !lz) - s = s00; - } - - /* Adjust exponent to take into account position of the point. */ - e -= nd - nd0; - if (nd0 <= 0) - nd0 = nd; - - /* Finished parsing. Set se to indicate how far we parsed */ - if (se) - *se = (char *)s; - - /* If all digits were zero, exit with return value +-0.0. Otherwise, - strip trailing zeros: scan back until we hit a nonzero digit. */ - if (!nd) - goto ret; - for (i = nd; i > 0; ) { - --i; - if (s0[i < nd0 ? i : i+1] != '0') { - ++i; - break; - } - } - e += nd - i; - nd = i; - if (nd0 > nd) - nd0 = nd; - - /* Summary of parsing results. After parsing, and dealing with zero - * inputs, we have values s0, nd0, nd, e, sign, where: - * - * - s0 points to the first significant digit of the input string - * - * - nd is the total number of significant digits (here, and - * below, 'significant digits' means the set of digits of the - * significand of the input that remain after ignoring leading - * and trailing zeros). - * - * - nd0 indicates the position of the decimal point, if present; it - * satisfies 1 <= nd0 <= nd. The nd significant digits are in - * s0[0:nd0] and s0[nd0+1:nd+1] using the usual Python half-open slice - * notation. (If nd0 < nd, then s0[nd0] contains a '.' character; if - * nd0 == nd, then s0[nd0] could be any non-digit character.) - * - * - e is the adjusted exponent: the absolute value of the number - * represented by the original input string is n * 10**e, where - * n is the integer represented by the concatenation of - * s0[0:nd0] and s0[nd0+1:nd+1] - * - * - sign gives the sign of the input: 1 for negative, 0 for positive - * - * - the first and last significant digits are nonzero - */ - - /* put first DBL_DIG+1 digits into integer y and z. - * - * - y contains the value represented by the first min(9, nd) - * significant digits - * - * - if nd > 9, z contains the value represented by significant digits - * with indices in [9, min(16, nd)). So y * 10**(min(16, nd) - 9) + z - * gives the value represented by the first min(16, nd) sig. digits. - */ - - bc.e0 = e1 = e; - y = z = 0; - for (i = 0; i < nd; i++) { - if (i < 9) - y = 10*y + s0[i < nd0 ? i : i+1] - '0'; - else if (i < DBL_DIG+1) - z = 10*z + s0[i < nd0 ? i : i+1] - '0'; - else - break; - } - - k = nd < DBL_DIG + 1 ? nd : DBL_DIG + 1; - dval(&rv) = y; - if (k > 9) { - dval(&rv) = tens[k - 9] * dval(&rv) + z; - } - bd0 = 0; - if (nd <= DBL_DIG - && Flt_Rounds == 1 - ) { - if (!e) - goto ret; - if (e > 0) { - if (e <= Ten_pmax) { - dval(&rv) *= tens[e]; - goto ret; - } - i = DBL_DIG - nd; - if (e <= Ten_pmax + i) { - /* A fancier test would sometimes let us do - * this for larger i values. - */ - e -= i; - dval(&rv) *= tens[i]; - dval(&rv) *= tens[e]; - goto ret; - } - } - else if (e >= -Ten_pmax) { - dval(&rv) /= tens[-e]; - goto ret; - } - } - e1 += nd - k; - - bc.scale = 0; - - /* 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) - goto ovfl; - 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) { - /* The input decimal value lies in [10**e1, 10**(e1+16)). - - If e1 <= -512, underflow immediately. - If e1 <= -256, set bc.scale to 2*P. - - So for input value < 1e-256, bc.scale is always set; - for input value >= 1e-240, bc.scale is never set. - For input values in [1e-256, 1e-240), bc.scale may or may - not be set. */ - - e1 = -e1; - if ((i = e1 & 15)) - dval(&rv) /= tens[i]; - if (e1 >>= 4) { - if (e1 >= 1 << n_bigtens) - goto undfl; - if (e1 & Scale_Bit) - bc.scale = 2*P; - for(j = 0; e1 > 0; j++, e1 >>= 1) - if (e1 & 1) - dval(&rv) *= tinytens[j]; - if (bc.scale && (j = 2*P + 1 - ((word0(&rv) & Exp_mask) - >> Exp_shift)) > 0) { - /* scaled rv is denormal; clear 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; - } - if (!dval(&rv)) - goto undfl; - } - } - - /* Now the hard part -- adjusting rv to the correct value.*/ - - /* Put digits into bd: true value = bd * 10^e */ - - bc.nd = nd; - bc.nd0 = nd0; /* Only needed if nd > STRTOD_DIGLIM, but done here */ - /* to silence an erroneous warning about bc.nd0 */ - /* possibly not being initialized. */ - if (nd > STRTOD_DIGLIM) { - /* ASSERT(STRTOD_DIGLIM >= 18); 18 == one more than the */ - /* minimum number of decimal digits to distinguish double values */ - /* in IEEE arithmetic. */ - - /* Truncate input to 18 significant digits, then discard any trailing - zeros on the result by updating nd, nd0, e and y suitably. (There's - no need to update z; it's not reused beyond this point.) */ - for (i = 18; i > 0; ) { - /* scan back until we hit a nonzero digit. significant digit 'i' - is s0[i] if i < nd0, s0[i+1] if i >= nd0. */ - --i; - if (s0[i < nd0 ? i : i+1] != '0') { - ++i; - break; - } - } - e += nd - i; - nd = i; - if (nd0 > nd) - nd0 = nd; - if (nd < 9) { /* must recompute y */ - y = 0; - for(i = 0; i < nd0; ++i) - y = 10*y + s0[i] - '0'; - for(; i < nd; ++i) - y = 10*y + s0[i+1] - '0'; - } - } - bd0 = s2b(s0, nd0, nd, y); - if (bd0 == NULL) - goto failed_malloc; - - /* Notation for the comments below. Write: - - - dv for the absolute value of the number represented by the original - decimal input string. - - - if we've truncated dv, write tdv for the truncated value. - Otherwise, set tdv == dv. - - - srv for the quantity rv/2^bc.scale; so srv is the current binary - approximation to tdv (and dv). It should be exactly representable - in an IEEE 754 double. - */ - - for(;;) { - - /* This is the main correction loop for sb_strtod. - - We've got a decimal value tdv, and a floating-point approximation - srv=rv/2^bc.scale to tdv. The aim is to determine whether srv is - close enough (i.e., within 0.5 ulps) to tdv, and to compute a new - approximation if not. - - To determine whether srv is close enough to tdv, compute integers - bd, bb and bs proportional to tdv, srv and 0.5 ulp(srv) - respectively, and then use integer arithmetic to determine whether - |tdv - srv| is less than, equal to, or greater than 0.5 ulp(srv). - */ - - bd = Balloc(bd0->k); - if (bd == NULL) { - Bfree(bd0); - goto failed_malloc; - } - Bcopy(bd, bd0); - bb = sd2b(&rv, bc.scale, &bbe); /* srv = bb * 2^bbe */ - if (bb == NULL) { - Bfree(bd); - Bfree(bd0); - goto failed_malloc; - } - /* Record whether lsb of bb is odd, in case we need this - for the round-to-even step later. */ - odd = bb->x[0] & 1; - - /* tdv = bd * 10**e; srv = bb * 2**bbe */ - bs = i2b(1); - if (bs == NULL) { - Bfree(bb); - Bfree(bd); - Bfree(bd0); - goto failed_malloc; - } - - 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; - bb2++; - bd2++; - - /* At this stage bd5 - bb5 == e == bd2 - bb2 + bbe, bb2 - bs2 == 1, - and bs == 1, so: - - tdv == bd * 10**e = bd * 2**(bbe - bb2 + bd2) * 5**(bd5 - bb5) - srv == bb * 2**bbe = bb * 2**(bbe - bb2 + bb2) - 0.5 ulp(srv) == 2**(bbe-1) = bs * 2**(bbe - bb2 + bs2) - - It follows that: - - M * tdv = bd * 2**bd2 * 5**bd5 - M * srv = bb * 2**bb2 * 5**bb5 - M * 0.5 ulp(srv) = bs * 2**bs2 * 5**bb5 - - for some constant M. (Actually, M == 2**(bb2 - bbe) * 5**bb5, but - this fact is not needed below.) - */ - - /* Remove factor of 2**i, where i = min(bb2, bd2, bs2). */ - i = bb2 < bd2 ? bb2 : bd2; - if (i > bs2) - i = bs2; - if (i > 0) { - bb2 -= i; - bd2 -= i; - bs2 -= i; - } - - /* Scale bb, bd, bs by the appropriate powers of 2 and 5. */ - if (bb5 > 0) { - bs = pow5mult(bs, bb5); - if (bs == NULL) { - Bfree(bb); - Bfree(bd); - Bfree(bd0); - goto failed_malloc; - } - bb1 = mult(bs, bb); - Bfree(bb); - bb = bb1; - if (bb == NULL) { - Bfree(bs); - Bfree(bd); - Bfree(bd0); - goto failed_malloc; - } - } - if (bb2 > 0) { - bb = lshift(bb, bb2); - if (bb == NULL) { - Bfree(bs); - Bfree(bd); - Bfree(bd0); - goto failed_malloc; - } - } - if (bd5 > 0) { - bd = pow5mult(bd, bd5); - if (bd == NULL) { - Bfree(bb); - Bfree(bs); - Bfree(bd0); - goto failed_malloc; - } - } - if (bd2 > 0) { - bd = lshift(bd, bd2); - if (bd == NULL) { - Bfree(bb); - Bfree(bs); - Bfree(bd0); - goto failed_malloc; - } - } - if (bs2 > 0) { - bs = lshift(bs, bs2); - if (bs == NULL) { - Bfree(bb); - Bfree(bd); - Bfree(bd0); - goto failed_malloc; - } - } - - /* Now bd, bb and bs are scaled versions of tdv, srv and 0.5 ulp(srv), - respectively. Compute the difference |tdv - srv|, and compare - with 0.5 ulp(srv). */ - - delta = diff(bb, bd); - if (delta == NULL) { - Bfree(bb); - Bfree(bs); - Bfree(bd); - Bfree(bd0); - goto failed_malloc; - } - dsign = delta->sign; - delta->sign = 0; - i = cmp(delta, bs); - if (bc.nd > nd && i <= 0) { - if (dsign) - break; /* Must use bigcomp(). */ - - /* Here rv overestimates the truncated decimal value by at most - 0.5 ulp(rv). Hence rv either overestimates the true decimal - value by <= 0.5 ulp(rv), or underestimates it by some small - amount (< 0.1 ulp(rv)); either way, rv is within 0.5 ulps of - the true decimal value, so it's possible to exit. - - Exception: if scaled rv is a normal exact power of 2, but not - DBL_MIN, then rv - 0.5 ulp(rv) takes us all the way down to the - next double, so the correctly rounded result is either rv - 0.5 - ulp(rv) or rv; in this case, use bigcomp to distinguish. */ - - if (!word1(&rv) && !(word0(&rv) & Bndry_mask)) { - /* rv can't be 0, since it's an overestimate for some - nonzero value. So rv is a normal power of 2. */ - j = (int)(word0(&rv) & Exp_mask) >> Exp_shift; - /* rv / 2^bc.scale = 2^(j - 1023 - bc.scale); use bigcomp if - rv / 2^bc.scale >= 2^-1021. */ - if (j - bc.scale >= 2) { - dval(&rv) -= 0.5 * sulp(&rv, &bc); - break; /* Use bigcomp. */ - } - } - - { - bc.nd = nd; - i = -1; /* Discarded digits make delta smaller. */ - } - } - - 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 - || (word0(&rv) & Exp_mask) <= (2*P+1)*Exp_msk1 - ) { - break; - } - if (!delta->x[0] && delta->wds <= 1) { - /* exact result */ - break; - } - delta = lshift(delta,Log2P); - if (delta == NULL) { - Bfree(bb); - Bfree(bs); - Bfree(bd); - Bfree(bd0); - goto failed_malloc; - } - 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) == ( - (bc.scale && - (y = word0(&rv) & Exp_mask) <= 2*P*Exp_msk1) ? - (0xffffffff & (0xffffffff << (2*P+1-(y>>Exp_shift)))) : - 0xffffffff)) { - /*boundary case -- increment exponent*/ - word0(&rv) = (word0(&rv) & Exp_mask) - + Exp_msk1 - ; - word1(&rv) = 0; - /* dsign = 0; */ - break; - } - } - else if (!(word0(&rv) & Bndry_mask) && !word1(&rv)) { - drop_down: - /* boundary case -- decrement exponent */ - if (bc.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 */ - if (bc.nd > nd) - break; - goto undfl; - } - } - L = (word0(&rv) & Exp_mask) - Exp_msk1; - word0(&rv) = L | Bndry_mask1; - word1(&rv) = 0xffffffff; - break; - } - if (!odd) - break; - if (dsign) - dval(&rv) += sulp(&rv, &bc); - else { - dval(&rv) -= sulp(&rv, &bc); - if (!dval(&rv)) { - if (bc.nd >nd) - break; - goto undfl; - } - } - /* dsign = 1 - dsign; */ - break; - } - if ((aadj = ratio(delta, bs)) <= 2.) { - if (dsign) - aadj = aadj1 = 1.; - else if (word1(&rv) || word0(&rv) & Bndry_mask) { - if (word1(&rv) == Tiny1 && !word0(&rv)) { - if (bc.nd >nd) - break; - goto undfl; - } - 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; - if (Flt_Rounds == 0) - aadj1 += 0.5; - } - 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.d = aadj1 * ulp(&rv); - dval(&rv) += adj.d; - if ((word0(&rv) & Exp_mask) >= - Exp_msk1*(DBL_MAX_EXP+Bias-P)) { - if (word0(&rv0) == Big0 && word1(&rv0) == Big1) { - Bfree(bb); - Bfree(bd); - Bfree(bs); - Bfree(bd0); - Bfree(delta); - goto ovfl; - } - word0(&rv) = Big0; - word1(&rv) = Big1; - goto cont; - } - else - word0(&rv) += P*Exp_msk1; - } - else { - if (bc.scale && y <= 2*P*Exp_msk1) { - if (aadj <= 0x7fffffff) { - if ((z = (ULong)aadj) <= 0) - z = 1; - aadj = z; - aadj1 = dsign ? aadj : -aadj; - } - dval(&aadj2) = aadj1; - word0(&aadj2) += (2*P+1)*Exp_msk1 - y; - aadj1 = dval(&aadj2); - } - adj.d = aadj1 * ulp(&rv); - dval(&rv) += adj.d; - } - z = word0(&rv) & Exp_mask; - if (bc.nd == nd) { - if (!bc.scale) - 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; - } - } - cont: - Bfree(bb); - Bfree(bd); - Bfree(bs); - Bfree(delta); - } - Bfree(bb); - Bfree(bd); - Bfree(bs); - Bfree(bd0); - Bfree(delta); - if (bc.nd > nd) { - error = bigcomp(&rv, s0, &bc); - if (error) - goto failed_malloc; - } - - if (bc.scale) { - word0(&rv0) = Exp_1 - 2*P*Exp_msk1; - word1(&rv0) = 0; - dval(&rv) *= dval(&rv0); - } - - ret: - return sign ? -dval(&rv) : dval(&rv); - - parse_error: - return 0.0; - - failed_malloc: - errno = ENOMEM; - return -1.0; - - undfl: - return sign ? -0.0 : 0.0; - - ovfl: - errno = ERANGE; - /* Can't trust HUGE_VAL */ - word0(&rv) = Exp_mask; - word1(&rv) = 0; - return sign ? -dval(&rv) : dval(&rv); - -} - -static char * -rv_alloc(int i) -{ - 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(k); - if (r == NULL) - return NULL; - *r = k; - return (char *)(r+1); -} - -static char * -nrv_alloc(char *s, char **rve, int n) -{ - char *rv, *t; - - rv = rv_alloc(n); - if (rv == NULL) - return NULL; - t = rv; - 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. - */ - -void -sb_freedtoa(char *s) -{ - Bigint *b = (Bigint *)((int *)s - 1); - b->maxwds = 1 << (b->k = *(int*)b); - Bfree(b); -} - -/* 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. - */ - -/* Additional notes (METD): (1) returns NULL on failure. (2) to avoid memory - leakage, a successful call to sb_dtoa should always be matched by a - call to sb_freedtoa. */ - -char * -sb_dtoa(double dd, int mode, int ndigits, - int *decpt, int *sign, char **rve) -{ - /* Arguments ndigits, decpt, sign are similar to those - of ecvt and fcvt; trailing zeros are suppressed from - the returned string. If not null, *rve is set to point - to the end of the return value. If d is +-Infinity or NaN, - then *decpt is set to 9999. - - mode: - 0 ==> shortest string that yields d when read in - and rounded to nearest. - 1 ==> like 0, but with Steele & White stopping rule; - e.g. with IEEE P754 arithmetic , mode 0 gives - 1e23 whereas mode 1 gives 9.999999999999999e22. - 2 ==> max(1,ndigits) significant digits. This gives a - return value similar to that of ecvt, except - that trailing zeros are suppressed. - 3 ==> through ndigits past the decimal point. This - gives a return value similar to that from fcvt, - except that trailing zeros are suppressed, and - ndigits can be negative. - 4,5 ==> similar to 2 and 3, respectively, but (in - round-nearest mode) with the tests of mode 0 to - possibly return a shorter string that rounds to d. - With IEEE arithmetic and compilation with - -DHonor_FLT_ROUNDS, modes 4 and 5 behave the same - as modes 2 and 3 when FLT_ROUNDS != 1. - 6-9 ==> Debugging modes similar to mode - 4: don't try - fast floating-point estimate (if applicable). - - Values of mode other than 0-9 are treated as mode 0. - - Sufficient space is allocated to the return value - to hold the suppressed trailing zeros. - */ - - int bbits, b2, b5, be, dig, i, ieps, ilim, ilim0, ilim1, - j, j1, k, k0, k_check, leftright, m2, m5, s2, s5, - spec_case, try_quick; - Long L; - int denorm; - ULong x; - Bigint *b, *b1, *delta, *mlo, *mhi, *S; - U d2, eps, u; - double ds; - char *s, *s0; - - /* set pointers to NULL, to silence gcc compiler warnings and make - cleanup easier on error */ - mlo = mhi = S = 0; - s0 = 0; - - u.d = dd; - if (word0(&u) & Sign_bit) { - /* set sign for everything, including 0's and NaNs */ - *sign = 1; - word0(&u) &= ~Sign_bit; /* clear sign bit */ - } - else - *sign = 0; - - /* quick return for Infinities, NaNs and zeros */ - if ((word0(&u) & Exp_mask) == Exp_mask) - { - /* Infinity or NaN */ - *decpt = 9999; - if (!word1(&u) && !(word0(&u) & 0xfffff)) - return nrv_alloc("Infinity", rve, 8); - return nrv_alloc("NaN", rve, 3); - } - if (!dval(&u)) { - *decpt = 1; - return nrv_alloc("0", rve, 1); - } - - /* compute k = floor(log10(d)). The computation may leave k - one too large, but should never leave k too small. */ - b = d2b(&u, &be, &bbits); - if (b == NULL) - goto failed_malloc; - if ((i = (int)(word0(&u) >> Exp_shift1 & (Exp_mask>>Exp_shift1)))) { - dval(&d2) = dval(&u); - word0(&d2) &= Frac_mask1; - word0(&d2) |= Exp_11; - - /* 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; - denorm = 0; - } - else { - /* d is denormalized */ - - i = bbits + be + (Bias + (P-1) - 1); - x = i > 32 ? word0(&u) << (64 - i) | word1(&u) >> (i - 32) - : word1(&u) << (32 - i); - dval(&d2) = x; - word0(&d2) -= 31*Exp_msk1; /* adjust exponent */ - i -= (Bias + (P-1) - 1) + 1; - denorm = 1; - } - 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(&u) < 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; - ilim = ilim1 = -1; /* Values for cases 0 and 1; done here to */ - /* silence erroneous "gcc -Wall" warning. */ - switch(mode) { - case 0: - case 1: - i = 18; - ndigits = 0; - break; - case 2: - leftright = 0; - /* no break */ - case 4: - if (ndigits <= 0) - ndigits = 1; - ilim = ilim1 = i = ndigits; - break; - case 3: - leftright = 0; - /* no break */ - case 5: - i = ndigits + k + 1; - ilim = i; - ilim1 = i - 1; - if (i <= 0) - i = 1; - } - s0 = rv_alloc(i); - if (s0 == NULL) - goto failed_malloc; - s = s0; - - - if (ilim >= 0 && ilim <= Quick_max && try_quick) { - - /* Try to get by with floating-point arithmetic. */ - - i = 0; - dval(&d2) = dval(&u); - 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(&u) /= bigtens[n_bigtens-1]; - ieps++; - } - for(; j; j >>= 1, i++) - if (j & 1) { - ieps++; - ds *= bigtens[i]; - } - dval(&u) /= ds; - } - else if ((j1 = -k)) { - dval(&u) *= tens[j1 & 0xf]; - for(j = j1 >> 4; j; j >>= 1, i++) - if (j & 1) { - ieps++; - dval(&u) *= bigtens[i]; - } - } - if (k_check && dval(&u) < 1. && ilim > 0) { - if (ilim1 <= 0) - goto fast_failed; - ilim = ilim1; - k--; - dval(&u) *= 10.; - ieps++; - } - dval(&eps) = ieps*dval(&u) + 7.; - word0(&eps) -= (P-1)*Exp_msk1; - if (ilim == 0) { - S = mhi = 0; - dval(&u) -= 5.; - if (dval(&u) > dval(&eps)) - goto one_digit; - if (dval(&u) < -dval(&eps)) - goto no_digits; - goto fast_failed; - } - if (leftright) { - /* Use Steele & White method of only - * generating digits needed. - */ - dval(&eps) = 0.5/tens[ilim-1] - dval(&eps); - for(i = 0;;) { - L = (Long)dval(&u); - dval(&u) -= L; - *s++ = '0' + (int)L; - if (dval(&u) < dval(&eps)) - goto ret1; - if (1. - dval(&u) < dval(&eps)) - goto bump_up; - if (++i >= ilim) - break; - dval(&eps) *= 10.; - dval(&u) *= 10.; - } - } - else { - /* Generate ilim digits, then fix them up. */ - dval(&eps) *= tens[ilim-1]; - for(i = 1;; i++, dval(&u) *= 10.) { - L = (Long)(dval(&u)); - if (!(dval(&u) -= L)) - ilim = i; - *s++ = '0' + (int)L; - if (i == ilim) { - if (dval(&u) > 0.5 + dval(&eps)) - goto bump_up; - else if (dval(&u) < 0.5 - dval(&eps)) { - while(*--s == '0'); - s++; - goto ret1; - } - break; - } - } - } - fast_failed: - s = s0; - dval(&u) = 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(&u) <= 5*ds) - goto no_digits; - goto one_digit; - } - for(i = 1;; i++, dval(&u) *= 10.) { - L = (Long)(dval(&u) / ds); - dval(&u) -= L*ds; - *s++ = '0' + (int)L; - if (!dval(&u)) { - break; - } - if (i == ilim) { - dval(&u) += dval(&u); - if (dval(&u) > ds || (dval(&u) == ds && L & 1)) { - bump_up: - while(*--s == '9') - if (s == s0) { - k++; - *s = '0'; - break; - } - ++*s++; - } - break; - } - } - goto ret1; - } - - m2 = b2; - m5 = b5; - if (leftright) { - i = - denorm ? be + (Bias + (P-1) - 1 + 1) : - 1 + P - bbits; - b2 += i; - s2 += i; - mhi = i2b(1); - if (mhi == NULL) - goto failed_malloc; - } - 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); - if (mhi == NULL) - goto failed_malloc; - b1 = mult(mhi, b); - Bfree(b); - b = b1; - if (b == NULL) - goto failed_malloc; - } - if ((j = b5 - m5)) { - b = pow5mult(b, j); - if (b == NULL) - goto failed_malloc; - } - } - else { - b = pow5mult(b, b5); - if (b == NULL) - goto failed_malloc; - } - } - S = i2b(1); - if (S == NULL) - goto failed_malloc; - if (s5 > 0) { - S = pow5mult(S, s5); - if (S == NULL) - goto failed_malloc; - } - - /* Check for special case that d is a normalized power of 2. */ - - spec_case = 0; - if ((mode < 2 || leftright) - ) { - if (!word1(&u) && !(word0(&u) & Bndry_mask) - && word0(&u) & (Exp_mask & ~Exp_msk1) - ) { - /* The special case */ - b2 += Log2P; - s2 += Log2P; - spec_case = 1; - } - } - - /* Arrange for convenient computation of quotients: - * shift left if necessary so divisor has 4 leading 0 bits. - * - * Perhaps we should just compute leading 28 bits of S once - * and for all and pass them and a shift to quorem, so it - * can do shifts and ors to compute the numerator for q. - */ -#define iInc 28 - i = dshift(S, s2); - b2 += i; - m2 += i; - s2 += i; - if (b2 > 0) { - b = lshift(b, b2); - if (b == NULL) - goto failed_malloc; - } - if (s2 > 0) { - S = lshift(S, s2); - if (S == NULL) - goto failed_malloc; - } - if (k_check) { - if (cmp(b,S) < 0) { - k--; - b = multadd(b, 10, 0); /* we botched the k estimate */ - if (b == NULL) - goto failed_malloc; - if (leftright) { - mhi = multadd(mhi, 10, 0); - if (mhi == NULL) - goto failed_malloc; - } - ilim = ilim1; - } - } - if (ilim <= 0 && (mode == 3 || mode == 5)) { - if (ilim < 0) { - /* no digits, fcvt style */ - no_digits: - k = -1 - ndigits; - goto ret; - } - else { - S = multadd(S, 5, 0); - if (S == NULL) - goto failed_malloc; - if (cmp(b, S) <= 0) - goto no_digits; - } - one_digit: - *s++ = '1'; - k++; - goto ret; - } - if (leftright) { - if (m2 > 0) { - mhi = lshift(mhi, m2); - if (mhi == NULL) - goto failed_malloc; - } - - /* Compute mlo -- check for special case - * that d is a normalized power of 2. - */ - - mlo = mhi; - if (spec_case) { - mhi = Balloc(mhi->k); - if (mhi == NULL) - goto failed_malloc; - Bcopy(mhi, mlo); - mhi = lshift(mhi, Log2P); - if (mhi == NULL) - goto failed_malloc; - } - - 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); - if (delta == NULL) - goto failed_malloc; - j1 = delta->sign ? 1 : cmp(b, delta); - Bfree(delta); - if (j1 == 0 && mode != 1 && !(word1(&u) & 1) - ) { - if (dig == '9') - goto round_9_up; - if (j > 0) - dig++; - *s++ = dig; - goto ret; - } - if (j < 0 || (j == 0 && mode != 1 - && !(word1(&u) & 1) - )) { - if (!b->x[0] && b->wds <= 1) { - goto accept_dig; - } - if (j1 > 0) { - b = lshift(b, 1); - if (b == NULL) - goto failed_malloc; - j1 = cmp(b, S); - if ((j1 > 0 || (j1 == 0 && dig & 1)) - && dig++ == '9') - goto round_9_up; - } - accept_dig: - *s++ = dig; - goto ret; - } - if (j1 > 0) { - 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 (b == NULL) - goto failed_malloc; - if (mlo == mhi) { - mlo = mhi = multadd(mhi, 10, 0); - if (mlo == NULL) - goto failed_malloc; - } - else { - mlo = multadd(mlo, 10, 0); - if (mlo == NULL) - goto failed_malloc; - mhi = multadd(mhi, 10, 0); - if (mhi == NULL) - goto failed_malloc; - } - } - } - else - for(i = 1;; i++) { - *s++ = dig = quorem(b,S) + '0'; - if (!b->x[0] && b->wds <= 1) { - goto ret; - } - if (i >= ilim) - break; - b = multadd(b, 10, 0); - if (b == NULL) - goto failed_malloc; - } - - /* Round off last digit */ - - b = lshift(b, 1); - if (b == NULL) - goto failed_malloc; - 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); - *s = 0; - *decpt = k + 1; - if (rve) - *rve = s; - return s0; - failed_malloc: - if (S) - Bfree(S); - if (mlo && mlo != mhi) - Bfree(mlo); - if (mhi) - Bfree(mhi); - if (b) - Bfree(b); - if (s0) - sb_freedtoa(s0); - return NULL; -} -#ifdef __cplusplus -} -#endif |