| /**************************************************************** |
| * |
| * 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. |
| * |
| * Please remember to check http://www.netlib.org/fp regularly (and especially |
| * before any Python release) for bugfixes and updates. |
| * |
| * The major modifications from Gay's original code are as follows: |
| * |
| * 0. The original code has been specialized to Python'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 PyMem_Malloc and PyMem_Free in place of malloc and free. |
| * |
| * 2. The public functions strtod, dtoa and freedtoa all now have |
| * a _Py_dg_ prefix. |
| * |
| * 3. Instead of assuming that PyMem_Malloc always succeeds, we thread |
| * PyMem_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. _Py_dg_dtoa returns NULL |
| * on failure. _Py_dg_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 |
| * _Py_dg_dtoa are expected to call _Py_dg_freedtoa to free |
| * the memory allocated by _Py_dg_dtoa. |
| * |
| * 5. The code has been reformatted to better fit with Python's |
| * C style guide (PEP 7). |
| * |
| * 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. |
| * |
| ***************************************************************/ |
| |
| /* 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 "."). |
| * Please report bugs for this modified version using the Python issue tracker |
| * (http://bugs.python.org). */ |
| |
| /* 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 Python's #defines to Gay's #defines starts here. */ |
| |
| #include "Python.h" |
| |
| /* if PY_NO_SHORT_FLOAT_REPR is defined, then don't even try to compile |
| the following code */ |
| #ifndef PY_NO_SHORT_FLOAT_REPR |
| |
| #include "float.h" |
| |
| #define MALLOC PyMem_Malloc |
| #define FREE PyMem_Free |
| |
| /* This code should also work for ARM mixed-endian format on little-endian |
| machines, where doubles have byte order 45670123 (in increasing address |
| order, 0 being the least significant byte). */ |
| #ifdef DOUBLE_IS_LITTLE_ENDIAN_IEEE754 |
| # define IEEE_8087 |
| #endif |
| #if defined(DOUBLE_IS_BIG_ENDIAN_IEEE754) || \ |
| defined(DOUBLE_IS_ARM_MIXED_ENDIAN_IEEE754) |
| # define IEEE_MC68k |
| #endif |
| #if defined(IEEE_8087) + defined(IEEE_MC68k) != 1 |
| #error "Exactly one of IEEE_8087 or IEEE_MC68k should be defined." |
| #endif |
| |
| /* The code below assumes that the endianness of integers matches the |
| endianness of the two 32-bit words of a double. Check this. */ |
| #if defined(WORDS_BIGENDIAN) && (defined(DOUBLE_IS_LITTLE_ENDIAN_IEEE754) || \ |
| defined(DOUBLE_IS_ARM_MIXED_ENDIAN_IEEE754)) |
| #error "doubles and ints have incompatible endianness" |
| #endif |
| |
| #if !defined(WORDS_BIGENDIAN) && defined(DOUBLE_IS_BIG_ENDIAN_IEEE754) |
| #error "doubles and ints have incompatible endianness" |
| #endif |
| |
| |
| #if defined(HAVE_UINT32_T) && defined(HAVE_INT32_T) |
| typedef PY_UINT32_T ULong; |
| typedef PY_INT32_T Long; |
| #else |
| #error "Failed to find an exact-width 32-bit integer type" |
| #endif |
| |
| #if defined(HAVE_UINT64_T) |
| #define ULLong PY_UINT64_T |
| #else |
| #undef ULLong |
| #endif |
| |
| #undef DEBUG |
| #ifdef Py_DEBUG |
| #define DEBUG |
| #endif |
| |
| /* End Python #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 |
| |
| #ifdef DIGLIM_DEBUG |
| extern int strtod_diglim; |
| #else |
| #define strtod_diglim STRTOD_DIGLIM |
| #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 Exp_1 0x3ff00000 |
| #define Exp_11 0x3ff00000 |
| #define Ebits 11 |
| #define Frac_mask 0xfffff |
| #define Frac_mask1 0xfffff |
| #define Ten_pmax 22 |
| #define Bletch 0x10 |
| #define Bndry_mask 0xfffff |
| #define Bndry_mask1 0xfffff |
| #define LSB 1 |
| #define Sign_bit 0x80000000 |
| #define Log2P 1 |
| #define Tiny0 0 |
| #define Tiny1 1 |
| #define Quick_max 14 |
| #define Int_max 14 |
| |
| #ifndef 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 |
| |
| #ifndef NAN_WORD0 |
| #define NAN_WORD0 0x7ff80000 |
| #endif |
| |
| #ifndef NAN_WORD1 |
| #define NAN_WORD1 0 |
| #endif |
| |
| |
| /* struct BCinfo is used to pass information from _Py_dg_strtod to bigcomp */ |
| |
| typedef struct BCinfo BCinfo; |
| struct |
| BCinfo { |
| int dp0, dp1, dplen, dsign, e0, inexact; |
| int nd, nd0, rounding, scale, uflchk; |
| }; |
| |
| #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; |
| |
| /* 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; |
| } |
| } |
| } |
| |
| #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 _Py_dg_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, int dplen) |
| { |
| 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; |
| |
| i = 9; |
| if (9 < nd0) { |
| s += 9; |
| do { |
| b = multadd(b, 10, *s++ - '0'); |
| if (b == NULL) |
| return NULL; |
| } while(++i < nd0); |
| s += dplen; |
| } |
| else |
| s += dplen + 9; |
| 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->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; |
| } |
| |
| /* 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; |
| } |
| |
| /* 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; |
| |
| 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 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 e; 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 |
| |
| /* case insensitive string match, for recognising 'inf[inity]' and |
| 'nan' strings. */ |
| |
| static int |
| match(const char **sp, char *t) |
| { |
| int c, d; |
| const char *s = *sp; |
| |
| while((d = *t++)) { |
| if ((c = *++s) >= 'A' && c <= 'Z') |
| c += 'a' - 'A'; |
| if (c != d) |
| return 0; |
| } |
| *sp = s + 1; |
| return 1; |
| } |
| |
| #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; |
| } |
| |
| |
| /* return 0 on success, -1 on failure */ |
| |
| static int |
| bigcomp(U *rv, const char *s0, BCinfo *bc) |
| { |
| Bigint *b, *d; |
| int b2, bbits, d2, dd, dig, dsign, i, j, nd, nd0, p2, p5, speccase; |
| |
| dsign = bc->dsign; |
| nd = bc->nd; |
| nd0 = bc->nd0; |
| p5 = nd + bc->e0 - 1; |
| speccase = 0; |
| if (rv->d == 0.) { /* special case: value near underflow-to-zero */ |
| /* threshold was rounded to zero */ |
| b = i2b(1); |
| if (b == NULL) |
| return -1; |
| p2 = Emin - P + 1; |
| bbits = 1; |
| word0(rv) = (P+2) << Exp_shift; |
| i = 0; |
| { |
| speccase = 1; |
| --p2; |
| dsign = 0; |
| goto have_i; |
| } |
| } |
| else |
| { |
| b = d2b(rv, &p2, &bbits); |
| if (b == NULL) |
| return -1; |
| } |
| p2 -= bc->scale; |
| /* floor(log2(rv)) == bbits - 1 + p2 */ |
| /* Check for denormal case. */ |
| i = P - bbits; |
| if (i > (j = P - Emin - 1 + p2)) { |
| i = j; |
| } |
| { |
| b = lshift(b, ++i); |
| if (b == NULL) |
| return -1; |
| b->x[0] |= 1; |
| } |
| have_i: |
| p2 -= p5 + i; |
| 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; |
| } |
| } |
| |
| /* Now b/d = exactly half-way between the two floating-point values */ |
| /* on either side of the input string. Compute first digit of b/d. */ |
| |
| if (!(dig = quorem(b,d))) { |
| b = multadd(b, 10, 0); /* very unlikely */ |
| if (b == NULL) { |
| Bfree(d); |
| return -1; |
| } |
| dig = quorem(b,d); |
| } |
| |
| /* Compare b/d with s0 */ |
| |
| assert(nd > 0); |
| dd = 9999; /* silence gcc compiler warning */ |
| for(i = 0; i < nd0; ) { |
| if ((dd = s0[i++] - '0' - dig)) |
| goto ret; |
| if (!b->x[0] && b->wds == 1) { |
| if (i < nd) |
| dd = 1; |
| goto ret; |
| } |
| b = multadd(b, 10, 0); |
| if (b == NULL) { |
| Bfree(d); |
| return -1; |
| } |
| dig = quorem(b,d); |
| } |
| for(j = bc->dp1; i++ < nd;) { |
| if ((dd = s0[j++] - '0' - dig)) |
| goto ret; |
| if (!b->x[0] && b->wds == 1) { |
| if (i < nd) |
| dd = 1; |
| goto ret; |
| } |
| b = multadd(b, 10, 0); |
| if (b == NULL) { |
| Bfree(d); |
| return -1; |
| } |
| dig = quorem(b,d); |
| } |
| if (b->x[0] || b->wds > 1) |
| dd = -1; |
| ret: |
| Bfree(b); |
| Bfree(d); |
| if (speccase) { |
| if (dd <= 0) |
| rv->d = 0.; |
| } |
| else if (dd < 0) { |
| if (!dsign) /* does not happen for round-near */ |
| retlow1: |
| dval(rv) -= ulp(rv); |
| } |
| else if (dd > 0) { |
| if (dsign) { |
| rethi1: |
| dval(rv) += ulp(rv); |
| } |
| } |
| else { |
| /* Exact half-way case: apply round-even rule. */ |
| if (word1(rv) & 1) { |
| if (dsign) |
| goto rethi1; |
| goto retlow1; |
| } |
| } |
| |
| return 0; |
| } |
| |
| double |
| _Py_dg_strtod(const char *s00, char **se) |
| { |
| int bb2, bb5, bbe, bd2, bd5, bbbits, bs2, c, e, e1, error; |
| int esign, i, j, k, nd, nd0, nf, nz, nz0, sign; |
| const char *s, *s0, *s1; |
| double aadj, aadj1; |
| Long L; |
| U aadj2, adj, rv, rv0; |
| ULong y, z; |
| BCinfo bc; |
| Bigint *bb, *bb1, *bd, *bd0, *bs, *delta; |
| |
| sign = nz0 = nz = bc.dplen = bc.uflchk = 0; |
| dval(&rv) = 0.; |
| for(s = s00;;s++) switch(*s) { |
| case '-': |
| sign = 1; |
| /* no break */ |
| case '+': |
| if (*++s) |
| goto break2; |
| /* no break */ |
| case 0: |
| goto ret0; |
| case '\t': |
| case '\n': |
| case '\v': |
| case '\f': |
| case '\r': |
| case ' ': |
| continue; |
| default: |
| goto break2; |
| } |
| break2: |
| if (*s == '0') { |
| nz0 = 1; |
| while(*++s == '0') ; |
| if (!*s) |
| goto ret; |
| } |
| s0 = s; |
| y = z = 0; |
| for(nd = nf = 0; (c = *s) >= '0' && c <= '9'; nd++, s++) |
| if (nd < 9) |
| y = 10*y + c - '0'; |
| else if (nd < 16) |
| z = 10*z + c - '0'; |
| nd0 = nd; |
| bc.dp0 = bc.dp1 = s - s0; |
| if (c == '.') { |
| c = *++s; |
| bc.dp1 = s - s0; |
| bc.dplen = bc.dp1 - bc.dp0; |
| if (!nd) { |
| for(; c == '0'; c = *++s) |
| nz++; |
| if (c > '0' && c <= '9') { |
| s0 = s; |
| nf += nz; |
| nz = 0; |
| goto have_dig; |
| } |
| goto dig_done; |
| } |
| for(; c >= '0' && c <= '9'; c = *++s) { |
| have_dig: |
| nz++; |
| if (c -= '0') { |
| nf += nz; |
| for(i = 1; i < nz; i++) |
| if (nd++ < 9) |
| y *= 10; |
| else if (nd <= DBL_DIG + 1) |
| z *= 10; |
| if (nd++ < 9) |
| y = 10*y + c; |
| else if (nd <= DBL_DIG + 1) |
| z = 10*z + c; |
| nz = 0; |
| } |
| } |
| } |
| dig_done: |
| e = 0; |
| if (c == 'e' || c == 'E') { |
| if (!nd && !nz && !nz0) { |
| goto ret0; |
| } |
| s00 = s; |
| esign = 0; |
| switch(c = *++s) { |
| case '-': |
| esign = 1; |
| case '+': |
| c = *++s; |
| } |
| if (c >= '0' && c <= '9') { |
| while(c == '0') |
| c = *++s; |
| if (c > '0' && c <= '9') { |
| L = c - '0'; |
| s1 = s; |
| while((c = *++s) >= '0' && c <= '9') |
| L = 10*L + c - '0'; |
| if (s - s1 > 8 || L > 19999) |
| /* Avoid confusion from exponents |
| * so large that e might overflow. |
| */ |
| e = 19999; /* safe for 16 bit ints */ |
| else |
| e = (int)L; |
| if (esign) |
| e = -e; |
| } |
| else |
| e = 0; |
| } |
| else |
| s = s00; |
| } |
| if (!nd) { |
| if (!nz && !nz0) { |
| /* Check for Nan and Infinity */ |
| if (!bc.dplen) |
| switch(c) { |
| case 'i': |
| case 'I': |
| if (match(&s,"nf")) { |
| --s; |
| if (!match(&s,"inity")) |
| ++s; |
| word0(&rv) = 0x7ff00000; |
| word1(&rv) = 0; |
| goto ret; |
| } |
| break; |
| case 'n': |
| case 'N': |
| if (match(&s, "an")) { |
| word0(&rv) = NAN_WORD0; |
| word1(&rv) = NAN_WORD1; |
| goto ret; |
| } |
| } |
| ret0: |
| s = s00; |
| sign = 0; |
| } |
| goto ret; |
| } |
| bc.e0 = e1 = e -= nf; |
| |
| /* Now we have nd0 digits, starting at s0, followed by a |
| * decimal point, followed by nd-nd0 digits. The number we're |
| * after is the integer represented by those digits times |
| * 10**e */ |
| |
| if (!nd0) |
| nd0 = nd; |
| k = nd < DBL_DIG + 1 ? nd : DBL_DIG + 1; |
| dval(&rv) = y; |
| if (k > 9) { |
| 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) { |
| ovfl: |
| errno = ERANGE; |
| /* Can't trust HUGE_VAL */ |
| word0(&rv) = Exp_mask; |
| word1(&rv) = 0; |
| goto ret; |
| } |
| e1 >>= 4; |
| for(j = 0; e1 > 1; j++, e1 >>= 1) |
| if (e1 & 1) |
| dval(&rv) *= bigtens[j]; |
| /* The last multiplication could overflow. */ |
| word0(&rv) -= P*Exp_msk1; |
| dval(&rv) *= bigtens[j]; |
| if ((z = word0(&rv) & Exp_mask) |
| > Exp_msk1*(DBL_MAX_EXP+Bias-P)) |
| goto ovfl; |
| if (z > Exp_msk1*(DBL_MAX_EXP+Bias-1-P)) { |
| /* set to largest number */ |
| /* (Can't trust DBL_MAX) */ |
| word0(&rv) = Big0; |
| word1(&rv) = Big1; |
| } |
| else |
| word0(&rv) += P*Exp_msk1; |
| } |
| } |
| else if (e1 < 0) { |
| e1 = -e1; |
| if ((i = e1 & 15)) |
| dval(&rv) /= tens[i]; |
| if (e1 >>= 4) { |
| if (e1 >= 1 << n_bigtens) |
| goto undfl; |
| 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)) { |
| undfl: |
| dval(&rv) = 0.; |
| errno = ERANGE; |
| goto ret; |
| } |
| } |
| } |
| |
| /* 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. */ |
| i = j = 18; |
| if (i > nd0) |
| j += bc.dplen; |
| for(;;) { |
| if (--j <= bc.dp1 && j >= bc.dp0) |
| j = bc.dp0 - 1; |
| if (s0[j] != '0') |
| break; |
| --i; |
| } |
| 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(j = bc.dp1; i < nd; ++i) |
| y = 10*y + s0[j++] - '0'; |
| } |
| } |
| bd0 = s2b(s0, nd0, nd, y, bc.dplen); |
| if (bd0 == NULL) |
| goto failed_malloc; |
| |
| for(;;) { |
| bd = Balloc(bd0->k); |
| if (bd == NULL) { |
| Bfree(bd0); |
| goto failed_malloc; |
| } |
| Bcopy(bd, bd0); |
| bb = d2b(&rv, &bbe, &bbbits); /* rv = bb * 2^bbe */ |
| if (bb == NULL) { |
| Bfree(bd); |
| Bfree(bd0); |
| goto failed_malloc; |
| } |
| 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; |
| j = bbe - bc.scale; |
| i = j + bbbits - 1; /* logb(rv) */ |
| if (i < Emin) /* denormal */ |
| j += P - Emin; |
| else |
| j = P + 1 - bbbits; |
| bb2 += j; |
| bd2 += j; |
| bd2 += bc.scale; |
| 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); |
| 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; |
| } |
| } |
| delta = diff(bb, bd); |
| if (delta == NULL) { |
| Bfree(bb); |
| Bfree(bs); |
| Bfree(bd); |
| Bfree(bd0); |
| goto failed_malloc; |
| } |
| bc.dsign = delta->sign; |
| delta->sign = 0; |
| i = cmp(delta, bs); |
| if (bc.nd > nd && i <= 0) { |
| if (bc.dsign) |
| break; /* Must 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 (bc.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 (bc.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; |
| bc.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) { |
| bc.uflchk = 1; |
| break; |
| } |
| goto undfl; |
| } |
| } |
| L = (word0(&rv) & Exp_mask) - Exp_msk1; |
| word0(&rv) = L | Bndry_mask1; |
| word1(&rv) = 0xffffffff; |
| break; |
| } |
| if (!(word1(&rv) & LSB)) |
| break; |
| if (bc.dsign) |
| dval(&rv) += ulp(&rv); |
| else { |
| dval(&rv) -= ulp(&rv); |
| if (!dval(&rv)) { |
| if (bc.nd >nd) { |
| bc.uflchk = 1; |
| break; |
| } |
| goto undfl; |
| } |
| } |
| bc.dsign = 1 - bc.dsign; |
| break; |
| } |
| if ((aadj = ratio(delta, bs)) <= 2.) { |
| if (bc.dsign) |
| aadj = aadj1 = 1.; |
| else if (word1(&rv) || word0(&rv) & Bndry_mask) { |
| if (word1(&rv) == Tiny1 && !word0(&rv)) { |
| if (bc.nd >nd) { |
| bc.uflchk = 1; |
| 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 = bc.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) |
| 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 = bc.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 (bc.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); |
| /* try to avoid the bug of testing an 8087 register value */ |
| if (!(word0(&rv) & Exp_mask)) |
| errno = ERANGE; |
| } |
| ret: |
| if (se) |
| *se = (char *)s; |
| return sign ? -dval(&rv) : dval(&rv); |
| |
| failed_malloc: |
| if (se) |
| *se = (char *)s00; |
| errno = ENOMEM; |
| return -1.0; |
| } |
| |
| 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 |
| _Py_dg_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 _Py_dg_dtoa should always be matched by a |
| call to _Py_dg_freedtoa. */ |
| |
| char * |
| _Py_dg_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 = b = 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. |
| */ |
| if ((i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0x1f)) |
| i = 32 - i; |
| #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) |
| _Py_dg_freedtoa(s0); |
| return NULL; |
| } |
| #ifdef __cplusplus |
| } |
| #endif |
| |
| #endif /* PY_NO_SHORT_FLOAT_REPR */ |