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+/****************************************************************
+ *
+ * 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.
+ *
+ * 7. _Py_dg_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 ".").
+ * 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
+
+/* 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 19999U
+#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
+
+/* struct BCinfo is used to pass information from _Py_dg_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 _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)
+{
+ 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 _Py_dg_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 _Py_dg_strtod.
+
+ The bigcomp function is only called after _Py_dg_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 _Py_dg_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 _Py_dg_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;
+}
+
+double
+_Py_dg_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;
+
+ 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). nd0 will be the position
+ of the point relative to s0. nd will be the total number of digits
+ ignoring leading zeros. */
+ s0 = s1 = s;
+ while ('0' <= c && c <= '9')
+ c = *++s;
+ nd0 = nd = s - s1;
+
+ /* Parse decimal point and following digits. */
+ if (c == '.') {
+ c = *++s;
+ if (!nd) {
+ s1 = s;
+ while (c == '0')
+ c = *++s;
+ lz = lz || s != s1;
+ nd0 -= s - s1;
+ s0 = s;
+ }
+ s1 = s;
+ while ('0' <= c && c <= '9')
+ c = *++s;
+ nd += s - s1;
+ }
+
+ /* Now lz is true if and only if there were leading zero digits, and nd
+ gives the total number of digits ignoring leading zeros. A valid input
+ must have at least one digit. */
+ if (!nd && !lz) {
+ if (se)
+ *se = (char *)s00;
+ goto parse_error;
+ }
+
+ /* 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 _Py_dg_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
+_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 = 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)
+ _Py_dg_freedtoa(s0);
+ return NULL;
+}
+#ifdef __cplusplus
+}
+#endif
+
+#endif /* PY_NO_SHORT_FLOAT_REPR */
generated by cgit v0.12 at 2025-10-31 04:26:54 (GMT)