Issue #7117: Prepare for backport of py3k float repr.

Add the Python/dtoa.c file containing the main algorithms;
add corresponding include file and include in Python.h;
include license information for Python/dtoa.c;
add dtoa.c and dtoa.h to Makefile.

1 files changed, 2609 insertions, 0 deletions

diff --git a/Python/dtoa.c b/Python/dtoa.c
new file mode 100644
index 0000000..1cac941
--- /dev/null
+++ b/Python/dtoa.c
@@ -0,0 +1,2609 @@
+/****************************************************************
+ *
+ * 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
+
+#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
+
+/* 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
+
+#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;
+        /* modify original dtoa.c so that it doesn't accept leading whitespace
+        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) {
+          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 */