2009-04-16 19:52:09 +00:00
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/****************************************************************
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*
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* The author of this software is David M. Gay.
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*
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* Copyright (c) 1991, 2000, 2001 by Lucent Technologies.
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*
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* Permission to use, copy, modify, and distribute this software for any
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* purpose without fee is hereby granted, provided that this entire notice
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* is included in all copies of any software which is or includes a copy
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* or modification of this software and in all copies of the supporting
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* documentation for such software.
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*
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* THIS SOFTWARE IS BEING PROVIDED "AS IS", WITHOUT ANY EXPRESS OR IMPLIED
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* WARRANTY. IN PARTICULAR, NEITHER THE AUTHOR NOR LUCENT MAKES ANY
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* REPRESENTATION OR WARRANTY OF ANY KIND CONCERNING THE MERCHANTABILITY
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* OF THIS SOFTWARE OR ITS FITNESS FOR ANY PARTICULAR PURPOSE.
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*
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***************************************************************/
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/****************************************************************
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* This is dtoa.c by David M. Gay, downloaded from
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* http://www.netlib.org/fp/dtoa.c on April 15, 2009 and modified for
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* inclusion into the Python core by Mark E. T. Dickinson and Eric V. Smith.
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2009-04-17 16:06:28 +00:00
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*
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* Please remember to check http://www.netlib.org/fp regularly (and especially
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* before any Python release) for bugfixes and updates.
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*
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* The major modifications from Gay's original code are as follows:
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2009-04-16 19:52:09 +00:00
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*
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* 0. The original code has been specialized to Python's needs by removing
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* many of the #ifdef'd sections. In particular, code to support VAX and
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* IBM floating-point formats, hex NaNs, hex floats, locale-aware
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* treatment of the decimal point, and setting of the inexact flag have
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* been removed.
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*
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* 1. We use PyMem_Malloc and PyMem_Free in place of malloc and free.
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*
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* 2. The public functions strtod, dtoa and freedtoa all now have
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* a _Py_dg_ prefix.
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*
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* 3. Instead of assuming that PyMem_Malloc always succeeds, we thread
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* PyMem_Malloc failures through the code. The functions
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*
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* Balloc, multadd, s2b, i2b, mult, pow5mult, lshift, diff, d2b
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*
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* of return type *Bigint all return NULL to indicate a malloc failure.
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* Similarly, rv_alloc and nrv_alloc (return type char *) return NULL on
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* failure. bigcomp now has return type int (it used to be void) and
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* returns -1 on failure and 0 otherwise. _Py_dg_dtoa returns NULL
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* on failure. _Py_dg_strtod indicates failure due to malloc failure
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* by returning -1.0, setting errno=ENOMEM and *se to s00.
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*
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* 4. The static variable dtoa_result has been removed. Callers of
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* _Py_dg_dtoa are expected to call _Py_dg_freedtoa to free
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* the memory allocated by _Py_dg_dtoa.
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*
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* 5. The code has been reformatted to better fit with Python's
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* C style guide (PEP 7).
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*
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2009-04-17 16:06:28 +00:00
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* 6. A bug in the memory allocation has been fixed: to avoid FREEing memory
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* that hasn't been MALLOC'ed, private_mem should only be used when k <=
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* Kmax.
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*
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2009-05-03 20:33:40 +00:00
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* 7. _Py_dg_strtod has been modified so that it doesn't accept strings with
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* leading whitespace.
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*
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2020-05-29 13:23:57 +00:00
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* 8. A corner case where _Py_dg_dtoa didn't strip trailing zeros has been
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* fixed. (bugs.python.org/issue40780)
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*
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2009-04-16 19:52:09 +00:00
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***************************************************************/
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/* Please send bug reports for the original dtoa.c code to David M. Gay (dmg
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* at acm dot org, with " at " changed at "@" and " dot " changed to ".").
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* Please report bugs for this modified version using the Python issue tracker
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* (http://bugs.python.org). */
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/* On a machine with IEEE extended-precision registers, it is
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* necessary to specify double-precision (53-bit) rounding precision
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* before invoking strtod or dtoa. If the machine uses (the equivalent
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* of) Intel 80x87 arithmetic, the call
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* _control87(PC_53, MCW_PC);
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* does this with many compilers. Whether this or another call is
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* appropriate depends on the compiler; for this to work, it may be
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* necessary to #include "float.h" or another system-dependent header
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* file.
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*/
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/* strtod for IEEE-, VAX-, and IBM-arithmetic machines.
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*
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* This strtod returns a nearest machine number to the input decimal
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* string (or sets errno to ERANGE). With IEEE arithmetic, ties are
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* broken by the IEEE round-even rule. Otherwise ties are broken by
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* biased rounding (add half and chop).
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*
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* Inspired loosely by William D. Clinger's paper "How to Read Floating
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* Point Numbers Accurately" [Proc. ACM SIGPLAN '90, pp. 92-101].
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*
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* Modifications:
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*
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* 1. We only require IEEE, IBM, or VAX double-precision
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* arithmetic (not IEEE double-extended).
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* 2. We get by with floating-point arithmetic in a case that
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* Clinger missed -- when we're computing d * 10^n
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* for a small integer d and the integer n is not too
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* much larger than 22 (the maximum integer k for which
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* we can represent 10^k exactly), we may be able to
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* compute (d*10^k) * 10^(e-k) with just one roundoff.
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* 3. Rather than a bit-at-a-time adjustment of the binary
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* result in the hard case, we use floating-point
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* arithmetic to determine the adjustment to within
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* one bit; only in really hard cases do we need to
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* compute a second residual.
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* 4. Because of 3., we don't need a large table of powers of 10
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* for ten-to-e (just some small tables, e.g. of 10^k
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* for 0 <= k <= 22).
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*/
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/* Linking of Python's #defines to Gay's #defines starts here. */
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#include "Python.h"
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2022-02-23 17:16:23 +00:00
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#include "pycore_dtoa.h" // _PY_SHORT_FLOAT_REPR
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2023-02-28 20:14:40 +00:00
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#include "pycore_pystate.h" // _PyInterpreterState_GET()
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2021-10-13 17:25:53 +00:00
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#include <stdlib.h> // exit()
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2009-04-16 19:52:09 +00:00
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2022-02-23 17:16:23 +00:00
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/* if _PY_SHORT_FLOAT_REPR == 0, then don't even try to compile
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2009-04-16 19:52:09 +00:00
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the following code */
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2022-02-23 17:16:23 +00:00
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#if _PY_SHORT_FLOAT_REPR == 1
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2009-04-16 19:52:09 +00:00
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#include "float.h"
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#define MALLOC PyMem_Malloc
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#define FREE PyMem_Free
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/* This code should also work for ARM mixed-endian format on little-endian
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machines, where doubles have byte order 45670123 (in increasing address
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order, 0 being the least significant byte). */
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#ifdef DOUBLE_IS_LITTLE_ENDIAN_IEEE754
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# define IEEE_8087
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#endif
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#if defined(DOUBLE_IS_BIG_ENDIAN_IEEE754) || \
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defined(DOUBLE_IS_ARM_MIXED_ENDIAN_IEEE754)
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# define IEEE_MC68k
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#endif
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#if defined(IEEE_8087) + defined(IEEE_MC68k) != 1
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#error "Exactly one of IEEE_8087 or IEEE_MC68k should be defined."
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#endif
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/* The code below assumes that the endianness of integers matches the
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endianness of the two 32-bit words of a double. Check this. */
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#if defined(WORDS_BIGENDIAN) && (defined(DOUBLE_IS_LITTLE_ENDIAN_IEEE754) || \
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defined(DOUBLE_IS_ARM_MIXED_ENDIAN_IEEE754))
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#error "doubles and ints have incompatible endianness"
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#endif
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#if !defined(WORDS_BIGENDIAN) && defined(DOUBLE_IS_BIG_ENDIAN_IEEE754)
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#error "doubles and ints have incompatible endianness"
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#endif
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2021-03-22 10:58:59 +00:00
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2022-11-15 16:45:11 +00:00
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// ULong is defined in pycore_dtoa.h.
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2021-03-22 10:58:59 +00:00
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typedef int32_t Long;
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typedef uint64_t ULLong;
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2009-04-16 19:52:09 +00:00
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#undef DEBUG
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#ifdef Py_DEBUG
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#define DEBUG
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#endif
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/* End Python #define linking */
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#ifdef DEBUG
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#define Bug(x) {fprintf(stderr, "%s\n", x); exit(1);}
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#endif
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typedef union { double d; ULong L[2]; } U;
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#ifdef IEEE_8087
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#define word0(x) (x)->L[1]
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#define word1(x) (x)->L[0]
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#else
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#define word0(x) (x)->L[0]
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#define word1(x) (x)->L[1]
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#endif
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#define dval(x) (x)->d
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#ifndef STRTOD_DIGLIM
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#define STRTOD_DIGLIM 40
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#endif
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2010-01-12 23:04:19 +00:00
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/* maximum permitted exponent value for strtod; exponents larger than
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MAX_ABS_EXP in absolute value get truncated to +-MAX_ABS_EXP. MAX_ABS_EXP
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should fit into an int. */
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#ifndef MAX_ABS_EXP
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2013-11-26 16:19:13 +00:00
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#define MAX_ABS_EXP 1100000000U
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#endif
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/* Bound on length of pieces of input strings in _Py_dg_strtod; specifically,
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this is used to bound the total number of digits ignoring leading zeros and
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the number of digits that follow the decimal point. Ideally, MAX_DIGITS
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should satisfy MAX_DIGITS + 400 < MAX_ABS_EXP; that ensures that the
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exponent clipping in _Py_dg_strtod can't affect the value of the output. */
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#ifndef MAX_DIGITS
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#define MAX_DIGITS 1000000000U
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#endif
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/* Guard against trying to use the above values on unusual platforms with ints
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* of width less than 32 bits. */
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#if MAX_ABS_EXP > INT_MAX
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#error "MAX_ABS_EXP should fit in an int"
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#endif
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#if MAX_DIGITS > INT_MAX
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#error "MAX_DIGITS should fit in an int"
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2009-04-16 19:52:09 +00:00
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#endif
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/* The following definition of Storeinc is appropriate for MIPS processors.
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* An alternative that might be better on some machines is
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* #define Storeinc(a,b,c) (*a++ = b << 16 | c & 0xffff)
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*/
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#if defined(IEEE_8087)
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#define Storeinc(a,b,c) (((unsigned short *)a)[1] = (unsigned short)b, \
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((unsigned short *)a)[0] = (unsigned short)c, a++)
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#else
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#define Storeinc(a,b,c) (((unsigned short *)a)[0] = (unsigned short)b, \
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((unsigned short *)a)[1] = (unsigned short)c, a++)
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#endif
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/* #define P DBL_MANT_DIG */
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/* Ten_pmax = floor(P*log(2)/log(5)) */
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/* Bletch = (highest power of 2 < DBL_MAX_10_EXP) / 16 */
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/* Quick_max = floor((P-1)*log(FLT_RADIX)/log(10) - 1) */
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/* Int_max = floor(P*log(FLT_RADIX)/log(10) - 1) */
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#define Exp_shift 20
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#define Exp_shift1 20
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#define Exp_msk1 0x100000
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#define Exp_msk11 0x100000
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#define Exp_mask 0x7ff00000
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#define P 53
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#define Nbits 53
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#define Bias 1023
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#define Emax 1023
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#define Emin (-1022)
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2010-01-24 10:16:29 +00:00
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#define Etiny (-1074) /* smallest denormal is 2**Etiny */
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2009-04-16 19:52:09 +00:00
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#define Exp_1 0x3ff00000
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#define Exp_11 0x3ff00000
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#define Ebits 11
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#define Frac_mask 0xfffff
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#define Frac_mask1 0xfffff
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#define Ten_pmax 22
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#define Bletch 0x10
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#define Bndry_mask 0xfffff
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#define Bndry_mask1 0xfffff
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#define Sign_bit 0x80000000
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#define Log2P 1
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#define Tiny0 0
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#define Tiny1 1
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#define Quick_max 14
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#define Int_max 14
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#ifndef Flt_Rounds
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#ifdef FLT_ROUNDS
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#define Flt_Rounds FLT_ROUNDS
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#else
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#define Flt_Rounds 1
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#endif
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#endif /*Flt_Rounds*/
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#define Rounding Flt_Rounds
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#define Big0 (Frac_mask1 | Exp_msk1*(DBL_MAX_EXP+Bias-1))
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#define Big1 0xffffffff
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2012-04-29 14:31:56 +00:00
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/* Bits of the representation of positive infinity. */
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#define POSINF_WORD0 0x7ff00000
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#define POSINF_WORD1 0
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2009-04-16 19:52:09 +00:00
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/* struct BCinfo is used to pass information from _Py_dg_strtod to bigcomp */
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typedef struct BCinfo BCinfo;
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struct
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BCinfo {
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2010-01-21 19:51:08 +00:00
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int e0, nd, nd0, scale;
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2009-04-16 19:52:09 +00:00
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};
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#define FFFFFFFF 0xffffffffUL
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/* struct Bigint is used to represent arbitrary-precision integers. These
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integers are stored in sign-magnitude format, with the magnitude stored as
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an array of base 2**32 digits. Bigints are always normalized: if x is a
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Bigint then x->wds >= 1, and either x->wds == 1 or x[wds-1] is nonzero.
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The Bigint fields are as follows:
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- next is a header used by Balloc and Bfree to keep track of lists
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of freed Bigints; it's also used for the linked list of
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powers of 5 of the form 5**2**i used by pow5mult.
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- k indicates which pool this Bigint was allocated from
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- maxwds is the maximum number of words space was allocated for
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(usually maxwds == 2**k)
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- sign is 1 for negative Bigints, 0 for positive. The sign is unused
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(ignored on inputs, set to 0 on outputs) in almost all operations
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involving Bigints: a notable exception is the diff function, which
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ignores signs on inputs but sets the sign of the output correctly.
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- wds is the actual number of significant words
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- x contains the vector of words (digits) for this Bigint, from least
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significant (x[0]) to most significant (x[wds-1]).
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*/
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2022-11-15 16:45:11 +00:00
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// struct Bigint is defined in pycore_dtoa.h.
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2021-03-22 10:58:59 +00:00
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typedef struct Bigint Bigint;
|
2009-04-16 19:52:09 +00:00
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2023-12-07 13:47:55 +00:00
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#if !defined(Py_GIL_DISABLED) && !defined(Py_USING_MEMORY_DEBUGGER)
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2010-01-17 21:02:55 +00:00
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2009-04-16 19:52:09 +00:00
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/* Memory management: memory is allocated from, and returned to, Kmax+1 pools
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of memory, where pool k (0 <= k <= Kmax) is for Bigints b with b->maxwds ==
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1 << k. These pools are maintained as linked lists, with freelist[k]
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pointing to the head of the list for pool k.
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On allocation, if there's no free slot in the appropriate pool, MALLOC is
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|
|
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. */
|
|
|
|
|
2023-02-28 20:14:40 +00:00
|
|
|
#define freelist interp->dtoa.freelist
|
|
|
|
#define private_mem interp->dtoa.preallocated
|
|
|
|
#define pmem_next interp->dtoa.preallocated_next
|
2009-04-16 19:52:09 +00:00
|
|
|
|
|
|
|
/* Allocate space for a Bigint with up to 1<<k digits */
|
|
|
|
|
|
|
|
static Bigint *
|
|
|
|
Balloc(int k)
|
|
|
|
{
|
|
|
|
int x;
|
|
|
|
Bigint *rv;
|
|
|
|
unsigned int len;
|
2023-02-28 20:14:40 +00:00
|
|
|
PyInterpreterState *interp = _PyInterpreterState_GET();
|
2021-03-22 10:58:59 +00:00
|
|
|
|
2022-11-15 16:45:11 +00:00
|
|
|
if (k <= Bigint_Kmax && (rv = freelist[k]))
|
2009-04-16 19:52:09 +00:00
|
|
|
freelist[k] = rv->next;
|
|
|
|
else {
|
|
|
|
x = 1 << k;
|
|
|
|
len = (sizeof(Bigint) + (x-1)*sizeof(ULong) + sizeof(double) - 1)
|
|
|
|
/sizeof(double);
|
2022-11-15 16:45:11 +00:00
|
|
|
if (k <= Bigint_Kmax &&
|
|
|
|
pmem_next - private_mem + len <= (Py_ssize_t)Bigint_PREALLOC_SIZE
|
|
|
|
) {
|
2009-04-16 19:52:09 +00:00
|
|
|
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) {
|
2022-11-15 16:45:11 +00:00
|
|
|
if (v->k > Bigint_Kmax)
|
2009-04-16 19:52:09 +00:00
|
|
|
FREE((void*)v);
|
|
|
|
else {
|
2023-02-28 20:14:40 +00:00
|
|
|
PyInterpreterState *interp = _PyInterpreterState_GET();
|
2009-04-16 19:52:09 +00:00
|
|
|
v->next = freelist[v->k];
|
|
|
|
freelist[v->k] = v;
|
|
|
|
}
|
|
|
|
}
|
|
|
|
}
|
|
|
|
|
2022-11-15 16:45:11 +00:00
|
|
|
#undef pmem_next
|
|
|
|
#undef private_mem
|
|
|
|
#undef freelist
|
|
|
|
|
2010-01-17 21:02:55 +00:00
|
|
|
#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);
|
|
|
|
}
|
|
|
|
}
|
|
|
|
|
2023-12-07 13:47:55 +00:00
|
|
|
#endif /* !defined(Py_GIL_DISABLED) && !defined(Py_USING_MEMORY_DEBUGGER) */
|
2010-01-17 21:02:55 +00:00
|
|
|
|
2009-04-16 19:52:09 +00:00
|
|
|
#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;
|
|
|
|
ULong *x;
|
|
|
|
ULLong carry, y;
|
|
|
|
Bigint *b1;
|
|
|
|
|
|
|
|
wds = b->wds;
|
|
|
|
x = b->x;
|
|
|
|
i = 0;
|
|
|
|
carry = a;
|
|
|
|
do {
|
|
|
|
y = *x * (ULLong)m + carry;
|
|
|
|
carry = y >> 32;
|
2009-04-17 19:29:46 +00:00
|
|
|
*x++ = (ULong)(y & FFFFFFFF);
|
2009-04-16 19:52:09 +00:00
|
|
|
}
|
|
|
|
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 *
|
Merged revisions 77477-77478,77481-77483,77490-77493 via svnmerge from
svn+ssh://pythondev@svn.python.org/python/trunk
........
r77477 | mark.dickinson | 2010-01-13 18:21:53 +0000 (Wed, 13 Jan 2010) | 1 line
Add comments explaining the role of the bigcomp function in dtoa.c.
........
r77478 | mark.dickinson | 2010-01-13 19:02:37 +0000 (Wed, 13 Jan 2010) | 1 line
Clarify that sulp expects a nonnegative input, but that +0.0 is fine.
........
r77481 | mark.dickinson | 2010-01-13 20:55:03 +0000 (Wed, 13 Jan 2010) | 1 line
Simplify and annotate the bigcomp function, removing unused special cases.
........
r77482 | mark.dickinson | 2010-01-13 22:15:53 +0000 (Wed, 13 Jan 2010) | 1 line
Fix buggy comparison: LHS of comparison was being treated as unsigned.
........
r77483 | mark.dickinson | 2010-01-13 22:20:10 +0000 (Wed, 13 Jan 2010) | 1 line
More dtoa.c cleanup; remove the need for bc.dplen, bc.dp0 and bc.dp1.
........
r77490 | mark.dickinson | 2010-01-14 13:02:36 +0000 (Thu, 14 Jan 2010) | 1 line
Fix off-by-one error introduced in r77483. I have a test for this, but it currently fails due to a different dtoa.c bug; I'll add the test once that bug is fixed.
........
r77491 | mark.dickinson | 2010-01-14 13:14:49 +0000 (Thu, 14 Jan 2010) | 1 line
Issue 7632: fix a dtoa.c bug (bug 6) causing incorrect rounding. Tests to follow.
........
r77492 | mark.dickinson | 2010-01-14 14:40:20 +0000 (Thu, 14 Jan 2010) | 1 line
Issue 7632: fix incorrect rounding for long input strings with values very close to a power of 2. (See Bug 4 in the tracker discussion.)
........
r77493 | mark.dickinson | 2010-01-14 15:22:33 +0000 (Thu, 14 Jan 2010) | 1 line
Issue #7632: add tests for bugs fixed so far.
........
2010-01-14 15:37:49 +00:00
|
|
|
s2b(const char *s, int nd0, int nd, ULong y9)
|
2009-04-16 19:52:09 +00:00
|
|
|
{
|
|
|
|
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;
|
|
|
|
|
Merged revisions 77477-77478,77481-77483,77490-77493 via svnmerge from
svn+ssh://pythondev@svn.python.org/python/trunk
........
r77477 | mark.dickinson | 2010-01-13 18:21:53 +0000 (Wed, 13 Jan 2010) | 1 line
Add comments explaining the role of the bigcomp function in dtoa.c.
........
r77478 | mark.dickinson | 2010-01-13 19:02:37 +0000 (Wed, 13 Jan 2010) | 1 line
Clarify that sulp expects a nonnegative input, but that +0.0 is fine.
........
r77481 | mark.dickinson | 2010-01-13 20:55:03 +0000 (Wed, 13 Jan 2010) | 1 line
Simplify and annotate the bigcomp function, removing unused special cases.
........
r77482 | mark.dickinson | 2010-01-13 22:15:53 +0000 (Wed, 13 Jan 2010) | 1 line
Fix buggy comparison: LHS of comparison was being treated as unsigned.
........
r77483 | mark.dickinson | 2010-01-13 22:20:10 +0000 (Wed, 13 Jan 2010) | 1 line
More dtoa.c cleanup; remove the need for bc.dplen, bc.dp0 and bc.dp1.
........
r77490 | mark.dickinson | 2010-01-14 13:02:36 +0000 (Thu, 14 Jan 2010) | 1 line
Fix off-by-one error introduced in r77483. I have a test for this, but it currently fails due to a different dtoa.c bug; I'll add the test once that bug is fixed.
........
r77491 | mark.dickinson | 2010-01-14 13:14:49 +0000 (Thu, 14 Jan 2010) | 1 line
Issue 7632: fix a dtoa.c bug (bug 6) causing incorrect rounding. Tests to follow.
........
r77492 | mark.dickinson | 2010-01-14 14:40:20 +0000 (Thu, 14 Jan 2010) | 1 line
Issue 7632: fix incorrect rounding for long input strings with values very close to a power of 2. (See Bug 4 in the tracker discussion.)
........
r77493 | mark.dickinson | 2010-01-14 15:22:33 +0000 (Thu, 14 Jan 2010) | 1 line
Issue #7632: add tests for bugs fixed so far.
........
2010-01-14 15:37:49 +00:00
|
|
|
if (nd <= 9)
|
|
|
|
return b;
|
|
|
|
|
|
|
|
s += 9;
|
|
|
|
for (i = 9; i < nd0; i++) {
|
|
|
|
b = multadd(b, 10, *s++ - '0');
|
|
|
|
if (b == NULL)
|
|
|
|
return NULL;
|
2009-04-16 19:52:09 +00:00
|
|
|
}
|
Merged revisions 77477-77478,77481-77483,77490-77493 via svnmerge from
svn+ssh://pythondev@svn.python.org/python/trunk
........
r77477 | mark.dickinson | 2010-01-13 18:21:53 +0000 (Wed, 13 Jan 2010) | 1 line
Add comments explaining the role of the bigcomp function in dtoa.c.
........
r77478 | mark.dickinson | 2010-01-13 19:02:37 +0000 (Wed, 13 Jan 2010) | 1 line
Clarify that sulp expects a nonnegative input, but that +0.0 is fine.
........
r77481 | mark.dickinson | 2010-01-13 20:55:03 +0000 (Wed, 13 Jan 2010) | 1 line
Simplify and annotate the bigcomp function, removing unused special cases.
........
r77482 | mark.dickinson | 2010-01-13 22:15:53 +0000 (Wed, 13 Jan 2010) | 1 line
Fix buggy comparison: LHS of comparison was being treated as unsigned.
........
r77483 | mark.dickinson | 2010-01-13 22:20:10 +0000 (Wed, 13 Jan 2010) | 1 line
More dtoa.c cleanup; remove the need for bc.dplen, bc.dp0 and bc.dp1.
........
r77490 | mark.dickinson | 2010-01-14 13:02:36 +0000 (Thu, 14 Jan 2010) | 1 line
Fix off-by-one error introduced in r77483. I have a test for this, but it currently fails due to a different dtoa.c bug; I'll add the test once that bug is fixed.
........
r77491 | mark.dickinson | 2010-01-14 13:14:49 +0000 (Thu, 14 Jan 2010) | 1 line
Issue 7632: fix a dtoa.c bug (bug 6) causing incorrect rounding. Tests to follow.
........
r77492 | mark.dickinson | 2010-01-14 14:40:20 +0000 (Thu, 14 Jan 2010) | 1 line
Issue 7632: fix incorrect rounding for long input strings with values very close to a power of 2. (See Bug 4 in the tracker discussion.)
........
r77493 | mark.dickinson | 2010-01-14 15:22:33 +0000 (Thu, 14 Jan 2010) | 1 line
Issue #7632: add tests for bugs fixed so far.
........
2010-01-14 15:37:49 +00:00
|
|
|
s++;
|
2009-04-16 19:52:09 +00:00
|
|
|
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;
|
|
|
|
ULLong carry, z;
|
|
|
|
|
2010-01-24 10:16:29 +00:00
|
|
|
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;
|
|
|
|
}
|
|
|
|
|
2009-04-16 19:52:09 +00:00
|
|
|
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;
|
|
|
|
for(; xb < xbe; xc0++) {
|
|
|
|
if ((y = *xb++)) {
|
|
|
|
x = xa;
|
|
|
|
xc = xc0;
|
|
|
|
carry = 0;
|
|
|
|
do {
|
|
|
|
z = *x++ * (ULLong)y + *xc + carry;
|
|
|
|
carry = z >> 32;
|
2009-04-17 19:29:46 +00:00
|
|
|
*xc++ = (ULong)(z & FFFFFFFF);
|
2009-04-16 19:52:09 +00:00
|
|
|
}
|
|
|
|
while(x < xae);
|
|
|
|
*xc = (ULong)carry;
|
|
|
|
}
|
|
|
|
}
|
|
|
|
for(xc0 = c->x, xc = xc0 + wc; wc > 0 && !*--xc; --wc) ;
|
|
|
|
c->wds = wc;
|
|
|
|
return c;
|
|
|
|
}
|
|
|
|
|
2010-01-17 21:02:55 +00:00
|
|
|
#ifndef Py_USING_MEMORY_DEBUGGER
|
|
|
|
|
2009-04-16 19:52:09 +00:00
|
|
|
/* 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)
|
|
|
|
{
|
2023-12-07 13:47:55 +00:00
|
|
|
Bigint *b1, *p5, **p5s;
|
2009-04-16 19:52:09 +00:00
|
|
|
int i;
|
2015-12-25 17:53:18 +00:00
|
|
|
static const int p05[3] = { 5, 25, 125 };
|
2009-04-16 19:52:09 +00:00
|
|
|
|
2023-12-07 13:47:55 +00:00
|
|
|
// For double-to-string conversion, the maximum value of k is limited by
|
|
|
|
// DBL_MAX_10_EXP (308), the maximum decimal base-10 exponent for binary64.
|
|
|
|
// For string-to-double conversion, the extreme case is constrained by our
|
|
|
|
// hardcoded exponent limit before we underflow of -512, adjusted by
|
|
|
|
// STRTOD_DIGLIM-DBL_DIG-1, giving a maximum of k=535.
|
|
|
|
assert(0 <= k && k < 1024);
|
|
|
|
|
2009-04-16 19:52:09 +00:00
|
|
|
if ((i = k & 3)) {
|
|
|
|
b = multadd(b, p05[i-1], 0);
|
|
|
|
if (b == NULL)
|
|
|
|
return NULL;
|
|
|
|
}
|
|
|
|
|
|
|
|
if (!(k >>= 2))
|
|
|
|
return b;
|
2023-02-28 20:14:40 +00:00
|
|
|
PyInterpreterState *interp = _PyInterpreterState_GET();
|
2023-12-07 13:47:55 +00:00
|
|
|
p5s = interp->dtoa.p5s;
|
2009-04-16 19:52:09 +00:00
|
|
|
for(;;) {
|
2023-12-07 13:47:55 +00:00
|
|
|
assert(p5s != interp->dtoa.p5s + Bigint_Pow5size);
|
|
|
|
p5 = *p5s;
|
|
|
|
p5s++;
|
2009-04-16 19:52:09 +00:00
|
|
|
if (k & 1) {
|
|
|
|
b1 = mult(b, p5);
|
|
|
|
Bfree(b);
|
|
|
|
b = b1;
|
|
|
|
if (b == NULL)
|
|
|
|
return NULL;
|
|
|
|
}
|
|
|
|
if (!(k >>= 1))
|
|
|
|
break;
|
|
|
|
}
|
|
|
|
return b;
|
|
|
|
}
|
|
|
|
|
2010-01-17 21:02:55 +00:00
|
|
|
#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;
|
2015-12-25 17:53:18 +00:00
|
|
|
static const int p05[3] = { 5, 25, 125 };
|
2010-01-17 21:02:55 +00:00
|
|
|
|
|
|
|
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 */
|
|
|
|
|
2009-04-16 19:52:09 +00:00
|
|
|
/* 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;
|
|
|
|
|
2010-01-24 10:16:29 +00:00
|
|
|
if (!k || (!b->x[0] && b->wds == 1))
|
|
|
|
return b;
|
|
|
|
|
2009-04-16 19:52:09 +00:00
|
|
|
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;
|
|
|
|
ULLong borrow, y;
|
|
|
|
|
|
|
|
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;
|
|
|
|
do {
|
|
|
|
y = (ULLong)*xa++ - *xb++ - borrow;
|
|
|
|
borrow = y >> 32 & (ULong)1;
|
2009-04-17 19:29:46 +00:00
|
|
|
*xc++ = (ULong)(y & FFFFFFFF);
|
2009-04-16 19:52:09 +00:00
|
|
|
}
|
|
|
|
while(xb < xbe);
|
|
|
|
while(xa < xae) {
|
|
|
|
y = *xa++ - borrow;
|
|
|
|
borrow = y >> 32 & (ULong)1;
|
2009-04-17 19:29:46 +00:00
|
|
|
*xc++ = (ULong)(y & FFFFFFFF);
|
2009-04-16 19:52:09 +00:00
|
|
|
}
|
|
|
|
while(!*--xc)
|
|
|
|
wa--;
|
|
|
|
c->wds = wa;
|
|
|
|
return c;
|
|
|
|
}
|
|
|
|
|
2010-01-21 19:51:08 +00:00
|
|
|
/* Given a positive normal double x, return the difference between x and the
|
|
|
|
next double up. Doesn't give correct results for subnormals. */
|
2009-04-16 19:52:09 +00:00
|
|
|
|
|
|
|
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);
|
|
|
|
}
|
|
|
|
|
2010-01-24 10:16:29 +00:00
|
|
|
/* 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;
|
2015-03-18 14:01:44 +00:00
|
|
|
|
2010-01-24 10:16:29 +00:00
|
|
|
/* 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;
|
|
|
|
}
|
|
|
|
|
2009-04-16 19:52:09 +00:00
|
|
|
/* 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
|
2010-01-04 21:33:31 +00:00
|
|
|
significant bits of b; that is, 2**(*bbits-1) <= b < 2**(*bbits).
|
2009-04-16 19:52:09 +00:00
|
|
|
|
|
|
|
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;
|
|
|
|
ULLong borrow, carry, y, ys;
|
|
|
|
|
|
|
|
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 {
|
|
|
|
ys = *sx++ * (ULLong)q + carry;
|
|
|
|
carry = ys >> 32;
|
|
|
|
y = *bx - (ys & FFFFFFFF) - borrow;
|
|
|
|
borrow = y >> 32 & (ULong)1;
|
2009-04-17 19:29:46 +00:00
|
|
|
*bx++ = (ULong)(y & FFFFFFFF);
|
2009-04-16 19:52:09 +00:00
|
|
|
}
|
|
|
|
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 {
|
|
|
|
ys = *sx++ + carry;
|
|
|
|
carry = ys >> 32;
|
|
|
|
y = *bx - (ys & FFFFFFFF) - borrow;
|
|
|
|
borrow = y >> 32 & (ULong)1;
|
2009-04-17 19:29:46 +00:00
|
|
|
*bx++ = (ULong)(y & FFFFFFFF);
|
2009-04-16 19:52:09 +00:00
|
|
|
}
|
|
|
|
while(sx <= sxe);
|
|
|
|
bx = b->x;
|
|
|
|
bxe = bx + n;
|
|
|
|
if (!*bxe) {
|
|
|
|
while(--bxe > bx && !*bxe)
|
|
|
|
--n;
|
|
|
|
b->wds = n;
|
|
|
|
}
|
|
|
|
}
|
|
|
|
return q;
|
|
|
|
}
|
|
|
|
|
Merged revisions 77477-77478,77481-77483,77490-77493 via svnmerge from
svn+ssh://pythondev@svn.python.org/python/trunk
........
r77477 | mark.dickinson | 2010-01-13 18:21:53 +0000 (Wed, 13 Jan 2010) | 1 line
Add comments explaining the role of the bigcomp function in dtoa.c.
........
r77478 | mark.dickinson | 2010-01-13 19:02:37 +0000 (Wed, 13 Jan 2010) | 1 line
Clarify that sulp expects a nonnegative input, but that +0.0 is fine.
........
r77481 | mark.dickinson | 2010-01-13 20:55:03 +0000 (Wed, 13 Jan 2010) | 1 line
Simplify and annotate the bigcomp function, removing unused special cases.
........
r77482 | mark.dickinson | 2010-01-13 22:15:53 +0000 (Wed, 13 Jan 2010) | 1 line
Fix buggy comparison: LHS of comparison was being treated as unsigned.
........
r77483 | mark.dickinson | 2010-01-13 22:20:10 +0000 (Wed, 13 Jan 2010) | 1 line
More dtoa.c cleanup; remove the need for bc.dplen, bc.dp0 and bc.dp1.
........
r77490 | mark.dickinson | 2010-01-14 13:02:36 +0000 (Thu, 14 Jan 2010) | 1 line
Fix off-by-one error introduced in r77483. I have a test for this, but it currently fails due to a different dtoa.c bug; I'll add the test once that bug is fixed.
........
r77491 | mark.dickinson | 2010-01-14 13:14:49 +0000 (Thu, 14 Jan 2010) | 1 line
Issue 7632: fix a dtoa.c bug (bug 6) causing incorrect rounding. Tests to follow.
........
r77492 | mark.dickinson | 2010-01-14 14:40:20 +0000 (Thu, 14 Jan 2010) | 1 line
Issue 7632: fix incorrect rounding for long input strings with values very close to a power of 2. (See Bug 4 in the tracker discussion.)
........
r77493 | mark.dickinson | 2010-01-14 15:22:33 +0000 (Thu, 14 Jan 2010) | 1 line
Issue #7632: add tests for bugs fixed so far.
........
2010-01-14 15:37:49 +00:00
|
|
|
/* sulp(x) is a version of ulp(x) that takes bc.scale into account.
|
2010-01-12 23:04:19 +00:00
|
|
|
|
Merged revisions 77477-77478,77481-77483,77490-77493 via svnmerge from
svn+ssh://pythondev@svn.python.org/python/trunk
........
r77477 | mark.dickinson | 2010-01-13 18:21:53 +0000 (Wed, 13 Jan 2010) | 1 line
Add comments explaining the role of the bigcomp function in dtoa.c.
........
r77478 | mark.dickinson | 2010-01-13 19:02:37 +0000 (Wed, 13 Jan 2010) | 1 line
Clarify that sulp expects a nonnegative input, but that +0.0 is fine.
........
r77481 | mark.dickinson | 2010-01-13 20:55:03 +0000 (Wed, 13 Jan 2010) | 1 line
Simplify and annotate the bigcomp function, removing unused special cases.
........
r77482 | mark.dickinson | 2010-01-13 22:15:53 +0000 (Wed, 13 Jan 2010) | 1 line
Fix buggy comparison: LHS of comparison was being treated as unsigned.
........
r77483 | mark.dickinson | 2010-01-13 22:20:10 +0000 (Wed, 13 Jan 2010) | 1 line
More dtoa.c cleanup; remove the need for bc.dplen, bc.dp0 and bc.dp1.
........
r77490 | mark.dickinson | 2010-01-14 13:02:36 +0000 (Thu, 14 Jan 2010) | 1 line
Fix off-by-one error introduced in r77483. I have a test for this, but it currently fails due to a different dtoa.c bug; I'll add the test once that bug is fixed.
........
r77491 | mark.dickinson | 2010-01-14 13:14:49 +0000 (Thu, 14 Jan 2010) | 1 line
Issue 7632: fix a dtoa.c bug (bug 6) causing incorrect rounding. Tests to follow.
........
r77492 | mark.dickinson | 2010-01-14 14:40:20 +0000 (Thu, 14 Jan 2010) | 1 line
Issue 7632: fix incorrect rounding for long input strings with values very close to a power of 2. (See Bug 4 in the tracker discussion.)
........
r77493 | mark.dickinson | 2010-01-14 15:22:33 +0000 (Thu, 14 Jan 2010) | 1 line
Issue #7632: add tests for bugs fixed so far.
........
2010-01-14 15:37:49 +00:00
|
|
|
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). */
|
2010-01-12 23:04:19 +00:00
|
|
|
|
|
|
|
static double
|
|
|
|
sulp(U *x, BCinfo *bc)
|
|
|
|
{
|
|
|
|
U u;
|
|
|
|
|
Merged revisions 77477-77478,77481-77483,77490-77493 via svnmerge from
svn+ssh://pythondev@svn.python.org/python/trunk
........
r77477 | mark.dickinson | 2010-01-13 18:21:53 +0000 (Wed, 13 Jan 2010) | 1 line
Add comments explaining the role of the bigcomp function in dtoa.c.
........
r77478 | mark.dickinson | 2010-01-13 19:02:37 +0000 (Wed, 13 Jan 2010) | 1 line
Clarify that sulp expects a nonnegative input, but that +0.0 is fine.
........
r77481 | mark.dickinson | 2010-01-13 20:55:03 +0000 (Wed, 13 Jan 2010) | 1 line
Simplify and annotate the bigcomp function, removing unused special cases.
........
r77482 | mark.dickinson | 2010-01-13 22:15:53 +0000 (Wed, 13 Jan 2010) | 1 line
Fix buggy comparison: LHS of comparison was being treated as unsigned.
........
r77483 | mark.dickinson | 2010-01-13 22:20:10 +0000 (Wed, 13 Jan 2010) | 1 line
More dtoa.c cleanup; remove the need for bc.dplen, bc.dp0 and bc.dp1.
........
r77490 | mark.dickinson | 2010-01-14 13:02:36 +0000 (Thu, 14 Jan 2010) | 1 line
Fix off-by-one error introduced in r77483. I have a test for this, but it currently fails due to a different dtoa.c bug; I'll add the test once that bug is fixed.
........
r77491 | mark.dickinson | 2010-01-14 13:14:49 +0000 (Thu, 14 Jan 2010) | 1 line
Issue 7632: fix a dtoa.c bug (bug 6) causing incorrect rounding. Tests to follow.
........
r77492 | mark.dickinson | 2010-01-14 14:40:20 +0000 (Thu, 14 Jan 2010) | 1 line
Issue 7632: fix incorrect rounding for long input strings with values very close to a power of 2. (See Bug 4 in the tracker discussion.)
........
r77493 | mark.dickinson | 2010-01-14 15:22:33 +0000 (Thu, 14 Jan 2010) | 1 line
Issue #7632: add tests for bugs fixed so far.
........
2010-01-14 15:37:49 +00:00
|
|
|
if (bc->scale && 2*P + 1 > (int)((word0(x) & Exp_mask) >> Exp_shift)) {
|
2010-01-12 23:04:19 +00:00
|
|
|
/* rv/2^bc->scale is subnormal */
|
|
|
|
word0(&u) = (P+2)*Exp_msk1;
|
|
|
|
word1(&u) = 0;
|
|
|
|
return u.d;
|
|
|
|
}
|
Merged revisions 77477-77478,77481-77483,77490-77493 via svnmerge from
svn+ssh://pythondev@svn.python.org/python/trunk
........
r77477 | mark.dickinson | 2010-01-13 18:21:53 +0000 (Wed, 13 Jan 2010) | 1 line
Add comments explaining the role of the bigcomp function in dtoa.c.
........
r77478 | mark.dickinson | 2010-01-13 19:02:37 +0000 (Wed, 13 Jan 2010) | 1 line
Clarify that sulp expects a nonnegative input, but that +0.0 is fine.
........
r77481 | mark.dickinson | 2010-01-13 20:55:03 +0000 (Wed, 13 Jan 2010) | 1 line
Simplify and annotate the bigcomp function, removing unused special cases.
........
r77482 | mark.dickinson | 2010-01-13 22:15:53 +0000 (Wed, 13 Jan 2010) | 1 line
Fix buggy comparison: LHS of comparison was being treated as unsigned.
........
r77483 | mark.dickinson | 2010-01-13 22:20:10 +0000 (Wed, 13 Jan 2010) | 1 line
More dtoa.c cleanup; remove the need for bc.dplen, bc.dp0 and bc.dp1.
........
r77490 | mark.dickinson | 2010-01-14 13:02:36 +0000 (Thu, 14 Jan 2010) | 1 line
Fix off-by-one error introduced in r77483. I have a test for this, but it currently fails due to a different dtoa.c bug; I'll add the test once that bug is fixed.
........
r77491 | mark.dickinson | 2010-01-14 13:14:49 +0000 (Thu, 14 Jan 2010) | 1 line
Issue 7632: fix a dtoa.c bug (bug 6) causing incorrect rounding. Tests to follow.
........
r77492 | mark.dickinson | 2010-01-14 14:40:20 +0000 (Thu, 14 Jan 2010) | 1 line
Issue 7632: fix incorrect rounding for long input strings with values very close to a power of 2. (See Bug 4 in the tracker discussion.)
........
r77493 | mark.dickinson | 2010-01-14 15:22:33 +0000 (Thu, 14 Jan 2010) | 1 line
Issue #7632: add tests for bugs fixed so far.
........
2010-01-14 15:37:49 +00:00
|
|
|
else {
|
|
|
|
assert(word0(x) || word1(x)); /* x != 0.0 */
|
2010-01-12 23:04:19 +00:00
|
|
|
return ulp(x);
|
Merged revisions 77477-77478,77481-77483,77490-77493 via svnmerge from
svn+ssh://pythondev@svn.python.org/python/trunk
........
r77477 | mark.dickinson | 2010-01-13 18:21:53 +0000 (Wed, 13 Jan 2010) | 1 line
Add comments explaining the role of the bigcomp function in dtoa.c.
........
r77478 | mark.dickinson | 2010-01-13 19:02:37 +0000 (Wed, 13 Jan 2010) | 1 line
Clarify that sulp expects a nonnegative input, but that +0.0 is fine.
........
r77481 | mark.dickinson | 2010-01-13 20:55:03 +0000 (Wed, 13 Jan 2010) | 1 line
Simplify and annotate the bigcomp function, removing unused special cases.
........
r77482 | mark.dickinson | 2010-01-13 22:15:53 +0000 (Wed, 13 Jan 2010) | 1 line
Fix buggy comparison: LHS of comparison was being treated as unsigned.
........
r77483 | mark.dickinson | 2010-01-13 22:20:10 +0000 (Wed, 13 Jan 2010) | 1 line
More dtoa.c cleanup; remove the need for bc.dplen, bc.dp0 and bc.dp1.
........
r77490 | mark.dickinson | 2010-01-14 13:02:36 +0000 (Thu, 14 Jan 2010) | 1 line
Fix off-by-one error introduced in r77483. I have a test for this, but it currently fails due to a different dtoa.c bug; I'll add the test once that bug is fixed.
........
r77491 | mark.dickinson | 2010-01-14 13:14:49 +0000 (Thu, 14 Jan 2010) | 1 line
Issue 7632: fix a dtoa.c bug (bug 6) causing incorrect rounding. Tests to follow.
........
r77492 | mark.dickinson | 2010-01-14 14:40:20 +0000 (Thu, 14 Jan 2010) | 1 line
Issue 7632: fix incorrect rounding for long input strings with values very close to a power of 2. (See Bug 4 in the tracker discussion.)
........
r77493 | mark.dickinson | 2010-01-14 15:22:33 +0000 (Thu, 14 Jan 2010) | 1 line
Issue #7632: add tests for bugs fixed so far.
........
2010-01-14 15:37:49 +00:00
|
|
|
}
|
2010-01-12 23:04:19 +00:00
|
|
|
}
|
2009-04-16 19:52:09 +00:00
|
|
|
|
Merged revisions 77477-77478,77481-77483,77490-77493 via svnmerge from
svn+ssh://pythondev@svn.python.org/python/trunk
........
r77477 | mark.dickinson | 2010-01-13 18:21:53 +0000 (Wed, 13 Jan 2010) | 1 line
Add comments explaining the role of the bigcomp function in dtoa.c.
........
r77478 | mark.dickinson | 2010-01-13 19:02:37 +0000 (Wed, 13 Jan 2010) | 1 line
Clarify that sulp expects a nonnegative input, but that +0.0 is fine.
........
r77481 | mark.dickinson | 2010-01-13 20:55:03 +0000 (Wed, 13 Jan 2010) | 1 line
Simplify and annotate the bigcomp function, removing unused special cases.
........
r77482 | mark.dickinson | 2010-01-13 22:15:53 +0000 (Wed, 13 Jan 2010) | 1 line
Fix buggy comparison: LHS of comparison was being treated as unsigned.
........
r77483 | mark.dickinson | 2010-01-13 22:20:10 +0000 (Wed, 13 Jan 2010) | 1 line
More dtoa.c cleanup; remove the need for bc.dplen, bc.dp0 and bc.dp1.
........
r77490 | mark.dickinson | 2010-01-14 13:02:36 +0000 (Thu, 14 Jan 2010) | 1 line
Fix off-by-one error introduced in r77483. I have a test for this, but it currently fails due to a different dtoa.c bug; I'll add the test once that bug is fixed.
........
r77491 | mark.dickinson | 2010-01-14 13:14:49 +0000 (Thu, 14 Jan 2010) | 1 line
Issue 7632: fix a dtoa.c bug (bug 6) causing incorrect rounding. Tests to follow.
........
r77492 | mark.dickinson | 2010-01-14 14:40:20 +0000 (Thu, 14 Jan 2010) | 1 line
Issue 7632: fix incorrect rounding for long input strings with values very close to a power of 2. (See Bug 4 in the tracker discussion.)
........
r77493 | mark.dickinson | 2010-01-14 15:22:33 +0000 (Thu, 14 Jan 2010) | 1 line
Issue #7632: add tests for bugs fixed so far.
........
2010-01-14 15:37:49 +00:00
|
|
|
/* 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). */
|
2009-04-16 19:52:09 +00:00
|
|
|
|
|
|
|
static int
|
|
|
|
bigcomp(U *rv, const char *s0, BCinfo *bc)
|
|
|
|
{
|
|
|
|
Bigint *b, *d;
|
2010-01-24 10:16:29 +00:00
|
|
|
int b2, d2, dd, i, nd, nd0, odd, p2, p5;
|
2009-04-16 19:52:09 +00:00
|
|
|
|
|
|
|
nd = bc->nd;
|
|
|
|
nd0 = bc->nd0;
|
2010-01-12 23:04:19 +00:00
|
|
|
p5 = nd + bc->e0;
|
2010-01-24 10:16:29 +00:00
|
|
|
b = sd2b(rv, bc->scale, &p2);
|
Merged revisions 77477-77478,77481-77483,77490-77493 via svnmerge from
svn+ssh://pythondev@svn.python.org/python/trunk
........
r77477 | mark.dickinson | 2010-01-13 18:21:53 +0000 (Wed, 13 Jan 2010) | 1 line
Add comments explaining the role of the bigcomp function in dtoa.c.
........
r77478 | mark.dickinson | 2010-01-13 19:02:37 +0000 (Wed, 13 Jan 2010) | 1 line
Clarify that sulp expects a nonnegative input, but that +0.0 is fine.
........
r77481 | mark.dickinson | 2010-01-13 20:55:03 +0000 (Wed, 13 Jan 2010) | 1 line
Simplify and annotate the bigcomp function, removing unused special cases.
........
r77482 | mark.dickinson | 2010-01-13 22:15:53 +0000 (Wed, 13 Jan 2010) | 1 line
Fix buggy comparison: LHS of comparison was being treated as unsigned.
........
r77483 | mark.dickinson | 2010-01-13 22:20:10 +0000 (Wed, 13 Jan 2010) | 1 line
More dtoa.c cleanup; remove the need for bc.dplen, bc.dp0 and bc.dp1.
........
r77490 | mark.dickinson | 2010-01-14 13:02:36 +0000 (Thu, 14 Jan 2010) | 1 line
Fix off-by-one error introduced in r77483. I have a test for this, but it currently fails due to a different dtoa.c bug; I'll add the test once that bug is fixed.
........
r77491 | mark.dickinson | 2010-01-14 13:14:49 +0000 (Thu, 14 Jan 2010) | 1 line
Issue 7632: fix a dtoa.c bug (bug 6) causing incorrect rounding. Tests to follow.
........
r77492 | mark.dickinson | 2010-01-14 14:40:20 +0000 (Thu, 14 Jan 2010) | 1 line
Issue 7632: fix incorrect rounding for long input strings with values very close to a power of 2. (See Bug 4 in the tracker discussion.)
........
r77493 | mark.dickinson | 2010-01-14 15:22:33 +0000 (Thu, 14 Jan 2010) | 1 line
Issue #7632: add tests for bugs fixed so far.
........
2010-01-14 15:37:49 +00:00
|
|
|
if (b == NULL)
|
|
|
|
return -1;
|
2010-01-24 10:16:29 +00:00
|
|
|
|
Merged revisions 77477-77478,77481-77483,77490-77493 via svnmerge from
svn+ssh://pythondev@svn.python.org/python/trunk
........
r77477 | mark.dickinson | 2010-01-13 18:21:53 +0000 (Wed, 13 Jan 2010) | 1 line
Add comments explaining the role of the bigcomp function in dtoa.c.
........
r77478 | mark.dickinson | 2010-01-13 19:02:37 +0000 (Wed, 13 Jan 2010) | 1 line
Clarify that sulp expects a nonnegative input, but that +0.0 is fine.
........
r77481 | mark.dickinson | 2010-01-13 20:55:03 +0000 (Wed, 13 Jan 2010) | 1 line
Simplify and annotate the bigcomp function, removing unused special cases.
........
r77482 | mark.dickinson | 2010-01-13 22:15:53 +0000 (Wed, 13 Jan 2010) | 1 line
Fix buggy comparison: LHS of comparison was being treated as unsigned.
........
r77483 | mark.dickinson | 2010-01-13 22:20:10 +0000 (Wed, 13 Jan 2010) | 1 line
More dtoa.c cleanup; remove the need for bc.dplen, bc.dp0 and bc.dp1.
........
r77490 | mark.dickinson | 2010-01-14 13:02:36 +0000 (Thu, 14 Jan 2010) | 1 line
Fix off-by-one error introduced in r77483. I have a test for this, but it currently fails due to a different dtoa.c bug; I'll add the test once that bug is fixed.
........
r77491 | mark.dickinson | 2010-01-14 13:14:49 +0000 (Thu, 14 Jan 2010) | 1 line
Issue 7632: fix a dtoa.c bug (bug 6) causing incorrect rounding. Tests to follow.
........
r77492 | mark.dickinson | 2010-01-14 14:40:20 +0000 (Thu, 14 Jan 2010) | 1 line
Issue 7632: fix incorrect rounding for long input strings with values very close to a power of 2. (See Bug 4 in the tracker discussion.)
........
r77493 | mark.dickinson | 2010-01-14 15:22:33 +0000 (Thu, 14 Jan 2010) | 1 line
Issue #7632: add tests for bugs fixed so far.
........
2010-01-14 15:37:49 +00:00
|
|
|
/* record whether the lsb of rv/2^(bc->scale) is odd: in the exact halfway
|
|
|
|
case, this is used for round to even. */
|
2010-01-24 10:16:29 +00:00
|
|
|
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;
|
Merged revisions 77477-77478,77481-77483,77490-77493 via svnmerge from
svn+ssh://pythondev@svn.python.org/python/trunk
........
r77477 | mark.dickinson | 2010-01-13 18:21:53 +0000 (Wed, 13 Jan 2010) | 1 line
Add comments explaining the role of the bigcomp function in dtoa.c.
........
r77478 | mark.dickinson | 2010-01-13 19:02:37 +0000 (Wed, 13 Jan 2010) | 1 line
Clarify that sulp expects a nonnegative input, but that +0.0 is fine.
........
r77481 | mark.dickinson | 2010-01-13 20:55:03 +0000 (Wed, 13 Jan 2010) | 1 line
Simplify and annotate the bigcomp function, removing unused special cases.
........
r77482 | mark.dickinson | 2010-01-13 22:15:53 +0000 (Wed, 13 Jan 2010) | 1 line
Fix buggy comparison: LHS of comparison was being treated as unsigned.
........
r77483 | mark.dickinson | 2010-01-13 22:20:10 +0000 (Wed, 13 Jan 2010) | 1 line
More dtoa.c cleanup; remove the need for bc.dplen, bc.dp0 and bc.dp1.
........
r77490 | mark.dickinson | 2010-01-14 13:02:36 +0000 (Thu, 14 Jan 2010) | 1 line
Fix off-by-one error introduced in r77483. I have a test for this, but it currently fails due to a different dtoa.c bug; I'll add the test once that bug is fixed.
........
r77491 | mark.dickinson | 2010-01-14 13:14:49 +0000 (Thu, 14 Jan 2010) | 1 line
Issue 7632: fix a dtoa.c bug (bug 6) causing incorrect rounding. Tests to follow.
........
r77492 | mark.dickinson | 2010-01-14 14:40:20 +0000 (Thu, 14 Jan 2010) | 1 line
Issue 7632: fix incorrect rounding for long input strings with values very close to a power of 2. (See Bug 4 in the tracker discussion.)
........
r77493 | mark.dickinson | 2010-01-14 15:22:33 +0000 (Thu, 14 Jan 2010) | 1 line
Issue #7632: add tests for bugs fixed so far.
........
2010-01-14 15:37:49 +00:00
|
|
|
b->x[0] |= 1;
|
2010-01-24 10:16:29 +00:00
|
|
|
p2--;
|
Merged revisions 77477-77478,77481-77483,77490-77493 via svnmerge from
svn+ssh://pythondev@svn.python.org/python/trunk
........
r77477 | mark.dickinson | 2010-01-13 18:21:53 +0000 (Wed, 13 Jan 2010) | 1 line
Add comments explaining the role of the bigcomp function in dtoa.c.
........
r77478 | mark.dickinson | 2010-01-13 19:02:37 +0000 (Wed, 13 Jan 2010) | 1 line
Clarify that sulp expects a nonnegative input, but that +0.0 is fine.
........
r77481 | mark.dickinson | 2010-01-13 20:55:03 +0000 (Wed, 13 Jan 2010) | 1 line
Simplify and annotate the bigcomp function, removing unused special cases.
........
r77482 | mark.dickinson | 2010-01-13 22:15:53 +0000 (Wed, 13 Jan 2010) | 1 line
Fix buggy comparison: LHS of comparison was being treated as unsigned.
........
r77483 | mark.dickinson | 2010-01-13 22:20:10 +0000 (Wed, 13 Jan 2010) | 1 line
More dtoa.c cleanup; remove the need for bc.dplen, bc.dp0 and bc.dp1.
........
r77490 | mark.dickinson | 2010-01-14 13:02:36 +0000 (Thu, 14 Jan 2010) | 1 line
Fix off-by-one error introduced in r77483. I have a test for this, but it currently fails due to a different dtoa.c bug; I'll add the test once that bug is fixed.
........
r77491 | mark.dickinson | 2010-01-14 13:14:49 +0000 (Thu, 14 Jan 2010) | 1 line
Issue 7632: fix a dtoa.c bug (bug 6) causing incorrect rounding. Tests to follow.
........
r77492 | mark.dickinson | 2010-01-14 14:40:20 +0000 (Thu, 14 Jan 2010) | 1 line
Issue 7632: fix incorrect rounding for long input strings with values very close to a power of 2. (See Bug 4 in the tracker discussion.)
........
r77493 | mark.dickinson | 2010-01-14 15:22:33 +0000 (Thu, 14 Jan 2010) | 1 line
Issue #7632: add tests for bugs fixed so far.
........
2010-01-14 15:37:49 +00:00
|
|
|
|
2010-01-24 10:16:29 +00:00
|
|
|
p2 -= p5;
|
2009-04-16 19:52:09 +00:00
|
|
|
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;
|
|
|
|
}
|
|
|
|
}
|
|
|
|
|
2010-01-21 19:51:08 +00:00
|
|
|
/* 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 */
|
2010-01-12 23:04:19 +00:00
|
|
|
dd = -1;
|
2010-01-21 19:51:08 +00:00
|
|
|
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++;
|
2009-04-16 19:52:09 +00:00
|
|
|
|
2010-01-21 19:51:08 +00:00
|
|
|
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;
|
|
|
|
}
|
Merged revisions 77477-77478,77481-77483,77490-77493 via svnmerge from
svn+ssh://pythondev@svn.python.org/python/trunk
........
r77477 | mark.dickinson | 2010-01-13 18:21:53 +0000 (Wed, 13 Jan 2010) | 1 line
Add comments explaining the role of the bigcomp function in dtoa.c.
........
r77478 | mark.dickinson | 2010-01-13 19:02:37 +0000 (Wed, 13 Jan 2010) | 1 line
Clarify that sulp expects a nonnegative input, but that +0.0 is fine.
........
r77481 | mark.dickinson | 2010-01-13 20:55:03 +0000 (Wed, 13 Jan 2010) | 1 line
Simplify and annotate the bigcomp function, removing unused special cases.
........
r77482 | mark.dickinson | 2010-01-13 22:15:53 +0000 (Wed, 13 Jan 2010) | 1 line
Fix buggy comparison: LHS of comparison was being treated as unsigned.
........
r77483 | mark.dickinson | 2010-01-13 22:20:10 +0000 (Wed, 13 Jan 2010) | 1 line
More dtoa.c cleanup; remove the need for bc.dplen, bc.dp0 and bc.dp1.
........
r77490 | mark.dickinson | 2010-01-14 13:02:36 +0000 (Thu, 14 Jan 2010) | 1 line
Fix off-by-one error introduced in r77483. I have a test for this, but it currently fails due to a different dtoa.c bug; I'll add the test once that bug is fixed.
........
r77491 | mark.dickinson | 2010-01-14 13:14:49 +0000 (Thu, 14 Jan 2010) | 1 line
Issue 7632: fix a dtoa.c bug (bug 6) causing incorrect rounding. Tests to follow.
........
r77492 | mark.dickinson | 2010-01-14 14:40:20 +0000 (Thu, 14 Jan 2010) | 1 line
Issue 7632: fix incorrect rounding for long input strings with values very close to a power of 2. (See Bug 4 in the tracker discussion.)
........
r77493 | mark.dickinson | 2010-01-14 15:22:33 +0000 (Thu, 14 Jan 2010) | 1 line
Issue #7632: add tests for bugs fixed so far.
........
2010-01-14 15:37:49 +00:00
|
|
|
}
|
2009-04-16 19:52:09 +00:00
|
|
|
}
|
|
|
|
Bfree(b);
|
|
|
|
Bfree(d);
|
Merged revisions 77477-77478,77481-77483,77490-77493 via svnmerge from
svn+ssh://pythondev@svn.python.org/python/trunk
........
r77477 | mark.dickinson | 2010-01-13 18:21:53 +0000 (Wed, 13 Jan 2010) | 1 line
Add comments explaining the role of the bigcomp function in dtoa.c.
........
r77478 | mark.dickinson | 2010-01-13 19:02:37 +0000 (Wed, 13 Jan 2010) | 1 line
Clarify that sulp expects a nonnegative input, but that +0.0 is fine.
........
r77481 | mark.dickinson | 2010-01-13 20:55:03 +0000 (Wed, 13 Jan 2010) | 1 line
Simplify and annotate the bigcomp function, removing unused special cases.
........
r77482 | mark.dickinson | 2010-01-13 22:15:53 +0000 (Wed, 13 Jan 2010) | 1 line
Fix buggy comparison: LHS of comparison was being treated as unsigned.
........
r77483 | mark.dickinson | 2010-01-13 22:20:10 +0000 (Wed, 13 Jan 2010) | 1 line
More dtoa.c cleanup; remove the need for bc.dplen, bc.dp0 and bc.dp1.
........
r77490 | mark.dickinson | 2010-01-14 13:02:36 +0000 (Thu, 14 Jan 2010) | 1 line
Fix off-by-one error introduced in r77483. I have a test for this, but it currently fails due to a different dtoa.c bug; I'll add the test once that bug is fixed.
........
r77491 | mark.dickinson | 2010-01-14 13:14:49 +0000 (Thu, 14 Jan 2010) | 1 line
Issue 7632: fix a dtoa.c bug (bug 6) causing incorrect rounding. Tests to follow.
........
r77492 | mark.dickinson | 2010-01-14 14:40:20 +0000 (Thu, 14 Jan 2010) | 1 line
Issue 7632: fix incorrect rounding for long input strings with values very close to a power of 2. (See Bug 4 in the tracker discussion.)
........
r77493 | mark.dickinson | 2010-01-14 15:22:33 +0000 (Thu, 14 Jan 2010) | 1 line
Issue #7632: add tests for bugs fixed so far.
........
2010-01-14 15:37:49 +00:00
|
|
|
if (dd > 0 || (dd == 0 && odd))
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dval(rv) += sulp(rv, bc);
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2009-04-16 19:52:09 +00:00
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|
return 0;
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}
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2012-04-29 14:31:56 +00:00
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2009-04-16 19:52:09 +00:00
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|
double
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_Py_dg_strtod(const char *s00, char **se)
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|
|
{
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2010-01-24 10:16:29 +00:00
|
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int bb2, bb5, bbe, bd2, bd5, bs2, c, dsign, e, e1, error;
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|
int esign, i, j, k, lz, nd, nd0, odd, sign;
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2009-04-16 19:52:09 +00:00
|
|
|
const char *s, *s0, *s1;
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|
double aadj, aadj1;
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|
|
U aadj2, adj, rv, rv0;
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2010-01-21 19:51:08 +00:00
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|
ULong y, z, abs_exp;
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2010-01-16 18:10:25 +00:00
|
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|
Long L;
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2009-04-16 19:52:09 +00:00
|
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|
BCinfo bc;
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2019-03-13 16:55:01 +00:00
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|
Bigint *bb = NULL, *bd = NULL, *bd0 = NULL, *bs = NULL, *delta = NULL;
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2013-11-26 16:19:13 +00:00
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|
size_t ndigits, fraclen;
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2019-03-13 16:55:01 +00:00
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|
double result;
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2009-04-16 19:52:09 +00:00
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|
dval(&rv) = 0.;
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2010-01-21 19:51:08 +00:00
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|
|
|
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|
/* Start parsing. */
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|
c = *(s = s00);
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|
|
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|
/* Parse optional sign, if present. */
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|
sign = 0;
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|
switch (c) {
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|
|
|
case '-':
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|
|
sign = 1;
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2017-08-21 11:09:59 +00:00
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|
/* fall through */
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2010-01-21 19:51:08 +00:00
|
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|
case '+':
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|
c = *++s;
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2009-04-16 19:52:09 +00:00
|
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|
}
|
2010-01-21 19:51:08 +00:00
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|
|
|
|
|
/* Skip leading zeros: lz is true iff there were leading zeros. */
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|
|
s1 = s;
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|
|
while (c == '0')
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|
c = *++s;
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|
lz = s != s1;
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|
|
|
2013-11-26 16:19:13 +00:00
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|
/* Point s0 at the first nonzero digit (if any). fraclen will be the
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|
|
|
number of digits between the decimal point and the end of the
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|
|
digit string. ndigits will be the total number of digits ignoring
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|
|
|
leading zeros. */
|
2010-01-21 19:51:08 +00:00
|
|
|
s0 = s1 = s;
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|
|
|
while ('0' <= c && c <= '9')
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|
|
|
c = *++s;
|
2013-11-26 16:19:13 +00:00
|
|
|
ndigits = s - s1;
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|
|
|
fraclen = 0;
|
2010-01-21 19:51:08 +00:00
|
|
|
|
|
|
|
/* Parse decimal point and following digits. */
|
2009-04-16 19:52:09 +00:00
|
|
|
if (c == '.') {
|
|
|
|
c = *++s;
|
2013-11-26 16:19:13 +00:00
|
|
|
if (!ndigits) {
|
2010-01-21 19:51:08 +00:00
|
|
|
s1 = s;
|
|
|
|
while (c == '0')
|
|
|
|
c = *++s;
|
|
|
|
lz = lz || s != s1;
|
2013-11-26 16:19:13 +00:00
|
|
|
fraclen += (s - s1);
|
2010-01-21 19:51:08 +00:00
|
|
|
s0 = s;
|
2009-04-16 19:52:09 +00:00
|
|
|
}
|
2010-01-21 19:51:08 +00:00
|
|
|
s1 = s;
|
|
|
|
while ('0' <= c && c <= '9')
|
|
|
|
c = *++s;
|
2013-11-26 16:19:13 +00:00
|
|
|
ndigits += s - s1;
|
|
|
|
fraclen += s - s1;
|
|
|
|
}
|
|
|
|
|
|
|
|
/* Now lz is true if and only if there were leading zero digits, and
|
|
|
|
ndigits gives the total number of digits ignoring leading zeros. A
|
|
|
|
valid input must have at least one digit. */
|
|
|
|
if (!ndigits && !lz) {
|
|
|
|
if (se)
|
|
|
|
*se = (char *)s00;
|
|
|
|
goto parse_error;
|
2010-01-21 19:51:08 +00:00
|
|
|
}
|
|
|
|
|
2013-11-26 16:19:13 +00:00
|
|
|
/* Range check ndigits and fraclen to make sure that they, and values
|
|
|
|
computed with them, can safely fit in an int. */
|
|
|
|
if (ndigits > MAX_DIGITS || fraclen > MAX_DIGITS) {
|
2010-01-21 19:51:08 +00:00
|
|
|
if (se)
|
|
|
|
*se = (char *)s00;
|
|
|
|
goto parse_error;
|
2009-04-16 19:52:09 +00:00
|
|
|
}
|
2013-11-26 16:19:13 +00:00
|
|
|
nd = (int)ndigits;
|
|
|
|
nd0 = (int)ndigits - (int)fraclen;
|
2010-01-21 19:51:08 +00:00
|
|
|
|
|
|
|
/* Parse exponent. */
|
2009-04-16 19:52:09 +00:00
|
|
|
e = 0;
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|
|
|
if (c == 'e' || c == 'E') {
|
|
|
|
s00 = s;
|
2010-01-21 19:51:08 +00:00
|
|
|
c = *++s;
|
|
|
|
|
|
|
|
/* Exponent sign. */
|
2009-04-16 19:52:09 +00:00
|
|
|
esign = 0;
|
2010-01-21 19:51:08 +00:00
|
|
|
switch (c) {
|
2009-04-16 19:52:09 +00:00
|
|
|
case '-':
|
|
|
|
esign = 1;
|
2017-08-21 11:09:59 +00:00
|
|
|
/* fall through */
|
2009-04-16 19:52:09 +00:00
|
|
|
case '+':
|
|
|
|
c = *++s;
|
|
|
|
}
|
2010-01-21 19:51:08 +00:00
|
|
|
|
|
|
|
/* 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;
|
2009-04-16 19:52:09 +00:00
|
|
|
}
|
2010-01-21 19:51:08 +00:00
|
|
|
|
|
|
|
/* 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;
|
2009-04-16 19:52:09 +00:00
|
|
|
else
|
2010-01-21 19:51:08 +00:00
|
|
|
e = (int)abs_exp;
|
|
|
|
if (esign)
|
|
|
|
e = -e;
|
|
|
|
|
|
|
|
/* A valid exponent must have at least one digit. */
|
|
|
|
if (s == s1 && !lz)
|
2009-04-16 19:52:09 +00:00
|
|
|
s = s00;
|
|
|
|
}
|
2010-01-21 19:51:08 +00:00
|
|
|
|
|
|
|
/* Adjust exponent to take into account position of the point. */
|
|
|
|
e -= nd - nd0;
|
|
|
|
if (nd0 <= 0)
|
2010-01-16 18:10:25 +00:00
|
|
|
nd0 = nd;
|
|
|
|
|
2010-01-21 19:51:08 +00:00
|
|
|
/* 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;
|
2010-01-16 18:10:25 +00:00
|
|
|
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;
|
2009-04-16 19:52:09 +00:00
|
|
|
|
2010-01-21 19:51:08 +00:00
|
|
|
/* Summary of parsing results. After parsing, and dealing with zero
|
|
|
|
* inputs, we have values s0, nd0, nd, e, sign, where:
|
2010-01-16 18:10:25 +00:00
|
|
|
*
|
2010-01-21 19:51:08 +00:00
|
|
|
* - s0 points to the first significant digit of the input string
|
2010-01-16 18:10:25 +00:00
|
|
|
*
|
|
|
|
* - 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
|
2010-01-21 19:51:08 +00:00
|
|
|
* and trailing zeros).
|
2010-01-16 18:10:25 +00:00
|
|
|
*
|
2010-01-21 19:51:08 +00:00
|
|
|
* - 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.)
|
2010-01-16 18:10:25 +00:00
|
|
|
*
|
|
|
|
* - 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.
|
|
|
|
*/
|
|
|
|
|
2010-01-21 19:51:08 +00:00
|
|
|
bc.e0 = e1 = e;
|
2010-01-16 18:10:25 +00:00
|
|
|
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;
|
|
|
|
}
|
|
|
|
|
2009-04-16 19:52:09 +00:00
|
|
|
k = nd < DBL_DIG + 1 ? nd : DBL_DIG + 1;
|
|
|
|
dval(&rv) = y;
|
|
|
|
if (k > 9) {
|
|
|
|
dval(&rv) = tens[k - 9] * dval(&rv) + z;
|
|
|
|
}
|
|
|
|
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) {
|
2010-01-21 19:51:08 +00:00
|
|
|
if (e1 > DBL_MAX_10_EXP)
|
|
|
|
goto ovfl;
|
2009-04-16 19:52:09 +00:00
|
|
|
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) {
|
2010-01-21 19:51:08 +00:00
|
|
|
/* 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. */
|
|
|
|
|
2009-04-16 19:52:09 +00:00
|
|
|
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;
|
|
|
|
}
|
2010-01-21 19:51:08 +00:00
|
|
|
if (!dval(&rv))
|
|
|
|
goto undfl;
|
2009-04-16 19:52:09 +00:00
|
|
|
}
|
|
|
|
}
|
|
|
|
|
|
|
|
/* Now the hard part -- adjusting rv to the correct value.*/
|
|
|
|
|
|
|
|
/* Put digits into bd: true value = bd * 10^e */
|
|
|
|
|
|
|
|
bc.nd = nd;
|
2010-01-12 23:04:19 +00:00
|
|
|
bc.nd0 = nd0; /* Only needed if nd > STRTOD_DIGLIM, but done here */
|
2009-04-16 19:52:09 +00:00
|
|
|
/* to silence an erroneous warning about bc.nd0 */
|
|
|
|
/* possibly not being initialized. */
|
2010-01-12 23:04:19 +00:00
|
|
|
if (nd > STRTOD_DIGLIM) {
|
|
|
|
/* ASSERT(STRTOD_DIGLIM >= 18); 18 == one more than the */
|
2009-04-16 19:52:09 +00:00
|
|
|
/* minimum number of decimal digits to distinguish double values */
|
|
|
|
/* in IEEE arithmetic. */
|
2010-01-16 18:10:25 +00:00
|
|
|
|
|
|
|
/* 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. */
|
2009-04-16 19:52:09 +00:00
|
|
|
--i;
|
2010-01-16 18:10:25 +00:00
|
|
|
if (s0[i < nd0 ? i : i+1] != '0') {
|
|
|
|
++i;
|
|
|
|
break;
|
|
|
|
}
|
2009-04-16 19:52:09 +00:00
|
|
|
}
|
|
|
|
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';
|
2010-01-16 18:10:25 +00:00
|
|
|
for(; i < nd; ++i)
|
|
|
|
y = 10*y + s0[i+1] - '0';
|
2009-04-16 19:52:09 +00:00
|
|
|
}
|
|
|
|
}
|
Merged revisions 77477-77478,77481-77483,77490-77493 via svnmerge from
svn+ssh://pythondev@svn.python.org/python/trunk
........
r77477 | mark.dickinson | 2010-01-13 18:21:53 +0000 (Wed, 13 Jan 2010) | 1 line
Add comments explaining the role of the bigcomp function in dtoa.c.
........
r77478 | mark.dickinson | 2010-01-13 19:02:37 +0000 (Wed, 13 Jan 2010) | 1 line
Clarify that sulp expects a nonnegative input, but that +0.0 is fine.
........
r77481 | mark.dickinson | 2010-01-13 20:55:03 +0000 (Wed, 13 Jan 2010) | 1 line
Simplify and annotate the bigcomp function, removing unused special cases.
........
r77482 | mark.dickinson | 2010-01-13 22:15:53 +0000 (Wed, 13 Jan 2010) | 1 line
Fix buggy comparison: LHS of comparison was being treated as unsigned.
........
r77483 | mark.dickinson | 2010-01-13 22:20:10 +0000 (Wed, 13 Jan 2010) | 1 line
More dtoa.c cleanup; remove the need for bc.dplen, bc.dp0 and bc.dp1.
........
r77490 | mark.dickinson | 2010-01-14 13:02:36 +0000 (Thu, 14 Jan 2010) | 1 line
Fix off-by-one error introduced in r77483. I have a test for this, but it currently fails due to a different dtoa.c bug; I'll add the test once that bug is fixed.
........
r77491 | mark.dickinson | 2010-01-14 13:14:49 +0000 (Thu, 14 Jan 2010) | 1 line
Issue 7632: fix a dtoa.c bug (bug 6) causing incorrect rounding. Tests to follow.
........
r77492 | mark.dickinson | 2010-01-14 14:40:20 +0000 (Thu, 14 Jan 2010) | 1 line
Issue 7632: fix incorrect rounding for long input strings with values very close to a power of 2. (See Bug 4 in the tracker discussion.)
........
r77493 | mark.dickinson | 2010-01-14 15:22:33 +0000 (Thu, 14 Jan 2010) | 1 line
Issue #7632: add tests for bugs fixed so far.
........
2010-01-14 15:37:49 +00:00
|
|
|
bd0 = s2b(s0, nd0, nd, y);
|
2009-04-16 19:52:09 +00:00
|
|
|
if (bd0 == NULL)
|
|
|
|
goto failed_malloc;
|
|
|
|
|
2010-01-21 19:51:08 +00:00
|
|
|
/* 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.
|
|
|
|
*/
|
|
|
|
|
2009-04-16 19:52:09 +00:00
|
|
|
for(;;) {
|
2010-01-21 19:51:08 +00:00
|
|
|
|
|
|
|
/* 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).
|
|
|
|
*/
|
|
|
|
|
2009-04-16 19:52:09 +00:00
|
|
|
bd = Balloc(bd0->k);
|
|
|
|
if (bd == NULL) {
|
|
|
|
goto failed_malloc;
|
|
|
|
}
|
|
|
|
Bcopy(bd, bd0);
|
2010-01-24 10:16:29 +00:00
|
|
|
bb = sd2b(&rv, bc.scale, &bbe); /* srv = bb * 2^bbe */
|
2009-04-16 19:52:09 +00:00
|
|
|
if (bb == NULL) {
|
|
|
|
goto failed_malloc;
|
|
|
|
}
|
2010-01-24 10:16:29 +00:00
|
|
|
/* 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 */
|
2009-04-16 19:52:09 +00:00
|
|
|
bs = i2b(1);
|
|
|
|
if (bs == NULL) {
|
|
|
|
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;
|
2010-01-24 10:16:29 +00:00
|
|
|
bb2++;
|
|
|
|
bd2++;
|
2010-01-21 19:51:08 +00:00
|
|
|
|
2010-01-24 10:16:29 +00:00
|
|
|
/* At this stage bd5 - bb5 == e == bd2 - bb2 + bbe, bb2 - bs2 == 1,
|
2012-04-29 14:31:56 +00:00
|
|
|
and bs == 1, so:
|
2010-01-21 19:51:08 +00:00
|
|
|
|
2010-01-24 10:16:29 +00:00
|
|
|
tdv == bd * 10**e = bd * 2**(bbe - bb2 + bd2) * 5**(bd5 - bb5)
|
|
|
|
srv == bb * 2**bbe = bb * 2**(bbe - bb2 + bb2)
|
2012-04-29 14:31:56 +00:00
|
|
|
0.5 ulp(srv) == 2**(bbe-1) = bs * 2**(bbe - bb2 + bs2)
|
2010-01-21 19:51:08 +00:00
|
|
|
|
2012-04-29 14:31:56 +00:00
|
|
|
It follows that:
|
2010-01-21 19:51:08 +00:00
|
|
|
|
2010-01-24 10:16:29 +00:00
|
|
|
M * tdv = bd * 2**bd2 * 5**bd5
|
|
|
|
M * srv = bb * 2**bb2 * 5**bb5
|
|
|
|
M * 0.5 ulp(srv) = bs * 2**bs2 * 5**bb5
|
2010-01-21 19:51:08 +00:00
|
|
|
|
2012-04-29 14:31:56 +00:00
|
|
|
for some constant M. (Actually, M == 2**(bb2 - bbe) * 5**bb5, but
|
|
|
|
this fact is not needed below.)
|
2010-01-24 10:16:29 +00:00
|
|
|
*/
|
2010-01-21 19:51:08 +00:00
|
|
|
|
2010-01-24 10:16:29 +00:00
|
|
|
/* Remove factor of 2**i, where i = min(bb2, bd2, bs2). */
|
2009-04-16 19:52:09 +00:00
|
|
|
i = bb2 < bd2 ? bb2 : bd2;
|
|
|
|
if (i > bs2)
|
|
|
|
i = bs2;
|
|
|
|
if (i > 0) {
|
|
|
|
bb2 -= i;
|
|
|
|
bd2 -= i;
|
|
|
|
bs2 -= i;
|
|
|
|
}
|
2010-01-21 19:51:08 +00:00
|
|
|
|
|
|
|
/* Scale bb, bd, bs by the appropriate powers of 2 and 5. */
|
2009-04-16 19:52:09 +00:00
|
|
|
if (bb5 > 0) {
|
|
|
|
bs = pow5mult(bs, bb5);
|
|
|
|
if (bs == NULL) {
|
|
|
|
goto failed_malloc;
|
|
|
|
}
|
2019-03-13 16:55:01 +00:00
|
|
|
Bigint *bb1 = mult(bs, bb);
|
2009-04-16 19:52:09 +00:00
|
|
|
Bfree(bb);
|
|
|
|
bb = bb1;
|
|
|
|
if (bb == NULL) {
|
|
|
|
goto failed_malloc;
|
|
|
|
}
|
|
|
|
}
|
|
|
|
if (bb2 > 0) {
|
|
|
|
bb = lshift(bb, bb2);
|
|
|
|
if (bb == NULL) {
|
|
|
|
goto failed_malloc;
|
|
|
|
}
|
|
|
|
}
|
|
|
|
if (bd5 > 0) {
|
|
|
|
bd = pow5mult(bd, bd5);
|
|
|
|
if (bd == NULL) {
|
|
|
|
goto failed_malloc;
|
|
|
|
}
|
|
|
|
}
|
|
|
|
if (bd2 > 0) {
|
|
|
|
bd = lshift(bd, bd2);
|
|
|
|
if (bd == NULL) {
|
|
|
|
goto failed_malloc;
|
|
|
|
}
|
|
|
|
}
|
|
|
|
if (bs2 > 0) {
|
|
|
|
bs = lshift(bs, bs2);
|
|
|
|
if (bs == NULL) {
|
|
|
|
goto failed_malloc;
|
|
|
|
}
|
|
|
|
}
|
2010-01-21 19:51:08 +00:00
|
|
|
|
|
|
|
/* 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). */
|
|
|
|
|
2009-04-16 19:52:09 +00:00
|
|
|
delta = diff(bb, bd);
|
|
|
|
if (delta == NULL) {
|
|
|
|
goto failed_malloc;
|
|
|
|
}
|
2010-01-21 19:51:08 +00:00
|
|
|
dsign = delta->sign;
|
2009-04-16 19:52:09 +00:00
|
|
|
delta->sign = 0;
|
|
|
|
i = cmp(delta, bs);
|
|
|
|
if (bc.nd > nd && i <= 0) {
|
2010-01-21 19:51:08 +00:00
|
|
|
if (dsign)
|
2009-04-16 19:52:09 +00:00
|
|
|
break; /* Must use bigcomp(). */
|
Merged revisions 77477-77478,77481-77483,77490-77493 via svnmerge from
svn+ssh://pythondev@svn.python.org/python/trunk
........
r77477 | mark.dickinson | 2010-01-13 18:21:53 +0000 (Wed, 13 Jan 2010) | 1 line
Add comments explaining the role of the bigcomp function in dtoa.c.
........
r77478 | mark.dickinson | 2010-01-13 19:02:37 +0000 (Wed, 13 Jan 2010) | 1 line
Clarify that sulp expects a nonnegative input, but that +0.0 is fine.
........
r77481 | mark.dickinson | 2010-01-13 20:55:03 +0000 (Wed, 13 Jan 2010) | 1 line
Simplify and annotate the bigcomp function, removing unused special cases.
........
r77482 | mark.dickinson | 2010-01-13 22:15:53 +0000 (Wed, 13 Jan 2010) | 1 line
Fix buggy comparison: LHS of comparison was being treated as unsigned.
........
r77483 | mark.dickinson | 2010-01-13 22:20:10 +0000 (Wed, 13 Jan 2010) | 1 line
More dtoa.c cleanup; remove the need for bc.dplen, bc.dp0 and bc.dp1.
........
r77490 | mark.dickinson | 2010-01-14 13:02:36 +0000 (Thu, 14 Jan 2010) | 1 line
Fix off-by-one error introduced in r77483. I have a test for this, but it currently fails due to a different dtoa.c bug; I'll add the test once that bug is fixed.
........
r77491 | mark.dickinson | 2010-01-14 13:14:49 +0000 (Thu, 14 Jan 2010) | 1 line
Issue 7632: fix a dtoa.c bug (bug 6) causing incorrect rounding. Tests to follow.
........
r77492 | mark.dickinson | 2010-01-14 14:40:20 +0000 (Thu, 14 Jan 2010) | 1 line
Issue 7632: fix incorrect rounding for long input strings with values very close to a power of 2. (See Bug 4 in the tracker discussion.)
........
r77493 | mark.dickinson | 2010-01-14 15:22:33 +0000 (Thu, 14 Jan 2010) | 1 line
Issue #7632: add tests for bugs fixed so far.
........
2010-01-14 15:37:49 +00:00
|
|
|
|
|
|
|
/* 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);
|
2010-01-21 19:51:08 +00:00
|
|
|
break; /* Use bigcomp. */
|
Merged revisions 77477-77478,77481-77483,77490-77493 via svnmerge from
svn+ssh://pythondev@svn.python.org/python/trunk
........
r77477 | mark.dickinson | 2010-01-13 18:21:53 +0000 (Wed, 13 Jan 2010) | 1 line
Add comments explaining the role of the bigcomp function in dtoa.c.
........
r77478 | mark.dickinson | 2010-01-13 19:02:37 +0000 (Wed, 13 Jan 2010) | 1 line
Clarify that sulp expects a nonnegative input, but that +0.0 is fine.
........
r77481 | mark.dickinson | 2010-01-13 20:55:03 +0000 (Wed, 13 Jan 2010) | 1 line
Simplify and annotate the bigcomp function, removing unused special cases.
........
r77482 | mark.dickinson | 2010-01-13 22:15:53 +0000 (Wed, 13 Jan 2010) | 1 line
Fix buggy comparison: LHS of comparison was being treated as unsigned.
........
r77483 | mark.dickinson | 2010-01-13 22:20:10 +0000 (Wed, 13 Jan 2010) | 1 line
More dtoa.c cleanup; remove the need for bc.dplen, bc.dp0 and bc.dp1.
........
r77490 | mark.dickinson | 2010-01-14 13:02:36 +0000 (Thu, 14 Jan 2010) | 1 line
Fix off-by-one error introduced in r77483. I have a test for this, but it currently fails due to a different dtoa.c bug; I'll add the test once that bug is fixed.
........
r77491 | mark.dickinson | 2010-01-14 13:14:49 +0000 (Thu, 14 Jan 2010) | 1 line
Issue 7632: fix a dtoa.c bug (bug 6) causing incorrect rounding. Tests to follow.
........
r77492 | mark.dickinson | 2010-01-14 14:40:20 +0000 (Thu, 14 Jan 2010) | 1 line
Issue 7632: fix incorrect rounding for long input strings with values very close to a power of 2. (See Bug 4 in the tracker discussion.)
........
r77493 | mark.dickinson | 2010-01-14 15:22:33 +0000 (Thu, 14 Jan 2010) | 1 line
Issue #7632: add tests for bugs fixed so far.
........
2010-01-14 15:37:49 +00:00
|
|
|
}
|
|
|
|
}
|
|
|
|
|
2009-04-16 19:52:09 +00:00
|
|
|
{
|
|
|
|
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.
|
|
|
|
*/
|
2010-01-21 19:51:08 +00:00
|
|
|
if (dsign || word1(&rv) || word0(&rv) & Bndry_mask
|
2009-04-16 19:52:09 +00:00
|
|
|
|| (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) {
|
|
|
|
goto failed_malloc;
|
|
|
|
}
|
|
|
|
if (cmp(delta, bs) > 0)
|
|
|
|
goto drop_down;
|
|
|
|
break;
|
|
|
|
}
|
|
|
|
if (i == 0) {
|
|
|
|
/* exactly half-way between */
|
2010-01-21 19:51:08 +00:00
|
|
|
if (dsign) {
|
2009-04-16 19:52:09 +00:00
|
|
|
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;
|
2011-02-22 20:15:44 +00:00
|
|
|
/* dsign = 0; */
|
2009-04-16 19:52:09 +00:00
|
|
|
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 */
|
2010-01-21 19:51:08 +00:00
|
|
|
if (bc.nd > nd)
|
2009-04-16 19:52:09 +00:00
|
|
|
break;
|
|
|
|
goto undfl;
|
|
|
|
}
|
|
|
|
}
|
|
|
|
L = (word0(&rv) & Exp_mask) - Exp_msk1;
|
|
|
|
word0(&rv) = L | Bndry_mask1;
|
|
|
|
word1(&rv) = 0xffffffff;
|
|
|
|
break;
|
|
|
|
}
|
2010-01-24 10:16:29 +00:00
|
|
|
if (!odd)
|
2009-04-16 19:52:09 +00:00
|
|
|
break;
|
2010-01-21 19:51:08 +00:00
|
|
|
if (dsign)
|
2010-01-24 10:16:29 +00:00
|
|
|
dval(&rv) += sulp(&rv, &bc);
|
2009-04-16 19:52:09 +00:00
|
|
|
else {
|
2010-01-24 10:16:29 +00:00
|
|
|
dval(&rv) -= sulp(&rv, &bc);
|
2009-04-16 19:52:09 +00:00
|
|
|
if (!dval(&rv)) {
|
2010-01-12 23:04:19 +00:00
|
|
|
if (bc.nd >nd)
|
2009-04-16 19:52:09 +00:00
|
|
|
break;
|
|
|
|
goto undfl;
|
|
|
|
}
|
|
|
|
}
|
2011-02-22 20:15:44 +00:00
|
|
|
/* dsign = 1 - dsign; */
|
2009-04-16 19:52:09 +00:00
|
|
|
break;
|
|
|
|
}
|
|
|
|
if ((aadj = ratio(delta, bs)) <= 2.) {
|
2010-01-21 19:51:08 +00:00
|
|
|
if (dsign)
|
2009-04-16 19:52:09 +00:00
|
|
|
aadj = aadj1 = 1.;
|
|
|
|
else if (word1(&rv) || word0(&rv) & Bndry_mask) {
|
|
|
|
if (word1(&rv) == Tiny1 && !word0(&rv)) {
|
2010-01-12 23:04:19 +00:00
|
|
|
if (bc.nd >nd)
|
2009-04-16 19:52:09 +00:00
|
|
|
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;
|
2010-01-21 19:51:08 +00:00
|
|
|
aadj1 = dsign ? aadj : -aadj;
|
2009-04-16 19:52:09 +00:00
|
|
|
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)) {
|
2010-01-17 14:39:12 +00:00
|
|
|
if (word0(&rv0) == Big0 && word1(&rv0) == Big1) {
|
2009-04-16 19:52:09 +00:00
|
|
|
goto ovfl;
|
2010-01-17 14:39:12 +00:00
|
|
|
}
|
2009-04-16 19:52:09 +00:00
|
|
|
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;
|
2010-01-21 19:51:08 +00:00
|
|
|
aadj1 = dsign ? aadj : -aadj;
|
2009-04-16 19:52:09 +00:00
|
|
|
}
|
|
|
|
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. */
|
2010-01-21 19:51:08 +00:00
|
|
|
if (dsign || word1(&rv) || word0(&rv) & Bndry_mask) {
|
2009-04-16 19:52:09 +00:00
|
|
|
if (aadj < .4999999 || aadj > .5000001)
|
|
|
|
break;
|
|
|
|
}
|
|
|
|
else if (aadj < .4999999/FLT_RADIX)
|
|
|
|
break;
|
|
|
|
}
|
|
|
|
}
|
|
|
|
cont:
|
2019-03-13 16:55:01 +00:00
|
|
|
Bfree(bb); bb = NULL;
|
|
|
|
Bfree(bd); bd = NULL;
|
|
|
|
Bfree(bs); bs = NULL;
|
|
|
|
Bfree(delta); delta = NULL;
|
2009-04-16 19:52:09 +00:00
|
|
|
}
|
|
|
|
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);
|
|
|
|
}
|
2010-01-21 19:51:08 +00:00
|
|
|
|
2009-04-16 19:52:09 +00:00
|
|
|
ret:
|
2019-03-13 16:55:01 +00:00
|
|
|
result = sign ? -dval(&rv) : dval(&rv);
|
|
|
|
goto done;
|
2009-04-16 19:52:09 +00:00
|
|
|
|
2010-01-21 19:51:08 +00:00
|
|
|
parse_error:
|
2019-03-13 16:55:01 +00:00
|
|
|
result = 0.0;
|
|
|
|
goto done;
|
2010-01-21 19:51:08 +00:00
|
|
|
|
2009-04-16 19:52:09 +00:00
|
|
|
failed_malloc:
|
|
|
|
errno = ENOMEM;
|
2019-03-13 16:55:01 +00:00
|
|
|
result = -1.0;
|
|
|
|
goto done;
|
2010-01-21 19:51:08 +00:00
|
|
|
|
|
|
|
undfl:
|
2019-03-13 16:55:01 +00:00
|
|
|
result = sign ? -0.0 : 0.0;
|
|
|
|
goto done;
|
2010-01-21 19:51:08 +00:00
|
|
|
|
|
|
|
ovfl:
|
|
|
|
errno = ERANGE;
|
|
|
|
/* Can't trust HUGE_VAL */
|
|
|
|
word0(&rv) = Exp_mask;
|
|
|
|
word1(&rv) = 0;
|
2019-03-13 16:55:01 +00:00
|
|
|
result = sign ? -dval(&rv) : dval(&rv);
|
|
|
|
goto done;
|
|
|
|
|
|
|
|
done:
|
|
|
|
Bfree(bb);
|
|
|
|
Bfree(bd);
|
|
|
|
Bfree(bs);
|
|
|
|
Bfree(bd0);
|
|
|
|
Bfree(delta);
|
|
|
|
return result;
|
2010-01-21 19:51:08 +00:00
|
|
|
|
2009-04-16 19:52:09 +00:00
|
|
|
}
|
|
|
|
|
|
|
|
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 *
|
2015-12-25 18:01:53 +00:00
|
|
|
nrv_alloc(const char *s, char **rve, int n)
|
2009-04-16 19:52:09 +00:00
|
|
|
{
|
|
|
|
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 */
|
2010-05-13 11:52:22 +00:00
|
|
|
mlo = mhi = S = 0;
|
2009-04-16 19:52:09 +00:00
|
|
|
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;
|
2017-08-21 11:09:59 +00:00
|
|
|
/* fall through */
|
2009-04-16 19:52:09 +00:00
|
|
|
case 4:
|
|
|
|
if (ndigits <= 0)
|
|
|
|
ndigits = 1;
|
|
|
|
ilim = ilim1 = i = ndigits;
|
|
|
|
break;
|
|
|
|
case 3:
|
|
|
|
leftright = 0;
|
2017-08-21 11:09:59 +00:00
|
|
|
/* fall through */
|
2009-04-16 19:52:09 +00:00
|
|
|
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++;
|
|
|
|
}
|
2020-05-29 13:23:57 +00:00
|
|
|
else {
|
|
|
|
/* Strip trailing zeros. This branch was missing from the
|
|
|
|
original dtoa.c, leading to surplus trailing zeros in
|
|
|
|
some cases. See bugs.python.org/issue40780. */
|
|
|
|
while (s > s0 && s[-1] == '0') {
|
|
|
|
--s;
|
|
|
|
}
|
|
|
|
}
|
2009-04-16 19:52:09 +00:00
|
|
|
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;
|
|
|
|
}
|
|
|
|
|
2022-02-23 17:16:23 +00:00
|
|
|
#endif // _PY_SHORT_FLOAT_REPR == 1
|
2023-12-07 13:47:55 +00:00
|
|
|
|
|
|
|
PyStatus
|
|
|
|
_PyDtoa_Init(PyInterpreterState *interp)
|
|
|
|
{
|
|
|
|
#if _PY_SHORT_FLOAT_REPR == 1 && !defined(Py_USING_MEMORY_DEBUGGER)
|
|
|
|
Bigint **p5s = interp->dtoa.p5s;
|
|
|
|
|
|
|
|
// 5**4 = 625
|
|
|
|
Bigint *p5 = i2b(625);
|
|
|
|
if (p5 == NULL) {
|
|
|
|
return PyStatus_NoMemory();
|
|
|
|
}
|
|
|
|
p5s[0] = p5;
|
|
|
|
|
|
|
|
// compute 5**8, 5**16, 5**32, ..., 5**512
|
|
|
|
for (Py_ssize_t i = 1; i < Bigint_Pow5size; i++) {
|
|
|
|
p5 = mult(p5, p5);
|
|
|
|
if (p5 == NULL) {
|
|
|
|
return PyStatus_NoMemory();
|
|
|
|
}
|
|
|
|
p5s[i] = p5;
|
|
|
|
}
|
|
|
|
|
|
|
|
#endif
|
|
|
|
return PyStatus_Ok();
|
|
|
|
}
|
|
|
|
|
|
|
|
void
|
|
|
|
_PyDtoa_Fini(PyInterpreterState *interp)
|
|
|
|
{
|
|
|
|
#if _PY_SHORT_FLOAT_REPR == 1 && !defined(Py_USING_MEMORY_DEBUGGER)
|
|
|
|
Bigint **p5s = interp->dtoa.p5s;
|
|
|
|
for (Py_ssize_t i = 0; i < Bigint_Pow5size; i++) {
|
|
|
|
Bigint *p5 = p5s[i];
|
|
|
|
p5s[i] = NULL;
|
|
|
|
Bfree(p5);
|
|
|
|
}
|
|
|
|
#endif
|
|
|
|
}
|