1bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson/**************************************************************** 2bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * 3bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * The author of this software is David M. Gay. 4bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * 5bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * Copyright (c) 1991, 2000, 2001 by Lucent Technologies. 6bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * 7bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * Permission to use, copy, modify, and distribute this software for any 8bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * purpose without fee is hereby granted, provided that this entire notice 9bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * is included in all copies of any software which is or includes a copy 10bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * or modification of this software and in all copies of the supporting 11bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * documentation for such software. 12bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * 13bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * THIS SOFTWARE IS BEING PROVIDED "AS IS", WITHOUT ANY EXPRESS OR IMPLIED 14bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * WARRANTY. IN PARTICULAR, NEITHER THE AUTHOR NOR LUCENT MAKES ANY 15bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * REPRESENTATION OR WARRANTY OF ANY KIND CONCERNING THE MERCHANTABILITY 16bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * OF THIS SOFTWARE OR ITS FITNESS FOR ANY PARTICULAR PURPOSE. 17bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * 18bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson ***************************************************************/ 19bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 20bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson/**************************************************************** 21bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * This is dtoa.c by David M. Gay, downloaded from 22bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * http://www.netlib.org/fp/dtoa.c on April 15, 2009 and modified for 23bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * inclusion into the Python core by Mark E. T. Dickinson and Eric V. Smith. 24bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * 25bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * Please remember to check http://www.netlib.org/fp regularly (and especially 26bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * before any Python release) for bugfixes and updates. 27bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * 28bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * The major modifications from Gay's original code are as follows: 29bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * 30bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * 0. The original code has been specialized to Python's needs by removing 31bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * many of the #ifdef'd sections. In particular, code to support VAX and 32bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * IBM floating-point formats, hex NaNs, hex floats, locale-aware 33bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * treatment of the decimal point, and setting of the inexact flag have 34bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * been removed. 35bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * 36bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * 1. We use PyMem_Malloc and PyMem_Free in place of malloc and free. 37bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * 38bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * 2. The public functions strtod, dtoa and freedtoa all now have 39bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * a _Py_dg_ prefix. 40bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * 41bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * 3. Instead of assuming that PyMem_Malloc always succeeds, we thread 42bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * PyMem_Malloc failures through the code. The functions 43bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * 44bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * Balloc, multadd, s2b, i2b, mult, pow5mult, lshift, diff, d2b 45bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * 46bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * of return type *Bigint all return NULL to indicate a malloc failure. 47bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * Similarly, rv_alloc and nrv_alloc (return type char *) return NULL on 48bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * failure. bigcomp now has return type int (it used to be void) and 49bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * returns -1 on failure and 0 otherwise. _Py_dg_dtoa returns NULL 50bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * on failure. _Py_dg_strtod indicates failure due to malloc failure 51bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * by returning -1.0, setting errno=ENOMEM and *se to s00. 52bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * 53bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * 4. The static variable dtoa_result has been removed. Callers of 54bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * _Py_dg_dtoa are expected to call _Py_dg_freedtoa to free 55bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * the memory allocated by _Py_dg_dtoa. 56bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * 57bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * 5. The code has been reformatted to better fit with Python's 58bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * C style guide (PEP 7). 59bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * 60bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * 6. A bug in the memory allocation has been fixed: to avoid FREEing memory 61bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * that hasn't been MALLOC'ed, private_mem should only be used when k <= 62bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * Kmax. 63bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * 64bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * 7. _Py_dg_strtod has been modified so that it doesn't accept strings with 65bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * leading whitespace. 66bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * 67bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson ***************************************************************/ 68bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 69bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson/* Please send bug reports for the original dtoa.c code to David M. Gay (dmg 70bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * at acm dot org, with " at " changed at "@" and " dot " changed to "."). 71bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * Please report bugs for this modified version using the Python issue tracker 72bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * (http://bugs.python.org). */ 73bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 74bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson/* On a machine with IEEE extended-precision registers, it is 75bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * necessary to specify double-precision (53-bit) rounding precision 76bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * before invoking strtod or dtoa. If the machine uses (the equivalent 77bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * of) Intel 80x87 arithmetic, the call 78bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * _control87(PC_53, MCW_PC); 79bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * does this with many compilers. Whether this or another call is 80bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * appropriate depends on the compiler; for this to work, it may be 81bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * necessary to #include "float.h" or another system-dependent header 82bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * file. 83bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson */ 84bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 85bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson/* strtod for IEEE-, VAX-, and IBM-arithmetic machines. 86bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * 87bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * This strtod returns a nearest machine number to the input decimal 88bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * string (or sets errno to ERANGE). With IEEE arithmetic, ties are 89bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * broken by the IEEE round-even rule. Otherwise ties are broken by 90bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * biased rounding (add half and chop). 91bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * 92bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * Inspired loosely by William D. Clinger's paper "How to Read Floating 93bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * Point Numbers Accurately" [Proc. ACM SIGPLAN '90, pp. 92-101]. 94bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * 95bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * Modifications: 96bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * 97bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * 1. We only require IEEE, IBM, or VAX double-precision 98bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * arithmetic (not IEEE double-extended). 99bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * 2. We get by with floating-point arithmetic in a case that 100bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * Clinger missed -- when we're computing d * 10^n 101bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * for a small integer d and the integer n is not too 102bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * much larger than 22 (the maximum integer k for which 103bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * we can represent 10^k exactly), we may be able to 104bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * compute (d*10^k) * 10^(e-k) with just one roundoff. 105bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * 3. Rather than a bit-at-a-time adjustment of the binary 106bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * result in the hard case, we use floating-point 107bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * arithmetic to determine the adjustment to within 108bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * one bit; only in really hard cases do we need to 109bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * compute a second residual. 110bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * 4. Because of 3., we don't need a large table of powers of 10 111bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * for ten-to-e (just some small tables, e.g. of 10^k 112bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * for 0 <= k <= 22). 113bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson */ 114bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 115bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson/* Linking of Python's #defines to Gay's #defines starts here. */ 116bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 117bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#include "Python.h" 118bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 119bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson/* if PY_NO_SHORT_FLOAT_REPR is defined, then don't even try to compile 120bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson the following code */ 121bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#ifndef PY_NO_SHORT_FLOAT_REPR 122bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 123bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#include "float.h" 124bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 125bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#define MALLOC PyMem_Malloc 126bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#define FREE PyMem_Free 127bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 128bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson/* This code should also work for ARM mixed-endian format on little-endian 129bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson machines, where doubles have byte order 45670123 (in increasing address 130bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson order, 0 being the least significant byte). */ 131bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#ifdef DOUBLE_IS_LITTLE_ENDIAN_IEEE754 132bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson# define IEEE_8087 133bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#endif 134bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#if defined(DOUBLE_IS_BIG_ENDIAN_IEEE754) || \ 135bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson defined(DOUBLE_IS_ARM_MIXED_ENDIAN_IEEE754) 136bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson# define IEEE_MC68k 137bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#endif 138bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#if defined(IEEE_8087) + defined(IEEE_MC68k) != 1 139bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#error "Exactly one of IEEE_8087 or IEEE_MC68k should be defined." 140bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#endif 141bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 142bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson/* The code below assumes that the endianness of integers matches the 143bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson endianness of the two 32-bit words of a double. Check this. */ 144bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#if defined(WORDS_BIGENDIAN) && (defined(DOUBLE_IS_LITTLE_ENDIAN_IEEE754) || \ 145bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson defined(DOUBLE_IS_ARM_MIXED_ENDIAN_IEEE754)) 146bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#error "doubles and ints have incompatible endianness" 147bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#endif 148bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 149bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#if !defined(WORDS_BIGENDIAN) && defined(DOUBLE_IS_BIG_ENDIAN_IEEE754) 150bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#error "doubles and ints have incompatible endianness" 151bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#endif 152bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 153bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 154bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#if defined(HAVE_UINT32_T) && defined(HAVE_INT32_T) 155bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinsontypedef PY_UINT32_T ULong; 156bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinsontypedef PY_INT32_T Long; 157bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#else 158bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#error "Failed to find an exact-width 32-bit integer type" 159bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#endif 160bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 161bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#if defined(HAVE_UINT64_T) 162bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#define ULLong PY_UINT64_T 163bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#else 164bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#undef ULLong 165bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#endif 166bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 167bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#undef DEBUG 168bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#ifdef Py_DEBUG 169bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#define DEBUG 170bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#endif 171bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 172bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson/* End Python #define linking */ 173bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 174bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#ifdef DEBUG 175bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#define Bug(x) {fprintf(stderr, "%s\n", x); exit(1);} 176bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#endif 177bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 178bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#ifndef PRIVATE_MEM 179bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#define PRIVATE_MEM 2304 180bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#endif 181bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#define PRIVATE_mem ((PRIVATE_MEM+sizeof(double)-1)/sizeof(double)) 182bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinsonstatic double private_mem[PRIVATE_mem], *pmem_next = private_mem; 183bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 184bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#ifdef __cplusplus 185bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinsonextern "C" { 186bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#endif 187bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 188bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinsontypedef union { double d; ULong L[2]; } U; 189bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 190bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#ifdef IEEE_8087 191bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#define word0(x) (x)->L[1] 192bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#define word1(x) (x)->L[0] 193bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#else 194bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#define word0(x) (x)->L[0] 195bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#define word1(x) (x)->L[1] 196bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#endif 197bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#define dval(x) (x)->d 198bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 199bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#ifndef STRTOD_DIGLIM 200bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#define STRTOD_DIGLIM 40 201bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#endif 202bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 2030ca7452794bef03b66f56cc996a73cac066d0ec1Mark Dickinson/* maximum permitted exponent value for strtod; exponents larger than 2040ca7452794bef03b66f56cc996a73cac066d0ec1Mark Dickinson MAX_ABS_EXP in absolute value get truncated to +-MAX_ABS_EXP. MAX_ABS_EXP 2050ca7452794bef03b66f56cc996a73cac066d0ec1Mark Dickinson should fit into an int. */ 2060ca7452794bef03b66f56cc996a73cac066d0ec1Mark Dickinson#ifndef MAX_ABS_EXP 207c2f8c81af02519952a857baebb5c0c9048033009Mark Dickinson#define MAX_ABS_EXP 1100000000U 208c2f8c81af02519952a857baebb5c0c9048033009Mark Dickinson#endif 209c2f8c81af02519952a857baebb5c0c9048033009Mark Dickinson/* Bound on length of pieces of input strings in _Py_dg_strtod; specifically, 210c2f8c81af02519952a857baebb5c0c9048033009Mark Dickinson this is used to bound the total number of digits ignoring leading zeros and 211c2f8c81af02519952a857baebb5c0c9048033009Mark Dickinson the number of digits that follow the decimal point. Ideally, MAX_DIGITS 212c2f8c81af02519952a857baebb5c0c9048033009Mark Dickinson should satisfy MAX_DIGITS + 400 < MAX_ABS_EXP; that ensures that the 213c2f8c81af02519952a857baebb5c0c9048033009Mark Dickinson exponent clipping in _Py_dg_strtod can't affect the value of the output. */ 214c2f8c81af02519952a857baebb5c0c9048033009Mark Dickinson#ifndef MAX_DIGITS 215c2f8c81af02519952a857baebb5c0c9048033009Mark Dickinson#define MAX_DIGITS 1000000000U 216c2f8c81af02519952a857baebb5c0c9048033009Mark Dickinson#endif 217c2f8c81af02519952a857baebb5c0c9048033009Mark Dickinson 218c2f8c81af02519952a857baebb5c0c9048033009Mark Dickinson/* Guard against trying to use the above values on unusual platforms with ints 219c2f8c81af02519952a857baebb5c0c9048033009Mark Dickinson * of width less than 32 bits. */ 220c2f8c81af02519952a857baebb5c0c9048033009Mark Dickinson#if MAX_ABS_EXP > INT_MAX 221c2f8c81af02519952a857baebb5c0c9048033009Mark Dickinson#error "MAX_ABS_EXP should fit in an int" 222c2f8c81af02519952a857baebb5c0c9048033009Mark Dickinson#endif 223c2f8c81af02519952a857baebb5c0c9048033009Mark Dickinson#if MAX_DIGITS > INT_MAX 224c2f8c81af02519952a857baebb5c0c9048033009Mark Dickinson#error "MAX_DIGITS should fit in an int" 2250ca7452794bef03b66f56cc996a73cac066d0ec1Mark Dickinson#endif 2260ca7452794bef03b66f56cc996a73cac066d0ec1Mark Dickinson 227bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson/* The following definition of Storeinc is appropriate for MIPS processors. 228bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * An alternative that might be better on some machines is 229bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * #define Storeinc(a,b,c) (*a++ = b << 16 | c & 0xffff) 230bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson */ 231bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#if defined(IEEE_8087) 232bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#define Storeinc(a,b,c) (((unsigned short *)a)[1] = (unsigned short)b, \ 233bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson ((unsigned short *)a)[0] = (unsigned short)c, a++) 234bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#else 235bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#define Storeinc(a,b,c) (((unsigned short *)a)[0] = (unsigned short)b, \ 236bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson ((unsigned short *)a)[1] = (unsigned short)c, a++) 237bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#endif 238bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 239bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson/* #define P DBL_MANT_DIG */ 240bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson/* Ten_pmax = floor(P*log(2)/log(5)) */ 241bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson/* Bletch = (highest power of 2 < DBL_MAX_10_EXP) / 16 */ 242bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson/* Quick_max = floor((P-1)*log(FLT_RADIX)/log(10) - 1) */ 243bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson/* Int_max = floor(P*log(FLT_RADIX)/log(10) - 1) */ 244bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 245bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#define Exp_shift 20 246bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#define Exp_shift1 20 247bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#define Exp_msk1 0x100000 248bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#define Exp_msk11 0x100000 249bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#define Exp_mask 0x7ff00000 250bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#define P 53 251bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#define Nbits 53 252bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#define Bias 1023 253bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#define Emax 1023 254bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#define Emin (-1022) 255adcda3400f8ae931139605b8d1fcfede4c1c6916Mark Dickinson#define Etiny (-1074) /* smallest denormal is 2**Etiny */ 256bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#define Exp_1 0x3ff00000 257bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#define Exp_11 0x3ff00000 258bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#define Ebits 11 259bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#define Frac_mask 0xfffff 260bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#define Frac_mask1 0xfffff 261bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#define Ten_pmax 22 262bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#define Bletch 0x10 263bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#define Bndry_mask 0xfffff 264bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#define Bndry_mask1 0xfffff 265bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#define Sign_bit 0x80000000 266bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#define Log2P 1 267bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#define Tiny0 0 268bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#define Tiny1 1 269bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#define Quick_max 14 270bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#define Int_max 14 271bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 272bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#ifndef Flt_Rounds 273bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#ifdef FLT_ROUNDS 274bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#define Flt_Rounds FLT_ROUNDS 275bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#else 276bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#define Flt_Rounds 1 277bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#endif 278bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#endif /*Flt_Rounds*/ 279bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 280bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#define Rounding Flt_Rounds 281bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 282bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#define Big0 (Frac_mask1 | Exp_msk1*(DBL_MAX_EXP+Bias-1)) 283bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#define Big1 0xffffffff 284bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 285bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson/* struct BCinfo is used to pass information from _Py_dg_strtod to bigcomp */ 286bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 287bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinsontypedef struct BCinfo BCinfo; 288bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinsonstruct 289bb28285ea2f01e97a26bc595d49da43fbee62913Mark DickinsonBCinfo { 2904141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson int e0, nd, nd0, scale; 291bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson}; 292bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 293bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#define FFFFFFFF 0xffffffffUL 294bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 295bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#define Kmax 7 296bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 297bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson/* struct Bigint is used to represent arbitrary-precision integers. These 298bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson integers are stored in sign-magnitude format, with the magnitude stored as 299bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson an array of base 2**32 digits. Bigints are always normalized: if x is a 300bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson Bigint then x->wds >= 1, and either x->wds == 1 or x[wds-1] is nonzero. 301bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 302bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson The Bigint fields are as follows: 303bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 304bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson - next is a header used by Balloc and Bfree to keep track of lists 305bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson of freed Bigints; it's also used for the linked list of 306bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson powers of 5 of the form 5**2**i used by pow5mult. 307bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson - k indicates which pool this Bigint was allocated from 308bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson - maxwds is the maximum number of words space was allocated for 309bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson (usually maxwds == 2**k) 310bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson - sign is 1 for negative Bigints, 0 for positive. The sign is unused 311bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson (ignored on inputs, set to 0 on outputs) in almost all operations 312bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson involving Bigints: a notable exception is the diff function, which 313bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson ignores signs on inputs but sets the sign of the output correctly. 314bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson - wds is the actual number of significant words 315bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson - x contains the vector of words (digits) for this Bigint, from least 316bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson significant (x[0]) to most significant (x[wds-1]). 317bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson*/ 318bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 319bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinsonstruct 320bb28285ea2f01e97a26bc595d49da43fbee62913Mark DickinsonBigint { 321bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson struct Bigint *next; 322bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson int k, maxwds, sign, wds; 323bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson ULong x[1]; 324bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson}; 325bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 326bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinsontypedef struct Bigint Bigint; 327bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 3289481c576cd5e820f2a23b57481366f37df3dbbf9Mark Dickinson#ifndef Py_USING_MEMORY_DEBUGGER 3299481c576cd5e820f2a23b57481366f37df3dbbf9Mark Dickinson 330bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson/* Memory management: memory is allocated from, and returned to, Kmax+1 pools 331bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson of memory, where pool k (0 <= k <= Kmax) is for Bigints b with b->maxwds == 332bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 1 << k. These pools are maintained as linked lists, with freelist[k] 333bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson pointing to the head of the list for pool k. 334bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 335bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson On allocation, if there's no free slot in the appropriate pool, MALLOC is 336bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson called to get more memory. This memory is not returned to the system until 337bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson Python quits. There's also a private memory pool that's allocated from 338bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson in preference to using MALLOC. 339bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 340bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson For Bigints with more than (1 << Kmax) digits (which implies at least 1233 341bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson decimal digits), memory is directly allocated using MALLOC, and freed using 342bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson FREE. 343bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 344bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson XXX: it would be easy to bypass this memory-management system and 345bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson translate each call to Balloc into a call to PyMem_Malloc, and each 346bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson Bfree to PyMem_Free. Investigate whether this has any significant 347bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson performance on impact. */ 348bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 349bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinsonstatic Bigint *freelist[Kmax+1]; 350bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 351bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson/* Allocate space for a Bigint with up to 1<<k digits */ 352bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 353bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinsonstatic Bigint * 354bb28285ea2f01e97a26bc595d49da43fbee62913Mark DickinsonBalloc(int k) 355bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson{ 356bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson int x; 357bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson Bigint *rv; 358bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson unsigned int len; 359bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 360bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (k <= Kmax && (rv = freelist[k])) 361bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson freelist[k] = rv->next; 362bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson else { 363bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson x = 1 << k; 364bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson len = (sizeof(Bigint) + (x-1)*sizeof(ULong) + sizeof(double) - 1) 365bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson /sizeof(double); 366bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (k <= Kmax && pmem_next - private_mem + len <= PRIVATE_mem) { 367bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson rv = (Bigint*)pmem_next; 368bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson pmem_next += len; 369bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 370bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson else { 371bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson rv = (Bigint*)MALLOC(len*sizeof(double)); 372bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (rv == NULL) 373bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson return NULL; 374bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 375bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson rv->k = k; 376bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson rv->maxwds = x; 377bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 378bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson rv->sign = rv->wds = 0; 379bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson return rv; 380bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson} 381bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 382bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson/* Free a Bigint allocated with Balloc */ 383bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 384bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinsonstatic void 385bb28285ea2f01e97a26bc595d49da43fbee62913Mark DickinsonBfree(Bigint *v) 386bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson{ 387bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (v) { 388bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (v->k > Kmax) 389bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson FREE((void*)v); 390bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson else { 391bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson v->next = freelist[v->k]; 392bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson freelist[v->k] = v; 393bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 394bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 395bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson} 396bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 3979481c576cd5e820f2a23b57481366f37df3dbbf9Mark Dickinson#else 3989481c576cd5e820f2a23b57481366f37df3dbbf9Mark Dickinson 3999481c576cd5e820f2a23b57481366f37df3dbbf9Mark Dickinson/* Alternative versions of Balloc and Bfree that use PyMem_Malloc and 4009481c576cd5e820f2a23b57481366f37df3dbbf9Mark Dickinson PyMem_Free directly in place of the custom memory allocation scheme above. 4019481c576cd5e820f2a23b57481366f37df3dbbf9Mark Dickinson These are provided for the benefit of memory debugging tools like 4029481c576cd5e820f2a23b57481366f37df3dbbf9Mark Dickinson Valgrind. */ 4039481c576cd5e820f2a23b57481366f37df3dbbf9Mark Dickinson 4049481c576cd5e820f2a23b57481366f37df3dbbf9Mark Dickinson/* Allocate space for a Bigint with up to 1<<k digits */ 4059481c576cd5e820f2a23b57481366f37df3dbbf9Mark Dickinson 4069481c576cd5e820f2a23b57481366f37df3dbbf9Mark Dickinsonstatic Bigint * 4079481c576cd5e820f2a23b57481366f37df3dbbf9Mark DickinsonBalloc(int k) 4089481c576cd5e820f2a23b57481366f37df3dbbf9Mark Dickinson{ 4099481c576cd5e820f2a23b57481366f37df3dbbf9Mark Dickinson int x; 4109481c576cd5e820f2a23b57481366f37df3dbbf9Mark Dickinson Bigint *rv; 4119481c576cd5e820f2a23b57481366f37df3dbbf9Mark Dickinson unsigned int len; 4129481c576cd5e820f2a23b57481366f37df3dbbf9Mark Dickinson 4139481c576cd5e820f2a23b57481366f37df3dbbf9Mark Dickinson x = 1 << k; 4149481c576cd5e820f2a23b57481366f37df3dbbf9Mark Dickinson len = (sizeof(Bigint) + (x-1)*sizeof(ULong) + sizeof(double) - 1) 4159481c576cd5e820f2a23b57481366f37df3dbbf9Mark Dickinson /sizeof(double); 4169481c576cd5e820f2a23b57481366f37df3dbbf9Mark Dickinson 4179481c576cd5e820f2a23b57481366f37df3dbbf9Mark Dickinson rv = (Bigint*)MALLOC(len*sizeof(double)); 4189481c576cd5e820f2a23b57481366f37df3dbbf9Mark Dickinson if (rv == NULL) 4199481c576cd5e820f2a23b57481366f37df3dbbf9Mark Dickinson return NULL; 4209481c576cd5e820f2a23b57481366f37df3dbbf9Mark Dickinson 4219481c576cd5e820f2a23b57481366f37df3dbbf9Mark Dickinson rv->k = k; 4229481c576cd5e820f2a23b57481366f37df3dbbf9Mark Dickinson rv->maxwds = x; 4239481c576cd5e820f2a23b57481366f37df3dbbf9Mark Dickinson rv->sign = rv->wds = 0; 4249481c576cd5e820f2a23b57481366f37df3dbbf9Mark Dickinson return rv; 4259481c576cd5e820f2a23b57481366f37df3dbbf9Mark Dickinson} 4269481c576cd5e820f2a23b57481366f37df3dbbf9Mark Dickinson 4279481c576cd5e820f2a23b57481366f37df3dbbf9Mark Dickinson/* Free a Bigint allocated with Balloc */ 4289481c576cd5e820f2a23b57481366f37df3dbbf9Mark Dickinson 4299481c576cd5e820f2a23b57481366f37df3dbbf9Mark Dickinsonstatic void 4309481c576cd5e820f2a23b57481366f37df3dbbf9Mark DickinsonBfree(Bigint *v) 4319481c576cd5e820f2a23b57481366f37df3dbbf9Mark Dickinson{ 4329481c576cd5e820f2a23b57481366f37df3dbbf9Mark Dickinson if (v) { 4339481c576cd5e820f2a23b57481366f37df3dbbf9Mark Dickinson FREE((void*)v); 4349481c576cd5e820f2a23b57481366f37df3dbbf9Mark Dickinson } 4359481c576cd5e820f2a23b57481366f37df3dbbf9Mark Dickinson} 4369481c576cd5e820f2a23b57481366f37df3dbbf9Mark Dickinson 4379481c576cd5e820f2a23b57481366f37df3dbbf9Mark Dickinson#endif /* Py_USING_MEMORY_DEBUGGER */ 4389481c576cd5e820f2a23b57481366f37df3dbbf9Mark Dickinson 439bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#define Bcopy(x,y) memcpy((char *)&x->sign, (char *)&y->sign, \ 440bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson y->wds*sizeof(Long) + 2*sizeof(int)) 441bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 442bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson/* Multiply a Bigint b by m and add a. Either modifies b in place and returns 443bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson a pointer to the modified b, or Bfrees b and returns a pointer to a copy. 444bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson On failure, return NULL. In this case, b will have been already freed. */ 445bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 446bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinsonstatic Bigint * 447bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinsonmultadd(Bigint *b, int m, int a) /* multiply by m and add a */ 448bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson{ 449bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson int i, wds; 450bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#ifdef ULLong 451bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson ULong *x; 452bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson ULLong carry, y; 453bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#else 454bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson ULong carry, *x, y; 455bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson ULong xi, z; 456bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#endif 457bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson Bigint *b1; 458bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 459bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson wds = b->wds; 460bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson x = b->x; 461bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson i = 0; 462bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson carry = a; 463bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson do { 464bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#ifdef ULLong 465bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson y = *x * (ULLong)m + carry; 466bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson carry = y >> 32; 467bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson *x++ = (ULong)(y & FFFFFFFF); 468bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#else 469bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson xi = *x; 470bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson y = (xi & 0xffff) * m + carry; 471bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson z = (xi >> 16) * m + (y >> 16); 472bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson carry = z >> 16; 473bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson *x++ = (z << 16) + (y & 0xffff); 474bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#endif 475bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 476bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson while(++i < wds); 477bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (carry) { 478bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (wds >= b->maxwds) { 479bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson b1 = Balloc(b->k+1); 480bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (b1 == NULL){ 481bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson Bfree(b); 482bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson return NULL; 483bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 484bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson Bcopy(b1, b); 485bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson Bfree(b); 486bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson b = b1; 487bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 488bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson b->x[wds++] = (ULong)carry; 489bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson b->wds = wds; 490bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 491bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson return b; 492bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson} 493bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 494bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson/* convert a string s containing nd decimal digits (possibly containing a 495bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson decimal separator at position nd0, which is ignored) to a Bigint. This 496bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson function carries on where the parsing code in _Py_dg_strtod leaves off: on 497bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson entry, y9 contains the result of converting the first 9 digits. Returns 498bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson NULL on failure. */ 499bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 500bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinsonstatic Bigint * 501d2a9940acbe6a74cc83e371baf2ef7c580e308bcMark Dickinsons2b(const char *s, int nd0, int nd, ULong y9) 502bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson{ 503bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson Bigint *b; 504bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson int i, k; 505bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson Long x, y; 506bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 507bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson x = (nd + 8) / 9; 508bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson for(k = 0, y = 1; x > y; y <<= 1, k++) ; 509bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson b = Balloc(k); 510bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (b == NULL) 511bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson return NULL; 512bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson b->x[0] = y9; 513bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson b->wds = 1; 514bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 515d2a9940acbe6a74cc83e371baf2ef7c580e308bcMark Dickinson if (nd <= 9) 516d2a9940acbe6a74cc83e371baf2ef7c580e308bcMark Dickinson return b; 517d2a9940acbe6a74cc83e371baf2ef7c580e308bcMark Dickinson 518d2a9940acbe6a74cc83e371baf2ef7c580e308bcMark Dickinson s += 9; 519d2a9940acbe6a74cc83e371baf2ef7c580e308bcMark Dickinson for (i = 9; i < nd0; i++) { 520d2a9940acbe6a74cc83e371baf2ef7c580e308bcMark Dickinson b = multadd(b, 10, *s++ - '0'); 521d2a9940acbe6a74cc83e371baf2ef7c580e308bcMark Dickinson if (b == NULL) 522d2a9940acbe6a74cc83e371baf2ef7c580e308bcMark Dickinson return NULL; 523bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 524d2a9940acbe6a74cc83e371baf2ef7c580e308bcMark Dickinson s++; 525bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson for(; i < nd; i++) { 526bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson b = multadd(b, 10, *s++ - '0'); 527bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (b == NULL) 528bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson return NULL; 529bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 530bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson return b; 531bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson} 532bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 533bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson/* count leading 0 bits in the 32-bit integer x. */ 534bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 535bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinsonstatic int 536bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinsonhi0bits(ULong x) 537bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson{ 538bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson int k = 0; 539bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 540bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (!(x & 0xffff0000)) { 541bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson k = 16; 542bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson x <<= 16; 543bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 544bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (!(x & 0xff000000)) { 545bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson k += 8; 546bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson x <<= 8; 547bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 548bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (!(x & 0xf0000000)) { 549bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson k += 4; 550bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson x <<= 4; 551bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 552bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (!(x & 0xc0000000)) { 553bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson k += 2; 554bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson x <<= 2; 555bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 556bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (!(x & 0x80000000)) { 557bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson k++; 558bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (!(x & 0x40000000)) 559bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson return 32; 560bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 561bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson return k; 562bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson} 563bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 564bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson/* count trailing 0 bits in the 32-bit integer y, and shift y right by that 565bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson number of bits. */ 566bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 567bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinsonstatic int 568bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinsonlo0bits(ULong *y) 569bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson{ 570bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson int k; 571bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson ULong x = *y; 572bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 573bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (x & 7) { 574bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (x & 1) 575bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson return 0; 576bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (x & 2) { 577bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson *y = x >> 1; 578bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson return 1; 579bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 580bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson *y = x >> 2; 581bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson return 2; 582bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 583bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson k = 0; 584bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (!(x & 0xffff)) { 585bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson k = 16; 586bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson x >>= 16; 587bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 588bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (!(x & 0xff)) { 589bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson k += 8; 590bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson x >>= 8; 591bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 592bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (!(x & 0xf)) { 593bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson k += 4; 594bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson x >>= 4; 595bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 596bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (!(x & 0x3)) { 597bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson k += 2; 598bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson x >>= 2; 599bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 600bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (!(x & 1)) { 601bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson k++; 602bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson x >>= 1; 603bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (!x) 604bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson return 32; 605bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 606bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson *y = x; 607bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson return k; 608bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson} 609bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 610bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson/* convert a small nonnegative integer to a Bigint */ 611bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 612bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinsonstatic Bigint * 613bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinsoni2b(int i) 614bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson{ 615bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson Bigint *b; 616bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 617bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson b = Balloc(1); 618bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (b == NULL) 619bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson return NULL; 620bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson b->x[0] = i; 621bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson b->wds = 1; 622bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson return b; 623bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson} 624bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 625bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson/* multiply two Bigints. Returns a new Bigint, or NULL on failure. Ignores 626bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson the signs of a and b. */ 627bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 628bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinsonstatic Bigint * 629bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinsonmult(Bigint *a, Bigint *b) 630bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson{ 631bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson Bigint *c; 632bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson int k, wa, wb, wc; 633bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson ULong *x, *xa, *xae, *xb, *xbe, *xc, *xc0; 634bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson ULong y; 635bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#ifdef ULLong 636bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson ULLong carry, z; 637bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#else 638bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson ULong carry, z; 639bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson ULong z2; 640bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#endif 641bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 642fc5290458d00e3eebf82dd914fd2848b7e3f7e87Mark Dickinson if ((!a->x[0] && a->wds == 1) || (!b->x[0] && b->wds == 1)) { 643fc5290458d00e3eebf82dd914fd2848b7e3f7e87Mark Dickinson c = Balloc(0); 644fc5290458d00e3eebf82dd914fd2848b7e3f7e87Mark Dickinson if (c == NULL) 645fc5290458d00e3eebf82dd914fd2848b7e3f7e87Mark Dickinson return NULL; 646fc5290458d00e3eebf82dd914fd2848b7e3f7e87Mark Dickinson c->wds = 1; 647fc5290458d00e3eebf82dd914fd2848b7e3f7e87Mark Dickinson c->x[0] = 0; 648fc5290458d00e3eebf82dd914fd2848b7e3f7e87Mark Dickinson return c; 649fc5290458d00e3eebf82dd914fd2848b7e3f7e87Mark Dickinson } 650fc5290458d00e3eebf82dd914fd2848b7e3f7e87Mark Dickinson 651bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (a->wds < b->wds) { 652bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson c = a; 653bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson a = b; 654bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson b = c; 655bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 656bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson k = a->k; 657bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson wa = a->wds; 658bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson wb = b->wds; 659bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson wc = wa + wb; 660bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (wc > a->maxwds) 661bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson k++; 662bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson c = Balloc(k); 663bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (c == NULL) 664bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson return NULL; 665bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson for(x = c->x, xa = x + wc; x < xa; x++) 666bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson *x = 0; 667bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson xa = a->x; 668bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson xae = xa + wa; 669bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson xb = b->x; 670bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson xbe = xb + wb; 671bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson xc0 = c->x; 672bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#ifdef ULLong 673bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson for(; xb < xbe; xc0++) { 674bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if ((y = *xb++)) { 675bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson x = xa; 676bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson xc = xc0; 677bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson carry = 0; 678bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson do { 679bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson z = *x++ * (ULLong)y + *xc + carry; 680bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson carry = z >> 32; 681bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson *xc++ = (ULong)(z & FFFFFFFF); 682bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 683bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson while(x < xae); 684bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson *xc = (ULong)carry; 685bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 686bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 687bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#else 688bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson for(; xb < xbe; xb++, xc0++) { 689bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (y = *xb & 0xffff) { 690bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson x = xa; 691bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson xc = xc0; 692bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson carry = 0; 693bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson do { 694bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson z = (*x & 0xffff) * y + (*xc & 0xffff) + carry; 695bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson carry = z >> 16; 696bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson z2 = (*x++ >> 16) * y + (*xc >> 16) + carry; 697bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson carry = z2 >> 16; 698bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson Storeinc(xc, z2, z); 699bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 700bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson while(x < xae); 701bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson *xc = carry; 702bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 703bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (y = *xb >> 16) { 704bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson x = xa; 705bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson xc = xc0; 706bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson carry = 0; 707bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson z2 = *xc; 708bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson do { 709bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson z = (*x & 0xffff) * y + (*xc >> 16) + carry; 710bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson carry = z >> 16; 711bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson Storeinc(xc, z, z2); 712bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson z2 = (*x++ >> 16) * y + (*xc & 0xffff) + carry; 713bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson carry = z2 >> 16; 714bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 715bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson while(x < xae); 716bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson *xc = z2; 717bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 718bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 719bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#endif 720bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson for(xc0 = c->x, xc = xc0 + wc; wc > 0 && !*--xc; --wc) ; 721bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson c->wds = wc; 722bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson return c; 723bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson} 724bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 7259481c576cd5e820f2a23b57481366f37df3dbbf9Mark Dickinson#ifndef Py_USING_MEMORY_DEBUGGER 7269481c576cd5e820f2a23b57481366f37df3dbbf9Mark Dickinson 727bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson/* p5s is a linked list of powers of 5 of the form 5**(2**i), i >= 2 */ 728bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 729bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinsonstatic Bigint *p5s; 730bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 731bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson/* multiply the Bigint b by 5**k. Returns a pointer to the result, or NULL on 732bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson failure; if the returned pointer is distinct from b then the original 733bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson Bigint b will have been Bfree'd. Ignores the sign of b. */ 734bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 735bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinsonstatic Bigint * 736bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinsonpow5mult(Bigint *b, int k) 737bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson{ 738bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson Bigint *b1, *p5, *p51; 739bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson int i; 740bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson static int p05[3] = { 5, 25, 125 }; 741bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 742bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if ((i = k & 3)) { 743bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson b = multadd(b, p05[i-1], 0); 744bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (b == NULL) 745bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson return NULL; 746bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 747bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 748bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (!(k >>= 2)) 749bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson return b; 750bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson p5 = p5s; 751bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (!p5) { 752bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson /* first time */ 753bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson p5 = i2b(625); 754bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (p5 == NULL) { 755bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson Bfree(b); 756bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson return NULL; 757bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 758bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson p5s = p5; 759bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson p5->next = 0; 760bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 761bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson for(;;) { 762bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (k & 1) { 763bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson b1 = mult(b, p5); 764bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson Bfree(b); 765bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson b = b1; 766bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (b == NULL) 767bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson return NULL; 768bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 769bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (!(k >>= 1)) 770bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson break; 771bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson p51 = p5->next; 772bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (!p51) { 773bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson p51 = mult(p5,p5); 774bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (p51 == NULL) { 775bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson Bfree(b); 776bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson return NULL; 777bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 778bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson p51->next = 0; 779bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson p5->next = p51; 780bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 781bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson p5 = p51; 782bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 783bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson return b; 784bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson} 785bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 7869481c576cd5e820f2a23b57481366f37df3dbbf9Mark Dickinson#else 7879481c576cd5e820f2a23b57481366f37df3dbbf9Mark Dickinson 7889481c576cd5e820f2a23b57481366f37df3dbbf9Mark Dickinson/* Version of pow5mult that doesn't cache powers of 5. Provided for 7899481c576cd5e820f2a23b57481366f37df3dbbf9Mark Dickinson the benefit of memory debugging tools like Valgrind. */ 7909481c576cd5e820f2a23b57481366f37df3dbbf9Mark Dickinson 7919481c576cd5e820f2a23b57481366f37df3dbbf9Mark Dickinsonstatic Bigint * 7929481c576cd5e820f2a23b57481366f37df3dbbf9Mark Dickinsonpow5mult(Bigint *b, int k) 7939481c576cd5e820f2a23b57481366f37df3dbbf9Mark Dickinson{ 7949481c576cd5e820f2a23b57481366f37df3dbbf9Mark Dickinson Bigint *b1, *p5, *p51; 7959481c576cd5e820f2a23b57481366f37df3dbbf9Mark Dickinson int i; 7969481c576cd5e820f2a23b57481366f37df3dbbf9Mark Dickinson static int p05[3] = { 5, 25, 125 }; 7979481c576cd5e820f2a23b57481366f37df3dbbf9Mark Dickinson 7989481c576cd5e820f2a23b57481366f37df3dbbf9Mark Dickinson if ((i = k & 3)) { 7999481c576cd5e820f2a23b57481366f37df3dbbf9Mark Dickinson b = multadd(b, p05[i-1], 0); 8009481c576cd5e820f2a23b57481366f37df3dbbf9Mark Dickinson if (b == NULL) 8019481c576cd5e820f2a23b57481366f37df3dbbf9Mark Dickinson return NULL; 8029481c576cd5e820f2a23b57481366f37df3dbbf9Mark Dickinson } 8039481c576cd5e820f2a23b57481366f37df3dbbf9Mark Dickinson 8049481c576cd5e820f2a23b57481366f37df3dbbf9Mark Dickinson if (!(k >>= 2)) 8059481c576cd5e820f2a23b57481366f37df3dbbf9Mark Dickinson return b; 8069481c576cd5e820f2a23b57481366f37df3dbbf9Mark Dickinson p5 = i2b(625); 8079481c576cd5e820f2a23b57481366f37df3dbbf9Mark Dickinson if (p5 == NULL) { 8089481c576cd5e820f2a23b57481366f37df3dbbf9Mark Dickinson Bfree(b); 8099481c576cd5e820f2a23b57481366f37df3dbbf9Mark Dickinson return NULL; 8109481c576cd5e820f2a23b57481366f37df3dbbf9Mark Dickinson } 8119481c576cd5e820f2a23b57481366f37df3dbbf9Mark Dickinson 8129481c576cd5e820f2a23b57481366f37df3dbbf9Mark Dickinson for(;;) { 8139481c576cd5e820f2a23b57481366f37df3dbbf9Mark Dickinson if (k & 1) { 8149481c576cd5e820f2a23b57481366f37df3dbbf9Mark Dickinson b1 = mult(b, p5); 8159481c576cd5e820f2a23b57481366f37df3dbbf9Mark Dickinson Bfree(b); 8169481c576cd5e820f2a23b57481366f37df3dbbf9Mark Dickinson b = b1; 8179481c576cd5e820f2a23b57481366f37df3dbbf9Mark Dickinson if (b == NULL) { 8189481c576cd5e820f2a23b57481366f37df3dbbf9Mark Dickinson Bfree(p5); 8199481c576cd5e820f2a23b57481366f37df3dbbf9Mark Dickinson return NULL; 8209481c576cd5e820f2a23b57481366f37df3dbbf9Mark Dickinson } 8219481c576cd5e820f2a23b57481366f37df3dbbf9Mark Dickinson } 8229481c576cd5e820f2a23b57481366f37df3dbbf9Mark Dickinson if (!(k >>= 1)) 8239481c576cd5e820f2a23b57481366f37df3dbbf9Mark Dickinson break; 8249481c576cd5e820f2a23b57481366f37df3dbbf9Mark Dickinson p51 = mult(p5, p5); 8259481c576cd5e820f2a23b57481366f37df3dbbf9Mark Dickinson Bfree(p5); 8269481c576cd5e820f2a23b57481366f37df3dbbf9Mark Dickinson p5 = p51; 8279481c576cd5e820f2a23b57481366f37df3dbbf9Mark Dickinson if (p5 == NULL) { 8289481c576cd5e820f2a23b57481366f37df3dbbf9Mark Dickinson Bfree(b); 8299481c576cd5e820f2a23b57481366f37df3dbbf9Mark Dickinson return NULL; 8309481c576cd5e820f2a23b57481366f37df3dbbf9Mark Dickinson } 8319481c576cd5e820f2a23b57481366f37df3dbbf9Mark Dickinson } 8329481c576cd5e820f2a23b57481366f37df3dbbf9Mark Dickinson Bfree(p5); 8339481c576cd5e820f2a23b57481366f37df3dbbf9Mark Dickinson return b; 8349481c576cd5e820f2a23b57481366f37df3dbbf9Mark Dickinson} 8359481c576cd5e820f2a23b57481366f37df3dbbf9Mark Dickinson 8369481c576cd5e820f2a23b57481366f37df3dbbf9Mark Dickinson#endif /* Py_USING_MEMORY_DEBUGGER */ 8379481c576cd5e820f2a23b57481366f37df3dbbf9Mark Dickinson 838bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson/* shift a Bigint b left by k bits. Return a pointer to the shifted result, 839bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson or NULL on failure. If the returned pointer is distinct from b then the 840bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson original b will have been Bfree'd. Ignores the sign of b. */ 841bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 842bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinsonstatic Bigint * 843bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinsonlshift(Bigint *b, int k) 844bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson{ 845bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson int i, k1, n, n1; 846bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson Bigint *b1; 847bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson ULong *x, *x1, *xe, z; 848bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 849fc5290458d00e3eebf82dd914fd2848b7e3f7e87Mark Dickinson if (!k || (!b->x[0] && b->wds == 1)) 850fc5290458d00e3eebf82dd914fd2848b7e3f7e87Mark Dickinson return b; 851fc5290458d00e3eebf82dd914fd2848b7e3f7e87Mark Dickinson 852bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson n = k >> 5; 853bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson k1 = b->k; 854bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson n1 = n + b->wds + 1; 855bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson for(i = b->maxwds; n1 > i; i <<= 1) 856bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson k1++; 857bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson b1 = Balloc(k1); 858bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (b1 == NULL) { 859bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson Bfree(b); 860bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson return NULL; 861bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 862bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson x1 = b1->x; 863bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson for(i = 0; i < n; i++) 864bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson *x1++ = 0; 865bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson x = b->x; 866bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson xe = x + b->wds; 867bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (k &= 0x1f) { 868bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson k1 = 32 - k; 869bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson z = 0; 870bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson do { 871bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson *x1++ = *x << k | z; 872bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson z = *x++ >> k1; 873bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 874bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson while(x < xe); 875bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if ((*x1 = z)) 876bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson ++n1; 877bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 878bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson else do 879bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson *x1++ = *x++; 880bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson while(x < xe); 881bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson b1->wds = n1 - 1; 882bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson Bfree(b); 883bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson return b1; 884bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson} 885bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 886bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson/* Do a three-way compare of a and b, returning -1 if a < b, 0 if a == b and 887bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 1 if a > b. Ignores signs of a and b. */ 888bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 889bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinsonstatic int 890bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinsoncmp(Bigint *a, Bigint *b) 891bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson{ 892bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson ULong *xa, *xa0, *xb, *xb0; 893bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson int i, j; 894bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 895bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson i = a->wds; 896bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson j = b->wds; 897bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#ifdef DEBUG 898bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (i > 1 && !a->x[i-1]) 899bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson Bug("cmp called with a->x[a->wds-1] == 0"); 900bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (j > 1 && !b->x[j-1]) 901bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson Bug("cmp called with b->x[b->wds-1] == 0"); 902bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#endif 903bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (i -= j) 904bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson return i; 905bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson xa0 = a->x; 906bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson xa = xa0 + j; 907bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson xb0 = b->x; 908bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson xb = xb0 + j; 909bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson for(;;) { 910bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (*--xa != *--xb) 911bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson return *xa < *xb ? -1 : 1; 912bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (xa <= xa0) 913bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson break; 914bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 915bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson return 0; 916bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson} 917bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 918bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson/* Take the difference of Bigints a and b, returning a new Bigint. Returns 919bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson NULL on failure. The signs of a and b are ignored, but the sign of the 920bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson result is set appropriately. */ 921bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 922bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinsonstatic Bigint * 923bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinsondiff(Bigint *a, Bigint *b) 924bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson{ 925bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson Bigint *c; 926bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson int i, wa, wb; 927bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson ULong *xa, *xae, *xb, *xbe, *xc; 928bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#ifdef ULLong 929bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson ULLong borrow, y; 930bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#else 931bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson ULong borrow, y; 932bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson ULong z; 933bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#endif 934bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 935bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson i = cmp(a,b); 936bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (!i) { 937bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson c = Balloc(0); 938bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (c == NULL) 939bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson return NULL; 940bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson c->wds = 1; 941bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson c->x[0] = 0; 942bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson return c; 943bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 944bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (i < 0) { 945bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson c = a; 946bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson a = b; 947bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson b = c; 948bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson i = 1; 949bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 950bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson else 951bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson i = 0; 952bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson c = Balloc(a->k); 953bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (c == NULL) 954bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson return NULL; 955bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson c->sign = i; 956bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson wa = a->wds; 957bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson xa = a->x; 958bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson xae = xa + wa; 959bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson wb = b->wds; 960bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson xb = b->x; 961bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson xbe = xb + wb; 962bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson xc = c->x; 963bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson borrow = 0; 964bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#ifdef ULLong 965bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson do { 966bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson y = (ULLong)*xa++ - *xb++ - borrow; 967bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson borrow = y >> 32 & (ULong)1; 968bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson *xc++ = (ULong)(y & FFFFFFFF); 969bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 970bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson while(xb < xbe); 971bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson while(xa < xae) { 972bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson y = *xa++ - borrow; 973bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson borrow = y >> 32 & (ULong)1; 974bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson *xc++ = (ULong)(y & FFFFFFFF); 975bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 976bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#else 977bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson do { 978bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson y = (*xa & 0xffff) - (*xb & 0xffff) - borrow; 979bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson borrow = (y & 0x10000) >> 16; 980bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson z = (*xa++ >> 16) - (*xb++ >> 16) - borrow; 981bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson borrow = (z & 0x10000) >> 16; 982bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson Storeinc(xc, z, y); 983bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 984bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson while(xb < xbe); 985bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson while(xa < xae) { 986bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson y = (*xa & 0xffff) - borrow; 987bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson borrow = (y & 0x10000) >> 16; 988bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson z = (*xa++ >> 16) - borrow; 989bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson borrow = (z & 0x10000) >> 16; 990bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson Storeinc(xc, z, y); 991bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 992bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#endif 993bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson while(!*--xc) 994bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson wa--; 995bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson c->wds = wa; 996bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson return c; 997bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson} 998bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 9994141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson/* Given a positive normal double x, return the difference between x and the 10004141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson next double up. Doesn't give correct results for subnormals. */ 1001bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 1002bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinsonstatic double 1003bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinsonulp(U *x) 1004bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson{ 1005bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson Long L; 1006bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson U u; 1007bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 1008bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson L = (word0(x) & Exp_mask) - (P-1)*Exp_msk1; 1009bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson word0(&u) = L; 1010bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson word1(&u) = 0; 1011bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson return dval(&u); 1012bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson} 1013bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 1014bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson/* Convert a Bigint to a double plus an exponent */ 1015bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 1016bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinsonstatic double 1017bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinsonb2d(Bigint *a, int *e) 1018bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson{ 1019bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson ULong *xa, *xa0, w, y, z; 1020bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson int k; 1021bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson U d; 1022bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 1023bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson xa0 = a->x; 1024bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson xa = xa0 + a->wds; 1025bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson y = *--xa; 1026bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#ifdef DEBUG 1027bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (!y) Bug("zero y in b2d"); 1028bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#endif 1029bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson k = hi0bits(y); 1030bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson *e = 32 - k; 1031bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (k < Ebits) { 1032bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson word0(&d) = Exp_1 | y >> (Ebits - k); 1033bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson w = xa > xa0 ? *--xa : 0; 1034bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson word1(&d) = y << ((32-Ebits) + k) | w >> (Ebits - k); 1035bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson goto ret_d; 1036bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 1037bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson z = xa > xa0 ? *--xa : 0; 1038bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (k -= Ebits) { 1039bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson word0(&d) = Exp_1 | y << k | z >> (32 - k); 1040bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson y = xa > xa0 ? *--xa : 0; 1041bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson word1(&d) = z << k | y >> (32 - k); 1042bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 1043bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson else { 1044bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson word0(&d) = Exp_1 | y; 1045bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson word1(&d) = z; 1046bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 1047bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson ret_d: 1048bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson return dval(&d); 1049bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson} 1050bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 1051adcda3400f8ae931139605b8d1fcfede4c1c6916Mark Dickinson/* Convert a scaled double to a Bigint plus an exponent. Similar to d2b, 1052adcda3400f8ae931139605b8d1fcfede4c1c6916Mark Dickinson except that it accepts the scale parameter used in _Py_dg_strtod (which 1053adcda3400f8ae931139605b8d1fcfede4c1c6916Mark Dickinson should be either 0 or 2*P), and the normalization for the return value is 1054adcda3400f8ae931139605b8d1fcfede4c1c6916Mark Dickinson different (see below). On input, d should be finite and nonnegative, and d 1055adcda3400f8ae931139605b8d1fcfede4c1c6916Mark Dickinson / 2**scale should be exactly representable as an IEEE 754 double. 1056adcda3400f8ae931139605b8d1fcfede4c1c6916Mark Dickinson 1057adcda3400f8ae931139605b8d1fcfede4c1c6916Mark Dickinson Returns a Bigint b and an integer e such that 1058adcda3400f8ae931139605b8d1fcfede4c1c6916Mark Dickinson 1059adcda3400f8ae931139605b8d1fcfede4c1c6916Mark Dickinson dval(d) / 2**scale = b * 2**e. 1060adcda3400f8ae931139605b8d1fcfede4c1c6916Mark Dickinson 1061adcda3400f8ae931139605b8d1fcfede4c1c6916Mark Dickinson Unlike d2b, b is not necessarily odd: b and e are normalized so 1062adcda3400f8ae931139605b8d1fcfede4c1c6916Mark Dickinson that either 2**(P-1) <= b < 2**P and e >= Etiny, or b < 2**P 1063adcda3400f8ae931139605b8d1fcfede4c1c6916Mark Dickinson and e == Etiny. This applies equally to an input of 0.0: in that 1064adcda3400f8ae931139605b8d1fcfede4c1c6916Mark Dickinson case the return values are b = 0 and e = Etiny. 1065adcda3400f8ae931139605b8d1fcfede4c1c6916Mark Dickinson 1066adcda3400f8ae931139605b8d1fcfede4c1c6916Mark Dickinson The above normalization ensures that for all possible inputs d, 1067adcda3400f8ae931139605b8d1fcfede4c1c6916Mark Dickinson 2**e gives ulp(d/2**scale). 1068adcda3400f8ae931139605b8d1fcfede4c1c6916Mark Dickinson 1069adcda3400f8ae931139605b8d1fcfede4c1c6916Mark Dickinson Returns NULL on failure. 1070adcda3400f8ae931139605b8d1fcfede4c1c6916Mark Dickinson*/ 1071adcda3400f8ae931139605b8d1fcfede4c1c6916Mark Dickinson 1072adcda3400f8ae931139605b8d1fcfede4c1c6916Mark Dickinsonstatic Bigint * 1073adcda3400f8ae931139605b8d1fcfede4c1c6916Mark Dickinsonsd2b(U *d, int scale, int *e) 1074adcda3400f8ae931139605b8d1fcfede4c1c6916Mark Dickinson{ 1075adcda3400f8ae931139605b8d1fcfede4c1c6916Mark Dickinson Bigint *b; 1076adcda3400f8ae931139605b8d1fcfede4c1c6916Mark Dickinson 1077adcda3400f8ae931139605b8d1fcfede4c1c6916Mark Dickinson b = Balloc(1); 1078adcda3400f8ae931139605b8d1fcfede4c1c6916Mark Dickinson if (b == NULL) 1079adcda3400f8ae931139605b8d1fcfede4c1c6916Mark Dickinson return NULL; 1080adcda3400f8ae931139605b8d1fcfede4c1c6916Mark Dickinson 1081adcda3400f8ae931139605b8d1fcfede4c1c6916Mark Dickinson /* First construct b and e assuming that scale == 0. */ 1082adcda3400f8ae931139605b8d1fcfede4c1c6916Mark Dickinson b->wds = 2; 1083adcda3400f8ae931139605b8d1fcfede4c1c6916Mark Dickinson b->x[0] = word1(d); 1084adcda3400f8ae931139605b8d1fcfede4c1c6916Mark Dickinson b->x[1] = word0(d) & Frac_mask; 1085adcda3400f8ae931139605b8d1fcfede4c1c6916Mark Dickinson *e = Etiny - 1 + (int)((word0(d) & Exp_mask) >> Exp_shift); 1086adcda3400f8ae931139605b8d1fcfede4c1c6916Mark Dickinson if (*e < Etiny) 1087adcda3400f8ae931139605b8d1fcfede4c1c6916Mark Dickinson *e = Etiny; 1088adcda3400f8ae931139605b8d1fcfede4c1c6916Mark Dickinson else 1089adcda3400f8ae931139605b8d1fcfede4c1c6916Mark Dickinson b->x[1] |= Exp_msk1; 1090adcda3400f8ae931139605b8d1fcfede4c1c6916Mark Dickinson 1091adcda3400f8ae931139605b8d1fcfede4c1c6916Mark Dickinson /* Now adjust for scale, provided that b != 0. */ 1092adcda3400f8ae931139605b8d1fcfede4c1c6916Mark Dickinson if (scale && (b->x[0] || b->x[1])) { 1093adcda3400f8ae931139605b8d1fcfede4c1c6916Mark Dickinson *e -= scale; 1094adcda3400f8ae931139605b8d1fcfede4c1c6916Mark Dickinson if (*e < Etiny) { 1095adcda3400f8ae931139605b8d1fcfede4c1c6916Mark Dickinson scale = Etiny - *e; 1096adcda3400f8ae931139605b8d1fcfede4c1c6916Mark Dickinson *e = Etiny; 1097adcda3400f8ae931139605b8d1fcfede4c1c6916Mark Dickinson /* We can't shift more than P-1 bits without shifting out a 1. */ 1098adcda3400f8ae931139605b8d1fcfede4c1c6916Mark Dickinson assert(0 < scale && scale <= P - 1); 1099adcda3400f8ae931139605b8d1fcfede4c1c6916Mark Dickinson if (scale >= 32) { 1100adcda3400f8ae931139605b8d1fcfede4c1c6916Mark Dickinson /* The bits shifted out should all be zero. */ 1101adcda3400f8ae931139605b8d1fcfede4c1c6916Mark Dickinson assert(b->x[0] == 0); 1102adcda3400f8ae931139605b8d1fcfede4c1c6916Mark Dickinson b->x[0] = b->x[1]; 1103adcda3400f8ae931139605b8d1fcfede4c1c6916Mark Dickinson b->x[1] = 0; 1104adcda3400f8ae931139605b8d1fcfede4c1c6916Mark Dickinson scale -= 32; 1105adcda3400f8ae931139605b8d1fcfede4c1c6916Mark Dickinson } 1106adcda3400f8ae931139605b8d1fcfede4c1c6916Mark Dickinson if (scale) { 1107adcda3400f8ae931139605b8d1fcfede4c1c6916Mark Dickinson /* The bits shifted out should all be zero. */ 1108adcda3400f8ae931139605b8d1fcfede4c1c6916Mark Dickinson assert(b->x[0] << (32 - scale) == 0); 1109adcda3400f8ae931139605b8d1fcfede4c1c6916Mark Dickinson b->x[0] = (b->x[0] >> scale) | (b->x[1] << (32 - scale)); 1110adcda3400f8ae931139605b8d1fcfede4c1c6916Mark Dickinson b->x[1] >>= scale; 1111adcda3400f8ae931139605b8d1fcfede4c1c6916Mark Dickinson } 1112adcda3400f8ae931139605b8d1fcfede4c1c6916Mark Dickinson } 1113adcda3400f8ae931139605b8d1fcfede4c1c6916Mark Dickinson } 1114adcda3400f8ae931139605b8d1fcfede4c1c6916Mark Dickinson /* Ensure b is normalized. */ 1115adcda3400f8ae931139605b8d1fcfede4c1c6916Mark Dickinson if (!b->x[1]) 1116adcda3400f8ae931139605b8d1fcfede4c1c6916Mark Dickinson b->wds = 1; 1117adcda3400f8ae931139605b8d1fcfede4c1c6916Mark Dickinson 1118adcda3400f8ae931139605b8d1fcfede4c1c6916Mark Dickinson return b; 1119adcda3400f8ae931139605b8d1fcfede4c1c6916Mark Dickinson} 1120adcda3400f8ae931139605b8d1fcfede4c1c6916Mark Dickinson 1121bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson/* Convert a double to a Bigint plus an exponent. Return NULL on failure. 1122bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 1123bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson Given a finite nonzero double d, return an odd Bigint b and exponent *e 1124bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson such that fabs(d) = b * 2**e. On return, *bbits gives the number of 11252bcd17727027b6c923340209f8c6b92e34c69556Mark Dickinson significant bits of b; that is, 2**(*bbits-1) <= b < 2**(*bbits). 1126bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 1127bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson If d is zero, then b == 0, *e == -1010, *bbits = 0. 1128bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson */ 1129bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 1130bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinsonstatic Bigint * 1131bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinsond2b(U *d, int *e, int *bits) 1132bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson{ 1133bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson Bigint *b; 1134bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson int de, k; 1135bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson ULong *x, y, z; 1136bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson int i; 1137bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 1138bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson b = Balloc(1); 1139bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (b == NULL) 1140bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson return NULL; 1141bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson x = b->x; 1142bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 1143bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson z = word0(d) & Frac_mask; 1144bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson word0(d) &= 0x7fffffff; /* clear sign bit, which we ignore */ 1145bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if ((de = (int)(word0(d) >> Exp_shift))) 1146bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson z |= Exp_msk1; 1147bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if ((y = word1(d))) { 1148bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if ((k = lo0bits(&y))) { 1149bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson x[0] = y | z << (32 - k); 1150bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson z >>= k; 1151bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 1152bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson else 1153bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson x[0] = y; 1154bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson i = 1155bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson b->wds = (x[1] = z) ? 2 : 1; 1156bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 1157bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson else { 1158bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson k = lo0bits(&z); 1159bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson x[0] = z; 1160bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson i = 1161bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson b->wds = 1; 1162bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson k += 32; 1163bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 1164bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (de) { 1165bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson *e = de - Bias - (P-1) + k; 1166bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson *bits = P - k; 1167bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 1168bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson else { 1169bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson *e = de - Bias - (P-1) + 1 + k; 1170bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson *bits = 32*i - hi0bits(x[i-1]); 1171bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 1172bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson return b; 1173bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson} 1174bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 1175bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson/* Compute the ratio of two Bigints, as a double. The result may have an 1176bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson error of up to 2.5 ulps. */ 1177bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 1178bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinsonstatic double 1179bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinsonratio(Bigint *a, Bigint *b) 1180bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson{ 1181bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson U da, db; 1182bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson int k, ka, kb; 1183bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 1184bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson dval(&da) = b2d(a, &ka); 1185bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson dval(&db) = b2d(b, &kb); 1186bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson k = ka - kb + 32*(a->wds - b->wds); 1187bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (k > 0) 1188bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson word0(&da) += k*Exp_msk1; 1189bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson else { 1190bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson k = -k; 1191bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson word0(&db) += k*Exp_msk1; 1192bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 1193bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson return dval(&da) / dval(&db); 1194bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson} 1195bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 1196bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinsonstatic const double 1197bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinsontens[] = { 1198bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9, 1199bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19, 1200bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 1e20, 1e21, 1e22 1201bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson}; 1202bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 1203bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinsonstatic const double 1204bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinsonbigtens[] = { 1e16, 1e32, 1e64, 1e128, 1e256 }; 1205bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinsonstatic const double tinytens[] = { 1e-16, 1e-32, 1e-64, 1e-128, 1206bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 9007199254740992.*9007199254740992.e-256 1207bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson /* = 2^106 * 1e-256 */ 1208bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson}; 1209bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson/* The factor of 2^53 in tinytens[4] helps us avoid setting the underflow */ 1210bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson/* flag unnecessarily. It leads to a song and dance at the end of strtod. */ 1211bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#define Scale_Bit 0x10 1212bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#define n_bigtens 5 1213bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 1214bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#define ULbits 32 1215bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#define kshift 5 1216bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#define kmask 31 1217bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 1218bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 1219bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinsonstatic int 1220bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinsondshift(Bigint *b, int p2) 1221bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson{ 1222bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson int rv = hi0bits(b->x[b->wds-1]) - 4; 1223bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (p2 > 0) 1224bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson rv -= p2; 1225bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson return rv & kmask; 1226bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson} 1227bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 1228bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson/* special case of Bigint division. The quotient is always in the range 0 <= 1229bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson quotient < 10, and on entry the divisor S is normalized so that its top 4 1230bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson bits (28--31) are zero and bit 27 is set. */ 1231bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 1232bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinsonstatic int 1233bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinsonquorem(Bigint *b, Bigint *S) 1234bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson{ 1235bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson int n; 1236bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson ULong *bx, *bxe, q, *sx, *sxe; 1237bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#ifdef ULLong 1238bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson ULLong borrow, carry, y, ys; 1239bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#else 1240bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson ULong borrow, carry, y, ys; 1241bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson ULong si, z, zs; 1242bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#endif 1243bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 1244bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson n = S->wds; 1245bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#ifdef DEBUG 1246bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson /*debug*/ if (b->wds > n) 1247bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson /*debug*/ Bug("oversize b in quorem"); 1248bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#endif 1249bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (b->wds < n) 1250bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson return 0; 1251bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson sx = S->x; 1252bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson sxe = sx + --n; 1253bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson bx = b->x; 1254bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson bxe = bx + n; 1255bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson q = *bxe / (*sxe + 1); /* ensure q <= true quotient */ 1256bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#ifdef DEBUG 1257bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson /*debug*/ if (q > 9) 1258bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson /*debug*/ Bug("oversized quotient in quorem"); 1259bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#endif 1260bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (q) { 1261bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson borrow = 0; 1262bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson carry = 0; 1263bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson do { 1264bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#ifdef ULLong 1265bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson ys = *sx++ * (ULLong)q + carry; 1266bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson carry = ys >> 32; 1267bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson y = *bx - (ys & FFFFFFFF) - borrow; 1268bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson borrow = y >> 32 & (ULong)1; 1269bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson *bx++ = (ULong)(y & FFFFFFFF); 1270bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#else 1271bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson si = *sx++; 1272bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson ys = (si & 0xffff) * q + carry; 1273bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson zs = (si >> 16) * q + (ys >> 16); 1274bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson carry = zs >> 16; 1275bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson y = (*bx & 0xffff) - (ys & 0xffff) - borrow; 1276bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson borrow = (y & 0x10000) >> 16; 1277bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson z = (*bx >> 16) - (zs & 0xffff) - borrow; 1278bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson borrow = (z & 0x10000) >> 16; 1279bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson Storeinc(bx, z, y); 1280bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#endif 1281bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 1282bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson while(sx <= sxe); 1283bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (!*bxe) { 1284bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson bx = b->x; 1285bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson while(--bxe > bx && !*bxe) 1286bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson --n; 1287bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson b->wds = n; 1288bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 1289bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 1290bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (cmp(b, S) >= 0) { 1291bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson q++; 1292bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson borrow = 0; 1293bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson carry = 0; 1294bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson bx = b->x; 1295bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson sx = S->x; 1296bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson do { 1297bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#ifdef ULLong 1298bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson ys = *sx++ + carry; 1299bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson carry = ys >> 32; 1300bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson y = *bx - (ys & FFFFFFFF) - borrow; 1301bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson borrow = y >> 32 & (ULong)1; 1302bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson *bx++ = (ULong)(y & FFFFFFFF); 1303bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#else 1304bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson si = *sx++; 1305bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson ys = (si & 0xffff) + carry; 1306bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson zs = (si >> 16) + (ys >> 16); 1307bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson carry = zs >> 16; 1308bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson y = (*bx & 0xffff) - (ys & 0xffff) - borrow; 1309bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson borrow = (y & 0x10000) >> 16; 1310bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson z = (*bx >> 16) - (zs & 0xffff) - borrow; 1311bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson borrow = (z & 0x10000) >> 16; 1312bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson Storeinc(bx, z, y); 1313bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#endif 1314bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 1315bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson while(sx <= sxe); 1316bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson bx = b->x; 1317bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson bxe = bx + n; 1318bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (!*bxe) { 1319bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson while(--bxe > bx && !*bxe) 1320bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson --n; 1321bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson b->wds = n; 1322bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 1323bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 1324bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson return q; 1325bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson} 1326bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 13275818e0125395b88b5e3c69dacdb50d5562628cd2Mark Dickinson/* sulp(x) is a version of ulp(x) that takes bc.scale into account. 13285ff4f279e6342bf142de22c91662b8eb70ce722aMark Dickinson 13295818e0125395b88b5e3c69dacdb50d5562628cd2Mark Dickinson Assuming that x is finite and nonnegative (positive zero is fine 13305818e0125395b88b5e3c69dacdb50d5562628cd2Mark Dickinson here) and x / 2^bc.scale is exactly representable as a double, 13315818e0125395b88b5e3c69dacdb50d5562628cd2Mark Dickinson sulp(x) is equivalent to 2^bc.scale * ulp(x / 2^bc.scale). */ 13325ff4f279e6342bf142de22c91662b8eb70ce722aMark Dickinson 13335ff4f279e6342bf142de22c91662b8eb70ce722aMark Dickinsonstatic double 13345ff4f279e6342bf142de22c91662b8eb70ce722aMark Dickinsonsulp(U *x, BCinfo *bc) 13355ff4f279e6342bf142de22c91662b8eb70ce722aMark Dickinson{ 13365ff4f279e6342bf142de22c91662b8eb70ce722aMark Dickinson U u; 13375ff4f279e6342bf142de22c91662b8eb70ce722aMark Dickinson 133802139d74bae1a77bbe4ad528762e1620486e3e36Mark Dickinson if (bc->scale && 2*P + 1 > (int)((word0(x) & Exp_mask) >> Exp_shift)) { 13395ff4f279e6342bf142de22c91662b8eb70ce722aMark Dickinson /* rv/2^bc->scale is subnormal */ 13405ff4f279e6342bf142de22c91662b8eb70ce722aMark Dickinson word0(&u) = (P+2)*Exp_msk1; 13415ff4f279e6342bf142de22c91662b8eb70ce722aMark Dickinson word1(&u) = 0; 13425ff4f279e6342bf142de22c91662b8eb70ce722aMark Dickinson return u.d; 13435ff4f279e6342bf142de22c91662b8eb70ce722aMark Dickinson } 13445818e0125395b88b5e3c69dacdb50d5562628cd2Mark Dickinson else { 13455818e0125395b88b5e3c69dacdb50d5562628cd2Mark Dickinson assert(word0(x) || word1(x)); /* x != 0.0 */ 13465ff4f279e6342bf142de22c91662b8eb70ce722aMark Dickinson return ulp(x); 13475818e0125395b88b5e3c69dacdb50d5562628cd2Mark Dickinson } 13485ff4f279e6342bf142de22c91662b8eb70ce722aMark Dickinson} 1349bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 1350b26d56ac18df454e373e01a405a622d412d5bd53Mark Dickinson/* The bigcomp function handles some hard cases for strtod, for inputs 1351b26d56ac18df454e373e01a405a622d412d5bd53Mark Dickinson with more than STRTOD_DIGLIM digits. It's called once an initial 1352b26d56ac18df454e373e01a405a622d412d5bd53Mark Dickinson estimate for the double corresponding to the input string has 1353b26d56ac18df454e373e01a405a622d412d5bd53Mark Dickinson already been obtained by the code in _Py_dg_strtod. 1354b26d56ac18df454e373e01a405a622d412d5bd53Mark Dickinson 1355b26d56ac18df454e373e01a405a622d412d5bd53Mark Dickinson The bigcomp function is only called after _Py_dg_strtod has found a 1356b26d56ac18df454e373e01a405a622d412d5bd53Mark Dickinson double value rv such that either rv or rv + 1ulp represents the 1357b26d56ac18df454e373e01a405a622d412d5bd53Mark Dickinson correctly rounded value corresponding to the original string. It 1358b26d56ac18df454e373e01a405a622d412d5bd53Mark Dickinson determines which of these two values is the correct one by 1359b26d56ac18df454e373e01a405a622d412d5bd53Mark Dickinson computing the decimal digits of rv + 0.5ulp and comparing them with 13606e0d3d67fb67cc80c4570e504890e03c2bc6efdeMark Dickinson the corresponding digits of s0. 1361b26d56ac18df454e373e01a405a622d412d5bd53Mark Dickinson 1362b26d56ac18df454e373e01a405a622d412d5bd53Mark Dickinson In the following, write dv for the absolute value of the number represented 1363b26d56ac18df454e373e01a405a622d412d5bd53Mark Dickinson by the input string. 1364b26d56ac18df454e373e01a405a622d412d5bd53Mark Dickinson 1365b26d56ac18df454e373e01a405a622d412d5bd53Mark Dickinson Inputs: 1366b26d56ac18df454e373e01a405a622d412d5bd53Mark Dickinson 1367b26d56ac18df454e373e01a405a622d412d5bd53Mark Dickinson s0 points to the first significant digit of the input string. 1368b26d56ac18df454e373e01a405a622d412d5bd53Mark Dickinson 1369b26d56ac18df454e373e01a405a622d412d5bd53Mark Dickinson rv is a (possibly scaled) estimate for the closest double value to the 1370b26d56ac18df454e373e01a405a622d412d5bd53Mark Dickinson value represented by the original input to _Py_dg_strtod. If 1371b26d56ac18df454e373e01a405a622d412d5bd53Mark Dickinson bc->scale is nonzero, then rv/2^(bc->scale) is the approximation to 1372b26d56ac18df454e373e01a405a622d412d5bd53Mark Dickinson the input value. 1373b26d56ac18df454e373e01a405a622d412d5bd53Mark Dickinson 1374b26d56ac18df454e373e01a405a622d412d5bd53Mark Dickinson bc is a struct containing information gathered during the parsing and 1375b26d56ac18df454e373e01a405a622d412d5bd53Mark Dickinson estimation steps of _Py_dg_strtod. Description of fields follows: 1376b26d56ac18df454e373e01a405a622d412d5bd53Mark Dickinson 1377b26d56ac18df454e373e01a405a622d412d5bd53Mark Dickinson bc->e0 gives the exponent of the input value, such that dv = (integer 1378b26d56ac18df454e373e01a405a622d412d5bd53Mark Dickinson given by the bd->nd digits of s0) * 10**e0 1379b26d56ac18df454e373e01a405a622d412d5bd53Mark Dickinson 1380d2a9940acbe6a74cc83e371baf2ef7c580e308bcMark Dickinson bc->nd gives the total number of significant digits of s0. It will 1381d2a9940acbe6a74cc83e371baf2ef7c580e308bcMark Dickinson be at least 1. 1382b26d56ac18df454e373e01a405a622d412d5bd53Mark Dickinson 1383b26d56ac18df454e373e01a405a622d412d5bd53Mark Dickinson bc->nd0 gives the number of significant digits of s0 before the 1384b26d56ac18df454e373e01a405a622d412d5bd53Mark Dickinson decimal separator. If there's no decimal separator, bc->nd0 == 1385b26d56ac18df454e373e01a405a622d412d5bd53Mark Dickinson bc->nd. 1386b26d56ac18df454e373e01a405a622d412d5bd53Mark Dickinson 1387b26d56ac18df454e373e01a405a622d412d5bd53Mark Dickinson bc->scale is the value used to scale rv to avoid doing arithmetic with 1388b26d56ac18df454e373e01a405a622d412d5bd53Mark Dickinson subnormal values. It's either 0 or 2*P (=106). 1389b26d56ac18df454e373e01a405a622d412d5bd53Mark Dickinson 1390b26d56ac18df454e373e01a405a622d412d5bd53Mark Dickinson Outputs: 1391b26d56ac18df454e373e01a405a622d412d5bd53Mark Dickinson 1392b26d56ac18df454e373e01a405a622d412d5bd53Mark Dickinson On successful exit, rv/2^(bc->scale) is the closest double to dv. 1393b26d56ac18df454e373e01a405a622d412d5bd53Mark Dickinson 1394b26d56ac18df454e373e01a405a622d412d5bd53Mark Dickinson Returns 0 on success, -1 on failure (e.g., due to a failed malloc call). */ 1395bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 1396bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinsonstatic int 1397bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinsonbigcomp(U *rv, const char *s0, BCinfo *bc) 1398bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson{ 1399bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson Bigint *b, *d; 1400adcda3400f8ae931139605b8d1fcfede4c1c6916Mark Dickinson int b2, d2, dd, i, nd, nd0, odd, p2, p5; 1401bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 1402bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson nd = bc->nd; 1403bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson nd0 = bc->nd0; 14048efef5ce9f6c0dfd2cb4720b61a37bbdfdb5e30eMark Dickinson p5 = nd + bc->e0; 1405adcda3400f8ae931139605b8d1fcfede4c1c6916Mark Dickinson b = sd2b(rv, bc->scale, &p2); 14066e0d3d67fb67cc80c4570e504890e03c2bc6efdeMark Dickinson if (b == NULL) 14076e0d3d67fb67cc80c4570e504890e03c2bc6efdeMark Dickinson return -1; 1408adcda3400f8ae931139605b8d1fcfede4c1c6916Mark Dickinson 140950b60c612e7eca3f815d362190ddb80a21a6d820Mark Dickinson /* record whether the lsb of rv/2^(bc->scale) is odd: in the exact halfway 141050b60c612e7eca3f815d362190ddb80a21a6d820Mark Dickinson case, this is used for round to even. */ 1411adcda3400f8ae931139605b8d1fcfede4c1c6916Mark Dickinson odd = b->x[0] & 1; 1412adcda3400f8ae931139605b8d1fcfede4c1c6916Mark Dickinson 1413adcda3400f8ae931139605b8d1fcfede4c1c6916Mark Dickinson /* left shift b by 1 bit and or a 1 into the least significant bit; 1414adcda3400f8ae931139605b8d1fcfede4c1c6916Mark Dickinson this gives us b * 2**p2 = rv/2^(bc->scale) + 0.5 ulp. */ 1415adcda3400f8ae931139605b8d1fcfede4c1c6916Mark Dickinson b = lshift(b, 1); 1416adcda3400f8ae931139605b8d1fcfede4c1c6916Mark Dickinson if (b == NULL) 1417adcda3400f8ae931139605b8d1fcfede4c1c6916Mark Dickinson return -1; 14186e0d3d67fb67cc80c4570e504890e03c2bc6efdeMark Dickinson b->x[0] |= 1; 1419adcda3400f8ae931139605b8d1fcfede4c1c6916Mark Dickinson p2--; 14206e0d3d67fb67cc80c4570e504890e03c2bc6efdeMark Dickinson 1421adcda3400f8ae931139605b8d1fcfede4c1c6916Mark Dickinson p2 -= p5; 1422bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson d = i2b(1); 1423bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (d == NULL) { 1424bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson Bfree(b); 1425bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson return -1; 1426bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 1427bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson /* Arrange for convenient computation of quotients: 1428bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * shift left if necessary so divisor has 4 leading 0 bits. 1429bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson */ 1430bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (p5 > 0) { 1431bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson d = pow5mult(d, p5); 1432bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (d == NULL) { 1433bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson Bfree(b); 1434bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson return -1; 1435bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 1436bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 1437bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson else if (p5 < 0) { 1438bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson b = pow5mult(b, -p5); 1439bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (b == NULL) { 1440bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson Bfree(d); 1441bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson return -1; 1442bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 1443bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 1444bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (p2 > 0) { 1445bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson b2 = p2; 1446bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson d2 = 0; 1447bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 1448bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson else { 1449bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson b2 = 0; 1450bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson d2 = -p2; 1451bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 1452bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson i = dshift(d, d2); 1453bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if ((b2 += i) > 0) { 1454bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson b = lshift(b, b2); 1455bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (b == NULL) { 1456bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson Bfree(d); 1457bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson return -1; 1458bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 1459bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 1460bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if ((d2 += i) > 0) { 1461bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson d = lshift(d, d2); 1462bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (d == NULL) { 1463bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson Bfree(b); 1464bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson return -1; 1465bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 1466bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 1467bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 14684141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson /* Compare s0 with b/d: set dd to -1, 0, or 1 according as s0 < b/d, s0 == 14694141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson * b/d, or s0 > b/d. Here the digits of s0 are thought of as representing 14704141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson * a number in the range [0.1, 1). */ 14714141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson if (cmp(b, d) >= 0) 14724141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson /* b/d >= 1 */ 14738efef5ce9f6c0dfd2cb4720b61a37bbdfdb5e30eMark Dickinson dd = -1; 14744141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson else { 14754141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson i = 0; 14764141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson for(;;) { 14774141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson b = multadd(b, 10, 0); 14784141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson if (b == NULL) { 14794141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson Bfree(d); 14804141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson return -1; 14814141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson } 14824141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson dd = s0[i < nd0 ? i : i+1] - '0' - quorem(b, d); 14834141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson i++; 148450b60c612e7eca3f815d362190ddb80a21a6d820Mark Dickinson 14854141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson if (dd) 14864141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson break; 14874141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson if (!b->x[0] && b->wds == 1) { 14884141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson /* b/d == 0 */ 14894141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson dd = i < nd; 14904141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson break; 14914141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson } 14924141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson if (!(i < nd)) { 14934141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson /* b/d != 0, but digits of s0 exhausted */ 14944141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson dd = -1; 14954141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson break; 14964141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson } 1497bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 1498bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 1499bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson Bfree(b); 1500bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson Bfree(d); 150150b60c612e7eca3f815d362190ddb80a21a6d820Mark Dickinson if (dd > 0 || (dd == 0 && odd)) 15026e0d3d67fb67cc80c4570e504890e03c2bc6efdeMark Dickinson dval(rv) += sulp(rv, bc); 1503bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson return 0; 1504bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson} 1505bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 1506bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinsondouble 1507bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson_Py_dg_strtod(const char *s00, char **se) 1508bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson{ 1509adcda3400f8ae931139605b8d1fcfede4c1c6916Mark Dickinson int bb2, bb5, bbe, bd2, bd5, bs2, c, dsign, e, e1, error; 1510adcda3400f8ae931139605b8d1fcfede4c1c6916Mark Dickinson int esign, i, j, k, lz, nd, nd0, odd, sign; 1511bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson const char *s, *s0, *s1; 1512bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson double aadj, aadj1; 1513bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson U aadj2, adj, rv, rv0; 15144141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson ULong y, z, abs_exp; 151518a818bc63d993c3d3433f69cf2b7d2b9bd63ebfMark Dickinson Long L; 1516bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson BCinfo bc; 1517bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson Bigint *bb, *bb1, *bd, *bd0, *bs, *delta; 1518c2f8c81af02519952a857baebb5c0c9048033009Mark Dickinson size_t ndigits, fraclen; 1519bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 1520bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson dval(&rv) = 0.; 15214141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson 15224141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson /* Start parsing. */ 15234141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson c = *(s = s00); 15244141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson 15254141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson /* Parse optional sign, if present. */ 15264141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson sign = 0; 15274141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson switch (c) { 15284141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson case '-': 15294141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson sign = 1; 15304141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson /* no break */ 15314141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson case '+': 15324141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson c = *++s; 1533bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 15344141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson 15354141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson /* Skip leading zeros: lz is true iff there were leading zeros. */ 15364141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson s1 = s; 15374141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson while (c == '0') 15384141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson c = *++s; 15394141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson lz = s != s1; 15404141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson 1541c2f8c81af02519952a857baebb5c0c9048033009Mark Dickinson /* Point s0 at the first nonzero digit (if any). fraclen will be the 1542c2f8c81af02519952a857baebb5c0c9048033009Mark Dickinson number of digits between the decimal point and the end of the 1543c2f8c81af02519952a857baebb5c0c9048033009Mark Dickinson digit string. ndigits will be the total number of digits ignoring 1544c2f8c81af02519952a857baebb5c0c9048033009Mark Dickinson leading zeros. */ 15454141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson s0 = s1 = s; 15464141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson while ('0' <= c && c <= '9') 15474141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson c = *++s; 1548c2f8c81af02519952a857baebb5c0c9048033009Mark Dickinson ndigits = s - s1; 1549c2f8c81af02519952a857baebb5c0c9048033009Mark Dickinson fraclen = 0; 15504141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson 15514141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson /* Parse decimal point and following digits. */ 1552bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (c == '.') { 1553bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson c = *++s; 1554c2f8c81af02519952a857baebb5c0c9048033009Mark Dickinson if (!ndigits) { 15554141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson s1 = s; 15564141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson while (c == '0') 15574141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson c = *++s; 15584141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson lz = lz || s != s1; 1559c2f8c81af02519952a857baebb5c0c9048033009Mark Dickinson fraclen += (s - s1); 15604141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson s0 = s; 1561bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 15624141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson s1 = s; 15634141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson while ('0' <= c && c <= '9') 15644141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson c = *++s; 1565c2f8c81af02519952a857baebb5c0c9048033009Mark Dickinson ndigits += s - s1; 1566c2f8c81af02519952a857baebb5c0c9048033009Mark Dickinson fraclen += s - s1; 1567c2f8c81af02519952a857baebb5c0c9048033009Mark Dickinson } 1568c2f8c81af02519952a857baebb5c0c9048033009Mark Dickinson 1569c2f8c81af02519952a857baebb5c0c9048033009Mark Dickinson /* Now lz is true if and only if there were leading zero digits, and 1570c2f8c81af02519952a857baebb5c0c9048033009Mark Dickinson ndigits gives the total number of digits ignoring leading zeros. A 1571c2f8c81af02519952a857baebb5c0c9048033009Mark Dickinson valid input must have at least one digit. */ 1572c2f8c81af02519952a857baebb5c0c9048033009Mark Dickinson if (!ndigits && !lz) { 1573c2f8c81af02519952a857baebb5c0c9048033009Mark Dickinson if (se) 1574c2f8c81af02519952a857baebb5c0c9048033009Mark Dickinson *se = (char *)s00; 1575c2f8c81af02519952a857baebb5c0c9048033009Mark Dickinson goto parse_error; 1576bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 15774141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson 1578c2f8c81af02519952a857baebb5c0c9048033009Mark Dickinson /* Range check ndigits and fraclen to make sure that they, and values 1579c2f8c81af02519952a857baebb5c0c9048033009Mark Dickinson computed with them, can safely fit in an int. */ 1580c2f8c81af02519952a857baebb5c0c9048033009Mark Dickinson if (ndigits > MAX_DIGITS || fraclen > MAX_DIGITS) { 158119428060139151e3047283f132e8baf16436745eMark Dickinson if (se) 158219428060139151e3047283f132e8baf16436745eMark Dickinson *se = (char *)s00; 15834141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson goto parse_error; 15844141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson } 1585c2f8c81af02519952a857baebb5c0c9048033009Mark Dickinson nd = (int)ndigits; 1586c2f8c81af02519952a857baebb5c0c9048033009Mark Dickinson nd0 = (int)ndigits - (int)fraclen; 15874141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson 15884141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson /* Parse exponent. */ 1589bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson e = 0; 1590bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (c == 'e' || c == 'E') { 1591bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson s00 = s; 15924141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson c = *++s; 15934141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson 15944141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson /* Exponent sign. */ 1595bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson esign = 0; 15964141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson switch (c) { 1597bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson case '-': 1598bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson esign = 1; 15994141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson /* no break */ 1600bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson case '+': 1601bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson c = *++s; 1602bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 16034141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson 16044141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson /* Skip zeros. lz is true iff there are leading zeros. */ 16054141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson s1 = s; 16064141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson while (c == '0') 16074141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson c = *++s; 16084141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson lz = s != s1; 16094141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson 16104141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson /* Get absolute value of the exponent. */ 16114141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson s1 = s; 16124141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson abs_exp = 0; 16134141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson while ('0' <= c && c <= '9') { 16144141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson abs_exp = 10*abs_exp + (c - '0'); 16154141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson c = *++s; 1616bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 16174141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson 16184141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson /* abs_exp will be correct modulo 2**32. But 10**9 < 2**32, so if 16194141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson there are at most 9 significant exponent digits then overflow is 16204141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson impossible. */ 16214141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson if (s - s1 > 9 || abs_exp > MAX_ABS_EXP) 16224141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson e = (int)MAX_ABS_EXP; 1623bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson else 16244141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson e = (int)abs_exp; 16254141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson if (esign) 16264141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson e = -e; 16274141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson 16284141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson /* A valid exponent must have at least one digit. */ 16294141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson if (s == s1 && !lz) 1630bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson s = s00; 1631bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 16324141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson 16334141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson /* Adjust exponent to take into account position of the point. */ 16344141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson e -= nd - nd0; 16354141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson if (nd0 <= 0) 1636811ff822f8cd87cf29867118cb3a74c5035a1a94Mark Dickinson nd0 = nd; 1637811ff822f8cd87cf29867118cb3a74c5035a1a94Mark Dickinson 16384141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson /* Finished parsing. Set se to indicate how far we parsed */ 16394141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson if (se) 16404141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson *se = (char *)s; 16414141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson 16424141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson /* If all digits were zero, exit with return value +-0.0. Otherwise, 16434141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson strip trailing zeros: scan back until we hit a nonzero digit. */ 16444141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson if (!nd) 16454141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson goto ret; 1646811ff822f8cd87cf29867118cb3a74c5035a1a94Mark Dickinson for (i = nd; i > 0; ) { 1647811ff822f8cd87cf29867118cb3a74c5035a1a94Mark Dickinson --i; 1648811ff822f8cd87cf29867118cb3a74c5035a1a94Mark Dickinson if (s0[i < nd0 ? i : i+1] != '0') { 1649811ff822f8cd87cf29867118cb3a74c5035a1a94Mark Dickinson ++i; 1650811ff822f8cd87cf29867118cb3a74c5035a1a94Mark Dickinson break; 1651811ff822f8cd87cf29867118cb3a74c5035a1a94Mark Dickinson } 1652811ff822f8cd87cf29867118cb3a74c5035a1a94Mark Dickinson } 1653811ff822f8cd87cf29867118cb3a74c5035a1a94Mark Dickinson e += nd - i; 1654811ff822f8cd87cf29867118cb3a74c5035a1a94Mark Dickinson nd = i; 1655811ff822f8cd87cf29867118cb3a74c5035a1a94Mark Dickinson if (nd0 > nd) 1656811ff822f8cd87cf29867118cb3a74c5035a1a94Mark Dickinson nd0 = nd; 1657bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 16584141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson /* Summary of parsing results. After parsing, and dealing with zero 16594141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson * inputs, we have values s0, nd0, nd, e, sign, where: 1660476279f18b1bbcc5939f6bb7a10dd937c933cfb3Mark Dickinson * 16614141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson * - s0 points to the first significant digit of the input string 1662476279f18b1bbcc5939f6bb7a10dd937c933cfb3Mark Dickinson * 1663811ff822f8cd87cf29867118cb3a74c5035a1a94Mark Dickinson * - nd is the total number of significant digits (here, and 1664811ff822f8cd87cf29867118cb3a74c5035a1a94Mark Dickinson * below, 'significant digits' means the set of digits of the 1665811ff822f8cd87cf29867118cb3a74c5035a1a94Mark Dickinson * significand of the input that remain after ignoring leading 16664141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson * and trailing zeros). 1667476279f18b1bbcc5939f6bb7a10dd937c933cfb3Mark Dickinson * 16684141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson * - nd0 indicates the position of the decimal point, if present; it 16694141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson * satisfies 1 <= nd0 <= nd. The nd significant digits are in 16704141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson * s0[0:nd0] and s0[nd0+1:nd+1] using the usual Python half-open slice 16714141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson * notation. (If nd0 < nd, then s0[nd0] contains a '.' character; if 16724141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson * nd0 == nd, then s0[nd0] could be any non-digit character.) 1673476279f18b1bbcc5939f6bb7a10dd937c933cfb3Mark Dickinson * 1674811ff822f8cd87cf29867118cb3a74c5035a1a94Mark Dickinson * - e is the adjusted exponent: the absolute value of the number 1675811ff822f8cd87cf29867118cb3a74c5035a1a94Mark Dickinson * represented by the original input string is n * 10**e, where 1676811ff822f8cd87cf29867118cb3a74c5035a1a94Mark Dickinson * n is the integer represented by the concatenation of 1677811ff822f8cd87cf29867118cb3a74c5035a1a94Mark Dickinson * s0[0:nd0] and s0[nd0+1:nd+1] 1678476279f18b1bbcc5939f6bb7a10dd937c933cfb3Mark Dickinson * 1679811ff822f8cd87cf29867118cb3a74c5035a1a94Mark Dickinson * - sign gives the sign of the input: 1 for negative, 0 for positive 1680811ff822f8cd87cf29867118cb3a74c5035a1a94Mark Dickinson * 1681811ff822f8cd87cf29867118cb3a74c5035a1a94Mark Dickinson * - the first and last significant digits are nonzero 1682811ff822f8cd87cf29867118cb3a74c5035a1a94Mark Dickinson */ 1683811ff822f8cd87cf29867118cb3a74c5035a1a94Mark Dickinson 1684811ff822f8cd87cf29867118cb3a74c5035a1a94Mark Dickinson /* put first DBL_DIG+1 digits into integer y and z. 1685476279f18b1bbcc5939f6bb7a10dd937c933cfb3Mark Dickinson * 1686476279f18b1bbcc5939f6bb7a10dd937c933cfb3Mark Dickinson * - y contains the value represented by the first min(9, nd) 1687476279f18b1bbcc5939f6bb7a10dd937c933cfb3Mark Dickinson * significant digits 1688476279f18b1bbcc5939f6bb7a10dd937c933cfb3Mark Dickinson * 1689476279f18b1bbcc5939f6bb7a10dd937c933cfb3Mark Dickinson * - if nd > 9, z contains the value represented by significant digits 1690476279f18b1bbcc5939f6bb7a10dd937c933cfb3Mark Dickinson * with indices in [9, min(16, nd)). So y * 10**(min(16, nd) - 9) + z 1691476279f18b1bbcc5939f6bb7a10dd937c933cfb3Mark Dickinson * gives the value represented by the first min(16, nd) sig. digits. 1692476279f18b1bbcc5939f6bb7a10dd937c933cfb3Mark Dickinson */ 1693476279f18b1bbcc5939f6bb7a10dd937c933cfb3Mark Dickinson 16944141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson bc.e0 = e1 = e; 1695811ff822f8cd87cf29867118cb3a74c5035a1a94Mark Dickinson y = z = 0; 1696811ff822f8cd87cf29867118cb3a74c5035a1a94Mark Dickinson for (i = 0; i < nd; i++) { 1697811ff822f8cd87cf29867118cb3a74c5035a1a94Mark Dickinson if (i < 9) 1698811ff822f8cd87cf29867118cb3a74c5035a1a94Mark Dickinson y = 10*y + s0[i < nd0 ? i : i+1] - '0'; 1699811ff822f8cd87cf29867118cb3a74c5035a1a94Mark Dickinson else if (i < DBL_DIG+1) 1700811ff822f8cd87cf29867118cb3a74c5035a1a94Mark Dickinson z = 10*z + s0[i < nd0 ? i : i+1] - '0'; 1701811ff822f8cd87cf29867118cb3a74c5035a1a94Mark Dickinson else 1702811ff822f8cd87cf29867118cb3a74c5035a1a94Mark Dickinson break; 1703811ff822f8cd87cf29867118cb3a74c5035a1a94Mark Dickinson } 1704811ff822f8cd87cf29867118cb3a74c5035a1a94Mark Dickinson 1705bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson k = nd < DBL_DIG + 1 ? nd : DBL_DIG + 1; 1706bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson dval(&rv) = y; 1707bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (k > 9) { 1708bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson dval(&rv) = tens[k - 9] * dval(&rv) + z; 1709bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 1710bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson bd0 = 0; 1711bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (nd <= DBL_DIG 1712bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson && Flt_Rounds == 1 1713bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson ) { 1714bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (!e) 1715bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson goto ret; 1716bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (e > 0) { 1717bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (e <= Ten_pmax) { 1718bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson dval(&rv) *= tens[e]; 1719bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson goto ret; 1720bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 1721bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson i = DBL_DIG - nd; 1722bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (e <= Ten_pmax + i) { 1723bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson /* A fancier test would sometimes let us do 1724bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * this for larger i values. 1725bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson */ 1726bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson e -= i; 1727bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson dval(&rv) *= tens[i]; 1728bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson dval(&rv) *= tens[e]; 1729bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson goto ret; 1730bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 1731bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 1732bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson else if (e >= -Ten_pmax) { 1733bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson dval(&rv) /= tens[-e]; 1734bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson goto ret; 1735bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 1736bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 1737bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson e1 += nd - k; 1738bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 1739bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson bc.scale = 0; 1740bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 1741bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson /* Get starting approximation = rv * 10**e1 */ 1742bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 1743bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (e1 > 0) { 1744bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if ((i = e1 & 15)) 1745bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson dval(&rv) *= tens[i]; 1746bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (e1 &= ~15) { 17474141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson if (e1 > DBL_MAX_10_EXP) 17484141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson goto ovfl; 1749bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson e1 >>= 4; 1750bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson for(j = 0; e1 > 1; j++, e1 >>= 1) 1751bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (e1 & 1) 1752bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson dval(&rv) *= bigtens[j]; 1753bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson /* The last multiplication could overflow. */ 1754bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson word0(&rv) -= P*Exp_msk1; 1755bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson dval(&rv) *= bigtens[j]; 1756bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if ((z = word0(&rv) & Exp_mask) 1757bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson > Exp_msk1*(DBL_MAX_EXP+Bias-P)) 1758bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson goto ovfl; 1759bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (z > Exp_msk1*(DBL_MAX_EXP+Bias-1-P)) { 1760bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson /* set to largest number */ 1761bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson /* (Can't trust DBL_MAX) */ 1762bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson word0(&rv) = Big0; 1763bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson word1(&rv) = Big1; 1764bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 1765bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson else 1766bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson word0(&rv) += P*Exp_msk1; 1767bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 1768bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 1769bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson else if (e1 < 0) { 1770ca6ea567184941a62f49f911a16d5bc3515c634cMark Dickinson /* The input decimal value lies in [10**e1, 10**(e1+16)). 1771ca6ea567184941a62f49f911a16d5bc3515c634cMark Dickinson 1772ca6ea567184941a62f49f911a16d5bc3515c634cMark Dickinson If e1 <= -512, underflow immediately. 1773ca6ea567184941a62f49f911a16d5bc3515c634cMark Dickinson If e1 <= -256, set bc.scale to 2*P. 1774ca6ea567184941a62f49f911a16d5bc3515c634cMark Dickinson 1775ca6ea567184941a62f49f911a16d5bc3515c634cMark Dickinson So for input value < 1e-256, bc.scale is always set; 1776ca6ea567184941a62f49f911a16d5bc3515c634cMark Dickinson for input value >= 1e-240, bc.scale is never set. 1777ca6ea567184941a62f49f911a16d5bc3515c634cMark Dickinson For input values in [1e-256, 1e-240), bc.scale may or may 1778ca6ea567184941a62f49f911a16d5bc3515c634cMark Dickinson not be set. */ 1779ca6ea567184941a62f49f911a16d5bc3515c634cMark Dickinson 1780bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson e1 = -e1; 1781bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if ((i = e1 & 15)) 1782bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson dval(&rv) /= tens[i]; 1783bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (e1 >>= 4) { 1784bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (e1 >= 1 << n_bigtens) 1785bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson goto undfl; 1786bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (e1 & Scale_Bit) 1787bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson bc.scale = 2*P; 1788bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson for(j = 0; e1 > 0; j++, e1 >>= 1) 1789bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (e1 & 1) 1790bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson dval(&rv) *= tinytens[j]; 1791bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (bc.scale && (j = 2*P + 1 - ((word0(&rv) & Exp_mask) 1792bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson >> Exp_shift)) > 0) { 1793bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson /* scaled rv is denormal; clear j low bits */ 1794bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (j >= 32) { 1795bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson word1(&rv) = 0; 1796bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (j >= 53) 1797bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson word0(&rv) = (P+2)*Exp_msk1; 1798bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson else 1799bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson word0(&rv) &= 0xffffffff << (j-32); 1800bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 1801bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson else 1802bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson word1(&rv) &= 0xffffffff << j; 1803bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 18044141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson if (!dval(&rv)) 18054141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson goto undfl; 1806bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 1807bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 1808bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 1809bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson /* Now the hard part -- adjusting rv to the correct value.*/ 1810bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 1811bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson /* Put digits into bd: true value = bd * 10^e */ 1812bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 1813bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson bc.nd = nd; 18145a0b399aa9d75d4d208394d80b4997c164435ecbMark Dickinson bc.nd0 = nd0; /* Only needed if nd > STRTOD_DIGLIM, but done here */ 1815bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson /* to silence an erroneous warning about bc.nd0 */ 1816bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson /* possibly not being initialized. */ 18175a0b399aa9d75d4d208394d80b4997c164435ecbMark Dickinson if (nd > STRTOD_DIGLIM) { 18185a0b399aa9d75d4d208394d80b4997c164435ecbMark Dickinson /* ASSERT(STRTOD_DIGLIM >= 18); 18 == one more than the */ 1819bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson /* minimum number of decimal digits to distinguish double values */ 1820bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson /* in IEEE arithmetic. */ 1821476279f18b1bbcc5939f6bb7a10dd937c933cfb3Mark Dickinson 1822476279f18b1bbcc5939f6bb7a10dd937c933cfb3Mark Dickinson /* Truncate input to 18 significant digits, then discard any trailing 1823476279f18b1bbcc5939f6bb7a10dd937c933cfb3Mark Dickinson zeros on the result by updating nd, nd0, e and y suitably. (There's 1824476279f18b1bbcc5939f6bb7a10dd937c933cfb3Mark Dickinson no need to update z; it's not reused beyond this point.) */ 1825476279f18b1bbcc5939f6bb7a10dd937c933cfb3Mark Dickinson for (i = 18; i > 0; ) { 1826476279f18b1bbcc5939f6bb7a10dd937c933cfb3Mark Dickinson /* scan back until we hit a nonzero digit. significant digit 'i' 1827476279f18b1bbcc5939f6bb7a10dd937c933cfb3Mark Dickinson is s0[i] if i < nd0, s0[i+1] if i >= nd0. */ 1828bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson --i; 1829476279f18b1bbcc5939f6bb7a10dd937c933cfb3Mark Dickinson if (s0[i < nd0 ? i : i+1] != '0') { 1830476279f18b1bbcc5939f6bb7a10dd937c933cfb3Mark Dickinson ++i; 1831476279f18b1bbcc5939f6bb7a10dd937c933cfb3Mark Dickinson break; 1832476279f18b1bbcc5939f6bb7a10dd937c933cfb3Mark Dickinson } 1833bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 1834bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson e += nd - i; 1835bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson nd = i; 1836bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (nd0 > nd) 1837bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson nd0 = nd; 1838bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (nd < 9) { /* must recompute y */ 1839bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson y = 0; 1840bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson for(i = 0; i < nd0; ++i) 1841bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson y = 10*y + s0[i] - '0'; 1842476279f18b1bbcc5939f6bb7a10dd937c933cfb3Mark Dickinson for(; i < nd; ++i) 1843476279f18b1bbcc5939f6bb7a10dd937c933cfb3Mark Dickinson y = 10*y + s0[i+1] - '0'; 1844bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 1845bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 1846d2a9940acbe6a74cc83e371baf2ef7c580e308bcMark Dickinson bd0 = s2b(s0, nd0, nd, y); 1847bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (bd0 == NULL) 1848bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson goto failed_malloc; 1849bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 1850ca6ea567184941a62f49f911a16d5bc3515c634cMark Dickinson /* Notation for the comments below. Write: 1851ca6ea567184941a62f49f911a16d5bc3515c634cMark Dickinson 1852ca6ea567184941a62f49f911a16d5bc3515c634cMark Dickinson - dv for the absolute value of the number represented by the original 1853ca6ea567184941a62f49f911a16d5bc3515c634cMark Dickinson decimal input string. 1854ca6ea567184941a62f49f911a16d5bc3515c634cMark Dickinson 1855ca6ea567184941a62f49f911a16d5bc3515c634cMark Dickinson - if we've truncated dv, write tdv for the truncated value. 1856ca6ea567184941a62f49f911a16d5bc3515c634cMark Dickinson Otherwise, set tdv == dv. 1857ca6ea567184941a62f49f911a16d5bc3515c634cMark Dickinson 1858ca6ea567184941a62f49f911a16d5bc3515c634cMark Dickinson - srv for the quantity rv/2^bc.scale; so srv is the current binary 1859ca6ea567184941a62f49f911a16d5bc3515c634cMark Dickinson approximation to tdv (and dv). It should be exactly representable 1860ca6ea567184941a62f49f911a16d5bc3515c634cMark Dickinson in an IEEE 754 double. 1861ca6ea567184941a62f49f911a16d5bc3515c634cMark Dickinson */ 1862ca6ea567184941a62f49f911a16d5bc3515c634cMark Dickinson 1863bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson for(;;) { 1864ca6ea567184941a62f49f911a16d5bc3515c634cMark Dickinson 1865ca6ea567184941a62f49f911a16d5bc3515c634cMark Dickinson /* This is the main correction loop for _Py_dg_strtod. 1866ca6ea567184941a62f49f911a16d5bc3515c634cMark Dickinson 1867ca6ea567184941a62f49f911a16d5bc3515c634cMark Dickinson We've got a decimal value tdv, and a floating-point approximation 1868ca6ea567184941a62f49f911a16d5bc3515c634cMark Dickinson srv=rv/2^bc.scale to tdv. The aim is to determine whether srv is 1869ca6ea567184941a62f49f911a16d5bc3515c634cMark Dickinson close enough (i.e., within 0.5 ulps) to tdv, and to compute a new 1870ca6ea567184941a62f49f911a16d5bc3515c634cMark Dickinson approximation if not. 1871ca6ea567184941a62f49f911a16d5bc3515c634cMark Dickinson 1872ca6ea567184941a62f49f911a16d5bc3515c634cMark Dickinson To determine whether srv is close enough to tdv, compute integers 1873ca6ea567184941a62f49f911a16d5bc3515c634cMark Dickinson bd, bb and bs proportional to tdv, srv and 0.5 ulp(srv) 1874ca6ea567184941a62f49f911a16d5bc3515c634cMark Dickinson respectively, and then use integer arithmetic to determine whether 1875ca6ea567184941a62f49f911a16d5bc3515c634cMark Dickinson |tdv - srv| is less than, equal to, or greater than 0.5 ulp(srv). 1876ca6ea567184941a62f49f911a16d5bc3515c634cMark Dickinson */ 1877ca6ea567184941a62f49f911a16d5bc3515c634cMark Dickinson 1878bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson bd = Balloc(bd0->k); 1879bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (bd == NULL) { 1880bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson Bfree(bd0); 1881bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson goto failed_malloc; 1882bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 1883bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson Bcopy(bd, bd0); 1884adcda3400f8ae931139605b8d1fcfede4c1c6916Mark Dickinson bb = sd2b(&rv, bc.scale, &bbe); /* srv = bb * 2^bbe */ 1885bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (bb == NULL) { 1886bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson Bfree(bd); 1887bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson Bfree(bd0); 1888bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson goto failed_malloc; 1889bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 1890adcda3400f8ae931139605b8d1fcfede4c1c6916Mark Dickinson /* Record whether lsb of bb is odd, in case we need this 1891adcda3400f8ae931139605b8d1fcfede4c1c6916Mark Dickinson for the round-to-even step later. */ 1892adcda3400f8ae931139605b8d1fcfede4c1c6916Mark Dickinson odd = bb->x[0] & 1; 1893adcda3400f8ae931139605b8d1fcfede4c1c6916Mark Dickinson 1894adcda3400f8ae931139605b8d1fcfede4c1c6916Mark Dickinson /* tdv = bd * 10**e; srv = bb * 2**bbe */ 1895bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson bs = i2b(1); 1896bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (bs == NULL) { 1897bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson Bfree(bb); 1898bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson Bfree(bd); 1899bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson Bfree(bd0); 1900bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson goto failed_malloc; 1901bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 1902bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 1903bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (e >= 0) { 1904bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson bb2 = bb5 = 0; 1905bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson bd2 = bd5 = e; 1906bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 1907bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson else { 1908bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson bb2 = bb5 = -e; 1909bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson bd2 = bd5 = 0; 1910bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 1911bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (bbe >= 0) 1912bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson bb2 += bbe; 1913bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson else 1914bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson bd2 -= bbe; 1915bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson bs2 = bb2; 1916adcda3400f8ae931139605b8d1fcfede4c1c6916Mark Dickinson bb2++; 1917adcda3400f8ae931139605b8d1fcfede4c1c6916Mark Dickinson bd2++; 1918ca6ea567184941a62f49f911a16d5bc3515c634cMark Dickinson 1919adcda3400f8ae931139605b8d1fcfede4c1c6916Mark Dickinson /* At this stage bd5 - bb5 == e == bd2 - bb2 + bbe, bb2 - bs2 == 1, 1920c2f8c81af02519952a857baebb5c0c9048033009Mark Dickinson and bs == 1, so: 1921ca6ea567184941a62f49f911a16d5bc3515c634cMark Dickinson 1922adcda3400f8ae931139605b8d1fcfede4c1c6916Mark Dickinson tdv == bd * 10**e = bd * 2**(bbe - bb2 + bd2) * 5**(bd5 - bb5) 1923adcda3400f8ae931139605b8d1fcfede4c1c6916Mark Dickinson srv == bb * 2**bbe = bb * 2**(bbe - bb2 + bb2) 1924c2f8c81af02519952a857baebb5c0c9048033009Mark Dickinson 0.5 ulp(srv) == 2**(bbe-1) = bs * 2**(bbe - bb2 + bs2) 1925ca6ea567184941a62f49f911a16d5bc3515c634cMark Dickinson 1926c2f8c81af02519952a857baebb5c0c9048033009Mark Dickinson It follows that: 1927ca6ea567184941a62f49f911a16d5bc3515c634cMark Dickinson 1928adcda3400f8ae931139605b8d1fcfede4c1c6916Mark Dickinson M * tdv = bd * 2**bd2 * 5**bd5 1929adcda3400f8ae931139605b8d1fcfede4c1c6916Mark Dickinson M * srv = bb * 2**bb2 * 5**bb5 1930adcda3400f8ae931139605b8d1fcfede4c1c6916Mark Dickinson M * 0.5 ulp(srv) = bs * 2**bs2 * 5**bb5 1931ca6ea567184941a62f49f911a16d5bc3515c634cMark Dickinson 1932c2f8c81af02519952a857baebb5c0c9048033009Mark Dickinson for some constant M. (Actually, M == 2**(bb2 - bbe) * 5**bb5, but 1933c2f8c81af02519952a857baebb5c0c9048033009Mark Dickinson this fact is not needed below.) 1934adcda3400f8ae931139605b8d1fcfede4c1c6916Mark Dickinson */ 1935ca6ea567184941a62f49f911a16d5bc3515c634cMark Dickinson 1936adcda3400f8ae931139605b8d1fcfede4c1c6916Mark Dickinson /* Remove factor of 2**i, where i = min(bb2, bd2, bs2). */ 1937bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson i = bb2 < bd2 ? bb2 : bd2; 1938bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (i > bs2) 1939bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson i = bs2; 1940bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (i > 0) { 1941bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson bb2 -= i; 1942bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson bd2 -= i; 1943bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson bs2 -= i; 1944bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 1945ca6ea567184941a62f49f911a16d5bc3515c634cMark Dickinson 1946ca6ea567184941a62f49f911a16d5bc3515c634cMark Dickinson /* Scale bb, bd, bs by the appropriate powers of 2 and 5. */ 1947bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (bb5 > 0) { 1948bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson bs = pow5mult(bs, bb5); 1949bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (bs == NULL) { 1950bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson Bfree(bb); 1951bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson Bfree(bd); 1952bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson Bfree(bd0); 1953bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson goto failed_malloc; 1954bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 1955bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson bb1 = mult(bs, bb); 1956bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson Bfree(bb); 1957bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson bb = bb1; 1958bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (bb == NULL) { 1959bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson Bfree(bs); 1960bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson Bfree(bd); 1961bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson Bfree(bd0); 1962bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson goto failed_malloc; 1963bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 1964bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 1965bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (bb2 > 0) { 1966bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson bb = lshift(bb, bb2); 1967bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (bb == NULL) { 1968bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson Bfree(bs); 1969bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson Bfree(bd); 1970bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson Bfree(bd0); 1971bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson goto failed_malloc; 1972bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 1973bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 1974bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (bd5 > 0) { 1975bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson bd = pow5mult(bd, bd5); 1976bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (bd == NULL) { 1977bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson Bfree(bb); 1978bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson Bfree(bs); 1979bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson Bfree(bd0); 1980bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson goto failed_malloc; 1981bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 1982bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 1983bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (bd2 > 0) { 1984bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson bd = lshift(bd, bd2); 1985bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (bd == NULL) { 1986bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson Bfree(bb); 1987bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson Bfree(bs); 1988bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson Bfree(bd0); 1989bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson goto failed_malloc; 1990bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 1991bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 1992bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (bs2 > 0) { 1993bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson bs = lshift(bs, bs2); 1994bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (bs == NULL) { 1995bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson Bfree(bb); 1996bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson Bfree(bd); 1997bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson Bfree(bd0); 1998bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson goto failed_malloc; 1999bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 2000bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 2001ca6ea567184941a62f49f911a16d5bc3515c634cMark Dickinson 2002ca6ea567184941a62f49f911a16d5bc3515c634cMark Dickinson /* Now bd, bb and bs are scaled versions of tdv, srv and 0.5 ulp(srv), 2003ca6ea567184941a62f49f911a16d5bc3515c634cMark Dickinson respectively. Compute the difference |tdv - srv|, and compare 2004ca6ea567184941a62f49f911a16d5bc3515c634cMark Dickinson with 0.5 ulp(srv). */ 2005ca6ea567184941a62f49f911a16d5bc3515c634cMark Dickinson 2006bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson delta = diff(bb, bd); 2007bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (delta == NULL) { 2008bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson Bfree(bb); 2009bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson Bfree(bs); 2010bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson Bfree(bd); 2011bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson Bfree(bd0); 2012bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson goto failed_malloc; 2013bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 20144141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson dsign = delta->sign; 2015bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson delta->sign = 0; 2016bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson i = cmp(delta, bs); 2017bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (bc.nd > nd && i <= 0) { 20184141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson if (dsign) 2019bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson break; /* Must use bigcomp(). */ 2020f8747c1f12577a4198d47f28eaf89a2983a13261Mark Dickinson 2021f8747c1f12577a4198d47f28eaf89a2983a13261Mark Dickinson /* Here rv overestimates the truncated decimal value by at most 2022f8747c1f12577a4198d47f28eaf89a2983a13261Mark Dickinson 0.5 ulp(rv). Hence rv either overestimates the true decimal 2023f8747c1f12577a4198d47f28eaf89a2983a13261Mark Dickinson value by <= 0.5 ulp(rv), or underestimates it by some small 2024f8747c1f12577a4198d47f28eaf89a2983a13261Mark Dickinson amount (< 0.1 ulp(rv)); either way, rv is within 0.5 ulps of 2025f8747c1f12577a4198d47f28eaf89a2983a13261Mark Dickinson the true decimal value, so it's possible to exit. 2026f8747c1f12577a4198d47f28eaf89a2983a13261Mark Dickinson 2027f8747c1f12577a4198d47f28eaf89a2983a13261Mark Dickinson Exception: if scaled rv is a normal exact power of 2, but not 2028f8747c1f12577a4198d47f28eaf89a2983a13261Mark Dickinson DBL_MIN, then rv - 0.5 ulp(rv) takes us all the way down to the 2029f8747c1f12577a4198d47f28eaf89a2983a13261Mark Dickinson next double, so the correctly rounded result is either rv - 0.5 2030f8747c1f12577a4198d47f28eaf89a2983a13261Mark Dickinson ulp(rv) or rv; in this case, use bigcomp to distinguish. */ 2031f8747c1f12577a4198d47f28eaf89a2983a13261Mark Dickinson 2032f8747c1f12577a4198d47f28eaf89a2983a13261Mark Dickinson if (!word1(&rv) && !(word0(&rv) & Bndry_mask)) { 2033f8747c1f12577a4198d47f28eaf89a2983a13261Mark Dickinson /* rv can't be 0, since it's an overestimate for some 2034f8747c1f12577a4198d47f28eaf89a2983a13261Mark Dickinson nonzero value. So rv is a normal power of 2. */ 2035f8747c1f12577a4198d47f28eaf89a2983a13261Mark Dickinson j = (int)(word0(&rv) & Exp_mask) >> Exp_shift; 2036f8747c1f12577a4198d47f28eaf89a2983a13261Mark Dickinson /* rv / 2^bc.scale = 2^(j - 1023 - bc.scale); use bigcomp if 2037f8747c1f12577a4198d47f28eaf89a2983a13261Mark Dickinson rv / 2^bc.scale >= 2^-1021. */ 2038f8747c1f12577a4198d47f28eaf89a2983a13261Mark Dickinson if (j - bc.scale >= 2) { 2039f8747c1f12577a4198d47f28eaf89a2983a13261Mark Dickinson dval(&rv) -= 0.5 * sulp(&rv, &bc); 20404141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson break; /* Use bigcomp. */ 2041f8747c1f12577a4198d47f28eaf89a2983a13261Mark Dickinson } 2042f8747c1f12577a4198d47f28eaf89a2983a13261Mark Dickinson } 2043f8747c1f12577a4198d47f28eaf89a2983a13261Mark Dickinson 2044bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson { 2045bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson bc.nd = nd; 2046bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson i = -1; /* Discarded digits make delta smaller. */ 2047bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 2048bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 2049bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 2050bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (i < 0) { 2051bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson /* Error is less than half an ulp -- check for 2052bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * special case of mantissa a power of two. 2053bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson */ 20544141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson if (dsign || word1(&rv) || word0(&rv) & Bndry_mask 2055bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson || (word0(&rv) & Exp_mask) <= (2*P+1)*Exp_msk1 2056bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson ) { 2057bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson break; 2058bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 2059bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (!delta->x[0] && delta->wds <= 1) { 2060bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson /* exact result */ 2061bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson break; 2062bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 2063bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson delta = lshift(delta,Log2P); 2064bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (delta == NULL) { 2065bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson Bfree(bb); 2066bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson Bfree(bs); 2067bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson Bfree(bd); 2068bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson Bfree(bd0); 2069bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson goto failed_malloc; 2070bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 2071bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (cmp(delta, bs) > 0) 2072bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson goto drop_down; 2073bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson break; 2074bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 2075bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (i == 0) { 2076bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson /* exactly half-way between */ 20774141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson if (dsign) { 2078bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if ((word0(&rv) & Bndry_mask1) == Bndry_mask1 2079bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson && word1(&rv) == ( 2080bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson (bc.scale && 2081bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson (y = word0(&rv) & Exp_mask) <= 2*P*Exp_msk1) ? 2082bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson (0xffffffff & (0xffffffff << (2*P+1-(y>>Exp_shift)))) : 2083bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 0xffffffff)) { 2084bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson /*boundary case -- increment exponent*/ 2085bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson word0(&rv) = (word0(&rv) & Exp_mask) 2086bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson + Exp_msk1 2087bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson ; 2088bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson word1(&rv) = 0; 20894141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson dsign = 0; 2090bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson break; 2091bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 2092bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 2093bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson else if (!(word0(&rv) & Bndry_mask) && !word1(&rv)) { 2094bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson drop_down: 2095bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson /* boundary case -- decrement exponent */ 2096bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (bc.scale) { 2097bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson L = word0(&rv) & Exp_mask; 2098bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (L <= (2*P+1)*Exp_msk1) { 2099bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (L > (P+2)*Exp_msk1) 2100bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson /* round even ==> */ 2101bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson /* accept rv */ 2102bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson break; 2103bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson /* rv = smallest denormal */ 21044141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson if (bc.nd > nd) 2105bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson break; 2106bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson goto undfl; 2107bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 2108bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 2109bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson L = (word0(&rv) & Exp_mask) - Exp_msk1; 2110bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson word0(&rv) = L | Bndry_mask1; 2111bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson word1(&rv) = 0xffffffff; 2112bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson break; 2113bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 2114adcda3400f8ae931139605b8d1fcfede4c1c6916Mark Dickinson if (!odd) 2115bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson break; 21164141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson if (dsign) 21178cd0a66a0fd7bb7d69153906942930c2e8c3dd17Mark Dickinson dval(&rv) += sulp(&rv, &bc); 2118bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson else { 21198cd0a66a0fd7bb7d69153906942930c2e8c3dd17Mark Dickinson dval(&rv) -= sulp(&rv, &bc); 2120bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (!dval(&rv)) { 21215a0b399aa9d75d4d208394d80b4997c164435ecbMark Dickinson if (bc.nd >nd) 2122bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson break; 2123bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson goto undfl; 2124bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 2125bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 21264141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson dsign = 1 - dsign; 2127bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson break; 2128bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 2129bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if ((aadj = ratio(delta, bs)) <= 2.) { 21304141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson if (dsign) 2131bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson aadj = aadj1 = 1.; 2132bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson else if (word1(&rv) || word0(&rv) & Bndry_mask) { 2133bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (word1(&rv) == Tiny1 && !word0(&rv)) { 21345a0b399aa9d75d4d208394d80b4997c164435ecbMark Dickinson if (bc.nd >nd) 2135bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson break; 2136bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson goto undfl; 2137bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 2138bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson aadj = 1.; 2139bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson aadj1 = -1.; 2140bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 2141bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson else { 2142bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson /* special case -- power of FLT_RADIX to be */ 2143bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson /* rounded down... */ 2144bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 2145bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (aadj < 2./FLT_RADIX) 2146bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson aadj = 1./FLT_RADIX; 2147bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson else 2148bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson aadj *= 0.5; 2149bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson aadj1 = -aadj; 2150bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 2151bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 2152bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson else { 2153bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson aadj *= 0.5; 21544141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson aadj1 = dsign ? aadj : -aadj; 2155bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (Flt_Rounds == 0) 2156bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson aadj1 += 0.5; 2157bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 2158bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson y = word0(&rv) & Exp_mask; 2159bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 2160bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson /* Check for overflow */ 2161bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 2162bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (y == Exp_msk1*(DBL_MAX_EXP+Bias-1)) { 2163bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson dval(&rv0) = dval(&rv); 2164bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson word0(&rv) -= P*Exp_msk1; 2165bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson adj.d = aadj1 * ulp(&rv); 2166bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson dval(&rv) += adj.d; 2167bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if ((word0(&rv) & Exp_mask) >= 2168bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson Exp_msk1*(DBL_MAX_EXP+Bias-P)) { 216923df3d270d3572c43638d15b63684405b66887f7Mark Dickinson if (word0(&rv0) == Big0 && word1(&rv0) == Big1) { 217023df3d270d3572c43638d15b63684405b66887f7Mark Dickinson Bfree(bb); 217123df3d270d3572c43638d15b63684405b66887f7Mark Dickinson Bfree(bd); 217223df3d270d3572c43638d15b63684405b66887f7Mark Dickinson Bfree(bs); 217323df3d270d3572c43638d15b63684405b66887f7Mark Dickinson Bfree(bd0); 217423df3d270d3572c43638d15b63684405b66887f7Mark Dickinson Bfree(delta); 2175bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson goto ovfl; 217623df3d270d3572c43638d15b63684405b66887f7Mark Dickinson } 2177bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson word0(&rv) = Big0; 2178bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson word1(&rv) = Big1; 2179bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson goto cont; 2180bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 2181bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson else 2182bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson word0(&rv) += P*Exp_msk1; 2183bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 2184bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson else { 2185bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (bc.scale && y <= 2*P*Exp_msk1) { 2186bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (aadj <= 0x7fffffff) { 2187bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if ((z = (ULong)aadj) <= 0) 2188bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson z = 1; 2189bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson aadj = z; 21904141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson aadj1 = dsign ? aadj : -aadj; 2191bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 2192bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson dval(&aadj2) = aadj1; 2193bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson word0(&aadj2) += (2*P+1)*Exp_msk1 - y; 2194bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson aadj1 = dval(&aadj2); 2195bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 2196bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson adj.d = aadj1 * ulp(&rv); 2197bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson dval(&rv) += adj.d; 2198bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 2199bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson z = word0(&rv) & Exp_mask; 2200bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (bc.nd == nd) { 2201bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (!bc.scale) 2202bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (y == z) { 2203bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson /* Can we stop now? */ 2204bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson L = (Long)aadj; 2205bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson aadj -= L; 2206bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson /* The tolerances below are conservative. */ 22074141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson if (dsign || word1(&rv) || word0(&rv) & Bndry_mask) { 2208bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (aadj < .4999999 || aadj > .5000001) 2209bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson break; 2210bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 2211bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson else if (aadj < .4999999/FLT_RADIX) 2212bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson break; 2213bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 2214bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 2215bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson cont: 2216bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson Bfree(bb); 2217bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson Bfree(bd); 2218bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson Bfree(bs); 2219bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson Bfree(delta); 2220bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 2221bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson Bfree(bb); 2222bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson Bfree(bd); 2223bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson Bfree(bs); 2224bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson Bfree(bd0); 2225bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson Bfree(delta); 2226bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (bc.nd > nd) { 2227bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson error = bigcomp(&rv, s0, &bc); 2228bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (error) 2229bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson goto failed_malloc; 2230bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 2231bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 2232bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (bc.scale) { 2233bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson word0(&rv0) = Exp_1 - 2*P*Exp_msk1; 2234bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson word1(&rv0) = 0; 2235bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson dval(&rv) *= dval(&rv0); 2236bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 22374141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson 2238bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson ret: 2239bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson return sign ? -dval(&rv) : dval(&rv); 2240bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 22414141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson parse_error: 22424141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson return 0.0; 22434141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson 2244bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson failed_malloc: 2245bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson errno = ENOMEM; 2246bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson return -1.0; 22474141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson 22484141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson undfl: 22494141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson return sign ? -0.0 : 0.0; 22504141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson 22514141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson ovfl: 22524141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson errno = ERANGE; 22534141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson /* Can't trust HUGE_VAL */ 22544141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson word0(&rv) = Exp_mask; 22554141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson word1(&rv) = 0; 22564141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson return sign ? -dval(&rv) : dval(&rv); 22574141d65fb7eacccee58b2fa462b56a2410e67777Mark Dickinson 2258bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson} 2259bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 2260bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinsonstatic char * 2261bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinsonrv_alloc(int i) 2262bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson{ 2263bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson int j, k, *r; 2264bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 2265bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson j = sizeof(ULong); 2266bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson for(k = 0; 2267bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson sizeof(Bigint) - sizeof(ULong) - sizeof(int) + j <= (unsigned)i; 2268bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson j <<= 1) 2269bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson k++; 2270bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson r = (int*)Balloc(k); 2271bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (r == NULL) 2272bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson return NULL; 2273bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson *r = k; 2274bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson return (char *)(r+1); 2275bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson} 2276bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 2277bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinsonstatic char * 2278bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinsonnrv_alloc(char *s, char **rve, int n) 2279bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson{ 2280bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson char *rv, *t; 2281bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 2282bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson rv = rv_alloc(n); 2283bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (rv == NULL) 2284bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson return NULL; 2285bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson t = rv; 2286bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson while((*t = *s++)) t++; 2287bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (rve) 2288bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson *rve = t; 2289bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson return rv; 2290bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson} 2291bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 2292bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson/* freedtoa(s) must be used to free values s returned by dtoa 2293bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * when MULTIPLE_THREADS is #defined. It should be used in all cases, 2294bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * but for consistency with earlier versions of dtoa, it is optional 2295bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * when MULTIPLE_THREADS is not defined. 2296bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson */ 2297bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 2298bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinsonvoid 2299bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson_Py_dg_freedtoa(char *s) 2300bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson{ 2301bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson Bigint *b = (Bigint *)((int *)s - 1); 2302bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson b->maxwds = 1 << (b->k = *(int*)b); 2303bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson Bfree(b); 2304bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson} 2305bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 2306bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson/* dtoa for IEEE arithmetic (dmg): convert double to ASCII string. 2307bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * 2308bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * Inspired by "How to Print Floating-Point Numbers Accurately" by 2309bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * Guy L. Steele, Jr. and Jon L. White [Proc. ACM SIGPLAN '90, pp. 112-126]. 2310bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * 2311bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * Modifications: 2312bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * 1. Rather than iterating, we use a simple numeric overestimate 2313bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * to determine k = floor(log10(d)). We scale relevant 2314bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * quantities using O(log2(k)) rather than O(k) multiplications. 2315bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * 2. For some modes > 2 (corresponding to ecvt and fcvt), we don't 2316bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * try to generate digits strictly left to right. Instead, we 2317bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * compute with fewer bits and propagate the carry if necessary 2318bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * when rounding the final digit up. This is often faster. 2319bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * 3. Under the assumption that input will be rounded nearest, 2320bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * mode 0 renders 1e23 as 1e23 rather than 9.999999999999999e22. 2321bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * That is, we allow equality in stopping tests when the 2322bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * round-nearest rule will give the same floating-point value 2323bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * as would satisfaction of the stopping test with strict 2324bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * inequality. 2325bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * 4. We remove common factors of powers of 2 from relevant 2326bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * quantities. 2327bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * 5. When converting floating-point integers less than 1e16, 2328bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * we use floating-point arithmetic rather than resorting 2329bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * to multiple-precision integers. 2330bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * 6. When asked to produce fewer than 15 digits, we first try 2331bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * to get by with floating-point arithmetic; we resort to 2332bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * multiple-precision integer arithmetic only if we cannot 2333bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * guarantee that the floating-point calculation has given 2334bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * the correctly rounded result. For k requested digits and 2335bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * "uniformly" distributed input, the probability is 2336bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * something like 10^(k-15) that we must resort to the Long 2337bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * calculation. 2338bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson */ 2339bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 2340bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson/* Additional notes (METD): (1) returns NULL on failure. (2) to avoid memory 2341bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson leakage, a successful call to _Py_dg_dtoa should always be matched by a 2342bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson call to _Py_dg_freedtoa. */ 2343bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 2344bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinsonchar * 2345bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson_Py_dg_dtoa(double dd, int mode, int ndigits, 2346bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson int *decpt, int *sign, char **rve) 2347bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson{ 2348bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson /* Arguments ndigits, decpt, sign are similar to those 2349bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson of ecvt and fcvt; trailing zeros are suppressed from 2350bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson the returned string. If not null, *rve is set to point 2351bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson to the end of the return value. If d is +-Infinity or NaN, 2352bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson then *decpt is set to 9999. 2353bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 2354bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson mode: 2355bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 0 ==> shortest string that yields d when read in 2356bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson and rounded to nearest. 2357bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 1 ==> like 0, but with Steele & White stopping rule; 2358bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson e.g. with IEEE P754 arithmetic , mode 0 gives 2359bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 1e23 whereas mode 1 gives 9.999999999999999e22. 2360bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 2 ==> max(1,ndigits) significant digits. This gives a 2361bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson return value similar to that of ecvt, except 2362bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson that trailing zeros are suppressed. 2363bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 3 ==> through ndigits past the decimal point. This 2364bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson gives a return value similar to that from fcvt, 2365bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson except that trailing zeros are suppressed, and 2366bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson ndigits can be negative. 2367bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 4,5 ==> similar to 2 and 3, respectively, but (in 2368bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson round-nearest mode) with the tests of mode 0 to 2369bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson possibly return a shorter string that rounds to d. 2370bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson With IEEE arithmetic and compilation with 2371bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson -DHonor_FLT_ROUNDS, modes 4 and 5 behave the same 2372bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson as modes 2 and 3 when FLT_ROUNDS != 1. 2373bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 6-9 ==> Debugging modes similar to mode - 4: don't try 2374bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson fast floating-point estimate (if applicable). 2375bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 2376bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson Values of mode other than 0-9 are treated as mode 0. 2377bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 2378bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson Sufficient space is allocated to the return value 2379bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson to hold the suppressed trailing zeros. 2380bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson */ 2381bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 2382bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson int bbits, b2, b5, be, dig, i, ieps, ilim, ilim0, ilim1, 2383bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson j, j1, k, k0, k_check, leftright, m2, m5, s2, s5, 2384bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson spec_case, try_quick; 2385bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson Long L; 2386bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson int denorm; 2387bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson ULong x; 2388bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson Bigint *b, *b1, *delta, *mlo, *mhi, *S; 2389bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson U d2, eps, u; 2390bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson double ds; 2391bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson char *s, *s0; 2392bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 2393bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson /* set pointers to NULL, to silence gcc compiler warnings and make 2394bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson cleanup easier on error */ 23950b03f10afb301560c711b953b6ca2ecef3181eedBrett Cannon mlo = mhi = S = 0; 2396bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson s0 = 0; 2397bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 2398bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson u.d = dd; 2399bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (word0(&u) & Sign_bit) { 2400bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson /* set sign for everything, including 0's and NaNs */ 2401bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson *sign = 1; 2402bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson word0(&u) &= ~Sign_bit; /* clear sign bit */ 2403bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 2404bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson else 2405bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson *sign = 0; 2406bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 2407bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson /* quick return for Infinities, NaNs and zeros */ 2408bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if ((word0(&u) & Exp_mask) == Exp_mask) 2409bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson { 2410bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson /* Infinity or NaN */ 2411bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson *decpt = 9999; 2412bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (!word1(&u) && !(word0(&u) & 0xfffff)) 2413bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson return nrv_alloc("Infinity", rve, 8); 2414bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson return nrv_alloc("NaN", rve, 3); 2415bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 2416bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (!dval(&u)) { 2417bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson *decpt = 1; 2418bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson return nrv_alloc("0", rve, 1); 2419bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 2420bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 2421bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson /* compute k = floor(log10(d)). The computation may leave k 2422bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson one too large, but should never leave k too small. */ 2423bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson b = d2b(&u, &be, &bbits); 2424bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (b == NULL) 2425bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson goto failed_malloc; 2426bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if ((i = (int)(word0(&u) >> Exp_shift1 & (Exp_mask>>Exp_shift1)))) { 2427bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson dval(&d2) = dval(&u); 2428bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson word0(&d2) &= Frac_mask1; 2429bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson word0(&d2) |= Exp_11; 2430bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 2431bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson /* log(x) ~=~ log(1.5) + (x-1.5)/1.5 2432bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * log10(x) = log(x) / log(10) 2433bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * ~=~ log(1.5)/log(10) + (x-1.5)/(1.5*log(10)) 2434bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * log10(d) = (i-Bias)*log(2)/log(10) + log10(d2) 2435bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * 2436bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * This suggests computing an approximation k to log10(d) by 2437bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * 2438bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * k = (i - Bias)*0.301029995663981 2439bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * + ( (d2-1.5)*0.289529654602168 + 0.176091259055681 ); 2440bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * 2441bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * We want k to be too large rather than too small. 2442bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * The error in the first-order Taylor series approximation 2443bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * is in our favor, so we just round up the constant enough 2444bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * to compensate for any error in the multiplication of 2445bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * (i - Bias) by 0.301029995663981; since |i - Bias| <= 1077, 2446bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * and 1077 * 0.30103 * 2^-52 ~=~ 7.2e-14, 2447bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * adding 1e-13 to the constant term more than suffices. 2448bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * Hence we adjust the constant term to 0.1760912590558. 2449bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * (We could get a more accurate k by invoking log10, 2450bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * but this is probably not worthwhile.) 2451bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson */ 2452bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 2453bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson i -= Bias; 2454bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson denorm = 0; 2455bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 2456bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson else { 2457bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson /* d is denormalized */ 2458bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 2459bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson i = bbits + be + (Bias + (P-1) - 1); 2460bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson x = i > 32 ? word0(&u) << (64 - i) | word1(&u) >> (i - 32) 2461bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson : word1(&u) << (32 - i); 2462bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson dval(&d2) = x; 2463bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson word0(&d2) -= 31*Exp_msk1; /* adjust exponent */ 2464bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson i -= (Bias + (P-1) - 1) + 1; 2465bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson denorm = 1; 2466bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 2467bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson ds = (dval(&d2)-1.5)*0.289529654602168 + 0.1760912590558 + 2468bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson i*0.301029995663981; 2469bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson k = (int)ds; 2470bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (ds < 0. && ds != k) 2471bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson k--; /* want k = floor(ds) */ 2472bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson k_check = 1; 2473bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (k >= 0 && k <= Ten_pmax) { 2474bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (dval(&u) < tens[k]) 2475bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson k--; 2476bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson k_check = 0; 2477bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 2478bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson j = bbits - i - 1; 2479bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (j >= 0) { 2480bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson b2 = 0; 2481bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson s2 = j; 2482bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 2483bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson else { 2484bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson b2 = -j; 2485bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson s2 = 0; 2486bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 2487bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (k >= 0) { 2488bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson b5 = 0; 2489bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson s5 = k; 2490bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson s2 += k; 2491bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 2492bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson else { 2493bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson b2 -= k; 2494bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson b5 = -k; 2495bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson s5 = 0; 2496bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 2497bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (mode < 0 || mode > 9) 2498bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson mode = 0; 2499bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 2500bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson try_quick = 1; 2501bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 2502bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (mode > 5) { 2503bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson mode -= 4; 2504bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson try_quick = 0; 2505bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 2506bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson leftright = 1; 2507bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson ilim = ilim1 = -1; /* Values for cases 0 and 1; done here to */ 2508bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson /* silence erroneous "gcc -Wall" warning. */ 2509bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson switch(mode) { 2510bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson case 0: 2511bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson case 1: 2512bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson i = 18; 2513bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson ndigits = 0; 2514bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson break; 2515bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson case 2: 2516bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson leftright = 0; 2517bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson /* no break */ 2518bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson case 4: 2519bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (ndigits <= 0) 2520bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson ndigits = 1; 2521bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson ilim = ilim1 = i = ndigits; 2522bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson break; 2523bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson case 3: 2524bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson leftright = 0; 2525bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson /* no break */ 2526bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson case 5: 2527bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson i = ndigits + k + 1; 2528bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson ilim = i; 2529bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson ilim1 = i - 1; 2530bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (i <= 0) 2531bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson i = 1; 2532bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 2533bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson s0 = rv_alloc(i); 2534bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (s0 == NULL) 2535bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson goto failed_malloc; 2536bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson s = s0; 2537bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 2538bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 2539bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (ilim >= 0 && ilim <= Quick_max && try_quick) { 2540bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 2541bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson /* Try to get by with floating-point arithmetic. */ 2542bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 2543bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson i = 0; 2544bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson dval(&d2) = dval(&u); 2545bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson k0 = k; 2546bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson ilim0 = ilim; 2547bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson ieps = 2; /* conservative */ 2548bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (k > 0) { 2549bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson ds = tens[k&0xf]; 2550bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson j = k >> 4; 2551bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (j & Bletch) { 2552bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson /* prevent overflows */ 2553bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson j &= Bletch - 1; 2554bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson dval(&u) /= bigtens[n_bigtens-1]; 2555bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson ieps++; 2556bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 2557bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson for(; j; j >>= 1, i++) 2558bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (j & 1) { 2559bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson ieps++; 2560bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson ds *= bigtens[i]; 2561bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 2562bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson dval(&u) /= ds; 2563bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 2564bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson else if ((j1 = -k)) { 2565bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson dval(&u) *= tens[j1 & 0xf]; 2566bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson for(j = j1 >> 4; j; j >>= 1, i++) 2567bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (j & 1) { 2568bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson ieps++; 2569bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson dval(&u) *= bigtens[i]; 2570bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 2571bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 2572bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (k_check && dval(&u) < 1. && ilim > 0) { 2573bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (ilim1 <= 0) 2574bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson goto fast_failed; 2575bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson ilim = ilim1; 2576bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson k--; 2577bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson dval(&u) *= 10.; 2578bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson ieps++; 2579bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 2580bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson dval(&eps) = ieps*dval(&u) + 7.; 2581bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson word0(&eps) -= (P-1)*Exp_msk1; 2582bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (ilim == 0) { 2583bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson S = mhi = 0; 2584bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson dval(&u) -= 5.; 2585bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (dval(&u) > dval(&eps)) 2586bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson goto one_digit; 2587bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (dval(&u) < -dval(&eps)) 2588bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson goto no_digits; 2589bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson goto fast_failed; 2590bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 2591bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (leftright) { 2592bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson /* Use Steele & White method of only 2593bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * generating digits needed. 2594bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson */ 2595bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson dval(&eps) = 0.5/tens[ilim-1] - dval(&eps); 2596bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson for(i = 0;;) { 2597bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson L = (Long)dval(&u); 2598bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson dval(&u) -= L; 2599bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson *s++ = '0' + (int)L; 2600bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (dval(&u) < dval(&eps)) 2601bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson goto ret1; 2602bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (1. - dval(&u) < dval(&eps)) 2603bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson goto bump_up; 2604bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (++i >= ilim) 2605bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson break; 2606bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson dval(&eps) *= 10.; 2607bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson dval(&u) *= 10.; 2608bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 2609bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 2610bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson else { 2611bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson /* Generate ilim digits, then fix them up. */ 2612bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson dval(&eps) *= tens[ilim-1]; 2613bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson for(i = 1;; i++, dval(&u) *= 10.) { 2614bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson L = (Long)(dval(&u)); 2615bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (!(dval(&u) -= L)) 2616bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson ilim = i; 2617bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson *s++ = '0' + (int)L; 2618bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (i == ilim) { 2619bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (dval(&u) > 0.5 + dval(&eps)) 2620bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson goto bump_up; 2621bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson else if (dval(&u) < 0.5 - dval(&eps)) { 2622bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson while(*--s == '0'); 2623bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson s++; 2624bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson goto ret1; 2625bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 2626bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson break; 2627bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 2628bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 2629bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 2630bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson fast_failed: 2631bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson s = s0; 2632bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson dval(&u) = dval(&d2); 2633bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson k = k0; 2634bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson ilim = ilim0; 2635bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 2636bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 2637bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson /* Do we have a "small" integer? */ 2638bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 2639bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (be >= 0 && k <= Int_max) { 2640bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson /* Yes. */ 2641bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson ds = tens[k]; 2642bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (ndigits < 0 && ilim <= 0) { 2643bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson S = mhi = 0; 2644bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (ilim < 0 || dval(&u) <= 5*ds) 2645bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson goto no_digits; 2646bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson goto one_digit; 2647bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 2648bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson for(i = 1;; i++, dval(&u) *= 10.) { 2649bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson L = (Long)(dval(&u) / ds); 2650bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson dval(&u) -= L*ds; 2651bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson *s++ = '0' + (int)L; 2652bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (!dval(&u)) { 2653bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson break; 2654bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 2655bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (i == ilim) { 2656bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson dval(&u) += dval(&u); 2657bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (dval(&u) > ds || (dval(&u) == ds && L & 1)) { 2658bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson bump_up: 2659bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson while(*--s == '9') 2660bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (s == s0) { 2661bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson k++; 2662bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson *s = '0'; 2663bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson break; 2664bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 2665bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson ++*s++; 2666bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 2667bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson break; 2668bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 2669bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 2670bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson goto ret1; 2671bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 2672bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 2673bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson m2 = b2; 2674bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson m5 = b5; 2675bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (leftright) { 2676bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson i = 2677bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson denorm ? be + (Bias + (P-1) - 1 + 1) : 2678bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 1 + P - bbits; 2679bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson b2 += i; 2680bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson s2 += i; 2681bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson mhi = i2b(1); 2682bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (mhi == NULL) 2683bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson goto failed_malloc; 2684bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 2685bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (m2 > 0 && s2 > 0) { 2686bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson i = m2 < s2 ? m2 : s2; 2687bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson b2 -= i; 2688bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson m2 -= i; 2689bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson s2 -= i; 2690bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 2691bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (b5 > 0) { 2692bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (leftright) { 2693bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (m5 > 0) { 2694bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson mhi = pow5mult(mhi, m5); 2695bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (mhi == NULL) 2696bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson goto failed_malloc; 2697bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson b1 = mult(mhi, b); 2698bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson Bfree(b); 2699bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson b = b1; 2700bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (b == NULL) 2701bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson goto failed_malloc; 2702bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 2703bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if ((j = b5 - m5)) { 2704bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson b = pow5mult(b, j); 2705bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (b == NULL) 2706bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson goto failed_malloc; 2707bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 2708bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 2709bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson else { 2710bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson b = pow5mult(b, b5); 2711bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (b == NULL) 2712bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson goto failed_malloc; 2713bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 2714bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 2715bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson S = i2b(1); 2716bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (S == NULL) 2717bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson goto failed_malloc; 2718bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (s5 > 0) { 2719bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson S = pow5mult(S, s5); 2720bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (S == NULL) 2721bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson goto failed_malloc; 2722bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 2723bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 2724bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson /* Check for special case that d is a normalized power of 2. */ 2725bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 2726bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson spec_case = 0; 2727bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if ((mode < 2 || leftright) 2728bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson ) { 2729bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (!word1(&u) && !(word0(&u) & Bndry_mask) 2730bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson && word0(&u) & (Exp_mask & ~Exp_msk1) 2731bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson ) { 2732bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson /* The special case */ 2733bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson b2 += Log2P; 2734bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson s2 += Log2P; 2735bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson spec_case = 1; 2736bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 2737bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 2738bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 2739bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson /* Arrange for convenient computation of quotients: 2740bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * shift left if necessary so divisor has 4 leading 0 bits. 2741bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * 2742bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * Perhaps we should just compute leading 28 bits of S once 2743bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * and for all and pass them and a shift to quorem, so it 2744bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * can do shifts and ors to compute the numerator for q. 2745bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson */ 2746bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#define iInc 28 2747bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson i = dshift(S, s2); 2748bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson b2 += i; 2749bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson m2 += i; 2750bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson s2 += i; 2751bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (b2 > 0) { 2752bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson b = lshift(b, b2); 2753bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (b == NULL) 2754bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson goto failed_malloc; 2755bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 2756bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (s2 > 0) { 2757bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson S = lshift(S, s2); 2758bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (S == NULL) 2759bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson goto failed_malloc; 2760bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 2761bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (k_check) { 2762bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (cmp(b,S) < 0) { 2763bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson k--; 2764bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson b = multadd(b, 10, 0); /* we botched the k estimate */ 2765bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (b == NULL) 2766bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson goto failed_malloc; 2767bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (leftright) { 2768bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson mhi = multadd(mhi, 10, 0); 2769bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (mhi == NULL) 2770bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson goto failed_malloc; 2771bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 2772bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson ilim = ilim1; 2773bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 2774bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 2775bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (ilim <= 0 && (mode == 3 || mode == 5)) { 2776bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (ilim < 0) { 2777bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson /* no digits, fcvt style */ 2778bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson no_digits: 2779bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson k = -1 - ndigits; 2780bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson goto ret; 2781bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 2782bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson else { 2783bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson S = multadd(S, 5, 0); 2784bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (S == NULL) 2785bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson goto failed_malloc; 2786bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (cmp(b, S) <= 0) 2787bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson goto no_digits; 2788bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 2789bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson one_digit: 2790bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson *s++ = '1'; 2791bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson k++; 2792bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson goto ret; 2793bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 2794bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (leftright) { 2795bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (m2 > 0) { 2796bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson mhi = lshift(mhi, m2); 2797bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (mhi == NULL) 2798bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson goto failed_malloc; 2799bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 2800bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 2801bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson /* Compute mlo -- check for special case 2802bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * that d is a normalized power of 2. 2803bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson */ 2804bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 2805bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson mlo = mhi; 2806bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (spec_case) { 2807bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson mhi = Balloc(mhi->k); 2808bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (mhi == NULL) 2809bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson goto failed_malloc; 2810bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson Bcopy(mhi, mlo); 2811bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson mhi = lshift(mhi, Log2P); 2812bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (mhi == NULL) 2813bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson goto failed_malloc; 2814bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 2815bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 2816bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson for(i = 1;;i++) { 2817bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson dig = quorem(b,S) + '0'; 2818bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson /* Do we yet have the shortest decimal string 2819bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson * that will round to d? 2820bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson */ 2821bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson j = cmp(b, mlo); 2822bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson delta = diff(S, mhi); 2823bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (delta == NULL) 2824bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson goto failed_malloc; 2825bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson j1 = delta->sign ? 1 : cmp(b, delta); 2826bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson Bfree(delta); 2827bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (j1 == 0 && mode != 1 && !(word1(&u) & 1) 2828bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson ) { 2829bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (dig == '9') 2830bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson goto round_9_up; 2831bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (j > 0) 2832bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson dig++; 2833bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson *s++ = dig; 2834bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson goto ret; 2835bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 2836bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (j < 0 || (j == 0 && mode != 1 2837bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson && !(word1(&u) & 1) 2838bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson )) { 2839bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (!b->x[0] && b->wds <= 1) { 2840bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson goto accept_dig; 2841bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 2842bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (j1 > 0) { 2843bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson b = lshift(b, 1); 2844bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (b == NULL) 2845bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson goto failed_malloc; 2846bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson j1 = cmp(b, S); 2847bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if ((j1 > 0 || (j1 == 0 && dig & 1)) 2848bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson && dig++ == '9') 2849bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson goto round_9_up; 2850bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 2851bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson accept_dig: 2852bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson *s++ = dig; 2853bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson goto ret; 2854bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 2855bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (j1 > 0) { 2856bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (dig == '9') { /* possible if i == 1 */ 2857bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson round_9_up: 2858bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson *s++ = '9'; 2859bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson goto roundoff; 2860bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 2861bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson *s++ = dig + 1; 2862bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson goto ret; 2863bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 2864bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson *s++ = dig; 2865bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (i == ilim) 2866bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson break; 2867bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson b = multadd(b, 10, 0); 2868bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (b == NULL) 2869bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson goto failed_malloc; 2870bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (mlo == mhi) { 2871bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson mlo = mhi = multadd(mhi, 10, 0); 2872bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (mlo == NULL) 2873bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson goto failed_malloc; 2874bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 2875bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson else { 2876bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson mlo = multadd(mlo, 10, 0); 2877bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (mlo == NULL) 2878bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson goto failed_malloc; 2879bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson mhi = multadd(mhi, 10, 0); 2880bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (mhi == NULL) 2881bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson goto failed_malloc; 2882bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 2883bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 2884bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 2885bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson else 2886bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson for(i = 1;; i++) { 2887bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson *s++ = dig = quorem(b,S) + '0'; 2888bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (!b->x[0] && b->wds <= 1) { 2889bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson goto ret; 2890bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 2891bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (i >= ilim) 2892bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson break; 2893bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson b = multadd(b, 10, 0); 2894bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (b == NULL) 2895bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson goto failed_malloc; 2896bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 2897bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 2898bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson /* Round off last digit */ 2899bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 2900bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson b = lshift(b, 1); 2901bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (b == NULL) 2902bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson goto failed_malloc; 2903bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson j = cmp(b, S); 2904bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (j > 0 || (j == 0 && dig & 1)) { 2905bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson roundoff: 2906bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson while(*--s == '9') 2907bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (s == s0) { 2908bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson k++; 2909bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson *s++ = '1'; 2910bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson goto ret; 2911bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 2912bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson ++*s++; 2913bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 2914bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson else { 2915bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson while(*--s == '0'); 2916bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson s++; 2917bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 2918bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson ret: 2919bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson Bfree(S); 2920bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (mhi) { 2921bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (mlo && mlo != mhi) 2922bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson Bfree(mlo); 2923bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson Bfree(mhi); 2924bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson } 2925bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson ret1: 2926bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson Bfree(b); 2927bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson *s = 0; 2928bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson *decpt = k + 1; 2929bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (rve) 2930bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson *rve = s; 2931bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson return s0; 2932bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson failed_malloc: 2933bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (S) 2934bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson Bfree(S); 2935bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (mlo && mlo != mhi) 2936bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson Bfree(mlo); 2937bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (mhi) 2938bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson Bfree(mhi); 2939bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (b) 2940bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson Bfree(b); 2941bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson if (s0) 2942bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson _Py_dg_freedtoa(s0); 2943bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson return NULL; 2944bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson} 2945bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#ifdef __cplusplus 2946bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson} 2947bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#endif 2948bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson 2949bb28285ea2f01e97a26bc595d49da43fbee62913Mark Dickinson#endif /* PY_NO_SHORT_FLOAT_REPR */ 2950