1 | /****************************************************************
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2 | *
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3 | * The author of this software is David M. Gay.
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4 | *
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5 | * Copyright (c) 1991, 2000, 2001 by Lucent Technologies.
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6 | *
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7 | * Permission to use, copy, modify, and distribute this software for any
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8 | * purpose without fee is hereby granted, provided that this entire notice
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9 | * is included in all copies of any software which is or includes a copy
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10 | * or modification of this software and in all copies of the supporting
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11 | * documentation for such software.
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12 | *
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13 | * THIS SOFTWARE IS BEING PROVIDED "AS IS", WITHOUT ANY EXPRESS OR IMPLIED
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14 | * WARRANTY. IN PARTICULAR, NEITHER THE AUTHOR NOR LUCENT MAKES ANY
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15 | * REPRESENTATION OR WARRANTY OF ANY KIND CONCERNING THE MERCHANTABILITY
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16 | * OF THIS SOFTWARE OR ITS FITNESS FOR ANY PARTICULAR PURPOSE.
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17 | *
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18 | ***************************************************************/
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19 |
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20 | /****************************************************************
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21 | * This is dtoa.c by David M. Gay, downloaded from
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22 | * http://www.netlib.org/fp/dtoa.c on April 15, 2009 and modified for
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23 | * inclusion into the Python core by Mark E. T. Dickinson and Eric V. Smith.
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24 | *
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25 | * Please remember to check http://www.netlib.org/fp regularly (and especially
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26 | * before any Python release) for bugfixes and updates.
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27 | *
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28 | * The major modifications from Gay's original code are as follows:
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29 | *
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30 | * 0. The original code has been specialized to Python's needs by removing
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31 | * many of the #ifdef'd sections. In particular, code to support VAX and
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32 | * IBM floating-point formats, hex NaNs, hex floats, locale-aware
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33 | * treatment of the decimal point, and setting of the inexact flag have
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34 | * been removed.
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35 | *
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36 | * 1. We use PyMem_Malloc and PyMem_Free in place of malloc and free.
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37 | *
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38 | * 2. The public functions strtod, dtoa and freedtoa all now have
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39 | * a _Py_dg_ prefix.
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40 | *
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41 | * 3. Instead of assuming that PyMem_Malloc always succeeds, we thread
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42 | * PyMem_Malloc failures through the code. The functions
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43 | *
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44 | * Balloc, multadd, s2b, i2b, mult, pow5mult, lshift, diff, d2b
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45 | *
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46 | * of return type *Bigint all return NULL to indicate a malloc failure.
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47 | * Similarly, rv_alloc and nrv_alloc (return type char *) return NULL on
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48 | * failure. bigcomp now has return type int (it used to be void) and
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49 | * returns -1 on failure and 0 otherwise. _Py_dg_dtoa returns NULL
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50 | * on failure. _Py_dg_strtod indicates failure due to malloc failure
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51 | * by returning -1.0, setting errno=ENOMEM and *se to s00.
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52 | *
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53 | * 4. The static variable dtoa_result has been removed. Callers of
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54 | * _Py_dg_dtoa are expected to call _Py_dg_freedtoa to free
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55 | * the memory allocated by _Py_dg_dtoa.
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56 | *
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57 | * 5. The code has been reformatted to better fit with Python's
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58 | * C style guide (PEP 7).
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59 | *
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60 | * 6. A bug in the memory allocation has been fixed: to avoid FREEing memory
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61 | * that hasn't been MALLOC'ed, private_mem should only be used when k <=
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62 | * Kmax.
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63 | *
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64 | * 7. _Py_dg_strtod has been modified so that it doesn't accept strings with
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65 | * leading whitespace.
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66 | *
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67 | ***************************************************************/
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68 |
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69 | /* Please send bug reports for the original dtoa.c code to David M. Gay (dmg
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70 | * at acm dot org, with " at " changed at "@" and " dot " changed to ".").
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71 | * Please report bugs for this modified version using the Python issue tracker
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72 | * (http://bugs.python.org). */
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73 |
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74 | /* On a machine with IEEE extended-precision registers, it is
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75 | * necessary to specify double-precision (53-bit) rounding precision
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76 | * before invoking strtod or dtoa. If the machine uses (the equivalent
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77 | * of) Intel 80x87 arithmetic, the call
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78 | * _control87(PC_53, MCW_PC);
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79 | * does this with many compilers. Whether this or another call is
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80 | * appropriate depends on the compiler; for this to work, it may be
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81 | * necessary to #include "float.h" or another system-dependent header
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82 | * file.
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83 | */
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84 |
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85 | /* strtod for IEEE-, VAX-, and IBM-arithmetic machines.
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86 | *
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87 | * This strtod returns a nearest machine number to the input decimal
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88 | * string (or sets errno to ERANGE). With IEEE arithmetic, ties are
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89 | * broken by the IEEE round-even rule. Otherwise ties are broken by
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90 | * biased rounding (add half and chop).
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91 | *
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92 | * Inspired loosely by William D. Clinger's paper "How to Read Floating
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93 | * Point Numbers Accurately" [Proc. ACM SIGPLAN '90, pp. 92-101].
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94 | *
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95 | * Modifications:
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96 | *
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97 | * 1. We only require IEEE, IBM, or VAX double-precision
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98 | * arithmetic (not IEEE double-extended).
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99 | * 2. We get by with floating-point arithmetic in a case that
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100 | * Clinger missed -- when we're computing d * 10^n
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101 | * for a small integer d and the integer n is not too
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102 | * much larger than 22 (the maximum integer k for which
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103 | * we can represent 10^k exactly), we may be able to
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104 | * compute (d*10^k) * 10^(e-k) with just one roundoff.
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105 | * 3. Rather than a bit-at-a-time adjustment of the binary
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106 | * result in the hard case, we use floating-point
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107 | * arithmetic to determine the adjustment to within
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108 | * one bit; only in really hard cases do we need to
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109 | * compute a second residual.
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110 | * 4. Because of 3., we don't need a large table of powers of 10
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111 | * for ten-to-e (just some small tables, e.g. of 10^k
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112 | * for 0 <= k <= 22).
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113 | */
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114 |
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115 | /* Linking of Python's #defines to Gay's #defines starts here. */
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116 |
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117 | #include "Python.h"
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118 |
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119 | /* if PY_NO_SHORT_FLOAT_REPR is defined, then don't even try to compile
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120 | the following code */
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121 | #ifndef PY_NO_SHORT_FLOAT_REPR
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122 |
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123 | #include "float.h"
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124 |
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125 | #define MALLOC PyMem_Malloc
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126 | #define FREE PyMem_Free
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127 |
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128 | /* This code should also work for ARM mixed-endian format on little-endian
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129 | machines, where doubles have byte order 45670123 (in increasing address
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130 | order, 0 being the least significant byte). */
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131 | #ifdef DOUBLE_IS_LITTLE_ENDIAN_IEEE754
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132 | # define IEEE_8087
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133 | #endif
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134 | #if defined(DOUBLE_IS_BIG_ENDIAN_IEEE754) || \
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135 | defined(DOUBLE_IS_ARM_MIXED_ENDIAN_IEEE754)
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136 | # define IEEE_MC68k
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137 | #endif
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138 | #if defined(IEEE_8087) + defined(IEEE_MC68k) != 1
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139 | #error "Exactly one of IEEE_8087 or IEEE_MC68k should be defined."
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140 | #endif
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141 |
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142 | /* The code below assumes that the endianness of integers matches the
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143 | endianness of the two 32-bit words of a double. Check this. */
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144 | #if defined(WORDS_BIGENDIAN) && (defined(DOUBLE_IS_LITTLE_ENDIAN_IEEE754) || \
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145 | defined(DOUBLE_IS_ARM_MIXED_ENDIAN_IEEE754))
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146 | #error "doubles and ints have incompatible endianness"
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147 | #endif
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148 |
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149 | #if !defined(WORDS_BIGENDIAN) && defined(DOUBLE_IS_BIG_ENDIAN_IEEE754)
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150 | #error "doubles and ints have incompatible endianness"
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151 | #endif
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152 |
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153 |
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154 | #if defined(HAVE_UINT32_T) && defined(HAVE_INT32_T)
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155 | typedef PY_UINT32_T ULong;
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156 | typedef PY_INT32_T Long;
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157 | #else
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158 | #error "Failed to find an exact-width 32-bit integer type"
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159 | #endif
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160 |
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161 | #if defined(HAVE_UINT64_T)
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162 | #define ULLong PY_UINT64_T
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163 | #else
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164 | #undef ULLong
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165 | #endif
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166 |
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167 | #undef DEBUG
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168 | #ifdef Py_DEBUG
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169 | #define DEBUG
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170 | #endif
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171 |
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172 | /* End Python #define linking */
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173 |
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174 | #ifdef DEBUG
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175 | #define Bug(x) {fprintf(stderr, "%s\n", x); exit(1);}
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176 | #endif
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177 |
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178 | #ifndef PRIVATE_MEM
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179 | #define PRIVATE_MEM 2304
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180 | #endif
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181 | #define PRIVATE_mem ((PRIVATE_MEM+sizeof(double)-1)/sizeof(double))
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182 | static double private_mem[PRIVATE_mem], *pmem_next = private_mem;
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183 |
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184 | #ifdef __cplusplus
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185 | extern "C" {
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186 | #endif
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187 |
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188 | typedef union { double d; ULong L[2]; } U;
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189 |
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190 | #ifdef IEEE_8087
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191 | #define word0(x) (x)->L[1]
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192 | #define word1(x) (x)->L[0]
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193 | #else
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194 | #define word0(x) (x)->L[0]
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195 | #define word1(x) (x)->L[1]
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196 | #endif
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197 | #define dval(x) (x)->d
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198 |
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199 | #ifndef STRTOD_DIGLIM
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200 | #define STRTOD_DIGLIM 40
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201 | #endif
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202 |
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203 | /* maximum permitted exponent value for strtod; exponents larger than
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204 | MAX_ABS_EXP in absolute value get truncated to +-MAX_ABS_EXP. MAX_ABS_EXP
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205 | should fit into an int. */
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206 | #ifndef MAX_ABS_EXP
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207 | #define MAX_ABS_EXP 19999U
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208 | #endif
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209 |
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210 | /* The following definition of Storeinc is appropriate for MIPS processors.
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211 | * An alternative that might be better on some machines is
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212 | * #define Storeinc(a,b,c) (*a++ = b << 16 | c & 0xffff)
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213 | */
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214 | #if defined(IEEE_8087)
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215 | #define Storeinc(a,b,c) (((unsigned short *)a)[1] = (unsigned short)b, \
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216 | ((unsigned short *)a)[0] = (unsigned short)c, a++)
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217 | #else
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218 | #define Storeinc(a,b,c) (((unsigned short *)a)[0] = (unsigned short)b, \
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219 | ((unsigned short *)a)[1] = (unsigned short)c, a++)
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220 | #endif
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221 |
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222 | /* #define P DBL_MANT_DIG */
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223 | /* Ten_pmax = floor(P*log(2)/log(5)) */
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224 | /* Bletch = (highest power of 2 < DBL_MAX_10_EXP) / 16 */
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225 | /* Quick_max = floor((P-1)*log(FLT_RADIX)/log(10) - 1) */
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226 | /* Int_max = floor(P*log(FLT_RADIX)/log(10) - 1) */
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227 |
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228 | #define Exp_shift 20
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229 | #define Exp_shift1 20
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230 | #define Exp_msk1 0x100000
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231 | #define Exp_msk11 0x100000
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232 | #define Exp_mask 0x7ff00000
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233 | #define P 53
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234 | #define Nbits 53
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235 | #define Bias 1023
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236 | #define Emax 1023
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237 | #define Emin (-1022)
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238 | #define Etiny (-1074) /* smallest denormal is 2**Etiny */
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239 | #define Exp_1 0x3ff00000
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240 | #define Exp_11 0x3ff00000
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241 | #define Ebits 11
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242 | #define Frac_mask 0xfffff
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243 | #define Frac_mask1 0xfffff
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244 | #define Ten_pmax 22
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245 | #define Bletch 0x10
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246 | #define Bndry_mask 0xfffff
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247 | #define Bndry_mask1 0xfffff
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248 | #define Sign_bit 0x80000000
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249 | #define Log2P 1
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250 | #define Tiny0 0
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251 | #define Tiny1 1
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252 | #define Quick_max 14
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253 | #define Int_max 14
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254 |
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255 | #ifndef Flt_Rounds
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256 | #ifdef FLT_ROUNDS
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257 | #define Flt_Rounds FLT_ROUNDS
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258 | #else
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259 | #define Flt_Rounds 1
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260 | #endif
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261 | #endif /*Flt_Rounds*/
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262 |
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263 | #define Rounding Flt_Rounds
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264 |
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265 | #define Big0 (Frac_mask1 | Exp_msk1*(DBL_MAX_EXP+Bias-1))
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266 | #define Big1 0xffffffff
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267 |
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268 | /* struct BCinfo is used to pass information from _Py_dg_strtod to bigcomp */
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269 |
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270 | typedef struct BCinfo BCinfo;
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271 | struct
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272 | BCinfo {
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273 | int e0, nd, nd0, scale;
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274 | };
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275 |
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276 | #define FFFFFFFF 0xffffffffUL
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277 |
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278 | #define Kmax 7
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279 |
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280 | /* struct Bigint is used to represent arbitrary-precision integers. These
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281 | integers are stored in sign-magnitude format, with the magnitude stored as
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282 | an array of base 2**32 digits. Bigints are always normalized: if x is a
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283 | Bigint then x->wds >= 1, and either x->wds == 1 or x[wds-1] is nonzero.
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284 |
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285 | The Bigint fields are as follows:
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286 |
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287 | - next is a header used by Balloc and Bfree to keep track of lists
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288 | of freed Bigints; it's also used for the linked list of
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289 | powers of 5 of the form 5**2**i used by pow5mult.
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290 | - k indicates which pool this Bigint was allocated from
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291 | - maxwds is the maximum number of words space was allocated for
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292 | (usually maxwds == 2**k)
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293 | - sign is 1 for negative Bigints, 0 for positive. The sign is unused
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294 | (ignored on inputs, set to 0 on outputs) in almost all operations
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295 | involving Bigints: a notable exception is the diff function, which
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296 | ignores signs on inputs but sets the sign of the output correctly.
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297 | - wds is the actual number of significant words
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298 | - x contains the vector of words (digits) for this Bigint, from least
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299 | significant (x[0]) to most significant (x[wds-1]).
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300 | */
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301 |
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302 | struct
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303 | Bigint {
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304 | struct Bigint *next;
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305 | int k, maxwds, sign, wds;
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306 | ULong x[1];
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307 | };
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308 |
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309 | typedef struct Bigint Bigint;
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310 |
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311 | #ifndef Py_USING_MEMORY_DEBUGGER
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312 |
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313 | /* Memory management: memory is allocated from, and returned to, Kmax+1 pools
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314 | of memory, where pool k (0 <= k <= Kmax) is for Bigints b with b->maxwds ==
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315 | 1 << k. These pools are maintained as linked lists, with freelist[k]
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316 | pointing to the head of the list for pool k.
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317 |
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318 | On allocation, if there's no free slot in the appropriate pool, MALLOC is
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319 | called to get more memory. This memory is not returned to the system until
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320 | Python quits. There's also a private memory pool that's allocated from
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321 | in preference to using MALLOC.
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322 |
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323 | For Bigints with more than (1 << Kmax) digits (which implies at least 1233
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324 | decimal digits), memory is directly allocated using MALLOC, and freed using
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325 | FREE.
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326 |
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327 | XXX: it would be easy to bypass this memory-management system and
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328 | translate each call to Balloc into a call to PyMem_Malloc, and each
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329 | Bfree to PyMem_Free. Investigate whether this has any significant
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330 | performance on impact. */
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331 |
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332 | static Bigint *freelist[Kmax+1];
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333 |
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334 | /* Allocate space for a Bigint with up to 1<<k digits */
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335 |
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336 | static Bigint *
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337 | Balloc(int k)
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338 | {
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339 | int x;
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340 | Bigint *rv;
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341 | unsigned int len;
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342 |
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343 | if (k <= Kmax && (rv = freelist[k]))
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344 | freelist[k] = rv->next;
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345 | else {
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346 | x = 1 << k;
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347 | len = (sizeof(Bigint) + (x-1)*sizeof(ULong) + sizeof(double) - 1)
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348 | /sizeof(double);
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349 | if (k <= Kmax && pmem_next - private_mem + len <= PRIVATE_mem) {
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350 | rv = (Bigint*)pmem_next;
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351 | pmem_next += len;
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352 | }
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353 | else {
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354 | rv = (Bigint*)MALLOC(len*sizeof(double));
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355 | if (rv == NULL)
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356 | return NULL;
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357 | }
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358 | rv->k = k;
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359 | rv->maxwds = x;
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360 | }
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361 | rv->sign = rv->wds = 0;
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362 | return rv;
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363 | }
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364 |
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365 | /* Free a Bigint allocated with Balloc */
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366 |
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367 | static void
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368 | Bfree(Bigint *v)
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369 | {
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370 | if (v) {
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371 | if (v->k > Kmax)
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372 | FREE((void*)v);
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373 | else {
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374 | v->next = freelist[v->k];
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375 | freelist[v->k] = v;
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376 | }
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377 | }
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378 | }
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379 |
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380 | #else
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381 |
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382 | /* Alternative versions of Balloc and Bfree that use PyMem_Malloc and
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383 | PyMem_Free directly in place of the custom memory allocation scheme above.
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384 | These are provided for the benefit of memory debugging tools like
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385 | Valgrind. */
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386 |
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387 | /* Allocate space for a Bigint with up to 1<<k digits */
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388 |
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389 | static Bigint *
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390 | Balloc(int k)
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391 | {
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392 | int x;
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393 | Bigint *rv;
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394 | unsigned int len;
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395 |
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396 | x = 1 << k;
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397 | len = (sizeof(Bigint) + (x-1)*sizeof(ULong) + sizeof(double) - 1)
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398 | /sizeof(double);
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399 |
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400 | rv = (Bigint*)MALLOC(len*sizeof(double));
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401 | if (rv == NULL)
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402 | return NULL;
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403 |
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404 | rv->k = k;
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405 | rv->maxwds = x;
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406 | rv->sign = rv->wds = 0;
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407 | return rv;
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408 | }
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409 |
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410 | /* Free a Bigint allocated with Balloc */
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411 |
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412 | static void
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413 | Bfree(Bigint *v)
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414 | {
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415 | if (v) {
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416 | FREE((void*)v);
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417 | }
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418 | }
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419 |
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420 | #endif /* Py_USING_MEMORY_DEBUGGER */
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421 |
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422 | #define Bcopy(x,y) memcpy((char *)&x->sign, (char *)&y->sign, \
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423 | y->wds*sizeof(Long) + 2*sizeof(int))
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424 |
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425 | /* Multiply a Bigint b by m and add a. Either modifies b in place and returns
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426 | a pointer to the modified b, or Bfrees b and returns a pointer to a copy.
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427 | On failure, return NULL. In this case, b will have been already freed. */
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428 |
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429 | static Bigint *
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430 | multadd(Bigint *b, int m, int a) /* multiply by m and add a */
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431 | {
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432 | int i, wds;
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433 | #ifdef ULLong
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434 | ULong *x;
|
---|
435 | ULLong carry, y;
|
---|
436 | #else
|
---|
437 | ULong carry, *x, y;
|
---|
438 | ULong xi, z;
|
---|
439 | #endif
|
---|
440 | Bigint *b1;
|
---|
441 |
|
---|
442 | wds = b->wds;
|
---|
443 | x = b->x;
|
---|
444 | i = 0;
|
---|
445 | carry = a;
|
---|
446 | do {
|
---|
447 | #ifdef ULLong
|
---|
448 | y = *x * (ULLong)m + carry;
|
---|
449 | carry = y >> 32;
|
---|
450 | *x++ = (ULong)(y & FFFFFFFF);
|
---|
451 | #else
|
---|
452 | xi = *x;
|
---|
453 | y = (xi & 0xffff) * m + carry;
|
---|
454 | z = (xi >> 16) * m + (y >> 16);
|
---|
455 | carry = z >> 16;
|
---|
456 | *x++ = (z << 16) + (y & 0xffff);
|
---|
457 | #endif
|
---|
458 | }
|
---|
459 | while(++i < wds);
|
---|
460 | if (carry) {
|
---|
461 | if (wds >= b->maxwds) {
|
---|
462 | b1 = Balloc(b->k+1);
|
---|
463 | if (b1 == NULL){
|
---|
464 | Bfree(b);
|
---|
465 | return NULL;
|
---|
466 | }
|
---|
467 | Bcopy(b1, b);
|
---|
468 | Bfree(b);
|
---|
469 | b = b1;
|
---|
470 | }
|
---|
471 | b->x[wds++] = (ULong)carry;
|
---|
472 | b->wds = wds;
|
---|
473 | }
|
---|
474 | return b;
|
---|
475 | }
|
---|
476 |
|
---|
477 | /* convert a string s containing nd decimal digits (possibly containing a
|
---|
478 | decimal separator at position nd0, which is ignored) to a Bigint. This
|
---|
479 | function carries on where the parsing code in _Py_dg_strtod leaves off: on
|
---|
480 | entry, y9 contains the result of converting the first 9 digits. Returns
|
---|
481 | NULL on failure. */
|
---|
482 |
|
---|
483 | static Bigint *
|
---|
484 | s2b(const char *s, int nd0, int nd, ULong y9)
|
---|
485 | {
|
---|
486 | Bigint *b;
|
---|
487 | int i, k;
|
---|
488 | Long x, y;
|
---|
489 |
|
---|
490 | x = (nd + 8) / 9;
|
---|
491 | for(k = 0, y = 1; x > y; y <<= 1, k++) ;
|
---|
492 | b = Balloc(k);
|
---|
493 | if (b == NULL)
|
---|
494 | return NULL;
|
---|
495 | b->x[0] = y9;
|
---|
496 | b->wds = 1;
|
---|
497 |
|
---|
498 | if (nd <= 9)
|
---|
499 | return b;
|
---|
500 |
|
---|
501 | s += 9;
|
---|
502 | for (i = 9; i < nd0; i++) {
|
---|
503 | b = multadd(b, 10, *s++ - '0');
|
---|
504 | if (b == NULL)
|
---|
505 | return NULL;
|
---|
506 | }
|
---|
507 | s++;
|
---|
508 | for(; i < nd; i++) {
|
---|
509 | b = multadd(b, 10, *s++ - '0');
|
---|
510 | if (b == NULL)
|
---|
511 | return NULL;
|
---|
512 | }
|
---|
513 | return b;
|
---|
514 | }
|
---|
515 |
|
---|
516 | /* count leading 0 bits in the 32-bit integer x. */
|
---|
517 |
|
---|
518 | static int
|
---|
519 | hi0bits(ULong x)
|
---|
520 | {
|
---|
521 | int k = 0;
|
---|
522 |
|
---|
523 | if (!(x & 0xffff0000)) {
|
---|
524 | k = 16;
|
---|
525 | x <<= 16;
|
---|
526 | }
|
---|
527 | if (!(x & 0xff000000)) {
|
---|
528 | k += 8;
|
---|
529 | x <<= 8;
|
---|
530 | }
|
---|
531 | if (!(x & 0xf0000000)) {
|
---|
532 | k += 4;
|
---|
533 | x <<= 4;
|
---|
534 | }
|
---|
535 | if (!(x & 0xc0000000)) {
|
---|
536 | k += 2;
|
---|
537 | x <<= 2;
|
---|
538 | }
|
---|
539 | if (!(x & 0x80000000)) {
|
---|
540 | k++;
|
---|
541 | if (!(x & 0x40000000))
|
---|
542 | return 32;
|
---|
543 | }
|
---|
544 | return k;
|
---|
545 | }
|
---|
546 |
|
---|
547 | /* count trailing 0 bits in the 32-bit integer y, and shift y right by that
|
---|
548 | number of bits. */
|
---|
549 |
|
---|
550 | static int
|
---|
551 | lo0bits(ULong *y)
|
---|
552 | {
|
---|
553 | int k;
|
---|
554 | ULong x = *y;
|
---|
555 |
|
---|
556 | if (x & 7) {
|
---|
557 | if (x & 1)
|
---|
558 | return 0;
|
---|
559 | if (x & 2) {
|
---|
560 | *y = x >> 1;
|
---|
561 | return 1;
|
---|
562 | }
|
---|
563 | *y = x >> 2;
|
---|
564 | return 2;
|
---|
565 | }
|
---|
566 | k = 0;
|
---|
567 | if (!(x & 0xffff)) {
|
---|
568 | k = 16;
|
---|
569 | x >>= 16;
|
---|
570 | }
|
---|
571 | if (!(x & 0xff)) {
|
---|
572 | k += 8;
|
---|
573 | x >>= 8;
|
---|
574 | }
|
---|
575 | if (!(x & 0xf)) {
|
---|
576 | k += 4;
|
---|
577 | x >>= 4;
|
---|
578 | }
|
---|
579 | if (!(x & 0x3)) {
|
---|
580 | k += 2;
|
---|
581 | x >>= 2;
|
---|
582 | }
|
---|
583 | if (!(x & 1)) {
|
---|
584 | k++;
|
---|
585 | x >>= 1;
|
---|
586 | if (!x)
|
---|
587 | return 32;
|
---|
588 | }
|
---|
589 | *y = x;
|
---|
590 | return k;
|
---|
591 | }
|
---|
592 |
|
---|
593 | /* convert a small nonnegative integer to a Bigint */
|
---|
594 |
|
---|
595 | static Bigint *
|
---|
596 | i2b(int i)
|
---|
597 | {
|
---|
598 | Bigint *b;
|
---|
599 |
|
---|
600 | b = Balloc(1);
|
---|
601 | if (b == NULL)
|
---|
602 | return NULL;
|
---|
603 | b->x[0] = i;
|
---|
604 | b->wds = 1;
|
---|
605 | return b;
|
---|
606 | }
|
---|
607 |
|
---|
608 | /* multiply two Bigints. Returns a new Bigint, or NULL on failure. Ignores
|
---|
609 | the signs of a and b. */
|
---|
610 |
|
---|
611 | static Bigint *
|
---|
612 | mult(Bigint *a, Bigint *b)
|
---|
613 | {
|
---|
614 | Bigint *c;
|
---|
615 | int k, wa, wb, wc;
|
---|
616 | ULong *x, *xa, *xae, *xb, *xbe, *xc, *xc0;
|
---|
617 | ULong y;
|
---|
618 | #ifdef ULLong
|
---|
619 | ULLong carry, z;
|
---|
620 | #else
|
---|
621 | ULong carry, z;
|
---|
622 | ULong z2;
|
---|
623 | #endif
|
---|
624 |
|
---|
625 | if ((!a->x[0] && a->wds == 1) || (!b->x[0] && b->wds == 1)) {
|
---|
626 | c = Balloc(0);
|
---|
627 | if (c == NULL)
|
---|
628 | return NULL;
|
---|
629 | c->wds = 1;
|
---|
630 | c->x[0] = 0;
|
---|
631 | return c;
|
---|
632 | }
|
---|
633 |
|
---|
634 | if (a->wds < b->wds) {
|
---|
635 | c = a;
|
---|
636 | a = b;
|
---|
637 | b = c;
|
---|
638 | }
|
---|
639 | k = a->k;
|
---|
640 | wa = a->wds;
|
---|
641 | wb = b->wds;
|
---|
642 | wc = wa + wb;
|
---|
643 | if (wc > a->maxwds)
|
---|
644 | k++;
|
---|
645 | c = Balloc(k);
|
---|
646 | if (c == NULL)
|
---|
647 | return NULL;
|
---|
648 | for(x = c->x, xa = x + wc; x < xa; x++)
|
---|
649 | *x = 0;
|
---|
650 | xa = a->x;
|
---|
651 | xae = xa + wa;
|
---|
652 | xb = b->x;
|
---|
653 | xbe = xb + wb;
|
---|
654 | xc0 = c->x;
|
---|
655 | #ifdef ULLong
|
---|
656 | for(; xb < xbe; xc0++) {
|
---|
657 | if ((y = *xb++)) {
|
---|
658 | x = xa;
|
---|
659 | xc = xc0;
|
---|
660 | carry = 0;
|
---|
661 | do {
|
---|
662 | z = *x++ * (ULLong)y + *xc + carry;
|
---|
663 | carry = z >> 32;
|
---|
664 | *xc++ = (ULong)(z & FFFFFFFF);
|
---|
665 | }
|
---|
666 | while(x < xae);
|
---|
667 | *xc = (ULong)carry;
|
---|
668 | }
|
---|
669 | }
|
---|
670 | #else
|
---|
671 | for(; xb < xbe; xb++, xc0++) {
|
---|
672 | if (y = *xb & 0xffff) {
|
---|
673 | x = xa;
|
---|
674 | xc = xc0;
|
---|
675 | carry = 0;
|
---|
676 | do {
|
---|
677 | z = (*x & 0xffff) * y + (*xc & 0xffff) + carry;
|
---|
678 | carry = z >> 16;
|
---|
679 | z2 = (*x++ >> 16) * y + (*xc >> 16) + carry;
|
---|
680 | carry = z2 >> 16;
|
---|
681 | Storeinc(xc, z2, z);
|
---|
682 | }
|
---|
683 | while(x < xae);
|
---|
684 | *xc = carry;
|
---|
685 | }
|
---|
686 | if (y = *xb >> 16) {
|
---|
687 | x = xa;
|
---|
688 | xc = xc0;
|
---|
689 | carry = 0;
|
---|
690 | z2 = *xc;
|
---|
691 | do {
|
---|
692 | z = (*x & 0xffff) * y + (*xc >> 16) + carry;
|
---|
693 | carry = z >> 16;
|
---|
694 | Storeinc(xc, z, z2);
|
---|
695 | z2 = (*x++ >> 16) * y + (*xc & 0xffff) + carry;
|
---|
696 | carry = z2 >> 16;
|
---|
697 | }
|
---|
698 | while(x < xae);
|
---|
699 | *xc = z2;
|
---|
700 | }
|
---|
701 | }
|
---|
702 | #endif
|
---|
703 | for(xc0 = c->x, xc = xc0 + wc; wc > 0 && !*--xc; --wc) ;
|
---|
704 | c->wds = wc;
|
---|
705 | return c;
|
---|
706 | }
|
---|
707 |
|
---|
708 | #ifndef Py_USING_MEMORY_DEBUGGER
|
---|
709 |
|
---|
710 | /* p5s is a linked list of powers of 5 of the form 5**(2**i), i >= 2 */
|
---|
711 |
|
---|
712 | static Bigint *p5s;
|
---|
713 |
|
---|
714 | /* multiply the Bigint b by 5**k. Returns a pointer to the result, or NULL on
|
---|
715 | failure; if the returned pointer is distinct from b then the original
|
---|
716 | Bigint b will have been Bfree'd. Ignores the sign of b. */
|
---|
717 |
|
---|
718 | static Bigint *
|
---|
719 | pow5mult(Bigint *b, int k)
|
---|
720 | {
|
---|
721 | Bigint *b1, *p5, *p51;
|
---|
722 | int i;
|
---|
723 | static int p05[3] = { 5, 25, 125 };
|
---|
724 |
|
---|
725 | if ((i = k & 3)) {
|
---|
726 | b = multadd(b, p05[i-1], 0);
|
---|
727 | if (b == NULL)
|
---|
728 | return NULL;
|
---|
729 | }
|
---|
730 |
|
---|
731 | if (!(k >>= 2))
|
---|
732 | return b;
|
---|
733 | p5 = p5s;
|
---|
734 | if (!p5) {
|
---|
735 | /* first time */
|
---|
736 | p5 = i2b(625);
|
---|
737 | if (p5 == NULL) {
|
---|
738 | Bfree(b);
|
---|
739 | return NULL;
|
---|
740 | }
|
---|
741 | p5s = p5;
|
---|
742 | p5->next = 0;
|
---|
743 | }
|
---|
744 | for(;;) {
|
---|
745 | if (k & 1) {
|
---|
746 | b1 = mult(b, p5);
|
---|
747 | Bfree(b);
|
---|
748 | b = b1;
|
---|
749 | if (b == NULL)
|
---|
750 | return NULL;
|
---|
751 | }
|
---|
752 | if (!(k >>= 1))
|
---|
753 | break;
|
---|
754 | p51 = p5->next;
|
---|
755 | if (!p51) {
|
---|
756 | p51 = mult(p5,p5);
|
---|
757 | if (p51 == NULL) {
|
---|
758 | Bfree(b);
|
---|
759 | return NULL;
|
---|
760 | }
|
---|
761 | p51->next = 0;
|
---|
762 | p5->next = p51;
|
---|
763 | }
|
---|
764 | p5 = p51;
|
---|
765 | }
|
---|
766 | return b;
|
---|
767 | }
|
---|
768 |
|
---|
769 | #else
|
---|
770 |
|
---|
771 | /* Version of pow5mult that doesn't cache powers of 5. Provided for
|
---|
772 | the benefit of memory debugging tools like Valgrind. */
|
---|
773 |
|
---|
774 | static Bigint *
|
---|
775 | pow5mult(Bigint *b, int k)
|
---|
776 | {
|
---|
777 | Bigint *b1, *p5, *p51;
|
---|
778 | int i;
|
---|
779 | static int p05[3] = { 5, 25, 125 };
|
---|
780 |
|
---|
781 | if ((i = k & 3)) {
|
---|
782 | b = multadd(b, p05[i-1], 0);
|
---|
783 | if (b == NULL)
|
---|
784 | return NULL;
|
---|
785 | }
|
---|
786 |
|
---|
787 | if (!(k >>= 2))
|
---|
788 | return b;
|
---|
789 | p5 = i2b(625);
|
---|
790 | if (p5 == NULL) {
|
---|
791 | Bfree(b);
|
---|
792 | return NULL;
|
---|
793 | }
|
---|
794 |
|
---|
795 | for(;;) {
|
---|
796 | if (k & 1) {
|
---|
797 | b1 = mult(b, p5);
|
---|
798 | Bfree(b);
|
---|
799 | b = b1;
|
---|
800 | if (b == NULL) {
|
---|
801 | Bfree(p5);
|
---|
802 | return NULL;
|
---|
803 | }
|
---|
804 | }
|
---|
805 | if (!(k >>= 1))
|
---|
806 | break;
|
---|
807 | p51 = mult(p5, p5);
|
---|
808 | Bfree(p5);
|
---|
809 | p5 = p51;
|
---|
810 | if (p5 == NULL) {
|
---|
811 | Bfree(b);
|
---|
812 | return NULL;
|
---|
813 | }
|
---|
814 | }
|
---|
815 | Bfree(p5);
|
---|
816 | return b;
|
---|
817 | }
|
---|
818 |
|
---|
819 | #endif /* Py_USING_MEMORY_DEBUGGER */
|
---|
820 |
|
---|
821 | /* shift a Bigint b left by k bits. Return a pointer to the shifted result,
|
---|
822 | or NULL on failure. If the returned pointer is distinct from b then the
|
---|
823 | original b will have been Bfree'd. Ignores the sign of b. */
|
---|
824 |
|
---|
825 | static Bigint *
|
---|
826 | lshift(Bigint *b, int k)
|
---|
827 | {
|
---|
828 | int i, k1, n, n1;
|
---|
829 | Bigint *b1;
|
---|
830 | ULong *x, *x1, *xe, z;
|
---|
831 |
|
---|
832 | if (!k || (!b->x[0] && b->wds == 1))
|
---|
833 | return b;
|
---|
834 |
|
---|
835 | n = k >> 5;
|
---|
836 | k1 = b->k;
|
---|
837 | n1 = n + b->wds + 1;
|
---|
838 | for(i = b->maxwds; n1 > i; i <<= 1)
|
---|
839 | k1++;
|
---|
840 | b1 = Balloc(k1);
|
---|
841 | if (b1 == NULL) {
|
---|
842 | Bfree(b);
|
---|
843 | return NULL;
|
---|
844 | }
|
---|
845 | x1 = b1->x;
|
---|
846 | for(i = 0; i < n; i++)
|
---|
847 | *x1++ = 0;
|
---|
848 | x = b->x;
|
---|
849 | xe = x + b->wds;
|
---|
850 | if (k &= 0x1f) {
|
---|
851 | k1 = 32 - k;
|
---|
852 | z = 0;
|
---|
853 | do {
|
---|
854 | *x1++ = *x << k | z;
|
---|
855 | z = *x++ >> k1;
|
---|
856 | }
|
---|
857 | while(x < xe);
|
---|
858 | if ((*x1 = z))
|
---|
859 | ++n1;
|
---|
860 | }
|
---|
861 | else do
|
---|
862 | *x1++ = *x++;
|
---|
863 | while(x < xe);
|
---|
864 | b1->wds = n1 - 1;
|
---|
865 | Bfree(b);
|
---|
866 | return b1;
|
---|
867 | }
|
---|
868 |
|
---|
869 | /* Do a three-way compare of a and b, returning -1 if a < b, 0 if a == b and
|
---|
870 | 1 if a > b. Ignores signs of a and b. */
|
---|
871 |
|
---|
872 | static int
|
---|
873 | cmp(Bigint *a, Bigint *b)
|
---|
874 | {
|
---|
875 | ULong *xa, *xa0, *xb, *xb0;
|
---|
876 | int i, j;
|
---|
877 |
|
---|
878 | i = a->wds;
|
---|
879 | j = b->wds;
|
---|
880 | #ifdef DEBUG
|
---|
881 | if (i > 1 && !a->x[i-1])
|
---|
882 | Bug("cmp called with a->x[a->wds-1] == 0");
|
---|
883 | if (j > 1 && !b->x[j-1])
|
---|
884 | Bug("cmp called with b->x[b->wds-1] == 0");
|
---|
885 | #endif
|
---|
886 | if (i -= j)
|
---|
887 | return i;
|
---|
888 | xa0 = a->x;
|
---|
889 | xa = xa0 + j;
|
---|
890 | xb0 = b->x;
|
---|
891 | xb = xb0 + j;
|
---|
892 | for(;;) {
|
---|
893 | if (*--xa != *--xb)
|
---|
894 | return *xa < *xb ? -1 : 1;
|
---|
895 | if (xa <= xa0)
|
---|
896 | break;
|
---|
897 | }
|
---|
898 | return 0;
|
---|
899 | }
|
---|
900 |
|
---|
901 | /* Take the difference of Bigints a and b, returning a new Bigint. Returns
|
---|
902 | NULL on failure. The signs of a and b are ignored, but the sign of the
|
---|
903 | result is set appropriately. */
|
---|
904 |
|
---|
905 | static Bigint *
|
---|
906 | diff(Bigint *a, Bigint *b)
|
---|
907 | {
|
---|
908 | Bigint *c;
|
---|
909 | int i, wa, wb;
|
---|
910 | ULong *xa, *xae, *xb, *xbe, *xc;
|
---|
911 | #ifdef ULLong
|
---|
912 | ULLong borrow, y;
|
---|
913 | #else
|
---|
914 | ULong borrow, y;
|
---|
915 | ULong z;
|
---|
916 | #endif
|
---|
917 |
|
---|
918 | i = cmp(a,b);
|
---|
919 | if (!i) {
|
---|
920 | c = Balloc(0);
|
---|
921 | if (c == NULL)
|
---|
922 | return NULL;
|
---|
923 | c->wds = 1;
|
---|
924 | c->x[0] = 0;
|
---|
925 | return c;
|
---|
926 | }
|
---|
927 | if (i < 0) {
|
---|
928 | c = a;
|
---|
929 | a = b;
|
---|
930 | b = c;
|
---|
931 | i = 1;
|
---|
932 | }
|
---|
933 | else
|
---|
934 | i = 0;
|
---|
935 | c = Balloc(a->k);
|
---|
936 | if (c == NULL)
|
---|
937 | return NULL;
|
---|
938 | c->sign = i;
|
---|
939 | wa = a->wds;
|
---|
940 | xa = a->x;
|
---|
941 | xae = xa + wa;
|
---|
942 | wb = b->wds;
|
---|
943 | xb = b->x;
|
---|
944 | xbe = xb + wb;
|
---|
945 | xc = c->x;
|
---|
946 | borrow = 0;
|
---|
947 | #ifdef ULLong
|
---|
948 | do {
|
---|
949 | y = (ULLong)*xa++ - *xb++ - borrow;
|
---|
950 | borrow = y >> 32 & (ULong)1;
|
---|
951 | *xc++ = (ULong)(y & FFFFFFFF);
|
---|
952 | }
|
---|
953 | while(xb < xbe);
|
---|
954 | while(xa < xae) {
|
---|
955 | y = *xa++ - borrow;
|
---|
956 | borrow = y >> 32 & (ULong)1;
|
---|
957 | *xc++ = (ULong)(y & FFFFFFFF);
|
---|
958 | }
|
---|
959 | #else
|
---|
960 | do {
|
---|
961 | y = (*xa & 0xffff) - (*xb & 0xffff) - borrow;
|
---|
962 | borrow = (y & 0x10000) >> 16;
|
---|
963 | z = (*xa++ >> 16) - (*xb++ >> 16) - borrow;
|
---|
964 | borrow = (z & 0x10000) >> 16;
|
---|
965 | Storeinc(xc, z, y);
|
---|
966 | }
|
---|
967 | while(xb < xbe);
|
---|
968 | while(xa < xae) {
|
---|
969 | y = (*xa & 0xffff) - borrow;
|
---|
970 | borrow = (y & 0x10000) >> 16;
|
---|
971 | z = (*xa++ >> 16) - borrow;
|
---|
972 | borrow = (z & 0x10000) >> 16;
|
---|
973 | Storeinc(xc, z, y);
|
---|
974 | }
|
---|
975 | #endif
|
---|
976 | while(!*--xc)
|
---|
977 | wa--;
|
---|
978 | c->wds = wa;
|
---|
979 | return c;
|
---|
980 | }
|
---|
981 |
|
---|
982 | /* Given a positive normal double x, return the difference between x and the
|
---|
983 | next double up. Doesn't give correct results for subnormals. */
|
---|
984 |
|
---|
985 | static double
|
---|
986 | ulp(U *x)
|
---|
987 | {
|
---|
988 | Long L;
|
---|
989 | U u;
|
---|
990 |
|
---|
991 | L = (word0(x) & Exp_mask) - (P-1)*Exp_msk1;
|
---|
992 | word0(&u) = L;
|
---|
993 | word1(&u) = 0;
|
---|
994 | return dval(&u);
|
---|
995 | }
|
---|
996 |
|
---|
997 | /* Convert a Bigint to a double plus an exponent */
|
---|
998 |
|
---|
999 | static double
|
---|
1000 | b2d(Bigint *a, int *e)
|
---|
1001 | {
|
---|
1002 | ULong *xa, *xa0, w, y, z;
|
---|
1003 | int k;
|
---|
1004 | U d;
|
---|
1005 |
|
---|
1006 | xa0 = a->x;
|
---|
1007 | xa = xa0 + a->wds;
|
---|
1008 | y = *--xa;
|
---|
1009 | #ifdef DEBUG
|
---|
1010 | if (!y) Bug("zero y in b2d");
|
---|
1011 | #endif
|
---|
1012 | k = hi0bits(y);
|
---|
1013 | *e = 32 - k;
|
---|
1014 | if (k < Ebits) {
|
---|
1015 | word0(&d) = Exp_1 | y >> (Ebits - k);
|
---|
1016 | w = xa > xa0 ? *--xa : 0;
|
---|
1017 | word1(&d) = y << ((32-Ebits) + k) | w >> (Ebits - k);
|
---|
1018 | goto ret_d;
|
---|
1019 | }
|
---|
1020 | z = xa > xa0 ? *--xa : 0;
|
---|
1021 | if (k -= Ebits) {
|
---|
1022 | word0(&d) = Exp_1 | y << k | z >> (32 - k);
|
---|
1023 | y = xa > xa0 ? *--xa : 0;
|
---|
1024 | word1(&d) = z << k | y >> (32 - k);
|
---|
1025 | }
|
---|
1026 | else {
|
---|
1027 | word0(&d) = Exp_1 | y;
|
---|
1028 | word1(&d) = z;
|
---|
1029 | }
|
---|
1030 | ret_d:
|
---|
1031 | return dval(&d);
|
---|
1032 | }
|
---|
1033 |
|
---|
1034 | /* Convert a scaled double to a Bigint plus an exponent. Similar to d2b,
|
---|
1035 | except that it accepts the scale parameter used in _Py_dg_strtod (which
|
---|
1036 | should be either 0 or 2*P), and the normalization for the return value is
|
---|
1037 | different (see below). On input, d should be finite and nonnegative, and d
|
---|
1038 | / 2**scale should be exactly representable as an IEEE 754 double.
|
---|
1039 |
|
---|
1040 | Returns a Bigint b and an integer e such that
|
---|
1041 |
|
---|
1042 | dval(d) / 2**scale = b * 2**e.
|
---|
1043 |
|
---|
1044 | Unlike d2b, b is not necessarily odd: b and e are normalized so
|
---|
1045 | that either 2**(P-1) <= b < 2**P and e >= Etiny, or b < 2**P
|
---|
1046 | and e == Etiny. This applies equally to an input of 0.0: in that
|
---|
1047 | case the return values are b = 0 and e = Etiny.
|
---|
1048 |
|
---|
1049 | The above normalization ensures that for all possible inputs d,
|
---|
1050 | 2**e gives ulp(d/2**scale).
|
---|
1051 |
|
---|
1052 | Returns NULL on failure.
|
---|
1053 | */
|
---|
1054 |
|
---|
1055 | static Bigint *
|
---|
1056 | sd2b(U *d, int scale, int *e)
|
---|
1057 | {
|
---|
1058 | Bigint *b;
|
---|
1059 |
|
---|
1060 | b = Balloc(1);
|
---|
1061 | if (b == NULL)
|
---|
1062 | return NULL;
|
---|
1063 |
|
---|
1064 | /* First construct b and e assuming that scale == 0. */
|
---|
1065 | b->wds = 2;
|
---|
1066 | b->x[0] = word1(d);
|
---|
1067 | b->x[1] = word0(d) & Frac_mask;
|
---|
1068 | *e = Etiny - 1 + (int)((word0(d) & Exp_mask) >> Exp_shift);
|
---|
1069 | if (*e < Etiny)
|
---|
1070 | *e = Etiny;
|
---|
1071 | else
|
---|
1072 | b->x[1] |= Exp_msk1;
|
---|
1073 |
|
---|
1074 | /* Now adjust for scale, provided that b != 0. */
|
---|
1075 | if (scale && (b->x[0] || b->x[1])) {
|
---|
1076 | *e -= scale;
|
---|
1077 | if (*e < Etiny) {
|
---|
1078 | scale = Etiny - *e;
|
---|
1079 | *e = Etiny;
|
---|
1080 | /* We can't shift more than P-1 bits without shifting out a 1. */
|
---|
1081 | assert(0 < scale && scale <= P - 1);
|
---|
1082 | if (scale >= 32) {
|
---|
1083 | /* The bits shifted out should all be zero. */
|
---|
1084 | assert(b->x[0] == 0);
|
---|
1085 | b->x[0] = b->x[1];
|
---|
1086 | b->x[1] = 0;
|
---|
1087 | scale -= 32;
|
---|
1088 | }
|
---|
1089 | if (scale) {
|
---|
1090 | /* The bits shifted out should all be zero. */
|
---|
1091 | assert(b->x[0] << (32 - scale) == 0);
|
---|
1092 | b->x[0] = (b->x[0] >> scale) | (b->x[1] << (32 - scale));
|
---|
1093 | b->x[1] >>= scale;
|
---|
1094 | }
|
---|
1095 | }
|
---|
1096 | }
|
---|
1097 | /* Ensure b is normalized. */
|
---|
1098 | if (!b->x[1])
|
---|
1099 | b->wds = 1;
|
---|
1100 |
|
---|
1101 | return b;
|
---|
1102 | }
|
---|
1103 |
|
---|
1104 | /* Convert a double to a Bigint plus an exponent. Return NULL on failure.
|
---|
1105 |
|
---|
1106 | Given a finite nonzero double d, return an odd Bigint b and exponent *e
|
---|
1107 | such that fabs(d) = b * 2**e. On return, *bbits gives the number of
|
---|
1108 | significant bits of b; that is, 2**(*bbits-1) <= b < 2**(*bbits).
|
---|
1109 |
|
---|
1110 | If d is zero, then b == 0, *e == -1010, *bbits = 0.
|
---|
1111 | */
|
---|
1112 |
|
---|
1113 | static Bigint *
|
---|
1114 | d2b(U *d, int *e, int *bits)
|
---|
1115 | {
|
---|
1116 | Bigint *b;
|
---|
1117 | int de, k;
|
---|
1118 | ULong *x, y, z;
|
---|
1119 | int i;
|
---|
1120 |
|
---|
1121 | b = Balloc(1);
|
---|
1122 | if (b == NULL)
|
---|
1123 | return NULL;
|
---|
1124 | x = b->x;
|
---|
1125 |
|
---|
1126 | z = word0(d) & Frac_mask;
|
---|
1127 | word0(d) &= 0x7fffffff; /* clear sign bit, which we ignore */
|
---|
1128 | if ((de = (int)(word0(d) >> Exp_shift)))
|
---|
1129 | z |= Exp_msk1;
|
---|
1130 | if ((y = word1(d))) {
|
---|
1131 | if ((k = lo0bits(&y))) {
|
---|
1132 | x[0] = y | z << (32 - k);
|
---|
1133 | z >>= k;
|
---|
1134 | }
|
---|
1135 | else
|
---|
1136 | x[0] = y;
|
---|
1137 | i =
|
---|
1138 | b->wds = (x[1] = z) ? 2 : 1;
|
---|
1139 | }
|
---|
1140 | else {
|
---|
1141 | k = lo0bits(&z);
|
---|
1142 | x[0] = z;
|
---|
1143 | i =
|
---|
1144 | b->wds = 1;
|
---|
1145 | k += 32;
|
---|
1146 | }
|
---|
1147 | if (de) {
|
---|
1148 | *e = de - Bias - (P-1) + k;
|
---|
1149 | *bits = P - k;
|
---|
1150 | }
|
---|
1151 | else {
|
---|
1152 | *e = de - Bias - (P-1) + 1 + k;
|
---|
1153 | *bits = 32*i - hi0bits(x[i-1]);
|
---|
1154 | }
|
---|
1155 | return b;
|
---|
1156 | }
|
---|
1157 |
|
---|
1158 | /* Compute the ratio of two Bigints, as a double. The result may have an
|
---|
1159 | error of up to 2.5 ulps. */
|
---|
1160 |
|
---|
1161 | static double
|
---|
1162 | ratio(Bigint *a, Bigint *b)
|
---|
1163 | {
|
---|
1164 | U da, db;
|
---|
1165 | int k, ka, kb;
|
---|
1166 |
|
---|
1167 | dval(&da) = b2d(a, &ka);
|
---|
1168 | dval(&db) = b2d(b, &kb);
|
---|
1169 | k = ka - kb + 32*(a->wds - b->wds);
|
---|
1170 | if (k > 0)
|
---|
1171 | word0(&da) += k*Exp_msk1;
|
---|
1172 | else {
|
---|
1173 | k = -k;
|
---|
1174 | word0(&db) += k*Exp_msk1;
|
---|
1175 | }
|
---|
1176 | return dval(&da) / dval(&db);
|
---|
1177 | }
|
---|
1178 |
|
---|
1179 | static const double
|
---|
1180 | tens[] = {
|
---|
1181 | 1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9,
|
---|
1182 | 1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19,
|
---|
1183 | 1e20, 1e21, 1e22
|
---|
1184 | };
|
---|
1185 |
|
---|
1186 | static const double
|
---|
1187 | bigtens[] = { 1e16, 1e32, 1e64, 1e128, 1e256 };
|
---|
1188 | static const double tinytens[] = { 1e-16, 1e-32, 1e-64, 1e-128,
|
---|
1189 | 9007199254740992.*9007199254740992.e-256
|
---|
1190 | /* = 2^106 * 1e-256 */
|
---|
1191 | };
|
---|
1192 | /* The factor of 2^53 in tinytens[4] helps us avoid setting the underflow */
|
---|
1193 | /* flag unnecessarily. It leads to a song and dance at the end of strtod. */
|
---|
1194 | #define Scale_Bit 0x10
|
---|
1195 | #define n_bigtens 5
|
---|
1196 |
|
---|
1197 | #define ULbits 32
|
---|
1198 | #define kshift 5
|
---|
1199 | #define kmask 31
|
---|
1200 |
|
---|
1201 |
|
---|
1202 | static int
|
---|
1203 | dshift(Bigint *b, int p2)
|
---|
1204 | {
|
---|
1205 | int rv = hi0bits(b->x[b->wds-1]) - 4;
|
---|
1206 | if (p2 > 0)
|
---|
1207 | rv -= p2;
|
---|
1208 | return rv & kmask;
|
---|
1209 | }
|
---|
1210 |
|
---|
1211 | /* special case of Bigint division. The quotient is always in the range 0 <=
|
---|
1212 | quotient < 10, and on entry the divisor S is normalized so that its top 4
|
---|
1213 | bits (28--31) are zero and bit 27 is set. */
|
---|
1214 |
|
---|
1215 | static int
|
---|
1216 | quorem(Bigint *b, Bigint *S)
|
---|
1217 | {
|
---|
1218 | int n;
|
---|
1219 | ULong *bx, *bxe, q, *sx, *sxe;
|
---|
1220 | #ifdef ULLong
|
---|
1221 | ULLong borrow, carry, y, ys;
|
---|
1222 | #else
|
---|
1223 | ULong borrow, carry, y, ys;
|
---|
1224 | ULong si, z, zs;
|
---|
1225 | #endif
|
---|
1226 |
|
---|
1227 | n = S->wds;
|
---|
1228 | #ifdef DEBUG
|
---|
1229 | /*debug*/ if (b->wds > n)
|
---|
1230 | /*debug*/ Bug("oversize b in quorem");
|
---|
1231 | #endif
|
---|
1232 | if (b->wds < n)
|
---|
1233 | return 0;
|
---|
1234 | sx = S->x;
|
---|
1235 | sxe = sx + --n;
|
---|
1236 | bx = b->x;
|
---|
1237 | bxe = bx + n;
|
---|
1238 | q = *bxe / (*sxe + 1); /* ensure q <= true quotient */
|
---|
1239 | #ifdef DEBUG
|
---|
1240 | /*debug*/ if (q > 9)
|
---|
1241 | /*debug*/ Bug("oversized quotient in quorem");
|
---|
1242 | #endif
|
---|
1243 | if (q) {
|
---|
1244 | borrow = 0;
|
---|
1245 | carry = 0;
|
---|
1246 | do {
|
---|
1247 | #ifdef ULLong
|
---|
1248 | ys = *sx++ * (ULLong)q + carry;
|
---|
1249 | carry = ys >> 32;
|
---|
1250 | y = *bx - (ys & FFFFFFFF) - borrow;
|
---|
1251 | borrow = y >> 32 & (ULong)1;
|
---|
1252 | *bx++ = (ULong)(y & FFFFFFFF);
|
---|
1253 | #else
|
---|
1254 | si = *sx++;
|
---|
1255 | ys = (si & 0xffff) * q + carry;
|
---|
1256 | zs = (si >> 16) * q + (ys >> 16);
|
---|
1257 | carry = zs >> 16;
|
---|
1258 | y = (*bx & 0xffff) - (ys & 0xffff) - borrow;
|
---|
1259 | borrow = (y & 0x10000) >> 16;
|
---|
1260 | z = (*bx >> 16) - (zs & 0xffff) - borrow;
|
---|
1261 | borrow = (z & 0x10000) >> 16;
|
---|
1262 | Storeinc(bx, z, y);
|
---|
1263 | #endif
|
---|
1264 | }
|
---|
1265 | while(sx <= sxe);
|
---|
1266 | if (!*bxe) {
|
---|
1267 | bx = b->x;
|
---|
1268 | while(--bxe > bx && !*bxe)
|
---|
1269 | --n;
|
---|
1270 | b->wds = n;
|
---|
1271 | }
|
---|
1272 | }
|
---|
1273 | if (cmp(b, S) >= 0) {
|
---|
1274 | q++;
|
---|
1275 | borrow = 0;
|
---|
1276 | carry = 0;
|
---|
1277 | bx = b->x;
|
---|
1278 | sx = S->x;
|
---|
1279 | do {
|
---|
1280 | #ifdef ULLong
|
---|
1281 | ys = *sx++ + carry;
|
---|
1282 | carry = ys >> 32;
|
---|
1283 | y = *bx - (ys & FFFFFFFF) - borrow;
|
---|
1284 | borrow = y >> 32 & (ULong)1;
|
---|
1285 | *bx++ = (ULong)(y & FFFFFFFF);
|
---|
1286 | #else
|
---|
1287 | si = *sx++;
|
---|
1288 | ys = (si & 0xffff) + carry;
|
---|
1289 | zs = (si >> 16) + (ys >> 16);
|
---|
1290 | carry = zs >> 16;
|
---|
1291 | y = (*bx & 0xffff) - (ys & 0xffff) - borrow;
|
---|
1292 | borrow = (y & 0x10000) >> 16;
|
---|
1293 | z = (*bx >> 16) - (zs & 0xffff) - borrow;
|
---|
1294 | borrow = (z & 0x10000) >> 16;
|
---|
1295 | Storeinc(bx, z, y);
|
---|
1296 | #endif
|
---|
1297 | }
|
---|
1298 | while(sx <= sxe);
|
---|
1299 | bx = b->x;
|
---|
1300 | bxe = bx + n;
|
---|
1301 | if (!*bxe) {
|
---|
1302 | while(--bxe > bx && !*bxe)
|
---|
1303 | --n;
|
---|
1304 | b->wds = n;
|
---|
1305 | }
|
---|
1306 | }
|
---|
1307 | return q;
|
---|
1308 | }
|
---|
1309 |
|
---|
1310 | /* sulp(x) is a version of ulp(x) that takes bc.scale into account.
|
---|
1311 |
|
---|
1312 | Assuming that x is finite and nonnegative (positive zero is fine
|
---|
1313 | here) and x / 2^bc.scale is exactly representable as a double,
|
---|
1314 | sulp(x) is equivalent to 2^bc.scale * ulp(x / 2^bc.scale). */
|
---|
1315 |
|
---|
1316 | static double
|
---|
1317 | sulp(U *x, BCinfo *bc)
|
---|
1318 | {
|
---|
1319 | U u;
|
---|
1320 |
|
---|
1321 | if (bc->scale && 2*P + 1 > (int)((word0(x) & Exp_mask) >> Exp_shift)) {
|
---|
1322 | /* rv/2^bc->scale is subnormal */
|
---|
1323 | word0(&u) = (P+2)*Exp_msk1;
|
---|
1324 | word1(&u) = 0;
|
---|
1325 | return u.d;
|
---|
1326 | }
|
---|
1327 | else {
|
---|
1328 | assert(word0(x) || word1(x)); /* x != 0.0 */
|
---|
1329 | return ulp(x);
|
---|
1330 | }
|
---|
1331 | }
|
---|
1332 |
|
---|
1333 | /* The bigcomp function handles some hard cases for strtod, for inputs
|
---|
1334 | with more than STRTOD_DIGLIM digits. It's called once an initial
|
---|
1335 | estimate for the double corresponding to the input string has
|
---|
1336 | already been obtained by the code in _Py_dg_strtod.
|
---|
1337 |
|
---|
1338 | The bigcomp function is only called after _Py_dg_strtod has found a
|
---|
1339 | double value rv such that either rv or rv + 1ulp represents the
|
---|
1340 | correctly rounded value corresponding to the original string. It
|
---|
1341 | determines which of these two values is the correct one by
|
---|
1342 | computing the decimal digits of rv + 0.5ulp and comparing them with
|
---|
1343 | the corresponding digits of s0.
|
---|
1344 |
|
---|
1345 | In the following, write dv for the absolute value of the number represented
|
---|
1346 | by the input string.
|
---|
1347 |
|
---|
1348 | Inputs:
|
---|
1349 |
|
---|
1350 | s0 points to the first significant digit of the input string.
|
---|
1351 |
|
---|
1352 | rv is a (possibly scaled) estimate for the closest double value to the
|
---|
1353 | value represented by the original input to _Py_dg_strtod. If
|
---|
1354 | bc->scale is nonzero, then rv/2^(bc->scale) is the approximation to
|
---|
1355 | the input value.
|
---|
1356 |
|
---|
1357 | bc is a struct containing information gathered during the parsing and
|
---|
1358 | estimation steps of _Py_dg_strtod. Description of fields follows:
|
---|
1359 |
|
---|
1360 | bc->e0 gives the exponent of the input value, such that dv = (integer
|
---|
1361 | given by the bd->nd digits of s0) * 10**e0
|
---|
1362 |
|
---|
1363 | bc->nd gives the total number of significant digits of s0. It will
|
---|
1364 | be at least 1.
|
---|
1365 |
|
---|
1366 | bc->nd0 gives the number of significant digits of s0 before the
|
---|
1367 | decimal separator. If there's no decimal separator, bc->nd0 ==
|
---|
1368 | bc->nd.
|
---|
1369 |
|
---|
1370 | bc->scale is the value used to scale rv to avoid doing arithmetic with
|
---|
1371 | subnormal values. It's either 0 or 2*P (=106).
|
---|
1372 |
|
---|
1373 | Outputs:
|
---|
1374 |
|
---|
1375 | On successful exit, rv/2^(bc->scale) is the closest double to dv.
|
---|
1376 |
|
---|
1377 | Returns 0 on success, -1 on failure (e.g., due to a failed malloc call). */
|
---|
1378 |
|
---|
1379 | static int
|
---|
1380 | bigcomp(U *rv, const char *s0, BCinfo *bc)
|
---|
1381 | {
|
---|
1382 | Bigint *b, *d;
|
---|
1383 | int b2, d2, dd, i, nd, nd0, odd, p2, p5;
|
---|
1384 |
|
---|
1385 | nd = bc->nd;
|
---|
1386 | nd0 = bc->nd0;
|
---|
1387 | p5 = nd + bc->e0;
|
---|
1388 | b = sd2b(rv, bc->scale, &p2);
|
---|
1389 | if (b == NULL)
|
---|
1390 | return -1;
|
---|
1391 |
|
---|
1392 | /* record whether the lsb of rv/2^(bc->scale) is odd: in the exact halfway
|
---|
1393 | case, this is used for round to even. */
|
---|
1394 | odd = b->x[0] & 1;
|
---|
1395 |
|
---|
1396 | /* left shift b by 1 bit and or a 1 into the least significant bit;
|
---|
1397 | this gives us b * 2**p2 = rv/2^(bc->scale) + 0.5 ulp. */
|
---|
1398 | b = lshift(b, 1);
|
---|
1399 | if (b == NULL)
|
---|
1400 | return -1;
|
---|
1401 | b->x[0] |= 1;
|
---|
1402 | p2--;
|
---|
1403 |
|
---|
1404 | p2 -= p5;
|
---|
1405 | d = i2b(1);
|
---|
1406 | if (d == NULL) {
|
---|
1407 | Bfree(b);
|
---|
1408 | return -1;
|
---|
1409 | }
|
---|
1410 | /* Arrange for convenient computation of quotients:
|
---|
1411 | * shift left if necessary so divisor has 4 leading 0 bits.
|
---|
1412 | */
|
---|
1413 | if (p5 > 0) {
|
---|
1414 | d = pow5mult(d, p5);
|
---|
1415 | if (d == NULL) {
|
---|
1416 | Bfree(b);
|
---|
1417 | return -1;
|
---|
1418 | }
|
---|
1419 | }
|
---|
1420 | else if (p5 < 0) {
|
---|
1421 | b = pow5mult(b, -p5);
|
---|
1422 | if (b == NULL) {
|
---|
1423 | Bfree(d);
|
---|
1424 | return -1;
|
---|
1425 | }
|
---|
1426 | }
|
---|
1427 | if (p2 > 0) {
|
---|
1428 | b2 = p2;
|
---|
1429 | d2 = 0;
|
---|
1430 | }
|
---|
1431 | else {
|
---|
1432 | b2 = 0;
|
---|
1433 | d2 = -p2;
|
---|
1434 | }
|
---|
1435 | i = dshift(d, d2);
|
---|
1436 | if ((b2 += i) > 0) {
|
---|
1437 | b = lshift(b, b2);
|
---|
1438 | if (b == NULL) {
|
---|
1439 | Bfree(d);
|
---|
1440 | return -1;
|
---|
1441 | }
|
---|
1442 | }
|
---|
1443 | if ((d2 += i) > 0) {
|
---|
1444 | d = lshift(d, d2);
|
---|
1445 | if (d == NULL) {
|
---|
1446 | Bfree(b);
|
---|
1447 | return -1;
|
---|
1448 | }
|
---|
1449 | }
|
---|
1450 |
|
---|
1451 | /* Compare s0 with b/d: set dd to -1, 0, or 1 according as s0 < b/d, s0 ==
|
---|
1452 | * b/d, or s0 > b/d. Here the digits of s0 are thought of as representing
|
---|
1453 | * a number in the range [0.1, 1). */
|
---|
1454 | if (cmp(b, d) >= 0)
|
---|
1455 | /* b/d >= 1 */
|
---|
1456 | dd = -1;
|
---|
1457 | else {
|
---|
1458 | i = 0;
|
---|
1459 | for(;;) {
|
---|
1460 | b = multadd(b, 10, 0);
|
---|
1461 | if (b == NULL) {
|
---|
1462 | Bfree(d);
|
---|
1463 | return -1;
|
---|
1464 | }
|
---|
1465 | dd = s0[i < nd0 ? i : i+1] - '0' - quorem(b, d);
|
---|
1466 | i++;
|
---|
1467 |
|
---|
1468 | if (dd)
|
---|
1469 | break;
|
---|
1470 | if (!b->x[0] && b->wds == 1) {
|
---|
1471 | /* b/d == 0 */
|
---|
1472 | dd = i < nd;
|
---|
1473 | break;
|
---|
1474 | }
|
---|
1475 | if (!(i < nd)) {
|
---|
1476 | /* b/d != 0, but digits of s0 exhausted */
|
---|
1477 | dd = -1;
|
---|
1478 | break;
|
---|
1479 | }
|
---|
1480 | }
|
---|
1481 | }
|
---|
1482 | Bfree(b);
|
---|
1483 | Bfree(d);
|
---|
1484 | if (dd > 0 || (dd == 0 && odd))
|
---|
1485 | dval(rv) += sulp(rv, bc);
|
---|
1486 | return 0;
|
---|
1487 | }
|
---|
1488 |
|
---|
1489 | double
|
---|
1490 | _Py_dg_strtod(const char *s00, char **se)
|
---|
1491 | {
|
---|
1492 | int bb2, bb5, bbe, bd2, bd5, bs2, c, dsign, e, e1, error;
|
---|
1493 | int esign, i, j, k, lz, nd, nd0, odd, sign;
|
---|
1494 | const char *s, *s0, *s1;
|
---|
1495 | double aadj, aadj1;
|
---|
1496 | U aadj2, adj, rv, rv0;
|
---|
1497 | ULong y, z, abs_exp;
|
---|
1498 | Long L;
|
---|
1499 | BCinfo bc;
|
---|
1500 | Bigint *bb, *bb1, *bd, *bd0, *bs, *delta;
|
---|
1501 |
|
---|
1502 | dval(&rv) = 0.;
|
---|
1503 |
|
---|
1504 | /* Start parsing. */
|
---|
1505 | c = *(s = s00);
|
---|
1506 |
|
---|
1507 | /* Parse optional sign, if present. */
|
---|
1508 | sign = 0;
|
---|
1509 | switch (c) {
|
---|
1510 | case '-':
|
---|
1511 | sign = 1;
|
---|
1512 | /* no break */
|
---|
1513 | case '+':
|
---|
1514 | c = *++s;
|
---|
1515 | }
|
---|
1516 |
|
---|
1517 | /* Skip leading zeros: lz is true iff there were leading zeros. */
|
---|
1518 | s1 = s;
|
---|
1519 | while (c == '0')
|
---|
1520 | c = *++s;
|
---|
1521 | lz = s != s1;
|
---|
1522 |
|
---|
1523 | /* Point s0 at the first nonzero digit (if any). nd0 will be the position
|
---|
1524 | of the point relative to s0. nd will be the total number of digits
|
---|
1525 | ignoring leading zeros. */
|
---|
1526 | s0 = s1 = s;
|
---|
1527 | while ('0' <= c && c <= '9')
|
---|
1528 | c = *++s;
|
---|
1529 | nd0 = nd = s - s1;
|
---|
1530 |
|
---|
1531 | /* Parse decimal point and following digits. */
|
---|
1532 | if (c == '.') {
|
---|
1533 | c = *++s;
|
---|
1534 | if (!nd) {
|
---|
1535 | s1 = s;
|
---|
1536 | while (c == '0')
|
---|
1537 | c = *++s;
|
---|
1538 | lz = lz || s != s1;
|
---|
1539 | nd0 -= s - s1;
|
---|
1540 | s0 = s;
|
---|
1541 | }
|
---|
1542 | s1 = s;
|
---|
1543 | while ('0' <= c && c <= '9')
|
---|
1544 | c = *++s;
|
---|
1545 | nd += s - s1;
|
---|
1546 | }
|
---|
1547 |
|
---|
1548 | /* Now lz is true if and only if there were leading zero digits, and nd
|
---|
1549 | gives the total number of digits ignoring leading zeros. A valid input
|
---|
1550 | must have at least one digit. */
|
---|
1551 | if (!nd && !lz) {
|
---|
1552 | if (se)
|
---|
1553 | *se = (char *)s00;
|
---|
1554 | goto parse_error;
|
---|
1555 | }
|
---|
1556 |
|
---|
1557 | /* Parse exponent. */
|
---|
1558 | e = 0;
|
---|
1559 | if (c == 'e' || c == 'E') {
|
---|
1560 | s00 = s;
|
---|
1561 | c = *++s;
|
---|
1562 |
|
---|
1563 | /* Exponent sign. */
|
---|
1564 | esign = 0;
|
---|
1565 | switch (c) {
|
---|
1566 | case '-':
|
---|
1567 | esign = 1;
|
---|
1568 | /* no break */
|
---|
1569 | case '+':
|
---|
1570 | c = *++s;
|
---|
1571 | }
|
---|
1572 |
|
---|
1573 | /* Skip zeros. lz is true iff there are leading zeros. */
|
---|
1574 | s1 = s;
|
---|
1575 | while (c == '0')
|
---|
1576 | c = *++s;
|
---|
1577 | lz = s != s1;
|
---|
1578 |
|
---|
1579 | /* Get absolute value of the exponent. */
|
---|
1580 | s1 = s;
|
---|
1581 | abs_exp = 0;
|
---|
1582 | while ('0' <= c && c <= '9') {
|
---|
1583 | abs_exp = 10*abs_exp + (c - '0');
|
---|
1584 | c = *++s;
|
---|
1585 | }
|
---|
1586 |
|
---|
1587 | /* abs_exp will be correct modulo 2**32. But 10**9 < 2**32, so if
|
---|
1588 | there are at most 9 significant exponent digits then overflow is
|
---|
1589 | impossible. */
|
---|
1590 | if (s - s1 > 9 || abs_exp > MAX_ABS_EXP)
|
---|
1591 | e = (int)MAX_ABS_EXP;
|
---|
1592 | else
|
---|
1593 | e = (int)abs_exp;
|
---|
1594 | if (esign)
|
---|
1595 | e = -e;
|
---|
1596 |
|
---|
1597 | /* A valid exponent must have at least one digit. */
|
---|
1598 | if (s == s1 && !lz)
|
---|
1599 | s = s00;
|
---|
1600 | }
|
---|
1601 |
|
---|
1602 | /* Adjust exponent to take into account position of the point. */
|
---|
1603 | e -= nd - nd0;
|
---|
1604 | if (nd0 <= 0)
|
---|
1605 | nd0 = nd;
|
---|
1606 |
|
---|
1607 | /* Finished parsing. Set se to indicate how far we parsed */
|
---|
1608 | if (se)
|
---|
1609 | *se = (char *)s;
|
---|
1610 |
|
---|
1611 | /* If all digits were zero, exit with return value +-0.0. Otherwise,
|
---|
1612 | strip trailing zeros: scan back until we hit a nonzero digit. */
|
---|
1613 | if (!nd)
|
---|
1614 | goto ret;
|
---|
1615 | for (i = nd; i > 0; ) {
|
---|
1616 | --i;
|
---|
1617 | if (s0[i < nd0 ? i : i+1] != '0') {
|
---|
1618 | ++i;
|
---|
1619 | break;
|
---|
1620 | }
|
---|
1621 | }
|
---|
1622 | e += nd - i;
|
---|
1623 | nd = i;
|
---|
1624 | if (nd0 > nd)
|
---|
1625 | nd0 = nd;
|
---|
1626 |
|
---|
1627 | /* Summary of parsing results. After parsing, and dealing with zero
|
---|
1628 | * inputs, we have values s0, nd0, nd, e, sign, where:
|
---|
1629 | *
|
---|
1630 | * - s0 points to the first significant digit of the input string
|
---|
1631 | *
|
---|
1632 | * - nd is the total number of significant digits (here, and
|
---|
1633 | * below, 'significant digits' means the set of digits of the
|
---|
1634 | * significand of the input that remain after ignoring leading
|
---|
1635 | * and trailing zeros).
|
---|
1636 | *
|
---|
1637 | * - nd0 indicates the position of the decimal point, if present; it
|
---|
1638 | * satisfies 1 <= nd0 <= nd. The nd significant digits are in
|
---|
1639 | * s0[0:nd0] and s0[nd0+1:nd+1] using the usual Python half-open slice
|
---|
1640 | * notation. (If nd0 < nd, then s0[nd0] contains a '.' character; if
|
---|
1641 | * nd0 == nd, then s0[nd0] could be any non-digit character.)
|
---|
1642 | *
|
---|
1643 | * - e is the adjusted exponent: the absolute value of the number
|
---|
1644 | * represented by the original input string is n * 10**e, where
|
---|
1645 | * n is the integer represented by the concatenation of
|
---|
1646 | * s0[0:nd0] and s0[nd0+1:nd+1]
|
---|
1647 | *
|
---|
1648 | * - sign gives the sign of the input: 1 for negative, 0 for positive
|
---|
1649 | *
|
---|
1650 | * - the first and last significant digits are nonzero
|
---|
1651 | */
|
---|
1652 |
|
---|
1653 | /* put first DBL_DIG+1 digits into integer y and z.
|
---|
1654 | *
|
---|
1655 | * - y contains the value represented by the first min(9, nd)
|
---|
1656 | * significant digits
|
---|
1657 | *
|
---|
1658 | * - if nd > 9, z contains the value represented by significant digits
|
---|
1659 | * with indices in [9, min(16, nd)). So y * 10**(min(16, nd) - 9) + z
|
---|
1660 | * gives the value represented by the first min(16, nd) sig. digits.
|
---|
1661 | */
|
---|
1662 |
|
---|
1663 | bc.e0 = e1 = e;
|
---|
1664 | y = z = 0;
|
---|
1665 | for (i = 0; i < nd; i++) {
|
---|
1666 | if (i < 9)
|
---|
1667 | y = 10*y + s0[i < nd0 ? i : i+1] - '0';
|
---|
1668 | else if (i < DBL_DIG+1)
|
---|
1669 | z = 10*z + s0[i < nd0 ? i : i+1] - '0';
|
---|
1670 | else
|
---|
1671 | break;
|
---|
1672 | }
|
---|
1673 |
|
---|
1674 | k = nd < DBL_DIG + 1 ? nd : DBL_DIG + 1;
|
---|
1675 | dval(&rv) = y;
|
---|
1676 | if (k > 9) {
|
---|
1677 | dval(&rv) = tens[k - 9] * dval(&rv) + z;
|
---|
1678 | }
|
---|
1679 | bd0 = 0;
|
---|
1680 | if (nd <= DBL_DIG
|
---|
1681 | && Flt_Rounds == 1
|
---|
1682 | ) {
|
---|
1683 | if (!e)
|
---|
1684 | goto ret;
|
---|
1685 | if (e > 0) {
|
---|
1686 | if (e <= Ten_pmax) {
|
---|
1687 | dval(&rv) *= tens[e];
|
---|
1688 | goto ret;
|
---|
1689 | }
|
---|
1690 | i = DBL_DIG - nd;
|
---|
1691 | if (e <= Ten_pmax + i) {
|
---|
1692 | /* A fancier test would sometimes let us do
|
---|
1693 | * this for larger i values.
|
---|
1694 | */
|
---|
1695 | e -= i;
|
---|
1696 | dval(&rv) *= tens[i];
|
---|
1697 | dval(&rv) *= tens[e];
|
---|
1698 | goto ret;
|
---|
1699 | }
|
---|
1700 | }
|
---|
1701 | else if (e >= -Ten_pmax) {
|
---|
1702 | dval(&rv) /= tens[-e];
|
---|
1703 | goto ret;
|
---|
1704 | }
|
---|
1705 | }
|
---|
1706 | e1 += nd - k;
|
---|
1707 |
|
---|
1708 | bc.scale = 0;
|
---|
1709 |
|
---|
1710 | /* Get starting approximation = rv * 10**e1 */
|
---|
1711 |
|
---|
1712 | if (e1 > 0) {
|
---|
1713 | if ((i = e1 & 15))
|
---|
1714 | dval(&rv) *= tens[i];
|
---|
1715 | if (e1 &= ~15) {
|
---|
1716 | if (e1 > DBL_MAX_10_EXP)
|
---|
1717 | goto ovfl;
|
---|
1718 | e1 >>= 4;
|
---|
1719 | for(j = 0; e1 > 1; j++, e1 >>= 1)
|
---|
1720 | if (e1 & 1)
|
---|
1721 | dval(&rv) *= bigtens[j];
|
---|
1722 | /* The last multiplication could overflow. */
|
---|
1723 | word0(&rv) -= P*Exp_msk1;
|
---|
1724 | dval(&rv) *= bigtens[j];
|
---|
1725 | if ((z = word0(&rv) & Exp_mask)
|
---|
1726 | > Exp_msk1*(DBL_MAX_EXP+Bias-P))
|
---|
1727 | goto ovfl;
|
---|
1728 | if (z > Exp_msk1*(DBL_MAX_EXP+Bias-1-P)) {
|
---|
1729 | /* set to largest number */
|
---|
1730 | /* (Can't trust DBL_MAX) */
|
---|
1731 | word0(&rv) = Big0;
|
---|
1732 | word1(&rv) = Big1;
|
---|
1733 | }
|
---|
1734 | else
|
---|
1735 | word0(&rv) += P*Exp_msk1;
|
---|
1736 | }
|
---|
1737 | }
|
---|
1738 | else if (e1 < 0) {
|
---|
1739 | /* The input decimal value lies in [10**e1, 10**(e1+16)).
|
---|
1740 |
|
---|
1741 | If e1 <= -512, underflow immediately.
|
---|
1742 | If e1 <= -256, set bc.scale to 2*P.
|
---|
1743 |
|
---|
1744 | So for input value < 1e-256, bc.scale is always set;
|
---|
1745 | for input value >= 1e-240, bc.scale is never set.
|
---|
1746 | For input values in [1e-256, 1e-240), bc.scale may or may
|
---|
1747 | not be set. */
|
---|
1748 |
|
---|
1749 | e1 = -e1;
|
---|
1750 | if ((i = e1 & 15))
|
---|
1751 | dval(&rv) /= tens[i];
|
---|
1752 | if (e1 >>= 4) {
|
---|
1753 | if (e1 >= 1 << n_bigtens)
|
---|
1754 | goto undfl;
|
---|
1755 | if (e1 & Scale_Bit)
|
---|
1756 | bc.scale = 2*P;
|
---|
1757 | for(j = 0; e1 > 0; j++, e1 >>= 1)
|
---|
1758 | if (e1 & 1)
|
---|
1759 | dval(&rv) *= tinytens[j];
|
---|
1760 | if (bc.scale && (j = 2*P + 1 - ((word0(&rv) & Exp_mask)
|
---|
1761 | >> Exp_shift)) > 0) {
|
---|
1762 | /* scaled rv is denormal; clear j low bits */
|
---|
1763 | if (j >= 32) {
|
---|
1764 | word1(&rv) = 0;
|
---|
1765 | if (j >= 53)
|
---|
1766 | word0(&rv) = (P+2)*Exp_msk1;
|
---|
1767 | else
|
---|
1768 | word0(&rv) &= 0xffffffff << (j-32);
|
---|
1769 | }
|
---|
1770 | else
|
---|
1771 | word1(&rv) &= 0xffffffff << j;
|
---|
1772 | }
|
---|
1773 | if (!dval(&rv))
|
---|
1774 | goto undfl;
|
---|
1775 | }
|
---|
1776 | }
|
---|
1777 |
|
---|
1778 | /* Now the hard part -- adjusting rv to the correct value.*/
|
---|
1779 |
|
---|
1780 | /* Put digits into bd: true value = bd * 10^e */
|
---|
1781 |
|
---|
1782 | bc.nd = nd;
|
---|
1783 | bc.nd0 = nd0; /* Only needed if nd > STRTOD_DIGLIM, but done here */
|
---|
1784 | /* to silence an erroneous warning about bc.nd0 */
|
---|
1785 | /* possibly not being initialized. */
|
---|
1786 | if (nd > STRTOD_DIGLIM) {
|
---|
1787 | /* ASSERT(STRTOD_DIGLIM >= 18); 18 == one more than the */
|
---|
1788 | /* minimum number of decimal digits to distinguish double values */
|
---|
1789 | /* in IEEE arithmetic. */
|
---|
1790 |
|
---|
1791 | /* Truncate input to 18 significant digits, then discard any trailing
|
---|
1792 | zeros on the result by updating nd, nd0, e and y suitably. (There's
|
---|
1793 | no need to update z; it's not reused beyond this point.) */
|
---|
1794 | for (i = 18; i > 0; ) {
|
---|
1795 | /* scan back until we hit a nonzero digit. significant digit 'i'
|
---|
1796 | is s0[i] if i < nd0, s0[i+1] if i >= nd0. */
|
---|
1797 | --i;
|
---|
1798 | if (s0[i < nd0 ? i : i+1] != '0') {
|
---|
1799 | ++i;
|
---|
1800 | break;
|
---|
1801 | }
|
---|
1802 | }
|
---|
1803 | e += nd - i;
|
---|
1804 | nd = i;
|
---|
1805 | if (nd0 > nd)
|
---|
1806 | nd0 = nd;
|
---|
1807 | if (nd < 9) { /* must recompute y */
|
---|
1808 | y = 0;
|
---|
1809 | for(i = 0; i < nd0; ++i)
|
---|
1810 | y = 10*y + s0[i] - '0';
|
---|
1811 | for(; i < nd; ++i)
|
---|
1812 | y = 10*y + s0[i+1] - '0';
|
---|
1813 | }
|
---|
1814 | }
|
---|
1815 | bd0 = s2b(s0, nd0, nd, y);
|
---|
1816 | if (bd0 == NULL)
|
---|
1817 | goto failed_malloc;
|
---|
1818 |
|
---|
1819 | /* Notation for the comments below. Write:
|
---|
1820 |
|
---|
1821 | - dv for the absolute value of the number represented by the original
|
---|
1822 | decimal input string.
|
---|
1823 |
|
---|
1824 | - if we've truncated dv, write tdv for the truncated value.
|
---|
1825 | Otherwise, set tdv == dv.
|
---|
1826 |
|
---|
1827 | - srv for the quantity rv/2^bc.scale; so srv is the current binary
|
---|
1828 | approximation to tdv (and dv). It should be exactly representable
|
---|
1829 | in an IEEE 754 double.
|
---|
1830 | */
|
---|
1831 |
|
---|
1832 | for(;;) {
|
---|
1833 |
|
---|
1834 | /* This is the main correction loop for _Py_dg_strtod.
|
---|
1835 |
|
---|
1836 | We've got a decimal value tdv, and a floating-point approximation
|
---|
1837 | srv=rv/2^bc.scale to tdv. The aim is to determine whether srv is
|
---|
1838 | close enough (i.e., within 0.5 ulps) to tdv, and to compute a new
|
---|
1839 | approximation if not.
|
---|
1840 |
|
---|
1841 | To determine whether srv is close enough to tdv, compute integers
|
---|
1842 | bd, bb and bs proportional to tdv, srv and 0.5 ulp(srv)
|
---|
1843 | respectively, and then use integer arithmetic to determine whether
|
---|
1844 | |tdv - srv| is less than, equal to, or greater than 0.5 ulp(srv).
|
---|
1845 | */
|
---|
1846 |
|
---|
1847 | bd = Balloc(bd0->k);
|
---|
1848 | if (bd == NULL) {
|
---|
1849 | Bfree(bd0);
|
---|
1850 | goto failed_malloc;
|
---|
1851 | }
|
---|
1852 | Bcopy(bd, bd0);
|
---|
1853 | bb = sd2b(&rv, bc.scale, &bbe); /* srv = bb * 2^bbe */
|
---|
1854 | if (bb == NULL) {
|
---|
1855 | Bfree(bd);
|
---|
1856 | Bfree(bd0);
|
---|
1857 | goto failed_malloc;
|
---|
1858 | }
|
---|
1859 | /* Record whether lsb of bb is odd, in case we need this
|
---|
1860 | for the round-to-even step later. */
|
---|
1861 | odd = bb->x[0] & 1;
|
---|
1862 |
|
---|
1863 | /* tdv = bd * 10**e; srv = bb * 2**bbe */
|
---|
1864 | bs = i2b(1);
|
---|
1865 | if (bs == NULL) {
|
---|
1866 | Bfree(bb);
|
---|
1867 | Bfree(bd);
|
---|
1868 | Bfree(bd0);
|
---|
1869 | goto failed_malloc;
|
---|
1870 | }
|
---|
1871 |
|
---|
1872 | if (e >= 0) {
|
---|
1873 | bb2 = bb5 = 0;
|
---|
1874 | bd2 = bd5 = e;
|
---|
1875 | }
|
---|
1876 | else {
|
---|
1877 | bb2 = bb5 = -e;
|
---|
1878 | bd2 = bd5 = 0;
|
---|
1879 | }
|
---|
1880 | if (bbe >= 0)
|
---|
1881 | bb2 += bbe;
|
---|
1882 | else
|
---|
1883 | bd2 -= bbe;
|
---|
1884 | bs2 = bb2;
|
---|
1885 | bb2++;
|
---|
1886 | bd2++;
|
---|
1887 |
|
---|
1888 | /* At this stage bd5 - bb5 == e == bd2 - bb2 + bbe, bb2 - bs2 == 1,
|
---|
1889 | and bs == 1, so:
|
---|
1890 |
|
---|
1891 | tdv == bd * 10**e = bd * 2**(bbe - bb2 + bd2) * 5**(bd5 - bb5)
|
---|
1892 | srv == bb * 2**bbe = bb * 2**(bbe - bb2 + bb2)
|
---|
1893 | 0.5 ulp(srv) == 2**(bbe-1) = bs * 2**(bbe - bb2 + bs2)
|
---|
1894 |
|
---|
1895 | It follows that:
|
---|
1896 |
|
---|
1897 | M * tdv = bd * 2**bd2 * 5**bd5
|
---|
1898 | M * srv = bb * 2**bb2 * 5**bb5
|
---|
1899 | M * 0.5 ulp(srv) = bs * 2**bs2 * 5**bb5
|
---|
1900 |
|
---|
1901 | for some constant M. (Actually, M == 2**(bb2 - bbe) * 5**bb5, but
|
---|
1902 | this fact is not needed below.)
|
---|
1903 | */
|
---|
1904 |
|
---|
1905 | /* Remove factor of 2**i, where i = min(bb2, bd2, bs2). */
|
---|
1906 | i = bb2 < bd2 ? bb2 : bd2;
|
---|
1907 | if (i > bs2)
|
---|
1908 | i = bs2;
|
---|
1909 | if (i > 0) {
|
---|
1910 | bb2 -= i;
|
---|
1911 | bd2 -= i;
|
---|
1912 | bs2 -= i;
|
---|
1913 | }
|
---|
1914 |
|
---|
1915 | /* Scale bb, bd, bs by the appropriate powers of 2 and 5. */
|
---|
1916 | if (bb5 > 0) {
|
---|
1917 | bs = pow5mult(bs, bb5);
|
---|
1918 | if (bs == NULL) {
|
---|
1919 | Bfree(bb);
|
---|
1920 | Bfree(bd);
|
---|
1921 | Bfree(bd0);
|
---|
1922 | goto failed_malloc;
|
---|
1923 | }
|
---|
1924 | bb1 = mult(bs, bb);
|
---|
1925 | Bfree(bb);
|
---|
1926 | bb = bb1;
|
---|
1927 | if (bb == NULL) {
|
---|
1928 | Bfree(bs);
|
---|
1929 | Bfree(bd);
|
---|
1930 | Bfree(bd0);
|
---|
1931 | goto failed_malloc;
|
---|
1932 | }
|
---|
1933 | }
|
---|
1934 | if (bb2 > 0) {
|
---|
1935 | bb = lshift(bb, bb2);
|
---|
1936 | if (bb == NULL) {
|
---|
1937 | Bfree(bs);
|
---|
1938 | Bfree(bd);
|
---|
1939 | Bfree(bd0);
|
---|
1940 | goto failed_malloc;
|
---|
1941 | }
|
---|
1942 | }
|
---|
1943 | if (bd5 > 0) {
|
---|
1944 | bd = pow5mult(bd, bd5);
|
---|
1945 | if (bd == NULL) {
|
---|
1946 | Bfree(bb);
|
---|
1947 | Bfree(bs);
|
---|
1948 | Bfree(bd0);
|
---|
1949 | goto failed_malloc;
|
---|
1950 | }
|
---|
1951 | }
|
---|
1952 | if (bd2 > 0) {
|
---|
1953 | bd = lshift(bd, bd2);
|
---|
1954 | if (bd == NULL) {
|
---|
1955 | Bfree(bb);
|
---|
1956 | Bfree(bs);
|
---|
1957 | Bfree(bd0);
|
---|
1958 | goto failed_malloc;
|
---|
1959 | }
|
---|
1960 | }
|
---|
1961 | if (bs2 > 0) {
|
---|
1962 | bs = lshift(bs, bs2);
|
---|
1963 | if (bs == NULL) {
|
---|
1964 | Bfree(bb);
|
---|
1965 | Bfree(bd);
|
---|
1966 | Bfree(bd0);
|
---|
1967 | goto failed_malloc;
|
---|
1968 | }
|
---|
1969 | }
|
---|
1970 |
|
---|
1971 | /* Now bd, bb and bs are scaled versions of tdv, srv and 0.5 ulp(srv),
|
---|
1972 | respectively. Compute the difference |tdv - srv|, and compare
|
---|
1973 | with 0.5 ulp(srv). */
|
---|
1974 |
|
---|
1975 | delta = diff(bb, bd);
|
---|
1976 | if (delta == NULL) {
|
---|
1977 | Bfree(bb);
|
---|
1978 | Bfree(bs);
|
---|
1979 | Bfree(bd);
|
---|
1980 | Bfree(bd0);
|
---|
1981 | goto failed_malloc;
|
---|
1982 | }
|
---|
1983 | dsign = delta->sign;
|
---|
1984 | delta->sign = 0;
|
---|
1985 | i = cmp(delta, bs);
|
---|
1986 | if (bc.nd > nd && i <= 0) {
|
---|
1987 | if (dsign)
|
---|
1988 | break; /* Must use bigcomp(). */
|
---|
1989 |
|
---|
1990 | /* Here rv overestimates the truncated decimal value by at most
|
---|
1991 | 0.5 ulp(rv). Hence rv either overestimates the true decimal
|
---|
1992 | value by <= 0.5 ulp(rv), or underestimates it by some small
|
---|
1993 | amount (< 0.1 ulp(rv)); either way, rv is within 0.5 ulps of
|
---|
1994 | the true decimal value, so it's possible to exit.
|
---|
1995 |
|
---|
1996 | Exception: if scaled rv is a normal exact power of 2, but not
|
---|
1997 | DBL_MIN, then rv - 0.5 ulp(rv) takes us all the way down to the
|
---|
1998 | next double, so the correctly rounded result is either rv - 0.5
|
---|
1999 | ulp(rv) or rv; in this case, use bigcomp to distinguish. */
|
---|
2000 |
|
---|
2001 | if (!word1(&rv) && !(word0(&rv) & Bndry_mask)) {
|
---|
2002 | /* rv can't be 0, since it's an overestimate for some
|
---|
2003 | nonzero value. So rv is a normal power of 2. */
|
---|
2004 | j = (int)(word0(&rv) & Exp_mask) >> Exp_shift;
|
---|
2005 | /* rv / 2^bc.scale = 2^(j - 1023 - bc.scale); use bigcomp if
|
---|
2006 | rv / 2^bc.scale >= 2^-1021. */
|
---|
2007 | if (j - bc.scale >= 2) {
|
---|
2008 | dval(&rv) -= 0.5 * sulp(&rv, &bc);
|
---|
2009 | break; /* Use bigcomp. */
|
---|
2010 | }
|
---|
2011 | }
|
---|
2012 |
|
---|
2013 | {
|
---|
2014 | bc.nd = nd;
|
---|
2015 | i = -1; /* Discarded digits make delta smaller. */
|
---|
2016 | }
|
---|
2017 | }
|
---|
2018 |
|
---|
2019 | if (i < 0) {
|
---|
2020 | /* Error is less than half an ulp -- check for
|
---|
2021 | * special case of mantissa a power of two.
|
---|
2022 | */
|
---|
2023 | if (dsign || word1(&rv) || word0(&rv) & Bndry_mask
|
---|
2024 | || (word0(&rv) & Exp_mask) <= (2*P+1)*Exp_msk1
|
---|
2025 | ) {
|
---|
2026 | break;
|
---|
2027 | }
|
---|
2028 | if (!delta->x[0] && delta->wds <= 1) {
|
---|
2029 | /* exact result */
|
---|
2030 | break;
|
---|
2031 | }
|
---|
2032 | delta = lshift(delta,Log2P);
|
---|
2033 | if (delta == NULL) {
|
---|
2034 | Bfree(bb);
|
---|
2035 | Bfree(bs);
|
---|
2036 | Bfree(bd);
|
---|
2037 | Bfree(bd0);
|
---|
2038 | goto failed_malloc;
|
---|
2039 | }
|
---|
2040 | if (cmp(delta, bs) > 0)
|
---|
2041 | goto drop_down;
|
---|
2042 | break;
|
---|
2043 | }
|
---|
2044 | if (i == 0) {
|
---|
2045 | /* exactly half-way between */
|
---|
2046 | if (dsign) {
|
---|
2047 | if ((word0(&rv) & Bndry_mask1) == Bndry_mask1
|
---|
2048 | && word1(&rv) == (
|
---|
2049 | (bc.scale &&
|
---|
2050 | (y = word0(&rv) & Exp_mask) <= 2*P*Exp_msk1) ?
|
---|
2051 | (0xffffffff & (0xffffffff << (2*P+1-(y>>Exp_shift)))) :
|
---|
2052 | 0xffffffff)) {
|
---|
2053 | /*boundary case -- increment exponent*/
|
---|
2054 | word0(&rv) = (word0(&rv) & Exp_mask)
|
---|
2055 | + Exp_msk1
|
---|
2056 | ;
|
---|
2057 | word1(&rv) = 0;
|
---|
2058 | dsign = 0;
|
---|
2059 | break;
|
---|
2060 | }
|
---|
2061 | }
|
---|
2062 | else if (!(word0(&rv) & Bndry_mask) && !word1(&rv)) {
|
---|
2063 | drop_down:
|
---|
2064 | /* boundary case -- decrement exponent */
|
---|
2065 | if (bc.scale) {
|
---|
2066 | L = word0(&rv) & Exp_mask;
|
---|
2067 | if (L <= (2*P+1)*Exp_msk1) {
|
---|
2068 | if (L > (P+2)*Exp_msk1)
|
---|
2069 | /* round even ==> */
|
---|
2070 | /* accept rv */
|
---|
2071 | break;
|
---|
2072 | /* rv = smallest denormal */
|
---|
2073 | if (bc.nd > nd)
|
---|
2074 | break;
|
---|
2075 | goto undfl;
|
---|
2076 | }
|
---|
2077 | }
|
---|
2078 | L = (word0(&rv) & Exp_mask) - Exp_msk1;
|
---|
2079 | word0(&rv) = L | Bndry_mask1;
|
---|
2080 | word1(&rv) = 0xffffffff;
|
---|
2081 | break;
|
---|
2082 | }
|
---|
2083 | if (!odd)
|
---|
2084 | break;
|
---|
2085 | if (dsign)
|
---|
2086 | dval(&rv) += sulp(&rv, &bc);
|
---|
2087 | else {
|
---|
2088 | dval(&rv) -= sulp(&rv, &bc);
|
---|
2089 | if (!dval(&rv)) {
|
---|
2090 | if (bc.nd >nd)
|
---|
2091 | break;
|
---|
2092 | goto undfl;
|
---|
2093 | }
|
---|
2094 | }
|
---|
2095 | dsign = 1 - dsign;
|
---|
2096 | break;
|
---|
2097 | }
|
---|
2098 | if ((aadj = ratio(delta, bs)) <= 2.) {
|
---|
2099 | if (dsign)
|
---|
2100 | aadj = aadj1 = 1.;
|
---|
2101 | else if (word1(&rv) || word0(&rv) & Bndry_mask) {
|
---|
2102 | if (word1(&rv) == Tiny1 && !word0(&rv)) {
|
---|
2103 | if (bc.nd >nd)
|
---|
2104 | break;
|
---|
2105 | goto undfl;
|
---|
2106 | }
|
---|
2107 | aadj = 1.;
|
---|
2108 | aadj1 = -1.;
|
---|
2109 | }
|
---|
2110 | else {
|
---|
2111 | /* special case -- power of FLT_RADIX to be */
|
---|
2112 | /* rounded down... */
|
---|
2113 |
|
---|
2114 | if (aadj < 2./FLT_RADIX)
|
---|
2115 | aadj = 1./FLT_RADIX;
|
---|
2116 | else
|
---|
2117 | aadj *= 0.5;
|
---|
2118 | aadj1 = -aadj;
|
---|
2119 | }
|
---|
2120 | }
|
---|
2121 | else {
|
---|
2122 | aadj *= 0.5;
|
---|
2123 | aadj1 = dsign ? aadj : -aadj;
|
---|
2124 | if (Flt_Rounds == 0)
|
---|
2125 | aadj1 += 0.5;
|
---|
2126 | }
|
---|
2127 | y = word0(&rv) & Exp_mask;
|
---|
2128 |
|
---|
2129 | /* Check for overflow */
|
---|
2130 |
|
---|
2131 | if (y == Exp_msk1*(DBL_MAX_EXP+Bias-1)) {
|
---|
2132 | dval(&rv0) = dval(&rv);
|
---|
2133 | word0(&rv) -= P*Exp_msk1;
|
---|
2134 | adj.d = aadj1 * ulp(&rv);
|
---|
2135 | dval(&rv) += adj.d;
|
---|
2136 | if ((word0(&rv) & Exp_mask) >=
|
---|
2137 | Exp_msk1*(DBL_MAX_EXP+Bias-P)) {
|
---|
2138 | if (word0(&rv0) == Big0 && word1(&rv0) == Big1) {
|
---|
2139 | Bfree(bb);
|
---|
2140 | Bfree(bd);
|
---|
2141 | Bfree(bs);
|
---|
2142 | Bfree(bd0);
|
---|
2143 | Bfree(delta);
|
---|
2144 | goto ovfl;
|
---|
2145 | }
|
---|
2146 | word0(&rv) = Big0;
|
---|
2147 | word1(&rv) = Big1;
|
---|
2148 | goto cont;
|
---|
2149 | }
|
---|
2150 | else
|
---|
2151 | word0(&rv) += P*Exp_msk1;
|
---|
2152 | }
|
---|
2153 | else {
|
---|
2154 | if (bc.scale && y <= 2*P*Exp_msk1) {
|
---|
2155 | if (aadj <= 0x7fffffff) {
|
---|
2156 | if ((z = (ULong)aadj) <= 0)
|
---|
2157 | z = 1;
|
---|
2158 | aadj = z;
|
---|
2159 | aadj1 = dsign ? aadj : -aadj;
|
---|
2160 | }
|
---|
2161 | dval(&aadj2) = aadj1;
|
---|
2162 | word0(&aadj2) += (2*P+1)*Exp_msk1 - y;
|
---|
2163 | aadj1 = dval(&aadj2);
|
---|
2164 | }
|
---|
2165 | adj.d = aadj1 * ulp(&rv);
|
---|
2166 | dval(&rv) += adj.d;
|
---|
2167 | }
|
---|
2168 | z = word0(&rv) & Exp_mask;
|
---|
2169 | if (bc.nd == nd) {
|
---|
2170 | if (!bc.scale)
|
---|
2171 | if (y == z) {
|
---|
2172 | /* Can we stop now? */
|
---|
2173 | L = (Long)aadj;
|
---|
2174 | aadj -= L;
|
---|
2175 | /* The tolerances below are conservative. */
|
---|
2176 | if (dsign || word1(&rv) || word0(&rv) & Bndry_mask) {
|
---|
2177 | if (aadj < .4999999 || aadj > .5000001)
|
---|
2178 | break;
|
---|
2179 | }
|
---|
2180 | else if (aadj < .4999999/FLT_RADIX)
|
---|
2181 | break;
|
---|
2182 | }
|
---|
2183 | }
|
---|
2184 | cont:
|
---|
2185 | Bfree(bb);
|
---|
2186 | Bfree(bd);
|
---|
2187 | Bfree(bs);
|
---|
2188 | Bfree(delta);
|
---|
2189 | }
|
---|
2190 | Bfree(bb);
|
---|
2191 | Bfree(bd);
|
---|
2192 | Bfree(bs);
|
---|
2193 | Bfree(bd0);
|
---|
2194 | Bfree(delta);
|
---|
2195 | if (bc.nd > nd) {
|
---|
2196 | error = bigcomp(&rv, s0, &bc);
|
---|
2197 | if (error)
|
---|
2198 | goto failed_malloc;
|
---|
2199 | }
|
---|
2200 |
|
---|
2201 | if (bc.scale) {
|
---|
2202 | word0(&rv0) = Exp_1 - 2*P*Exp_msk1;
|
---|
2203 | word1(&rv0) = 0;
|
---|
2204 | dval(&rv) *= dval(&rv0);
|
---|
2205 | }
|
---|
2206 |
|
---|
2207 | ret:
|
---|
2208 | return sign ? -dval(&rv) : dval(&rv);
|
---|
2209 |
|
---|
2210 | parse_error:
|
---|
2211 | return 0.0;
|
---|
2212 |
|
---|
2213 | failed_malloc:
|
---|
2214 | errno = ENOMEM;
|
---|
2215 | return -1.0;
|
---|
2216 |
|
---|
2217 | undfl:
|
---|
2218 | return sign ? -0.0 : 0.0;
|
---|
2219 |
|
---|
2220 | ovfl:
|
---|
2221 | errno = ERANGE;
|
---|
2222 | /* Can't trust HUGE_VAL */
|
---|
2223 | word0(&rv) = Exp_mask;
|
---|
2224 | word1(&rv) = 0;
|
---|
2225 | return sign ? -dval(&rv) : dval(&rv);
|
---|
2226 |
|
---|
2227 | }
|
---|
2228 |
|
---|
2229 | static char *
|
---|
2230 | rv_alloc(int i)
|
---|
2231 | {
|
---|
2232 | int j, k, *r;
|
---|
2233 |
|
---|
2234 | j = sizeof(ULong);
|
---|
2235 | for(k = 0;
|
---|
2236 | sizeof(Bigint) - sizeof(ULong) - sizeof(int) + j <= (unsigned)i;
|
---|
2237 | j <<= 1)
|
---|
2238 | k++;
|
---|
2239 | r = (int*)Balloc(k);
|
---|
2240 | if (r == NULL)
|
---|
2241 | return NULL;
|
---|
2242 | *r = k;
|
---|
2243 | return (char *)(r+1);
|
---|
2244 | }
|
---|
2245 |
|
---|
2246 | static char *
|
---|
2247 | nrv_alloc(char *s, char **rve, int n)
|
---|
2248 | {
|
---|
2249 | char *rv, *t;
|
---|
2250 |
|
---|
2251 | rv = rv_alloc(n);
|
---|
2252 | if (rv == NULL)
|
---|
2253 | return NULL;
|
---|
2254 | t = rv;
|
---|
2255 | while((*t = *s++)) t++;
|
---|
2256 | if (rve)
|
---|
2257 | *rve = t;
|
---|
2258 | return rv;
|
---|
2259 | }
|
---|
2260 |
|
---|
2261 | /* freedtoa(s) must be used to free values s returned by dtoa
|
---|
2262 | * when MULTIPLE_THREADS is #defined. It should be used in all cases,
|
---|
2263 | * but for consistency with earlier versions of dtoa, it is optional
|
---|
2264 | * when MULTIPLE_THREADS is not defined.
|
---|
2265 | */
|
---|
2266 |
|
---|
2267 | void
|
---|
2268 | _Py_dg_freedtoa(char *s)
|
---|
2269 | {
|
---|
2270 | Bigint *b = (Bigint *)((int *)s - 1);
|
---|
2271 | b->maxwds = 1 << (b->k = *(int*)b);
|
---|
2272 | Bfree(b);
|
---|
2273 | }
|
---|
2274 |
|
---|
2275 | /* dtoa for IEEE arithmetic (dmg): convert double to ASCII string.
|
---|
2276 | *
|
---|
2277 | * Inspired by "How to Print Floating-Point Numbers Accurately" by
|
---|
2278 | * Guy L. Steele, Jr. and Jon L. White [Proc. ACM SIGPLAN '90, pp. 112-126].
|
---|
2279 | *
|
---|
2280 | * Modifications:
|
---|
2281 | * 1. Rather than iterating, we use a simple numeric overestimate
|
---|
2282 | * to determine k = floor(log10(d)). We scale relevant
|
---|
2283 | * quantities using O(log2(k)) rather than O(k) multiplications.
|
---|
2284 | * 2. For some modes > 2 (corresponding to ecvt and fcvt), we don't
|
---|
2285 | * try to generate digits strictly left to right. Instead, we
|
---|
2286 | * compute with fewer bits and propagate the carry if necessary
|
---|
2287 | * when rounding the final digit up. This is often faster.
|
---|
2288 | * 3. Under the assumption that input will be rounded nearest,
|
---|
2289 | * mode 0 renders 1e23 as 1e23 rather than 9.999999999999999e22.
|
---|
2290 | * That is, we allow equality in stopping tests when the
|
---|
2291 | * round-nearest rule will give the same floating-point value
|
---|
2292 | * as would satisfaction of the stopping test with strict
|
---|
2293 | * inequality.
|
---|
2294 | * 4. We remove common factors of powers of 2 from relevant
|
---|
2295 | * quantities.
|
---|
2296 | * 5. When converting floating-point integers less than 1e16,
|
---|
2297 | * we use floating-point arithmetic rather than resorting
|
---|
2298 | * to multiple-precision integers.
|
---|
2299 | * 6. When asked to produce fewer than 15 digits, we first try
|
---|
2300 | * to get by with floating-point arithmetic; we resort to
|
---|
2301 | * multiple-precision integer arithmetic only if we cannot
|
---|
2302 | * guarantee that the floating-point calculation has given
|
---|
2303 | * the correctly rounded result. For k requested digits and
|
---|
2304 | * "uniformly" distributed input, the probability is
|
---|
2305 | * something like 10^(k-15) that we must resort to the Long
|
---|
2306 | * calculation.
|
---|
2307 | */
|
---|
2308 |
|
---|
2309 | /* Additional notes (METD): (1) returns NULL on failure. (2) to avoid memory
|
---|
2310 | leakage, a successful call to _Py_dg_dtoa should always be matched by a
|
---|
2311 | call to _Py_dg_freedtoa. */
|
---|
2312 |
|
---|
2313 | char *
|
---|
2314 | _Py_dg_dtoa(double dd, int mode, int ndigits,
|
---|
2315 | int *decpt, int *sign, char **rve)
|
---|
2316 | {
|
---|
2317 | /* Arguments ndigits, decpt, sign are similar to those
|
---|
2318 | of ecvt and fcvt; trailing zeros are suppressed from
|
---|
2319 | the returned string. If not null, *rve is set to point
|
---|
2320 | to the end of the return value. If d is +-Infinity or NaN,
|
---|
2321 | then *decpt is set to 9999.
|
---|
2322 |
|
---|
2323 | mode:
|
---|
2324 | 0 ==> shortest string that yields d when read in
|
---|
2325 | and rounded to nearest.
|
---|
2326 | 1 ==> like 0, but with Steele & White stopping rule;
|
---|
2327 | e.g. with IEEE P754 arithmetic , mode 0 gives
|
---|
2328 | 1e23 whereas mode 1 gives 9.999999999999999e22.
|
---|
2329 | 2 ==> max(1,ndigits) significant digits. This gives a
|
---|
2330 | return value similar to that of ecvt, except
|
---|
2331 | that trailing zeros are suppressed.
|
---|
2332 | 3 ==> through ndigits past the decimal point. This
|
---|
2333 | gives a return value similar to that from fcvt,
|
---|
2334 | except that trailing zeros are suppressed, and
|
---|
2335 | ndigits can be negative.
|
---|
2336 | 4,5 ==> similar to 2 and 3, respectively, but (in
|
---|
2337 | round-nearest mode) with the tests of mode 0 to
|
---|
2338 | possibly return a shorter string that rounds to d.
|
---|
2339 | With IEEE arithmetic and compilation with
|
---|
2340 | -DHonor_FLT_ROUNDS, modes 4 and 5 behave the same
|
---|
2341 | as modes 2 and 3 when FLT_ROUNDS != 1.
|
---|
2342 | 6-9 ==> Debugging modes similar to mode - 4: don't try
|
---|
2343 | fast floating-point estimate (if applicable).
|
---|
2344 |
|
---|
2345 | Values of mode other than 0-9 are treated as mode 0.
|
---|
2346 |
|
---|
2347 | Sufficient space is allocated to the return value
|
---|
2348 | to hold the suppressed trailing zeros.
|
---|
2349 | */
|
---|
2350 |
|
---|
2351 | int bbits, b2, b5, be, dig, i, ieps, ilim, ilim0, ilim1,
|
---|
2352 | j, j1, k, k0, k_check, leftright, m2, m5, s2, s5,
|
---|
2353 | spec_case, try_quick;
|
---|
2354 | Long L;
|
---|
2355 | int denorm;
|
---|
2356 | ULong x;
|
---|
2357 | Bigint *b, *b1, *delta, *mlo, *mhi, *S;
|
---|
2358 | U d2, eps, u;
|
---|
2359 | double ds;
|
---|
2360 | char *s, *s0;
|
---|
2361 |
|
---|
2362 | /* set pointers to NULL, to silence gcc compiler warnings and make
|
---|
2363 | cleanup easier on error */
|
---|
2364 | mlo = mhi = S = 0;
|
---|
2365 | s0 = 0;
|
---|
2366 |
|
---|
2367 | u.d = dd;
|
---|
2368 | if (word0(&u) & Sign_bit) {
|
---|
2369 | /* set sign for everything, including 0's and NaNs */
|
---|
2370 | *sign = 1;
|
---|
2371 | word0(&u) &= ~Sign_bit; /* clear sign bit */
|
---|
2372 | }
|
---|
2373 | else
|
---|
2374 | *sign = 0;
|
---|
2375 |
|
---|
2376 | /* quick return for Infinities, NaNs and zeros */
|
---|
2377 | if ((word0(&u) & Exp_mask) == Exp_mask)
|
---|
2378 | {
|
---|
2379 | /* Infinity or NaN */
|
---|
2380 | *decpt = 9999;
|
---|
2381 | if (!word1(&u) && !(word0(&u) & 0xfffff))
|
---|
2382 | return nrv_alloc("Infinity", rve, 8);
|
---|
2383 | return nrv_alloc("NaN", rve, 3);
|
---|
2384 | }
|
---|
2385 | if (!dval(&u)) {
|
---|
2386 | *decpt = 1;
|
---|
2387 | return nrv_alloc("0", rve, 1);
|
---|
2388 | }
|
---|
2389 |
|
---|
2390 | /* compute k = floor(log10(d)). The computation may leave k
|
---|
2391 | one too large, but should never leave k too small. */
|
---|
2392 | b = d2b(&u, &be, &bbits);
|
---|
2393 | if (b == NULL)
|
---|
2394 | goto failed_malloc;
|
---|
2395 | if ((i = (int)(word0(&u) >> Exp_shift1 & (Exp_mask>>Exp_shift1)))) {
|
---|
2396 | dval(&d2) = dval(&u);
|
---|
2397 | word0(&d2) &= Frac_mask1;
|
---|
2398 | word0(&d2) |= Exp_11;
|
---|
2399 |
|
---|
2400 | /* log(x) ~=~ log(1.5) + (x-1.5)/1.5
|
---|
2401 | * log10(x) = log(x) / log(10)
|
---|
2402 | * ~=~ log(1.5)/log(10) + (x-1.5)/(1.5*log(10))
|
---|
2403 | * log10(d) = (i-Bias)*log(2)/log(10) + log10(d2)
|
---|
2404 | *
|
---|
2405 | * This suggests computing an approximation k to log10(d) by
|
---|
2406 | *
|
---|
2407 | * k = (i - Bias)*0.301029995663981
|
---|
2408 | * + ( (d2-1.5)*0.289529654602168 + 0.176091259055681 );
|
---|
2409 | *
|
---|
2410 | * We want k to be too large rather than too small.
|
---|
2411 | * The error in the first-order Taylor series approximation
|
---|
2412 | * is in our favor, so we just round up the constant enough
|
---|
2413 | * to compensate for any error in the multiplication of
|
---|
2414 | * (i - Bias) by 0.301029995663981; since |i - Bias| <= 1077,
|
---|
2415 | * and 1077 * 0.30103 * 2^-52 ~=~ 7.2e-14,
|
---|
2416 | * adding 1e-13 to the constant term more than suffices.
|
---|
2417 | * Hence we adjust the constant term to 0.1760912590558.
|
---|
2418 | * (We could get a more accurate k by invoking log10,
|
---|
2419 | * but this is probably not worthwhile.)
|
---|
2420 | */
|
---|
2421 |
|
---|
2422 | i -= Bias;
|
---|
2423 | denorm = 0;
|
---|
2424 | }
|
---|
2425 | else {
|
---|
2426 | /* d is denormalized */
|
---|
2427 |
|
---|
2428 | i = bbits + be + (Bias + (P-1) - 1);
|
---|
2429 | x = i > 32 ? word0(&u) << (64 - i) | word1(&u) >> (i - 32)
|
---|
2430 | : word1(&u) << (32 - i);
|
---|
2431 | dval(&d2) = x;
|
---|
2432 | word0(&d2) -= 31*Exp_msk1; /* adjust exponent */
|
---|
2433 | i -= (Bias + (P-1) - 1) + 1;
|
---|
2434 | denorm = 1;
|
---|
2435 | }
|
---|
2436 | ds = (dval(&d2)-1.5)*0.289529654602168 + 0.1760912590558 +
|
---|
2437 | i*0.301029995663981;
|
---|
2438 | k = (int)ds;
|
---|
2439 | if (ds < 0. && ds != k)
|
---|
2440 | k--; /* want k = floor(ds) */
|
---|
2441 | k_check = 1;
|
---|
2442 | if (k >= 0 && k <= Ten_pmax) {
|
---|
2443 | if (dval(&u) < tens[k])
|
---|
2444 | k--;
|
---|
2445 | k_check = 0;
|
---|
2446 | }
|
---|
2447 | j = bbits - i - 1;
|
---|
2448 | if (j >= 0) {
|
---|
2449 | b2 = 0;
|
---|
2450 | s2 = j;
|
---|
2451 | }
|
---|
2452 | else {
|
---|
2453 | b2 = -j;
|
---|
2454 | s2 = 0;
|
---|
2455 | }
|
---|
2456 | if (k >= 0) {
|
---|
2457 | b5 = 0;
|
---|
2458 | s5 = k;
|
---|
2459 | s2 += k;
|
---|
2460 | }
|
---|
2461 | else {
|
---|
2462 | b2 -= k;
|
---|
2463 | b5 = -k;
|
---|
2464 | s5 = 0;
|
---|
2465 | }
|
---|
2466 | if (mode < 0 || mode > 9)
|
---|
2467 | mode = 0;
|
---|
2468 |
|
---|
2469 | try_quick = 1;
|
---|
2470 |
|
---|
2471 | if (mode > 5) {
|
---|
2472 | mode -= 4;
|
---|
2473 | try_quick = 0;
|
---|
2474 | }
|
---|
2475 | leftright = 1;
|
---|
2476 | ilim = ilim1 = -1; /* Values for cases 0 and 1; done here to */
|
---|
2477 | /* silence erroneous "gcc -Wall" warning. */
|
---|
2478 | switch(mode) {
|
---|
2479 | case 0:
|
---|
2480 | case 1:
|
---|
2481 | i = 18;
|
---|
2482 | ndigits = 0;
|
---|
2483 | break;
|
---|
2484 | case 2:
|
---|
2485 | leftright = 0;
|
---|
2486 | /* no break */
|
---|
2487 | case 4:
|
---|
2488 | if (ndigits <= 0)
|
---|
2489 | ndigits = 1;
|
---|
2490 | ilim = ilim1 = i = ndigits;
|
---|
2491 | break;
|
---|
2492 | case 3:
|
---|
2493 | leftright = 0;
|
---|
2494 | /* no break */
|
---|
2495 | case 5:
|
---|
2496 | i = ndigits + k + 1;
|
---|
2497 | ilim = i;
|
---|
2498 | ilim1 = i - 1;
|
---|
2499 | if (i <= 0)
|
---|
2500 | i = 1;
|
---|
2501 | }
|
---|
2502 | s0 = rv_alloc(i);
|
---|
2503 | if (s0 == NULL)
|
---|
2504 | goto failed_malloc;
|
---|
2505 | s = s0;
|
---|
2506 |
|
---|
2507 |
|
---|
2508 | if (ilim >= 0 && ilim <= Quick_max && try_quick) {
|
---|
2509 |
|
---|
2510 | /* Try to get by with floating-point arithmetic. */
|
---|
2511 |
|
---|
2512 | i = 0;
|
---|
2513 | dval(&d2) = dval(&u);
|
---|
2514 | k0 = k;
|
---|
2515 | ilim0 = ilim;
|
---|
2516 | ieps = 2; /* conservative */
|
---|
2517 | if (k > 0) {
|
---|
2518 | ds = tens[k&0xf];
|
---|
2519 | j = k >> 4;
|
---|
2520 | if (j & Bletch) {
|
---|
2521 | /* prevent overflows */
|
---|
2522 | j &= Bletch - 1;
|
---|
2523 | dval(&u) /= bigtens[n_bigtens-1];
|
---|
2524 | ieps++;
|
---|
2525 | }
|
---|
2526 | for(; j; j >>= 1, i++)
|
---|
2527 | if (j & 1) {
|
---|
2528 | ieps++;
|
---|
2529 | ds *= bigtens[i];
|
---|
2530 | }
|
---|
2531 | dval(&u) /= ds;
|
---|
2532 | }
|
---|
2533 | else if ((j1 = -k)) {
|
---|
2534 | dval(&u) *= tens[j1 & 0xf];
|
---|
2535 | for(j = j1 >> 4; j; j >>= 1, i++)
|
---|
2536 | if (j & 1) {
|
---|
2537 | ieps++;
|
---|
2538 | dval(&u) *= bigtens[i];
|
---|
2539 | }
|
---|
2540 | }
|
---|
2541 | if (k_check && dval(&u) < 1. && ilim > 0) {
|
---|
2542 | if (ilim1 <= 0)
|
---|
2543 | goto fast_failed;
|
---|
2544 | ilim = ilim1;
|
---|
2545 | k--;
|
---|
2546 | dval(&u) *= 10.;
|
---|
2547 | ieps++;
|
---|
2548 | }
|
---|
2549 | dval(&eps) = ieps*dval(&u) + 7.;
|
---|
2550 | word0(&eps) -= (P-1)*Exp_msk1;
|
---|
2551 | if (ilim == 0) {
|
---|
2552 | S = mhi = 0;
|
---|
2553 | dval(&u) -= 5.;
|
---|
2554 | if (dval(&u) > dval(&eps))
|
---|
2555 | goto one_digit;
|
---|
2556 | if (dval(&u) < -dval(&eps))
|
---|
2557 | goto no_digits;
|
---|
2558 | goto fast_failed;
|
---|
2559 | }
|
---|
2560 | if (leftright) {
|
---|
2561 | /* Use Steele & White method of only
|
---|
2562 | * generating digits needed.
|
---|
2563 | */
|
---|
2564 | dval(&eps) = 0.5/tens[ilim-1] - dval(&eps);
|
---|
2565 | for(i = 0;;) {
|
---|
2566 | L = (Long)dval(&u);
|
---|
2567 | dval(&u) -= L;
|
---|
2568 | *s++ = '0' + (int)L;
|
---|
2569 | if (dval(&u) < dval(&eps))
|
---|
2570 | goto ret1;
|
---|
2571 | if (1. - dval(&u) < dval(&eps))
|
---|
2572 | goto bump_up;
|
---|
2573 | if (++i >= ilim)
|
---|
2574 | break;
|
---|
2575 | dval(&eps) *= 10.;
|
---|
2576 | dval(&u) *= 10.;
|
---|
2577 | }
|
---|
2578 | }
|
---|
2579 | else {
|
---|
2580 | /* Generate ilim digits, then fix them up. */
|
---|
2581 | dval(&eps) *= tens[ilim-1];
|
---|
2582 | for(i = 1;; i++, dval(&u) *= 10.) {
|
---|
2583 | L = (Long)(dval(&u));
|
---|
2584 | if (!(dval(&u) -= L))
|
---|
2585 | ilim = i;
|
---|
2586 | *s++ = '0' + (int)L;
|
---|
2587 | if (i == ilim) {
|
---|
2588 | if (dval(&u) > 0.5 + dval(&eps))
|
---|
2589 | goto bump_up;
|
---|
2590 | else if (dval(&u) < 0.5 - dval(&eps)) {
|
---|
2591 | while(*--s == '0');
|
---|
2592 | s++;
|
---|
2593 | goto ret1;
|
---|
2594 | }
|
---|
2595 | break;
|
---|
2596 | }
|
---|
2597 | }
|
---|
2598 | }
|
---|
2599 | fast_failed:
|
---|
2600 | s = s0;
|
---|
2601 | dval(&u) = dval(&d2);
|
---|
2602 | k = k0;
|
---|
2603 | ilim = ilim0;
|
---|
2604 | }
|
---|
2605 |
|
---|
2606 | /* Do we have a "small" integer? */
|
---|
2607 |
|
---|
2608 | if (be >= 0 && k <= Int_max) {
|
---|
2609 | /* Yes. */
|
---|
2610 | ds = tens[k];
|
---|
2611 | if (ndigits < 0 && ilim <= 0) {
|
---|
2612 | S = mhi = 0;
|
---|
2613 | if (ilim < 0 || dval(&u) <= 5*ds)
|
---|
2614 | goto no_digits;
|
---|
2615 | goto one_digit;
|
---|
2616 | }
|
---|
2617 | for(i = 1;; i++, dval(&u) *= 10.) {
|
---|
2618 | L = (Long)(dval(&u) / ds);
|
---|
2619 | dval(&u) -= L*ds;
|
---|
2620 | *s++ = '0' + (int)L;
|
---|
2621 | if (!dval(&u)) {
|
---|
2622 | break;
|
---|
2623 | }
|
---|
2624 | if (i == ilim) {
|
---|
2625 | dval(&u) += dval(&u);
|
---|
2626 | if (dval(&u) > ds || (dval(&u) == ds && L & 1)) {
|
---|
2627 | bump_up:
|
---|
2628 | while(*--s == '9')
|
---|
2629 | if (s == s0) {
|
---|
2630 | k++;
|
---|
2631 | *s = '0';
|
---|
2632 | break;
|
---|
2633 | }
|
---|
2634 | ++*s++;
|
---|
2635 | }
|
---|
2636 | break;
|
---|
2637 | }
|
---|
2638 | }
|
---|
2639 | goto ret1;
|
---|
2640 | }
|
---|
2641 |
|
---|
2642 | m2 = b2;
|
---|
2643 | m5 = b5;
|
---|
2644 | if (leftright) {
|
---|
2645 | i =
|
---|
2646 | denorm ? be + (Bias + (P-1) - 1 + 1) :
|
---|
2647 | 1 + P - bbits;
|
---|
2648 | b2 += i;
|
---|
2649 | s2 += i;
|
---|
2650 | mhi = i2b(1);
|
---|
2651 | if (mhi == NULL)
|
---|
2652 | goto failed_malloc;
|
---|
2653 | }
|
---|
2654 | if (m2 > 0 && s2 > 0) {
|
---|
2655 | i = m2 < s2 ? m2 : s2;
|
---|
2656 | b2 -= i;
|
---|
2657 | m2 -= i;
|
---|
2658 | s2 -= i;
|
---|
2659 | }
|
---|
2660 | if (b5 > 0) {
|
---|
2661 | if (leftright) {
|
---|
2662 | if (m5 > 0) {
|
---|
2663 | mhi = pow5mult(mhi, m5);
|
---|
2664 | if (mhi == NULL)
|
---|
2665 | goto failed_malloc;
|
---|
2666 | b1 = mult(mhi, b);
|
---|
2667 | Bfree(b);
|
---|
2668 | b = b1;
|
---|
2669 | if (b == NULL)
|
---|
2670 | goto failed_malloc;
|
---|
2671 | }
|
---|
2672 | if ((j = b5 - m5)) {
|
---|
2673 | b = pow5mult(b, j);
|
---|
2674 | if (b == NULL)
|
---|
2675 | goto failed_malloc;
|
---|
2676 | }
|
---|
2677 | }
|
---|
2678 | else {
|
---|
2679 | b = pow5mult(b, b5);
|
---|
2680 | if (b == NULL)
|
---|
2681 | goto failed_malloc;
|
---|
2682 | }
|
---|
2683 | }
|
---|
2684 | S = i2b(1);
|
---|
2685 | if (S == NULL)
|
---|
2686 | goto failed_malloc;
|
---|
2687 | if (s5 > 0) {
|
---|
2688 | S = pow5mult(S, s5);
|
---|
2689 | if (S == NULL)
|
---|
2690 | goto failed_malloc;
|
---|
2691 | }
|
---|
2692 |
|
---|
2693 | /* Check for special case that d is a normalized power of 2. */
|
---|
2694 |
|
---|
2695 | spec_case = 0;
|
---|
2696 | if ((mode < 2 || leftright)
|
---|
2697 | ) {
|
---|
2698 | if (!word1(&u) && !(word0(&u) & Bndry_mask)
|
---|
2699 | && word0(&u) & (Exp_mask & ~Exp_msk1)
|
---|
2700 | ) {
|
---|
2701 | /* The special case */
|
---|
2702 | b2 += Log2P;
|
---|
2703 | s2 += Log2P;
|
---|
2704 | spec_case = 1;
|
---|
2705 | }
|
---|
2706 | }
|
---|
2707 |
|
---|
2708 | /* Arrange for convenient computation of quotients:
|
---|
2709 | * shift left if necessary so divisor has 4 leading 0 bits.
|
---|
2710 | *
|
---|
2711 | * Perhaps we should just compute leading 28 bits of S once
|
---|
2712 | * and for all and pass them and a shift to quorem, so it
|
---|
2713 | * can do shifts and ors to compute the numerator for q.
|
---|
2714 | */
|
---|
2715 | #define iInc 28
|
---|
2716 | i = dshift(S, s2);
|
---|
2717 | b2 += i;
|
---|
2718 | m2 += i;
|
---|
2719 | s2 += i;
|
---|
2720 | if (b2 > 0) {
|
---|
2721 | b = lshift(b, b2);
|
---|
2722 | if (b == NULL)
|
---|
2723 | goto failed_malloc;
|
---|
2724 | }
|
---|
2725 | if (s2 > 0) {
|
---|
2726 | S = lshift(S, s2);
|
---|
2727 | if (S == NULL)
|
---|
2728 | goto failed_malloc;
|
---|
2729 | }
|
---|
2730 | if (k_check) {
|
---|
2731 | if (cmp(b,S) < 0) {
|
---|
2732 | k--;
|
---|
2733 | b = multadd(b, 10, 0); /* we botched the k estimate */
|
---|
2734 | if (b == NULL)
|
---|
2735 | goto failed_malloc;
|
---|
2736 | if (leftright) {
|
---|
2737 | mhi = multadd(mhi, 10, 0);
|
---|
2738 | if (mhi == NULL)
|
---|
2739 | goto failed_malloc;
|
---|
2740 | }
|
---|
2741 | ilim = ilim1;
|
---|
2742 | }
|
---|
2743 | }
|
---|
2744 | if (ilim <= 0 && (mode == 3 || mode == 5)) {
|
---|
2745 | if (ilim < 0) {
|
---|
2746 | /* no digits, fcvt style */
|
---|
2747 | no_digits:
|
---|
2748 | k = -1 - ndigits;
|
---|
2749 | goto ret;
|
---|
2750 | }
|
---|
2751 | else {
|
---|
2752 | S = multadd(S, 5, 0);
|
---|
2753 | if (S == NULL)
|
---|
2754 | goto failed_malloc;
|
---|
2755 | if (cmp(b, S) <= 0)
|
---|
2756 | goto no_digits;
|
---|
2757 | }
|
---|
2758 | one_digit:
|
---|
2759 | *s++ = '1';
|
---|
2760 | k++;
|
---|
2761 | goto ret;
|
---|
2762 | }
|
---|
2763 | if (leftright) {
|
---|
2764 | if (m2 > 0) {
|
---|
2765 | mhi = lshift(mhi, m2);
|
---|
2766 | if (mhi == NULL)
|
---|
2767 | goto failed_malloc;
|
---|
2768 | }
|
---|
2769 |
|
---|
2770 | /* Compute mlo -- check for special case
|
---|
2771 | * that d is a normalized power of 2.
|
---|
2772 | */
|
---|
2773 |
|
---|
2774 | mlo = mhi;
|
---|
2775 | if (spec_case) {
|
---|
2776 | mhi = Balloc(mhi->k);
|
---|
2777 | if (mhi == NULL)
|
---|
2778 | goto failed_malloc;
|
---|
2779 | Bcopy(mhi, mlo);
|
---|
2780 | mhi = lshift(mhi, Log2P);
|
---|
2781 | if (mhi == NULL)
|
---|
2782 | goto failed_malloc;
|
---|
2783 | }
|
---|
2784 |
|
---|
2785 | for(i = 1;;i++) {
|
---|
2786 | dig = quorem(b,S) + '0';
|
---|
2787 | /* Do we yet have the shortest decimal string
|
---|
2788 | * that will round to d?
|
---|
2789 | */
|
---|
2790 | j = cmp(b, mlo);
|
---|
2791 | delta = diff(S, mhi);
|
---|
2792 | if (delta == NULL)
|
---|
2793 | goto failed_malloc;
|
---|
2794 | j1 = delta->sign ? 1 : cmp(b, delta);
|
---|
2795 | Bfree(delta);
|
---|
2796 | if (j1 == 0 && mode != 1 && !(word1(&u) & 1)
|
---|
2797 | ) {
|
---|
2798 | if (dig == '9')
|
---|
2799 | goto round_9_up;
|
---|
2800 | if (j > 0)
|
---|
2801 | dig++;
|
---|
2802 | *s++ = dig;
|
---|
2803 | goto ret;
|
---|
2804 | }
|
---|
2805 | if (j < 0 || (j == 0 && mode != 1
|
---|
2806 | && !(word1(&u) & 1)
|
---|
2807 | )) {
|
---|
2808 | if (!b->x[0] && b->wds <= 1) {
|
---|
2809 | goto accept_dig;
|
---|
2810 | }
|
---|
2811 | if (j1 > 0) {
|
---|
2812 | b = lshift(b, 1);
|
---|
2813 | if (b == NULL)
|
---|
2814 | goto failed_malloc;
|
---|
2815 | j1 = cmp(b, S);
|
---|
2816 | if ((j1 > 0 || (j1 == 0 && dig & 1))
|
---|
2817 | && dig++ == '9')
|
---|
2818 | goto round_9_up;
|
---|
2819 | }
|
---|
2820 | accept_dig:
|
---|
2821 | *s++ = dig;
|
---|
2822 | goto ret;
|
---|
2823 | }
|
---|
2824 | if (j1 > 0) {
|
---|
2825 | if (dig == '9') { /* possible if i == 1 */
|
---|
2826 | round_9_up:
|
---|
2827 | *s++ = '9';
|
---|
2828 | goto roundoff;
|
---|
2829 | }
|
---|
2830 | *s++ = dig + 1;
|
---|
2831 | goto ret;
|
---|
2832 | }
|
---|
2833 | *s++ = dig;
|
---|
2834 | if (i == ilim)
|
---|
2835 | break;
|
---|
2836 | b = multadd(b, 10, 0);
|
---|
2837 | if (b == NULL)
|
---|
2838 | goto failed_malloc;
|
---|
2839 | if (mlo == mhi) {
|
---|
2840 | mlo = mhi = multadd(mhi, 10, 0);
|
---|
2841 | if (mlo == NULL)
|
---|
2842 | goto failed_malloc;
|
---|
2843 | }
|
---|
2844 | else {
|
---|
2845 | mlo = multadd(mlo, 10, 0);
|
---|
2846 | if (mlo == NULL)
|
---|
2847 | goto failed_malloc;
|
---|
2848 | mhi = multadd(mhi, 10, 0);
|
---|
2849 | if (mhi == NULL)
|
---|
2850 | goto failed_malloc;
|
---|
2851 | }
|
---|
2852 | }
|
---|
2853 | }
|
---|
2854 | else
|
---|
2855 | for(i = 1;; i++) {
|
---|
2856 | *s++ = dig = quorem(b,S) + '0';
|
---|
2857 | if (!b->x[0] && b->wds <= 1) {
|
---|
2858 | goto ret;
|
---|
2859 | }
|
---|
2860 | if (i >= ilim)
|
---|
2861 | break;
|
---|
2862 | b = multadd(b, 10, 0);
|
---|
2863 | if (b == NULL)
|
---|
2864 | goto failed_malloc;
|
---|
2865 | }
|
---|
2866 |
|
---|
2867 | /* Round off last digit */
|
---|
2868 |
|
---|
2869 | b = lshift(b, 1);
|
---|
2870 | if (b == NULL)
|
---|
2871 | goto failed_malloc;
|
---|
2872 | j = cmp(b, S);
|
---|
2873 | if (j > 0 || (j == 0 && dig & 1)) {
|
---|
2874 | roundoff:
|
---|
2875 | while(*--s == '9')
|
---|
2876 | if (s == s0) {
|
---|
2877 | k++;
|
---|
2878 | *s++ = '1';
|
---|
2879 | goto ret;
|
---|
2880 | }
|
---|
2881 | ++*s++;
|
---|
2882 | }
|
---|
2883 | else {
|
---|
2884 | while(*--s == '0');
|
---|
2885 | s++;
|
---|
2886 | }
|
---|
2887 | ret:
|
---|
2888 | Bfree(S);
|
---|
2889 | if (mhi) {
|
---|
2890 | if (mlo && mlo != mhi)
|
---|
2891 | Bfree(mlo);
|
---|
2892 | Bfree(mhi);
|
---|
2893 | }
|
---|
2894 | ret1:
|
---|
2895 | Bfree(b);
|
---|
2896 | *s = 0;
|
---|
2897 | *decpt = k + 1;
|
---|
2898 | if (rve)
|
---|
2899 | *rve = s;
|
---|
2900 | return s0;
|
---|
2901 | failed_malloc:
|
---|
2902 | if (S)
|
---|
2903 | Bfree(S);
|
---|
2904 | if (mlo && mlo != mhi)
|
---|
2905 | Bfree(mlo);
|
---|
2906 | if (mhi)
|
---|
2907 | Bfree(mhi);
|
---|
2908 | if (b)
|
---|
2909 | Bfree(b);
|
---|
2910 | if (s0)
|
---|
2911 | _Py_dg_freedtoa(s0);
|
---|
2912 | return NULL;
|
---|
2913 | }
|
---|
2914 | #ifdef __cplusplus
|
---|
2915 | }
|
---|
2916 | #endif
|
---|
2917 |
|
---|
2918 | #endif /* PY_NO_SHORT_FLOAT_REPR */
|
---|