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) 1998-2001 by Lucent Technologies |
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6 | All Rights Reserved |
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7 | |
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8 | Permission to use, copy, modify, and distribute this software and |
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9 | its documentation for any purpose and without fee is hereby |
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10 | granted, provided that the above copyright notice appear in all |
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11 | copies and that both that the copyright notice and this |
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12 | permission notice and warranty disclaimer appear in supporting |
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13 | documentation, and that the name of Lucent or any of its entities |
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14 | not be used in advertising or publicity pertaining to |
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15 | distribution of the software without specific, written prior |
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16 | permission. |
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17 | |
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18 | LUCENT DISCLAIMS ALL WARRANTIES WITH REGARD TO THIS SOFTWARE, |
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19 | INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS. |
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20 | IN NO EVENT SHALL LUCENT OR ANY OF ITS ENTITIES BE LIABLE FOR ANY |
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21 | SPECIAL, INDIRECT OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES |
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22 | WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER |
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23 | IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, |
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24 | ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE OF |
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25 | THIS SOFTWARE. |
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26 | |
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27 | ****************************************************************/ |
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28 | |
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29 | /* Please send bug reports to David M. Gay (dmg at acm dot org, |
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30 | * with " at " changed at "@" and " dot " changed to "."). */ |
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31 | |
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32 | #include <_ansi.h> |
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33 | #include <errno.h> |
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34 | #include <stdlib.h> |
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35 | #include <string.h> |
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36 | #include "mprec.h" |
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37 | #include "gdtoa.h" |
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38 | #include "gd_qnan.h" |
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39 | |
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40 | #include "locale.h" |
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41 | |
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42 | #if defined (_HAVE_LONG_DOUBLE) && !defined (_LDBL_EQ_DBL) |
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43 | |
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44 | #define USE_LOCALE |
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45 | |
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46 | static const int |
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47 | fivesbits[] = { 0, 3, 5, 7, 10, 12, 14, 17, 19, 21, |
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48 | 24, 26, 28, 31, 33, 35, 38, 40, 42, 45, |
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49 | 47, 49, 52 |
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50 | #ifdef VAX |
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51 | , 54, 56 |
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52 | #endif |
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53 | }; |
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54 | |
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55 | static _Bigint * |
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56 | sum (struct _reent *p, _Bigint *a, _Bigint *b) |
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57 | { |
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58 | _Bigint *c; |
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59 | __ULong carry, *xc, *xa, *xb, *xe, y; |
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60 | #ifdef Pack_32 |
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61 | __ULong z; |
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62 | #endif |
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63 | |
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64 | if (a->_wds < b->_wds) { |
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65 | c = b; b = a; a = c; |
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66 | } |
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67 | c = Balloc(p, a->_k); |
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68 | c->_wds = a->_wds; |
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69 | carry = 0; |
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70 | xa = a->_x; |
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71 | xb = b->_x; |
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72 | xc = c->_x; |
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73 | xe = xc + b->_wds; |
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74 | #ifdef Pack_32 |
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75 | do { |
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76 | y = (*xa & 0xffff) + (*xb & 0xffff) + carry; |
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77 | carry = (y & 0x10000) >> 16; |
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78 | z = (*xa++ >> 16) + (*xb++ >> 16) + carry; |
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79 | carry = (z & 0x10000) >> 16; |
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80 | Storeinc(xc, z, y); |
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81 | } |
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82 | while(xc < xe); |
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83 | xe += a->_wds - b->_wds; |
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84 | while(xc < xe) { |
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85 | y = (*xa & 0xffff) + carry; |
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86 | carry = (y & 0x10000) >> 16; |
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87 | z = (*xa++ >> 16) + carry; |
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88 | carry = (z & 0x10000) >> 16; |
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89 | Storeinc(xc, z, y); |
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90 | } |
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91 | #else |
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92 | do { |
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93 | y = *xa++ + *xb++ + carry; |
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94 | carry = (y & 0x10000) >> 16; |
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95 | *xc++ = y & 0xffff; |
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96 | } |
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97 | while(xc < xe); |
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98 | xe += a->_wds - b->_wds; |
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99 | while(xc < xe) { |
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100 | y = *xa++ + carry; |
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101 | carry = (y & 0x10000) >> 16; |
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102 | *xc++ = y & 0xffff; |
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103 | } |
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104 | #endif |
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105 | if (carry) { |
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106 | if (c->_wds == c->_maxwds) { |
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107 | b = Balloc(p, c->_k + 1); |
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108 | Bcopy(b, c); |
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109 | Bfree(p, c); |
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110 | c = b; |
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111 | } |
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112 | c->_x[c->_wds++] = 1; |
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113 | } |
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114 | return c; |
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115 | } |
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116 | |
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117 | static void |
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118 | rshift (_Bigint *b, int k) |
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119 | { |
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120 | __ULong *x, *x1, *xe, y; |
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121 | int n; |
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122 | |
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123 | x = x1 = b->_x; |
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124 | n = k >> kshift; |
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125 | if (n < b->_wds) { |
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126 | xe = x + b->_wds; |
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127 | x += n; |
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128 | if (k &= kmask) { |
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129 | n = ULbits - k; |
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130 | y = *x++ >> k; |
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131 | while(x < xe) { |
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132 | *x1++ = (y | (*x << n)) & ALL_ON; |
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133 | y = *x++ >> k; |
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134 | } |
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135 | if ((*x1 = y) !=0) |
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136 | x1++; |
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137 | } |
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138 | else |
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139 | while(x < xe) |
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140 | *x1++ = *x++; |
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141 | } |
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142 | if ((b->_wds = x1 - b->_x) == 0) |
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143 | b->_x[0] = 0; |
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144 | } |
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145 | |
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146 | static int |
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147 | trailz (_Bigint *b) |
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148 | { |
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149 | __ULong L, *x, *xe; |
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150 | int n = 0; |
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151 | |
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152 | x = b->_x; |
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153 | xe = x + b->_wds; |
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154 | for(n = 0; x < xe && !*x; x++) |
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155 | n += ULbits; |
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156 | if (x < xe) { |
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157 | L = *x; |
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158 | n += lo0bits(&L); |
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159 | } |
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160 | return n; |
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161 | } |
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162 | |
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163 | _Bigint * |
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164 | increment (struct _reent *p, _Bigint *b) |
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165 | { |
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166 | __ULong *x, *xe; |
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167 | _Bigint *b1; |
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168 | #ifdef Pack_16 |
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169 | __ULong carry = 1, y; |
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170 | #endif |
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171 | |
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172 | x = b->_x; |
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173 | xe = x + b->_wds; |
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174 | #ifdef Pack_32 |
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175 | do { |
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176 | if (*x < (__ULong)0xffffffffL) { |
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177 | ++*x; |
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178 | return b; |
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179 | } |
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180 | *x++ = 0; |
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181 | } while(x < xe); |
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182 | #else |
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183 | do { |
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184 | y = *x + carry; |
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185 | carry = y >> 16; |
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186 | *x++ = y & 0xffff; |
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187 | if (!carry) |
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188 | return b; |
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189 | } while(x < xe); |
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190 | if (carry) |
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191 | #endif |
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192 | { |
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193 | if (b->_wds >= b->_maxwds) { |
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194 | b1 = Balloc(p,b->_k+1); |
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195 | Bcopy(b1,b); |
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196 | Bfree(p,b); |
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197 | b = b1; |
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198 | } |
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199 | b->_x[b->_wds++] = 1; |
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200 | } |
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201 | return b; |
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202 | } |
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203 | |
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204 | int |
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205 | decrement (_Bigint *b) |
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206 | { |
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207 | __ULong *x, *xe; |
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208 | #ifdef Pack_16 |
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209 | __ULong borrow = 1, y; |
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210 | #endif |
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211 | |
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212 | x = b->_x; |
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213 | xe = x + b->_wds; |
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214 | #ifdef Pack_32 |
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215 | do { |
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216 | if (*x) { |
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217 | --*x; |
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218 | break; |
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219 | } |
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220 | *x++ = 0xffffffffL; |
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221 | } |
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222 | while(x < xe); |
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223 | #else |
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224 | do { |
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225 | y = *x - borrow; |
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226 | borrow = (y & 0x10000) >> 16; |
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227 | *x++ = y & 0xffff; |
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228 | } while(borrow && x < xe); |
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229 | #endif |
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230 | return STRTOG_Inexlo; |
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231 | } |
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232 | |
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233 | static int |
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234 | all_on (_Bigint *b, int n) |
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235 | { |
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236 | __ULong *x, *xe; |
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237 | |
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238 | x = b->_x; |
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239 | xe = x + (n >> kshift); |
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240 | while(x < xe) |
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241 | if ((*x++ & ALL_ON) != ALL_ON) |
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242 | return 0; |
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243 | if (n &= kmask) |
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244 | return ((*x | (ALL_ON << n)) & ALL_ON) == ALL_ON; |
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245 | return 1; |
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246 | } |
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247 | |
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248 | _Bigint * |
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249 | set_ones (struct _reent *p, _Bigint *b, int n) |
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250 | { |
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251 | int k; |
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252 | __ULong *x, *xe; |
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253 | |
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254 | k = (n + ((1 << kshift) - 1)) >> kshift; |
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255 | if (b->_k < k) { |
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256 | Bfree(p,b); |
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257 | b = Balloc(p,k); |
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258 | } |
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259 | k = n >> kshift; |
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260 | if (n &= kmask) |
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261 | k++; |
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262 | b->_wds = k; |
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263 | x = b->_x; |
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264 | xe = x + k; |
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265 | while(x < xe) |
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266 | *x++ = ALL_ON; |
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267 | if (n) |
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268 | x[-1] >>= ULbits - n; |
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269 | return b; |
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270 | } |
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271 | |
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272 | static int |
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273 | rvOK (struct _reent *p, double d, FPI *fpi, Long *exp, __ULong *bits, int exact, |
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274 | int rd, int *irv) |
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275 | { |
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276 | _Bigint *b; |
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277 | __ULong carry, inex, lostbits; |
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278 | int bdif, e, j, k, k1, nb, rv; |
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279 | |
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280 | carry = rv = 0; |
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281 | b = d2b(p, d, &e, &bdif); |
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282 | bdif -= nb = fpi->nbits; |
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283 | e += bdif; |
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284 | if (bdif <= 0) { |
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285 | if (exact) |
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286 | goto trunc; |
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287 | goto ret; |
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288 | } |
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289 | if (P == nb) { |
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290 | if ( |
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291 | #ifndef IMPRECISE_INEXACT |
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292 | exact && |
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293 | #endif |
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294 | fpi->rounding == |
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295 | #ifdef RND_PRODQUOT |
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296 | FPI_Round_near |
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297 | #else |
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298 | Flt_Rounds |
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299 | #endif |
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300 | ) goto trunc; |
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301 | goto ret; |
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302 | } |
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303 | switch(rd) { |
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304 | case 1: |
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305 | goto trunc; |
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306 | case 2: |
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307 | break; |
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308 | default: /* round near */ |
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309 | k = bdif - 1; |
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310 | if (k < 0) |
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311 | goto trunc; |
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312 | if (!k) { |
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313 | if (!exact) |
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314 | goto ret; |
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315 | if (b->_x[0] & 2) |
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316 | break; |
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317 | goto trunc; |
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318 | } |
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319 | if (b->_x[k>>kshift] & ((__ULong)1 << (k & kmask))) |
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320 | break; |
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321 | goto trunc; |
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322 | } |
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323 | /* "break" cases: round up 1 bit, then truncate; bdif > 0 */ |
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324 | carry = 1; |
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325 | trunc: |
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326 | inex = lostbits = 0; |
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327 | if (bdif > 0) { |
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328 | if ( (lostbits = any_on(b, bdif)) !=0) |
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329 | inex = STRTOG_Inexlo; |
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330 | rshift(b, bdif); |
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331 | if (carry) { |
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332 | inex = STRTOG_Inexhi; |
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333 | b = increment(p, b); |
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334 | if ( (j = nb & kmask) !=0) |
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335 | j = ULbits - j; |
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336 | if (hi0bits(b->_x[b->_wds - 1]) != j) { |
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337 | if (!lostbits) |
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338 | lostbits = b->_x[0] & 1; |
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339 | rshift(b, 1); |
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340 | e++; |
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341 | } |
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342 | } |
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343 | } |
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344 | else if (bdif < 0) |
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345 | b = lshift(p, b, -bdif); |
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346 | if (e < fpi->emin) { |
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347 | k = fpi->emin - e; |
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348 | e = fpi->emin; |
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349 | if (k > nb || fpi->sudden_underflow) { |
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350 | b->_wds = inex = 0; |
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351 | *irv = STRTOG_Underflow | STRTOG_Inexlo; |
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352 | } |
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353 | else { |
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354 | k1 = k - 1; |
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355 | if (k1 > 0 && !lostbits) |
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356 | lostbits = any_on(b, k1); |
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357 | if (!lostbits && !exact) |
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358 | goto ret; |
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359 | lostbits |= |
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360 | carry = b->_x[k1>>kshift] & (1 << (k1 & kmask)); |
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361 | rshift(b, k); |
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362 | *irv = STRTOG_Denormal; |
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363 | if (carry) { |
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364 | b = increment(p, b); |
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365 | inex = STRTOG_Inexhi | STRTOG_Underflow; |
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366 | } |
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367 | else if (lostbits) |
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368 | inex = STRTOG_Inexlo | STRTOG_Underflow; |
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369 | } |
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370 | } |
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371 | else if (e > fpi->emax) { |
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372 | e = fpi->emax + 1; |
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373 | *irv = STRTOG_Infinite | STRTOG_Overflow | STRTOG_Inexhi; |
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374 | #ifndef NO_ERRNO |
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375 | errno = ERANGE; |
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376 | #endif |
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377 | b->_wds = inex = 0; |
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378 | } |
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379 | *exp = e; |
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380 | copybits(bits, nb, b); |
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381 | *irv |= inex; |
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382 | rv = 1; |
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383 | ret: |
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384 | Bfree(p,b); |
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385 | return rv; |
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386 | } |
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387 | |
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388 | static int |
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389 | mantbits (U d) |
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390 | { |
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391 | __ULong L; |
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392 | #ifdef VAX |
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393 | L = word1(d) << 16 | word1(d) >> 16; |
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394 | if (L) |
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395 | #else |
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396 | if ( (L = word1(d)) !=0) |
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397 | #endif |
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398 | return P - lo0bits(&L); |
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399 | #ifdef VAX |
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400 | L = word0(d) << 16 | word0(d) >> 16 | Exp_msk11; |
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401 | #else |
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402 | L = word0(d) | Exp_msk1; |
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403 | #endif |
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404 | return P - 32 - lo0bits(&L); |
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405 | } |
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406 | |
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407 | int |
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408 | _strtodg_l (struct _reent *p, const char *s00, char **se, FPI *fpi, Long *exp, |
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409 | __ULong *bits, locale_t loc) |
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410 | { |
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411 | int abe, abits, asub; |
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412 | int bb0, bb2, bb5, bbe, bd2, bd5, bbbits, bs2, c, decpt, denorm; |
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413 | int dsign, e, e1, e2, emin, esign, finished, i, inex, irv; |
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414 | int j, k, nbits, nd, nd0, nf, nz, nz0, rd, rvbits, rve, rve1, sign; |
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415 | int sudden_underflow; |
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416 | const char *s, *s0, *s1; |
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417 | //double adj, adj0, rv, tol; |
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418 | double adj0, tol; |
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419 | U adj, rv; |
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420 | Long L; |
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421 | __ULong y, z; |
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422 | _Bigint *ab, *bb, *bb1, *bd, *bd0, *bs, *delta, *rvb, *rvb0; |
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423 | struct lconv *lconv = __localeconv_l (loc); |
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424 | int dec_len = strlen (lconv->decimal_point); |
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425 | |
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426 | irv = STRTOG_Zero; |
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427 | denorm = sign = nz0 = nz = 0; |
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428 | dval(rv) = 0.; |
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429 | rvb = 0; |
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430 | nbits = fpi->nbits; |
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431 | for(s = s00;;s++) switch(*s) { |
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432 | case '-': |
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433 | sign = 1; |
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434 | /* no break */ |
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435 | case '+': |
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436 | if (*++s) |
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437 | goto break2; |
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438 | /* no break */ |
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439 | case 0: |
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440 | sign = 0; |
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441 | irv = STRTOG_NoNumber; |
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442 | s = s00; |
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443 | goto ret; |
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444 | case '\t': |
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445 | case '\n': |
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446 | case '\v': |
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447 | case '\f': |
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448 | case '\r': |
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449 | case ' ': |
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450 | continue; |
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451 | default: |
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452 | goto break2; |
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453 | } |
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454 | break2: |
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455 | if (*s == '0') { |
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456 | #ifndef NO_HEX_FP |
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457 | switch(s[1]) { |
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458 | case 'x': |
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459 | case 'X': |
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460 | irv = gethex(p, &s, fpi, exp, &rvb, sign, loc); |
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461 | if (irv == STRTOG_NoNumber) { |
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462 | s = s00; |
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463 | sign = 0; |
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464 | } |
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465 | goto ret; |
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466 | } |
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467 | #endif |
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468 | nz0 = 1; |
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469 | while(*++s == '0') ; |
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470 | if (!*s) |
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471 | goto ret; |
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472 | } |
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473 | sudden_underflow = fpi->sudden_underflow; |
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474 | s0 = s; |
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475 | y = z = 0; |
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476 | for(decpt = nd = nf = 0; (c = *s) >= '0' && c <= '9'; nd++, s++) |
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477 | if (nd < 9) |
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478 | y = 10*y + c - '0'; |
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479 | else if (nd < 16) |
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480 | z = 10*z + c - '0'; |
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481 | nd0 = nd; |
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482 | #ifdef USE_LOCALE |
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483 | if (strncmp (s, lconv->decimal_point, dec_len) == 0) |
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484 | #else |
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485 | if (c == '.') |
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486 | #endif |
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487 | { |
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488 | decpt = 1; |
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489 | #ifdef USE_LOCALE |
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490 | c = *(s += dec_len); |
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491 | #else |
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492 | c = *++s; |
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493 | #endif |
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494 | if (!nd) { |
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495 | for(; c == '0'; c = *++s) |
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496 | nz++; |
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497 | if (c > '0' && c <= '9') { |
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498 | s0 = s; |
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499 | nf += nz; |
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500 | nz = 0; |
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501 | goto have_dig; |
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502 | } |
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503 | goto dig_done; |
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504 | } |
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505 | for(; c >= '0' && c <= '9'; c = *++s) { |
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506 | have_dig: |
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507 | nz++; |
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508 | if (c -= '0') { |
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509 | nf += nz; |
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510 | for(i = 1; i < nz; i++) |
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511 | if (nd++ < 9) |
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512 | y *= 10; |
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513 | else if (nd <= DBL_DIG + 1) |
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514 | z *= 10; |
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515 | if (nd++ < 9) |
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516 | y = 10*y + c; |
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517 | else if (nd <= DBL_DIG + 1) |
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518 | z = 10*z + c; |
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519 | nz = 0; |
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520 | } |
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521 | } |
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522 | } |
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523 | dig_done: |
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524 | e = 0; |
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525 | if (c == 'e' || c == 'E') { |
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526 | if (!nd && !nz && !nz0) { |
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527 | irv = STRTOG_NoNumber; |
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528 | s = s00; |
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529 | goto ret; |
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530 | } |
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531 | s00 = s; |
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532 | esign = 0; |
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533 | switch(c = *++s) { |
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534 | case '-': |
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535 | esign = 1; |
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536 | case '+': |
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537 | c = *++s; |
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538 | } |
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539 | if (c >= '0' && c <= '9') { |
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540 | while(c == '0') |
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541 | c = *++s; |
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542 | if (c > '0' && c <= '9') { |
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543 | L = c - '0'; |
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544 | s1 = s; |
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545 | while((c = *++s) >= '0' && c <= '9') |
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546 | L = 10*L + c - '0'; |
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547 | if (s - s1 > 8 || L > 19999) |
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548 | /* Avoid confusion from exponents |
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549 | * so large that e might overflow. |
---|
550 | */ |
---|
551 | e = 19999; /* safe for 16 bit ints */ |
---|
552 | else |
---|
553 | e = (int)L; |
---|
554 | if (esign) |
---|
555 | e = -e; |
---|
556 | } |
---|
557 | else |
---|
558 | e = 0; |
---|
559 | } |
---|
560 | else |
---|
561 | s = s00; |
---|
562 | } |
---|
563 | if (!nd) { |
---|
564 | if (!nz && !nz0) { |
---|
565 | #ifdef INFNAN_CHECK |
---|
566 | /* Check for Nan and Infinity */ |
---|
567 | if (!decpt) |
---|
568 | switch(c) { |
---|
569 | case 'i': |
---|
570 | case 'I': |
---|
571 | if (match(&s,"nf")) { |
---|
572 | --s; |
---|
573 | if (!match(&s,"inity")) |
---|
574 | ++s; |
---|
575 | irv = STRTOG_Infinite; |
---|
576 | goto infnanexp; |
---|
577 | } |
---|
578 | break; |
---|
579 | case 'n': |
---|
580 | case 'N': |
---|
581 | if (match(&s, "an")) { |
---|
582 | irv = STRTOG_NaN; |
---|
583 | *exp = fpi->emax + 1; |
---|
584 | #ifndef No_Hex_NaN |
---|
585 | if (*s == '(') /*)*/ |
---|
586 | irv = hexnan(&s, fpi, bits); |
---|
587 | #endif |
---|
588 | goto infnanexp; |
---|
589 | } |
---|
590 | } |
---|
591 | #endif /* INFNAN_CHECK */ |
---|
592 | irv = STRTOG_NoNumber; |
---|
593 | s = s00; |
---|
594 | } |
---|
595 | goto ret; |
---|
596 | } |
---|
597 | |
---|
598 | irv = STRTOG_Normal; |
---|
599 | e1 = e -= nf; |
---|
600 | rd = 0; |
---|
601 | switch(fpi->rounding & 3) { |
---|
602 | case FPI_Round_up: |
---|
603 | rd = 2 - sign; |
---|
604 | break; |
---|
605 | case FPI_Round_zero: |
---|
606 | rd = 1; |
---|
607 | break; |
---|
608 | case FPI_Round_down: |
---|
609 | rd = 1 + sign; |
---|
610 | } |
---|
611 | |
---|
612 | /* Now we have nd0 digits, starting at s0, followed by a |
---|
613 | * decimal point, followed by nd-nd0 digits. The number we're |
---|
614 | * after is the integer represented by those digits times |
---|
615 | * 10**e */ |
---|
616 | |
---|
617 | if (!nd0) |
---|
618 | nd0 = nd; |
---|
619 | k = nd < DBL_DIG + 1 ? nd : DBL_DIG + 1; |
---|
620 | dval(rv) = y; |
---|
621 | if (k > 9) |
---|
622 | dval(rv) = tens[k - 9] * dval(rv) + z; |
---|
623 | bd0 = 0; |
---|
624 | if (nbits <= P && nd <= DBL_DIG) { |
---|
625 | if (!e) { |
---|
626 | if (rvOK(p, dval(rv), fpi, exp, bits, 1, rd, &irv)) |
---|
627 | goto ret; |
---|
628 | } |
---|
629 | else if (e > 0) { |
---|
630 | if (e <= Ten_pmax) { |
---|
631 | #ifdef VAX |
---|
632 | goto vax_ovfl_check; |
---|
633 | #else |
---|
634 | i = fivesbits[e] + mantbits(rv) <= P; |
---|
635 | /* rv = */ rounded_product(dval(rv), tens[e]); |
---|
636 | if (rvOK(p, dval(rv), fpi, exp, bits, i, rd, &irv)) |
---|
637 | goto ret; |
---|
638 | e1 -= e; |
---|
639 | goto rv_notOK; |
---|
640 | #endif |
---|
641 | } |
---|
642 | i = DBL_DIG - nd; |
---|
643 | if (e <= Ten_pmax + i) { |
---|
644 | /* A fancier test would sometimes let us do |
---|
645 | * this for larger i values. |
---|
646 | */ |
---|
647 | e2 = e - i; |
---|
648 | e1 -= i; |
---|
649 | dval(rv) *= tens[i]; |
---|
650 | #ifdef VAX |
---|
651 | /* VAX exponent range is so narrow we must |
---|
652 | * worry about overflow here... |
---|
653 | */ |
---|
654 | vax_ovfl_check: |
---|
655 | dval(adj) = dval(rv); |
---|
656 | word0(adj) -= P*Exp_msk1; |
---|
657 | /* adj = */ rounded_product(dval(adj), tens[e2]); |
---|
658 | if ((word0(adj) & Exp_mask) |
---|
659 | > Exp_msk1*(DBL_MAX_EXP+Bias-1-P)) |
---|
660 | goto rv_notOK; |
---|
661 | word0(adj) += P*Exp_msk1; |
---|
662 | dval(rv) = dval(adj); |
---|
663 | #else |
---|
664 | /* rv = */ rounded_product(dval(rv), tens[e2]); |
---|
665 | #endif |
---|
666 | if (rvOK(p, dval(rv), fpi, exp, bits, 0, rd, &irv)) |
---|
667 | goto ret; |
---|
668 | e1 -= e2; |
---|
669 | } |
---|
670 | } |
---|
671 | #ifndef Inaccurate_Divide |
---|
672 | else if (e >= -Ten_pmax) { |
---|
673 | /* rv = */ rounded_quotient(dval(rv), tens[-e]); |
---|
674 | if (rvOK(p, dval(rv), fpi, exp, bits, 0, rd, &irv)) |
---|
675 | goto ret; |
---|
676 | e1 -= e; |
---|
677 | } |
---|
678 | #endif |
---|
679 | } |
---|
680 | rv_notOK: |
---|
681 | e1 += nd - k; |
---|
682 | |
---|
683 | /* Get starting approximation = rv * 10**e1 */ |
---|
684 | |
---|
685 | e2 = 0; |
---|
686 | if (e1 > 0) { |
---|
687 | if ( (i = e1 & 15) !=0) |
---|
688 | dval(rv) *= tens[i]; |
---|
689 | if (e1 &= ~15) { |
---|
690 | e1 >>= 4; |
---|
691 | while(e1 >= (1 << n_bigtens-1)) { |
---|
692 | e2 += ((word0(rv) & Exp_mask) |
---|
693 | >> Exp_shift1) - Bias; |
---|
694 | word0(rv) &= ~Exp_mask; |
---|
695 | word0(rv) |= Bias << Exp_shift1; |
---|
696 | dval(rv) *= bigtens[n_bigtens-1]; |
---|
697 | e1 -= 1 << n_bigtens-1; |
---|
698 | } |
---|
699 | e2 += ((word0(rv) & Exp_mask) >> Exp_shift1) - Bias; |
---|
700 | word0(rv) &= ~Exp_mask; |
---|
701 | word0(rv) |= Bias << Exp_shift1; |
---|
702 | for(j = 0; e1 > 0; j++, e1 >>= 1) |
---|
703 | if (e1 & 1) |
---|
704 | dval(rv) *= bigtens[j]; |
---|
705 | } |
---|
706 | } |
---|
707 | else if (e1 < 0) { |
---|
708 | e1 = -e1; |
---|
709 | if ( (i = e1 & 15) !=0) |
---|
710 | dval(rv) /= tens[i]; |
---|
711 | if (e1 &= ~15) { |
---|
712 | e1 >>= 4; |
---|
713 | while(e1 >= (1 << n_bigtens-1)) { |
---|
714 | e2 += ((word0(rv) & Exp_mask) |
---|
715 | >> Exp_shift1) - Bias; |
---|
716 | word0(rv) &= ~Exp_mask; |
---|
717 | word0(rv) |= Bias << Exp_shift1; |
---|
718 | dval(rv) *= tinytens[n_bigtens-1]; |
---|
719 | e1 -= 1 << n_bigtens-1; |
---|
720 | } |
---|
721 | e2 += ((word0(rv) & Exp_mask) >> Exp_shift1) - Bias; |
---|
722 | word0(rv) &= ~Exp_mask; |
---|
723 | word0(rv) |= Bias << Exp_shift1; |
---|
724 | for(j = 0; e1 > 0; j++, e1 >>= 1) |
---|
725 | if (e1 & 1) |
---|
726 | dval(rv) *= tinytens[j]; |
---|
727 | } |
---|
728 | } |
---|
729 | #ifdef IBM |
---|
730 | /* e2 is a correction to the (base 2) exponent of the return |
---|
731 | * value, reflecting adjustments above to avoid overflow in the |
---|
732 | * native arithmetic. For native IBM (base 16) arithmetic, we |
---|
733 | * must multiply e2 by 4 to change from base 16 to 2. |
---|
734 | */ |
---|
735 | e2 <<= 2; |
---|
736 | #endif |
---|
737 | rvb = d2b(p, dval(rv), &rve, &rvbits); /* rv = rvb * 2^rve */ |
---|
738 | rve += e2; |
---|
739 | if ((j = rvbits - nbits) > 0) { |
---|
740 | rshift(rvb, j); |
---|
741 | rvbits = nbits; |
---|
742 | rve += j; |
---|
743 | } |
---|
744 | bb0 = 0; /* trailing zero bits in rvb */ |
---|
745 | e2 = rve + rvbits - nbits; |
---|
746 | if (e2 > fpi->emax + 1) |
---|
747 | goto huge; |
---|
748 | rve1 = rve + rvbits - nbits; |
---|
749 | if (e2 < (emin = fpi->emin)) { |
---|
750 | denorm = 1; |
---|
751 | j = rve - emin; |
---|
752 | if (j > 0) { |
---|
753 | rvb = lshift(p, rvb, j); |
---|
754 | rvbits += j; |
---|
755 | } |
---|
756 | else if (j < 0) { |
---|
757 | rvbits += j; |
---|
758 | if (rvbits <= 0) { |
---|
759 | if (rvbits < -1) { |
---|
760 | ufl: |
---|
761 | rvb->_wds = 0; |
---|
762 | rvb->_x[0] = 0; |
---|
763 | *exp = emin; |
---|
764 | irv = STRTOG_Underflow | STRTOG_Inexlo; |
---|
765 | goto ret; |
---|
766 | } |
---|
767 | rvb->_x[0] = rvb->_wds = rvbits = 1; |
---|
768 | } |
---|
769 | else |
---|
770 | rshift(rvb, -j); |
---|
771 | } |
---|
772 | rve = rve1 = emin; |
---|
773 | if (sudden_underflow && e2 + 1 < emin) |
---|
774 | goto ufl; |
---|
775 | } |
---|
776 | |
---|
777 | /* Now the hard part -- adjusting rv to the correct value.*/ |
---|
778 | |
---|
779 | /* Put digits into bd: true value = bd * 10^e */ |
---|
780 | |
---|
781 | bd0 = s2b(p, s0, nd0, nd, y); |
---|
782 | |
---|
783 | for(;;) { |
---|
784 | bd = Balloc(p,bd0->_k); |
---|
785 | Bcopy(bd, bd0); |
---|
786 | bb = Balloc(p,rvb->_k); |
---|
787 | Bcopy(bb, rvb); |
---|
788 | bbbits = rvbits - bb0; |
---|
789 | bbe = rve + bb0; |
---|
790 | bs = i2b(p, 1); |
---|
791 | |
---|
792 | if (e >= 0) { |
---|
793 | bb2 = bb5 = 0; |
---|
794 | bd2 = bd5 = e; |
---|
795 | } |
---|
796 | else { |
---|
797 | bb2 = bb5 = -e; |
---|
798 | bd2 = bd5 = 0; |
---|
799 | } |
---|
800 | if (bbe >= 0) |
---|
801 | bb2 += bbe; |
---|
802 | else |
---|
803 | bd2 -= bbe; |
---|
804 | bs2 = bb2; |
---|
805 | j = nbits + 1 - bbbits; |
---|
806 | i = bbe + bbbits - nbits; |
---|
807 | if (i < emin) /* denormal */ |
---|
808 | j += i - emin; |
---|
809 | bb2 += j; |
---|
810 | bd2 += j; |
---|
811 | i = bb2 < bd2 ? bb2 : bd2; |
---|
812 | if (i > bs2) |
---|
813 | i = bs2; |
---|
814 | if (i > 0) { |
---|
815 | bb2 -= i; |
---|
816 | bd2 -= i; |
---|
817 | bs2 -= i; |
---|
818 | } |
---|
819 | if (bb5 > 0) { |
---|
820 | bs = pow5mult(p, bs, bb5); |
---|
821 | bb1 = mult(p, bs, bb); |
---|
822 | Bfree(p,bb); |
---|
823 | bb = bb1; |
---|
824 | } |
---|
825 | bb2 -= bb0; |
---|
826 | if (bb2 > 0) |
---|
827 | bb = lshift(p, bb, bb2); |
---|
828 | else if (bb2 < 0) |
---|
829 | rshift(bb, -bb2); |
---|
830 | if (bd5 > 0) |
---|
831 | bd = pow5mult(p, bd, bd5); |
---|
832 | if (bd2 > 0) |
---|
833 | bd = lshift(p, bd, bd2); |
---|
834 | if (bs2 > 0) |
---|
835 | bs = lshift(p, bs, bs2); |
---|
836 | asub = 1; |
---|
837 | inex = STRTOG_Inexhi; |
---|
838 | delta = diff(p, bb, bd); |
---|
839 | if (delta->_wds <= 1 && !delta->_x[0]) |
---|
840 | break; |
---|
841 | dsign = delta->_sign; |
---|
842 | delta->_sign = finished = 0; |
---|
843 | L = 0; |
---|
844 | i = cmp(delta, bs); |
---|
845 | if (rd && i <= 0) { |
---|
846 | irv = STRTOG_Normal; |
---|
847 | if ( (finished = dsign ^ (rd&1)) !=0) { |
---|
848 | if (dsign != 0) { |
---|
849 | irv |= STRTOG_Inexhi; |
---|
850 | goto adj1; |
---|
851 | } |
---|
852 | irv |= STRTOG_Inexlo; |
---|
853 | if (rve1 == emin) |
---|
854 | goto adj1; |
---|
855 | for(i = 0, j = nbits; j >= ULbits; |
---|
856 | i++, j -= ULbits) { |
---|
857 | if (rvb->_x[i] & ALL_ON) |
---|
858 | goto adj1; |
---|
859 | } |
---|
860 | if (j > 1 && lo0bits(rvb->_x + i) < j - 1) |
---|
861 | goto adj1; |
---|
862 | rve = rve1 - 1; |
---|
863 | rvb = set_ones(p, rvb, rvbits = nbits); |
---|
864 | break; |
---|
865 | } |
---|
866 | irv |= dsign ? STRTOG_Inexlo : STRTOG_Inexhi; |
---|
867 | break; |
---|
868 | } |
---|
869 | if (i < 0) { |
---|
870 | /* Error is less than half an ulp -- check for |
---|
871 | * special case of mantissa a power of two. |
---|
872 | */ |
---|
873 | irv = dsign |
---|
874 | ? STRTOG_Normal | STRTOG_Inexlo |
---|
875 | : STRTOG_Normal | STRTOG_Inexhi; |
---|
876 | if (dsign || bbbits > 1 || denorm || rve1 == emin) |
---|
877 | break; |
---|
878 | delta = lshift(p, delta,1); |
---|
879 | if (cmp(delta, bs) > 0) { |
---|
880 | irv = STRTOG_Normal | STRTOG_Inexlo; |
---|
881 | goto drop_down; |
---|
882 | } |
---|
883 | break; |
---|
884 | } |
---|
885 | if (i == 0) { |
---|
886 | /* exactly half-way between */ |
---|
887 | if (dsign) { |
---|
888 | if (denorm && all_on(rvb, rvbits)) { |
---|
889 | /*boundary case -- increment exponent*/ |
---|
890 | rvb->_wds = 1; |
---|
891 | rvb->_x[0] = 1; |
---|
892 | rve = emin + nbits - (rvbits = 1); |
---|
893 | irv = STRTOG_Normal | STRTOG_Inexhi; |
---|
894 | denorm = 0; |
---|
895 | break; |
---|
896 | } |
---|
897 | irv = STRTOG_Normal | STRTOG_Inexlo; |
---|
898 | } |
---|
899 | else if (bbbits == 1) { |
---|
900 | irv = STRTOG_Normal; |
---|
901 | drop_down: |
---|
902 | /* boundary case -- decrement exponent */ |
---|
903 | if (rve1 == emin) { |
---|
904 | irv = STRTOG_Normal | STRTOG_Inexhi; |
---|
905 | if (rvb->_wds == 1 && rvb->_x[0] == 1) |
---|
906 | sudden_underflow = 1; |
---|
907 | break; |
---|
908 | } |
---|
909 | rve -= nbits; |
---|
910 | rvb = set_ones(p, rvb, rvbits = nbits); |
---|
911 | break; |
---|
912 | } |
---|
913 | else |
---|
914 | irv = STRTOG_Normal | STRTOG_Inexhi; |
---|
915 | if (bbbits < nbits && !denorm || !(rvb->_x[0] & 1)) |
---|
916 | break; |
---|
917 | if (dsign) { |
---|
918 | rvb = increment(p, rvb); |
---|
919 | j = kmask & (ULbits - (rvbits & kmask)); |
---|
920 | if (hi0bits(rvb->_x[rvb->_wds - 1]) != j) |
---|
921 | rvbits++; |
---|
922 | irv = STRTOG_Normal | STRTOG_Inexhi; |
---|
923 | } |
---|
924 | else { |
---|
925 | if (bbbits == 1) |
---|
926 | goto undfl; |
---|
927 | decrement(rvb); |
---|
928 | irv = STRTOG_Normal | STRTOG_Inexlo; |
---|
929 | } |
---|
930 | break; |
---|
931 | } |
---|
932 | if ((dval(adj) = ratio(delta, bs)) <= 2.) { |
---|
933 | adj1: |
---|
934 | inex = STRTOG_Inexlo; |
---|
935 | if (dsign) { |
---|
936 | asub = 0; |
---|
937 | inex = STRTOG_Inexhi; |
---|
938 | } |
---|
939 | else if (denorm && bbbits <= 1) { |
---|
940 | undfl: |
---|
941 | rvb->_wds = 0; |
---|
942 | rve = emin; |
---|
943 | irv = STRTOG_Underflow | STRTOG_Inexlo; |
---|
944 | break; |
---|
945 | } |
---|
946 | adj0 = dval(adj) = 1.; |
---|
947 | } |
---|
948 | else { |
---|
949 | adj0 = dval(adj) *= 0.5; |
---|
950 | if (dsign) { |
---|
951 | asub = 0; |
---|
952 | inex = STRTOG_Inexlo; |
---|
953 | } |
---|
954 | if (dval(adj) < 2147483647.) { |
---|
955 | L = adj0; |
---|
956 | adj0 -= L; |
---|
957 | switch(rd) { |
---|
958 | case 0: |
---|
959 | if (adj0 >= .5) |
---|
960 | goto inc_L; |
---|
961 | break; |
---|
962 | case 1: |
---|
963 | if (asub && adj0 > 0.) |
---|
964 | goto inc_L; |
---|
965 | break; |
---|
966 | case 2: |
---|
967 | if (!asub && adj0 > 0.) { |
---|
968 | inc_L: |
---|
969 | L++; |
---|
970 | inex = STRTOG_Inexact - inex; |
---|
971 | } |
---|
972 | } |
---|
973 | dval(adj) = L; |
---|
974 | } |
---|
975 | } |
---|
976 | y = rve + rvbits; |
---|
977 | |
---|
978 | /* adj *= ulp(dval(rv)); */ |
---|
979 | /* if (asub) rv -= adj; else rv += adj; */ |
---|
980 | |
---|
981 | if (!denorm && rvbits < nbits) { |
---|
982 | rvb = lshift(p, rvb, j = nbits - rvbits); |
---|
983 | rve -= j; |
---|
984 | rvbits = nbits; |
---|
985 | } |
---|
986 | ab = d2b(p, dval(adj), &abe, &abits); |
---|
987 | if (abe < 0) |
---|
988 | rshift(ab, -abe); |
---|
989 | else if (abe > 0) |
---|
990 | ab = lshift(p, ab, abe); |
---|
991 | rvb0 = rvb; |
---|
992 | if (asub) { |
---|
993 | /* rv -= adj; */ |
---|
994 | j = hi0bits(rvb->_x[rvb->_wds-1]); |
---|
995 | rvb = diff(p, rvb, ab); |
---|
996 | k = rvb0->_wds - 1; |
---|
997 | if (denorm) |
---|
998 | /* do nothing */; |
---|
999 | else if (rvb->_wds <= k |
---|
1000 | || hi0bits( rvb->_x[k]) > |
---|
1001 | hi0bits(rvb0->_x[k])) { |
---|
1002 | /* unlikely; can only have lost 1 high bit */ |
---|
1003 | if (rve1 == emin) { |
---|
1004 | --rvbits; |
---|
1005 | denorm = 1; |
---|
1006 | } |
---|
1007 | else { |
---|
1008 | rvb = lshift(p, rvb, 1); |
---|
1009 | --rve; |
---|
1010 | --rve1; |
---|
1011 | L = finished = 0; |
---|
1012 | } |
---|
1013 | } |
---|
1014 | } |
---|
1015 | else { |
---|
1016 | rvb = sum(p, rvb, ab); |
---|
1017 | k = rvb->_wds - 1; |
---|
1018 | if (k >= rvb0->_wds |
---|
1019 | || hi0bits(rvb->_x[k]) < hi0bits(rvb0->_x[k])) { |
---|
1020 | if (denorm) { |
---|
1021 | if (++rvbits == nbits) |
---|
1022 | denorm = 0; |
---|
1023 | } |
---|
1024 | else { |
---|
1025 | rshift(rvb, 1); |
---|
1026 | rve++; |
---|
1027 | rve1++; |
---|
1028 | L = 0; |
---|
1029 | } |
---|
1030 | } |
---|
1031 | } |
---|
1032 | Bfree(p,ab); |
---|
1033 | Bfree(p,rvb0); |
---|
1034 | if (finished) |
---|
1035 | break; |
---|
1036 | |
---|
1037 | z = rve + rvbits; |
---|
1038 | if (y == z && L) { |
---|
1039 | /* Can we stop now? */ |
---|
1040 | tol = dval(adj) * 5e-16; /* > max rel error */ |
---|
1041 | dval(adj) = adj0 - .5; |
---|
1042 | if (dval(adj) < -tol) { |
---|
1043 | if (adj0 > tol) { |
---|
1044 | irv |= inex; |
---|
1045 | break; |
---|
1046 | } |
---|
1047 | } |
---|
1048 | else if (dval(adj) > tol && adj0 < 1. - tol) { |
---|
1049 | irv |= inex; |
---|
1050 | break; |
---|
1051 | } |
---|
1052 | } |
---|
1053 | bb0 = denorm ? 0 : trailz(rvb); |
---|
1054 | Bfree(p,bb); |
---|
1055 | Bfree(p,bd); |
---|
1056 | Bfree(p,bs); |
---|
1057 | Bfree(p,delta); |
---|
1058 | } |
---|
1059 | if (!denorm && (j = nbits - rvbits)) { |
---|
1060 | if (j > 0) |
---|
1061 | rvb = lshift(p, rvb, j); |
---|
1062 | else |
---|
1063 | rshift(rvb, -j); |
---|
1064 | rve -= j; |
---|
1065 | } |
---|
1066 | *exp = rve; |
---|
1067 | Bfree(p,bb); |
---|
1068 | Bfree(p,bd); |
---|
1069 | Bfree(p,bs); |
---|
1070 | Bfree(p,bd0); |
---|
1071 | Bfree(p,delta); |
---|
1072 | if (rve > fpi->emax) { |
---|
1073 | huge: |
---|
1074 | rvb->_wds = 0; |
---|
1075 | irv = STRTOG_Infinite | STRTOG_Overflow | STRTOG_Inexhi; |
---|
1076 | #ifndef NO_ERRNO |
---|
1077 | errno = ERANGE; |
---|
1078 | #endif |
---|
1079 | infnanexp: |
---|
1080 | *exp = fpi->emax + 1; |
---|
1081 | } |
---|
1082 | ret: |
---|
1083 | if (denorm) { |
---|
1084 | if (sudden_underflow) { |
---|
1085 | rvb->_wds = 0; |
---|
1086 | irv = STRTOG_Underflow | STRTOG_Inexlo; |
---|
1087 | } |
---|
1088 | else { |
---|
1089 | irv = (irv & ~STRTOG_Retmask) | |
---|
1090 | (rvb->_wds > 0 ? STRTOG_Denormal : STRTOG_Zero); |
---|
1091 | if (irv & STRTOG_Inexact) |
---|
1092 | irv |= STRTOG_Underflow; |
---|
1093 | } |
---|
1094 | } |
---|
1095 | if (se) |
---|
1096 | *se = (char *)s; |
---|
1097 | if (sign) |
---|
1098 | irv |= STRTOG_Neg; |
---|
1099 | if (rvb) { |
---|
1100 | copybits(bits, nbits, rvb); |
---|
1101 | Bfree(p,rvb); |
---|
1102 | } |
---|
1103 | return irv; |
---|
1104 | } |
---|
1105 | |
---|
1106 | #endif /* _HAVE_LONG_DOUBLE && !_LDBL_EQ_DBL */ |
---|