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1 /* Copyright (C) 2007, 2009 Free Software Foundation, Inc.
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2
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3 This file is part of GCC.
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4
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5 GCC is free software; you can redistribute it and/or modify it under
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6 the terms of the GNU General Public License as published by the Free
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7 Software Foundation; either version 3, or (at your option) any later
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8 version.
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9
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10 GCC is distributed in the hope that it will be useful, but WITHOUT ANY
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11 WARRANTY; without even the implied warranty of MERCHANTABILITY or
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12 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
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13 for more details.
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14
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15 Under Section 7 of GPL version 3, you are granted additional
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16 permissions described in the GCC Runtime Library Exception, version
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17 3.1, as published by the Free Software Foundation.
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18
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19 You should have received a copy of the GNU General Public License and
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20 a copy of the GCC Runtime Library Exception along with this program;
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21 see the files COPYING3 and COPYING.RUNTIME respectively. If not, see
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22 <http://www.gnu.org/licenses/>. */
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23
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24 /*****************************************************************************
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25 * BID64 remainder
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26 *****************************************************************************
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27 *
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28 * Algorithm description:
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29 *
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30 * if(exponent_x < exponent_y)
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31 * scale coefficient_y so exponents are aligned
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32 * perform coefficient divide (64-bit integer divide), unless
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33 * coefficient_y is longer than 64 bits (clearly larger
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34 * than coefficient_x)
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35 * else // exponent_x > exponent_y
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36 * use a loop to scale coefficient_x to 18_digits, divide by
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37 * coefficient_y (64-bit integer divide), calculate remainder
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38 * as new_coefficient_x and repeat until final remainder is obtained
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39 * (when new_exponent_x < exponent_y)
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40 *
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41 ****************************************************************************/
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42
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43 #include "bid_internal.h"
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44
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45 #define MAX_FORMAT_DIGITS 16
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46 #define DECIMAL_EXPONENT_BIAS 398
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47 #define MASK_BINARY_EXPONENT 0x7ff0000000000000ull
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48 #define BINARY_EXPONENT_BIAS 0x3ff
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49 #define UPPER_EXPON_LIMIT 51
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50
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51 #if DECIMAL_CALL_BY_REFERENCE
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52
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53 void
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54 bid64_rem (UINT64 * pres, UINT64 * px,
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55 UINT64 *
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56 py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
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57 UINT64 x, y;
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58 #else
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59
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60 UINT64
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61 bid64_rem (UINT64 x,
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62 UINT64 y _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
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63 #endif
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64 UINT128 CY;
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65 UINT64 sign_x, sign_y, coefficient_x, coefficient_y, res;
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66 UINT64 Q, R, R2, T, valid_y, valid_x;
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67 int_float tempx;
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68 int exponent_x, exponent_y, bin_expon, e_scale;
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69 int digits_x, diff_expon;
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70
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71 #if DECIMAL_CALL_BY_REFERENCE
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72 x = *px;
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73 y = *py;
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74 #endif
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75
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76 valid_y = unpack_BID64 (&sign_y, &exponent_y, &coefficient_y, y);
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77 valid_x = unpack_BID64 (&sign_x, &exponent_x, &coefficient_x, x);
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78
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79 // unpack arguments, check for NaN or Infinity
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80 if (!valid_x) {
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81 // x is Inf. or NaN or 0
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82 #ifdef SET_STATUS_FLAGS
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83 if ((y & SNAN_MASK64) == SNAN_MASK64) // y is sNaN
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84 __set_status_flags (pfpsf, INVALID_EXCEPTION);
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85 #endif
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86
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87 // test if x is NaN
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88 if ((x & 0x7c00000000000000ull) == 0x7c00000000000000ull) {
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89 #ifdef SET_STATUS_FLAGS
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90 if (((x & SNAN_MASK64) == SNAN_MASK64))
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91 __set_status_flags (pfpsf, INVALID_EXCEPTION);
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92 #endif
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93 res = coefficient_x & QUIET_MASK64;;
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94 BID_RETURN (res);
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95 }
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96 // x is Infinity?
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97 if ((x & 0x7800000000000000ull) == 0x7800000000000000ull) {
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98 if (((y & NAN_MASK64) != NAN_MASK64)) {
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99 #ifdef SET_STATUS_FLAGS
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100 __set_status_flags (pfpsf, INVALID_EXCEPTION);
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101 #endif
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102 // return NaN
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103 res = 0x7c00000000000000ull;
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104 BID_RETURN (res);
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105 }
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106 }
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107 // x is 0
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108 // return x if y != 0
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109 if (((y & 0x7800000000000000ull) < 0x7800000000000000ull) &&
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110 coefficient_y) {
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111 if ((y & 0x6000000000000000ull) == 0x6000000000000000ull)
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112 exponent_y = (y >> 51) & 0x3ff;
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113 else
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114 exponent_y = (y >> 53) & 0x3ff;
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115
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116 if (exponent_y < exponent_x)
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117 exponent_x = exponent_y;
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118
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119 x = exponent_x;
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120 x <<= 53;
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121
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122 res = x | sign_x;
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123 BID_RETURN (res);
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124 }
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125
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126 }
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127 if (!valid_y) {
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128 // y is Inf. or NaN
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129
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130 // test if y is NaN
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131 if ((y & 0x7c00000000000000ull) == 0x7c00000000000000ull) {
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132 #ifdef SET_STATUS_FLAGS
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133 if (((y & SNAN_MASK64) == SNAN_MASK64))
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134 __set_status_flags (pfpsf, INVALID_EXCEPTION);
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135 #endif
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136 res = coefficient_y & QUIET_MASK64;;
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137 BID_RETURN (res);
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138 }
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139 // y is Infinity?
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140 if ((y & 0x7800000000000000ull) == 0x7800000000000000ull) {
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141 res = very_fast_get_BID64 (sign_x, exponent_x, coefficient_x);
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142 BID_RETURN (res);
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143 }
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144 // y is 0, return NaN
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145 {
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146 #ifdef SET_STATUS_FLAGS
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147 __set_status_flags (pfpsf, INVALID_EXCEPTION);
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148 #endif
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149 res = 0x7c00000000000000ull;
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150 BID_RETURN (res);
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151 }
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152 }
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153
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154
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155 diff_expon = exponent_x - exponent_y;
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156 if (diff_expon <= 0) {
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157 diff_expon = -diff_expon;
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158
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159 if (diff_expon > 16) {
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160 // |x|<|y| in this case
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161 res = x;
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162 BID_RETURN (res);
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163 }
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164 // set exponent of y to exponent_x, scale coefficient_y
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165 T = power10_table_128[diff_expon].w[0];
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166 __mul_64x64_to_128 (CY, coefficient_y, T);
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167
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168 if (CY.w[1] || CY.w[0] > (coefficient_x << 1)) {
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169 res = x;
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170 BID_RETURN (res);
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171 }
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172
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173 Q = coefficient_x / CY.w[0];
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174 R = coefficient_x - Q * CY.w[0];
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175
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176 R2 = R + R;
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177 if (R2 > CY.w[0] || (R2 == CY.w[0] && (Q & 1))) {
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178 R = CY.w[0] - R;
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179 sign_x ^= 0x8000000000000000ull;
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180 }
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181
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182 res = very_fast_get_BID64 (sign_x, exponent_x, R);
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183 BID_RETURN (res);
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184 }
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185
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186
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187 while (diff_expon > 0) {
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188 // get number of digits in coeff_x
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189 tempx.d = (float) coefficient_x;
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190 bin_expon = ((tempx.i >> 23) & 0xff) - 0x7f;
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191 digits_x = estimate_decimal_digits[bin_expon];
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192 // will not use this test, dividend will have 18 or 19 digits
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193 //if(coefficient_x >= power10_table_128[digits_x].w[0])
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194 // digits_x++;
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195
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196 e_scale = 18 - digits_x;
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197 if (diff_expon >= e_scale) {
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198 diff_expon -= e_scale;
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199 } else {
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200 e_scale = diff_expon;
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201 diff_expon = 0;
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202 }
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203
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204 // scale dividend to 18 or 19 digits
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205 coefficient_x *= power10_table_128[e_scale].w[0];
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206
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207 // quotient
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208 Q = coefficient_x / coefficient_y;
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209 // remainder
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210 coefficient_x -= Q * coefficient_y;
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211
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212 // check for remainder == 0
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213 if (!coefficient_x) {
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214 res = very_fast_get_BID64_small_mantissa (sign_x, exponent_y, 0);
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215 BID_RETURN (res);
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216 }
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217 }
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218
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219 R2 = coefficient_x + coefficient_x;
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220 if (R2 > coefficient_y || (R2 == coefficient_y && (Q & 1))) {
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221 coefficient_x = coefficient_y - coefficient_x;
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222 sign_x ^= 0x8000000000000000ull;
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223 }
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224
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225 res = very_fast_get_BID64 (sign_x, exponent_y, coefficient_x);
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226 BID_RETURN (res);
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227
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228 }
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