1 | /*
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2 | * Copyright (c) 2005 Josef Cejka
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3 | * Copyright (c) 2011 Petr Koupy
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4 | * All rights reserved.
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5 | *
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6 | * Redistribution and use in source and binary forms, with or without
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7 | * modification, are permitted provided that the following conditions
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8 | * are met:
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9 | *
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10 | * - Redistributions of source code must retain the above copyright
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11 | * notice, this list of conditions and the following disclaimer.
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12 | * - Redistributions in binary form must reproduce the above copyright
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13 | * notice, this list of conditions and the following disclaimer in the
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14 | * documentation and/or other materials provided with the distribution.
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15 | * - The name of the author may not be used to endorse or promote products
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16 | * derived from this software without specific prior written permission.
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17 | *
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18 | * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
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19 | * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
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20 | * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
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21 | * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
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22 | * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
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23 | * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
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24 | * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
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25 | * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
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26 | * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
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27 | * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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28 | */
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29 |
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30 | /** @addtogroup softfloat
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31 | * @{
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32 | */
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33 | /** @file Multiplication functions.
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34 | */
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35 |
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36 | #include <sftypes.h>
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37 | #include <mul.h>
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38 | #include <comparison.h>
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39 | #include <common.h>
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40 |
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41 | /** Multiply two single-precision floats.
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42 | *
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43 | * @param a First input operand.
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44 | * @param b Second input operand.
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45 | *
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46 | * @return Result of multiplication.
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47 | *
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48 | */
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49 | float32 mul_float32(float32 a, float32 b)
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50 | {
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51 | float32 result;
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52 | uint64_t frac1, frac2;
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53 | int32_t exp;
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54 |
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55 | result.parts.sign = a.parts.sign ^ b.parts.sign;
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56 |
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57 | if (is_float32_nan(a) || is_float32_nan(b)) {
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58 | /* TODO: fix SigNaNs */
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59 | if (is_float32_signan(a)) {
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60 | result.parts.fraction = a.parts.fraction;
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61 | result.parts.exp = a.parts.exp;
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62 | return result;
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63 | }
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64 | if (is_float32_signan(b)) { /* TODO: fix SigNaN */
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65 | result.parts.fraction = b.parts.fraction;
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66 | result.parts.exp = b.parts.exp;
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67 | return result;
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68 | }
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69 | /* set NaN as result */
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70 | result.bin = FLOAT32_NAN;
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71 | return result;
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72 | }
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73 |
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74 | if (is_float32_infinity(a)) {
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75 | if (is_float32_zero(b)) {
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76 | /* FIXME: zero * infinity */
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77 | result.bin = FLOAT32_NAN;
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78 | return result;
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79 | }
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80 | result.parts.fraction = a.parts.fraction;
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81 | result.parts.exp = a.parts.exp;
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82 | return result;
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83 | }
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84 |
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85 | if (is_float32_infinity(b)) {
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86 | if (is_float32_zero(a)) {
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87 | /* FIXME: zero * infinity */
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88 | result.bin = FLOAT32_NAN;
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89 | return result;
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90 | }
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91 | result.parts.fraction = b.parts.fraction;
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92 | result.parts.exp = b.parts.exp;
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93 | return result;
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94 | }
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95 |
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96 | /* exp is signed so we can easy detect underflow */
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97 | exp = a.parts.exp + b.parts.exp;
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98 | exp -= FLOAT32_BIAS;
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99 |
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100 | if (exp >= FLOAT32_MAX_EXPONENT) {
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101 | /* FIXME: overflow */
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102 | /* set infinity as result */
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103 | result.bin = FLOAT32_INF;
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104 | result.parts.sign = a.parts.sign ^ b.parts.sign;
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105 | return result;
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106 | }
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107 |
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108 | if (exp < 0) {
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109 | /* FIXME: underflow */
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110 | /* return signed zero */
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111 | result.parts.fraction = 0x0;
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112 | result.parts.exp = 0x0;
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113 | return result;
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114 | }
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115 |
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116 | frac1 = a.parts.fraction;
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117 | if (a.parts.exp > 0) {
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118 | frac1 |= FLOAT32_HIDDEN_BIT_MASK;
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119 | } else {
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120 | ++exp;
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121 | }
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122 |
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123 | frac2 = b.parts.fraction;
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124 |
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125 | if (b.parts.exp > 0) {
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126 | frac2 |= FLOAT32_HIDDEN_BIT_MASK;
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127 | } else {
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128 | ++exp;
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129 | }
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130 |
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131 | frac1 <<= 1; /* one bit space for rounding */
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132 |
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133 | frac1 = frac1 * frac2;
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134 |
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135 | /* round and return */
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136 | while ((exp < FLOAT32_MAX_EXPONENT) &&
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137 | (frac1 >= (1 << (FLOAT32_FRACTION_SIZE + 2)))) {
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138 | /* 23 bits of fraction + one more for hidden bit (all shifted 1 bit left) */
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139 | ++exp;
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140 | frac1 >>= 1;
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141 | }
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142 |
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143 | /* rounding */
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144 | /* ++frac1; FIXME: not works - without it is ok */
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145 | frac1 >>= 1; /* shift off rounding space */
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146 |
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147 | if ((exp < FLOAT32_MAX_EXPONENT) &&
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148 | (frac1 >= (1 << (FLOAT32_FRACTION_SIZE + 1)))) {
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149 | ++exp;
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150 | frac1 >>= 1;
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151 | }
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152 |
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153 | if (exp >= FLOAT32_MAX_EXPONENT) {
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154 | /* TODO: fix overflow */
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155 | /* return infinity*/
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156 | result.parts.exp = FLOAT32_MAX_EXPONENT;
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157 | result.parts.fraction = 0x0;
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158 | return result;
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159 | }
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160 |
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161 | exp -= FLOAT32_FRACTION_SIZE;
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162 |
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163 | if (exp <= FLOAT32_FRACTION_SIZE) {
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164 | /* denormalized number */
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165 | frac1 >>= 1; /* denormalize */
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166 | while ((frac1 > 0) && (exp < 0)) {
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167 | frac1 >>= 1;
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168 | ++exp;
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169 | }
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170 | if (frac1 == 0) {
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171 | /* FIXME : underflow */
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172 | result.parts.exp = 0;
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173 | result.parts.fraction = 0;
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174 | return result;
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175 | }
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176 | }
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177 | result.parts.exp = exp;
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178 | result.parts.fraction = frac1 & ((1 << FLOAT32_FRACTION_SIZE) - 1);
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179 |
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180 | return result;
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181 | }
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182 |
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183 | /** Multiply two double-precision floats.
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184 | *
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185 | * @param a First input operand.
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186 | * @param b Second input operand.
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187 | *
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188 | * @return Result of multiplication.
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189 | *
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190 | */
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191 | float64 mul_float64(float64 a, float64 b)
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192 | {
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193 | float64 result;
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194 | uint64_t frac1, frac2;
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195 | int32_t exp;
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196 |
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197 | result.parts.sign = a.parts.sign ^ b.parts.sign;
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198 |
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199 | if (is_float64_nan(a) || is_float64_nan(b)) {
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200 | /* TODO: fix SigNaNs */
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201 | if (is_float64_signan(a)) {
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202 | result.parts.fraction = a.parts.fraction;
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203 | result.parts.exp = a.parts.exp;
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204 | return result;
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205 | }
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206 | if (is_float64_signan(b)) { /* TODO: fix SigNaN */
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207 | result.parts.fraction = b.parts.fraction;
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208 | result.parts.exp = b.parts.exp;
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209 | return result;
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210 | }
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211 | /* set NaN as result */
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212 | result.bin = FLOAT64_NAN;
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213 | return result;
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214 | }
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215 |
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216 | if (is_float64_infinity(a)) {
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217 | if (is_float64_zero(b)) {
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218 | /* FIXME: zero * infinity */
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219 | result.bin = FLOAT64_NAN;
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220 | return result;
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221 | }
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222 | result.parts.fraction = a.parts.fraction;
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223 | result.parts.exp = a.parts.exp;
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224 | return result;
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225 | }
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226 |
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227 | if (is_float64_infinity(b)) {
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228 | if (is_float64_zero(a)) {
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229 | /* FIXME: zero * infinity */
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230 | result.bin = FLOAT64_NAN;
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231 | return result;
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232 | }
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233 | result.parts.fraction = b.parts.fraction;
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234 | result.parts.exp = b.parts.exp;
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235 | return result;
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236 | }
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237 |
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238 | /* exp is signed so we can easy detect underflow */
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239 | exp = a.parts.exp + b.parts.exp - FLOAT64_BIAS;
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240 |
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241 | frac1 = a.parts.fraction;
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242 |
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243 | if (a.parts.exp > 0) {
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244 | frac1 |= FLOAT64_HIDDEN_BIT_MASK;
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245 | } else {
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246 | ++exp;
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247 | }
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248 |
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249 | frac2 = b.parts.fraction;
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250 |
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251 | if (b.parts.exp > 0) {
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252 | frac2 |= FLOAT64_HIDDEN_BIT_MASK;
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253 | } else {
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254 | ++exp;
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255 | }
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256 |
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257 | frac1 <<= (64 - FLOAT64_FRACTION_SIZE - 1);
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258 | frac2 <<= (64 - FLOAT64_FRACTION_SIZE - 2);
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259 |
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260 | mul64(frac1, frac2, &frac1, &frac2);
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261 |
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262 | frac1 |= (frac2 != 0);
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263 | if (frac1 & (0x1ll << 62)) {
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264 | frac1 <<= 1;
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265 | exp--;
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266 | }
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267 |
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268 | result = finish_float64(exp, frac1, result.parts.sign);
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269 | return result;
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270 | }
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271 |
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272 | /** Multiply two quadruple-precision floats.
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273 | *
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274 | * @param a First input operand.
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275 | * @param b Second input operand.
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276 | *
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277 | * @return Result of multiplication.
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278 | *
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279 | */
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280 | float128 mul_float128(float128 a, float128 b)
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281 | {
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282 | float128 result;
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283 | uint64_t frac1_hi, frac1_lo, frac2_hi, frac2_lo, tmp_hi, tmp_lo;
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284 | int32_t exp;
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285 |
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286 | result.parts.sign = a.parts.sign ^ b.parts.sign;
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287 |
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288 | if (is_float128_nan(a) || is_float128_nan(b)) {
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289 | /* TODO: fix SigNaNs */
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290 | if (is_float128_signan(a)) {
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291 | result.parts.frac_hi = a.parts.frac_hi;
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292 | result.parts.frac_lo = a.parts.frac_lo;
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293 | result.parts.exp = a.parts.exp;
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294 | return result;
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295 | }
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296 | if (is_float128_signan(b)) { /* TODO: fix SigNaN */
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297 | result.parts.frac_hi = b.parts.frac_hi;
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298 | result.parts.frac_lo = b.parts.frac_lo;
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299 | result.parts.exp = b.parts.exp;
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300 | return result;
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301 | }
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302 | /* set NaN as result */
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303 | result.bin.hi = FLOAT128_NAN_HI;
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304 | result.bin.lo = FLOAT128_NAN_LO;
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305 | return result;
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306 | }
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307 |
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308 | if (is_float128_infinity(a)) {
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309 | if (is_float128_zero(b)) {
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310 | /* FIXME: zero * infinity */
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311 | result.bin.hi = FLOAT128_NAN_HI;
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312 | result.bin.lo = FLOAT128_NAN_LO;
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313 | return result;
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314 | }
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315 | result.parts.frac_hi = a.parts.frac_hi;
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316 | result.parts.frac_lo = a.parts.frac_lo;
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317 | result.parts.exp = a.parts.exp;
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318 | return result;
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319 | }
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320 |
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321 | if (is_float128_infinity(b)) {
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322 | if (is_float128_zero(a)) {
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323 | /* FIXME: zero * infinity */
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324 | result.bin.hi = FLOAT128_NAN_HI;
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325 | result.bin.lo = FLOAT128_NAN_LO;
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326 | return result;
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327 | }
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328 | result.parts.frac_hi = b.parts.frac_hi;
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329 | result.parts.frac_lo = b.parts.frac_lo;
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330 | result.parts.exp = b.parts.exp;
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331 | return result;
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332 | }
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333 |
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334 | /* exp is signed so we can easy detect underflow */
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335 | exp = a.parts.exp + b.parts.exp - FLOAT128_BIAS - 1;
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336 |
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337 | frac1_hi = a.parts.frac_hi;
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338 | frac1_lo = a.parts.frac_lo;
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339 |
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340 | if (a.parts.exp > 0) {
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341 | or128(frac1_hi, frac1_lo,
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342 | FLOAT128_HIDDEN_BIT_MASK_HI, FLOAT128_HIDDEN_BIT_MASK_LO,
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343 | &frac1_hi, &frac1_lo);
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344 | } else {
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345 | ++exp;
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346 | }
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347 |
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348 | frac2_hi = b.parts.frac_hi;
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349 | frac2_lo = b.parts.frac_lo;
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350 |
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351 | if (b.parts.exp > 0) {
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352 | or128(frac2_hi, frac2_lo,
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353 | FLOAT128_HIDDEN_BIT_MASK_HI, FLOAT128_HIDDEN_BIT_MASK_LO,
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354 | &frac2_hi, &frac2_lo);
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355 | } else {
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356 | ++exp;
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357 | }
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358 |
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359 | lshift128(frac2_hi, frac2_lo,
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360 | 128 - FLOAT128_FRACTION_SIZE, &frac2_hi, &frac2_lo);
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361 |
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362 | tmp_hi = frac1_hi;
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363 | tmp_lo = frac1_lo;
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364 | mul128(frac1_hi, frac1_lo, frac2_hi, frac2_lo,
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365 | &frac1_hi, &frac1_lo, &frac2_hi, &frac2_lo);
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366 | add128(frac1_hi, frac1_lo, tmp_hi, tmp_lo, &frac1_hi, &frac1_lo);
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367 | frac2_hi |= (frac2_lo != 0x0ll);
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368 |
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369 | if ((FLOAT128_HIDDEN_BIT_MASK_HI << 1) <= frac1_hi) {
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370 | frac2_hi >>= 1;
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371 | if (frac1_lo & 0x1ll) {
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372 | frac2_hi |= (0x1ull < 64);
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373 | }
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374 | rshift128(frac1_hi, frac1_lo, 1, &frac1_hi, &frac1_lo);
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375 | ++exp;
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376 | }
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377 |
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378 | result = finish_float128(exp, frac1_hi, frac1_lo, result.parts.sign, frac2_hi);
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379 | return result;
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380 | }
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381 |
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382 | /** @}
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383 | */
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