1 | /*
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2 | * Copyright (c) 2005 Josef Cejka
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3 | * All rights reserved.
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4 | *
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5 | * Redistribution and use in source and binary forms, with or without
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6 | * modification, are permitted provided that the following conditions
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7 | * are met:
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8 | *
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9 | * - Redistributions of source code must retain the above copyright
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10 | * notice, this list of conditions and the following disclaimer.
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11 | * - Redistributions in binary form must reproduce the above copyright
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12 | * notice, this list of conditions and the following disclaimer in the
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13 | * documentation and/or other materials provided with the distribution.
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14 | * - The name of the author may not be used to endorse or promote products
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15 | * derived from this software without specific prior written permission.
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16 | *
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17 | * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
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18 | * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
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19 | * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
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20 | * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
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21 | * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
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22 | * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
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23 | * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
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24 | * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
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25 | * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
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26 | * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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27 | */
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28 |
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29 | /** @addtogroup softfloat
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30 | * @{
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31 | */
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32 | /** @file
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33 | */
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34 |
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35 | #include<sftypes.h>
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36 | #include<common.h>
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37 |
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38 | /* Table for fast leading zeroes counting */
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39 | char zeroTable[256] = {
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40 | 8, 7, 7, 6, 6, 6, 6, 4, 4, 4, 4, 4, 4, 4, 4, \
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41 | 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, \
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42 | 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, \
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43 | 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, \
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44 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, \
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45 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, \
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46 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, \
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47 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, \
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48 | 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \
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49 | 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \
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50 | 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \
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51 | 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \
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52 | 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \
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53 | 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \
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54 | 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \
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55 | 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
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56 | };
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57 |
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58 |
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59 |
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60 | /** Take fraction shifted by 10 bits to left, round it, normalize it and detect exceptions
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61 | * @param cexp exponent with bias
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62 | * @param cfrac fraction shifted 10 places left with added hidden bit
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63 | * @param sign
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64 | * @return valied float64
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65 | */
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66 | float64 finishFloat64(int32_t cexp, uint64_t cfrac, char sign)
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67 | {
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68 | float64 result;
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69 |
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70 | result.parts.sign = sign;
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71 |
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72 | /* find first nonzero digit and shift result and detect possibly underflow */
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73 | while ((cexp > 0) && (cfrac) && (!(cfrac & (FLOAT64_HIDDEN_BIT_MASK << (64 - FLOAT64_FRACTION_SIZE - 1 ) )))) {
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74 | cexp--;
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75 | cfrac <<= 1;
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76 | /* TODO: fix underflow */
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77 | };
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78 |
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79 | if ((cexp < 0) || ( cexp == 0 && (!(cfrac & (FLOAT64_HIDDEN_BIT_MASK << (64 - FLOAT64_FRACTION_SIZE - 1)))))) {
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80 | /* FIXME: underflow */
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81 | result.parts.exp = 0;
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82 | if ((cexp + FLOAT64_FRACTION_SIZE + 1) < 0) { /* +1 is place for rounding */
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83 | result.parts.fraction = 0;
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84 | return result;
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85 | }
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86 |
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87 | while (cexp < 0) {
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88 | cexp++;
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89 | cfrac >>= 1;
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90 | }
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91 |
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92 | cfrac += (0x1 << (64 - FLOAT64_FRACTION_SIZE - 3));
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93 |
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94 | if (!(cfrac & (FLOAT64_HIDDEN_BIT_MASK << (64 - FLOAT64_FRACTION_SIZE - 1)))) {
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95 |
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96 | result.parts.fraction = ((cfrac >>(64 - FLOAT64_FRACTION_SIZE - 2) ) & (~FLOAT64_HIDDEN_BIT_MASK));
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97 | return result;
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98 | }
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99 | } else {
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100 | cfrac += (0x1 << (64 - FLOAT64_FRACTION_SIZE - 3));
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101 | }
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102 |
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103 | ++cexp;
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104 |
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105 | if (cfrac & (FLOAT64_HIDDEN_BIT_MASK << (64 - FLOAT64_FRACTION_SIZE - 1 ))) {
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106 | ++cexp;
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107 | cfrac >>= 1;
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108 | }
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109 |
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110 | /* check overflow */
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111 | if (cexp >= FLOAT64_MAX_EXPONENT ) {
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112 | /* FIXME: overflow, return infinity */
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113 | result.parts.exp = FLOAT64_MAX_EXPONENT;
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114 | result.parts.fraction = 0;
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115 | return result;
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116 | }
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117 |
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118 | result.parts.exp = (uint32_t)cexp;
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119 |
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120 | result.parts.fraction = ((cfrac >>(64 - FLOAT64_FRACTION_SIZE - 2 ) ) & (~FLOAT64_HIDDEN_BIT_MASK));
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121 |
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122 | return result;
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123 | }
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124 |
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125 | /** Counts leading zeroes in 64bit unsigned integer
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126 | * @param i
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127 | */
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128 | int countZeroes64(uint64_t i)
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129 | {
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130 | int j;
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131 | for (j =0; j < 64; j += 8) {
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132 | if ( i & (0xFFll << (56 - j))) {
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133 | return (j + countZeroes8(i >> (56 - j)));
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134 | }
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135 | }
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136 |
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137 | return 64;
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138 | }
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139 |
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140 | /** Counts leading zeroes in 32bit unsigned integer
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141 | * @param i
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142 | */
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143 | int countZeroes32(uint32_t i)
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144 | {
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145 | int j;
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146 | for (j =0; j < 32; j += 8) {
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147 | if ( i & (0xFF << (24 - j))) {
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148 | return (j + countZeroes8(i >> (24 - j)));
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149 | }
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150 | }
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151 |
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152 | return 32;
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153 | }
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154 |
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155 | /** Counts leading zeroes in byte
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156 | * @param i
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157 | */
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158 | int countZeroes8(uint8_t i)
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159 | {
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160 | return zeroTable[i];
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161 | }
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162 |
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163 | /** Round and normalize number expressed by exponent and fraction with first bit (equal to hidden bit) at 30. bit
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164 | * @param exp exponent
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165 | * @param fraction part with hidden bit shifted to 30. bit
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166 | */
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167 | void roundFloat32(int32_t *exp, uint32_t *fraction)
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168 | {
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169 | /* rounding - if first bit after fraction is set then round up */
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170 | (*fraction) += (0x1 << 6);
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171 |
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172 | if ((*fraction) & (FLOAT32_HIDDEN_BIT_MASK << 8)) {
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173 | /* rounding overflow */
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174 | ++(*exp);
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175 | (*fraction) >>= 1;
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176 | };
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177 |
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178 | if (((*exp) >= FLOAT32_MAX_EXPONENT ) || ((*exp) < 0)) {
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179 | /* overflow - set infinity as result */
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180 | (*exp) = FLOAT32_MAX_EXPONENT;
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181 | (*fraction) = 0;
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182 | return;
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183 | }
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184 |
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185 | return;
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186 | }
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187 |
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188 | /** Round and normalize number expressed by exponent and fraction with first bit (equal to hidden bit) at 62. bit
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189 | * @param exp exponent
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190 | * @param fraction part with hidden bit shifted to 62. bit
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191 | */
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192 | void roundFloat64(int32_t *exp, uint64_t *fraction)
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193 | {
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194 | /* rounding - if first bit after fraction is set then round up */
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195 | (*fraction) += (0x1 << 9);
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196 |
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197 | if ((*fraction) & (FLOAT64_HIDDEN_BIT_MASK << 11)) {
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198 | /* rounding overflow */
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199 | ++(*exp);
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200 | (*fraction) >>= 1;
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201 | };
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202 |
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203 | if (((*exp) >= FLOAT64_MAX_EXPONENT ) || ((*exp) < 0)) {
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204 | /* overflow - set infinity as result */
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205 | (*exp) = FLOAT64_MAX_EXPONENT;
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206 | (*fraction) = 0;
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207 | return;
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208 | }
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209 |
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210 | return;
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211 | }
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212 |
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213 | /** @}
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214 | */
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215 |
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