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| 829 | cejka | 1 | /* |
| 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 | |||
| 1740 | jermar | 29 | /** @addtogroup softfloat |
| 1657 | cejka | 30 | * @{ |
| 31 | */ |
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| 32 | /** @file |
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| 33 | */ |
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| 34 | |||
| 829 | cejka | 35 | #include<sftypes.h> |
| 36 | #include<common.h> |
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| 37 | |||
| 874 | cejka | 38 | /* Table for fast leading zeroes counting */ |
| 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 | |||
| 58 | |||
| 59 | |||
| 829 | cejka | 60 | /** Take fraction shifted by 10 bits to left, round it, normalize it and detect exceptions |
| 1653 | cejka | 61 | * @param cexp exponent with bias |
| 829 | cejka | 62 | * @param cfrac fraction shifted 10 places left with added hidden bit |
| 1653 | cejka | 63 | * @param sign |
| 829 | cejka | 64 | * @return valied float64 |
| 65 | */ |
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| 1031 | cejka | 66 | float64 finishFloat64(int32_t cexp, uint64_t cfrac, char sign) |
| 829 | cejka | 67 | { |
| 68 | float64 result; |
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| 69 | |||
| 70 | result.parts.sign = sign; |
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| 71 | |||
| 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 | |||
| 834 | cejka | 79 | if ((cexp < 0) || ( cexp == 0 && (!(cfrac & (FLOAT64_HIDDEN_BIT_MASK << (64 - FLOAT64_FRACTION_SIZE - 1)))))) { |
| 80 | /* FIXME: underflow */ |
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| 81 | result.parts.exp = 0; |
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| 835 | cejka | 82 | if ((cexp + FLOAT64_FRACTION_SIZE + 1) < 0) { /* +1 is place for rounding */ |
| 834 | cejka | 83 | result.parts.fraction = 0; |
| 84 | return result; |
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| 85 | } |
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| 835 | cejka | 86 | |
| 834 | cejka | 87 | while (cexp < 0) { |
| 88 | cexp++; |
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| 89 | cfrac >>= 1; |
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| 90 | } |
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| 835 | cejka | 91 | |
| 92 | cfrac += (0x1 << (64 - FLOAT64_FRACTION_SIZE - 3)); |
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| 93 | |||
| 874 | cejka | 94 | if (!(cfrac & (FLOAT64_HIDDEN_BIT_MASK << (64 - FLOAT64_FRACTION_SIZE - 1)))) { |
| 834 | cejka | 95 | |
| 835 | cejka | 96 | result.parts.fraction = ((cfrac >>(64 - FLOAT64_FRACTION_SIZE - 2) ) & (~FLOAT64_HIDDEN_BIT_MASK)); |
| 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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| 834 | cejka | 101 | } |
| 102 | |||
| 103 | ++cexp; |
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| 104 | |||
| 829 | cejka | 105 | if (cfrac & (FLOAT64_HIDDEN_BIT_MASK << (64 - FLOAT64_FRACTION_SIZE - 1 ))) { |
| 106 | ++cexp; |
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| 107 | cfrac >>= 1; |
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| 834 | cejka | 108 | } |
| 829 | cejka | 109 | |
| 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 | |||
| 1031 | cejka | 118 | result.parts.exp = (uint32_t)cexp; |
| 829 | cejka | 119 | |
| 120 | result.parts.fraction = ((cfrac >>(64 - FLOAT64_FRACTION_SIZE - 2 ) ) & (~FLOAT64_HIDDEN_BIT_MASK)); |
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| 121 | |||
| 122 | return result; |
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| 123 | } |
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| 834 | cejka | 124 | |
| 874 | cejka | 125 | /** Counts leading zeroes in 64bit unsigned integer |
| 126 | * @param i |
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| 127 | */ |
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| 1031 | cejka | 128 | int countZeroes64(uint64_t i) |
| 874 | cejka | 129 | { |
| 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 | |||
| 137 | return 64; |
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| 138 | } |
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| 139 | |||
| 140 | /** Counts leading zeroes in 32bit unsigned integer |
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| 141 | * @param i |
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| 142 | */ |
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| 1031 | cejka | 143 | int countZeroes32(uint32_t i) |
| 874 | cejka | 144 | { |
| 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 | |||
| 152 | return 32; |
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| 153 | } |
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| 154 | |||
| 155 | /** Counts leading zeroes in byte |
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| 156 | * @param i |
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| 157 | */ |
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| 1031 | cejka | 158 | int countZeroes8(uint8_t i) |
| 874 | cejka | 159 | { |
| 160 | return zeroTable[i]; |
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| 161 | } |
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| 162 | |||
| 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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| 1031 | cejka | 167 | void roundFloat32(int32_t *exp, uint32_t *fraction) |
| 874 | cejka | 168 | { |
| 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 | |||
| 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 | |||
| 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 | |||
| 185 | return; |
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| 186 | } |
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| 187 | |||
| 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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| 1031 | cejka | 192 | void roundFloat64(int32_t *exp, uint64_t *fraction) |
| 874 | cejka | 193 | { |
| 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 | |||
| 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 | |||
| 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 | |||
| 210 | return; |
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| 211 | } |
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| 212 | |||
| 1740 | jermar | 213 | /** @} |
| 1657 | cejka | 214 | */ |
| 215 |