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1 | /* |
1 | /* |
2 | * Copyright (C) 2005 Josef Cejka |
2 | * Copyright (C) 2005 Josef Cejka |
3 | * All rights reserved. |
3 | * All rights reserved. |
4 | * |
4 | * |
5 | * Redistribution and use in source and binary forms, with or without |
5 | * Redistribution and use in source and binary forms, with or without |
6 | * modification, are permitted provided that the following conditions |
6 | * modification, are permitted provided that the following conditions |
7 | * are met: |
7 | * are met: |
8 | * |
8 | * |
9 | * - Redistributions of source code must retain the above copyright |
9 | * - Redistributions of source code must retain the above copyright |
10 | * notice, this list of conditions and the following disclaimer. |
10 | * notice, this list of conditions and the following disclaimer. |
11 | * - Redistributions in binary form must reproduce the above copyright |
11 | * - Redistributions in binary form must reproduce the above copyright |
12 | * notice, this list of conditions and the following disclaimer in the |
12 | * notice, this list of conditions and the following disclaimer in the |
13 | * documentation and/or other materials provided with the distribution. |
13 | * documentation and/or other materials provided with the distribution. |
14 | * - The name of the author may not be used to endorse or promote products |
14 | * - The name of the author may not be used to endorse or promote products |
15 | * derived from this software without specific prior written permission. |
15 | * derived from this software without specific prior written permission. |
16 | * |
16 | * |
17 | * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR |
17 | * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR |
18 | * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES |
18 | * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES |
19 | * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. |
19 | * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. |
20 | * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT, |
20 | * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT, |
21 | * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT |
21 | * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT |
22 | * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, |
22 | * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, |
23 | * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY |
23 | * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY |
24 | * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT |
24 | * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT |
25 | * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF |
25 | * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF |
26 | * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. |
26 | * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. |
27 | */ |
27 | */ |
28 | 28 | ||
29 | /** @addtogroup softfloat |
29 | /** @addtogroup softfloat |
30 | * @{ |
30 | * @{ |
31 | */ |
31 | */ |
32 | /** @file |
32 | /** @file |
33 | */ |
33 | */ |
34 | 34 | ||
35 | #include<sftypes.h> |
35 | #include<sftypes.h> |
36 | #include<common.h> |
36 | #include<common.h> |
37 | 37 | ||
38 | /* Table for fast leading zeroes counting */ |
38 | /* Table for fast leading zeroes counting */ |
39 | char zeroTable[256] = { |
39 | char zeroTable[256] = { |
40 | 8, 7, 7, 6, 6, 6, 6, 4, 4, 4, 4, 4, 4, 4, 4, \ |
40 | 8, 7, 7, 6, 6, 6, 6, 4, 4, 4, 4, 4, 4, 4, 4, \ |
41 | 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, \ |
41 | 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, \ |
42 | 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, \ |
42 | 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, \ |
43 | 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, \ |
43 | 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, \ |
44 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, \ |
44 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, \ |
45 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, \ |
45 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, \ |
46 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, \ |
46 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, \ |
47 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, \ |
47 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, \ |
48 | 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \ |
48 | 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \ |
49 | 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \ |
49 | 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \ |
50 | 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \ |
50 | 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \ |
51 | 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \ |
51 | 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \ |
52 | 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \ |
52 | 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \ |
53 | 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \ |
53 | 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \ |
54 | 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \ |
54 | 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \ |
55 | 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 |
55 | 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 |
56 | }; |
56 | }; |
57 | 57 | ||
58 | 58 | ||
59 | 59 | ||
60 | /** Take fraction shifted by 10 bits to left, round it, normalize it and detect exceptions |
60 | /** Take fraction shifted by 10 bits to left, round it, normalize it and detect exceptions |
61 | * @param cexp exponent with bias |
61 | * @param cexp exponent with bias |
62 | * @param cfrac fraction shifted 10 places left with added hidden bit |
62 | * @param cfrac fraction shifted 10 places left with added hidden bit |
63 | * @param sign |
63 | * @param sign |
64 | * @return valied float64 |
64 | * @return valied float64 |
65 | */ |
65 | */ |
66 | float64 finishFloat64(int32_t cexp, uint64_t cfrac, char sign) |
66 | float64 finishFloat64(int32_t cexp, uint64_t cfrac, char sign) |
67 | { |
67 | { |
68 | float64 result; |
68 | float64 result; |
69 | 69 | ||
70 | result.parts.sign = sign; |
70 | result.parts.sign = sign; |
71 | 71 | ||
72 | /* find first nonzero digit and shift result and detect possibly underflow */ |
72 | /* find first nonzero digit and shift result and detect possibly underflow */ |
73 | while ((cexp > 0) && (cfrac) && (!(cfrac & (FLOAT64_HIDDEN_BIT_MASK << (64 - FLOAT64_FRACTION_SIZE - 1 ) )))) { |
73 | while ((cexp > 0) && (cfrac) && (!(cfrac & (FLOAT64_HIDDEN_BIT_MASK << (64 - FLOAT64_FRACTION_SIZE - 1 ) )))) { |
74 | cexp--; |
74 | cexp--; |
75 | cfrac <<= 1; |
75 | cfrac <<= 1; |
76 | /* TODO: fix underflow */ |
76 | /* TODO: fix underflow */ |
77 | }; |
77 | }; |
78 | 78 | ||
79 | if ((cexp < 0) || ( cexp == 0 && (!(cfrac & (FLOAT64_HIDDEN_BIT_MASK << (64 - FLOAT64_FRACTION_SIZE - 1)))))) { |
79 | if ((cexp < 0) || ( cexp == 0 && (!(cfrac & (FLOAT64_HIDDEN_BIT_MASK << (64 - FLOAT64_FRACTION_SIZE - 1)))))) { |
80 | /* FIXME: underflow */ |
80 | /* FIXME: underflow */ |
81 | result.parts.exp = 0; |
81 | result.parts.exp = 0; |
82 | if ((cexp + FLOAT64_FRACTION_SIZE + 1) < 0) { /* +1 is place for rounding */ |
82 | if ((cexp + FLOAT64_FRACTION_SIZE + 1) < 0) { /* +1 is place for rounding */ |
83 | result.parts.fraction = 0; |
83 | result.parts.fraction = 0; |
84 | return result; |
84 | return result; |
85 | } |
85 | } |
86 | 86 | ||
87 | while (cexp < 0) { |
87 | while (cexp < 0) { |
88 | cexp++; |
88 | cexp++; |
89 | cfrac >>= 1; |
89 | cfrac >>= 1; |
90 | } |
90 | } |
91 | 91 | ||
92 | cfrac += (0x1 << (64 - FLOAT64_FRACTION_SIZE - 3)); |
92 | cfrac += (0x1 << (64 - FLOAT64_FRACTION_SIZE - 3)); |
93 | 93 | ||
94 | if (!(cfrac & (FLOAT64_HIDDEN_BIT_MASK << (64 - FLOAT64_FRACTION_SIZE - 1)))) { |
94 | if (!(cfrac & (FLOAT64_HIDDEN_BIT_MASK << (64 - FLOAT64_FRACTION_SIZE - 1)))) { |
95 | 95 | ||
96 | result.parts.fraction = ((cfrac >>(64 - FLOAT64_FRACTION_SIZE - 2) ) & (~FLOAT64_HIDDEN_BIT_MASK)); |
96 | result.parts.fraction = ((cfrac >>(64 - FLOAT64_FRACTION_SIZE - 2) ) & (~FLOAT64_HIDDEN_BIT_MASK)); |
97 | return result; |
97 | return result; |
98 | } |
98 | } |
99 | } else { |
99 | } else { |
100 | cfrac += (0x1 << (64 - FLOAT64_FRACTION_SIZE - 3)); |
100 | cfrac += (0x1 << (64 - FLOAT64_FRACTION_SIZE - 3)); |
101 | } |
101 | } |
102 | 102 | ||
103 | ++cexp; |
103 | ++cexp; |
104 | 104 | ||
105 | if (cfrac & (FLOAT64_HIDDEN_BIT_MASK << (64 - FLOAT64_FRACTION_SIZE - 1 ))) { |
105 | if (cfrac & (FLOAT64_HIDDEN_BIT_MASK << (64 - FLOAT64_FRACTION_SIZE - 1 ))) { |
106 | ++cexp; |
106 | ++cexp; |
107 | cfrac >>= 1; |
107 | cfrac >>= 1; |
108 | } |
108 | } |
109 | 109 | ||
110 | /* check overflow */ |
110 | /* check overflow */ |
111 | if (cexp >= FLOAT64_MAX_EXPONENT ) { |
111 | if (cexp >= FLOAT64_MAX_EXPONENT ) { |
112 | /* FIXME: overflow, return infinity */ |
112 | /* FIXME: overflow, return infinity */ |
113 | result.parts.exp = FLOAT64_MAX_EXPONENT; |
113 | result.parts.exp = FLOAT64_MAX_EXPONENT; |
114 | result.parts.fraction = 0; |
114 | result.parts.fraction = 0; |
115 | return result; |
115 | return result; |
116 | } |
116 | } |
117 | 117 | ||
118 | result.parts.exp = (uint32_t)cexp; |
118 | result.parts.exp = (uint32_t)cexp; |
119 | 119 | ||
120 | result.parts.fraction = ((cfrac >>(64 - FLOAT64_FRACTION_SIZE - 2 ) ) & (~FLOAT64_HIDDEN_BIT_MASK)); |
120 | result.parts.fraction = ((cfrac >>(64 - FLOAT64_FRACTION_SIZE - 2 ) ) & (~FLOAT64_HIDDEN_BIT_MASK)); |
121 | 121 | ||
122 | return result; |
122 | return result; |
123 | } |
123 | } |
124 | 124 | ||
125 | /** Counts leading zeroes in 64bit unsigned integer |
125 | /** Counts leading zeroes in 64bit unsigned integer |
126 | * @param i |
126 | * @param i |
127 | */ |
127 | */ |
128 | int countZeroes64(uint64_t i) |
128 | int countZeroes64(uint64_t i) |
129 | { |
129 | { |
130 | int j; |
130 | int j; |
131 | for (j =0; j < 64; j += 8) { |
131 | for (j =0; j < 64; j += 8) { |
132 | if ( i & (0xFFll << (56 - j))) { |
132 | if ( i & (0xFFll << (56 - j))) { |
133 | return (j + countZeroes8(i >> (56 - j))); |
133 | return (j + countZeroes8(i >> (56 - j))); |
134 | } |
134 | } |
135 | } |
135 | } |
136 | 136 | ||
137 | return 64; |
137 | return 64; |
138 | } |
138 | } |
139 | 139 | ||
140 | /** Counts leading zeroes in 32bit unsigned integer |
140 | /** Counts leading zeroes in 32bit unsigned integer |
141 | * @param i |
141 | * @param i |
142 | */ |
142 | */ |
143 | int countZeroes32(uint32_t i) |
143 | int countZeroes32(uint32_t i) |
144 | { |
144 | { |
145 | int j; |
145 | int j; |
146 | for (j =0; j < 32; j += 8) { |
146 | for (j =0; j < 32; j += 8) { |
147 | if ( i & (0xFF << (24 - j))) { |
147 | if ( i & (0xFF << (24 - j))) { |
148 | return (j + countZeroes8(i >> (24 - j))); |
148 | return (j + countZeroes8(i >> (24 - j))); |
149 | } |
149 | } |
150 | } |
150 | } |
151 | 151 | ||
152 | return 32; |
152 | return 32; |
153 | } |
153 | } |
154 | 154 | ||
155 | /** Counts leading zeroes in byte |
155 | /** Counts leading zeroes in byte |
156 | * @param i |
156 | * @param i |
157 | */ |
157 | */ |
158 | int countZeroes8(uint8_t i) |
158 | int countZeroes8(uint8_t i) |
159 | { |
159 | { |
160 | return zeroTable[i]; |
160 | return zeroTable[i]; |
161 | } |
161 | } |
162 | 162 | ||
163 | /** Round and normalize number expressed by exponent and fraction with first bit (equal to hidden bit) at 30. bit |
163 | /** Round and normalize number expressed by exponent and fraction with first bit (equal to hidden bit) at 30. bit |
164 | * @param exp exponent |
164 | * @param exp exponent |
165 | * @param fraction part with hidden bit shifted to 30. bit |
165 | * @param fraction part with hidden bit shifted to 30. bit |
166 | */ |
166 | */ |
167 | void roundFloat32(int32_t *exp, uint32_t *fraction) |
167 | void roundFloat32(int32_t *exp, uint32_t *fraction) |
168 | { |
168 | { |
169 | /* rounding - if first bit after fraction is set then round up */ |
169 | /* rounding - if first bit after fraction is set then round up */ |
170 | (*fraction) += (0x1 << 6); |
170 | (*fraction) += (0x1 << 6); |
171 | 171 | ||
172 | if ((*fraction) & (FLOAT32_HIDDEN_BIT_MASK << 8)) { |
172 | if ((*fraction) & (FLOAT32_HIDDEN_BIT_MASK << 8)) { |
173 | /* rounding overflow */ |
173 | /* rounding overflow */ |
174 | ++(*exp); |
174 | ++(*exp); |
175 | (*fraction) >>= 1; |
175 | (*fraction) >>= 1; |
176 | }; |
176 | }; |
177 | 177 | ||
178 | if (((*exp) >= FLOAT32_MAX_EXPONENT ) || ((*exp) < 0)) { |
178 | if (((*exp) >= FLOAT32_MAX_EXPONENT ) || ((*exp) < 0)) { |
179 | /* overflow - set infinity as result */ |
179 | /* overflow - set infinity as result */ |
180 | (*exp) = FLOAT32_MAX_EXPONENT; |
180 | (*exp) = FLOAT32_MAX_EXPONENT; |
181 | (*fraction) = 0; |
181 | (*fraction) = 0; |
182 | return; |
182 | return; |
183 | } |
183 | } |
184 | 184 | ||
185 | return; |
185 | return; |
186 | } |
186 | } |
187 | 187 | ||
188 | /** Round and normalize number expressed by exponent and fraction with first bit (equal to hidden bit) at 62. bit |
188 | /** Round and normalize number expressed by exponent and fraction with first bit (equal to hidden bit) at 62. bit |
189 | * @param exp exponent |
189 | * @param exp exponent |
190 | * @param fraction part with hidden bit shifted to 62. bit |
190 | * @param fraction part with hidden bit shifted to 62. bit |
191 | */ |
191 | */ |
192 | void roundFloat64(int32_t *exp, uint64_t *fraction) |
192 | void roundFloat64(int32_t *exp, uint64_t *fraction) |
193 | { |
193 | { |
194 | /* rounding - if first bit after fraction is set then round up */ |
194 | /* rounding - if first bit after fraction is set then round up */ |
195 | (*fraction) += (0x1 << 9); |
195 | (*fraction) += (0x1 << 9); |
196 | 196 | ||
197 | if ((*fraction) & (FLOAT64_HIDDEN_BIT_MASK << 11)) { |
197 | if ((*fraction) & (FLOAT64_HIDDEN_BIT_MASK << 11)) { |
198 | /* rounding overflow */ |
198 | /* rounding overflow */ |
199 | ++(*exp); |
199 | ++(*exp); |
200 | (*fraction) >>= 1; |
200 | (*fraction) >>= 1; |
201 | }; |
201 | }; |
202 | 202 | ||
203 | if (((*exp) >= FLOAT64_MAX_EXPONENT ) || ((*exp) < 0)) { |
203 | if (((*exp) >= FLOAT64_MAX_EXPONENT ) || ((*exp) < 0)) { |
204 | /* overflow - set infinity as result */ |
204 | /* overflow - set infinity as result */ |
205 | (*exp) = FLOAT64_MAX_EXPONENT; |
205 | (*exp) = FLOAT64_MAX_EXPONENT; |
206 | (*fraction) = 0; |
206 | (*fraction) = 0; |
207 | return; |
207 | return; |
208 | } |
208 | } |
209 | 209 | ||
210 | return; |
210 | return; |
211 | } |
211 | } |
212 | 212 | ||
213 | - | ||
214 | /** @} |
213 | /** @} |
215 | */ |
214 | */ |
216 | 215 | ||
217 | 216 |