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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<sub.h> |
36 | #include<sub.h> |
37 | #include<comparison.h> |
37 | #include<comparison.h> |
38 | 38 | ||
39 | /** Subtract two float32 numbers with same signs |
39 | /** Subtract two float32 numbers with same signs |
40 | */ |
40 | */ |
41 | float32 subFloat32(float32 a, float32 b) |
41 | float32 subFloat32(float32 a, float32 b) |
42 | { |
42 | { |
43 | int expdiff; |
43 | int expdiff; |
44 | uint32_t exp1, exp2, frac1, frac2; |
44 | uint32_t exp1, exp2, frac1, frac2; |
45 | float32 result; |
45 | float32 result; |
46 | 46 | ||
47 | result.f = 0; |
47 | result.f = 0; |
48 | 48 | ||
49 | expdiff = a.parts.exp - b.parts.exp; |
49 | expdiff = a.parts.exp - b.parts.exp; |
50 | if ((expdiff < 0 ) || ((expdiff == 0) && (a.parts.fraction < b.parts.fraction))) { |
50 | if ((expdiff < 0 ) || ((expdiff == 0) && (a.parts.fraction < b.parts.fraction))) { |
51 | if (isFloat32NaN(b)) { |
51 | if (isFloat32NaN(b)) { |
52 | /* TODO: fix SigNaN */ |
52 | /* TODO: fix SigNaN */ |
53 | if (isFloat32SigNaN(b)) { |
53 | if (isFloat32SigNaN(b)) { |
54 | }; |
54 | }; |
55 | return b; |
55 | return b; |
56 | }; |
56 | }; |
57 | 57 | ||
58 | if (b.parts.exp == FLOAT32_MAX_EXPONENT) { |
58 | if (b.parts.exp == FLOAT32_MAX_EXPONENT) { |
59 | b.parts.sign = !b.parts.sign; /* num -(+-inf) = -+inf */ |
59 | b.parts.sign = !b.parts.sign; /* num -(+-inf) = -+inf */ |
60 | return b; |
60 | return b; |
61 | } |
61 | } |
62 | 62 | ||
63 | result.parts.sign = !a.parts.sign; |
63 | result.parts.sign = !a.parts.sign; |
64 | 64 | ||
65 | frac1 = b.parts.fraction; |
65 | frac1 = b.parts.fraction; |
66 | exp1 = b.parts.exp; |
66 | exp1 = b.parts.exp; |
67 | frac2 = a.parts.fraction; |
67 | frac2 = a.parts.fraction; |
68 | exp2 = a.parts.exp; |
68 | exp2 = a.parts.exp; |
69 | expdiff *= -1; |
69 | expdiff *= -1; |
70 | } else { |
70 | } else { |
71 | if (isFloat32NaN(a)) { |
71 | if (isFloat32NaN(a)) { |
72 | /* TODO: fix SigNaN */ |
72 | /* TODO: fix SigNaN */ |
73 | if (isFloat32SigNaN(a) || isFloat32SigNaN(b)) { |
73 | if (isFloat32SigNaN(a) || isFloat32SigNaN(b)) { |
74 | }; |
74 | }; |
75 | return a; |
75 | return a; |
76 | }; |
76 | }; |
77 | 77 | ||
78 | if (a.parts.exp == FLOAT32_MAX_EXPONENT) { |
78 | if (a.parts.exp == FLOAT32_MAX_EXPONENT) { |
79 | if (b.parts.exp == FLOAT32_MAX_EXPONENT) { |
79 | if (b.parts.exp == FLOAT32_MAX_EXPONENT) { |
80 | /* inf - inf => nan */ |
80 | /* inf - inf => nan */ |
81 | /* TODO: fix exception */ |
81 | /* TODO: fix exception */ |
82 | result.binary = FLOAT32_NAN; |
82 | result.binary = FLOAT32_NAN; |
83 | return result; |
83 | return result; |
84 | }; |
84 | }; |
85 | return a; |
85 | return a; |
86 | } |
86 | } |
87 | 87 | ||
88 | result.parts.sign = a.parts.sign; |
88 | result.parts.sign = a.parts.sign; |
89 | 89 | ||
90 | frac1 = a.parts.fraction; |
90 | frac1 = a.parts.fraction; |
91 | exp1 = a.parts.exp; |
91 | exp1 = a.parts.exp; |
92 | frac2 = b.parts.fraction; |
92 | frac2 = b.parts.fraction; |
93 | exp2 = b.parts.exp; |
93 | exp2 = b.parts.exp; |
94 | }; |
94 | }; |
95 | 95 | ||
96 | if (exp1 == 0) { |
96 | if (exp1 == 0) { |
97 | /* both are denormalized */ |
97 | /* both are denormalized */ |
98 | result.parts.fraction = frac1-frac2; |
98 | result.parts.fraction = frac1-frac2; |
99 | if (result.parts.fraction > frac1) { |
99 | if (result.parts.fraction > frac1) { |
100 | /* TODO: underflow exception */ |
100 | /* TODO: underflow exception */ |
101 | return result; |
101 | return result; |
102 | }; |
102 | }; |
103 | result.parts.exp = 0; |
103 | result.parts.exp = 0; |
104 | return result; |
104 | return result; |
105 | }; |
105 | }; |
106 | 106 | ||
107 | /* add hidden bit */ |
107 | /* add hidden bit */ |
108 | frac1 |= FLOAT32_HIDDEN_BIT_MASK; |
108 | frac1 |= FLOAT32_HIDDEN_BIT_MASK; |
109 | 109 | ||
110 | if (exp2 == 0) { |
110 | if (exp2 == 0) { |
111 | /* denormalized */ |
111 | /* denormalized */ |
112 | --expdiff; |
112 | --expdiff; |
113 | } else { |
113 | } else { |
114 | /* normalized */ |
114 | /* normalized */ |
115 | frac2 |= FLOAT32_HIDDEN_BIT_MASK; |
115 | frac2 |= FLOAT32_HIDDEN_BIT_MASK; |
116 | }; |
116 | }; |
117 | 117 | ||
118 | /* create some space for rounding */ |
118 | /* create some space for rounding */ |
119 | frac1 <<= 6; |
119 | frac1 <<= 6; |
120 | frac2 <<= 6; |
120 | frac2 <<= 6; |
121 | 121 | ||
122 | if (expdiff > FLOAT32_FRACTION_SIZE + 1) { |
122 | if (expdiff > FLOAT32_FRACTION_SIZE + 1) { |
123 | goto done; |
123 | goto done; |
124 | }; |
124 | }; |
125 | 125 | ||
126 | frac1 = frac1 - (frac2 >> expdiff); |
126 | frac1 = frac1 - (frac2 >> expdiff); |
127 | done: |
127 | done: |
128 | /* TODO: find first nonzero digit and shift result and detect possibly underflow */ |
128 | /* TODO: find first nonzero digit and shift result and detect possibly underflow */ |
129 | while ((exp1 > 0) && (!(frac1 & (FLOAT32_HIDDEN_BIT_MASK << 6 )))) { |
129 | while ((exp1 > 0) && (!(frac1 & (FLOAT32_HIDDEN_BIT_MASK << 6 )))) { |
130 | --exp1; |
130 | --exp1; |
131 | frac1 <<= 1; |
131 | frac1 <<= 1; |
132 | /* TODO: fix underflow - frac1 == 0 does not necessary means underflow... */ |
132 | /* TODO: fix underflow - frac1 == 0 does not necessary means underflow... */ |
133 | }; |
133 | }; |
134 | 134 | ||
135 | /* rounding - if first bit after fraction is set then round up */ |
135 | /* rounding - if first bit after fraction is set then round up */ |
136 | frac1 += 0x20; |
136 | frac1 += 0x20; |
137 | 137 | ||
138 | if (frac1 & (FLOAT32_HIDDEN_BIT_MASK << 7)) { |
138 | if (frac1 & (FLOAT32_HIDDEN_BIT_MASK << 7)) { |
139 | ++exp1; |
139 | ++exp1; |
140 | frac1 >>= 1; |
140 | frac1 >>= 1; |
141 | }; |
141 | }; |
142 | 142 | ||
143 | /*Clear hidden bit and shift */ |
143 | /*Clear hidden bit and shift */ |
144 | result.parts.fraction = ((frac1 >> 6) & (~FLOAT32_HIDDEN_BIT_MASK)); |
144 | result.parts.fraction = ((frac1 >> 6) & (~FLOAT32_HIDDEN_BIT_MASK)); |
145 | result.parts.exp = exp1; |
145 | result.parts.exp = exp1; |
146 | 146 | ||
147 | return result; |
147 | return result; |
148 | } |
148 | } |
149 | 149 | ||
150 | /** Subtract two float64 numbers with same signs |
150 | /** Subtract two float64 numbers with same signs |
151 | */ |
151 | */ |
152 | float64 subFloat64(float64 a, float64 b) |
152 | float64 subFloat64(float64 a, float64 b) |
153 | { |
153 | { |
154 | int expdiff; |
154 | int expdiff; |
155 | uint32_t exp1, exp2; |
155 | uint32_t exp1, exp2; |
156 | uint64_t frac1, frac2; |
156 | uint64_t frac1, frac2; |
157 | float64 result; |
157 | float64 result; |
158 | 158 | ||
159 | result.d = 0; |
159 | result.d = 0; |
160 | 160 | ||
161 | expdiff = a.parts.exp - b.parts.exp; |
161 | expdiff = a.parts.exp - b.parts.exp; |
162 | if ((expdiff < 0 ) || ((expdiff == 0) && (a.parts.fraction < b.parts.fraction))) { |
162 | if ((expdiff < 0 ) || ((expdiff == 0) && (a.parts.fraction < b.parts.fraction))) { |
163 | if (isFloat64NaN(b)) { |
163 | if (isFloat64NaN(b)) { |
164 | /* TODO: fix SigNaN */ |
164 | /* TODO: fix SigNaN */ |
165 | if (isFloat64SigNaN(b)) { |
165 | if (isFloat64SigNaN(b)) { |
166 | }; |
166 | }; |
167 | return b; |
167 | return b; |
168 | }; |
168 | }; |
169 | 169 | ||
170 | if (b.parts.exp == FLOAT64_MAX_EXPONENT) { |
170 | if (b.parts.exp == FLOAT64_MAX_EXPONENT) { |
171 | b.parts.sign = !b.parts.sign; /* num -(+-inf) = -+inf */ |
171 | b.parts.sign = !b.parts.sign; /* num -(+-inf) = -+inf */ |
172 | return b; |
172 | return b; |
173 | } |
173 | } |
174 | 174 | ||
175 | result.parts.sign = !a.parts.sign; |
175 | result.parts.sign = !a.parts.sign; |
176 | 176 | ||
177 | frac1 = b.parts.fraction; |
177 | frac1 = b.parts.fraction; |
178 | exp1 = b.parts.exp; |
178 | exp1 = b.parts.exp; |
179 | frac2 = a.parts.fraction; |
179 | frac2 = a.parts.fraction; |
180 | exp2 = a.parts.exp; |
180 | exp2 = a.parts.exp; |
181 | expdiff *= -1; |
181 | expdiff *= -1; |
182 | } else { |
182 | } else { |
183 | if (isFloat64NaN(a)) { |
183 | if (isFloat64NaN(a)) { |
184 | /* TODO: fix SigNaN */ |
184 | /* TODO: fix SigNaN */ |
185 | if (isFloat64SigNaN(a) || isFloat64SigNaN(b)) { |
185 | if (isFloat64SigNaN(a) || isFloat64SigNaN(b)) { |
186 | }; |
186 | }; |
187 | return a; |
187 | return a; |
188 | }; |
188 | }; |
189 | 189 | ||
190 | if (a.parts.exp == FLOAT64_MAX_EXPONENT) { |
190 | if (a.parts.exp == FLOAT64_MAX_EXPONENT) { |
191 | if (b.parts.exp == FLOAT64_MAX_EXPONENT) { |
191 | if (b.parts.exp == FLOAT64_MAX_EXPONENT) { |
192 | /* inf - inf => nan */ |
192 | /* inf - inf => nan */ |
193 | /* TODO: fix exception */ |
193 | /* TODO: fix exception */ |
194 | result.binary = FLOAT64_NAN; |
194 | result.binary = FLOAT64_NAN; |
195 | return result; |
195 | return result; |
196 | }; |
196 | }; |
197 | return a; |
197 | return a; |
198 | } |
198 | } |
199 | 199 | ||
200 | result.parts.sign = a.parts.sign; |
200 | result.parts.sign = a.parts.sign; |
201 | 201 | ||
202 | frac1 = a.parts.fraction; |
202 | frac1 = a.parts.fraction; |
203 | exp1 = a.parts.exp; |
203 | exp1 = a.parts.exp; |
204 | frac2 = b.parts.fraction; |
204 | frac2 = b.parts.fraction; |
205 | exp2 = b.parts.exp; |
205 | exp2 = b.parts.exp; |
206 | }; |
206 | }; |
207 | 207 | ||
208 | if (exp1 == 0) { |
208 | if (exp1 == 0) { |
209 | /* both are denormalized */ |
209 | /* both are denormalized */ |
210 | result.parts.fraction = frac1 - frac2; |
210 | result.parts.fraction = frac1 - frac2; |
211 | if (result.parts.fraction > frac1) { |
211 | if (result.parts.fraction > frac1) { |
212 | /* TODO: underflow exception */ |
212 | /* TODO: underflow exception */ |
213 | return result; |
213 | return result; |
214 | }; |
214 | }; |
215 | result.parts.exp = 0; |
215 | result.parts.exp = 0; |
216 | return result; |
216 | return result; |
217 | }; |
217 | }; |
218 | 218 | ||
219 | /* add hidden bit */ |
219 | /* add hidden bit */ |
220 | frac1 |= FLOAT64_HIDDEN_BIT_MASK; |
220 | frac1 |= FLOAT64_HIDDEN_BIT_MASK; |
221 | 221 | ||
222 | if (exp2 == 0) { |
222 | if (exp2 == 0) { |
223 | /* denormalized */ |
223 | /* denormalized */ |
224 | --expdiff; |
224 | --expdiff; |
225 | } else { |
225 | } else { |
226 | /* normalized */ |
226 | /* normalized */ |
227 | frac2 |= FLOAT64_HIDDEN_BIT_MASK; |
227 | frac2 |= FLOAT64_HIDDEN_BIT_MASK; |
228 | }; |
228 | }; |
229 | 229 | ||
230 | /* create some space for rounding */ |
230 | /* create some space for rounding */ |
231 | frac1 <<= 6; |
231 | frac1 <<= 6; |
232 | frac2 <<= 6; |
232 | frac2 <<= 6; |
233 | 233 | ||
234 | if (expdiff > FLOAT64_FRACTION_SIZE + 1) { |
234 | if (expdiff > FLOAT64_FRACTION_SIZE + 1) { |
235 | goto done; |
235 | goto done; |
236 | }; |
236 | }; |
237 | 237 | ||
238 | frac1 = frac1 - (frac2 >> expdiff); |
238 | frac1 = frac1 - (frac2 >> expdiff); |
239 | done: |
239 | done: |
240 | /* TODO: find first nonzero digit and shift result and detect possibly underflow */ |
240 | /* TODO: find first nonzero digit and shift result and detect possibly underflow */ |
241 | while ((exp1 > 0) && (!(frac1 & (FLOAT64_HIDDEN_BIT_MASK << 6 )))) { |
241 | while ((exp1 > 0) && (!(frac1 & (FLOAT64_HIDDEN_BIT_MASK << 6 )))) { |
242 | --exp1; |
242 | --exp1; |
243 | frac1 <<= 1; |
243 | frac1 <<= 1; |
244 | /* TODO: fix underflow - frac1 == 0 does not necessary means underflow... */ |
244 | /* TODO: fix underflow - frac1 == 0 does not necessary means underflow... */ |
245 | }; |
245 | }; |
246 | 246 | ||
247 | /* rounding - if first bit after fraction is set then round up */ |
247 | /* rounding - if first bit after fraction is set then round up */ |
248 | frac1 += 0x20; |
248 | frac1 += 0x20; |
249 | 249 | ||
250 | if (frac1 & (FLOAT64_HIDDEN_BIT_MASK << 7)) { |
250 | if (frac1 & (FLOAT64_HIDDEN_BIT_MASK << 7)) { |
251 | ++exp1; |
251 | ++exp1; |
252 | frac1 >>= 1; |
252 | frac1 >>= 1; |
253 | }; |
253 | }; |
254 | 254 | ||
255 | /*Clear hidden bit and shift */ |
255 | /*Clear hidden bit and shift */ |
256 | result.parts.fraction = ((frac1 >> 6) & (~FLOAT64_HIDDEN_BIT_MASK)); |
256 | result.parts.fraction = ((frac1 >> 6) & (~FLOAT64_HIDDEN_BIT_MASK)); |
257 | result.parts.exp = exp1; |
257 | result.parts.exp = exp1; |
258 | 258 | ||
259 | return result; |
259 | return result; |
260 | } |
260 | } |
261 | 261 | ||
262 | 262 | ||
263 | /** @} |
263 | /** @} |
264 | */ |
264 | */ |
265 | 265 | ||
266 | 266 |