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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 | #include<sftypes.h> |
29 | #include<sftypes.h> |
30 | #include<sub.h> |
30 | #include<sub.h> |
31 | #include<comparison.h> |
31 | #include<comparison.h> |
32 | 32 | ||
33 | /** Subtract two float32 numbers with same signs |
33 | /** Subtract two float32 numbers with same signs |
34 | */ |
34 | */ |
35 | float32 subFloat32(float32 a, float32 b) |
35 | float32 subFloat32(float32 a, float32 b) |
36 | { |
36 | { |
37 | int expdiff; |
37 | int expdiff; |
38 | __u32 exp1, exp2, frac1, frac2; |
38 | uint32_t exp1, exp2, frac1, frac2; |
39 | float32 result; |
39 | float32 result; |
40 | 40 | ||
41 | result.f = 0; |
41 | result.f = 0; |
42 | 42 | ||
43 | expdiff = a.parts.exp - b.parts.exp; |
43 | expdiff = a.parts.exp - b.parts.exp; |
44 | if ((expdiff < 0 ) || ((expdiff == 0) && (a.parts.fraction < b.parts.fraction))) { |
44 | if ((expdiff < 0 ) || ((expdiff == 0) && (a.parts.fraction < b.parts.fraction))) { |
45 | if (isFloat32NaN(b)) { |
45 | if (isFloat32NaN(b)) { |
46 | /* TODO: fix SigNaN */ |
46 | /* TODO: fix SigNaN */ |
47 | if (isFloat32SigNaN(b)) { |
47 | if (isFloat32SigNaN(b)) { |
48 | }; |
48 | }; |
49 | return b; |
49 | return b; |
50 | }; |
50 | }; |
51 | 51 | ||
52 | if (b.parts.exp == FLOAT32_MAX_EXPONENT) { |
52 | if (b.parts.exp == FLOAT32_MAX_EXPONENT) { |
53 | b.parts.sign = !b.parts.sign; /* num -(+-inf) = -+inf */ |
53 | b.parts.sign = !b.parts.sign; /* num -(+-inf) = -+inf */ |
54 | return b; |
54 | return b; |
55 | } |
55 | } |
56 | 56 | ||
57 | result.parts.sign = !a.parts.sign; |
57 | result.parts.sign = !a.parts.sign; |
58 | 58 | ||
59 | frac1 = b.parts.fraction; |
59 | frac1 = b.parts.fraction; |
60 | exp1 = b.parts.exp; |
60 | exp1 = b.parts.exp; |
61 | frac2 = a.parts.fraction; |
61 | frac2 = a.parts.fraction; |
62 | exp2 = a.parts.exp; |
62 | exp2 = a.parts.exp; |
63 | expdiff *= -1; |
63 | expdiff *= -1; |
64 | } else { |
64 | } else { |
65 | if (isFloat32NaN(a)) { |
65 | if (isFloat32NaN(a)) { |
66 | /* TODO: fix SigNaN */ |
66 | /* TODO: fix SigNaN */ |
67 | if (isFloat32SigNaN(a) || isFloat32SigNaN(b)) { |
67 | if (isFloat32SigNaN(a) || isFloat32SigNaN(b)) { |
68 | }; |
68 | }; |
69 | return a; |
69 | return a; |
70 | }; |
70 | }; |
71 | 71 | ||
72 | if (a.parts.exp == FLOAT32_MAX_EXPONENT) { |
72 | if (a.parts.exp == FLOAT32_MAX_EXPONENT) { |
73 | if (b.parts.exp == FLOAT32_MAX_EXPONENT) { |
73 | if (b.parts.exp == FLOAT32_MAX_EXPONENT) { |
74 | /* inf - inf => nan */ |
74 | /* inf - inf => nan */ |
75 | /* TODO: fix exception */ |
75 | /* TODO: fix exception */ |
76 | result.binary = FLOAT32_NAN; |
76 | result.binary = FLOAT32_NAN; |
77 | return result; |
77 | return result; |
78 | }; |
78 | }; |
79 | return a; |
79 | return a; |
80 | } |
80 | } |
81 | 81 | ||
82 | result.parts.sign = a.parts.sign; |
82 | result.parts.sign = a.parts.sign; |
83 | 83 | ||
84 | frac1 = a.parts.fraction; |
84 | frac1 = a.parts.fraction; |
85 | exp1 = a.parts.exp; |
85 | exp1 = a.parts.exp; |
86 | frac2 = b.parts.fraction; |
86 | frac2 = b.parts.fraction; |
87 | exp2 = b.parts.exp; |
87 | exp2 = b.parts.exp; |
88 | }; |
88 | }; |
89 | 89 | ||
90 | if (exp1 == 0) { |
90 | if (exp1 == 0) { |
91 | /* both are denormalized */ |
91 | /* both are denormalized */ |
92 | result.parts.fraction = frac1-frac2; |
92 | result.parts.fraction = frac1-frac2; |
93 | if (result.parts.fraction > frac1) { |
93 | if (result.parts.fraction > frac1) { |
94 | /* TODO: underflow exception */ |
94 | /* TODO: underflow exception */ |
95 | return result; |
95 | return result; |
96 | }; |
96 | }; |
97 | result.parts.exp = 0; |
97 | result.parts.exp = 0; |
98 | return result; |
98 | return result; |
99 | }; |
99 | }; |
100 | 100 | ||
101 | /* add hidden bit */ |
101 | /* add hidden bit */ |
102 | frac1 |= FLOAT32_HIDDEN_BIT_MASK; |
102 | frac1 |= FLOAT32_HIDDEN_BIT_MASK; |
103 | 103 | ||
104 | if (exp2 == 0) { |
104 | if (exp2 == 0) { |
105 | /* denormalized */ |
105 | /* denormalized */ |
106 | --expdiff; |
106 | --expdiff; |
107 | } else { |
107 | } else { |
108 | /* normalized */ |
108 | /* normalized */ |
109 | frac2 |= FLOAT32_HIDDEN_BIT_MASK; |
109 | frac2 |= FLOAT32_HIDDEN_BIT_MASK; |
110 | }; |
110 | }; |
111 | 111 | ||
112 | /* create some space for rounding */ |
112 | /* create some space for rounding */ |
113 | frac1 <<= 6; |
113 | frac1 <<= 6; |
114 | frac2 <<= 6; |
114 | frac2 <<= 6; |
115 | 115 | ||
116 | if (expdiff > FLOAT32_FRACTION_SIZE + 1) { |
116 | if (expdiff > FLOAT32_FRACTION_SIZE + 1) { |
117 | goto done; |
117 | goto done; |
118 | }; |
118 | }; |
119 | 119 | ||
120 | frac1 = frac1 - (frac2 >> expdiff); |
120 | frac1 = frac1 - (frac2 >> expdiff); |
121 | done: |
121 | done: |
122 | /* TODO: find first nonzero digit and shift result and detect possibly underflow */ |
122 | /* TODO: find first nonzero digit and shift result and detect possibly underflow */ |
123 | while ((exp1 > 0) && (!(frac1 & (FLOAT32_HIDDEN_BIT_MASK << 6 )))) { |
123 | while ((exp1 > 0) && (!(frac1 & (FLOAT32_HIDDEN_BIT_MASK << 6 )))) { |
124 | --exp1; |
124 | --exp1; |
125 | frac1 <<= 1; |
125 | frac1 <<= 1; |
126 | /* TODO: fix underflow - frac1 == 0 does not necessary means underflow... */ |
126 | /* TODO: fix underflow - frac1 == 0 does not necessary means underflow... */ |
127 | }; |
127 | }; |
128 | 128 | ||
129 | /* rounding - if first bit after fraction is set then round up */ |
129 | /* rounding - if first bit after fraction is set then round up */ |
130 | frac1 += 0x20; |
130 | frac1 += 0x20; |
131 | 131 | ||
132 | if (frac1 & (FLOAT32_HIDDEN_BIT_MASK << 7)) { |
132 | if (frac1 & (FLOAT32_HIDDEN_BIT_MASK << 7)) { |
133 | ++exp1; |
133 | ++exp1; |
134 | frac1 >>= 1; |
134 | frac1 >>= 1; |
135 | }; |
135 | }; |
136 | 136 | ||
137 | /*Clear hidden bit and shift */ |
137 | /*Clear hidden bit and shift */ |
138 | result.parts.fraction = ((frac1 >> 6) & (~FLOAT32_HIDDEN_BIT_MASK)); |
138 | result.parts.fraction = ((frac1 >> 6) & (~FLOAT32_HIDDEN_BIT_MASK)); |
139 | result.parts.exp = exp1; |
139 | result.parts.exp = exp1; |
140 | 140 | ||
141 | return result; |
141 | return result; |
142 | } |
142 | } |
143 | 143 | ||
144 | /** Subtract two float64 numbers with same signs |
144 | /** Subtract two float64 numbers with same signs |
145 | */ |
145 | */ |
146 | float64 subFloat64(float64 a, float64 b) |
146 | float64 subFloat64(float64 a, float64 b) |
147 | { |
147 | { |
148 | int expdiff; |
148 | int expdiff; |
149 | __u32 exp1, exp2; |
149 | uint32_t exp1, exp2; |
150 | __u64 frac1, frac2; |
150 | uint64_t frac1, frac2; |
151 | float64 result; |
151 | float64 result; |
152 | 152 | ||
153 | result.d = 0; |
153 | result.d = 0; |
154 | 154 | ||
155 | expdiff = a.parts.exp - b.parts.exp; |
155 | expdiff = a.parts.exp - b.parts.exp; |
156 | if ((expdiff < 0 ) || ((expdiff == 0) && (a.parts.fraction < b.parts.fraction))) { |
156 | if ((expdiff < 0 ) || ((expdiff == 0) && (a.parts.fraction < b.parts.fraction))) { |
157 | if (isFloat64NaN(b)) { |
157 | if (isFloat64NaN(b)) { |
158 | /* TODO: fix SigNaN */ |
158 | /* TODO: fix SigNaN */ |
159 | if (isFloat64SigNaN(b)) { |
159 | if (isFloat64SigNaN(b)) { |
160 | }; |
160 | }; |
161 | return b; |
161 | return b; |
162 | }; |
162 | }; |
163 | 163 | ||
164 | if (b.parts.exp == FLOAT64_MAX_EXPONENT) { |
164 | if (b.parts.exp == FLOAT64_MAX_EXPONENT) { |
165 | b.parts.sign = !b.parts.sign; /* num -(+-inf) = -+inf */ |
165 | b.parts.sign = !b.parts.sign; /* num -(+-inf) = -+inf */ |
166 | return b; |
166 | return b; |
167 | } |
167 | } |
168 | 168 | ||
169 | result.parts.sign = !a.parts.sign; |
169 | result.parts.sign = !a.parts.sign; |
170 | 170 | ||
171 | frac1 = b.parts.fraction; |
171 | frac1 = b.parts.fraction; |
172 | exp1 = b.parts.exp; |
172 | exp1 = b.parts.exp; |
173 | frac2 = a.parts.fraction; |
173 | frac2 = a.parts.fraction; |
174 | exp2 = a.parts.exp; |
174 | exp2 = a.parts.exp; |
175 | expdiff *= -1; |
175 | expdiff *= -1; |
176 | } else { |
176 | } else { |
177 | if (isFloat64NaN(a)) { |
177 | if (isFloat64NaN(a)) { |
178 | /* TODO: fix SigNaN */ |
178 | /* TODO: fix SigNaN */ |
179 | if (isFloat64SigNaN(a) || isFloat64SigNaN(b)) { |
179 | if (isFloat64SigNaN(a) || isFloat64SigNaN(b)) { |
180 | }; |
180 | }; |
181 | return a; |
181 | return a; |
182 | }; |
182 | }; |
183 | 183 | ||
184 | if (a.parts.exp == FLOAT64_MAX_EXPONENT) { |
184 | if (a.parts.exp == FLOAT64_MAX_EXPONENT) { |
185 | if (b.parts.exp == FLOAT64_MAX_EXPONENT) { |
185 | if (b.parts.exp == FLOAT64_MAX_EXPONENT) { |
186 | /* inf - inf => nan */ |
186 | /* inf - inf => nan */ |
187 | /* TODO: fix exception */ |
187 | /* TODO: fix exception */ |
188 | result.binary = FLOAT64_NAN; |
188 | result.binary = FLOAT64_NAN; |
189 | return result; |
189 | return result; |
190 | }; |
190 | }; |
191 | return a; |
191 | return a; |
192 | } |
192 | } |
193 | 193 | ||
194 | result.parts.sign = a.parts.sign; |
194 | result.parts.sign = a.parts.sign; |
195 | 195 | ||
196 | frac1 = a.parts.fraction; |
196 | frac1 = a.parts.fraction; |
197 | exp1 = a.parts.exp; |
197 | exp1 = a.parts.exp; |
198 | frac2 = b.parts.fraction; |
198 | frac2 = b.parts.fraction; |
199 | exp2 = b.parts.exp; |
199 | exp2 = b.parts.exp; |
200 | }; |
200 | }; |
201 | 201 | ||
202 | if (exp1 == 0) { |
202 | if (exp1 == 0) { |
203 | /* both are denormalized */ |
203 | /* both are denormalized */ |
204 | result.parts.fraction = frac1 - frac2; |
204 | result.parts.fraction = frac1 - frac2; |
205 | if (result.parts.fraction > frac1) { |
205 | if (result.parts.fraction > frac1) { |
206 | /* TODO: underflow exception */ |
206 | /* TODO: underflow exception */ |
207 | return result; |
207 | return result; |
208 | }; |
208 | }; |
209 | result.parts.exp = 0; |
209 | result.parts.exp = 0; |
210 | return result; |
210 | return result; |
211 | }; |
211 | }; |
212 | 212 | ||
213 | /* add hidden bit */ |
213 | /* add hidden bit */ |
214 | frac1 |= FLOAT64_HIDDEN_BIT_MASK; |
214 | frac1 |= FLOAT64_HIDDEN_BIT_MASK; |
215 | 215 | ||
216 | if (exp2 == 0) { |
216 | if (exp2 == 0) { |
217 | /* denormalized */ |
217 | /* denormalized */ |
218 | --expdiff; |
218 | --expdiff; |
219 | } else { |
219 | } else { |
220 | /* normalized */ |
220 | /* normalized */ |
221 | frac2 |= FLOAT64_HIDDEN_BIT_MASK; |
221 | frac2 |= FLOAT64_HIDDEN_BIT_MASK; |
222 | }; |
222 | }; |
223 | 223 | ||
224 | /* create some space for rounding */ |
224 | /* create some space for rounding */ |
225 | frac1 <<= 6; |
225 | frac1 <<= 6; |
226 | frac2 <<= 6; |
226 | frac2 <<= 6; |
227 | 227 | ||
228 | if (expdiff > FLOAT64_FRACTION_SIZE + 1) { |
228 | if (expdiff > FLOAT64_FRACTION_SIZE + 1) { |
229 | goto done; |
229 | goto done; |
230 | }; |
230 | }; |
231 | 231 | ||
232 | frac1 = frac1 - (frac2 >> expdiff); |
232 | frac1 = frac1 - (frac2 >> expdiff); |
233 | done: |
233 | done: |
234 | /* TODO: find first nonzero digit and shift result and detect possibly underflow */ |
234 | /* TODO: find first nonzero digit and shift result and detect possibly underflow */ |
235 | while ((exp1 > 0) && (!(frac1 & (FLOAT64_HIDDEN_BIT_MASK << 6 )))) { |
235 | while ((exp1 > 0) && (!(frac1 & (FLOAT64_HIDDEN_BIT_MASK << 6 )))) { |
236 | --exp1; |
236 | --exp1; |
237 | frac1 <<= 1; |
237 | frac1 <<= 1; |
238 | /* TODO: fix underflow - frac1 == 0 does not necessary means underflow... */ |
238 | /* TODO: fix underflow - frac1 == 0 does not necessary means underflow... */ |
239 | }; |
239 | }; |
240 | 240 | ||
241 | /* rounding - if first bit after fraction is set then round up */ |
241 | /* rounding - if first bit after fraction is set then round up */ |
242 | frac1 += 0x20; |
242 | frac1 += 0x20; |
243 | 243 | ||
244 | if (frac1 & (FLOAT64_HIDDEN_BIT_MASK << 7)) { |
244 | if (frac1 & (FLOAT64_HIDDEN_BIT_MASK << 7)) { |
245 | ++exp1; |
245 | ++exp1; |
246 | frac1 >>= 1; |
246 | frac1 >>= 1; |
247 | }; |
247 | }; |
248 | 248 | ||
249 | /*Clear hidden bit and shift */ |
249 | /*Clear hidden bit and shift */ |
250 | result.parts.fraction = ((frac1 >> 6) & (~FLOAT64_HIDDEN_BIT_MASK)); |
250 | result.parts.fraction = ((frac1 >> 6) & (~FLOAT64_HIDDEN_BIT_MASK)); |
251 | result.parts.exp = exp1; |
251 | result.parts.exp = exp1; |
252 | 252 | ||
253 | return result; |
253 | return result; |
254 | } |
254 | } |
255 | 255 | ||
256 | 256 |