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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<arithmetic.h>
30
#include<arithmetic.h>
31
#include<comparison.h>
31
#include<comparison.h>
32
 
32
 
33
/** Add two Float32 numbers with same signs
33
/** Add two Float32 numbers with same signs
34
 */
34
 */
35
float32 addFloat32(float32 a, float32 b)
35
float32 addFloat32(float32 a, float32 b)
36
{
36
{
37
    int expdiff;
37
    int expdiff;
38
    __u32 exp1,exp2,mant1,mant2;
38
    __u32 exp1,exp2,mant1,mant2;
39
   
39
   
40
    expdiff=a.parts.exp - b.parts.exp;
40
    expdiff=a.parts.exp - b.parts.exp;
41
    if (expdiff<0) {
41
    if (expdiff<0) {
42
        if (isFloat32NaN(b)) {
42
        if (isFloat32NaN(b)) {
43
            //TODO: fix SigNaN
43
            //TODO: fix SigNaN
44
            if (isFloat32SigNaN(b)) {
44
            if (isFloat32SigNaN(b)) {
45
            };
45
            };
-
 
46
 
46
            return b;
47
            return b;
47
        };
48
        };
48
       
49
       
49
        if (b.parts.exp==0xFF) {
50
        if (b.parts.exp==0xFF) {
50
            return b;
51
            return b;
51
        }
52
        }
52
       
53
       
53
        mant1=b.parts.mantisa;
54
        mant1=b.parts.mantisa;
54
        exp1=b.parts.exp;
55
        exp1=b.parts.exp;
55
        mant2=a.parts.mantisa;
56
        mant2=a.parts.mantisa;
56
        exp2=a.parts.exp;
57
        exp2=a.parts.exp;
57
        expdiff*=-1;
58
        expdiff*=-1;
58
    } else {
59
    } else {
59
        if (isFloat32NaN(a)) {
60
        if (isFloat32NaN(a)) {
60
            //TODO: fix SigNaN
61
            //TODO: fix SigNaN
61
            if ((isFloat32SigNaN(a))||(isFloat32SigNaN(b))) {
62
            if ((isFloat32SigNaN(a))||(isFloat32SigNaN(b))) {
62
            };
63
            };
63
            return a;
64
            return a;
64
        };
65
        };
65
       
66
       
66
        if (a.parts.exp==0xFF) {
67
        if (a.parts.exp==0xFF) {
67
            return a;
68
            return a;
68
        }
69
        }
69
       
70
       
70
        mant1=a.parts.mantisa;
71
        mant1=a.parts.mantisa;
71
        exp1=a.parts.exp;
72
        exp1=a.parts.exp;
72
        mant2=b.parts.mantisa;
73
        mant2=b.parts.mantisa;
73
        exp2=b.parts.exp;
74
        exp2=b.parts.exp;
74
    };
75
    };
75
   
76
   
76
    if (exp1==0) {
77
    if (exp1==0) {
77
        //both are denormalized
78
        //both are denormalized
78
        mant1+=mant2;
79
        mant1+=mant2;
79
        if (mant1&0xF00000) {
80
        if (mant1&0xF00000) {
80
            a.parts.exp=1;
81
            a.parts.exp=1;
81
        };
82
        };
82
        a.parts.mantisa=mant1;
83
        a.parts.mantisa=mant1;
83
        return a;
84
        return a;
84
    };
85
    };
85
   
86
   
86
    // create some space for rounding
87
    // create some space for rounding
87
    mant1<<=6;
88
    mant1<<=6;
88
    mant2<<=6;
89
    mant2<<=6;
89
   
90
   
90
    mant1|=0x20000000; //add hidden bit
91
    mant1|=0x20000000; //add hidden bit
91
   
92
   
92
   
93
   
93
    if (exp2==0) {
94
    if (exp2==0) {
94
        --expdiff; 
95
        --expdiff; 
95
    } else {
96
    } else {
96
        mant2|=0x20000000; //hidden bit
97
        mant2|=0x20000000; //hidden bit
97
    };
98
    };
98
   
99
   
99
    if (expdiff>24) {
100
    if (expdiff>24) {
100
         goto done;
101
         goto done;
101
         };
102
         };
102
   
103
   
103
    mant2>>=expdiff;
104
    mant2>>=expdiff;
104
    mant1+=mant2;
105
    mant1+=mant2;
105
done:
106
done:
106
    if (mant1&0x40000000) {
107
    if (mant1&0x40000000) {
107
        ++exp1;
108
        ++exp1;
108
        mant1>>=1;
109
        mant1>>=1;
109
    };
110
    };
110
   
111
   
111
    //rounding - if first bit after mantisa is set then round up
112
    //rounding - if first bit after mantisa is set then round up
112
    mant1+=0x20;
113
    mant1+=0x20;
113
   
114
   
114
    if (mant1&0x40000000) {
115
    if (mant1&0x40000000) {
115
        ++exp1;
116
        ++exp1;
116
        mant1>>=1;
117
        mant1>>=1;
117
    };
118
    };
118
   
119
   
119
    a.parts.exp=exp1;
120
    a.parts.exp=exp1;
120
    a.parts.mantisa = ((mant1&(~0x20000000))>>6); /*Clear hidden bit and shift */
121
    a.parts.mantisa = ((mant1&(~0x20000000))>>6); /*Clear hidden bit and shift */
121
    return a;
122
    return a;
122
};
123
};
123
 
124
 
124
/** Subtract two float32 numbers with same signs
125
/** Subtract two float32 numbers with same signs
125
 */
126
 */
126
float32 subFloat32(float32 a, float32 b)
127
float32 subFloat32(float32 a, float32 b)
127
{
128
{
128
    int expdiff;
129
    int expdiff;
129
    __u32 exp1,exp2,mant1,mant2;
130
    __u32 exp1,exp2,mant1,mant2;
130
    float32 result;
131
    float32 result;
131
 
132
 
132
    result.f = 0;
133
    result.f = 0;
133
   
134
   
134
    expdiff=a.parts.exp - b.parts.exp;
135
    expdiff=a.parts.exp - b.parts.exp;
135
    if ((expdiff<0)||((expdiff==0)&&(a.parts.mantisa<b.parts.mantisa))) {
136
    if ((expdiff<0)||((expdiff==0)&&(a.parts.mantisa<b.parts.mantisa))) {
136
        if (isFloat32NaN(b)) {
137
        if (isFloat32NaN(b)) {
137
            //TODO: fix SigNaN
138
            //TODO: fix SigNaN
138
            if (isFloat32SigNaN(b)) {
139
            if (isFloat32SigNaN(b)) {
139
            };
140
            };
140
            return b;
141
            return b;
141
        };
142
        };
142
       
143
       
143
        if (b.parts.exp==0xFF) {
144
        if (b.parts.exp==0xFF) {
144
            b.parts.sign=!b.parts.sign; /* num -(+-inf) = -+inf */
145
            b.parts.sign=!b.parts.sign; /* num -(+-inf) = -+inf */
145
            return b;
146
            return b;
146
        }
147
        }
147
       
148
       
148
        result.parts.sign = !a.parts.sign;
149
        result.parts.sign = !a.parts.sign;
149
       
150
       
150
        mant1=b.parts.mantisa;
151
        mant1=b.parts.mantisa;
151
        exp1=b.parts.exp;
152
        exp1=b.parts.exp;
152
        mant2=a.parts.mantisa;
153
        mant2=a.parts.mantisa;
153
        exp2=a.parts.exp;
154
        exp2=a.parts.exp;
154
        expdiff*=-1;
155
        expdiff*=-1;
155
    } else {
156
    } else {
156
        if (isFloat32NaN(a)) {
157
        if (isFloat32NaN(a)) {
157
            //TODO: fix SigNaN
158
            //TODO: fix SigNaN
158
            if ((isFloat32SigNaN(a))||(isFloat32SigNaN(b))) {
159
            if ((isFloat32SigNaN(a))||(isFloat32SigNaN(b))) {
159
            };
160
            };
160
            return a;
161
            return a;
161
        };
162
        };
162
       
163
       
163
        if (a.parts.exp==0xFF) {
164
        if (a.parts.exp==0xFF) {
164
            if (b.parts.exp==0xFF) {
165
            if (b.parts.exp==0xFF) {
165
                /* inf - inf => nan */
166
                /* inf - inf => nan */
166
                //TODO: fix exception
167
                //TODO: fix exception
167
                result.binary = FLOAT32_NAN;
168
                result.binary = FLOAT32_NAN;
168
                return result;
169
                return result;
169
            };
170
            };
170
            return a;
171
            return a;
171
        }
172
        }
172
       
173
       
173
        result.parts.sign = a.parts.sign;
174
        result.parts.sign = a.parts.sign;
174
       
175
       
175
        mant1=a.parts.mantisa;
176
        mant1=a.parts.mantisa;
176
        exp1=a.parts.exp;
177
        exp1=a.parts.exp;
177
        mant2=b.parts.mantisa;
178
        mant2=b.parts.mantisa;
178
        exp2=b.parts.exp;
179
        exp2=b.parts.exp;
179
       
180
       
180
 
181
 
181
       
182
       
182
    };
183
    };
183
   
184
   
184
    if (exp1==0) {
185
    if (exp1==0) {
185
        //both are denormalized
186
        //both are denormalized
186
        result.parts.mantisa=mant1-mant2;
187
        result.parts.mantisa=mant1-mant2;
187
        if (result.parts.mantisa>mant1) {
188
        if (result.parts.mantisa>mant1) {
188
            //TODO: underflow exception
189
            //TODO: underflow exception
189
            return result;
190
            return result;
190
        };
191
        };
191
        result.parts.exp=0;
192
        result.parts.exp=0;
192
        return result;
193
        return result;
193
    };
194
    };
194
   
195
   
195
    // create some space for rounding
196
    // create some space for rounding
196
    mant1<<=6;
197
    mant1<<=6;
197
    mant2<<=6;
198
    mant2<<=6;
198
   
199
   
199
    mant1|=0x20000000; //add hidden bit
200
    mant1|=0x20000000; //add hidden bit
200
   
201
   
201
   
202
   
202
    if (exp2==0) {
203
    if (exp2==0) {
203
        --expdiff; 
204
        --expdiff; 
204
    } else {
205
    } else {
205
        mant2|=0x20000000; //hidden bit
206
        mant2|=0x20000000; //hidden bit
206
    };
207
    };
207
   
208
   
208
    if (expdiff>24) {
209
    if (expdiff>24) {
209
         goto done;
210
         goto done;
210
         };
211
         };
211
   
212
   
212
    mant1 = mant1-(mant2>>expdiff);
213
    mant1 = mant1-(mant2>>expdiff);
213
done:
214
done:
214
   
215
   
215
    //TODO: find first nonzero digit and shift result and detect possibly underflow
216
    //TODO: find first nonzero digit and shift result and detect possibly underflow
216
    while ((exp1>0)&&(!(mant1&0x20000000))) {
217
    while ((exp1>0)&&(!(mant1&0x20000000))) {
217
        exp1--;
218
        exp1--;
218
        mant1 <<= 1;
219
        mant1 <<= 1;
219
        if(mant1 == 0) {
220
        if(mant1 == 0) {
220
            /* Realy is it an underflow? ... */
221
            /* Realy is it an underflow? ... */
221
            //TODO: fix underflow
222
            /* TODO: fix underflow */
222
        };
223
        };
223
    };
224
    };
224
   
225
   
225
    //rounding - if first bit after mantisa is set then round up    
226
    //rounding - if first bit after mantisa is set then round up    
226
    mant1 += 0x20;
227
    mant1 += 0x20;
227
 
228
 
228
    if (mant1&0x40000000) {
229
    if (mant1&0x40000000) {
229
        ++exp1;
230
        ++exp1;
230
        mant1>>=1;
231
        mant1>>=1;
231
    };
232
    };
232
   
233
   
233
    result.parts.mantisa = ((mant1&(~0x20000000))>>6); /*Clear hidden bit and shift */
234
    result.parts.mantisa = ((mant1&(~0x20000000))>>6); /*Clear hidden bit and shift */
234
    result.parts.exp = exp1;
235
    result.parts.exp = exp1;
235
   
236
   
236
    return result;
237
    return result;
237
};
238
};
238
 
239
 
-
 
240
/** Multiply two 32 bit float numbers
-
 
241
 *
-
 
242
 */
-
 
243
float32 mulFloat32(float32 a, float32 b)
-
 
244
{
-
 
245
    float32 result;
-
 
246
    __u64 mant1, mant2;
-
 
247
    __s32 exp;
-
 
248
 
-
 
249
    result.parts.sign = a.parts.sign ^ b.parts.sign;
-
 
250
   
-
 
251
    if ((isFloat32NaN(a))||(isFloat32NaN(b))) {
-
 
252
        /* TODO: fix SigNaNs */
-
 
253
        if (isFloat32SigNaN(a)) {
-
 
254
            result.parts.mantisa = a.parts.mantisa;
-
 
255
            result.parts.exp = a.parts.exp;
-
 
256
            return result;
-
 
257
        };
-
 
258
        if (isFloat32SigNaN(b)) { /* TODO: fix SigNaN */
-
 
259
            result.parts.mantisa = b.parts.mantisa;
-
 
260
            result.parts.exp = b.parts.exp;
-
 
261
            return result;
-
 
262
        };
-
 
263
        /* set NaN as result */
-
 
264
        result.parts.mantisa = 0x1;
-
 
265
        result.parts.exp = 0xFF;
-
 
266
        return result;
-
 
267
    };
-
 
268
       
-
 
269
    if (isFloat32Infinity(a)) {
-
 
270
        if (isFloat32Zero(b)) {
-
 
271
            /* FIXME: zero * infinity */
-
 
272
            result.parts.mantisa = 0x1;
-
 
273
            result.parts.exp = 0xFF;
-
 
274
            return result;
-
 
275
        }
-
 
276
        result.parts.mantisa = a.parts.mantisa;
-
 
277
        result.parts.exp = a.parts.exp;
-
 
278
        return result;
-
 
279
    }
-
 
280
 
-
 
281
    if (isFloat32Infinity(b)) {
-
 
282
        if (isFloat32Zero(a)) {
-
 
283
            /* FIXME: zero * infinity */
-
 
284
            result.parts.mantisa = 0x1;
-
 
285
            result.parts.exp = 0xFF;
-
 
286
            return result;
-
 
287
        }
-
 
288
        result.parts.mantisa = b.parts.mantisa;
-
 
289
        result.parts.exp = b.parts.exp;
-
 
290
        return result;
-
 
291
    }
-
 
292
 
-
 
293
    /* exp is signed so we can easy detect underflow */
-
 
294
    exp = a.parts.exp + b.parts.exp;
-
 
295
    exp -= FLOAT32_BIAS;
-
 
296
   
-
 
297
    if (exp >= 0xFF ) {
-
 
298
        /* FIXME: overflow */
-
 
299
        /* set infinity as result */
-
 
300
        result.parts.mantisa = 0x0;
-
 
301
        result.parts.exp = 0xFF;
-
 
302
        return result;
-
 
303
    };
-
 
304
   
-
 
305
    if (exp < 0) {
-
 
306
        /* FIXME: underflow */
-
 
307
        /* return signed zero */
-
 
308
        result.parts.mantisa = 0x0;
-
 
309
        result.parts.exp = 0x0;
-
 
310
        return result;
-
 
311
    };
-
 
312
   
-
 
313
    mant1 = a.parts.mantisa;
-
 
314
    if (a.parts.exp>0) {
-
 
315
        mant1 |= 0x800000;
-
 
316
    } else {
-
 
317
        ++exp;
-
 
318
    };
-
 
319
   
-
 
320
    mant2 = b.parts.mantisa;
-
 
321
    if (b.parts.exp>0) {
-
 
322
        mant2 |= 0x800000;
-
 
323
    } else {
-
 
324
        ++exp;
-
 
325
    };
-
 
326
 
-
 
327
    mant1 <<= 1; /* one bit space for rounding */
-
 
328
 
-
 
329
    mant1 = mant1 * mant2;
-
 
330
/* round and return */
-
 
331
   
-
 
332
    while ((exp < 0xFF )&&(mant1 > 0x1FFFFFF )) { /* 0xFFFFFF is 23 bits of mantisa + one more for hidden bit (all shifted 1 bit left)*/
-
 
333
        ++exp;
-
 
334
        mant1 >>= 1;
-
 
335
    };
-
 
336
 
-
 
337
    /* rounding */
-
 
338
    //++mant1; /* FIXME: not works - without it is ok */
-
 
339
    mant1 >>= 1; /* shift off rounding space */
-
 
340
   
-
 
341
    if ((exp < 0xFF )&&(mant1 > 0xFFFFFF )) {
-
 
342
        ++exp;
-
 
343
        mant1 >>= 1;
-
 
344
    };
-
 
345
 
-
 
346
    if (exp >= 0xFF ) {
-
 
347
        /* TODO: fix overflow */
-
 
348
        /* return infinity*/
-
 
349
        result.parts.exp = 0xFF;
-
 
350
        result.parts.mantisa = 0x0;
-
 
351
        return result;
-
 
352
    }
-
 
353
   
-
 
354
    exp -= FLOAT32_MANTISA_SIZE;
-
 
355
 
-
 
356
    if (exp <= FLOAT32_MANTISA_SIZE) {
-
 
357
        /* denormalized number */
-
 
358
        mant1 >>= 1; /* denormalize */
-
 
359
        while ((mant1 > 0) && (exp < 0)) {
-
 
360
            mant1 >>= 1;
-
 
361
            ++exp;
-
 
362
        };
-
 
363
        if (mant1 == 0) {
-
 
364
            /* FIXME : underflow */
-
 
365
        result.parts.exp = 0;
-
 
366
        result.parts.mantisa = 0;
-
 
367
        return result;
-
 
368
        };
-
 
369
    };
-
 
370
    result.parts.exp = exp;
-
 
371
    result.parts.mantisa = mant1 & 0x7FFFFF;
-
 
372
   
-
 
373
    return result; 
-
 
374
   
-
 
375
};
-
 
376
 
-
 
377
 
239
 
378