xref: /third_party/ffmpeg/libavutil/softfloat.h (revision cabdff1a) 
1/*
2 * Copyright (c) 2006 Michael Niedermayer <michaelni@gmx.at>
3 *
4 * This file is part of FFmpeg.
5 *
6 * FFmpeg is free software; you can redistribute it and/or
7 * modify it under the terms of the GNU Lesser General Public
8 * License as published by the Free Software Foundation; either
9 * version 2.1 of the License, or (at your option) any later version.
10 *
11 * FFmpeg is distributed in the hope that it will be useful,
12 * but WITHOUT ANY WARRANTY; without even the implied warranty of
13 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
14 * Lesser General Public License for more details.
15 *
16 * You should have received a copy of the GNU Lesser General Public
17 * License along with FFmpeg; if not, write to the Free Software
18 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
19 */
20
21#ifndef AVUTIL_SOFTFLOAT_H
22#define AVUTIL_SOFTFLOAT_H
23
24#include <stdint.h>
25#include "common.h"
26
27#include "avassert.h"
28#include "softfloat_tables.h"
29
30#define MIN_EXP -149
31#define MAX_EXP  126
32#define ONE_BITS 29
33
34typedef struct SoftFloat{
35    int32_t mant;
36    int32_t  exp;
37}SoftFloat;
38
39static const SoftFloat FLOAT_0          = {          0,   MIN_EXP};             ///< 0.0
40static const SoftFloat FLOAT_05         = { 0x20000000,   0};                   ///< 0.5
41static const SoftFloat FLOAT_1          = { 0x20000000,   1};                   ///< 1.0
42static const SoftFloat FLOAT_EPSILON    = { 0x29F16B12, -16};                   ///< A small value
43static const SoftFloat FLOAT_1584893192 = { 0x32B771ED,   1};                   ///< 1.584893192 (10^.2)
44static const SoftFloat FLOAT_100000     = { 0x30D40000,  17};                   ///< 100000
45static const SoftFloat FLOAT_0999999    = { 0x3FFFFBCE,   0};                   ///< 0.999999
46static const SoftFloat FLOAT_MIN        = { 0x20000000,   MIN_EXP};
47
48
49/**
50 * Convert a SoftFloat to a double precision float.
51 */
52static inline av_const double av_sf2double(SoftFloat v) {
53    v.exp -= ONE_BITS +1;
54    return ldexp(v.mant, v.exp);
55}
56
57static av_const SoftFloat av_normalize_sf(SoftFloat a){
58    if(a.mant){
59#if 1
60        while((a.mant + 0x1FFFFFFFU)<0x3FFFFFFFU){
61            a.mant += a.mant;
62            a.exp  -= 1;
63        }
64#else
65        int s=ONE_BITS - av_log2(FFABS(a.mant));
66        a.exp   -= s;
67        a.mant <<= s;
68#endif
69        if(a.exp < MIN_EXP){
70            a.exp = MIN_EXP;
71            a.mant= 0;
72        }
73    }else{
74        a.exp= MIN_EXP;
75    }
76    return a;
77}
78
79static inline av_const SoftFloat av_normalize1_sf(SoftFloat a){
80#if 1
81    if((int32_t)(a.mant + 0x40000000U) <= 0){
82        a.exp++;
83        a.mant>>=1;
84    }
85    av_assert2(a.mant < 0x40000000 && a.mant > -0x40000000);
86    av_assert2(a.exp <= MAX_EXP);
87    return a;
88#elif 1
89    int t= a.mant + 0x40000000 < 0;
90    return (SoftFloat){ a.mant>>t, a.exp+t};
91#else
92    int t= (a.mant + 0x3FFFFFFFU)>>31;
93    return (SoftFloat){a.mant>>t, a.exp+t};
94#endif
95}
96
97/**
98 * @return Will not be more denormalized than a*b. So if either input is
99 *         normalized, then the output will not be worse then the other input.
100 *         If both are normalized, then the output will be normalized.
101 */
102static inline av_const SoftFloat av_mul_sf(SoftFloat a, SoftFloat b){
103    a.exp += b.exp;
104    av_assert2((int32_t)((a.mant * (int64_t)b.mant) >> ONE_BITS) == (a.mant * (int64_t)b.mant) >> ONE_BITS);
105    a.mant = (a.mant * (int64_t)b.mant) >> ONE_BITS;
106    a = av_normalize1_sf((SoftFloat){a.mant, a.exp - 1});
107    if (!a.mant || a.exp < MIN_EXP)
108        return FLOAT_0;
109    return a;
110}
111
112/**
113 * b has to be normalized and not zero.
114 * @return Will not be more denormalized than a.
115 */
116static inline av_const SoftFloat av_div_sf(SoftFloat a, SoftFloat b){
117    int64_t temp = (int64_t)a.mant * (1<<(ONE_BITS+1));
118    temp /= b.mant;
119    a.exp -= b.exp;
120    a.mant = temp;
121    while (a.mant != temp) {
122        temp /= 2;
123        a.exp--;
124        a.mant = temp;
125    }
126    a = av_normalize1_sf(a);
127    if (!a.mant || a.exp < MIN_EXP)
128        return FLOAT_0;
129    return a;
130}
131
132/**
133 * Compares two SoftFloats.
134 * @returns < 0 if the first is less
135 *          > 0 if the first is greater
136 *            0 if they are equal
137 */
138static inline av_const int av_cmp_sf(SoftFloat a, SoftFloat b){
139    int t= a.exp - b.exp;
140    if      (t <-31) return                  -  b.mant      ;
141    else if (t <  0) return (a.mant >> (-t)) -  b.mant      ;
142    else if (t < 32) return  a.mant          - (b.mant >> t);
143    else             return  a.mant                         ;
144}
145
146/**
147 * Compares two SoftFloats.
148 * @returns 1 if a is greater than b, 0 otherwise
149 */
150static inline av_const int av_gt_sf(SoftFloat a, SoftFloat b)
151{
152    int t= a.exp - b.exp;
153    if      (t <-31) return 0                >  b.mant      ;
154    else if (t <  0) return (a.mant >> (-t)) >  b.mant      ;
155    else if (t < 32) return  a.mant          > (b.mant >> t);
156    else             return  a.mant          >  0           ;
157}
158
159/**
160 * @returns the sum of 2 SoftFloats.
161 */
162static inline av_const SoftFloat av_add_sf(SoftFloat a, SoftFloat b){
163    int t= a.exp - b.exp;
164    if      (t <-31) return b;
165    else if (t <  0) return av_normalize_sf(av_normalize1_sf((SoftFloat){ b.mant + (a.mant >> (-t)), b.exp}));
166    else if (t < 32) return av_normalize_sf(av_normalize1_sf((SoftFloat){ a.mant + (b.mant >>   t ), a.exp}));
167    else             return a;
168}
169
170/**
171 * @returns the difference of 2 SoftFloats.
172 */
173static inline av_const SoftFloat av_sub_sf(SoftFloat a, SoftFloat b){
174    return av_add_sf(a, (SoftFloat){ -b.mant, b.exp});
175}
176
177//FIXME log, exp, pow
178
179/**
180 * Converts a mantisse and exponent to a SoftFloat.
181 * This converts a fixed point value v with frac_bits fractional bits to a
182 * SoftFloat.
183 * @returns a SoftFloat with value v * 2^-frac_bits
184 */
185static inline av_const SoftFloat av_int2sf(int v, int frac_bits){
186    int exp_offset = 0;
187    if(v <= INT_MIN + 1){
188        exp_offset = 1;
189        v>>=1;
190    }
191    return av_normalize_sf(av_normalize1_sf((SoftFloat){v, ONE_BITS + 1 - frac_bits + exp_offset}));
192}
193
194/**
195 * Converts a SoftFloat to an integer.
196 * Rounding is to -inf.
197 */
198static inline av_const int av_sf2int(SoftFloat v, int frac_bits){
199    v.exp += frac_bits - (ONE_BITS + 1);
200    if(v.exp >= 0) return v.mant <<  v.exp ;
201    else           return v.mant >>(-v.exp);
202}
203
204/**
205 * Rounding-to-nearest used.
206 */
207static av_always_inline SoftFloat av_sqrt_sf(SoftFloat val)
208{
209    int tabIndex, rem;
210
211    if (val.mant == 0)
212        val.exp = MIN_EXP;
213    else if (val.mant < 0)
214        abort();
215    else
216    {
217        tabIndex = (val.mant - 0x20000000) >> 20;
218
219        rem = val.mant & 0xFFFFF;
220        val.mant  = (int)(((int64_t)av_sqrttbl_sf[tabIndex] * (0x100000 - rem) +
221                           (int64_t)av_sqrttbl_sf[tabIndex + 1] * rem +
222                           0x80000) >> 20);
223        val.mant = (int)(((int64_t)av_sqr_exp_multbl_sf[val.exp & 1] * val.mant +
224                          0x10000000) >> 29);
225
226        if (val.mant < 0x40000000)
227            val.exp -= 2;
228        else
229            val.mant >>= 1;
230
231        val.exp = (val.exp >> 1) + 1;
232    }
233
234    return val;
235}
236
237/**
238 * Rounding-to-nearest used.
239 *
240 * @param a angle in units of (1ULL<<30)/M_PI radians
241 * @param s pointer to where   sine in units of (1<<30) is returned
242 * @param c pointer to where cosine in units of (1<<30) is returned
243 */
244static av_unused void av_sincos_sf(int a, int *s, int *c)
245{
246    int idx, sign;
247    int sv, cv;
248    int st, ct;
249
250    idx = a >> 26;
251    sign = (int32_t)((unsigned)idx << 27) >> 31;
252    cv = av_costbl_1_sf[idx & 0xf];
253    cv = (cv ^ sign) - sign;
254
255    idx -= 8;
256    sign = (int32_t)((unsigned)idx << 27) >> 31;
257    sv = av_costbl_1_sf[idx & 0xf];
258    sv = (sv ^ sign) - sign;
259
260    idx = a >> 21;
261    ct = av_costbl_2_sf[idx & 0x1f];
262    st = av_sintbl_2_sf[idx & 0x1f];
263
264    idx = (int)(((int64_t)cv * ct - (int64_t)sv * st + 0x20000000) >> 30);
265
266    sv = (int)(((int64_t)cv * st + (int64_t)sv * ct + 0x20000000) >> 30);
267
268    cv = idx;
269
270    idx = a >> 16;
271    ct = av_costbl_3_sf[idx & 0x1f];
272    st = av_sintbl_3_sf[idx & 0x1f];
273
274    idx = (int)(((int64_t)cv * ct - (int64_t)sv * st + 0x20000000) >> 30);
275
276    sv = (int)(((int64_t)cv * st + (int64_t)sv * ct + 0x20000000) >> 30);
277    cv = idx;
278
279    idx = a >> 11;
280
281    ct = (int)(((int64_t)av_costbl_4_sf[idx & 0x1f] * (0x800 - (a & 0x7ff)) +
282                (int64_t)av_costbl_4_sf[(idx & 0x1f)+1]*(a & 0x7ff) +
283                0x400) >> 11);
284    st = (int)(((int64_t)av_sintbl_4_sf[idx & 0x1f] * (0x800 - (a & 0x7ff)) +
285                (int64_t)av_sintbl_4_sf[(idx & 0x1f) + 1] * (a & 0x7ff) +
286                0x400) >> 11);
287
288    *c = (int)(((int64_t)cv * ct - (int64_t)sv * st + 0x20000000) >> 30);
289
290    *s = (int)(((int64_t)cv * st + (int64_t)sv * ct + 0x20000000) >> 30);
291}
292
293#endif /* AVUTIL_SOFTFLOAT_H */
294