libavutil/softfloat.h

   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
  34 typedef struct SoftFloat{
  35     int32_t mant;
  36     int32_t  exp;
  37 }SoftFloat;
  38
  39 static const SoftFloat FLOAT_0          = {          0,   MIN_EXP};             ///< 0.0
  40 static const SoftFloat FLOAT_05         = { 0x20000000,   0};                   ///< 0.5
  41 static const SoftFloat FLOAT_1          = { 0x20000000,   1};                   ///< 1.0
  42 static const SoftFloat FLOAT_EPSILON    = { 0x29F16B12, -16};                   ///< A small value
  43 static const SoftFloat FLOAT_1584893192 = { 0x32B771ED,   1};                   ///< 1.584893192 (10^.2)
  44 static const SoftFloat FLOAT_100000     = { 0x30D40000,  17};                   ///< 100000
  45 static const SoftFloat FLOAT_0999999    = { 0x3FFFFBCE,   0};                   ///< 0.999999
  46 static const SoftFloat FLOAT_MIN        = { 0x20000000,   MIN_EXP};
  47
  48
  49 /**
  50  * Convert a SoftFloat to a double precision float.
  51  */
  52 static inline av_const double av_sf2double(SoftFloat v) {
  53     v.exp -= ONE_BITS +1;
  54     return ldexp(v.mant, v.exp);
  55 }
  56
  57 static 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
  79 static 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  */
 102 static 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  */
 116 static 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  */
 138 static 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  */
 150 static 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  */
 162 static 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  */
 173 static 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  */
 185 static 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  */
 198 static 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  */
 207 static 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  */
 244 static 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 */