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  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 -126
  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};
  40. static const SoftFloat FLOAT_05         = { 0x20000000,   0};
  41. static const SoftFloat FLOAT_1          = { 0x20000000,   1};
  42. static const SoftFloat FLOAT_EPSILON    = { 0x29F16B12, -16};
  43. static const SoftFloat FLOAT_1584893192 = { 0x32B771ED,   1};
  44. static const SoftFloat FLOAT_100000     = { 0x30D40000,  17};
  45. static const SoftFloat FLOAT_0999999    = { 0x3FFFFBCE,   0};
  46.  
  47. static inline av_const double av_sf2double(SoftFloat v) {
  48.     v.exp -= ONE_BITS +1;
  49.     if(v.exp > 0) return (double)v.mant * (double)(1 << v.exp);
  50.     else          return (double)v.mant / (double)(1 << (-v.exp));
  51. }
  52.  
  53. static av_const SoftFloat av_normalize_sf(SoftFloat a){
  54.     if(a.mant){
  55. #if 1
  56.         while((a.mant + 0x1FFFFFFFU)<0x3FFFFFFFU){
  57.             a.mant += a.mant;
  58.             a.exp  -= 1;
  59.         }
  60. #else
  61.         int s=ONE_BITS - av_log2(FFABS(a.mant));
  62.         a.exp   -= s;
  63.         a.mant <<= s;
  64. #endif
  65.         if(a.exp < MIN_EXP){
  66.             a.exp = MIN_EXP;
  67.             a.mant= 0;
  68.         }
  69.     }else{
  70.         a.exp= MIN_EXP;
  71.     }
  72.     return a;
  73. }
  74.  
  75. static inline av_const SoftFloat av_normalize1_sf(SoftFloat a){
  76. #if 1
  77.     if((int32_t)(a.mant + 0x40000000U) <= 0){
  78.         a.exp++;
  79.         a.mant>>=1;
  80.     }
  81.     av_assert2(a.mant < 0x40000000 && a.mant > -0x40000000);
  82.     return a;
  83. #elif 1
  84.     int t= a.mant + 0x40000000 < 0;
  85.     return (SoftFloat){ a.mant>>t, a.exp+t};
  86. #else
  87.     int t= (a.mant + 0x3FFFFFFFU)>>31;
  88.     return (SoftFloat){a.mant>>t, a.exp+t};
  89. #endif
  90. }
  91.  
  92. /**
  93.  * @return Will not be more denormalized than a*b. So if either input is
  94.  *         normalized, then the output will not be worse then the other input.
  95.  *         If both are normalized, then the output will be normalized.
  96.  */
  97. static inline av_const SoftFloat av_mul_sf(SoftFloat a, SoftFloat b){
  98.     a.exp += b.exp;
  99.     av_assert2((int32_t)((a.mant * (int64_t)b.mant) >> ONE_BITS) == (a.mant * (int64_t)b.mant) >> ONE_BITS);
  100.     a.mant = (a.mant * (int64_t)b.mant) >> ONE_BITS;
  101.     a = av_normalize1_sf((SoftFloat){a.mant, a.exp - 1});
  102.     if (!a.mant || a.exp < MIN_EXP)
  103.         return FLOAT_0;
  104.     return a;
  105. }
  106.  
  107. /**
  108.  * b has to be normalized and not zero.
  109.  * @return Will not be more denormalized than a.
  110.  */
  111. static inline av_const SoftFloat av_div_sf(SoftFloat a, SoftFloat b){
  112.     a.exp -= b.exp;
  113.     a.mant = ((int64_t)a.mant<<(ONE_BITS+1)) / b.mant;
  114.     a = av_normalize1_sf(a);
  115.     if (!a.mant || a.exp < MIN_EXP)
  116.         return FLOAT_0;
  117.     return a;
  118. }
  119.  
  120. static inline av_const int av_cmp_sf(SoftFloat a, SoftFloat b){
  121.     int t= a.exp - b.exp;
  122.     if      (t <-31) return                  -  b.mant      ;
  123.     else if (t <  0) return (a.mant >> (-t)) -  b.mant      ;
  124.     else if (t < 32) return  a.mant          - (b.mant >> t);
  125.     else             return  a.mant                         ;
  126. }
  127.  
  128. static inline av_const int av_gt_sf(SoftFloat a, SoftFloat b)
  129. {
  130.     int t= a.exp - b.exp;
  131.     if      (t <-31) return 0                >  b.mant      ;
  132.     else if (t <  0) return (a.mant >> (-t)) >  b.mant      ;
  133.     else if (t < 32) return  a.mant          > (b.mant >> t);
  134.     else             return  a.mant          >  0           ;
  135. }
  136.  
  137. static inline av_const SoftFloat av_add_sf(SoftFloat a, SoftFloat b){
  138.     int t= a.exp - b.exp;
  139.     if      (t <-31) return b;
  140.     else if (t <  0) return av_normalize_sf(av_normalize1_sf((SoftFloat){ b.mant + (a.mant >> (-t)), b.exp}));
  141.     else if (t < 32) return av_normalize_sf(av_normalize1_sf((SoftFloat){ a.mant + (b.mant >>   t ), a.exp}));
  142.     else             return a;
  143. }
  144.  
  145. static inline av_const SoftFloat av_sub_sf(SoftFloat a, SoftFloat b){
  146.     return av_add_sf(a, (SoftFloat){ -b.mant, b.exp});
  147. }
  148.  
  149. //FIXME log, exp, pow
  150.  
  151. /**
  152.  * Converts a mantisse and exponent to a SoftFloat
  153.  * @returns a SoftFloat with value v * 2^frac_bits
  154.  */
  155. static inline av_const SoftFloat av_int2sf(int v, int frac_bits){
  156.     int exp_offset = 0;
  157.     if(v == INT_MIN){
  158.         exp_offset = 1;
  159.         v>>=1;
  160.     }
  161.     return av_normalize_sf(av_normalize1_sf((SoftFloat){v, ONE_BITS + 1 - frac_bits + exp_offset}));
  162. }
  163.  
  164. /**
  165.  * Rounding is to -inf.
  166.  */
  167. static inline av_const int av_sf2int(SoftFloat v, int frac_bits){
  168.     v.exp += frac_bits - (ONE_BITS + 1);
  169.     if(v.exp >= 0) return v.mant <<  v.exp ;
  170.     else           return v.mant >>(-v.exp);
  171. }
  172.  
  173. /**
  174.  * Rounding-to-nearest used.
  175.  */
  176. static av_always_inline SoftFloat av_sqrt_sf(SoftFloat val)
  177. {
  178.     int tabIndex, rem;
  179.  
  180.     if (val.mant == 0)
  181.         val.exp = MIN_EXP;
  182.     else if (val.mant < 0)
  183.         abort();
  184.     else
  185.     {
  186.         tabIndex = (val.mant - 0x20000000) >> 20;
  187.  
  188.         rem = val.mant & 0xFFFFF;
  189.         val.mant  = (int)(((int64_t)av_sqrttbl_sf[tabIndex] * (0x100000 - rem) +
  190.                            (int64_t)av_sqrttbl_sf[tabIndex + 1] * rem +
  191.                            0x80000) >> 20);
  192.         val.mant = (int)(((int64_t)av_sqr_exp_multbl_sf[val.exp & 1] * val.mant +
  193.                           0x10000000) >> 29);
  194.  
  195.         if (val.mant < 0x40000000)
  196.             val.exp -= 2;
  197.         else
  198.             val.mant >>= 1;
  199.  
  200.         val.exp = (val.exp >> 1) + 1;
  201.     }
  202.  
  203.     return val;
  204. }
  205.  
  206. /**
  207.  * Rounding-to-nearest used.
  208.  */
  209. static av_unused void av_sincos_sf(int a, int *s, int *c)
  210. {
  211.     int idx, sign;
  212.     int sv, cv;
  213.     int st, ct;
  214.  
  215.     idx = a >> 26;
  216.     sign = (idx << 27) >> 31;
  217.     cv = av_costbl_1_sf[idx & 0xf];
  218.     cv = (cv ^ sign) - sign;
  219.  
  220.     idx -= 8;
  221.     sign = (idx << 27) >> 31;
  222.     sv = av_costbl_1_sf[idx & 0xf];
  223.     sv = (sv ^ sign) - sign;
  224.  
  225.     idx = a >> 21;
  226.     ct = av_costbl_2_sf[idx & 0x1f];
  227.     st = av_sintbl_2_sf[idx & 0x1f];
  228.  
  229.     idx = (int)(((int64_t)cv * ct - (int64_t)sv * st + 0x20000000) >> 30);
  230.  
  231.     sv = (int)(((int64_t)cv * st + (int64_t)sv * ct + 0x20000000) >> 30);
  232.  
  233.     cv = idx;
  234.  
  235.     idx = a >> 16;
  236.     ct = av_costbl_3_sf[idx & 0x1f];
  237.     st = av_sintbl_3_sf[idx & 0x1f];
  238.  
  239.     idx = (int)(((int64_t)cv * ct - (int64_t)sv * st + 0x20000000) >> 30);
  240.  
  241.     sv = (int)(((int64_t)cv * st + (int64_t)sv * ct + 0x20000000) >> 30);
  242.     cv = idx;
  243.  
  244.     idx = a >> 11;
  245.  
  246.     ct = (int)(((int64_t)av_costbl_4_sf[idx & 0x1f] * (0x800 - (a & 0x7ff)) +
  247.                 (int64_t)av_costbl_4_sf[(idx & 0x1f)+1]*(a & 0x7ff) +
  248.                 0x400) >> 11);
  249.     st = (int)(((int64_t)av_sintbl_4_sf[idx & 0x1f] * (0x800 - (a & 0x7ff)) +
  250.                 (int64_t)av_sintbl_4_sf[(idx & 0x1f) + 1] * (a & 0x7ff) +
  251.                 0x400) >> 11);
  252.  
  253.     *c = (int)(((int64_t)cv * ct + (int64_t)sv * st + 0x20000000) >> 30);
  254.  
  255.     *s = (int)(((int64_t)cv * st + (int64_t)sv * ct + 0x20000000) >> 30);
  256. }
  257.  
  258. #endif /* AVUTIL_SOFTFLOAT_H */
  259.