Merge commit '6151e9128ce2a84a443c82b78f5b5cb364ba2ab4'
[ffmpeg.git] / libavutil / mathematics.c
index 00b81f1..1bf044c 100644 (file)
@@ -1,5 +1,5 @@
 /*
- * Copyright (c) 2005 Michael Niedermayer <michaelni@gmx.at>
+ * Copyright (c) 2005-2012 Michael Niedermayer <michaelni@gmx.at>
  *
  * This file is part of FFmpeg.
  *
  * miscellaneous math routines and tables
  */
 
-#include <assert.h>
 #include <stdint.h>
 #include <limits.h>
-#include "mathematics.h"
 
-const uint8_t ff_sqrt_tab[256]={
-  0, 16, 23, 28, 32, 36, 40, 43, 46, 48, 51, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 77, 79, 80, 82, 84, 85, 87, 88, 90,
- 91, 92, 94, 95, 96, 98, 99,100,102,103,104,105,107,108,109,110,111,112,114,115,116,117,118,119,120,121,122,123,124,125,126,127,
-128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,144,145,146,147,148,149,150,151,151,152,153,154,155,156,156,
-157,158,159,160,160,161,162,163,164,164,165,166,167,168,168,169,170,171,171,172,173,174,174,175,176,176,177,178,179,179,180,181,
-182,182,183,184,184,185,186,186,187,188,188,189,190,190,191,192,192,193,194,194,195,196,196,197,198,198,199,200,200,201,202,202,
-203,204,204,205,205,206,207,207,208,208,209,210,210,211,212,212,213,213,214,215,215,216,216,217,218,218,219,219,220,220,221,222,
-222,223,223,224,224,225,226,226,227,227,228,228,229,230,230,231,231,232,232,233,233,234,235,235,236,236,237,237,238,238,239,239,
-240,240,241,242,242,243,243,244,244,245,245,246,246,247,247,248,248,249,249,250,250,251,251,252,252,253,253,254,254,255,255,255
-};
-
-const uint8_t ff_log2_tab[256]={
-        0,0,1,1,2,2,2,2,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,
-        5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,
-        6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,
-        6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,
-        7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,
-        7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,
-        7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,
-        7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7
-};
-
-const uint8_t av_reverse[256]={
-0x00,0x80,0x40,0xC0,0x20,0xA0,0x60,0xE0,0x10,0x90,0x50,0xD0,0x30,0xB0,0x70,0xF0,
-0x08,0x88,0x48,0xC8,0x28,0xA8,0x68,0xE8,0x18,0x98,0x58,0xD8,0x38,0xB8,0x78,0xF8,
-0x04,0x84,0x44,0xC4,0x24,0xA4,0x64,0xE4,0x14,0x94,0x54,0xD4,0x34,0xB4,0x74,0xF4,
-0x0C,0x8C,0x4C,0xCC,0x2C,0xAC,0x6C,0xEC,0x1C,0x9C,0x5C,0xDC,0x3C,0xBC,0x7C,0xFC,
-0x02,0x82,0x42,0xC2,0x22,0xA2,0x62,0xE2,0x12,0x92,0x52,0xD2,0x32,0xB2,0x72,0xF2,
-0x0A,0x8A,0x4A,0xCA,0x2A,0xAA,0x6A,0xEA,0x1A,0x9A,0x5A,0xDA,0x3A,0xBA,0x7A,0xFA,
-0x06,0x86,0x46,0xC6,0x26,0xA6,0x66,0xE6,0x16,0x96,0x56,0xD6,0x36,0xB6,0x76,0xF6,
-0x0E,0x8E,0x4E,0xCE,0x2E,0xAE,0x6E,0xEE,0x1E,0x9E,0x5E,0xDE,0x3E,0xBE,0x7E,0xFE,
-0x01,0x81,0x41,0xC1,0x21,0xA1,0x61,0xE1,0x11,0x91,0x51,0xD1,0x31,0xB1,0x71,0xF1,
-0x09,0x89,0x49,0xC9,0x29,0xA9,0x69,0xE9,0x19,0x99,0x59,0xD9,0x39,0xB9,0x79,0xF9,
-0x05,0x85,0x45,0xC5,0x25,0xA5,0x65,0xE5,0x15,0x95,0x55,0xD5,0x35,0xB5,0x75,0xF5,
-0x0D,0x8D,0x4D,0xCD,0x2D,0xAD,0x6D,0xED,0x1D,0x9D,0x5D,0xDD,0x3D,0xBD,0x7D,0xFD,
-0x03,0x83,0x43,0xC3,0x23,0xA3,0x63,0xE3,0x13,0x93,0x53,0xD3,0x33,0xB3,0x73,0xF3,
-0x0B,0x8B,0x4B,0xCB,0x2B,0xAB,0x6B,0xEB,0x1B,0x9B,0x5B,0xDB,0x3B,0xBB,0x7B,0xFB,
-0x07,0x87,0x47,0xC7,0x27,0xA7,0x67,0xE7,0x17,0x97,0x57,0xD7,0x37,0xB7,0x77,0xF7,
-0x0F,0x8F,0x4F,0xCF,0x2F,0xAF,0x6F,0xEF,0x1F,0x9F,0x5F,0xDF,0x3F,0xBF,0x7F,0xFF,
-};
-
-int64_t av_gcd(int64_t a, int64_t b){
-    if(b) return av_gcd(b, a%b);
-    else  return a;
+#include "mathematics.h"
+#include "libavutil/intmath.h"
+#include "libavutil/common.h"
+#include "avassert.h"
+#include "version.h"
+
+/* Stein's binary GCD algorithm:
+ * https://en.wikipedia.org/wiki/Binary_GCD_algorithm */
+int64_t av_gcd(int64_t a, int64_t b) {
+    int za, zb, k;
+    int64_t u, v;
+    if (a == 0)
+        return b;
+    if (b == 0)
+        return a;
+    za = ff_ctzll(a);
+    zb = ff_ctzll(b);
+    k  = FFMIN(za, zb);
+    u = llabs(a >> za);
+    v = llabs(b >> zb);
+    while (u != v) {
+        if (u > v)
+            FFSWAP(int64_t, v, u);
+        v -= u;
+        v >>= ff_ctzll(v);
+    }
+    return (uint64_t)u << k;
 }
 
-int64_t av_rescale_rnd(int64_t a, int64_t b, int64_t c, enum AVRounding rnd){
-    int64_t r=0;
-    assert(c > 0);
-    assert(b >=0);
-    assert(rnd >=0 && rnd<=5 && rnd!=4);
+int64_t av_rescale_rnd(int64_t a, int64_t b, int64_t c, enum AVRounding rnd)
+{
+    int64_t r = 0;
+    av_assert2(c > 0);
+    av_assert2(b >=0);
+    av_assert2((unsigned)(rnd&~AV_ROUND_PASS_MINMAX)<=5 && (rnd&~AV_ROUND_PASS_MINMAX)!=4);
 
-    if(a<0 && a != INT64_MIN) return -av_rescale_rnd(-a, b, c, rnd ^ ((rnd>>1)&1));
+    if (c <= 0 || b < 0 || !((unsigned)(rnd&~AV_ROUND_PASS_MINMAX)<=5 && (rnd&~AV_ROUND_PASS_MINMAX)!=4))
+        return INT64_MIN;
 
-    if(rnd==AV_ROUND_NEAR_INF) r= c/2;
-    else if(rnd&1)             r= c-1;
+    if (rnd & AV_ROUND_PASS_MINMAX) {
+        if (a == INT64_MIN || a == INT64_MAX)
+            return a;
+        rnd -= AV_ROUND_PASS_MINMAX;
+    }
 
-    if(b<=INT_MAX && c<=INT_MAX){
-        if(a<=INT_MAX)
-            return (a * b + r)/c;
-        else
-            return a/c*b + (a%c*b + r)/c;
-    }else{
+    if (a < 0)
+        return -(uint64_t)av_rescale_rnd(-FFMAX(a, -INT64_MAX), b, c, rnd ^ ((rnd >> 1) & 1));
+
+    if (rnd == AV_ROUND_NEAR_INF)
+        r = c / 2;
+    else if (rnd & 1)
+        r = c - 1;
+
+    if (b <= INT_MAX && c <= INT_MAX) {
+        if (a <= INT_MAX)
+            return (a * b + r) / c;
+        else {
+            int64_t ad = a / c;
+            int64_t a2 = (a % c * b + r) / c;
+            if (ad >= INT32_MAX && b && ad > (INT64_MAX - a2) / b)
+                return INT64_MIN;
+            return ad * b + a2;
+        }
+    } else {
 #if 1
-        uint64_t a0= a&0xFFFFFFFF;
-        uint64_t a1= a>>32;
-        uint64_t b0= b&0xFFFFFFFF;
-        uint64_t b1= b>>32;
-        uint64_t t1= a0*b1 + a1*b0;
-        uint64_t t1a= t1<<32;
+        uint64_t a0  = a & 0xFFFFFFFF;
+        uint64_t a1  = a >> 32;
+        uint64_t b0  = b & 0xFFFFFFFF;
+        uint64_t b1  = b >> 32;
+        uint64_t t1  = a0 * b1 + a1 * b0;
+        uint64_t t1a = t1 << 32;
         int i;
 
-        a0 = a0*b0 + t1a;
-        a1 = a1*b1 + (t1>>32) + (a0<t1a);
+        a0  = a0 * b0 + t1a;
+        a1  = a1 * b1 + (t1 >> 32) + (a0 < t1a);
         a0 += r;
-        a1 += a0<r;
+        a1 += a0 < r;
 
-        for(i=63; i>=0; i--){
-//            int o= a1 & 0x8000000000000000ULL;
-            a1+= a1 + ((a0>>i)&1);
-            t1+=t1;
-            if(/*o || */c <= a1){
+        for (i = 63; i >= 0; i--) {
+            a1 += a1 + ((a0 >> i) & 1);
+            t1 += t1;
+            if (c <= a1) {
                 a1 -= c;
                 t1++;
             }
         }
+        if (t1 > INT64_MAX)
+            return INT64_MIN;
         return t1;
-    }
 #else
+        /* reference code doing (a*b + r) / c, requires libavutil/integer.h */
         AVInteger ai;
-        ai= av_mul_i(av_int2i(a), av_int2i(b));
-        ai= av_add_i(ai, av_int2i(r));
+        ai = av_mul_i(av_int2i(a), av_int2i(b));
+        ai = av_add_i(ai, av_int2i(r));
 
         return av_i2int(av_div_i(ai, av_int2i(c)));
-    }
 #endif
+    }
 }
 
-int64_t av_rescale(int64_t a, int64_t b, int64_t c){
+int64_t av_rescale(int64_t a, int64_t b, int64_t c)
+{
     return av_rescale_rnd(a, b, c, AV_ROUND_NEAR_INF);
 }
 
-int64_t av_rescale_q(int64_t a, AVRational bq, AVRational cq){
-    int64_t b= bq.num * (int64_t)cq.den;
-    int64_t c= cq.num * (int64_t)bq.den;
-    return av_rescale_rnd(a, b, c, AV_ROUND_NEAR_INF);
+int64_t av_rescale_q_rnd(int64_t a, AVRational bq, AVRational cq,
+                         enum AVRounding rnd)
+{
+    int64_t b = bq.num * (int64_t)cq.den;
+    int64_t c = cq.num * (int64_t)bq.den;
+    return av_rescale_rnd(a, b, c, rnd);
+}
+
+int64_t av_rescale_q(int64_t a, AVRational bq, AVRational cq)
+{
+    return av_rescale_q_rnd(a, bq, cq, AV_ROUND_NEAR_INF);
 }
 
-int av_compare_ts(int64_t ts_a, AVRational tb_a, int64_t ts_b, AVRational tb_b){
-    int64_t a= tb_a.num * (int64_t)tb_b.den;
-    int64_t b= tb_b.num * (int64_t)tb_a.den;
-    if (av_rescale_rnd(ts_a, a, b, AV_ROUND_DOWN) < ts_b) return -1;
-    if (av_rescale_rnd(ts_b, b, a, AV_ROUND_DOWN) < ts_a) return  1;
+int av_compare_ts(int64_t ts_a, AVRational tb_a, int64_t ts_b, AVRational tb_b)
+{
+    int64_t a = tb_a.num * (int64_t)tb_b.den;
+    int64_t b = tb_b.num * (int64_t)tb_a.den;
+    if ((FFABS(ts_a)|a|FFABS(ts_b)|b) <= INT_MAX)
+        return (ts_a*a > ts_b*b) - (ts_a*a < ts_b*b);
+    if (av_rescale_rnd(ts_a, a, b, AV_ROUND_DOWN) < ts_b)
+        return -1;
+    if (av_rescale_rnd(ts_b, b, a, AV_ROUND_DOWN) < ts_a)
+        return 1;
     return 0;
 }
 
-int64_t av_compare_mod(uint64_t a, uint64_t b, uint64_t mod){
-    int64_t c= (a-b) & (mod-1);
-    if(c > (mod>>1))
-        c-= mod;
+int64_t av_compare_mod(uint64_t a, uint64_t b, uint64_t mod)
+{
+    int64_t c = (a - b) & (mod - 1);
+    if (c > (mod >> 1))
+        c -= mod;
     return c;
 }
 
-#ifdef TEST
-#include "integer.h"
-#undef printf
-int main(void){
-    int64_t a,b,c,d,e;
+int64_t av_rescale_delta(AVRational in_tb, int64_t in_ts,  AVRational fs_tb, int duration, int64_t *last, AVRational out_tb){
+    int64_t a, b, this;
 
-    for(a=7; a<(1LL<<62); a+=a/3+1){
-        for(b=3; b<(1LL<<62); b+=b/4+1){
-            for(c=9; c<(1LL<<62); c+=(c*2)/5+3){
-                int64_t r= c/2;
-                AVInteger ai;
-                ai= av_mul_i(av_int2i(a), av_int2i(b));
-                ai= av_add_i(ai, av_int2i(r));
+    av_assert0(in_ts != AV_NOPTS_VALUE);
+    av_assert0(duration >= 0);
 
-                d= av_i2int(av_div_i(ai, av_int2i(c)));
+    if (*last == AV_NOPTS_VALUE || !duration || in_tb.num*(int64_t)out_tb.den <= out_tb.num*(int64_t)in_tb.den) {
+simple_round:
+        *last = av_rescale_q(in_ts, in_tb, fs_tb) + duration;
+        return av_rescale_q(in_ts, in_tb, out_tb);
+    }
 
-                e= av_rescale(a,b,c);
+    a =  av_rescale_q_rnd(2*in_ts-1, in_tb, fs_tb, AV_ROUND_DOWN)   >>1;
+    b = (av_rescale_q_rnd(2*in_ts+1, in_tb, fs_tb, AV_ROUND_UP  )+1)>>1;
+    if (*last < 2*a - b || *last > 2*b - a)
+        goto simple_round;
 
-                if((double)a * (double)b / (double)c > (1LL<<63))
-                    continue;
+    this = av_clip64(*last, a, b);
+    *last = this + duration;
 
-                if(d!=e) printf("%"PRId64"*%"PRId64"/%"PRId64"= %"PRId64"=%"PRId64"\n", a, b, c, d, e);
-            }
-        }
+    return av_rescale_q(this, fs_tb, out_tb);
+}
+
+int64_t av_add_stable(AVRational ts_tb, int64_t ts, AVRational inc_tb, int64_t inc)
+{
+    int64_t m, d;
+
+    if (inc != 1)
+        inc_tb = av_mul_q(inc_tb, (AVRational) {inc, 1});
+
+    m = inc_tb.num * (int64_t)ts_tb.den;
+    d = inc_tb.den * (int64_t)ts_tb.num;
+
+    if (m % d == 0)
+        return ts + m / d;
+    if (m < d)
+        return ts;
+
+    {
+        int64_t old = av_rescale_q(ts, ts_tb, inc_tb);
+        int64_t old_ts = av_rescale_q(old, inc_tb, ts_tb);
+        return av_rescale_q(old + 1, inc_tb, ts_tb) + (ts - old_ts);
     }
-    return 0;
 }
-#endif