optimized integer square root

diff --git a/images/Makefile b/images/Makefile
index efd5aec15ea8722c3188cfa72e4b89ec647753f5..47e267d1b61e6cce4d5af6652e57d456a6e9c5c9 100644 (file)
--- a/images/Makefile
+++ b/images/Makefile
@@ -6,7 +6,7 @@ PROGS+=$(addprefix $(o)/images/,image-tool image-dup-test image-sim-test)
 
 CONFIGS+=images
 
-LIBIMAGES_MODS=config image scale color alpha io-main dup-init dup-cmp sig-dump sig-init sig-cmp object
+LIBIMAGES_MODS=math config image scale color alpha io-main dup-init dup-cmp sig-dump sig-init sig-cmp object
 
 LIBIMAGES_LIBS=-lm
 

diff --git a/images/math.c b/images/math.c
new file mode 100644 (file)
index 0000000..f88daa6
--- /dev/null
+++ b/images/math.c
@@ -0,0 +1,64 @@
+/*
+ *     Image Library -- Math routines
+ *
+ *     (c) 2006 Pavel Charvat <pchar@ucw.cz>
+ *
+ *     This software may be freely distributed and used according to the terms
+ *     of the GNU General Public License.
+ */
+
+#include "lib/lib.h"
+#include "images/math.h"
+
+const u32 fast_div_tab[] = {
+          0, 4294967295U,2147483648U,1431655766, 1073741824,  858993460,  715827883,  613566757,
+  536870912,  477218589,  429496730,  390451573,  357913942,  330382100,  306783379,  286331154,
+  268435456,  252645136,  238609295,  226050911,  214748365,  204522253,  195225787,  186737709,
+  178956971,  171798692,  165191050,  159072863,  153391690,  148102321,  143165577,  138547333,
+  134217728,  130150525,  126322568,  122713352,  119304648,  116080198,  113025456,  110127367,
+  107374183,  104755300,  102261127,   99882961,   97612894,   95443718,   93368855,   91382283,
+   89478486,   87652394,   85899346,   84215046,   82595525,   81037119,   79536432,   78090315,
+   76695845,   75350304,   74051161,   72796056,   71582789,   70409300,   69273667,   68174085,
+   67108864,   66076420,   65075263,   64103990,   63161284,   62245903,   61356676,   60492498,
+   59652324,   58835169,   58040099,   57266231,   56512728,   55778797,   55063684,   54366675,
+   53687092,   53024288,   52377650,   51746594,   51130564,   50529028,   49941481,   49367441,
+   48806447,   48258060,   47721859,   47197443,   46684428,   46182445,   45691142,   45210183,
+   44739243,   44278014,   43826197,   43383509,   42949673,   42524429,   42107523,   41698712,
+   41297763,   40904451,   40518560,   40139882,   39768216,   39403370,   39045158,   38693400,
+   38347923,   38008561,   37675152,   37347542,   37025581,   36709123,   36398028,   36092163,
+   35791395,   35495598,   35204650,   34918434,   34636834,   34359739,   34087043,   33818641,
+   33554432,   33294321,   33038210,   32786010,   32537632,   32292988,   32051995,   31814573,
+   31580642,   31350127,   31122952,   30899046,   30678338,   30460761,   30246249,   30034737,
+   29826162,   29620465,   29417585,   29217465,   29020050,   28825284,   28633116,   28443493,
+   28256364,   28071682,   27889399,   27709467,   27531842,   27356480,   27183338,   27012373,
+   26843546,   26676816,   26512144,   26349493,   26188825,   26030105,   25873297,   25718368,
+   25565282,   25414008,   25264514,   25116768,   24970741,   24826401,   24683721,   24542671,
+   24403224,   24265352,   24129030,   23994231,   23860930,   23729102,   23598722,   23469767,
+   23342214,   23216040,   23091223,   22967740,   22845571,   22724695,   22605092,   22486740,
+   22369622,   22253717,   22139007,   22025474,   21913099,   21801865,   21691755,   21582751,
+   21474837,   21367997,   21262215,   21157475,   21053762,   20951060,   20849356,   20748635,
+   20648882,   20550083,   20452226,   20355296,   20259280,   20164166,   20069941,   19976593,
+   19884108,   19792477,   19701685,   19611723,   19522579,   19434242,   19346700,   19259944,
+   19173962,   19088744,   19004281,   18920561,   18837576,   18755316,   18673771,   18592933,
+   18512791,   18433337,   18354562,   18276457,   18199014,   18122225,   18046082,   17970575,
+   17895698,   17821442,   17747799,   17674763,   17602325,   17530479,   17459217,   17388532,
+   17318417,   17248865,   17179870,   17111424,   17043522,   16976156,   16909321,   16843010 };
+
+const byte fast_sqrt_tab[] = {
+    0,   16,   23,   28,   32,   36,   39,   43,   46,   48,   51,   53,   56,   58,   60,   62,
+   64,   66,   68,   70,   72,   74,   75,   77,   79,   80,   82,   83,   85,   86,   88,   89,
+   91,   92,   94,   95,   96,   98,   99,  100,  101,  103,  104,  105,  106,  108,  109,  110,
+  111,  112,  113,  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,
+  143,  144,  145,  146,  147,  148,  149,  150,  150,  151,  152,  153,  154,  155,  155,  156,
+  157,  158,  159,  159,  160,  161,  162,  163,  163,  164,  165,  166,  167,  167,  168,  169,
+  170,  170,  171,  172,  173,  173,  174,  175,  176,  176,  177,  178,  178,  179,  180,  181,
+  181,  182,  183,  183,  184,  185,  186,  186,  187,  188,  188,  189,  190,  190,  191,  192,
+  192,  193,  194,  194,  195,  196,  196,  197,  198,  198,  199,  199,  200,  201,  201,  202,
+  203,  203,  204,  205,  205,  206,  206,  207,  208,  208,  209,  210,  210,  211,  211,  212,
+  213,  213,  214,  214,  215,  216,  216,  217,  217,  218,  219,  219,  220,  220,  221,  221,
+  222,  223,  223,  224,  224,  225,  225,  226,  227,  227,  228,  228,  229,  229,  230,  230,
+  231,  232,  232,  233,  233,  234,  234,  235,  235,  236,  237,  237,  238,  238,  239,  239,
+  240,  240,  241,  241,  242,  242,  243,  243,  244,  245,  245,  246,  246,  247,  247,  248,
+  248,  249,  249,  250,  250,  251,  251,  252,  252,  253,  253,  254,  254,  255,  255,  255 };
+

diff --git a/images/math.h b/images/math.h
new file mode 100644 (file)
index 0000000..1824c95
--- /dev/null
+++ b/images/math.h
@@ -0,0 +1,103 @@
+#ifndef _IMAGES_MATH_H
+#define _IMAGES_MATH_H
+
+extern const u32 fast_div_tab[];
+extern const byte fast_sqrt_tab[];
+
+static inline uns
+isqr(int x)
+{
+  return x * x;
+}
+
+static inline uns
+fast_div_u32_u8(uns x, uns y)
+{
+#ifdef CPU_I386
+  int ret, dmy;
+  asm volatile (
+    "mull %3"
+    :"=d"(ret),"=a"(dmy)
+    :"1"(x),"g"(fast_div_tab[y])
+  );
+  return ret;
+#else
+  return ((u64)(x) * fast_div_tab[y]) >> 32;
+#endif
+}
+
+static inline uns
+fast_sqrt_u16(uns x)
+{
+  uns y;
+  if (x < (1 << 10) - 3)
+    y = fast_sqrt_tab[(x + 3) >> 2] >> 3;
+  else if (x < (1 << 14) - 28)
+    y = fast_sqrt_tab[(x + 28) >> 6] >> 1;
+  else
+    y = fast_sqrt_tab[x >> 8];
+  return (x < y * y) ? y - 1 : y;
+}
+
+static inline uns
+fast_sqrt_u32(uns x)
+{
+  uns y;
+  if (x < (1 << 16))
+    {
+      if (x < (1 << 10) - 3)
+       y = fast_sqrt_tab[(x + 3) >> 2] >> 3;
+      else if (x < (1 << 14) - 28)
+       y = fast_sqrt_tab[(x + 28) >> 6] >> 1;
+      else
+        y = fast_sqrt_tab[x >> 8];
+    }
+  else
+    {
+      if (x < (1 << 24))
+        {
+         if (x < (1 << 20))
+           {
+              y = fast_sqrt_tab[x >> 12];
+              y = (fast_div_u32_u8(x, y) >> 3) + (y << 1);
+            }
+         else
+           {
+              y = fast_sqrt_tab[x >> 16];
+              y = (fast_div_u32_u8(x, y) >> 5) + (y << 3);
+            }
+        }
+      else
+        {
+          if (x < (1 << 28))
+           {
+              if (x < (1 << 26))
+               {
+                  y = fast_sqrt_tab[x >> 18];
+                  y = (fast_div_u32_u8(x, y) >> 6) + (y << 4);
+                }
+             else
+               {
+                  y = fast_sqrt_tab[x >> 20];
+                  y = (fast_div_u32_u8(x, y) >> 7) + (y << 5);
+                }
+            }
+         else
+           {
+              if (x < (1 << 30))
+               {
+                  y = fast_sqrt_tab[x >> 22];
+                  y = (fast_div_u32_u8(x, y) >> 8) + (y << 6);
+                }
+             else
+               {
+                  y = fast_sqrt_tab[x >> 24];
+                  y = (fast_div_u32_u8(x, y) >> 9) + (y << 7);
+                }
+            }
+        }
+    }
+  return (x < y * y) ? y - 1 : y;
+}
+
+#endif

diff --git a/images/sig-cmp.c b/images/sig-cmp.c
index 6367643be36aeaa96646989dee076ecc7aefffce..ec3f1e865303beac7c058ef1bf262976e97493f7 100644 (file)
--- a/images/sig-cmp.c
+++ b/images/sig-cmp.c
@@ -11,6 +11,7 @@
 
 #include "lib/lib.h"
 #include "lib/math.h"
+#include "images/math.h"
 #include "images/images.h"
 #include "images/signature.h"
 #include <stdio.h>
@@ -57,8 +58,8 @@ image_signatures_dist(struct image_signature *sig1, struct image_signature *sig2
          f = MIN(f, mf[i][j]);
          h = MIN(h, mh[i][j]);
        }
-      lf[i] = (df * 0x10000) / (df + (int)sqrt(f));
-      lh[i] = (dh * 0x10000) / (dh + (int)sqrt(h));
+      lf[i] = (df * 0x10000) / (df + fast_sqrt_u32(f));
+      lh[i] = (dh * 0x10000) / (dh + fast_sqrt_u32(h));
       lfs += lf[i] * (6 * reg1[i].wa + 2 * reg1[i].wb);
       lhs += lh[i] * reg1[i].wa;
     }
@@ -70,8 +71,8 @@ image_signatures_dist(struct image_signature *sig1, struct image_signature *sig2
          f = MIN(f, mf[j][i]);
          h = MIN(h, mh[j][i]);
        }
-      lf[i + cnt1] = (df * 0x10000) / (df + (int)sqrt(f));
-      lh[i + cnt1] = (dh * 0x10000) / (dh + (int)sqrt(h));
+      lf[i + cnt1] = (df * 0x10000) / (df + fast_sqrt_u32(f));
+      lh[i + cnt1] = (dh * 0x10000) / (dh + fast_sqrt_u32(h));
       lfs += lf[i] * (6 * reg2[i].wa + 2 * reg2[i].wb);
       lhs += lh[i] * reg2[i].wa;
     }

diff --git a/images/sig-init.c b/images/sig-init.c
index 585210af9363c778f94f2e01320ab2113355cff4..41b47723092e5340da0b905599aa05a92b997e87 100644 (file)
--- a/images/sig-init.c
+++ b/images/sig-init.c
@@ -12,6 +12,7 @@
 #include "sherlock/sherlock.h"
 #include "lib/math.h"
 #include "lib/fastbuf.h"
+#include "images/math.h"
 #include "images/images.h"
 #include "images/color.h"
 #include "images/signature.h"
@@ -283,9 +284,9 @@ compute_image_signature(struct image_thread *thread UNUSED, struct image_signatu
            }
 
          /* Extract energies in LH, HL and HH bands */
-         block->lh = CLAMP((int)(sqrt(t[8] * t[8] + t[9] * t[9] + t[12] * t[12] + t[13] * t[13]) / 16), 0, 255);
-         block->hl = CLAMP((int)(sqrt(t[2] * t[2] + t[3] * t[3] + t[6] * t[6] + t[7] * t[7]) / 16), 0, 255);
-         block->hh = CLAMP((int)(sqrt(t[10] * t[10] + t[11] * t[11] + t[14] * t[14] + t[15] * t[15]) / 16), 0, 255);
+         block->lh = fast_sqrt_u16(isqr(t[8]) + isqr(t[9]) + isqr(t[12]) + isqr(t[13]));
+         block->hl = fast_sqrt_u16(isqr(t[2]) + isqr(t[3]) + isqr(t[6]) + isqr(t[7]));
+         block->hh = fast_sqrt_u16(isqr(t[10]) + isqr(t[11]) + isqr(t[14]) + isqr(t[15]));
         }
     }