util: implement table-based + linear interpolation linear-to-srgb conversion

Should be much faster, seems to work in softpipe.
While here (also it's now disabled) fix up the pow factor - the former value
is what is in GL core it is however not actually accurate to fp32 standard
(as it is 1.0/2.4), and if someone would do all the accurate math there's no
reason to waste 8 mantissa bits or so...

v2: use real table generating function instead of just printing the values
(might take a bit longer as it does calculations on some 3+ million floats
but much more descriptive obviously).
Also fix up another inaccurate pow factor (this time in the python code) -
wondering where the couple one bit errors came from :-(.

Reviewed-by: Jose Fonseca <jfonseca@vmware.com>
Reviewed-by: Zack Rusin <zackr@vmware.com>

src/gallium/auxiliary/util/u_format_srgb.h

@@ -39,6 +39,7 @@
 
 
 #include "pipe/p_compiler.h"
+#include "u_pack_color.h"
 #include "u_math.h"
 
 
@@ -51,23 +52,58 @@ util_format_srgb_to_linear_8unorm_table[256];
 extern const uint8_t
 util_format_linear_to_srgb_8unorm_table[256];
 
+extern const unsigned
+util_format_linear_to_srgb_helper_table[104];
+
 
 /**
  * Convert a unclamped linear float to srgb value in the [0,255].
- * XXX this hasn't been tested (render to srgb surface).
- * XXX this needs optimization.
  */
 static INLINE uint8_t
 util_format_linear_float_to_srgb_8unorm(float x)
 {
-   if (x >= 1.0f)
-      return 255;
-   else if (x >= 0.0031308f)
-      return float_to_ubyte(1.055f * powf(x, 0.41666f) - 0.055f);
-   else if (x > 0.0f)
-      return float_to_ubyte(12.92f * x);
-   else
-      return 0;
+   /* this would be exact but (probably much) slower */
+   if (0) {
+      if (x >= 1.0f)
+         return 255;
+      else if (x >= 0.0031308f)
+         return float_to_ubyte(1.055f * powf(x, 0.41666666f) - 0.055f);
+      else if (x > 0.0f)
+         return float_to_ubyte(12.92f * x);
+      else
+         return 0;
+   }
+   else {
+      /*
+       * This is taken from https://gist.github.com/rygorous/2203834
+       * Use LUT and do linear interpolation.
+       */
+      union fi almostone, minval, f;
+      unsigned tab, bias, scale, t;
+
+      almostone.ui = 0x3f7fffff;
+      minval.ui = (127-13) << 23;
+
+      /*
+       * Clamp to [2^(-13), 1-eps]; these two values map to 0 and 1, respectively.
+       * The tests are carefully written so that NaNs map to 0, same as in the
+       * reference implementation.
+       */
+      if (!(x > minval.f))
+         x = minval.f;
+      if (x > almostone.f)
+         x = almostone.f;
+
+      /* Do the table lookup and unpack bias, scale */
+      f.f = x;
+      tab = util_format_linear_to_srgb_helper_table[(f.ui - minval.ui) >> 20];
+      bias = (tab >> 16) << 9;
+      scale = tab & 0xffff;
+
+      /* Grab next-highest mantissa bits and perform linear interpolation */
+      t = (f.ui >> 12) & 0xff;
+      return (uint8_t) ((bias + scale*t) >> 16);
+   }
 }
 
 

src/gallium/auxiliary/util/u_format_srgb.py

@@ -40,6 +40,7 @@ CopyRight = '''
 
 
 import math
+import struct
 
 
 def srgb_to_linear(x):
@@ -51,10 +52,11 @@ def srgb_to_linear(x):
 
 def linear_to_srgb(x):
     if x >= 0.0031308:
-        return 1.055 * math.pow(x, 0.41666) - 0.055
+        return 1.055 * math.pow(x, 0.41666666) - 0.055
     else:
         return 12.92 * x
 
+
 def generate_srgb_tables():
     print 'const float'
     print 'util_format_srgb_8unorm_to_linear_float_table[256] = {'
@@ -84,6 +86,59 @@ def generate_srgb_tables():
     print '};'
     print
 
+# calculate the table interpolation values used in float linear to unorm8 srgb
+    numexp = 13
+    mantissa_msb = 3
+# stepshift is just used to only use every x-th float to make things faster,
+# 5 is largest value which still gives exact same table as 0
+    stepshift = 5
+    nbuckets = numexp << mantissa_msb
+    bucketsize = (1 << (23 - mantissa_msb)) >> stepshift
+    mantshift = 12
+    valtable = []
+    sum_aa = float(bucketsize)
+    sum_ab = 0.0
+    sum_bb = 0.0
+    for i in range(0, bucketsize):
+        j = (i << stepshift) >> mantshift
+        sum_ab += j
+        sum_bb += j*j
+    inv_det = 1.0 / (sum_aa * sum_bb - sum_ab * sum_ab)
+
+    for bucket in range(0, nbuckets):
+        start = ((127 - numexp) << 23) + bucket*(bucketsize << stepshift)
+        sum_a = 0.0
+        sum_b = 0.0
+ 
+        for i in range(0, bucketsize):
+            j = (i << stepshift) >> mantshift
+            fint = start + (i << stepshift)
+            ffloat = struct.unpack('f', struct.pack('I', fint))[0]
+            val = linear_to_srgb(ffloat) * 255.0 + 0.5
+            sum_a += val
+            sum_b += j*val
+
+        solved_a = inv_det * (sum_bb*sum_a - sum_ab*sum_b)
+        solved_b = inv_det * (sum_aa*sum_b - sum_ab*sum_a)
+
+        scaled_a = solved_a * 65536.0 / 512.0
+        scaled_b = solved_b * 65536.0
+ 
+        int_a = int(scaled_a + 0.5)
+        int_b = int(scaled_b + 0.5)
+
+        valtable.append((int_a << 16) + int_b)
+
+    print 'const unsigned'
+    print 'util_format_linear_to_srgb_helper_table[104] = {'
+
+    for j in range(0, nbuckets, 4):
+        print '   ',
+        for i in range(j, j + 4):
+            print '0x%08x,' % (valtable[i],),
+        print
+    print '};'
+    print
 
 def main():
     print '/* This file is autogenerated by u_format_srgb.py. Do not edit directly. */'