gallium: new u_math.[ch] files for math functions

So far, optimized/low-precision versions of exp(), exp2(), log2(), pow().

src/gallium/auxiliary/util/Makefile

@@ -12,6 +12,7 @@ C_SOURCES = \
 	u_gen_mipmap.c \
 	u_handle_table.c \
 	u_hash_table.c \
+	u_math.c \
 	u_mm.c \
 	u_simple_shaders.c \
 	u_snprintf.c \

src/gallium/auxiliary/util/SConscript

@@ -13,6 +13,7 @@ util = env.ConvenienceLibrary(
 		'u_gen_mipmap.c',
 		'u_handle_table.c',
 		'u_hash_table.c',
+		'u_math.c',
 		'u_mm.c',
 		'u_simple_shaders.c',
 		'u_snprintf.c',

src/gallium/auxiliary/util/u_math.c

@@ -0,0 +1,60 @@
+/**************************************************************************
+ * 
+ * Copyright 2008 Tungsten Graphics, Inc., Cedar Park, Texas.
+ * All Rights Reserved.
+ * 
+ * Permission is hereby granted, free of charge, to any person obtaining a
+ * copy of this software and associated documentation files (the
+ * "Software"), to deal in the Software without restriction, including
+ * without limitation the rights to use, copy, modify, merge, publish,
+ * distribute, sub license, and/or sell copies of the Software, and to
+ * permit persons to whom the Software is furnished to do so, subject to
+ * the following conditions:
+ * 
+ * The above copyright notice and this permission notice (including the
+ * next paragraph) shall be included in all copies or substantial portions
+ * of the Software.
+ * 
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
+ * OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
+ * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT.
+ * IN NO EVENT SHALL TUNGSTEN GRAPHICS AND/OR ITS SUPPLIERS BE LIABLE FOR
+ * ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,
+ * TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE
+ * SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
+ * 
+ **************************************************************************/
+
+
+
+#include "util/u_math.h"
+
+
+
+float pow2_table[POW2_TABLE_SIZE];
+
+
+static void
+init_pow2_table(void)
+{
+   int i;
+   for (i = 0; i < POW2_TABLE_SIZE; i++) {
+      pow2_table[i] = pow(2.0, i / POW2_TABLE_SCALE);
+   }
+}
+
+
+/**
+ * One time init for math utilities.
+ */
+void
+util_init_math(void)
+{
+   static boolean initialized = FALSE;
+   if (!initialized) {
+      init_pow2_table();
+      initialized = TRUE;
+   }
+}
+
+

src/gallium/auxiliary/util/u_math.h

@@ -0,0 +1,144 @@
+/**************************************************************************
+ * 
+ * Copyright 2008 Tungsten Graphics, Inc., Cedar Park, Texas.
+ * All Rights Reserved.
+ * 
+ * Permission is hereby granted, free of charge, to any person obtaining a
+ * copy of this software and associated documentation files (the
+ * "Software"), to deal in the Software without restriction, including
+ * without limitation the rights to use, copy, modify, merge, publish,
+ * distribute, sub license, and/or sell copies of the Software, and to
+ * permit persons to whom the Software is furnished to do so, subject to
+ * the following conditions:
+ * 
+ * The above copyright notice and this permission notice (including the
+ * next paragraph) shall be included in all copies or substantial portions
+ * of the Software.
+ * 
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
+ * OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
+ * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT.
+ * IN NO EVENT SHALL TUNGSTEN GRAPHICS AND/OR ITS SUPPLIERS BE LIABLE FOR
+ * ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,
+ * TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE
+ * SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
+ * 
+ **************************************************************************/
+
+
+/**
+ * Math utilities and approximations for common math functions.
+ * Reduced precision is usually acceptable in shaders...
+ */
+
+
+#ifndef U_MATH_H
+#define U_MATH_H
+
+
+#include "pipe/p_util.h"
+#include "util/u_math.h"
+
+
+
+#define POW2_TABLE_SIZE 256
+#define POW2_TABLE_SCALE ((float) (POW2_TABLE_SIZE-1))
+extern float pow2_table[POW2_TABLE_SIZE];
+
+
+extern void
+util_init_math(void);
+
+
+
+
+/**
+ * Fast approximation to exp(x).
+ * Compute with base 2 exponents:  exp(x) = exp2(log2(e) * x)
+ * Note: log2(e) is a constant, k = 1.44269
+ * So, exp(x) = exp2(k * x);
+ * Identity: exp2(a + b) = exp2(a) * exp2(b)
+ * Let ipart = int(k*x)
+ * Let fpart = k*x - ipart;
+ * So, exp2(k*x) = exp2(ipart) * exp2(fpart)
+ * Compute exp2(ipart) with i << ipart
+ * Compute exp2(fpart) with lookup table.
+ */
+static INLINE float
+util_fast_exp(float x)
+{
+   if (x >= 0.0f) {
+      float k = 1.44269f; /* = log2(e) */
+      float kx = k * x;
+      int ipart = (int) kx;
+      float fpart = kx - (float) ipart;
+      float y = (float) (1 << ipart)
+         * pow2_table[(int) (fpart * POW2_TABLE_SCALE)];
+      return y;
+   }
+   else {
+      /* exp(-x) = 1.0 / exp(x) */
+      float k = -1.44269f;
+      float kx = k * x;
+      int ipart = (int) kx;
+      float fpart = kx - (float) ipart;
+      float y = (float) (1 << ipart)
+         * pow2_table[(int) (fpart * POW2_TABLE_SCALE)];
+      return 1.0f / y;
+   }
+}
+
+
+/**
+ * Fast version of 2^x
+ * XXX the above function could be implemented in terms of this one.
+ */
+static INLINE float
+util_fast_exp2(float x)
+{
+   if (x >= 0.0f) {
+      int ipart = (int) x;
+      float fpart = x - (float) ipart;
+      float y = (float) (1 << ipart)
+         * pow2_table[(int) (fpart * POW2_TABLE_SCALE)];
+      return y;
+   }
+   else {
+      /* exp(-x) = 1.0 / exp(x) */
+      int ipart = (int) -x;
+      float fpart = -x - (float) ipart;
+      float y = (float) (1 << ipart)
+         * pow2_table[(int) (fpart * POW2_TABLE_SCALE)];
+      return 1.0f / y;
+   }
+}
+
+
+/**
+ * Based on code from http://www.flipcode.com/totd/
+ */
+static INLINE float
+util_fast_log2(float val)
+{
+   union fi num;
+   int log_2;
+   num.f = val;
+   log_2 = ((num.i >> 23) & 255) - 128;
+   num.i &= ~(255 << 23);
+   num.i += 127 << 23;
+   num.f = ((-1.0f/3) * num.f + 2) * num.f - 2.0f/3;
+   return num.f + log_2;
+}
+
+
+static INLINE float
+util_fast_pow(float x, float y)
+{
+   /* XXX this test may need adjustment */
+   if (y >= 3.0 && -0.02f <= x && x <= 0.02f)
+      return 0.0f;
+   return util_fast_exp2(util_fast_log2(x) * y);
+}
+
+
+#endif /* U_MATH_H */