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+/**************************************************************************
+ *
+ * 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...
+ *
+ * "fast" is used in the names of functions which are low-precision,
+ * or at least lower-precision than the normal C lib functions.
+ */
+
+
+#ifndef U_MATH_H
+#define U_MATH_H
+
+
+#include "pipe/p_compiler.h"
+#include "util/u_debug.h"
+
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+
+#if defined(PIPE_SUBSYSTEM_WINDOWS_MINIPORT)
+__inline double ceil(double val)
+{
+ double ceil_val;
+
+ if ((val - (long) val) == 0) {
+ ceil_val = val;
+ }
+ else {
+ if (val > 0) {
+ ceil_val = (long) val + 1;
+ }
+ else {
+ ceil_val = (long) val;
+ }
+ }
+
+ return ceil_val;
+}
+
+#ifndef PIPE_SUBSYSTEM_WINDOWS_CE_OGL
+__inline double floor(double val)
+{
+ double floor_val;
+
+ if ((val - (long) val) == 0) {
+ floor_val = val;
+ }
+ else {
+ if (val > 0) {
+ floor_val = (long) val;
+ }
+ else {
+ floor_val = (long) val - 1;
+ }
+ }
+
+ return floor_val;
+}
+#endif
+
+#pragma function(pow)
+__inline double __cdecl pow(double val, double exponent)
+{
+ /* XXX */
+ assert(0);
+ return 0;
+}
+
+#pragma function(log)
+__inline double __cdecl log(double val)
+{
+ /* XXX */
+ assert(0);
+ return 0;
+}
+
+#pragma function(atan2)
+__inline double __cdecl atan2(double val)
+{
+ /* XXX */
+ assert(0);
+ return 0;
+}
+#else
+#include <math.h>
+#include <stdarg.h>
+#endif
+
+
+#if defined(_MSC_VER)
+
+#if _MSC_VER < 1400 && !defined(__cplusplus) || defined(PIPE_SUBSYSTEM_WINDOWS_CE)
+
+static INLINE float cosf( float f )
+{
+ return (float) cos( (double) f );
+}
+
+static INLINE float sinf( float f )
+{
+ return (float) sin( (double) f );
+}
+
+static INLINE float ceilf( float f )
+{
+ return (float) ceil( (double) f );
+}
+
+static INLINE float floorf( float f )
+{
+ return (float) floor( (double) f );
+}
+
+static INLINE float powf( float f, float g )
+{
+ return (float) pow( (double) f, (double) g );
+}
+
+static INLINE float sqrtf( float f )
+{
+ return (float) sqrt( (double) f );
+}
+
+static INLINE float fabsf( float f )
+{
+ return (float) fabs( (double) f );
+}
+
+static INLINE float logf( float f )
+{
+ return (float) log( (double) f );
+}
+
+#else
+/* Work-around an extra semi-colon in VS 2005 logf definition */
+#ifdef logf
+#undef logf
+#define logf(x) ((float)log((double)(x)))
+#endif /* logf */
+#endif
+
+static INLINE double log2( double x )
+{
+ const double invln2 = 1.442695041;
+ return log( x ) * invln2;
+}
+
+#endif /* _MSC_VER */
+
+
+
+
+
+#define POW2_TABLE_SIZE_LOG2 9
+#define POW2_TABLE_SIZE (1 << POW2_TABLE_SIZE_LOG2)
+#define POW2_TABLE_OFFSET (POW2_TABLE_SIZE/2)
+#define POW2_TABLE_SCALE ((float)(POW2_TABLE_SIZE/2))
+extern float pow2_table[POW2_TABLE_SIZE];
+
+
+/**
+ * Initialize math module. This should be called before using any
+ * other functions in this module.
+ */
+extern void
+util_init_math(void);
+
+
+union fi {
+ float f;
+ int32_t i;
+ uint32_t ui;
+};
+
+
+/**
+ * Fast version of 2^x
+ * Identity: exp2(a + b) = exp2(a) * exp2(b)
+ * Let ipart = int(x)
+ * Let fpart = x - ipart;
+ * So, exp2(x) = exp2(ipart) * exp2(fpart)
+ * Compute exp2(ipart) with i << ipart
+ * Compute exp2(fpart) with lookup table.
+ */
+static INLINE float
+util_fast_exp2(float x)
+{
+ int32_t ipart;
+ float fpart, mpart;
+ union fi epart;
+
+ if(x > 129.00000f)
+ return 3.402823466e+38f;
+
+ if (x < -126.99999f)
+ return 0.0f;
+
+ ipart = (int32_t) x;
+ fpart = x - (float) ipart;
+
+ /* same as
+ * epart.f = (float) (1 << ipart)
+ * but faster and without integer overflow for ipart > 31
+ */
+ epart.i = (ipart + 127 ) << 23;
+
+ mpart = pow2_table[POW2_TABLE_OFFSET + (int)(fpart * POW2_TABLE_SCALE)];
+
+ return epart.f * mpart;
+}
+
+
+/**
+ * Fast approximation to exp(x).
+ */
+static INLINE float
+util_fast_exp(float x)
+{
+ const float k = 1.44269f; /* = log2(e) */
+ return util_fast_exp2(k * x);
+}
+
+
+#define LOG2_TABLE_SIZE_LOG2 16
+#define LOG2_TABLE_SCALE (1 << LOG2_TABLE_SIZE_LOG2)
+#define LOG2_TABLE_SIZE (LOG2_TABLE_SCALE + 1)
+extern float log2_table[LOG2_TABLE_SIZE];
+
+
+/**
+ * Fast approximation to log2(x).
+ */
+static INLINE float
+util_fast_log2(float x)
+{
+ union fi num;
+ float epart, mpart;
+ num.f = x;
+ epart = (float)(((num.i & 0x7f800000) >> 23) - 127);
+ /* mpart = log2_table[mantissa*LOG2_TABLE_SCALE + 0.5] */
+ mpart = log2_table[((num.i & 0x007fffff) + (1 << (22 - LOG2_TABLE_SIZE_LOG2))) >> (23 - LOG2_TABLE_SIZE_LOG2)];
+ return epart + mpart;
+}
+
+
+/**
+ * Fast approximation to x^y.
+ */
+static INLINE float
+util_fast_pow(float x, float y)
+{
+ return util_fast_exp2(util_fast_log2(x) * y);
+}
+
+
+/**
+ * Floor(x), returned as int.
+ */
+static INLINE int
+util_ifloor(float f)
+{
+ int ai, bi;
+ double af, bf;
+ union fi u;
+ af = (3 << 22) + 0.5 + (double) f;
+ bf = (3 << 22) + 0.5 - (double) f;
+ u.f = (float) af; ai = u.i;
+ u.f = (float) bf; bi = u.i;
+ return (ai - bi) >> 1;
+}
+
+
+/**
+ * Round float to nearest int.
+ */
+static INLINE int
+util_iround(float f)
+{
+#if defined(PIPE_CC_GCC) && defined(PIPE_ARCH_X86)
+ int r;
+ __asm__ ("fistpl %0" : "=m" (r) : "t" (f) : "st");
+ return r;
+#elif defined(PIPE_CC_MSVC) && defined(PIPE_ARCH_X86)
+ int r;
+ _asm {
+ fld f
+ fistp r
+ }
+ return r;
+#else
+ if (f >= 0.0f)
+ return (int) (f + 0.5f);
+ else
+ return (int) (f - 0.5f);
+#endif
+}
+
+
+
+/**
+ * Test if x is NaN or +/- infinity.
+ */
+static INLINE boolean
+util_is_inf_or_nan(float x)
+{
+ union fi tmp;
+ tmp.f = x;
+ return !(int)((unsigned int)((tmp.i & 0x7fffffff)-0x7f800000) >> 31);
+}
+
+
+/**
+ * Test whether x is a power of two.
+ */
+static INLINE boolean
+util_is_pot(unsigned x)
+{
+ return (x & (x - 1)) == 0;
+}
+
+
+/**
+ * Find first bit set in word. Least significant bit is 1.
+ * Return 0 if no bits set.
+ */
+#if defined(_MSC_VER) && _MSC_VER >= 1300
+static INLINE
+unsigned long ffs( unsigned long u )
+{
+ unsigned long i;
+ if (_BitScanForward(&i, u))
+ return i + 1;
+ else
+ return 0;
+}
+#elif defined(PIPE_CC_MSVC) && defined(PIPE_ARCH_X86)
+static INLINE
+unsigned ffs( unsigned u )
+{
+ unsigned i;
+
+ if (u == 0) {
+ return 0;
+ }
+
+ __asm bsf eax, [u]
+ __asm inc eax
+ __asm mov [i], eax
+
+ return i;
+}
+#elif defined(__MINGW32__)
+#define ffs __builtin_ffs
+#endif
+
+#ifdef __MINGW32__
+#define ffs __builtin_ffs
+#endif
+
+
+/* Could also binary search for the highest bit.
+ */
+static INLINE unsigned
+util_unsigned_logbase2(unsigned n)
+{
+ unsigned log2 = 0;
+ while (n >>= 1)
+ ++log2;
+ return log2;
+}
+
+
+/**
+ * Return float bits.
+ */
+static INLINE unsigned
+fui( float f )
+{
+ union fi fi;
+ fi.f = f;
+ return fi.ui;
+}
+
+
+/**
+ * Convert ubyte to float in [0, 1].
+ * XXX a 256-entry lookup table would be slightly faster.
+ */
+static INLINE float
+ubyte_to_float(ubyte ub)
+{
+ return (float) ub * (1.0f / 255.0f);
+}
+
+
+/**
+ * Convert float in [0,1] to ubyte in [0,255] with clamping.
+ */
+static INLINE ubyte
+float_to_ubyte(float f)
+{
+ const int ieee_0996 = 0x3f7f0000; /* 0.996 or so */
+ union fi tmp;
+
+ tmp.f = f;
+ if (tmp.i < 0) {
+ return (ubyte) 0;
+ }
+ else if (tmp.i >= ieee_0996) {
+ return (ubyte) 255;
+ }
+ else {
+ tmp.f = tmp.f * (255.0f/256.0f) + 32768.0f;
+ return (ubyte) tmp.i;
+ }
+}
+
+
+/**
+ * Calc log base 2
+ */
+static INLINE unsigned
+util_logbase2(unsigned n)
+{
+ unsigned log2 = 0;
+ while (n >>= 1)
+ ++log2;
+ return log2;
+}
+
+
+/**
+ * Clamp X to [MIN, MAX].
+ * This is a macro to allow float, int, uint, etc. types.
+ */
+#define CLAMP( X, MIN, MAX ) ( (X)<(MIN) ? (MIN) : ((X)>(MAX) ? (MAX) : (X)) )
+
+#define MIN2( A, B ) ( (A)<(B) ? (A) : (B) )
+#define MAX2( A, B ) ( (A)>(B) ? (A) : (B) )
+
+
+static INLINE int
+align(int value, int alignment)
+{
+ return (value + alignment - 1) & ~(alignment - 1);
+}
+
+static INLINE unsigned
+minify(unsigned value)
+{
+ return MAX2(1, value >> 1);
+}
+
+#ifndef COPY_4V
+#define COPY_4V( DST, SRC ) \
+do { \
+ (DST)[0] = (SRC)[0]; \
+ (DST)[1] = (SRC)[1]; \
+ (DST)[2] = (SRC)[2]; \
+ (DST)[3] = (SRC)[3]; \
+} while (0)
+#endif
+
+
+#ifndef COPY_4FV
+#define COPY_4FV( DST, SRC ) COPY_4V(DST, SRC)
+#endif
+
+
+#ifndef ASSIGN_4V
+#define ASSIGN_4V( DST, V0, V1, V2, V3 ) \
+do { \
+ (DST)[0] = (V0); \
+ (DST)[1] = (V1); \
+ (DST)[2] = (V2); \
+ (DST)[3] = (V3); \
+} while (0)
+#endif
+
+
+#ifdef __cplusplus
+}
+#endif
+
+#endif /* U_MATH_H */
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