/**************************************************************************
*
* 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
#include <math.h>
#include <stdarg.h>
#ifdef PIPE_OS_UNIX
#include <strings.h> /* for ffs */
#endif
#ifndef M_SQRT2
#define M_SQRT2 1.41421356237309504880
#endif
#if defined(_MSC_VER)
#if _MSC_VER < 1400 && !defined(__cplusplus)
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 */
#define isfinite(x) _finite((double)(x))
#define isnan(x) _isnan((double)(x))
#endif /* _MSC_VER < 1400 && !defined(__cplusplus) */
static INLINE double log2( double x )
{
const double invln2 = 1.442695041;
return log( x ) * invln2;
}
static INLINE double
round(double x)
{
return x >= 0.0 ? floor(x + 0.5) : ceil(x - 0.5);
}
static INLINE float
roundf(float x)
{
return x >= 0.0f ? floorf(x + 0.5f) : ceilf(x - 0.5f);
}
#endif /* _MSC_VER */
#ifdef PIPE_OS_ANDROID
static INLINE
double log2(double d)
{
return log(d) * (1.0 / M_LN2);
}
/* workaround a conflict with main/imports.h */
#ifdef log2f
#undef log2f
#endif
static INLINE
float log2f(float f)
{
return logf(f) * (float) (1.0 / M_LN2);
}
#endif
#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;
};
union di {
double d;
int64_t i;
uint64_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);
}
/* Note that this counts zero as a power of two.
*/
static INLINE boolean
util_is_power_of_two( unsigned v )
{
return (v & (v-1)) == 0;
}
/**
* 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
}
/**
* Approximate floating point comparison
*/
static INLINE boolean
util_is_approx(float a, float b, float tol)
{
return fabs(b - a) <= tol;
}
/**
* util_is_X_inf_or_nan = test if x is NaN or +/- Inf
* util_is_X_nan = test if x is NaN
* util_X_inf_sign = return +1 for +Inf, -1 for -Inf, or 0 for not Inf
*
* NaN can be checked with x != x, however this fails with the fast math flag
**/
/**
* Single-float
*/
static INLINE boolean
util_is_inf_or_nan(float x)
{
union fi tmp;
tmp.f = x;
return (tmp.ui & 0x7f800000) == 0x7f800000;
}
static INLINE boolean
util_is_nan(float x)
{
union fi tmp;
tmp.f = x;
return (tmp.ui & 0x7fffffff) > 0x7f800000;
}
static INLINE int
util_inf_sign(float x)
{
union fi tmp;
tmp.f = x;
if ((tmp.ui & 0x7fffffff) != 0x7f800000) {
return 0;
}
return (x < 0) ? -1 : 1;
}
/**
* Double-float
*/
static INLINE boolean
util_is_double_inf_or_nan(double x)
{
union di tmp;
tmp.d = x;
return (tmp.ui & 0x7ff0000000000000ULL) == 0x7ff0000000000000ULL;
}
static INLINE boolean
util_is_double_nan(double x)
{
union di tmp;
tmp.d = x;
return (tmp.ui & 0x7fffffffffffffffULL) > 0x7ff0000000000000ULL;
}
static INLINE int
util_double_inf_sign(double x)
{
union di tmp;
tmp.d = x;
if ((tmp.ui & 0x7fffffffffffffffULL) != 0x7ff0000000000000ULL) {
return 0;
}
return (x < 0) ? -1 : 1;
}
/**
* Half-float
*/
static INLINE boolean
util_is_half_inf_or_nan(int16_t x)
{
return (x & 0x7c00) == 0x7c00;
}
static INLINE boolean
util_is_half_nan(int16_t x)
{
return (x & 0x7fff) > 0x7c00;
}
static INLINE int
util_half_inf_sign(int16_t x)
{
if ((x & 0x7fff) != 0x7c00) {
return 0;
}
return (x < 0) ? -1 : 1;
}
/**
* Find first bit set in word. Least significant bit is 1.
* Return 0 if no bits set.
*/
#ifndef FFS_DEFINED
#define FFS_DEFINED 1
#if defined(_MSC_VER) && _MSC_VER >= 1300 && (_M_IX86 || _M_AMD64 || _M_IA64)
unsigned char _BitScanForward(unsigned long* Index, unsigned long Mask);
#pragma intrinsic(_BitScanForward)
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__) || defined(PIPE_OS_ANDROID)
#define ffs __builtin_ffs
#endif
#endif /* FFS_DEFINED */
/**
* Find last bit set in a word. The least significant bit is 1.
* Return 0 if no bits are set.
*/
static INLINE unsigned util_last_bit(unsigned u)
{
unsigned r = 0;
while (u) {
r++;
u >>= 1;
}
return r;
}
/* Destructively loop over all of the bits in a mask as in:
*
* while (mymask) {
* int i = u_bit_scan(&mymask);
* ... process element i
* }
*
*/
static INLINE int u_bit_scan(unsigned *mask)
{
int i = ffs(*mask) - 1;
*mask &= ~(1 << i);
return i;
}
/**
* 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;
}
}
static INLINE float
byte_to_float_tex(int8_t b)
{
return (b == -128) ? -1.0F : b * 1.0F / 127.0F;
}
static INLINE int8_t
float_to_byte_tex(float f)
{
return (int8_t) (127.0F * f);
}
/**
* Calc log base 2
*/
static INLINE unsigned
util_logbase2(unsigned n)
{
#if defined(PIPE_CC_GCC) && (PIPE_CC_GCC_VERSION >= 304)
return ((sizeof(unsigned) * 8 - 1) - __builtin_clz(n | 1));
#else
unsigned pos = 0;
if (n >= 1<<16) { n >>= 16; pos += 16; }
if (n >= 1<< 8) { n >>= 8; pos += 8; }
if (n >= 1<< 4) { n >>= 4; pos += 4; }
if (n >= 1<< 2) { n >>= 2; pos += 2; }
if (n >= 1<< 1) { pos += 1; }
return pos;
#endif
}
/**
* Returns the smallest power of two >= x
*/
static INLINE unsigned
util_next_power_of_two(unsigned x)
{
#if defined(PIPE_CC_GCC) && (PIPE_CC_GCC_VERSION >= 304)
if (x <= 1)
return 1;
return (1 << ((sizeof(unsigned) * 8) - __builtin_clz(x - 1)));
#else
unsigned val = x;
if (x <= 1)
return 1;
if (util_is_power_of_two(x))
return x;
val--;
val = (val >> 1) | val;
val = (val >> 2) | val;
val = (val >> 4) | val;
val = (val >> 8) | val;
val = (val >> 16) | val;
val++;
return val;
#endif
}
/**
* Return number of bits set in n.
*/
static INLINE unsigned
util_bitcount(unsigned n)
{
#if defined(PIPE_CC_GCC) && (PIPE_CC_GCC_VERSION >= 304)
return __builtin_popcount(n);
#else
/* K&R classic bitcount.
*
* For each iteration, clear the LSB from the bitfield.
* Requires only one iteration per set bit, instead of
* one iteration per bit less than highest set bit.
*/
unsigned bits = 0;
for (bits; n; bits++) {
n &= n - 1;
}
return bits;
#endif
}
/**
* Convert from little endian to CPU byte order.
*/
#ifdef PIPE_ARCH_BIG_ENDIAN
#define util_le32_to_cpu(x) util_bswap32(x)
#define util_le16_to_cpu(x) util_bswap16(x)
#else
#define util_le32_to_cpu(x) (x)
#define util_le16_to_cpu(x) (x)
#endif
/**
* Reverse byte order of a 32 bit word.
*/
static INLINE uint32_t
util_bswap32(uint32_t n)
{
#if defined(PIPE_CC_GCC) && (PIPE_CC_GCC_VERSION >= 403)
return __builtin_bswap32(n);
#else
return (n >> 24) |
((n >> 8) & 0x0000ff00) |
((n << 8) & 0x00ff0000) |
(n << 24);
#endif
}
/**
* Reverse byte order of a 16 bit word.
*/
static INLINE uint16_t
util_bswap16(uint16_t n)
{
return (n >> 8) |
(n << 8);
}
/**
* 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) )
#define MIN3( A, B, C ) ((A) < (B) ? MIN2(A, C) : MIN2(B, C))
#define MAX3( A, B, C ) ((A) > (B) ? MAX2(A, C) : MAX2(B, C))
#define MIN4( A, B, C, D ) ((A) < (B) ? MIN3(A, C, D) : MIN3(B, C, D))
#define MAX4( A, B, C, D ) ((A) > (B) ? MAX3(A, C, D) : MAX3(B, C, D))
/**
* Align a value, only works pot alignemnts.
*/
static INLINE int
align(int value, int alignment)
{
return (value + alignment - 1) & ~(alignment - 1);
}
/**
* Works like align but on npot alignments.
*/
static INLINE size_t
util_align_npot(size_t value, size_t alignment)
{
if (value % alignment)
return value + (alignment - (value % alignment));
return value;
}
static INLINE unsigned
u_minify(unsigned value, unsigned levels)
{
return MAX2(1, value >> levels);
}
#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
static INLINE uint32_t util_unsigned_fixed(float value, unsigned frac_bits)
{
return value < 0 ? 0 : (uint32_t)(value * (1<<frac_bits));
}
static INLINE int32_t util_signed_fixed(float value, unsigned frac_bits)
{
return (int32_t)(value * (1<<frac_bits));
}
#ifdef __cplusplus
}
#endif
#endif /* U_MATH_H */