773 lines
14 KiB
C
773 lines
14 KiB
C
/**************************************************************************
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*
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* Copyright 2008 Tungsten Graphics, Inc., Cedar Park, Texas.
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* All Rights Reserved.
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*
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* Permission is hereby granted, free of charge, to any person obtaining a
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* copy of this software and associated documentation files (the
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* "Software"), to deal in the Software without restriction, including
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* without limitation the rights to use, copy, modify, merge, publish,
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* distribute, sub license, and/or sell copies of the Software, and to
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* permit persons to whom the Software is furnished to do so, subject to
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* the following conditions:
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*
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* The above copyright notice and this permission notice (including the
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* next paragraph) shall be included in all copies or substantial portions
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* of the Software.
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*
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* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
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* OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
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* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT.
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* IN NO EVENT SHALL TUNGSTEN GRAPHICS AND/OR ITS SUPPLIERS BE LIABLE FOR
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* ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,
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* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE
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* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
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*
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**************************************************************************/
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/**
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* Math utilities and approximations for common math functions.
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* Reduced precision is usually acceptable in shaders...
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*
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* "fast" is used in the names of functions which are low-precision,
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* or at least lower-precision than the normal C lib functions.
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*/
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#ifndef U_MATH_H
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#define U_MATH_H
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#include "pipe/p_compiler.h"
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#ifdef __cplusplus
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extern "C" {
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#endif
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#include <math.h>
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#include <stdarg.h>
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#ifdef PIPE_OS_UNIX
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#include <strings.h> /* for ffs */
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#endif
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#ifndef M_SQRT2
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#define M_SQRT2 1.41421356237309504880
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#endif
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#if defined(_MSC_VER)
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#if _MSC_VER < 1400 && !defined(__cplusplus)
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static INLINE float cosf( float f )
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{
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return (float) cos( (double) f );
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}
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static INLINE float sinf( float f )
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{
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return (float) sin( (double) f );
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}
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static INLINE float ceilf( float f )
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{
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return (float) ceil( (double) f );
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}
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static INLINE float floorf( float f )
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{
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return (float) floor( (double) f );
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}
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static INLINE float powf( float f, float g )
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{
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return (float) pow( (double) f, (double) g );
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}
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static INLINE float sqrtf( float f )
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{
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return (float) sqrt( (double) f );
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}
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static INLINE float fabsf( float f )
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{
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return (float) fabs( (double) f );
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}
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static INLINE float logf( float f )
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{
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return (float) log( (double) f );
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}
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#else
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/* Work-around an extra semi-colon in VS 2005 logf definition */
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#ifdef logf
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#undef logf
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#define logf(x) ((float)log((double)(x)))
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#endif /* logf */
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#define isfinite(x) _finite((double)(x))
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#define isnan(x) _isnan((double)(x))
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#endif /* _MSC_VER < 1400 && !defined(__cplusplus) */
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static INLINE double log2( double x )
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{
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const double invln2 = 1.442695041;
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return log( x ) * invln2;
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}
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static INLINE double
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round(double x)
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{
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return x >= 0.0 ? floor(x + 0.5) : ceil(x - 0.5);
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}
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static INLINE float
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roundf(float x)
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{
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return x >= 0.0f ? floorf(x + 0.5f) : ceilf(x - 0.5f);
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}
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#endif /* _MSC_VER */
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#ifdef PIPE_OS_ANDROID
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static INLINE
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double log2(double d)
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{
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return log(d) * (1.0 / M_LN2);
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}
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/* workaround a conflict with main/imports.h */
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#ifdef log2f
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#undef log2f
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#endif
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static INLINE
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float log2f(float f)
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{
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return logf(f) * (float) (1.0 / M_LN2);
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}
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#endif
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#define POW2_TABLE_SIZE_LOG2 9
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#define POW2_TABLE_SIZE (1 << POW2_TABLE_SIZE_LOG2)
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#define POW2_TABLE_OFFSET (POW2_TABLE_SIZE/2)
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#define POW2_TABLE_SCALE ((float)(POW2_TABLE_SIZE/2))
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extern float pow2_table[POW2_TABLE_SIZE];
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/**
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* Initialize math module. This should be called before using any
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* other functions in this module.
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*/
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extern void
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util_init_math(void);
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union fi {
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float f;
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int32_t i;
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uint32_t ui;
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};
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union di {
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double d;
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int64_t i;
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uint64_t ui;
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};
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/**
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* Fast version of 2^x
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* Identity: exp2(a + b) = exp2(a) * exp2(b)
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* Let ipart = int(x)
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* Let fpart = x - ipart;
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* So, exp2(x) = exp2(ipart) * exp2(fpart)
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* Compute exp2(ipart) with i << ipart
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* Compute exp2(fpart) with lookup table.
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*/
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static INLINE float
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util_fast_exp2(float x)
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{
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int32_t ipart;
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float fpart, mpart;
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union fi epart;
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if(x > 129.00000f)
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return 3.402823466e+38f;
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if (x < -126.99999f)
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return 0.0f;
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ipart = (int32_t) x;
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fpart = x - (float) ipart;
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/* same as
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* epart.f = (float) (1 << ipart)
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* but faster and without integer overflow for ipart > 31
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*/
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epart.i = (ipart + 127 ) << 23;
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mpart = pow2_table[POW2_TABLE_OFFSET + (int)(fpart * POW2_TABLE_SCALE)];
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return epart.f * mpart;
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}
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/**
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* Fast approximation to exp(x).
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*/
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static INLINE float
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util_fast_exp(float x)
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{
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const float k = 1.44269f; /* = log2(e) */
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return util_fast_exp2(k * x);
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}
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#define LOG2_TABLE_SIZE_LOG2 16
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#define LOG2_TABLE_SCALE (1 << LOG2_TABLE_SIZE_LOG2)
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#define LOG2_TABLE_SIZE (LOG2_TABLE_SCALE + 1)
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extern float log2_table[LOG2_TABLE_SIZE];
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/**
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* Fast approximation to log2(x).
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*/
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static INLINE float
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util_fast_log2(float x)
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{
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union fi num;
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float epart, mpart;
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num.f = x;
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epart = (float)(((num.i & 0x7f800000) >> 23) - 127);
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/* mpart = log2_table[mantissa*LOG2_TABLE_SCALE + 0.5] */
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mpart = log2_table[((num.i & 0x007fffff) + (1 << (22 - LOG2_TABLE_SIZE_LOG2))) >> (23 - LOG2_TABLE_SIZE_LOG2)];
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return epart + mpart;
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}
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/**
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* Fast approximation to x^y.
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*/
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static INLINE float
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util_fast_pow(float x, float y)
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{
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return util_fast_exp2(util_fast_log2(x) * y);
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}
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/* Note that this counts zero as a power of two.
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*/
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static INLINE boolean
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util_is_power_of_two( unsigned v )
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{
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return (v & (v-1)) == 0;
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}
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/**
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* Floor(x), returned as int.
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*/
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static INLINE int
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util_ifloor(float f)
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{
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int ai, bi;
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double af, bf;
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union fi u;
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af = (3 << 22) + 0.5 + (double) f;
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bf = (3 << 22) + 0.5 - (double) f;
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u.f = (float) af; ai = u.i;
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u.f = (float) bf; bi = u.i;
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return (ai - bi) >> 1;
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}
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/**
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* Round float to nearest int.
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*/
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static INLINE int
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util_iround(float f)
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{
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#if defined(PIPE_CC_GCC) && defined(PIPE_ARCH_X86)
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int r;
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__asm__ ("fistpl %0" : "=m" (r) : "t" (f) : "st");
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return r;
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#elif defined(PIPE_CC_MSVC) && defined(PIPE_ARCH_X86)
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int r;
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_asm {
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fld f
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fistp r
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}
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return r;
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#else
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if (f >= 0.0f)
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return (int) (f + 0.5f);
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else
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return (int) (f - 0.5f);
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#endif
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}
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/**
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* Approximate floating point comparison
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*/
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static INLINE boolean
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util_is_approx(float a, float b, float tol)
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{
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return fabs(b - a) <= tol;
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}
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/**
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* util_is_X_inf_or_nan = test if x is NaN or +/- Inf
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* util_is_X_nan = test if x is NaN
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* util_X_inf_sign = return +1 for +Inf, -1 for -Inf, or 0 for not Inf
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*
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* NaN can be checked with x != x, however this fails with the fast math flag
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**/
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/**
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* Single-float
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*/
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static INLINE boolean
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util_is_inf_or_nan(float x)
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{
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union fi tmp;
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tmp.f = x;
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return (tmp.ui & 0x7f800000) == 0x7f800000;
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}
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static INLINE boolean
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util_is_nan(float x)
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{
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union fi tmp;
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tmp.f = x;
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return (tmp.ui & 0x7fffffff) > 0x7f800000;
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}
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static INLINE int
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util_inf_sign(float x)
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{
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union fi tmp;
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tmp.f = x;
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if ((tmp.ui & 0x7fffffff) != 0x7f800000) {
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return 0;
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}
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return (x < 0) ? -1 : 1;
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}
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/**
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* Double-float
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*/
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static INLINE boolean
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util_is_double_inf_or_nan(double x)
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{
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union di tmp;
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tmp.d = x;
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return (tmp.ui & 0x7ff0000000000000ULL) == 0x7ff0000000000000ULL;
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}
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static INLINE boolean
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util_is_double_nan(double x)
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{
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union di tmp;
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tmp.d = x;
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return (tmp.ui & 0x7fffffffffffffffULL) > 0x7ff0000000000000ULL;
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}
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static INLINE int
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util_double_inf_sign(double x)
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{
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union di tmp;
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tmp.d = x;
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if ((tmp.ui & 0x7fffffffffffffffULL) != 0x7ff0000000000000ULL) {
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return 0;
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}
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return (x < 0) ? -1 : 1;
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}
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/**
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* Half-float
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*/
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static INLINE boolean
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util_is_half_inf_or_nan(int16_t x)
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{
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return (x & 0x7c00) == 0x7c00;
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}
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static INLINE boolean
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util_is_half_nan(int16_t x)
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{
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return (x & 0x7fff) > 0x7c00;
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}
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static INLINE int
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util_half_inf_sign(int16_t x)
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{
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if ((x & 0x7fff) != 0x7c00) {
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return 0;
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}
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return (x < 0) ? -1 : 1;
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}
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/**
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* Find first bit set in word. Least significant bit is 1.
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* Return 0 if no bits set.
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*/
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#ifndef FFS_DEFINED
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#define FFS_DEFINED 1
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#if defined(_MSC_VER) && _MSC_VER >= 1300 && (_M_IX86 || _M_AMD64 || _M_IA64)
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unsigned char _BitScanForward(unsigned long* Index, unsigned long Mask);
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#pragma intrinsic(_BitScanForward)
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static INLINE
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unsigned long ffs( unsigned long u )
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{
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unsigned long i;
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if (_BitScanForward(&i, u))
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return i + 1;
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else
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return 0;
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}
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#elif defined(PIPE_CC_MSVC) && defined(PIPE_ARCH_X86)
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static INLINE
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unsigned ffs( unsigned u )
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{
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unsigned i;
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if (u == 0) {
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return 0;
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}
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__asm bsf eax, [u]
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__asm inc eax
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__asm mov [i], eax
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return i;
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}
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#elif defined(__MINGW32__) || defined(PIPE_OS_ANDROID)
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#define ffs __builtin_ffs
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#endif
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#endif /* FFS_DEFINED */
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/**
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* Find last bit set in a word. The least significant bit is 1.
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* Return 0 if no bits are set.
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*/
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static INLINE unsigned util_last_bit(unsigned u)
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{
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#if defined(__GNUC__) && ((__GNUC__ * 100 + __GNUC_MINOR__) >= 304)
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return u == 0 ? 0 : 32 - __builtin_clz(u);
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#else
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unsigned r = 0;
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while (u) {
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r++;
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u >>= 1;
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}
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return r;
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#endif
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}
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/* Destructively loop over all of the bits in a mask as in:
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*
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* while (mymask) {
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* int i = u_bit_scan(&mymask);
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* ... process element i
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* }
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*
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*/
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static INLINE int u_bit_scan(unsigned *mask)
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{
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int i = ffs(*mask) - 1;
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*mask &= ~(1 << i);
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return i;
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}
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/**
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* Return float bits.
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*/
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static INLINE unsigned
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fui( float f )
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{
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union fi fi;
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fi.f = f;
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return fi.ui;
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}
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/**
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* Convert ubyte to float in [0, 1].
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* XXX a 256-entry lookup table would be slightly faster.
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*/
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static INLINE float
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ubyte_to_float(ubyte ub)
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{
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return (float) ub * (1.0f / 255.0f);
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}
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/**
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* Convert float in [0,1] to ubyte in [0,255] with clamping.
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*/
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static INLINE ubyte
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float_to_ubyte(float f)
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{
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union fi tmp;
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tmp.f = f;
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if (tmp.i < 0) {
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return (ubyte) 0;
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}
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else if (tmp.i >= 0x3f800000 /* 1.0f */) {
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return (ubyte) 255;
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}
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else {
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tmp.f = tmp.f * (255.0f/256.0f) + 32768.0f;
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return (ubyte) tmp.i;
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}
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}
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static INLINE float
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byte_to_float_tex(int8_t b)
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{
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return (b == -128) ? -1.0F : b * 1.0F / 127.0F;
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}
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static INLINE int8_t
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float_to_byte_tex(float f)
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{
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return (int8_t) (127.0F * f);
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}
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/**
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* Calc log base 2
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*/
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static INLINE unsigned
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util_logbase2(unsigned n)
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{
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#if defined(PIPE_CC_GCC) && (PIPE_CC_GCC_VERSION >= 304)
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return ((sizeof(unsigned) * 8 - 1) - __builtin_clz(n | 1));
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#else
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unsigned pos = 0;
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if (n >= 1<<16) { n >>= 16; pos += 16; }
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if (n >= 1<< 8) { n >>= 8; pos += 8; }
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if (n >= 1<< 4) { n >>= 4; pos += 4; }
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if (n >= 1<< 2) { n >>= 2; pos += 2; }
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if (n >= 1<< 1) { pos += 1; }
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return pos;
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#endif
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}
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/**
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* Returns the smallest power of two >= x
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*/
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static INLINE unsigned
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util_next_power_of_two(unsigned x)
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{
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#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 */
|