0,0 → 1,805 |
/************************************************************************** |
* |
* Copyright 2008 VMware, Inc. |
* 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 VMWARE 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. |
* |
**************************************************************************/ |
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/** |
* 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. |
*/ |
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#ifndef U_MATH_H |
#define U_MATH_H |
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#include "pipe/p_compiler.h" |
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#include "c99_math.h" |
#include <assert.h> |
#include <float.h> |
#include <stdarg.h> |
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#ifdef PIPE_OS_UNIX |
#include <strings.h> /* for ffs */ |
#endif |
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#ifdef __cplusplus |
extern "C" { |
#endif |
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#ifndef M_SQRT2 |
#define M_SQRT2 1.41421356237309504880 |
#endif |
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#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]; |
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/** |
* Initialize math module. This should be called before using any |
* other functions in this module. |
*/ |
extern void |
util_init_math(void); |
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union fi { |
float f; |
int32_t i; |
uint32_t ui; |
}; |
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union di { |
double d; |
int64_t i; |
uint64_t ui; |
}; |
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/** |
* Extract the IEEE float32 exponent. |
*/ |
static INLINE signed |
util_get_float32_exponent(float x) |
{ |
union fi f; |
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f.f = x; |
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return ((f.ui >> 23) & 0xff) - 127; |
} |
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/** |
* 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; |
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if(x > 129.00000f) |
return 3.402823466e+38f; |
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if (x < -126.99999f) |
return 0.0f; |
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ipart = (int32_t) x; |
fpart = x - (float) ipart; |
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/* same as |
* epart.f = (float) (1 << ipart) |
* but faster and without integer overflow for ipart > 31 |
*/ |
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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/** |
* 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); |
} |
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#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]; |
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/** |
* 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; |
} |
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/** |
* Fast approximation to x^y. |
*/ |
static INLINE float |
util_fast_pow(float x, float y) |
{ |
return util_fast_exp2(util_fast_log2(x) * y); |
} |
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/* 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; |
} |
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/** |
* 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; |
} |
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/** |
* 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 |
} |
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/** |
* Approximate floating point comparison |
*/ |
static INLINE boolean |
util_is_approx(float a, float b, float tol) |
{ |
return fabs(b - a) <= tol; |
} |
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/** |
* 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 |
**/ |
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/** |
* Single-float |
*/ |
static INLINE boolean |
util_is_inf_or_nan(float x) |
{ |
union fi tmp; |
tmp.f = x; |
return (tmp.ui & 0x7f800000) == 0x7f800000; |
} |
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static INLINE boolean |
util_is_nan(float x) |
{ |
union fi tmp; |
tmp.f = x; |
return (tmp.ui & 0x7fffffff) > 0x7f800000; |
} |
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static INLINE int |
util_inf_sign(float x) |
{ |
union fi tmp; |
tmp.f = x; |
if ((tmp.ui & 0x7fffffff) != 0x7f800000) { |
return 0; |
} |
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return (x < 0) ? -1 : 1; |
} |
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/** |
* Double-float |
*/ |
static INLINE boolean |
util_is_double_inf_or_nan(double x) |
{ |
union di tmp; |
tmp.d = x; |
return (tmp.ui & 0x7ff0000000000000ULL) == 0x7ff0000000000000ULL; |
} |
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static INLINE boolean |
util_is_double_nan(double x) |
{ |
union di tmp; |
tmp.d = x; |
return (tmp.ui & 0x7fffffffffffffffULL) > 0x7ff0000000000000ULL; |
} |
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static INLINE int |
util_double_inf_sign(double x) |
{ |
union di tmp; |
tmp.d = x; |
if ((tmp.ui & 0x7fffffffffffffffULL) != 0x7ff0000000000000ULL) { |
return 0; |
} |
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return (x < 0) ? -1 : 1; |
} |
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/** |
* Half-float |
*/ |
static INLINE boolean |
util_is_half_inf_or_nan(int16_t x) |
{ |
return (x & 0x7c00) == 0x7c00; |
} |
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static INLINE boolean |
util_is_half_nan(int16_t x) |
{ |
return (x & 0x7fff) > 0x7c00; |
} |
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static INLINE int |
util_half_inf_sign(int16_t x) |
{ |
if ((x & 0x7fff) != 0x7c00) { |
return 0; |
} |
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return (x < 0) ? -1 : 1; |
} |
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/** |
* Find first bit set in word. Least significant bit is 1. |
* Return 0 if no bits set. |
*/ |
#ifndef FFS_DEFINED |
#define FFS_DEFINED 1 |
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#if defined(_MSC_VER) && (_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; |
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if (u == 0) { |
return 0; |
} |
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__asm bsf eax, [u] |
__asm inc eax |
__asm mov [i], eax |
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return i; |
} |
#elif defined(__MINGW32__) || defined(PIPE_OS_ANDROID) || \ |
defined(HAVE___BUILTIN_FFS) |
#define ffs __builtin_ffs |
#endif |
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#endif /* FFS_DEFINED */ |
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/** |
* Find first bit set in long long. Least significant bit is 1. |
* Return 0 if no bits set. |
*/ |
#ifndef FFSLL_DEFINED |
#define FFSLL_DEFINED 1 |
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#if defined(__MINGW32__) || defined(PIPE_OS_ANDROID) || \ |
defined(HAVE___BUILTIN_FFSLL) |
#define ffsll __builtin_ffsll |
#endif |
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#endif /* FFSLL_DEFINED */ |
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/** |
* 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) |
{ |
#if defined(HAVE___BUILTIN_CLZ) |
return u == 0 ? 0 : 32 - __builtin_clz(u); |
#else |
unsigned r = 0; |
while (u) { |
r++; |
u >>= 1; |
} |
return r; |
#endif |
} |
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/** |
* Find last bit in a word that does not match the sign bit. The least |
* significant bit is 1. |
* Return 0 if no bits are set. |
*/ |
static INLINE unsigned |
util_last_bit_signed(int i) |
{ |
if (i >= 0) |
return util_last_bit(i); |
else |
return util_last_bit(~(unsigned)i); |
} |
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/* 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; |
} |
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#ifndef _MSC_VER |
static INLINE int |
u_bit_scan64(uint64_t *mask) |
{ |
int i = ffsll(*mask) - 1; |
*mask &= ~(1llu << i); |
return i; |
} |
#endif |
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/** |
* Return float bits. |
*/ |
static INLINE unsigned |
fui( float f ) |
{ |
union fi fi; |
fi.f = f; |
return fi.ui; |
} |
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static INLINE float |
uif(uint32_t ui) |
{ |
union fi fi; |
fi.ui = ui; |
return fi.f; |
} |
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/** |
* 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); |
} |
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/** |
* Convert float in [0,1] to ubyte in [0,255] with clamping. |
*/ |
static INLINE ubyte |
float_to_ubyte(float f) |
{ |
union fi tmp; |
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tmp.f = f; |
if (tmp.i < 0) { |
return (ubyte) 0; |
} |
else if (tmp.i >= 0x3f800000 /* 1.0f */) { |
return (ubyte) 255; |
} |
else { |
tmp.f = tmp.f * (255.0f/256.0f) + 32768.0f; |
return (ubyte) tmp.i; |
} |
} |
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static INLINE float |
byte_to_float_tex(int8_t b) |
{ |
return (b == -128) ? -1.0F : b * 1.0F / 127.0F; |
} |
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static INLINE int8_t |
float_to_byte_tex(float f) |
{ |
return (int8_t) (127.0F * f); |
} |
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/** |
* Calc log base 2 |
*/ |
static INLINE unsigned |
util_logbase2(unsigned n) |
{ |
#if defined(HAVE___BUILTIN_CLZ) |
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 |
} |
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/** |
* Returns the smallest power of two >= x |
*/ |
static INLINE unsigned |
util_next_power_of_two(unsigned x) |
{ |
#if defined(HAVE___BUILTIN_CLZ) |
if (x <= 1) |
return 1; |
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return (1 << ((sizeof(unsigned) * 8) - __builtin_clz(x - 1))); |
#else |
unsigned val = x; |
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if (x <= 1) |
return 1; |
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if (util_is_power_of_two(x)) |
return x; |
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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 |
} |
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/** |
* Return number of bits set in n. |
*/ |
static INLINE unsigned |
util_bitcount(unsigned n) |
{ |
#if defined(HAVE___BUILTIN_POPCOUNT) |
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; |
for (bits = 0; n; bits++) { |
n &= n - 1; |
} |
return bits; |
#endif |
} |
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static INLINE unsigned |
util_bitcount64(uint64_t n) |
{ |
#ifdef HAVE___BUILTIN_POPCOUNTLL |
return __builtin_popcountll(n); |
#else |
return util_bitcount(n) + util_bitcount(n >> 32); |
#endif |
} |
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/** |
* Reverse bits in n |
* Algorithm taken from: |
* http://stackoverflow.com/questions/9144800/c-reverse-bits-in-unsigned-integer |
*/ |
static INLINE unsigned |
util_bitreverse(unsigned n) |
{ |
n = ((n >> 1) & 0x55555555u) | ((n & 0x55555555u) << 1); |
n = ((n >> 2) & 0x33333333u) | ((n & 0x33333333u) << 2); |
n = ((n >> 4) & 0x0f0f0f0fu) | ((n & 0x0f0f0f0fu) << 4); |
n = ((n >> 8) & 0x00ff00ffu) | ((n & 0x00ff00ffu) << 8); |
n = ((n >> 16) & 0xffffu) | ((n & 0xffffu) << 16); |
return n; |
} |
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/** |
* Convert from little endian to CPU byte order. |
*/ |
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#ifdef PIPE_ARCH_BIG_ENDIAN |
#define util_le64_to_cpu(x) util_bswap64(x) |
#define util_le32_to_cpu(x) util_bswap32(x) |
#define util_le16_to_cpu(x) util_bswap16(x) |
#else |
#define util_le64_to_cpu(x) (x) |
#define util_le32_to_cpu(x) (x) |
#define util_le16_to_cpu(x) (x) |
#endif |
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#define util_cpu_to_le64(x) util_le64_to_cpu(x) |
#define util_cpu_to_le32(x) util_le32_to_cpu(x) |
#define util_cpu_to_le16(x) util_le16_to_cpu(x) |
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/** |
* Reverse byte order of a 32 bit word. |
*/ |
static INLINE uint32_t |
util_bswap32(uint32_t n) |
{ |
#if defined(HAVE___BUILTIN_BSWAP32) |
return __builtin_bswap32(n); |
#else |
return (n >> 24) | |
((n >> 8) & 0x0000ff00) | |
((n << 8) & 0x00ff0000) | |
(n << 24); |
#endif |
} |
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/** |
* Reverse byte order of a 64bit word. |
*/ |
static INLINE uint64_t |
util_bswap64(uint64_t n) |
{ |
#if defined(HAVE___BUILTIN_BSWAP64) |
return __builtin_bswap64(n); |
#else |
return ((uint64_t)util_bswap32((uint32_t)n) << 32) | |
util_bswap32((n >> 32)); |
#endif |
} |
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/** |
* Reverse byte order of a 16 bit word. |
*/ |
static INLINE uint16_t |
util_bswap16(uint16_t n) |
{ |
return (n >> 8) | |
(n << 8); |
} |
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static INLINE void* |
util_memcpy_cpu_to_le32(void * restrict dest, const void * restrict src, size_t n) |
{ |
#ifdef PIPE_ARCH_BIG_ENDIAN |
size_t i, e; |
assert(n % 4 == 0); |
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for (i = 0, e = n / 4; i < e; i++) { |
uint32_t * restrict d = (uint32_t* restrict)dest; |
const uint32_t * restrict s = (const uint32_t* restrict)src; |
d[i] = util_bswap32(s[i]); |
} |
return dest; |
#else |
return memcpy(dest, src, n); |
#endif |
} |
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/** |
* 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)) ) |
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#define MIN2( A, B ) ( (A)<(B) ? (A) : (B) ) |
#define MAX2( A, B ) ( (A)>(B) ? (A) : (B) ) |
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#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)) |
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#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)) |
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/** |
* Align a value, only works pot alignemnts. |
*/ |
static INLINE int |
align(int value, int alignment) |
{ |
return (value + alignment - 1) & ~(alignment - 1); |
} |
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/** |
* 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; |
} |
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static INLINE unsigned |
u_minify(unsigned value, unsigned levels) |
{ |
return MAX2(1, value >> levels); |
} |
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#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 |
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#ifndef COPY_4FV |
#define COPY_4FV( DST, SRC ) COPY_4V(DST, SRC) |
#endif |
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#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 |
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static INLINE uint32_t |
util_unsigned_fixed(float value, unsigned frac_bits) |
{ |
return value < 0 ? 0 : (uint32_t)(value * (1<<frac_bits)); |
} |
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static INLINE int32_t |
util_signed_fixed(float value, unsigned frac_bits) |
{ |
return (int32_t)(value * (1<<frac_bits)); |
} |
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unsigned |
util_fpstate_get(void); |
unsigned |
util_fpstate_set_denorms_to_zero(unsigned current_fpstate); |
void |
util_fpstate_set(unsigned fpstate); |
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#ifdef __cplusplus |
} |
#endif |
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#endif /* U_MATH_H */ |