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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"

#ifdef __cplusplus

extern "C" {

#endif

#include 

#include 

#ifdef PIPE_OS_UNIX

#include  /* 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

#define ffs __builtin_ffs

#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)

{

#if defined(__GNUC__) && ((__GNUC__ * 100 + __GNUC_MINOR__) >= 304)

   return u == 0 ? 0 : 32 - __builtin_clz(u);

#else

   unsigned r = 0;

   while (u) {

       r++;

       u >>= 1;

   }

   return r;

#endif

}

/* 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)

{

   union fi tmp;

   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;

   }

}

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<

}

static INLINE int32_t util_signed_fixed(float value, unsigned frac_bits)

{

   return (int32_t)(value * (1<

}

unsigned

util_fpstate_get(void);

unsigned

util_fpstate_set_denorms_to_zero(unsigned current_fpstate);

void

util_fpstate_set(unsigned fpstate);

#ifdef __cplusplus

}

#endif

#endif /* U_MATH_H */