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  1. /**************************************************************************
  2.  *
  3.  * Copyright 2008 Tungsten Graphics, Inc., Cedar Park, Texas.
  4.  * All Rights Reserved.
  5.  *
  6.  * Permission is hereby granted, free of charge, to any person obtaining a
  7.  * copy of this software and associated documentation files (the
  8.  * "Software"), to deal in the Software without restriction, including
  9.  * without limitation the rights to use, copy, modify, merge, publish,
  10.  * distribute, sub license, and/or sell copies of the Software, and to
  11.  * permit persons to whom the Software is furnished to do so, subject to
  12.  * the following conditions:
  13.  *
  14.  * The above copyright notice and this permission notice (including the
  15.  * next paragraph) shall be included in all copies or substantial portions
  16.  * of the Software.
  17.  *
  18.  * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
  19.  * OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
  20.  * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT.
  21.  * IN NO EVENT SHALL TUNGSTEN GRAPHICS AND/OR ITS SUPPLIERS BE LIABLE FOR
  22.  * ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,
  23.  * TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE
  24.  * SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
  25.  *
  26.  **************************************************************************/
  27.  
  28.  
  29. /**
  30.  * Math utilities and approximations for common math functions.
  31.  * Reduced precision is usually acceptable in shaders...
  32.  *
  33.  * "fast" is used in the names of functions which are low-precision,
  34.  * or at least lower-precision than the normal C lib functions.
  35.  */
  36.  
  37.  
  38. #ifndef U_MATH_H
  39. #define U_MATH_H
  40.  
  41.  
  42. #include "pipe/p_compiler.h"
  43.  
  44.  
  45. #ifdef __cplusplus
  46. extern "C" {
  47. #endif
  48.  
  49.  
  50. #include <math.h>
  51. #include <stdarg.h>
  52.  
  53. #ifdef PIPE_OS_UNIX
  54. #include <strings.h> /* for ffs */
  55. #endif
  56.  
  57.  
  58. #ifndef M_SQRT2
  59. #define M_SQRT2 1.41421356237309504880
  60. #endif
  61.  
  62.  
  63. #if defined(_MSC_VER)
  64.  
  65. #if _MSC_VER < 1400 && !defined(__cplusplus)
  66.  
  67. static INLINE float cosf( float f )
  68. {
  69.    return (float) cos( (double) f );
  70. }
  71.  
  72. static INLINE float sinf( float f )
  73. {
  74.    return (float) sin( (double) f );
  75. }
  76.  
  77. static INLINE float ceilf( float f )
  78. {
  79.    return (float) ceil( (double) f );
  80. }
  81.  
  82. static INLINE float floorf( float f )
  83. {
  84.    return (float) floor( (double) f );
  85. }
  86.  
  87. static INLINE float powf( float f, float g )
  88. {
  89.    return (float) pow( (double) f, (double) g );
  90. }
  91.  
  92. static INLINE float sqrtf( float f )
  93. {
  94.    return (float) sqrt( (double) f );
  95. }
  96.  
  97. static INLINE float fabsf( float f )
  98. {
  99.    return (float) fabs( (double) f );
  100. }
  101.  
  102. static INLINE float logf( float f )
  103. {
  104.    return (float) log( (double) f );
  105. }
  106.  
  107. #else
  108. /* Work-around an extra semi-colon in VS 2005 logf definition */
  109. #ifdef logf
  110. #undef logf
  111. #define logf(x) ((float)log((double)(x)))
  112. #endif /* logf */
  113.  
  114. #define isfinite(x) _finite((double)(x))
  115. #define isnan(x) _isnan((double)(x))
  116. #endif /* _MSC_VER < 1400 && !defined(__cplusplus) */
  117.  
  118. static INLINE double log2( double x )
  119. {
  120.    const double invln2 = 1.442695041;
  121.    return log( x ) * invln2;
  122. }
  123.  
  124. static INLINE double
  125. round(double x)
  126. {
  127.    return x >= 0.0 ? floor(x + 0.5) : ceil(x - 0.5);
  128. }
  129.  
  130. static INLINE float
  131. roundf(float x)
  132. {
  133.    return x >= 0.0f ? floorf(x + 0.5f) : ceilf(x - 0.5f);
  134. }
  135.  
  136. #endif /* _MSC_VER */
  137.  
  138.  
  139. #ifdef PIPE_OS_ANDROID
  140.  
  141. static INLINE
  142. double log2(double d)
  143. {
  144.    return log(d) * (1.0 / M_LN2);
  145. }
  146.  
  147. /* workaround a conflict with main/imports.h */
  148. #ifdef log2f
  149. #undef log2f
  150. #endif
  151.  
  152. static INLINE
  153. float log2f(float f)
  154. {
  155.    return logf(f) * (float) (1.0 / M_LN2);
  156. }
  157.  
  158. #endif
  159.  
  160.  
  161.  
  162.  
  163. #define POW2_TABLE_SIZE_LOG2 9
  164. #define POW2_TABLE_SIZE (1 << POW2_TABLE_SIZE_LOG2)
  165. #define POW2_TABLE_OFFSET (POW2_TABLE_SIZE/2)
  166. #define POW2_TABLE_SCALE ((float)(POW2_TABLE_SIZE/2))
  167. extern float pow2_table[POW2_TABLE_SIZE];
  168.  
  169.  
  170. /**
  171.  * Initialize math module.  This should be called before using any
  172.  * other functions in this module.
  173.  */
  174. extern void
  175. util_init_math(void);
  176.  
  177.  
  178. union fi {
  179.    float f;
  180.    int32_t i;
  181.    uint32_t ui;
  182. };
  183.  
  184.  
  185. union di {
  186.    double d;
  187.    int64_t i;
  188.    uint64_t ui;
  189. };
  190.  
  191.  
  192. /**
  193.  * Fast version of 2^x
  194.  * Identity: exp2(a + b) = exp2(a) * exp2(b)
  195.  * Let ipart = int(x)
  196.  * Let fpart = x - ipart;
  197.  * So, exp2(x) = exp2(ipart) * exp2(fpart)
  198.  * Compute exp2(ipart) with i << ipart
  199.  * Compute exp2(fpart) with lookup table.
  200.  */
  201. static INLINE float
  202. util_fast_exp2(float x)
  203. {
  204.    int32_t ipart;
  205.    float fpart, mpart;
  206.    union fi epart;
  207.  
  208.    if(x > 129.00000f)
  209.       return 3.402823466e+38f;
  210.  
  211.    if (x < -126.99999f)
  212.       return 0.0f;
  213.  
  214.    ipart = (int32_t) x;
  215.    fpart = x - (float) ipart;
  216.  
  217.    /* same as
  218.     *   epart.f = (float) (1 << ipart)
  219.     * but faster and without integer overflow for ipart > 31
  220.     */
  221.    epart.i = (ipart + 127 ) << 23;
  222.  
  223.    mpart = pow2_table[POW2_TABLE_OFFSET + (int)(fpart * POW2_TABLE_SCALE)];
  224.  
  225.    return epart.f * mpart;
  226. }
  227.  
  228.  
  229. /**
  230.  * Fast approximation to exp(x).
  231.  */
  232. static INLINE float
  233. util_fast_exp(float x)
  234. {
  235.    const float k = 1.44269f; /* = log2(e) */
  236.    return util_fast_exp2(k * x);
  237. }
  238.  
  239.  
  240. #define LOG2_TABLE_SIZE_LOG2 16
  241. #define LOG2_TABLE_SCALE (1 << LOG2_TABLE_SIZE_LOG2)
  242. #define LOG2_TABLE_SIZE (LOG2_TABLE_SCALE + 1)
  243. extern float log2_table[LOG2_TABLE_SIZE];
  244.  
  245.  
  246. /**
  247.  * Fast approximation to log2(x).
  248.  */
  249. static INLINE float
  250. util_fast_log2(float x)
  251. {
  252.    union fi num;
  253.    float epart, mpart;
  254.    num.f = x;
  255.    epart = (float)(((num.i & 0x7f800000) >> 23) - 127);
  256.    /* mpart = log2_table[mantissa*LOG2_TABLE_SCALE + 0.5] */
  257.    mpart = log2_table[((num.i & 0x007fffff) + (1 << (22 - LOG2_TABLE_SIZE_LOG2))) >> (23 - LOG2_TABLE_SIZE_LOG2)];
  258.    return epart + mpart;
  259. }
  260.  
  261.  
  262. /**
  263.  * Fast approximation to x^y.
  264.  */
  265. static INLINE float
  266. util_fast_pow(float x, float y)
  267. {
  268.    return util_fast_exp2(util_fast_log2(x) * y);
  269. }
  270.  
  271. /* Note that this counts zero as a power of two.
  272.  */
  273. static INLINE boolean
  274. util_is_power_of_two( unsigned v )
  275. {
  276.    return (v & (v-1)) == 0;
  277. }
  278.  
  279.  
  280. /**
  281.  * Floor(x), returned as int.
  282.  */
  283. static INLINE int
  284. util_ifloor(float f)
  285. {
  286.    int ai, bi;
  287.    double af, bf;
  288.    union fi u;
  289.    af = (3 << 22) + 0.5 + (double) f;
  290.    bf = (3 << 22) + 0.5 - (double) f;
  291.    u.f = (float) af;  ai = u.i;
  292.    u.f = (float) bf;  bi = u.i;
  293.    return (ai - bi) >> 1;
  294. }
  295.  
  296.  
  297. /**
  298.  * Round float to nearest int.
  299.  */
  300. static INLINE int
  301. util_iround(float f)
  302. {
  303. #if defined(PIPE_CC_GCC) && defined(PIPE_ARCH_X86)
  304.    int r;
  305.    __asm__ ("fistpl %0" : "=m" (r) : "t" (f) : "st");
  306.    return r;
  307. #elif defined(PIPE_CC_MSVC) && defined(PIPE_ARCH_X86)
  308.    int r;
  309.    _asm {
  310.       fld f
  311.       fistp r
  312.    }
  313.    return r;
  314. #else
  315.    if (f >= 0.0f)
  316.       return (int) (f + 0.5f);
  317.    else
  318.       return (int) (f - 0.5f);
  319. #endif
  320. }
  321.  
  322.  
  323. /**
  324.  * Approximate floating point comparison
  325.  */
  326. static INLINE boolean
  327. util_is_approx(float a, float b, float tol)
  328. {
  329.    return fabs(b - a) <= tol;
  330. }
  331.  
  332.  
  333. /**
  334.  * util_is_X_inf_or_nan = test if x is NaN or +/- Inf
  335.  * util_is_X_nan        = test if x is NaN
  336.  * util_X_inf_sign      = return +1 for +Inf, -1 for -Inf, or 0 for not Inf
  337.  *
  338.  * NaN can be checked with x != x, however this fails with the fast math flag
  339.  **/
  340.  
  341.  
  342. /**
  343.  * Single-float
  344.  */
  345. static INLINE boolean
  346. util_is_inf_or_nan(float x)
  347. {
  348.    union fi tmp;
  349.    tmp.f = x;
  350.    return (tmp.ui & 0x7f800000) == 0x7f800000;
  351. }
  352.  
  353.  
  354. static INLINE boolean
  355. util_is_nan(float x)
  356. {
  357.    union fi tmp;
  358.    tmp.f = x;
  359.    return (tmp.ui & 0x7fffffff) > 0x7f800000;
  360. }
  361.  
  362.  
  363. static INLINE int
  364. util_inf_sign(float x)
  365. {
  366.    union fi tmp;
  367.    tmp.f = x;
  368.    if ((tmp.ui & 0x7fffffff) != 0x7f800000) {
  369.       return 0;
  370.    }
  371.  
  372.    return (x < 0) ? -1 : 1;
  373. }
  374.  
  375.  
  376. /**
  377.  * Double-float
  378.  */
  379. static INLINE boolean
  380. util_is_double_inf_or_nan(double x)
  381. {
  382.    union di tmp;
  383.    tmp.d = x;
  384.    return (tmp.ui & 0x7ff0000000000000ULL) == 0x7ff0000000000000ULL;
  385. }
  386.  
  387.  
  388. static INLINE boolean
  389. util_is_double_nan(double x)
  390. {
  391.    union di tmp;
  392.    tmp.d = x;
  393.    return (tmp.ui & 0x7fffffffffffffffULL) > 0x7ff0000000000000ULL;
  394. }
  395.  
  396.  
  397. static INLINE int
  398. util_double_inf_sign(double x)
  399. {
  400.    union di tmp;
  401.    tmp.d = x;
  402.    if ((tmp.ui & 0x7fffffffffffffffULL) != 0x7ff0000000000000ULL) {
  403.       return 0;
  404.    }
  405.  
  406.    return (x < 0) ? -1 : 1;
  407. }
  408.  
  409.  
  410. /**
  411.  * Half-float
  412.  */
  413. static INLINE boolean
  414. util_is_half_inf_or_nan(int16_t x)
  415. {
  416.    return (x & 0x7c00) == 0x7c00;
  417. }
  418.  
  419.  
  420. static INLINE boolean
  421. util_is_half_nan(int16_t x)
  422. {
  423.    return (x & 0x7fff) > 0x7c00;
  424. }
  425.  
  426.  
  427. static INLINE int
  428. util_half_inf_sign(int16_t x)
  429. {
  430.    if ((x & 0x7fff) != 0x7c00) {
  431.       return 0;
  432.    }
  433.  
  434.    return (x < 0) ? -1 : 1;
  435. }
  436.  
  437.  
  438. /**
  439.  * Find first bit set in word.  Least significant bit is 1.
  440.  * Return 0 if no bits set.
  441.  */
  442. #ifndef FFS_DEFINED
  443. #define FFS_DEFINED 1
  444.  
  445. #define ffs __builtin_ffs
  446.  
  447. #endif /* FFS_DEFINED */
  448.  
  449. /**
  450.  * Find last bit set in a word.  The least significant bit is 1.
  451.  * Return 0 if no bits are set.
  452.  */
  453. static INLINE unsigned util_last_bit(unsigned u)
  454. {
  455. #if defined(__GNUC__) && ((__GNUC__ * 100 + __GNUC_MINOR__) >= 304)
  456.    return u == 0 ? 0 : 32 - __builtin_clz(u);
  457. #else
  458.    unsigned r = 0;
  459.    while (u) {
  460.        r++;
  461.        u >>= 1;
  462.    }
  463.    return r;
  464. #endif
  465. }
  466.  
  467.  
  468. /* Destructively loop over all of the bits in a mask as in:
  469.  *
  470.  * while (mymask) {
  471.  *   int i = u_bit_scan(&mymask);
  472.  *   ... process element i
  473.  * }
  474.  *
  475.  */
  476. static INLINE int u_bit_scan(unsigned *mask)
  477. {
  478.    int i = ffs(*mask) - 1;
  479.    *mask &= ~(1 << i);
  480.    return i;
  481. }
  482.  
  483.  
  484. /**
  485.  * Return float bits.
  486.  */
  487. static INLINE unsigned
  488. fui( float f )
  489. {
  490.    union fi fi;
  491.    fi.f = f;
  492.    return fi.ui;
  493. }
  494.  
  495.  
  496. /**
  497.  * Convert ubyte to float in [0, 1].
  498.  * XXX a 256-entry lookup table would be slightly faster.
  499.  */
  500. static INLINE float
  501. ubyte_to_float(ubyte ub)
  502. {
  503.    return (float) ub * (1.0f / 255.0f);
  504. }
  505.  
  506.  
  507. /**
  508.  * Convert float in [0,1] to ubyte in [0,255] with clamping.
  509.  */
  510. static INLINE ubyte
  511. float_to_ubyte(float f)
  512. {
  513.    union fi tmp;
  514.  
  515.    tmp.f = f;
  516.    if (tmp.i < 0) {
  517.       return (ubyte) 0;
  518.    }
  519.    else if (tmp.i >= 0x3f800000 /* 1.0f */) {
  520.       return (ubyte) 255;
  521.    }
  522.    else {
  523.       tmp.f = tmp.f * (255.0f/256.0f) + 32768.0f;
  524.       return (ubyte) tmp.i;
  525.    }
  526. }
  527.  
  528. static INLINE float
  529. byte_to_float_tex(int8_t b)
  530. {
  531.    return (b == -128) ? -1.0F : b * 1.0F / 127.0F;
  532. }
  533.  
  534. static INLINE int8_t
  535. float_to_byte_tex(float f)
  536. {
  537.    return (int8_t) (127.0F * f);
  538. }
  539.  
  540. /**
  541.  * Calc log base 2
  542.  */
  543. static INLINE unsigned
  544. util_logbase2(unsigned n)
  545. {
  546. #if defined(PIPE_CC_GCC) && (PIPE_CC_GCC_VERSION >= 304)
  547.    return ((sizeof(unsigned) * 8 - 1) - __builtin_clz(n | 1));
  548. #else
  549.    unsigned pos = 0;
  550.    if (n >= 1<<16) { n >>= 16; pos += 16; }
  551.    if (n >= 1<< 8) { n >>=  8; pos +=  8; }
  552.    if (n >= 1<< 4) { n >>=  4; pos +=  4; }
  553.    if (n >= 1<< 2) { n >>=  2; pos +=  2; }
  554.    if (n >= 1<< 1) {           pos +=  1; }
  555.    return pos;
  556. #endif
  557. }
  558.  
  559.  
  560. /**
  561.  * Returns the smallest power of two >= x
  562.  */
  563. static INLINE unsigned
  564. util_next_power_of_two(unsigned x)
  565. {
  566. #if defined(PIPE_CC_GCC) && (PIPE_CC_GCC_VERSION >= 304)
  567.    if (x <= 1)
  568.        return 1;
  569.  
  570.    return (1 << ((sizeof(unsigned) * 8) - __builtin_clz(x - 1)));
  571. #else
  572.    unsigned val = x;
  573.  
  574.    if (x <= 1)
  575.       return 1;
  576.  
  577.    if (util_is_power_of_two(x))
  578.       return x;
  579.  
  580.    val--;
  581.    val = (val >> 1) | val;
  582.    val = (val >> 2) | val;
  583.    val = (val >> 4) | val;
  584.    val = (val >> 8) | val;
  585.    val = (val >> 16) | val;
  586.    val++;
  587.    return val;
  588. #endif
  589. }
  590.  
  591.  
  592. /**
  593.  * Return number of bits set in n.
  594.  */
  595. static INLINE unsigned
  596. util_bitcount(unsigned n)
  597. {
  598. #if defined(PIPE_CC_GCC) && (PIPE_CC_GCC_VERSION >= 304)
  599.    return __builtin_popcount(n);
  600. #else
  601.    /* K&R classic bitcount.
  602.     *
  603.     * For each iteration, clear the LSB from the bitfield.
  604.     * Requires only one iteration per set bit, instead of
  605.     * one iteration per bit less than highest set bit.
  606.     */
  607.    unsigned bits = 0;
  608.    for (bits; n; bits++) {
  609.       n &= n - 1;
  610.    }
  611.    return bits;
  612. #endif
  613. }
  614.  
  615.  
  616. /**
  617.  * Convert from little endian to CPU byte order.
  618.  */
  619.  
  620. #ifdef PIPE_ARCH_BIG_ENDIAN
  621. #define util_le32_to_cpu(x) util_bswap32(x)
  622. #define util_le16_to_cpu(x) util_bswap16(x)
  623. #else
  624. #define util_le32_to_cpu(x) (x)
  625. #define util_le16_to_cpu(x) (x)
  626. #endif
  627.  
  628.  
  629. /**
  630.  * Reverse byte order of a 32 bit word.
  631.  */
  632. static INLINE uint32_t
  633. util_bswap32(uint32_t n)
  634. {
  635. #if defined(PIPE_CC_GCC) && (PIPE_CC_GCC_VERSION >= 403)
  636.    return __builtin_bswap32(n);
  637. #else
  638.    return (n >> 24) |
  639.           ((n >> 8) & 0x0000ff00) |
  640.           ((n << 8) & 0x00ff0000) |
  641.           (n << 24);
  642. #endif
  643. }
  644.  
  645.  
  646. /**
  647.  * Reverse byte order of a 16 bit word.
  648.  */
  649. static INLINE uint16_t
  650. util_bswap16(uint16_t n)
  651. {
  652.    return (n >> 8) |
  653.           (n << 8);
  654. }
  655.  
  656.  
  657. /**
  658.  * Clamp X to [MIN, MAX].
  659.  * This is a macro to allow float, int, uint, etc. types.
  660.  */
  661. #define CLAMP( X, MIN, MAX )  ( (X)<(MIN) ? (MIN) : ((X)>(MAX) ? (MAX) : (X)) )
  662.  
  663. #define MIN2( A, B )   ( (A)<(B) ? (A) : (B) )
  664. #define MAX2( A, B )   ( (A)>(B) ? (A) : (B) )
  665.  
  666. #define MIN3( A, B, C ) ((A) < (B) ? MIN2(A, C) : MIN2(B, C))
  667. #define MAX3( A, B, C ) ((A) > (B) ? MAX2(A, C) : MAX2(B, C))
  668.  
  669. #define MIN4( A, B, C, D ) ((A) < (B) ? MIN3(A, C, D) : MIN3(B, C, D))
  670. #define MAX4( A, B, C, D ) ((A) > (B) ? MAX3(A, C, D) : MAX3(B, C, D))
  671.  
  672.  
  673. /**
  674.  * Align a value, only works pot alignemnts.
  675.  */
  676. static INLINE int
  677. align(int value, int alignment)
  678. {
  679.    return (value + alignment - 1) & ~(alignment - 1);
  680. }
  681.  
  682. /**
  683.  * Works like align but on npot alignments.
  684.  */
  685. static INLINE size_t
  686. util_align_npot(size_t value, size_t alignment)
  687. {
  688.    if (value % alignment)
  689.       return value + (alignment - (value % alignment));
  690.    return value;
  691. }
  692.  
  693. static INLINE unsigned
  694. u_minify(unsigned value, unsigned levels)
  695. {
  696.     return MAX2(1, value >> levels);
  697. }
  698.  
  699. #ifndef COPY_4V
  700. #define COPY_4V( DST, SRC )         \
  701. do {                                \
  702.    (DST)[0] = (SRC)[0];             \
  703.    (DST)[1] = (SRC)[1];             \
  704.    (DST)[2] = (SRC)[2];             \
  705.    (DST)[3] = (SRC)[3];             \
  706. } while (0)
  707. #endif
  708.  
  709.  
  710. #ifndef COPY_4FV
  711. #define COPY_4FV( DST, SRC )  COPY_4V(DST, SRC)
  712. #endif
  713.  
  714.  
  715. #ifndef ASSIGN_4V
  716. #define ASSIGN_4V( DST, V0, V1, V2, V3 ) \
  717. do {                                     \
  718.    (DST)[0] = (V0);                      \
  719.    (DST)[1] = (V1);                      \
  720.    (DST)[2] = (V2);                      \
  721.    (DST)[3] = (V3);                      \
  722. } while (0)
  723. #endif
  724.  
  725.  
  726. static INLINE uint32_t util_unsigned_fixed(float value, unsigned frac_bits)
  727. {
  728.    return value < 0 ? 0 : (uint32_t)(value * (1<<frac_bits));
  729. }
  730.  
  731. static INLINE int32_t util_signed_fixed(float value, unsigned frac_bits)
  732. {
  733.    return (int32_t)(value * (1<<frac_bits));
  734. }
  735.  
  736. unsigned
  737. util_fpstate_get(void);
  738. unsigned
  739. util_fpstate_set_denorms_to_zero(unsigned current_fpstate);
  740. void
  741. util_fpstate_set(unsigned fpstate);
  742.  
  743.  
  744.  
  745. #ifdef __cplusplus
  746. }
  747. #endif
  748.  
  749. #endif /* U_MATH_H */
  750.