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+/**************************************************************************
+ *
+ * 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.
+ *
+ **************************************************************************/
+
+
+/**
+ * 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 "c99_math.h"
+#include <assert.h>
+#include <float.h>
+#include <stdarg.h>
+
+#include "bitscan.h"
+#include "u_endian.h" /* for UTIL_ARCH_BIG_ENDIAN */
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+
+#ifndef M_SQRT2
+#define M_SQRT2 1.41421356237309504880
+#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;
+};
+
+
+/**
+ * Extract the IEEE float32 exponent.
+ */
+static inline signed
+util_get_float32_exponent(float x)
+{
+ union fi f;
+
+ f.f = x;
+
+ return ((f.ui >> 23) & 0xff) - 127;
+}
+
+
+/**
+ * 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);
+}
+
+
+/**
+ * Floor(x), returned as int.
+ */
+static inline int
+util_ifloor(float f)
+{
+#if defined(USE_X86_ASM) && defined(__GNUC__) && defined(__i386__)
+ /*
+ * IEEE floor for computers that round to nearest or even.
+ * 'f' must be between -4194304 and 4194303.
+ * This floor operation is done by "(iround(f + .5) + iround(f - .5)) >> 1",
+ * but uses some IEEE specific tricks for better speed.
+ * Contributed by Josh Vanderhoof
+ */
+ int ai, bi;
+ double af, bf;
+ af = (3 << 22) + 0.5 + (double)f;
+ bf = (3 << 22) + 0.5 - (double)f;
+ /* GCC generates an extra fstp/fld without this. */
+ __asm__ ("fstps %0" : "=m" (ai) : "t" (af) : "st");
+ __asm__ ("fstps %0" : "=m" (bi) : "t" (bf) : "st");
+ return (ai - bi) >> 1;
+#else
+ 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;
+#endif
+}
+
+
+/**
+ * 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 bool
+util_is_approx(float a, float b, float tol)
+{
+ return fabsf(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 bool
+util_is_inf_or_nan(float x)
+{
+ union fi tmp;
+ tmp.f = x;
+ return (tmp.ui & 0x7f800000) == 0x7f800000;
+}
+
+
+static inline bool
+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 bool
+util_is_double_inf_or_nan(double x)
+{
+ union di tmp;
+ tmp.d = x;
+ return (tmp.ui & 0x7ff0000000000000ULL) == 0x7ff0000000000000ULL;
+}
+
+
+static inline bool
+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 bool
+util_is_half_inf_or_nan(int16_t x)
+{
+ return (x & 0x7c00) == 0x7c00;
+}
+
+
+static inline bool
+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;
+}
+
+
+/**
+ * Return float bits.
+ */
+static inline unsigned
+fui( float f )
+{
+ union fi fi;
+ fi.f = f;
+ return fi.ui;
+}
+
+static inline float
+uif(uint32_t ui)
+{
+ union fi fi;
+ fi.ui = ui;
+ return fi.f;
+}
+
+
+/**
+ * Convert uint8_t to float in [0, 1].
+ */
+static inline float
+ubyte_to_float(uint8_t ub)
+{
+ return (float) ub * (1.0f / 255.0f);
+}
+
+
+/**
+ * Convert float in [0,1] to uint8_t in [0,255] with clamping.
+ */
+static inline uint8_t
+float_to_ubyte(float f)
+{
+ /* return 0 for NaN too */
+ if (!(f > 0.0f)) {
+ return (uint8_t) 0;
+ }
+ else if (f >= 1.0f) {
+ return (uint8_t) 255;
+ }
+ else {
+ union fi tmp;
+ tmp.f = f;
+ tmp.f = tmp.f * (255.0f/256.0f) + 32768.0f;
+ return (uint8_t) tmp.i;
+ }
+}
+
+/**
+ * Convert uint16_t to float in [0, 1].
+ */
+static inline float
+ushort_to_float(uint16_t us)
+{
+ return (float) us * (1.0f / 65535.0f);
+}
+
+
+/**
+ * Convert float in [0,1] to uint16_t in [0,65535] with clamping.
+ */
+static inline uint16_t
+float_to_ushort(float f)
+{
+ /* return 0 for NaN too */
+ if (!(f > 0.0f)) {
+ return (uint16_t) 0;
+ }
+ else if (f >= 1.0f) {
+ return (uint16_t) 65535;
+ }
+ else {
+ union fi tmp;
+ tmp.f = f;
+ tmp.f = tmp.f * (65535.0f/65536.0f) + 128.0f;
+ return (uint16_t) 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(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
+}
+
+static inline uint64_t
+util_logbase2_64(uint64_t n)
+{
+#if defined(HAVE___BUILTIN_CLZLL)
+ return ((sizeof(uint64_t) * 8 - 1) - __builtin_clzll(n | 1));
+#else
+ uint64_t pos = 0ull;
+ if (n >= 1ull<<32) { n >>= 32; pos += 32; }
+ if (n >= 1ull<<16) { n >>= 16; pos += 16; }
+ if (n >= 1ull<< 8) { n >>= 8; pos += 8; }
+ if (n >= 1ull<< 4) { n >>= 4; pos += 4; }
+ if (n >= 1ull<< 2) { n >>= 2; pos += 2; }
+ if (n >= 1ull<< 1) { pos += 1; }
+ return pos;
+#endif
+}
+
+/**
+ * Returns the ceiling of log n base 2, and 0 when n == 0. Equivalently,
+ * returns the smallest x such that n <= 2**x.
+ */
+static inline unsigned
+util_logbase2_ceil(unsigned n)
+{
+ if (n <= 1)
+ return 0;
+
+ return 1 + util_logbase2(n - 1);
+}
+
+static inline uint64_t
+util_logbase2_ceil64(uint64_t n)
+{
+ if (n <= 1)
+ return 0;
+
+ return 1ull + util_logbase2_64(n - 1);
+}
+
+/**
+ * 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;
+
+ return (1 << ((sizeof(unsigned) * 8) - __builtin_clz(x - 1)));
+#else
+ unsigned val = x;
+
+ if (x <= 1)
+ return 1;
+
+ if (util_is_power_of_two_or_zero(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
+}
+
+static inline uint64_t
+util_next_power_of_two64(uint64_t x)
+{
+#if defined(HAVE___BUILTIN_CLZLL)
+ if (x <= 1)
+ return 1;
+
+ return (1ull << ((sizeof(uint64_t) * 8) - __builtin_clzll(x - 1)));
+#else
+ uint64_t val = x;
+
+ if (x <= 1)
+ return 1;
+
+ if (util_is_power_of_two_or_zero64(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 = (val >> 32) | val;
+ val++;
+ return val;
+#endif
+}
+
+/**
+ * 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;
+}
+
+/**
+ * Convert from little endian to CPU byte order.
+ */
+
+#if UTIL_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
+
+#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)
+
+/**
+ * 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
+}
+
+/**
+ * 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
+}
+
+
+/**
+ * Reverse byte order of a 16 bit word.
+ */
+static inline uint16_t
+util_bswap16(uint16_t n)
+{
+ return (n >> 8) |
+ (n << 8);
+}
+
+static inline void*
+util_memcpy_cpu_to_le32(void * restrict dest, const void * restrict src, size_t n)
+{
+#if UTIL_ARCH_BIG_ENDIAN
+ size_t i, e;
+ assert(n % 4 == 0);
+
+ 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
+}
+
+/**
+ * Clamp X to [MIN, MAX].
+ * This is a macro to allow float, int, uint, etc. types.
+ * We arbitrarily turn NaN into MIN.
+ */
+#define CLAMP( X, MIN, MAX ) ( (X)>(MIN) ? ((X)>(MAX) ? (MAX) : (X)) : (MIN) )
+
+#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 up to an alignment value
+ *
+ * If \c value is not already aligned to the requested alignment value, it
+ * will be rounded up.
+ *
+ * \param value Value to be rounded
+ * \param alignment Alignment value to be used. This must be a power of two.
+ *
+ * \sa ROUND_DOWN_TO()
+ */
+static inline uintptr_t
+ALIGN(uintptr_t value, int32_t alignment)
+{
+ assert(util_is_power_of_two_nonzero(alignment));
+ return (((value) + (alignment) - 1) & ~((alignment) - 1));
+}
+
+/**
+ * Like ALIGN(), but works with a non-power-of-two alignment.
+ */
+static inline uintptr_t
+ALIGN_NPOT(uintptr_t value, int32_t alignment)
+{
+ assert(alignment > 0);
+ return (value + alignment - 1) / alignment * alignment;
+}
+
+/**
+ * Align a value down to an alignment value
+ *
+ * If \c value is not already aligned to the requested alignment value, it
+ * will be rounded down.
+ *
+ * \param value Value to be rounded
+ * \param alignment Alignment value to be used. This must be a power of two.
+ *
+ * \sa ALIGN()
+ */
+static inline uintptr_t
+ROUND_DOWN_TO(uintptr_t value, int32_t alignment)
+{
+ assert(util_is_power_of_two_nonzero(alignment));
+ return ((value) & ~(alignment - 1));
+}
+
+/**
+ * Align a value, only works pot alignemnts.
+ */
+static inline int
+align(int value, int alignment)
+{
+ return (value + alignment - 1) & ~(alignment - 1);
+}
+
+static inline uint64_t
+align64(uint64_t value, unsigned alignment)
+{
+ return (value + alignment - 1) & ~((uint64_t)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));
+}
+
+unsigned
+util_fpstate_get(void);
+unsigned
+util_fpstate_set_denorms_to_zero(unsigned current_fpstate);
+void
+util_fpstate_set(unsigned fpstate);
+
+/**
+ * For indexed draw calls, return true if the vertex count to be drawn is
+ * much lower than the vertex count that has to be uploaded, meaning
+ * that the driver should flatten indices instead of trying to upload
+ * a too big range.
+ *
+ * This is used by vertex upload code in u_vbuf and glthread.
+ */
+static inline bool
+util_is_vbo_upload_ratio_too_large(unsigned draw_vertex_count,
+ unsigned upload_vertex_count)
+{
+ if (draw_vertex_count > 1024)
+ return upload_vertex_count > draw_vertex_count * 4;
+ else if (draw_vertex_count > 32)
+ return upload_vertex_count > draw_vertex_count * 8;
+ else
+ return upload_vertex_count > draw_vertex_count * 16;
+}
+
+#ifdef __cplusplus
+}
+#endif
+
+#endif /* U_MATH_H */
generated by cgit v1.2.3 (git 2.39.1) at 2024-08-15 18:55:08 +0000