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ispc/stdlib.ispc

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// -*- mode: c++ -*-
/*
Copyright (c) 2010-2011, Intel Corporation
All rights reserved.
Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions are
met:
* Redistributions of source code must retain the above copyright
notice, this list of conditions and the following disclaimer.
* Redistributions in binary form must reproduce the above copyright
notice, this list of conditions and the following disclaimer in the
documentation and/or other materials provided with the distribution.
* Neither the name of Intel Corporation nor the names of its
contributors may be used to endorse or promote products derived from
this software without specific prior written permission.
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS
IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A
PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER
OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*/
/** @file stdlib.ispc
@brief Portion of the ispc standard library implementation that's in
ispc code
*/
///////////////////////////////////////////////////////////////////////////
// Low level primitives
static inline float floatbits(unsigned int a) {
return __floatbits_varying_int32(a);
}
static inline uniform float floatbits(uniform unsigned int a) {
return __floatbits_uniform_int32(a);
}
static inline float floatbits(int a) {
return __floatbits_varying_int32(a);
}
static inline uniform float floatbits(uniform int a) {
return __floatbits_uniform_int32(a);
}
static inline double doublebits(unsigned int64 a) {
return __doublebits_varying_int64(a);
}
static inline uniform double doublebits(uniform unsigned int64 a) {
return __doublebits_uniform_int64(a);
}
static inline unsigned int intbits(float a) {
return __intbits_varying_float(a);
}
static inline uniform unsigned int intbits(uniform float a) {
return __intbits_uniform_float(a);
}
static inline unsigned int64 intbits(double d) {
return __intbits_varying_double(d);
}
static inline uniform unsigned int64 intbits(uniform double d) {
return __intbits_uniform_double(d);
}
static inline float broadcast(float v, uniform int i) {
return __broadcast_float(v, i);
}
static inline int32 broadcast(int32 v, uniform int i) {
return __broadcast_int32(v, i);
}
static inline double broadcast(double v, uniform int i) {
return __broadcast_double(v, i);
}
static inline int64 broadcast(int64 v, uniform int i) {
return __broadcast_int64(v, i);
}
static inline float rotate(float v, uniform int i) {
return __rotate_float(v, i);
}
static inline int32 rotate(int32 v, uniform int i) {
return __rotate_int32(v, i);
}
static inline double rotate(double v, uniform int i) {
return __rotate_double(v, i);
}
static inline int64 rotate(int64 v, uniform int i) {
return __rotate_int64(v, i);
}
static inline float shuffle(float v, int i) {
return __shuffle_float(v, i);
}
static inline int32 shuffle(int32 v, int i) {
return __shuffle_int32(v, i);
}
static inline double shuffle(double v, int i) {
return __shuffle_double(v, i);
}
static inline int64 shuffle(int64 v, int i) {
return __shuffle_int64(v, i);
}
// x[i]
static inline uniform float extract(float x, uniform int i) {
return __extract(x, i);
}
// x[i] = v
static inline float insert(float x, uniform int i, uniform float v) {
return __insert(x, i, v);
}
static inline uniform int extract(int x, uniform int i) {
return intbits(extract(floatbits(x), i));
}
static inline int insert(int x, uniform int i, uniform int v) {
return intbits(insert(floatbits(x), i, floatbits(v)));
}
static inline uniform unsigned int extract(unsigned int x, uniform int i) {
return intbits(extract(floatbits(x), i));
}
static inline unsigned int insert(unsigned int x, uniform int i, uniform unsigned int v) {
return intbits(insert(floatbits(x), i, floatbits(v)));
}
static inline uniform bool any(bool v) {
// We only care about whether "any" is true for the active program instances,
// so we have to make v with the current program mask.
return __movmsk(v & __mask) != 0;
}
static inline uniform bool all(bool v) {
// As with any(), we need to explicitly mask v with the current program mask
// so we're only looking at the current lanes
bool match = ((v & __mask) == __mask);
return __movmsk(match) == (1 << programCount) - 1;
}
static inline uniform int popcnt(uniform int v) {
return __popcnt(v);
}
static inline int popcnt(int v) {
int r;
uniform int i;
for (i = 0; i < programCount; ++i)
r = insert(r, i, popcnt(extract(v, i)));
return (r & __mask);
}
static inline uniform int popcnt(bool v) {
// As with any() and all(), only count across the active lanes
return __popcnt(__movmsk(v & __mask));
}
static inline uniform int lanemask() {
return __movmsk(__mask);
}
///////////////////////////////////////////////////////////////////////////
// Horizontal ops / reductions
static inline uniform float reduce_add(float x) {
// zero the lanes where the mask is off
return __reduce_add_float(__mask ? x : 0.);
}
static inline uniform float reduce_min(float v) {
// For the lanes where the mask is off, replace the given value with
// infinity, so that it doesn't affect the result.
int iflt_max = 0x7f800000; // infinity
// Must use __floatbits_varying_int32, not floatbits(), since with the
// latter the current mask enters into the returned result...
return __reduce_min_float(__mask ? v : __floatbits_varying_int32(iflt_max));
}
static inline uniform float reduce_max(float v) {
// For the lanes where the mask is off, replace the given value with
// negative infinity, so that it doesn't affect the result.
const uniform int iflt_neg_max = 0xff800000; // -infinity
// Must use __floatbits_varying_int32, not floatbits(), since with the
// latter the current mask enters into the returned result...
return __reduce_max_float(__mask ? v : __floatbits_varying_int32(iflt_neg_max));
}
static inline uniform int reduce_add(int x) {
// Zero out the values for lanes that aren't running
return __reduce_add_int32(x & (int)__mask);
}
static inline uniform int reduce_min(int v) {
// Set values for non-running lanes to the maximum integer value so
// they don't affect the result.
int int_max = 0x7fffffff;
return __reduce_min_int32(__mask ? v : int_max);
}
static inline uniform int reduce_max(int v) {
// Set values for non-running lanes to the minimum integer value so
// they don't affect the result.
int int_min = 0x80000000;
return __reduce_max_int32(__mask ? v : int_min);
}
static inline uniform unsigned int reduce_add(unsigned int x) {
// Set values for non-running lanes to zero so they don't affect the
// result.
return __reduce_add_uint32(x & (int)__mask);
}
static inline uniform unsigned int reduce_min(unsigned int v) {
// Set values for non-running lanes to the maximum unsigned integer
// value so they don't affect the result.
unsigned int uint_max = 0xffffffff;
return __reduce_min_uint32(__mask ? v : uint_max);
}
static inline uniform unsigned int reduce_max(unsigned int v) {
// Set values for non-running lanes to zero so they don't affect the
// result.
return __reduce_max_uint32(__mask ? v : 0);
}
///////////////////////////////////////////////////////////////////////////
// packed load, store
static inline uniform unsigned int packed_load_active(uniform int a[], uniform int start,
reference int vals) {
return __packed_load_active(a, start, vals, __mask);
}
static inline uniform unsigned int packed_store_active(uniform int a[], uniform int start,
int vals) {
return __packed_store_active(a, start, vals, __mask);
}
///////////////////////////////////////////////////////////////////////////
// Load/store from/to 8/16-bit types
static inline unsigned int load_from_int8(uniform int a[], uniform int offset) {
return __load_uint8(a, offset);
}
static inline void store_to_int8(uniform int a[], uniform int offset,
unsigned int val) {
__store_uint8(a, offset, val, __mask);
}
static inline unsigned int load_from_int16(uniform int a[], uniform int offset) {
return __load_uint16(a, offset);
}
static inline void store_to_int16(uniform int a[], uniform int offset,
unsigned int val) {
__store_uint16(a, offset, val, __mask);
}
///////////////////////////////////////////////////////////////////////////
// Math
static inline float abs(float a) {
// Floating-point hack: zeroing the high bit clears the sign
unsigned int i = intbits(a);
i &= 0x7fffffff;
return floatbits(i);
}
static inline uniform float abs(uniform float a) {
uniform unsigned int i = intbits(a);
i &= 0x7fffffff;
return floatbits(i);
}
static inline unsigned int signbits(float x) {
unsigned int i = intbits(x);
return (i & 0x80000000u);
}
static inline uniform unsigned int signbits(uniform float x) {
uniform unsigned int i = intbits(x);
return (i & 0x80000000u);
}
static inline float round(float x) {
return __round_varying_float(x);
}
static inline uniform float round(uniform float x) {
return __round_uniform_float(x);
}
static inline float floor(float x) {
return __floor_varying_float(x);
}
static inline uniform float floor(uniform float x) {
return __floor_uniform_float(x);
}
static inline float ceil(float x) {
return __ceil_varying_float(x);
}
static inline uniform float ceil(uniform float x) {
return __ceil_uniform_float(x);
}
static inline float rcp(float v) {
return __rcp_varying_float(v);
}
static inline uniform float rcp(uniform float v) {
return __rcp_uniform_float(v);
}
static inline float sqrt(float v) {
return __sqrt_varying_float(v);
}
static inline uniform float sqrt(uniform float v) {
return __sqrt_uniform_float(v);
}
static inline float min(float a, float b) {
return __min_varying_float(a, b);
}
static inline uniform float min(uniform float a, uniform float b) {
return __min_uniform_float(a, b);
}
static inline float max(float a, float b) {
return __max_varying_float(a, b);
}
static inline uniform float max(uniform float a, uniform float b) {
return __max_uniform_float(a, b);
}
static inline unsigned int min(unsigned int a, unsigned int b) {
return __min_varying_uint32(a, b);
}
static inline uniform unsigned int min(uniform unsigned int a, uniform unsigned int b) {
return __min_uniform_uint32(a, b);
}
static inline unsigned int max(unsigned int a, unsigned int b) {
return __max_varying_uint32(a, b);
}
static inline uniform unsigned int max(uniform unsigned int a, uniform unsigned int b) {
return __max_uniform_uint32(a, b);
}
static inline int min(int a, int b) {
return __min_varying_int32(a, b);
}
static inline uniform int min(uniform int a, uniform int b) {
return __min_uniform_int32(a, b);
}
static inline int max(int a, int b) {
return __max_varying_int32(a, b);
}
static inline uniform int max(uniform int a, uniform int b) {
return __max_uniform_int32(a, b);
}
static inline float clamp(float v, float low, float high) {
return min(max(v, low), high);
}
static inline uniform float clamp(uniform float v, uniform float low, uniform float high) {
return min(max(v, low), high);
}
static inline unsigned int clamp(unsigned int v, unsigned int low, unsigned int high) {
return min(max(v, low), high);
}
static inline uniform unsigned int clamp(uniform unsigned int v, uniform unsigned int low,
uniform unsigned int high) {
return min(max(v, low), high);
}
static inline int clamp(int v, int low, int high) {
return min(max(v, low), high);
}
static inline uniform int clamp(uniform int v, uniform int low, uniform int high) {
return min(max(v, low), high);
}
///////////////////////////////////////////////////////////////////////////
// Transcendentals
static inline float rsqrt(float v) {
return __rsqrt_varying_float(v);
}
static inline uniform float rsqrt(uniform float v) {
return __rsqrt_uniform_float(v);
}
static inline float ldexp(float x, int n) {
unsigned int ex = 0x7F800000u;
unsigned int ix = intbits(x);
ex &= ix; // extract old exponent;
ix = ix & ~0x7F800000u; // clear exponent
n = (n << 23) + ex;
ix |= n; // insert new exponent
return floatbits(ix);
}
static inline uniform float ldexp(uniform float x, uniform int n) {
uniform unsigned int ex = 0x7F800000u;
uniform unsigned int ix = intbits(x);
ex &= ix; // extract old exponent;
ix = ix & ~0x7F800000u; // clear exponent
n = (n << 23) + ex;
ix |= n; // insert new exponent
return floatbits(ix);
}
static inline float frexp(float x, reference int pw2) {
unsigned int ex = 0x7F800000u; // exponent mask
unsigned int ix = intbits(x);
ex &= ix;
ix &= ~0x7F800000u; // clear exponent
pw2 = (int)(ex >> 23) - 126; // compute exponent
ix |= 0x3F000000u; // insert exponent +1 in x
return floatbits(ix);
}
static inline uniform float frexp(uniform float x, reference uniform int pw2) {
uniform unsigned int ex = 0x7F800000u; // exponent mask
uniform unsigned int ix = intbits(x);
ex &= ix;
ix &= ~0x7F800000u; // clear exponent
pw2 = (uniform int)(ex >> 23) - 126; // compute exponent
ix |= 0x3F000000u; // insert exponent +1 in x
return floatbits(ix);
}
// Most of the transcendental implementations in ispc code here come from
// Solomon Boulos's "syrah": https://github.com/boulos/syrah/
static inline float sin(float x_full) {
if (__math_lib == __math_lib_svml) {
return __svml_sin(x_full);
}
else if (__math_lib == __math_lib_system) {
float ret;
uniform int mask = lanemask();
for (uniform int i = 0; i < programCount; ++i) {
if ((mask & (1 << i)) == 0)
continue;
uniform float r = __stdlib_sin(extract(x_full, i));
ret = insert(ret, i, r);
}
return ret;
}
else if (__math_lib == __math_lib_ispc ||
__math_lib == __math_lib_ispc_fast) {
static const float pi_over_two_vec = 1.57079637050628662109375;
static const float two_over_pi_vec = 0.636619746685028076171875;
float scaled = x_full * two_over_pi_vec;
float k_real = floor(scaled);
int k = (int)k_real;
// Reduced range version of x
float x = x_full - k_real * pi_over_two_vec;
int k_mod4 = k & 3;
bool sin_usecos = (k_mod4 == 1 || k_mod4 == 3);
bool flip_sign = (k_mod4 > 1);
// These coefficients are from sollya with fpminimax(sin(x)/x, [|0, 2,
// 4, 6, 8, 10|], [|single...|], [0;Pi/2]);
static const float sin_c2 = -0.16666667163372039794921875;
static const float sin_c4 = 8.333347737789154052734375e-3;
static const float sin_c6 = -1.9842604524455964565277099609375e-4;
static const float sin_c8 = 2.760012648650445044040679931640625e-6;
static const float sin_c10 = -2.50293279435709337121807038784027099609375e-8;
static const float cos_c2 = -0.5;
static const float cos_c4 = 4.166664183139801025390625e-2;
static const float cos_c6 = -1.388833043165504932403564453125e-3;
static const float cos_c8 = 2.47562347794882953166961669921875e-5;
static const float cos_c10 = -2.59630184018533327616751194000244140625e-7;
float outside = sin_usecos ? 1 : x;
float c2 = sin_usecos ? cos_c2 : sin_c2;
float c4 = sin_usecos ? cos_c4 : sin_c4;
float c6 = sin_usecos ? cos_c6 : sin_c6;
float c8 = sin_usecos ? cos_c8 : sin_c8;
float c10 = sin_usecos ? cos_c10 : sin_c10;
float x2 = x * x;
float formula = x2 * c10 + c8;
formula = x2 * formula + c6;
formula = x2 * formula + c4;
formula = x2 * formula + c2;
formula = x2 * formula + 1;
formula *= outside;
formula = flip_sign ? -formula : formula;
return formula;
}
}
static inline uniform float sin(uniform float x_full) {
if (__math_lib == __math_lib_system ||
__math_lib == __math_lib_svml) {
return __stdlib_sin(x_full);
}
else if (__math_lib == __math_lib_ispc ||
__math_lib == __math_lib_ispc_fast) {
static const uniform float pi_over_two_vec = 1.57079637050628662109375;
static const uniform float two_over_pi_vec = 0.636619746685028076171875;
uniform float scaled = x_full * two_over_pi_vec;
uniform float k_real = floor(scaled);
uniform int k = (int)k_real;
// Reduced range version of x
uniform float x = x_full - k_real * pi_over_two_vec;
uniform int k_mod4 = k & 3;
uniform bool sin_usecos = (k_mod4 == 1 || k_mod4 == 3);
uniform bool flip_sign = (k_mod4 > 1);
// These coefficients are from sollya with fpminimax(sin(x)/x, [|0, 2,
// 4, 6, 8, 10|], [|single...|], [0;Pi/2]);
static const uniform float sin_c2 = -0.16666667163372039794921875;
static const uniform float sin_c4 = 8.333347737789154052734375e-3;
static const uniform float sin_c6 = -1.9842604524455964565277099609375e-4;
static const uniform float sin_c8 = 2.760012648650445044040679931640625e-6;
static const uniform float sin_c10 = -2.50293279435709337121807038784027099609375e-8;
static const uniform float cos_c2 = -0.5;
static const uniform float cos_c4 = 4.166664183139801025390625e-2;
static const uniform float cos_c6 = -1.388833043165504932403564453125e-3;
static const uniform float cos_c8 = 2.47562347794882953166961669921875e-5;
static const uniform float cos_c10 = -2.59630184018533327616751194000244140625e-7;
uniform float outside, c2, c4, c6, c8, c10;
if (sin_usecos) {
outside = 1.;
c2 = cos_c2;
c4 = cos_c4;
c6 = cos_c6;
c8 = cos_c8;
c10 = cos_c10;
}
else {
outside = x;
c2 = sin_c2;
c4 = sin_c4;
c6 = sin_c6;
c8 = sin_c8;
c10 = sin_c10;
}
uniform float x2 = x * x;
uniform float formula = x2 * c10 + c8;
formula = x2 * formula + c6;
formula = x2 * formula + c4;
formula = x2 * formula + c2;
formula = x2 * formula + 1.;
formula *= outside;
formula = flip_sign ? -formula : formula;
return formula;
}
}
static inline float cos(float x_full) {
if (__math_lib == __math_lib_svml) {
return __svml_cos(x_full);
}
else if (__math_lib == __math_lib_system) {
float ret;
uniform int mask = lanemask();
for (uniform int i = 0; i < programCount; ++i) {
if ((mask & (1 << i)) == 0)
continue;
uniform float r = __stdlib_cos(extract(x_full, i));
ret = insert(ret, i, r);
}
return ret;
}
else if (__math_lib == __math_lib_ispc ||
__math_lib == __math_lib_ispc_fast) {
static const float pi_over_two_vec = 1.57079637050628662109375;
static const float two_over_pi_vec = 0.636619746685028076171875;
float scaled = x_full * two_over_pi_vec;
float k_real = floor(scaled);
int k = (int)k_real;
// Reduced range version of x
float x = x_full - k_real * pi_over_two_vec;
int k_mod4 = k & 3;
bool cos_usecos = (k_mod4 == 0 || k_mod4 == 2);
bool flip_sign = (k_mod4 == 1 || k_mod4 == 2);
const float sin_c2 = -0.16666667163372039794921875;
const float sin_c4 = 8.333347737789154052734375e-3;
const float sin_c6 = -1.9842604524455964565277099609375e-4;
const float sin_c8 = 2.760012648650445044040679931640625e-6;
const float sin_c10 = -2.50293279435709337121807038784027099609375e-8;
const float cos_c2 = -0.5;
const float cos_c4 = 4.166664183139801025390625e-2;
const float cos_c6 = -1.388833043165504932403564453125e-3;
const float cos_c8 = 2.47562347794882953166961669921875e-5;
const float cos_c10 = -2.59630184018533327616751194000244140625e-7;
float outside = cos_usecos ? 1. : x;
float c2 = cos_usecos ? cos_c2 : sin_c2;
float c4 = cos_usecos ? cos_c4 : sin_c4;
float c6 = cos_usecos ? cos_c6 : sin_c6;
float c8 = cos_usecos ? cos_c8 : sin_c8;
float c10 = cos_usecos ? cos_c10 : sin_c10;
float x2 = x * x;
float formula = x2 * c10 + c8;
formula = x2 * formula + c6;
formula = x2 * formula + c4;
formula = x2 * formula + c2;
formula = x2 * formula + 1.;
formula *= outside;
formula = flip_sign ? -formula : formula;
return formula;
}
}
static inline uniform float cos(uniform float x_full) {
if (__math_lib == __math_lib_system ||
__math_lib == __math_lib_svml) {
return __stdlib_cos(x_full);
}
else if (__math_lib == __math_lib_ispc ||
__math_lib == __math_lib_ispc_fast) {
static const uniform float pi_over_two_vec = 1.57079637050628662109375;
static const uniform float two_over_pi_vec = 0.636619746685028076171875;
uniform float scaled = x_full * two_over_pi_vec;
uniform float k_real = floor(scaled);
uniform int k = (int)k_real;
// Reduced range version of x
uniform float x = x_full - k_real * pi_over_two_vec;
uniform int k_mod4 = k & 3;
uniform bool cos_usecos = (k_mod4 == 0 || k_mod4 == 2);
uniform bool flip_sign = (k_mod4 == 1 || k_mod4 == 2);
const uniform float sin_c2 = -0.16666667163372039794921875;
const uniform float sin_c4 = 8.333347737789154052734375e-3;
const uniform float sin_c6 = -1.9842604524455964565277099609375e-4;
const uniform float sin_c8 = 2.760012648650445044040679931640625e-6;
const uniform float sin_c10 = -2.50293279435709337121807038784027099609375e-8;
const uniform float cos_c2 = -0.5;
const uniform float cos_c4 = 4.166664183139801025390625e-2;
const uniform float cos_c6 = -1.388833043165504932403564453125e-3;
const uniform float cos_c8 = 2.47562347794882953166961669921875e-5;
const uniform float cos_c10 = -2.59630184018533327616751194000244140625e-7;
uniform float outside, c2, c4, c6, c8, c10;
if (cos_usecos) {
outside = 1.;
c2 = cos_c2;
c4 = cos_c4;
c6 = cos_c6;
c8 = cos_c8;
c10 = cos_c10;
}
else {
outside = x;
c2 = sin_c2;
c4 = sin_c4;
c6 = sin_c6;
c8 = sin_c8;
c10 = sin_c10;
}
uniform float x2 = x * x;
uniform float formula = x2 * c10 + c8;
formula = x2 * formula + c6;
formula = x2 * formula + c4;
formula = x2 * formula + c2;
formula = x2 * formula + 1.;
formula *= outside;
formula = flip_sign ? -formula : formula;
return formula;
}
}
static inline void sincos(float x_full, reference float sin_result, reference float cos_result) {
if (__math_lib == __math_lib_svml) {
__svml_sincos(x_full, sin_result, cos_result);
}
else if (__math_lib == __math_lib_system) {
uniform int mask = lanemask();
for (uniform int i = 0; i < programCount; ++i) {
if ((mask & (1 << i)) == 0)
continue;
uniform float s, c;
__stdlib_sincos(extract(x_full, i), s, c);
sin_result = insert(sin_result, i, s);
cos_result = insert(cos_result, i, c);
}
}
else if (__math_lib == __math_lib_ispc ||
__math_lib == __math_lib_ispc_fast) {
const float pi_over_two_vec = 1.57079637050628662109375;
const float two_over_pi_vec = 0.636619746685028076171875;
float scaled = x_full * two_over_pi_vec;
float k_real = floor(scaled);
int k = (int)k_real;
// Reduced range version of x
float x = x_full - k_real * pi_over_two_vec;
int k_mod4 = k & 3;
bool cos_usecos = (k_mod4 == 0 || k_mod4 == 2);
bool sin_usecos = (k_mod4 == 1 || k_mod4 == 3);
bool sin_flipsign = (k_mod4 > 1);
bool cos_flipsign = (k_mod4 == 1 || k_mod4 == 2);
const float one_vec = 1.;
const float sin_c2 = -0.16666667163372039794921875;
const float sin_c4 = 8.333347737789154052734375e-3;
const float sin_c6 = -1.9842604524455964565277099609375e-4;
const float sin_c8 = 2.760012648650445044040679931640625e-6;
const float sin_c10 = -2.50293279435709337121807038784027099609375e-8;
const float cos_c2 = -0.5;
const float cos_c4 = 4.166664183139801025390625e-2;
const float cos_c6 = -1.388833043165504932403564453125e-3;
const float cos_c8 = 2.47562347794882953166961669921875e-5;
const float cos_c10 = -2.59630184018533327616751194000244140625e-7;
float x2 = x * x;
float sin_formula = x2 * sin_c10 + sin_c8;
float cos_formula = x2 * cos_c10 + cos_c8;
sin_formula = x2 * sin_formula + sin_c6;
cos_formula = x2 * cos_formula + cos_c6;
sin_formula = x2 * sin_formula + sin_c4;
cos_formula = x2 * cos_formula + cos_c4;
sin_formula = x2 * sin_formula + sin_c2;
cos_formula = x2 * cos_formula + cos_c2;
sin_formula = x2 * sin_formula + one_vec;
cos_formula = x2 * cos_formula + one_vec;
sin_formula *= x;
sin_result = sin_usecos ? cos_formula : sin_formula;
cos_result = cos_usecos ? cos_formula : sin_formula;
sin_result = sin_flipsign ? -sin_result : sin_result;
cos_result = cos_flipsign ? -cos_result : cos_result;
}
}
static inline void sincos(uniform float x_full, reference uniform float sin_result,
reference uniform float cos_result) {
if (__math_lib == __math_lib_system ||
__math_lib == __math_lib_svml) {
__stdlib_sincos(x_full, sin_result, cos_result);
}
else if (__math_lib == __math_lib_ispc ||
__math_lib == __math_lib_ispc_fast) {
const uniform float pi_over_two_vec = 1.57079637050628662109375;
const uniform float two_over_pi_vec = 0.636619746685028076171875;
uniform float scaled = x_full * two_over_pi_vec;
uniform float k_real = floor(scaled);
uniform int k = (uniform int)k_real;
// Reduced range version of x
uniform float x = x_full - k_real * pi_over_two_vec;
uniform int k_mod4 = k & 3;
uniform bool cos_usecos = (k_mod4 == 0 || k_mod4 == 2);
uniform bool sin_usecos = (k_mod4 == 1 || k_mod4 == 3);
uniform bool sin_flipsign = (k_mod4 > 1);
uniform bool cos_flipsign = (k_mod4 == 1 || k_mod4 == 2);
const uniform float one_vec = 1.;
const uniform float sin_c2 = -0.16666667163372039794921875;
const uniform float sin_c4 = 8.333347737789154052734375e-3;
const uniform float sin_c6 = -1.9842604524455964565277099609375e-4;
const uniform float sin_c8 = 2.760012648650445044040679931640625e-6;
const uniform float sin_c10 = -2.50293279435709337121807038784027099609375e-8;
const uniform float cos_c2 = -0.5;
const uniform float cos_c4 = 4.166664183139801025390625e-2;
const uniform float cos_c6 = -1.388833043165504932403564453125e-3;
const uniform float cos_c8 = 2.47562347794882953166961669921875e-5;
const uniform float cos_c10 = -2.59630184018533327616751194000244140625e-7;
uniform float x2 = x * x;
uniform float sin_formula = x2 * sin_c10 + sin_c8;
uniform float cos_formula = x2 * cos_c10 + cos_c8;
sin_formula = x2 * sin_formula + sin_c6;
cos_formula = x2 * cos_formula + cos_c6;
sin_formula = x2 * sin_formula + sin_c4;
cos_formula = x2 * cos_formula + cos_c4;
sin_formula = x2 * sin_formula + sin_c2;
cos_formula = x2 * cos_formula + cos_c2;
sin_formula = x2 * sin_formula + one_vec;
cos_formula = x2 * cos_formula + one_vec;
sin_formula *= x;
sin_result = sin_usecos ? cos_formula : sin_formula;
cos_result = cos_usecos ? cos_formula : sin_formula;
sin_result = sin_flipsign ? -sin_result : sin_result;
cos_result = cos_flipsign ? -cos_result : cos_result;
}
}
static inline float tan(float x_full) {
if (__math_lib == __math_lib_svml) {
return __svml_tan(x_full);
}
else if (__math_lib == __math_lib_system) {
float ret;
uniform int mask = lanemask();
for (uniform int i = 0; i < programCount; ++i) {
if ((mask & (1 << i)) == 0)
continue;
uniform float r = __stdlib_tan(extract(x_full, i));
ret = insert(ret, i, r);
}
return ret;
}
else if (__math_lib == __math_lib_ispc ||
__math_lib == __math_lib_ispc_fast) {
const float pi_over_four_vec = 0.785398185253143310546875;
const float four_over_pi_vec = 1.27323949337005615234375;
bool x_lt_0 = x_full < 0.;
float y = x_lt_0 ? -x_full : x_full;
float scaled = y * four_over_pi_vec;
float k_real = floor(scaled);
int k = (int)k_real;
float x = y - k_real * pi_over_four_vec;
// if k & 1, x -= Pi/4
bool need_offset = (k & 1) != 0;
x = need_offset ? x - pi_over_four_vec : x;
// if k & 3 == (0 or 3) let z = tan_In...(y) otherwise z = -cot_In0To...
int k_mod4 = k & 3;
bool use_cotan = (k_mod4 == 1) || (k_mod4 == 2);
const float one_vec = 1.0;
const float tan_c2 = 0.33333075046539306640625;
const float tan_c4 = 0.13339905440807342529296875;
const float tan_c6 = 5.3348250687122344970703125e-2;
const float tan_c8 = 2.46033705770969390869140625e-2;
const float tan_c10 = 2.892402000725269317626953125e-3;
const float tan_c12 = 9.500005282461643218994140625e-3;
const float cot_c2 = -0.3333333432674407958984375;
const float cot_c4 = -2.222204394638538360595703125e-2;
const float cot_c6 = -2.11752182804048061370849609375e-3;
const float cot_c8 = -2.0846328698098659515380859375e-4;
const float cot_c10 = -2.548247357481159269809722900390625e-5;
const float cot_c12 = -3.5257363606433500535786151885986328125e-7;
float x2 = x * x;
float z;
cif (use_cotan) {
float cot_val = x2 * cot_c12 + cot_c10;
cot_val = x2 * cot_val + cot_c8;
cot_val = x2 * cot_val + cot_c6;
cot_val = x2 * cot_val + cot_c4;
cot_val = x2 * cot_val + cot_c2;
cot_val = x2 * cot_val + one_vec;
// The equation is for x * cot(x) but we need -x * cot(x) for the tan part.
cot_val /= -x;
z = cot_val;
} else {
float tan_val = x2 * tan_c12 + tan_c10;
tan_val = x2 * tan_val + tan_c8;
tan_val = x2 * tan_val + tan_c6;
tan_val = x2 * tan_val + tan_c4;
tan_val = x2 * tan_val + tan_c2;
tan_val = x2 * tan_val + one_vec;
// Equation was for tan(x)/x
tan_val *= x;
z = tan_val;
}
return x_lt_0 ? -z : z;
}
}
static inline uniform float tan(uniform float x_full) {
if (__math_lib == __math_lib_system ||
__math_lib == __math_lib_svml) {
return __stdlib_tan(x_full);
}
else if (__math_lib == __math_lib_ispc ||
__math_lib == __math_lib_ispc_fast) {
const uniform float pi_over_four_vec = 0.785398185253143310546875;
const uniform float four_over_pi_vec = 1.27323949337005615234375;
uniform bool x_lt_0 = x_full < 0.;
uniform float y = x_lt_0 ? -x_full : x_full;
uniform float scaled = y * four_over_pi_vec;
uniform float k_real = floor(scaled);
uniform int k = (int)k_real;
uniform float x = y - k_real * pi_over_four_vec;
// if k & 1, x -= Pi/4
uniform bool need_offset = (k & 1) != 0;
x = need_offset ? x - pi_over_four_vec : x;
// if k & 3 == (0 or 3) let z = tan_In...(y) otherwise z = -cot_In0To...
uniform int k_mod4 = k & 3;
uniform bool use_cotan = (k_mod4 == 1) || (k_mod4 == 2);
const uniform float one_vec = 1.0;
const uniform float tan_c2 = 0.33333075046539306640625;
const uniform float tan_c4 = 0.13339905440807342529296875;
const uniform float tan_c6 = 5.3348250687122344970703125e-2;
const uniform float tan_c8 = 2.46033705770969390869140625e-2;
const uniform float tan_c10 = 2.892402000725269317626953125e-3;
const uniform float tan_c12 = 9.500005282461643218994140625e-3;
const uniform float cot_c2 = -0.3333333432674407958984375;
const uniform float cot_c4 = -2.222204394638538360595703125e-2;
const uniform float cot_c6 = -2.11752182804048061370849609375e-3;
const uniform float cot_c8 = -2.0846328698098659515380859375e-4;
const uniform float cot_c10 = -2.548247357481159269809722900390625e-5;
const uniform float cot_c12 = -3.5257363606433500535786151885986328125e-7;
uniform float x2 = x * x;
uniform float z;
if (use_cotan) {
uniform float cot_val = x2 * cot_c12 + cot_c10;
cot_val = x2 * cot_val + cot_c8;
cot_val = x2 * cot_val + cot_c6;
cot_val = x2 * cot_val + cot_c4;
cot_val = x2 * cot_val + cot_c2;
cot_val = x2 * cot_val + one_vec;
// The equation is for x * cot(x) but we need -x * cot(x) for the tan part.
cot_val /= -x;
z = cot_val;
} else {
uniform float tan_val = x2 * tan_c12 + tan_c10;
tan_val = x2 * tan_val + tan_c8;
tan_val = x2 * tan_val + tan_c6;
tan_val = x2 * tan_val + tan_c4;
tan_val = x2 * tan_val + tan_c2;
tan_val = x2 * tan_val + one_vec;
// Equation was for tan(x)/x
tan_val *= x;
z = tan_val;
}
return x_lt_0 ? -z : z;
}
}
static inline float atan(float x_full) {
if (__math_lib == __math_lib_svml) {
return __svml_atan(x_full);
}
else if (__math_lib == __math_lib_system) {
float ret;
uniform int mask = lanemask();
for (uniform int i = 0; i < programCount; ++i) {
if ((mask & (1 << i)) == 0)
continue;
uniform float r = __stdlib_atan(extract(x_full, i));
ret = insert(ret, i, r);
}
return ret;
}
else if (__math_lib == __math_lib_ispc ||
__math_lib == __math_lib_ispc_fast) {
const float pi_over_two_vec = 1.57079637050628662109375;
// atan(-x) = -atan(x) (so flip from negative to positive first)
// if x > 1 -> atan(x) = Pi/2 - atan(1/x)
bool x_neg = x_full < 0;
float x_flipped = x_neg ? -x_full : x_full;
bool x_gt_1 = x_flipped > 1.;
float x = x_gt_1 ? 1./x_flipped : x_flipped;
// These coefficients approximate atan(x)/x
const float atan_c0 = 0.99999988079071044921875;
const float atan_c2 = -0.3333191573619842529296875;
const float atan_c4 = 0.199689209461212158203125;
const float atan_c6 = -0.14015688002109527587890625;
const float atan_c8 = 9.905083477497100830078125e-2;
const float atan_c10 = -5.93664981424808502197265625e-2;
const float atan_c12 = 2.417283318936824798583984375e-2;
const float atan_c14 = -4.6721356920897960662841796875e-3;
float x2 = x * x;
float result = x2 * atan_c14 + atan_c12;
result = x2 * result + atan_c10;
result = x2 * result + atan_c8;
result = x2 * result + atan_c6;
result = x2 * result + atan_c4;
result = x2 * result + atan_c2;
result = x2 * result + atan_c0;
result *= x;
result = x_gt_1 ? pi_over_two_vec - result : result;
result = x_neg ? -result : result;
return result;
}
}
static inline uniform float atan(uniform float x_full) {
if (__math_lib == __math_lib_system ||
__math_lib == __math_lib_svml) {
return __stdlib_atan(x_full);
}
else if (__math_lib == __math_lib_ispc ||
__math_lib == __math_lib_ispc_fast) {
const uniform float pi_over_two_vec = 1.57079637050628662109375;
// atan(-x) = -atan(x) (so flip from negative to positive first)
// if x > 1 -> atan(x) = Pi/2 - atan(1/x)
uniform bool x_neg = x_full < 0;
uniform float x_flipped = x_neg ? -x_full : x_full;
uniform bool x_gt_1 = x_flipped > 1.;
uniform float x = x_gt_1 ? 1./x_flipped : x_flipped;
// These coefficients approximate atan(x)/x
const uniform float atan_c0 = 0.99999988079071044921875;
const uniform float atan_c2 = -0.3333191573619842529296875;
const uniform float atan_c4 = 0.199689209461212158203125;
const uniform float atan_c6 = -0.14015688002109527587890625;
const uniform float atan_c8 = 9.905083477497100830078125e-2;
const uniform float atan_c10 = -5.93664981424808502197265625e-2;
const uniform float atan_c12 = 2.417283318936824798583984375e-2;
const uniform float atan_c14 = -4.6721356920897960662841796875e-3;
uniform float x2 = x * x;
uniform float result = x2 * atan_c14 + atan_c12;
result = x2 * result + atan_c10;
result = x2 * result + atan_c8;
result = x2 * result + atan_c6;
result = x2 * result + atan_c4;
result = x2 * result + atan_c2;
result = x2 * result + atan_c0;
result *= x;
result = x_gt_1 ? pi_over_two_vec - result : result;
result = x_neg ? -result : result;
return result;
}
}
static inline float atan2(float y, float x) {
if (__math_lib == __math_lib_svml) {
return __svml_atan2(y, x);
}
else if (__math_lib == __math_lib_system) {
float ret;
uniform int mask = lanemask();
for (uniform int i = 0; i < programCount; ++i) {
if ((mask & (1 << i)) == 0)
continue;
uniform float r = __stdlib_atan2(extract(y, i), extract(x, i));
ret = insert(ret, i, r);
}
return ret;
}
else if (__math_lib == __math_lib_ispc ||
__math_lib == __math_lib_ispc_fast) {
const float pi_vec = 3.1415926536;
const float pi_over_two_vec = 1.5707963267;
// atan2(y, x) =
//
// atan2(y > 0, x = +-0) -> Pi/2
// atan2(y < 0, x = +-0) -> -Pi/2
// atan2(y = +-0, x < +0) -> +-Pi
// atan2(y = +-0, x >= +0) -> +-0
//
// atan2(y >= 0, x < 0) -> Pi + atan(y/x)
// atan2(y < 0, x < 0) -> -Pi + atan(y/x)
// atan2(y, x > 0) -> atan(y/x)
//
// and then a bunch of code for dealing with infinities.
float y_over_x = y/x;
float atan_arg = atan(y_over_x);
bool x_lt_0 = x < 0;
bool y_lt_0 = y < 0;
float offset = x_lt_0 ? (y_lt_0 ? -pi_vec : pi_vec) : 0;
return offset + atan_arg;
}
}
static inline uniform float atan2(uniform float y, uniform float x) {
if (__math_lib == __math_lib_system ||
__math_lib == __math_lib_svml) {
return __stdlib_atan2(y, x);
}
else if (__math_lib == __math_lib_ispc ||
__math_lib == __math_lib_ispc_fast) {
const uniform float pi_vec = 3.1415927410125732421875;
const uniform float pi_over_two_vec = 1.57079637050628662109375;
uniform float y_over_x = y/x;
uniform float atan_arg = atan(y_over_x);
uniform bool x_lt_0 = x < 0;
uniform bool y_lt_0 = y < 0;
uniform float offset = x_lt_0 ? (y_lt_0 ? -pi_vec : pi_vec) : 0;
return offset + atan_arg;
}
}
static inline float exp(float x_full) {
if (__math_lib == __math_lib_svml) {
return __svml_exp(x_full);
}
else if (__math_lib == __math_lib_system) {
float ret;
uniform int mask = lanemask();
for (uniform int i = 0; i < programCount; ++i) {
if ((mask & (1 << i)) == 0)
continue;
uniform float r = __stdlib_exp(extract(x_full, i));
ret = insert(ret, i, r);
}
return ret;
}
else if (__math_lib == __math_lib_ispc_fast) {
float z = floor(1.44269504088896341f * x_full + 0.5f);
int n;
x_full -= z * 0.693359375f;
x_full -= z * -2.12194440e-4f;
n = (int)z;
z = x_full * x_full;
z = (((((1.9875691500E-4f * x_full + 1.3981999507E-3f) * x_full +
8.3334519073E-3f) * x_full + 4.1665795894E-2f) * x_full +
1.6666665459E-1f) * x_full + 5.0000001201E-1f) * z + x_full + 1.f;
x_full = ldexp(z, n);
return x_full;
}
else if (__math_lib == __math_lib_ispc) {
const float ln2_part1 = 0.6931457519;
const float ln2_part2 = 1.4286067653e-6;
const float one_over_ln2 = 1.44269502162933349609375;
float scaled = x_full * one_over_ln2;
float k_real = floor(scaled);
int k = (int)k_real;
// Reduced range version of x
float x = x_full - k_real * ln2_part1;
x -= k_real * ln2_part2;
// These coefficients are for e^x in [0, ln(2)]
const float one = 1.;
const float c2 = 0.4999999105930328369140625;
const float c3 = 0.166668415069580078125;
const float c4 = 4.16539050638675689697265625e-2;
const float c5 = 8.378830738365650177001953125e-3;
const float c6 = 1.304379315115511417388916015625e-3;
const float c7 = 2.7555381529964506626129150390625e-4;
float result = x * c7 + c6;
result = x * result + c5;
result = x * result + c4;
result = x * result + c3;
result = x * result + c2;
result = x * result + one;
result = x * result + one;
// Compute 2^k (should differ for float and double, but I'll avoid
// it for now and just do floats)
const int fpbias = 127;
int biased_n = k + fpbias;
bool overflow = k > fpbias;
// Minimum exponent is -126, so if k is <= -127 (k + 127 <= 0)
// we've got underflow. -127 * ln(2) -> -88.02. So the most
// negative float input that doesn't result in zero is like -88.
bool underflow = (biased_n <= 0);
const int InfBits = 0x7f800000;
biased_n <<= 23;
// Reinterpret this thing as float
float two_to_the_n = floatbits(biased_n);
// Handle both doubles and floats (hopefully eliding the copy for float)
float elemtype_2n = two_to_the_n;
result *= elemtype_2n;
result = overflow ? floatbits(InfBits) : result;
result = underflow ? 0. : result;
return result;
}
}
static inline uniform float exp(uniform float x_full) {
if (__math_lib == __math_lib_system ||
__math_lib == __math_lib_svml) {
return __stdlib_exp(x_full);
}
else if (__math_lib == __math_lib_ispc_fast) {
uniform float z = floor(1.44269504088896341f * x_full + 0.5f);
uniform int n;
x_full -= z * 0.693359375f;
x_full -= z * -2.12194440e-4f;
n = (int)z;
z = x_full * x_full;
z = (((((1.9875691500E-4f * x_full + 1.3981999507E-3f) * x_full +
8.3334519073E-3f) * x_full + 4.1665795894E-2f) * x_full +
1.6666665459E-1f) * x_full + 5.0000001201E-1f) * z + x_full + 1.f;
x_full = ldexp(z, n);
return x_full;
}
else if (__math_lib == __math_lib_ispc) {
const uniform float ln2_part1 = 0.6931457519;
const uniform float ln2_part2 = 1.4286067653e-6;
const uniform float one_over_ln2 = 1.44269502162933349609375;
uniform float scaled = x_full * one_over_ln2;
uniform float k_real = floor(scaled);
uniform int k = (uniform int)k_real;
// Reduced range version of x
uniform float x = x_full - k_real * ln2_part1;
x -= k_real * ln2_part2;
// These coefficients are for e^x in [0, ln(2)]
const uniform float one = 1.;
const uniform float c2 = 0.4999999105930328369140625;
const uniform float c3 = 0.166668415069580078125;
const uniform float c4 = 4.16539050638675689697265625e-2;
const uniform float c5 = 8.378830738365650177001953125e-3;
const uniform float c6 = 1.304379315115511417388916015625e-3;
const uniform float c7 = 2.7555381529964506626129150390625e-4;
uniform float result = x * c7 + c6;
result = x * result + c5;
result = x * result + c4;
result = x * result + c3;
result = x * result + c2;
result = x * result + one;
result = x * result + one;
// Compute 2^k (should differ for uniform float and double, but I'll avoid
// it for now and just do uniform floats)
const uniform int fpbias = 127;
uniform int biased_n = k + fpbias;
uniform bool overflow = k > fpbias;
// Minimum exponent is -126, so if k is <= -127 (k + 127 <= 0)
// we've got underflow. -127 * ln(2) -> -88.02. So the most
// negative uniform float input that doesn't result in zero is like -88.
uniform bool underflow = (biased_n <= 0);
const uniform int InfBits = 0x7f800000;
biased_n <<= 23;
// Reuniform interpret this thing as uniform float
uniform float two_to_the_n = floatbits(biased_n);
// Handle both doubles and uniform floats (hopefully eliding the copy for uniform float)
uniform float elemtype_2n = two_to_the_n;
result *= elemtype_2n;
result = overflow ? floatbits(InfBits) : result;
result = underflow ? 0. : result;
return result;
}
}
// Range reduction for logarithms takes log(x) -> log(2^n * y) -> n
// * log(2) + log(y) where y is the reduced range (usually in [1/2,
// 1)).
static inline void __range_reduce_log(float input, reference float reduced, reference int exponent) {
int int_version = intbits(input);
// single precision = SEEE EEEE EMMM MMMM MMMM MMMM MMMM MMMM
// exponent mask = 0111 1111 1000 0000 0000 0000 0000 0000
// 0x7 0xF 0x8 0x0 0x0 0x0 0x0 0x0
// non-exponent = 1000 0000 0111 1111 1111 1111 1111 1111
// = 0x8 0x0 0x7 0xF 0xF 0xF 0xF 0xF
//const int exponent_mask(0x7F800000)
static const int nonexponent_mask = 0x807FFFFF;
// We want the reduced version to have an exponent of -1 which is -1 + 127 after biasing or 126
static const int exponent_neg1 = (126 << 23);
// NOTE(boulos): We don't need to mask anything out since we know
// the sign bit has to be 0. If it's 1, we need to return infinity/nan
// anyway (log(x), x = +-0 -> infinity, x < 0 -> NaN).
int biased_exponent = int_version >> 23; // This number is [0, 255] but it means [-127, 128]
int offset_exponent = biased_exponent + 1; // Treat the number as if it were 2^{e+1} * (1.m)/2
exponent = offset_exponent - 127; // get the real value
// Blend the offset_exponent with the original input (do this in
// int for now, until I decide if float can have & and &not)
int blended = (int_version & nonexponent_mask) | (exponent_neg1);
reduced = floatbits(blended);
}
static inline void __range_reduce_log(uniform float input, reference uniform float reduced,
reference uniform int exponent) {
uniform int int_version = intbits(input);
static const uniform int nonexponent_mask = 0x807FFFFF;
static const uniform int exponent_neg1 = (126 << 23);
uniform int biased_exponent = int_version >> 23;
uniform int offset_exponent = biased_exponent + 1;
exponent = offset_exponent - 127; // get the real value
uniform int blended = (int_version & nonexponent_mask) | (exponent_neg1);
reduced = floatbits(blended);
}
static inline float log(float x_full) {
if (__math_lib == __math_lib_svml) {
return __svml_log(x_full);
}
else if (__math_lib == __math_lib_system) {
float ret;
uniform int mask = lanemask();
for (uniform int i = 0; i < programCount; ++i) {
if ((mask & (1 << i)) == 0)
continue;
uniform float r = __stdlib_log(extract(x_full, i));
ret = insert(ret, i, r);
}
return ret;
}
else if (__math_lib == __math_lib_ispc_fast) {
int e;
x_full = frexp(x_full, e);
int x_smaller_SQRTHF = (0.707106781186547524f > x_full) ? 0xffffffff : 0;
e += x_smaller_SQRTHF;
int ix_add = intbits(x_full);
ix_add &= x_smaller_SQRTHF;
x_full += floatbits(ix_add) - 1.f;
float z = x_full * x_full;
float y =
((((((((7.0376836292E-2f * x_full
+ -1.1514610310E-1f) * x_full
+ 1.1676998740E-1f) * x_full
+ -1.2420140846E-1f) * x_full
+ 1.4249322787E-1f) * x_full
+ -1.6668057665E-1f) * x_full
+ 2.0000714765E-1f) * x_full
+ -2.4999993993E-1f) * x_full
+ 3.3333331174E-1f) * x_full * z;
float fe = (float)e;
y += fe * -2.12194440e-4;
y -= 0.5f * z;
z = x_full + y;
return z + 0.693359375 * fe;
}
else if (__math_lib == __math_lib_ispc) {
float reduced;
int exponent;
const int NaN_bits = 0x7fc00000;
const int Neg_Inf_bits = 0xFF800000;
const float NaN = floatbits(NaN_bits);
const float neg_inf = floatbits(Neg_Inf_bits);
bool use_nan = x_full < 0.;
bool use_inf = x_full == 0.;
bool exceptional = use_nan || use_inf;
const float one = 1.0;
float patched = exceptional ? one : x_full;
__range_reduce_log(patched, reduced, exponent);
const float ln2 = 0.693147182464599609375;
float x1 = one - reduced;
const float c1 = 0.50000095367431640625;
const float c2 = 0.33326041698455810546875;
const float c3 = 0.2519190013408660888671875;
const float c4 = 0.17541764676570892333984375;
const float c5 = 0.3424419462680816650390625;
const float c6 = -0.599632322788238525390625;
const float c7 = +1.98442304134368896484375;
const float c8 = -2.4899270534515380859375;
const float c9 = +1.7491014003753662109375;
float result = x1 * c9 + c8;
result = x1 * result + c7;
result = x1 * result + c6;
result = x1 * result + c5;
result = x1 * result + c4;
result = x1 * result + c3;
result = x1 * result + c2;
result = x1 * result + c1;
result = x1 * result + one;
// Equation was for -(ln(red)/(1-red))
result *= -x1;
result += (float)(exponent) * ln2;
return exceptional ? (use_nan ? NaN : neg_inf) : result;
}
}
static inline uniform float log(uniform float x_full) {
if (__math_lib == __math_lib_system ||
__math_lib == __math_lib_svml) {
return __stdlib_log(x_full);
}
else if (__math_lib == __math_lib_ispc_fast) {
uniform int e;
x_full = frexp(x_full, e);
uniform int x_smaller_SQRTHF = (0.707106781186547524f > x_full) ? 0xffffffff : 0;
e += x_smaller_SQRTHF;
uniform int ix_add = intbits(x_full);
ix_add &= x_smaller_SQRTHF;
x_full += floatbits(ix_add) - 1.f;
uniform float z = x_full * x_full;
uniform float y =
((((((((7.0376836292E-2f * x_full
+ -1.1514610310E-1f) * x_full
+ 1.1676998740E-1f) * x_full
+ -1.2420140846E-1f) * x_full
+ 1.4249322787E-1f) * x_full
+ -1.6668057665E-1f) * x_full
+ 2.0000714765E-1f) * x_full
+ -2.4999993993E-1f) * x_full
+ 3.3333331174E-1f) * x_full * z;
uniform float fe = (uniform float)e;
y += fe * -2.12194440e-4;
y -= 0.5f * z;
z = x_full + y;
return z + 0.693359375 * fe;
}
else if (__math_lib == __math_lib_ispc) {
uniform float reduced;
uniform int exponent;
const uniform int NaN_bits = 0x7fc00000;
const uniform int Neg_Inf_bits = 0xFF800000;
const uniform float NaN = floatbits(NaN_bits);
const uniform float neg_inf = floatbits(Neg_Inf_bits);
uniform bool use_nan = x_full < 0.;
uniform bool use_inf = x_full == 0.;
uniform bool exceptional = use_nan || use_inf;
const uniform float one = 1.0;
uniform float patched = exceptional ? one : x_full;
__range_reduce_log(patched, reduced, exponent);
const uniform float ln2 = 0.693147182464599609375;
uniform float x1 = one - reduced;
const uniform float c1 = 0.50000095367431640625;
const uniform float c2 = 0.33326041698455810546875;
const uniform float c3 = 0.2519190013408660888671875;
const uniform float c4 = 0.17541764676570892333984375;
const uniform float c5 = 0.3424419462680816650390625;
const uniform float c6 = -0.599632322788238525390625;
const uniform float c7 = +1.98442304134368896484375;
const uniform float c8 = -2.4899270534515380859375;
const uniform float c9 = +1.7491014003753662109375;
uniform float result = x1 * c9 + c8;
result = x1 * result + c7;
result = x1 * result + c6;
result = x1 * result + c5;
result = x1 * result + c4;
result = x1 * result + c3;
result = x1 * result + c2;
result = x1 * result + c1;
result = x1 * result + one;
// Equation was for -(ln(red)/(1-red))
result *= -x1;
result += (uniform float)(exponent) * ln2;
return exceptional ? (use_nan ? NaN : neg_inf) : result;
}
}
static inline float pow(float a, float b) {
if (__math_lib == __math_lib_svml) {
return __svml_pow(a, b);
}
else if (__math_lib == __math_lib_system) {
float ret;
uniform int mask = lanemask();
for (uniform int i = 0; i < programCount; ++i) {
if ((mask & (1 << i)) == 0)
continue;
uniform float r = __stdlib_pow(extract(a, i), extract(b, i));
ret = insert(ret, i, r);
}
return ret;
}
else if (__math_lib == __math_lib_ispc ||
__math_lib == __math_lib_ispc_fast) {
return exp(b * log(a));
}
}
static inline uniform float pow(uniform float a, uniform float b) {
if (__math_lib == __math_lib_system ||
__math_lib == __math_lib_svml) {
return __stdlib_pow(a, b);
}
else if (__math_lib == __math_lib_ispc ||
__math_lib == __math_lib_ispc_fast) {
return exp(b * log(a));
}
}
///////////////////////////////////////////////////////////////////////////
// RNG stuff
struct RNGState {
unsigned int z1, z2, z3, z4;
};
static inline unsigned int random(reference uniform RNGState state)
{
unsigned int b;
b = ((state.z1 << 6) ^ state.z1) >> 13;
state.z1 = ((state.z1 & 4294967294U) << 18) ^ b;
b = ((state.z2 << 2) ^ state.z2) >> 27;
state.z2 = ((state.z2 & 4294967288U) << 2) ^ b;
b = ((state.z3 << 13) ^ state.z3) >> 21;
state.z3 = ((state.z3 & 4294967280U) << 7) ^ b;
b = ((state.z4 << 3) ^ state.z4) >> 12;
state.z4 = ((state.z4 & 4294967168U) << 13) ^ b;
return (state.z1 ^ state.z2 ^ state.z3 ^ state.z4);
}
static inline float frandom(reference uniform RNGState state)
{
return ((int)(random(state) & ((1<<24)-1))) / (float)(1 << 24);
}
static inline uniform unsigned int __seed4(reference uniform RNGState state,
uniform int start,
uniform unsigned int seed) {
uniform unsigned int c1 = 0xf0f0f0f0;
uniform unsigned int c2 = 0x0f0f0f0f;
state.z1 = insert(state.z1, start + 0, seed);
state.z1 = insert(state.z1, start + 1, seed ^ c1);
state.z1 = insert(state.z1, start + 2, (seed << 3) ^ c1);
state.z1 = insert(state.z1, start + 3, (seed << 2) ^ c2);
seed += 131;
state.z2 = insert(state.z2, start + 0, seed);
state.z2 = insert(state.z2, start + 1, seed ^ c1);
state.z2 = insert(state.z2, start + 2, (seed << 3) ^ c1);
state.z2 = insert(state.z2, start + 3, (seed << 2) ^ c2);
seed ^= extract(state.z2, 2);
state.z3 = insert(state.z3, start + 0, seed);
state.z3 = insert(state.z3, start + 1, seed ^ c1);
state.z3 = insert(state.z3, start + 2, (seed << 3) ^ c1);
state.z3 = insert(state.z3, start + 3, (seed << 2) ^ c2);
seed <<= 4;
seed += 3;
seed ^= extract(state.z1, 3);
state.z4 = insert(state.z4, start + 0, seed);
state.z4 = insert(state.z4, start + 1, seed ^ c1);
state.z4 = insert(state.z4, start + 2, (seed << 3) ^ c1);
state.z4 = insert(state.z4, start + 3, (seed << 2) ^ c2);
return seed;
}
static inline void seed_rng(reference uniform RNGState state, uniform unsigned int seed) {
seed = __seed4(state, 0, seed);
if (programCount == 8)
__seed4(state, 4, seed ^ 0xbeeff00d);
}
static inline void fastmath() {
__fastmath();
}
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