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m/fast: add some fast maths approximations

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This commit is contained in:
Danny Robson 2015-07-29 16:11:48 +10:00
parent 48d6a007a2
commit eb155d5bb0
4 changed files with 193 additions and 0 deletions
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3
Makefile.am
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@ -127,6 +127,8 @@ UTIL_FILES = \
maths.cpp \
maths.hpp \
maths.ipp \
maths/fast.hpp \
maths/fast.ipp \
matrix.cpp \
matrix.hpp \
matrix.ipp \
@ -335,6 +337,7 @@ TEST_BIN = \
test/json_types \
test/ray \
test/maths \
test/maths_fast \
test/matrix \
test/md2 \
test/md4 \

44
maths/fast.hpp Normal file
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@ -0,0 +1,44 @@
/*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*
* Copyright 2015 Danny Robson <danny@nerdcruft.net>
*/
#ifndef __UTIL_MATHS_FAST_HPP
#define __UTIL_MATHS_FAST_HPP
namespace util { namespace maths { namespace fast {
///////////////////////////////////////////////////////////////////////////
constexpr float pow (float, float);
constexpr float pow2 (float);
///////////////////////////////////////////////////////////////////////////
constexpr float exp (float);
///////////////////////////////////////////////////////////////////////////
constexpr float log (float);
constexpr float log2 (float);
///////////////////////////////////////////////////////////////////////////
constexpr float sqrt (float);
constexpr float invsqrt (float);
} } }
#include "fast.ipp"
#endif

107
maths/fast.ipp Normal file
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@ -0,0 +1,107 @@
/*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*
* Copyright 2015 Danny Robson <danny@nerdcruft.net>
*/
#ifdef __UTIL_MATHS_FAST_IPP
#error
#endif
#define __UTIL_MATHS_FAST_IPP
namespace util { namespace maths { namespace fast {
///////////////////////////////////////////////////////////////////////////
constexpr float
pow2 (float p)
{
float offset = (p < 0) ? 1.0f : 0.0f;
float clipp = (p < -126) ? -126.0f : p;
int32_t w = static_cast<int32_t> (clipp);
float z = clipp - w + offset;
union { uint32_t i; float f; } v = { static_cast<uint32_t> ( (1 << 23) * (clipp + 121.2740575f + 27.7280233f / (4.84252568f - z) - 1.49012907f * z) ) };
return v.f;
//float clipp = (p < -126) ? -126.0f : p;
//union { uint32_t i; float f; } v = { static_cast<uint32_t> ( (1 << 23) * (clipp + 126.94269504f) ) };
//return v.f;
}
constexpr float
log2 (float x)
{
union { float f; uint32_t i; } vx = { x };
union { uint32_t i; float f; } mx = { (vx.i & 0x007FFFFF) | 0x3f000000 };
float y = vx.i;
y *= 1.1920928955078125e-7f;
return y - 124.22551499f
- 1.498030302f * mx.f
- 1.72587999f / (0.3520887068f + mx.f);
//union { float f; uint32_t i; } vx = { x };
//float y = vx.i;
//y *= 1.1920928955078125e-7f;
//return y - 126.94269504f;
}
constexpr float
log (float x)
{
return 0.69314718f * log2 (x);
}
constexpr float
pow (float a, float b)
{
return pow2 (b * log2 (a));
}
constexpr float
sqrt (float x)
{
//return pow (x, 0.5f);
union { float f; int32_t i; } u = { x };
int32_t v = u.i;
v -= 1 << 23;
v >>= 1;
v += 1 << 29;
u.i = v;
return u.f;
}
constexpr float
invsqrt (float x)
{
union
{
float x;
int32_t i;
} u = { x };
u.i = 0x5f3759df - (u.i >> 1);
// refine estimate. repeat as necessary.
u.x = u.x * (1.5f - x * 0.5f * u.x * u.x);
return u.x;
}
} } }

39
test/maths_fast.cpp Normal file
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@ -0,0 +1,39 @@
#include "tap.hpp"
#include "maths/fast.hpp"
constexpr float
threshold (float a, float b)
{
constexpr float PARTS = 100;
return std::abs (a + b) / 2 / PARTS;
}
int
main (void)
{
util::TAP::logger tap;
{
auto a = util::maths::fast::log2 (3.456f);
auto b = std::log2 (3.456f);
tap.expect_lt (std::abs (a - b), threshold (a, b), "fast log2");
}
{
auto a = util::maths::fast::pow2 (-100.f);
auto b = std::pow (2.f, -100.f);
tap.expect_lt (std::abs (a - b), threshold (a, b), "fast pow2");
}
{
auto a = util::maths::fast::pow (0.8f, 100.f);
auto b = std::pow (0.8f, 100.f);
tap.expect_lt (std::abs (a - b), threshold (a, b), "fast pow");
}
return tap.status ();
}