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