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/*=====================================================================*
* Copyright (C) 2011 Paul Mineiro *
* 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 Paul Mineiro nor the names *
* of other 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. *
* *
* Contact: Paul Mineiro <paul@mineiro.com> *
*=====================================================================*/
#ifndef __FAST_GAMMA_H_
#define __FAST_GAMMA_H_
#include <stdint.h>
#include "sse.h"
#include "fastlog.h"
/* gamma/digamma functions only work for positive inputs */
static inline float
fastlgamma (float x)
{
float logterm = fastlog (x * (1.0f + x) * (2.0f + x));
float xp3 = 3.0f + x;
return - 2.081061466f
- x
+ 0.0833333f / xp3
- logterm
+ (2.5f + x) * fastlog (xp3);
}
static inline float
fasterlgamma (float x)
{
return - 0.0810614667f
- x
- fasterlog (x)
+ (0.5f + x) * fasterlog (1.0f + x);
}
static inline float
fastdigamma (float x)
{
float twopx = 2.0f + x;
float logterm = fastlog (twopx);
return (-48.0f + x * (-157.0f + x * (-127.0f - 30.0f * x))) /
(12.0f * x * (1.0f + x) * twopx * twopx)
+ logterm;
}
static inline float
fasterdigamma (float x)
{
float onepx = 1.0f + x;
return -1.0f / x - 1.0f / (2 * onepx) + fasterlog (onepx);
}
#ifdef __SSE2__
static inline v4sf
vfastlgamma (v4sf x)
{
const v4sf c_1_0 = v4sfl (1.0f);
const v4sf c_2_0 = v4sfl (2.0f);
const v4sf c_3_0 = v4sfl (3.0f);
const v4sf c_2_081061466 = v4sfl (2.081061466f);
const v4sf c_0_0833333 = v4sfl (0.0833333f);
const v4sf c_2_5 = v4sfl (2.5f);
v4sf logterm = vfastlog (x * (c_1_0 + x) * (c_2_0 + x));
v4sf xp3 = c_3_0 + x;
return - c_2_081061466
- x
+ c_0_0833333 / xp3
- logterm
+ (c_2_5 + x) * vfastlog (xp3);
}
static inline v4sf
vfasterlgamma (v4sf x)
{
const v4sf c_0_0810614667 = v4sfl (0.0810614667f);
const v4sf c_0_5 = v4sfl (0.5f);
const v4sf c_1 = v4sfl (1.0f);
return - c_0_0810614667
- x
- vfasterlog (x)
+ (c_0_5 + x) * vfasterlog (c_1 + x);
}
static inline v4sf
vfastdigamma (v4sf x)
{
v4sf twopx = v4sfl (2.0f) + x;
v4sf logterm = vfastlog (twopx);
return (v4sfl (-48.0f) + x * (v4sfl (-157.0f) + x * (v4sfl (-127.0f) - v4sfl (30.0f) * x))) /
(v4sfl (12.0f) * x * (v4sfl (1.0f) + x) * twopx * twopx)
+ logterm;
}
static inline v4sf
vfasterdigamma (v4sf x)
{
const v4sf c_1_0 = v4sfl (1.0f);
const v4sf c_2_0 = v4sfl (2.0f);
v4sf onepx = c_1_0 + x;
return -c_1_0 / x - c_1_0 / (c_2_0 * onepx) + vfasterlog (onepx);
}
#endif //__SSE2__
#endif // __FAST_GAMMA_H_
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