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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_ERF_H_
#define __FAST_ERF_H_
#include <math.h>
#include <stdint.h>
#include "sse.h"
#include "fastexp.h"
#include "fastlog.h"
// fasterfc: not actually faster than erfcf(3) on newer machines!
// ... although vectorized version is interesting
// and fastererfc is very fast
static inline float
fasterfc (float x)
{
static const float k = 3.3509633149424609f;
static const float a = 0.07219054755431126f;
static const float b = 15.418191568719577f;
static const float c = 5.609846028328545f;
union { float f; uint32_t i; } vc = { c * x };
float xsq = x * x;
float xquad = xsq * xsq;
vc.i |= 0x80000000;
return 2.0f / (1.0f + fastpow2 (k * x)) - a * x * (b * xquad - 1.0f) * fasterpow2 (vc.f);
}
static inline float
fastererfc (float x)
{
static const float k = 3.3509633149424609f;
return 2.0f / (1.0f + fasterpow2 (k * x));
}
// fasterf: not actually faster than erff(3) on newer machines!
// ... although vectorized version is interesting
// and fastererf is very fast
static inline float
fasterf (float x)
{
return 1.0f - fasterfc (x);
}
static inline float
fastererf (float x)
{
return 1.0f - fastererfc (x);
}
static inline float
fastinverseerf (float x)
{
static const float invk = 0.30004578719350504f;
static const float a = 0.020287853348211326f;
static const float b = 0.07236892874789555f;
static const float c = 0.9913030456864257f;
static const float d = 0.8059775923760193f;
float xsq = x * x;
return invk * fastlog2 ((1.0f + x) / (1.0f - x))
+ x * (a - b * xsq) / (c - d * xsq);
}
static inline float
fasterinverseerf (float x)
{
static const float invk = 0.30004578719350504f;
return invk * fasterlog2 ((1.0f + x) / (1.0f - x));
}
#ifdef __SSE2__
static inline v4sf
vfasterfc (v4sf x)
{
const v4sf k = v4sfl (3.3509633149424609f);
const v4sf a = v4sfl (0.07219054755431126f);
const v4sf b = v4sfl (15.418191568719577f);
const v4sf c = v4sfl (5.609846028328545f);
union { v4sf f; v4si i; } vc; vc.f = c * x;
vc.i |= v4sil (0x80000000);
v4sf xsq = x * x;
v4sf xquad = xsq * xsq;
return v4sfl (2.0f) / (v4sfl (1.0f) + vfastpow2 (k * x)) - a * x * (b * xquad - v4sfl (1.0f)) * vfasterpow2 (vc.f);
}
static inline v4sf
vfastererfc (const v4sf x)
{
const v4sf k = v4sfl (3.3509633149424609f);
return v4sfl (2.0f) / (v4sfl (1.0f) + vfasterpow2 (k * x));
}
static inline v4sf
vfasterf (v4sf x)
{
return v4sfl (1.0f) - vfasterfc (x);
}
static inline v4sf
vfastererf (const v4sf x)
{
return v4sfl (1.0f) - vfastererfc (x);
}
static inline v4sf
vfastinverseerf (v4sf x)
{
const v4sf invk = v4sfl (0.30004578719350504f);
const v4sf a = v4sfl (0.020287853348211326f);
const v4sf b = v4sfl (0.07236892874789555f);
const v4sf c = v4sfl (0.9913030456864257f);
const v4sf d = v4sfl (0.8059775923760193f);
v4sf xsq = x * x;
return invk * vfastlog2 ((v4sfl (1.0f) + x) / (v4sfl (1.0f) - x))
+ x * (a - b * xsq) / (c - d * xsq);
}
static inline v4sf
vfasterinverseerf (v4sf x)
{
const v4sf invk = v4sfl (0.30004578719350504f);
return invk * vfasterlog2 ((v4sfl (1.0f) + x) / (v4sfl (1.0f) - x));
}
#endif //__SSE2__
#endif // __FAST_ERF_H_
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