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121d608c3a
* Add fast fma functions * Use fast fma functions * Add fast pow function * Use fast pow function * Fix build * Remove fastFma * Avoid UB in fastPow On GCC with -O1 or -O2 optimizations, this new implementation generates identical assembly to the old union-based implementation
143 lines
3.7 KiB
C++
143 lines
3.7 KiB
C++
/*
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* interpolation.h - fast implementations of several interpolation-algorithms
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*
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* Copyright (c) 2004-2005 Tobias Doerffel <tobydox/at/users.sourceforge.net>
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*
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* This file is part of LMMS - https://lmms.io
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*
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* This program is free software; you can redistribute it and/or
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* modify it under the terms of the GNU General Public
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* License as published by the Free Software Foundation; either
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* version 2 of the License, or (at your option) any later version.
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*
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* This program is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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* General Public License for more details.
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*
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* You should have received a copy of the GNU General Public
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* License along with this program (see COPYING); if not, write to the
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* Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
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* Boston, MA 02110-1301 USA.
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*
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*/
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#ifndef LMMS_INTERPOLATION_H
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#define LMMS_INTERPOLATION_H
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#ifndef __USE_XOPEN
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#define __USE_XOPEN
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#endif
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#include <cmath>
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#include "lmms_constants.h"
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#include "lmms_math.h"
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namespace lmms
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{
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inline float hermiteInterpolate( float x0, float x1, float x2, float x3,
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float frac_pos )
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{
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const float frsq = frac_pos*frac_pos;
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const float frsq2 = 2*frsq;
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return( ( (x2-x0) *0.5f ) * ( frac_pos * (frsq+1) -frsq2 ) +
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( frsq2*frac_pos - 3*frsq ) * ( x1-x2 ) +
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frsq2 * (frac_pos-1) * ( ( x3-x1 ) * 0.25f ) + x1 );
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/*
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const float frsq = frac_pos*frac_pos;
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//const float frsq2 = 2*frsq;
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frac_pos *= 0.5;
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const float frcu = frsq*frac_pos;
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return (
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(frcu - frsq + frac_pos) * ((x2 - x0)) +
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(4*frcu - 3*frsq) * (x1 - x2)
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//frsq*(2*frac_pos-3) * (x1 - x2)
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+ (frcu - 0.5*frsq)*((x3 - x1))
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+ x1
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);
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*/
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}
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inline float cubicInterpolate( float v0, float v1, float v2, float v3, float x )
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{
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float frsq = x * x;
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float frcu = frsq * v0;
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float t1 = v1 * 3.f + v3;
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return v1 + (0.5f * frcu + x) * (v2 - frcu * (1.0f / 6.0f) -
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(t1 * (1.0f / 6.0f) - v0) * (1.0f / 3.0f)) + frsq * x * (t1 *
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(1.0f / 6.0f) - 0.5f * v2) + frsq * (0.5f * v2 - v1);
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}
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inline float cosinusInterpolate( float v0, float v1, float x )
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{
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const float f = ( 1.0f - cosf( x * F_PI ) ) * 0.5f;
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return f * (v1 - v0) + v0;
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}
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inline float linearInterpolate( float v0, float v1, float x )
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{
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return x * (v1 - v0) + v0;
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}
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inline float optimalInterpolate( float v0, float v1, float x )
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{
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const float z = x - 0.5f;
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const float even = v1 + v0;
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const float odd = v1 - v0;
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const float c0 = even * 0.50037842517188658;
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const float c1 = odd * 1.00621089801788210;
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const float c2 = even * -0.004541102062639801;
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const float c3 = odd * -1.57015627178718420;
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return ((c3 * z + c2) * z + c1) * z + c0;
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}
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inline float optimal4pInterpolate( float v0, float v1, float v2, float v3, float x )
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{
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const float z = x - 0.5f;
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const float even1 = v2 + v1;
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const float odd1 = v2 - v1;
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const float even2 = v3 + v0;
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const float odd2 = v3 - v0;
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const float c0 = even1 * 0.45868970870461956 + even2 * 0.04131401926395584;
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const float c1 = odd1 * 0.48068024766578432 + odd2 * 0.17577925564495955;
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const float c2 = even1 * -0.246185007019907091 + even2 * 0.24614027139700284;
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const float c3 = odd1 * -0.36030925263849456 + odd2 * 0.10174985775982505;
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return ((c3 * z + c2) * z + c1) * z + c0;
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}
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inline float lagrangeInterpolate( float v0, float v1, float v2, float v3, float x )
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{
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const float c0 = v1;
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const float c1 = v2 - v0 * ( 1.0f / 3.0f ) - v1 * 0.5f - v3 * ( 1.0f / 6.0f );
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const float c2 = 0.5f * (v0 + v2) - v1;
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const float c3 = ( 1.0f/6.0f ) * ( v3 - v0 ) + 0.5f * ( v1 - v2 );
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return ((c3 * x + c2) * x + c1) * x + c0;
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}
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} // namespace lmms
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#endif // LMMS_INTERPOLATION_H
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