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113 lines
3.4 KiB
C
113 lines
3.4 KiB
C
/*
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(C) Copyright 2001,2006,
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International Business Machines Corporation,
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Sony Computer Entertainment, Incorporated,
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Toshiba Corporation,
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All rights reserved.
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Redistribution and use in source and binary forms, with or without
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modification, are permitted provided that the following conditions are met:
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* Redistributions of source code must retain the above copyright notice,
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this list of conditions and the following disclaimer.
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* Redistributions in binary form must reproduce the above copyright
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notice, this list of conditions and the following disclaimer in the
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documentation and/or other materials provided with the distribution.
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* Neither the names of the copyright holders nor the names of their
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contributors may be used to endorse or promote products derived from this
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software without specific prior written permission.
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THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS
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IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
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TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A
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PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER
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OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
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EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
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PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
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PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
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LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
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NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
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SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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*/
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#ifndef _ATANF_H_
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#define _ATANF_H_ 1
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#ifndef M_PI_2
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#define M_PI_2 1.5707963267949f
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#endif /* M_PI_2 */
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/*
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* FUNCTION
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* float _atanf(float x)
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*
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* DESCRIPTION
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* _atanf computes the arc tangent of the value x; that is the value
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* whose tangent is x.
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*
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* _atanf returns the arc tangent in radians and the value is
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* mathematically defined to be in the range -PI/2 to PI/2.
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*
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* The arc tangent function is computed using a polynomial approximation
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* (B. Carlson, M. Goldstein, Los Alamos Scientific Laboratiry, 1955).
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* __8__
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* \
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* \
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* atanf(x) = / Ci*x^(2*i+1)
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* /____
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* i=0
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*
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* for x in the range -1 to 1. The remaining regions are defined to be:
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*
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* [1, infinity] : PI/2 + atanf(-1/x)
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* [-infinity, -1] : -PI/2 + atanf(-1/x)
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*/
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static __inline float _atanf(float x)
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{
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float xabs;
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float bias;
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float x2, x3, x4, x8, x9;
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float hi, lo;
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float result;
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bias = 0.0f;
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xabs = (x < 0.0f) ? -x : x;
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if (xabs >= 1.0f) {
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bias = M_PI_2;
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if (x < 0.0f) {
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bias = -bias;
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}
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x = -1.0f / x;
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}
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/* Instruction counts can be reduced if the polynomial was
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* computed entirely from nested (dependent) fma's. However,
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* to reduce the number of pipeline stalls, the polygon is evaluated
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* in two halves(hi and lo).
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*/
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bias += x;
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x2 = x * x;
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x3 = x2 * x;
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x4 = x2 * x2;
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x8 = x4 * x4;
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x9 = x8 * x;
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hi = 0.0028662257f * x2 - 0.0161657367f;
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hi = hi * x2 + 0.0429096138f;
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hi = hi * x2 - 0.0752896400f;
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hi = hi * x2 + 0.1065626393f;
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lo = -0.1420889944f * x2 + 0.1999355085f;
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lo = lo * x2 - 0.3333314528f;
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lo = lo * x3 + bias;
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result = hi * x9 + lo;
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return (result);
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}
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#endif /* _ATANF_H_ */
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