125 lines
3.8 KiB
C
125 lines
3.8 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 _EXP2F_H_
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#define _EXP2F_H_ 1
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#ifndef M_LN2
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#define M_LN2 0.69314718055994530942 /* ln(2) */
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#endif /* M_LN2 */
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/*
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* FUNCTION
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* float _exp2f(float x)
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*
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* DESCRIPTION
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* _exp2f computes 2 raised to the input x. Computation is
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* performed by observing the 2^(a+b) = 2^a * 2^b.
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* We decompose x into a and b (above) by letting.
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* a = ceil(x), b = x - a;
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*
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* 2^a is easilty computed by placing a into the exponent
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* or a floating point number whose mantissa is all zeros.
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*
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* 2^b is computed using the following polynomial approximation.
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* (C. Hastings, Jr, 1955).
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*
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* __7__
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* \
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* \
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* 2^x = / Ci*x^i
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* /____
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* i=0
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*
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* for x in the range 0.0 to 1.0
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*
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* C0 = 1.0
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* C1 = -0.9999999995
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* C2 = 0.4999999206
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* C3 = -0.1666653019
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* C4 = 0.0416573475
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* C5 = -0.0083013598
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* C6 = 0.0013298820
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* C7 = -0.0001413161
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*
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*/
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static __inline float _exp2f(float x)
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{
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union {
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float f;
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unsigned int ui;
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} bias, exp_int, exp_frac;
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unsigned int overflow, underflow;
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int ix;
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float frac, frac2, frac4;
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float hi, lo;
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/* Break in the input x into two parts ceil(x), x - ceil(x).
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*/
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bias.f = x;
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bias.ui = ~(unsigned int)((signed)(bias.ui) >> 31) & 0x3F7FFFFF;
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ix = (int)(x + bias.f);
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frac = (float)ix - x;
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frac *= (float)(M_LN2);
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exp_int.ui = (ix + 127) << 23;
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overflow = (ix > 128) ? 0x7FFFFFFF : 0x0;
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underflow = (ix < -127) ? 0xFFFFFFFF : 0x0;
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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 amd lo).
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*/
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frac2 = frac * frac;
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frac4 = frac2 * frac2;
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hi = -0.0001413161f * frac + 0.0013298820f;
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hi = hi * frac - 0.0083013598f;
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hi = hi * frac + 0.0416573475f;
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lo = -0.1666653019f * frac + 0.4999999206f;
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lo = lo * frac - 0.9999999995f;
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lo = lo * frac + 1.0f;
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exp_frac.f = hi * frac4 + lo;
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ix += exp_frac.ui >> 23;
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exp_frac.f *= exp_int.f;
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exp_frac.ui = (exp_frac.ui | overflow) & ~underflow;
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return (exp_frac.f);
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}
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#endif /* _EXP2F_H_ */
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