mirror of https://gitlab.com/rnger/amath
118 lines
4.0 KiB
C
118 lines
4.0 KiB
C
/*-
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* Copyright (c) 2014-2017 Carsten Sonne Larsen <cs@innolan.net>
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* All rights reserved.
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*
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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
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* are met:
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* 1. Redistributions of source code must retain the above copyright
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* notice, this list of conditions and the following disclaimer.
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* 2. 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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*
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* THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
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* IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
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* OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
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* IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
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* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
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* NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
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* DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
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* THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
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* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
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* THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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*
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* Project homepage:
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* https://amath.innolan.net
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*
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* The original source code can be obtained from:
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* http://www.netlib.org/fdlibm/k_sin.c
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*
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* =================================================================
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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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*
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* Developed at SunSoft, a Sun Microsystems, Inc. business.
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* Permission to use, copy, modify, and distribute this
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* software is freely granted, provided that this notice
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* is preserved.
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* =================================================================
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*/
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/**
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* @file ksin.c
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* @brief Kernel sin function
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*/
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#include "prim.h"
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static const double
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half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
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S1 = -1.66666666666666324348e-01, /* 0xBFC55555, 0x55555549 */
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S2 = 8.33333333332248946124e-03, /* 0x3F811111, 0x1110F8A6 */
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S3 = -1.98412698298579493134e-04, /* 0xBF2A01A0, 0x19C161D5 */
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S4 = 2.75573137070700676789e-06, /* 0x3EC71DE3, 0x57B1FE7D */
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S5 = -2.50507602534068634195e-08, /* 0xBE5AE5E6, 0x8A2B9CEB */
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S6 = 1.58969099521155010221e-10; /* 0x3DE5D93A, 0x5ACFD57C */
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/**
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* @brief Kernel sin function
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* @details
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* <pre>
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* Kernel sin function on [-pi/4, pi/4], pi/4 ~ 0.7854
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* Input x is assumed to be bounded by ~pi/4 in magnitude.
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* Input y is the tail of x.
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* Input iy indicates whether y is 0. (if iy=0, y assume to be 0).
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*
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* Algorithm
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* 1. Since sin(-x) = -sin(x), we need only to consider positive x.
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* 2. if x < 2^-27 (hx<0X3E400000 0), return x with inexact if x!=0.
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* 3. sin(x) is approximated by a polynomial of degree 13 on [0,pi/4]
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* 3 13
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* sin(x) ~ x + S1*x + ... + S6*x
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*
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* where
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*
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* |sin(x) 2 4 6 8 10 12 | -58
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* |----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x +S6*x )| <= 2
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* | x |
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*
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* 4. sin(x+y) = sin(x) + sin'(x')*y
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* ~ sin(x) + (1-x*x/2)*y
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*
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* For better accuracy, let
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* 3 2 2 2 2
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* r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6))))
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* then 3 2
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* sin(x) = x + (S1*x + (x *(r-y/2)+y))
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* </pre>
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*/
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double __kernel_sin(double x, double y, int iy)
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{
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double z, r, v;
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int32_t ix;
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GET_HIGH_WORD(ix, x);
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ix &= 0x7FFFFFFF;
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// |x| < 2**-27
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if (ix < 0x3E400000)
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{
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// generate inexact
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if ((int)x == 0)
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{
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return x;
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}
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}
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z = x * x;
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v = z * x;
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r = S2 + z * (S3 + z * (S4 + z * (S5 + z * S6)));
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if (iy == 0)
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{
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return x + v * (S1 + z * r);
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}
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return x - ((z * (half * y - v * r) - y) - v * S1);
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}
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