src/libm/k_sin.c
author Sam Lantinga <slouken@libsdl.org>
Sat, 04 Nov 2017 15:53:19 -0700
changeset 11683 48bcba563d9c
parent 6044 35448a5ea044
permissions -rw-r--r--
Updated math code from the uClibc 0.9.33 release
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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 SunPro, 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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/* __kernel_sin( x, y, iy)
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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
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 *	   [0,pi/4]
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 *		  	         3            13
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 *	   	sin(x) ~ x + S1*x + ... + S6*x
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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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 *	   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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 */
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#include "math_libm.h"
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#include "math_private.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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double attribute_hidden __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;			/* high word of x */
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	if(ix<0x3e400000)			/* |x| < 2**-27 */
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	   {if((int)x==0) return x;}		/* generate inexact */
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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) return x+v*(S1+z*r);
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	else      return x-((z*(half*y-v*r)-y)-v*S1);
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}