1141296Sdas 2141296Sdas/* @(#)k_sin.c 1.3 95/01/18 */ 32116Sjkh/* 42116Sjkh * ==================================================== 52116Sjkh * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 62116Sjkh * 7141296Sdas * Developed at SunSoft, a Sun Microsystems, Inc. business. 82116Sjkh * Permission to use, copy, modify, and distribute this 9141296Sdas * software is freely granted, provided that this notice 102116Sjkh * is preserved. 112116Sjkh * ==================================================== 122116Sjkh */ 132116Sjkh 14176408Sbde#include <sys/cdefs.h> 15176408Sbde__FBSDID("$FreeBSD$"); 162116Sjkh 172116Sjkh/* __kernel_sin( x, y, iy) 18151966Sbde * kernel sin function on ~[-pi/4, pi/4] (except on -0), pi/4 ~ 0.7854 192116Sjkh * Input x is assumed to be bounded by ~pi/4 in magnitude. 202116Sjkh * Input y is the tail of x. 21141296Sdas * Input iy indicates whether y is 0. (if iy=0, y assume to be 0). 222116Sjkh * 232116Sjkh * Algorithm 24141296Sdas * 1. Since sin(-x) = -sin(x), we need only to consider positive x. 25151966Sbde * 2. Callers must return sin(-0) = -0 without calling here since our 26151966Sbde * odd polynomial is not evaluated in a way that preserves -0. 27151966Sbde * Callers may do the optimization sin(x) ~ x for tiny x. 282116Sjkh * 3. sin(x) is approximated by a polynomial of degree 13 on 292116Sjkh * [0,pi/4] 302116Sjkh * 3 13 312116Sjkh * sin(x) ~ x + S1*x + ... + S6*x 322116Sjkh * where 33141296Sdas * 342116Sjkh * |sin(x) 2 4 6 8 10 12 | -58 352116Sjkh * |----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x +S6*x )| <= 2 36141296Sdas * | x | 37141296Sdas * 382116Sjkh * 4. sin(x+y) = sin(x) + sin'(x')*y 392116Sjkh * ~ sin(x) + (1-x*x/2)*y 40141296Sdas * For better accuracy, let 412116Sjkh * 3 2 2 2 2 422116Sjkh * r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6)))) 432116Sjkh * then 3 2 442116Sjkh * sin(x) = x + (S1*x + (x *(r-y/2)+y)) 452116Sjkh */ 462116Sjkh 472116Sjkh#include "math.h" 482116Sjkh#include "math_private.h" 492116Sjkh 508870Srgrimesstatic const double 512116Sjkhhalf = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */ 522116SjkhS1 = -1.66666666666666324348e-01, /* 0xBFC55555, 0x55555549 */ 532116SjkhS2 = 8.33333333332248946124e-03, /* 0x3F811111, 0x1110F8A6 */ 542116SjkhS3 = -1.98412698298579493134e-04, /* 0xBF2A01A0, 0x19C161D5 */ 552116SjkhS4 = 2.75573137070700676789e-06, /* 0x3EC71DE3, 0x57B1FE7D */ 562116SjkhS5 = -2.50507602534068634195e-08, /* 0xBE5AE5E6, 0x8A2B9CEB */ 572116SjkhS6 = 1.58969099521155010221e-10; /* 0x3DE5D93A, 0x5ACFD57C */ 582116Sjkh 5997413Salfreddouble 6097413Salfred__kernel_sin(double x, double y, int iy) 612116Sjkh{ 62176408Sbde double z,r,v,w; 63151620Sbde 642116Sjkh z = x*x; 65176408Sbde w = z*z; 66176408Sbde r = S2+z*(S3+z*S4) + z*w*(S5+z*S6); 672116Sjkh v = z*x; 682116Sjkh if(iy==0) return x+v*(S1+z*r); 692116Sjkh else return x-((z*(half*y-v*r)-y)-v*S1); 702116Sjkh} 71