11dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 21dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project/* @(#)k_sin.c 1.3 95/01/18 */ 31dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project/* 41dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * ==================================================== 51dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 61dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * 71dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * Developed at SunSoft, a Sun Microsystems, Inc. business. 81dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * Permission to use, copy, modify, and distribute this 91dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * software is freely granted, provided that this notice 101dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * is preserved. 111dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * ==================================================== 121dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project */ 131dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 14a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes#include <sys/cdefs.h> 15a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes__FBSDID("$FreeBSD$"); 161dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 171dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project/* __kernel_sin( x, y, iy) 181dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * kernel sin function on ~[-pi/4, pi/4] (except on -0), pi/4 ~ 0.7854 191dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * Input x is assumed to be bounded by ~pi/4 in magnitude. 201dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * Input y is the tail of x. 211dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * Input iy indicates whether y is 0. (if iy=0, y assume to be 0). 221dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * 231dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * Algorithm 241dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * 1. Since sin(-x) = -sin(x), we need only to consider positive x. 251dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * 2. Callers must return sin(-0) = -0 without calling here since our 261dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * odd polynomial is not evaluated in a way that preserves -0. 271dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * Callers may do the optimization sin(x) ~ x for tiny x. 281dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * 3. sin(x) is approximated by a polynomial of degree 13 on 291dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * [0,pi/4] 301dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * 3 13 311dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * sin(x) ~ x + S1*x + ... + S6*x 321dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * where 331dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * 341dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * |sin(x) 2 4 6 8 10 12 | -58 351dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * |----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x +S6*x )| <= 2 361dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * | x | 371dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * 381dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * 4. sin(x+y) = sin(x) + sin'(x')*y 391dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * ~ sin(x) + (1-x*x/2)*y 401dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * For better accuracy, let 411dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * 3 2 2 2 2 421dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6)))) 431dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * then 3 2 441dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * sin(x) = x + (S1*x + (x *(r-y/2)+y)) 451dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project */ 461dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 471dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project#include "math.h" 481dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project#include "math_private.h" 491dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 501dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projectstatic const double 511dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projecthalf = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */ 521dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source ProjectS1 = -1.66666666666666324348e-01, /* 0xBFC55555, 0x55555549 */ 531dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source ProjectS2 = 8.33333333332248946124e-03, /* 0x3F811111, 0x1110F8A6 */ 541dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source ProjectS3 = -1.98412698298579493134e-04, /* 0xBF2A01A0, 0x19C161D5 */ 551dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source ProjectS4 = 2.75573137070700676789e-06, /* 0x3EC71DE3, 0x57B1FE7D */ 561dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source ProjectS5 = -2.50507602534068634195e-08, /* 0xBE5AE5E6, 0x8A2B9CEB */ 571dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source ProjectS6 = 1.58969099521155010221e-10; /* 0x3DE5D93A, 0x5ACFD57C */ 581dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 591dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projectdouble 601dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project__kernel_sin(double x, double y, int iy) 611dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project{ 62a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes double z,r,v,w; 631dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 641dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project z = x*x; 65a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes w = z*z; 66a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes r = S2+z*(S3+z*S4) + z*w*(S5+z*S6); 671dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project v = z*x; 681dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if(iy==0) return x+v*(S1+z*r); 691dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project else return x-((z*(half*y-v*r)-y)-v*S1); 701dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project} 71