Details | Last modification | View Log | RSS feed
| Rev | Author | Line No. | Line |
|---|---|---|---|
| 2 | pj | 1 | /* @(#)k_sin.c 5.1 93/09/24 */ |
| 2 | /* |
||
| 3 | * ==================================================== |
||
| 4 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
||
| 5 | * |
||
| 6 | * Developed at SunPro, a Sun Microsystems, Inc. business. |
||
| 7 | * Permission to use, copy, modify, and distribute this |
||
| 8 | * software is freely granted, provided that this notice |
||
| 9 | * is preserved. |
||
| 10 | * ==================================================== |
||
| 11 | */ |
||
| 12 | |||
| 13 | #ifndef lint |
||
| 14 | static char rcsid[] = "$\Id: k_sin.c,v 1.2 1995/05/30 05:49:05 rgrimes Exp $"; |
||
| 15 | #endif |
||
| 16 | |||
| 17 | /* __kernel_sin( x, y, iy) |
||
| 18 | * kernel sin function on [-pi/4, pi/4], pi/4 ~ 0.7854 |
||
| 19 | * Input x is assumed to be bounded by ~pi/4 in magnitude. |
||
| 20 | * Input y is the tail of x. |
||
| 21 | * Input iy indicates whether y is 0. (if iy=0, y assume to be 0). |
||
| 22 | * |
||
| 23 | * Algorithm |
||
| 24 | * 1. Since sin(-x) = -sin(x), we need only to consider positive x. |
||
| 25 | * 2. if x < 2^-27 (hx<0x3e400000 0), return x with inexact if x!=0. |
||
| 26 | * 3. sin(x) is approximated by a polynomial of degree 13 on |
||
| 27 | * [0,pi/4] |
||
| 28 | * 3 13 |
||
| 29 | * sin(x) ~ x + S1*x + ... + S6*x |
||
| 30 | * where |
||
| 31 | * |
||
| 32 | * |sin(x) 2 4 6 8 10 12 | -58 |
||
| 33 | * |----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x +S6*x )| <= 2 |
||
| 34 | * | x | |
||
| 35 | * |
||
| 36 | * 4. sin(x+y) = sin(x) + sin'(x')*y |
||
| 37 | * ~ sin(x) + (1-x*x/2)*y |
||
| 38 | * For better accuracy, let |
||
| 39 | * 3 2 2 2 2 |
||
| 40 | * r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6)))) |
||
| 41 | * then 3 2 |
||
| 42 | * sin(x) = x + (S1*x + (x *(r-y/2)+y)) |
||
| 43 | */ |
||
| 44 | |||
| 45 | #include "math.h" |
||
| 46 | #include "math_private.h" |
||
| 47 | |||
| 48 | #ifdef __STDC__ |
||
| 49 | static const double |
||
| 50 | #else |
||
| 51 | static double |
||
| 52 | #endif |
||
| 53 | half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */ |
||
| 54 | S1 = -1.66666666666666324348e-01, /* 0xBFC55555, 0x55555549 */ |
||
| 55 | S2 = 8.33333333332248946124e-03, /* 0x3F811111, 0x1110F8A6 */ |
||
| 56 | S3 = -1.98412698298579493134e-04, /* 0xBF2A01A0, 0x19C161D5 */ |
||
| 57 | S4 = 2.75573137070700676789e-06, /* 0x3EC71DE3, 0x57B1FE7D */ |
||
| 58 | S5 = -2.50507602534068634195e-08, /* 0xBE5AE5E6, 0x8A2B9CEB */ |
||
| 59 | S6 = 1.58969099521155010221e-10; /* 0x3DE5D93A, 0x5ACFD57C */ |
||
| 60 | |||
| 61 | #ifdef __STDC__ |
||
| 62 | double __kernel_sin(double x, double y, int iy) |
||
| 63 | #else |
||
| 64 | double __kernel_sin(x, y, iy) |
||
| 65 | double x,y; int iy; /* iy=0 if y is zero */ |
||
| 66 | #endif |
||
| 67 | { |
||
| 68 | double z,r,v; |
||
| 69 | int32_t ix; |
||
| 70 | GET_HIGH_WORD(ix,x); |
||
| 71 | ix &= 0x7fffffff; /* high word of x */ |
||
| 72 | if(ix<0x3e400000) /* |x| < 2**-27 */ |
||
| 73 | {if((int)x==0) return x;} /* generate inexact */ |
||
| 74 | z = x*x; |
||
| 75 | v = z*x; |
||
| 76 | r = S2+z*(S3+z*(S4+z*(S5+z*S6))); |
||
| 77 | if(iy==0) return x+v*(S1+z*r); |
||
| 78 | else return x-((z*(half*y-v*r)-y)-v*S1); |
||
| 79 | } |