diff options
Diffstat (limited to 'sysdeps/ieee754/dbl-64/k_sin.c')
-rw-r--r-- | sysdeps/ieee754/dbl-64/k_sin.c | 91 |
1 files changed, 91 insertions, 0 deletions
diff --git a/sysdeps/ieee754/dbl-64/k_sin.c b/sysdeps/ieee754/dbl-64/k_sin.c new file mode 100644 index 0000000..49c5922 --- /dev/null +++ b/sysdeps/ieee754/dbl-64/k_sin.c @@ -0,0 +1,91 @@ +/* @(#)k_sin.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ +/* Modified by Naohiko Shimizu/Tokai University, Japan 1997/08/25, + for performance improvement on pipelined processors. +*/ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: k_sin.c,v 1.8 1995/05/10 20:46:31 jtc Exp $"; +#endif + +/* __kernel_sin( x, y, iy) + * kernel sin function on [-pi/4, pi/4], pi/4 ~ 0.7854 + * Input x is assumed to be bounded by ~pi/4 in magnitude. + * Input y is the tail of x. + * Input iy indicates whether y is 0. (if iy=0, y assume to be 0). + * + * Algorithm + * 1. Since sin(-x) = -sin(x), we need only to consider positive x. + * 2. if x < 2^-27 (hx<0x3e400000 0), return x with inexact if x!=0. + * 3. sin(x) is approximated by a polynomial of degree 13 on + * [0,pi/4] + * 3 13 + * sin(x) ~ x + S1*x + ... + S6*x + * where + * + * |sin(x) 2 4 6 8 10 12 | -58 + * |----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x +S6*x )| <= 2 + * | x | + * + * 4. sin(x+y) = sin(x) + sin'(x')*y + * ~ sin(x) + (1-x*x/2)*y + * For better accuracy, let + * 3 2 2 2 2 + * r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6)))) + * then 3 2 + * sin(x) = x + (S1*x + (x *(r-y/2)+y)) + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const double +#else +static double +#endif +S[] = { + 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */ + -1.66666666666666324348e-01, /* 0xBFC55555, 0x55555549 */ + 8.33333333332248946124e-03, /* 0x3F811111, 0x1110F8A6 */ + -1.98412698298579493134e-04, /* 0xBF2A01A0, 0x19C161D5 */ + 2.75573137070700676789e-06, /* 0x3EC71DE3, 0x57B1FE7D */ + -2.50507602534068634195e-08, /* 0xBE5AE5E6, 0x8A2B9CEB */ + 1.58969099521155010221e-10}; /* 0x3DE5D93A, 0x5ACFD57C */ + +#ifdef __STDC__ + double __kernel_sin(double x, double y, int iy) +#else + double __kernel_sin(x, y, iy) + double x,y; int iy; /* iy=0 if y is zero */ +#endif +{ + double z,r,v,z1,r1,r2; + int32_t ix; + GET_HIGH_WORD(ix,x); + ix &= 0x7fffffff; /* high word of x */ + if(ix<0x3e400000) /* |x| < 2**-27 */ + {if((int)x==0) return x;} /* generate inexact */ + z = x*x; + v = z*x; +#ifdef DO_NOT_USE_THIS + r = S2+z*(S3+z*(S4+z*(S5+z*S6))); + if(iy==0) return x+v*(S1+z*r); + else return x-((z*(half*y-v*r)-y)-v*S1); +#else + r1 = S[5]+z*S[6]; z1 = z*z*z; + r2 = S[3]+z*S[4]; + r = S[2] + z*r2 + z1*r1; + if(iy==0) return x+v*(S[1]+z*r); + else return x-((z*(S[0]*y-v*r)-y)-v*S[1]); +#endif +} |