diff options
Diffstat (limited to 'sysdeps/libm-ieee754/k_cos.c')
| -rw-r--r-- | sysdeps/libm-ieee754/k_cos.c | 55 |
1 files changed, 33 insertions, 22 deletions
diff --git a/sysdeps/libm-ieee754/k_cos.c b/sysdeps/libm-ieee754/k_cos.c index d8740b3508..7e38ef7915 100644 --- a/sysdeps/libm-ieee754/k_cos.c +++ b/sysdeps/libm-ieee754/k_cos.c @@ -5,10 +5,13 @@ * * Developed at SunPro, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice + * 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_cos.c,v 1.8 1995/05/10 20:46:22 jtc Exp $"; @@ -18,7 +21,7 @@ static char rcsid[] = "$NetBSD: k_cos.c,v 1.8 1995/05/10 20:46:22 jtc Exp $"; * __kernel_cos( x, y ) * kernel cos function on [-pi/4, pi/4], pi/4 ~ 0.785398164 * Input x is assumed to be bounded by ~pi/4 in magnitude. - * Input y is the tail of x. + * Input y is the tail of x. * * Algorithm * 1. Since cos(-x) = cos(x), we need only to consider positive x. @@ -28,15 +31,15 @@ static char rcsid[] = "$NetBSD: k_cos.c,v 1.8 1995/05/10 20:46:22 jtc Exp $"; * 4 14 * cos(x) ~ 1 - x*x/2 + C1*x + ... + C6*x * where the remez error is - * + * * | 2 4 6 8 10 12 14 | -58 * |cos(x)-(1-.5*x +C1*x +C2*x +C3*x +C4*x +C5*x +C6*x )| <= 2 - * | | - * - * 4 6 8 10 12 14 + * | | + * + * 4 6 8 10 12 14 * 4. let r = C1*x +C2*x +C3*x +C4*x +C5*x +C6*x , then * cos(x) = 1 - x*x/2 + r - * since cos(x+y) ~ cos(x) - sin(x)*y + * since cos(x+y) ~ cos(x) - sin(x)*y * ~ cos(x) - x*y, * a correction term is necessary in cos(x) and hence * cos(x+y) = 1 - (x*x/2 - (r - x*y)) @@ -53,17 +56,18 @@ static char rcsid[] = "$NetBSD: k_cos.c,v 1.8 1995/05/10 20:46:22 jtc Exp $"; #include "math_private.h" #ifdef __STDC__ -static const double +static const double #else -static double +static double #endif -one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ -C1 = 4.16666666666666019037e-02, /* 0x3FA55555, 0x5555554C */ -C2 = -1.38888888888741095749e-03, /* 0xBF56C16C, 0x16C15177 */ -C3 = 2.48015872894767294178e-05, /* 0x3EFA01A0, 0x19CB1590 */ -C4 = -2.75573143513906633035e-07, /* 0xBE927E4F, 0x809C52AD */ -C5 = 2.08757232129817482790e-09, /* 0x3E21EE9E, 0xBDB4B1C4 */ -C6 = -1.13596475577881948265e-11; /* 0xBDA8FAE9, 0xBE8838D4 */ +C[] = { + 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ + 4.16666666666666019037e-02, /* 0x3FA55555, 0x5555554C */ + -1.38888888888741095749e-03, /* 0xBF56C16C, 0x16C15177 */ + 2.48015872894767294178e-05, /* 0x3EFA01A0, 0x19CB1590 */ + -2.75573143513906633035e-07, /* 0xBE927E4F, 0x809C52AD */ + 2.08757232129817482790e-09, /* 0x3E21EE9E, 0xBDB4B1C4 */ + -1.13596475577881948265e-11}; /* 0xBDA8FAE9, 0xBE8838D4 */ #ifdef __STDC__ double __kernel_cos(double x, double y) @@ -72,17 +76,24 @@ C6 = -1.13596475577881948265e-11; /* 0xBDA8FAE9, 0xBE8838D4 */ double x,y; #endif { - double a,hz,z,r,qx; + double a,hz,z,r,qx,r1,r2,r3,z1,z2,z3; int32_t ix; + z = x*x; GET_HIGH_WORD(ix,x); ix &= 0x7fffffff; /* ix = |x|'s high word*/ if(ix<0x3e400000) { /* if x < 2**27 */ - if(((int)x)==0) return one; /* generate inexact */ + if(((int)x)==0) return C[0]; /* generate inexact */ } - z = x*x; +#ifdef DO_NOT_USE_THIS r = z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*C6))))); - if(ix < 0x3FD33333) /* if |x| < 0.3 */ - return one - (0.5*z - (z*r - x*y)); +#else + r1=z*C[6];r1=r1+C[5];z1=z*z; + r2=z*C[4];r2=r2+C[3];z2=z1*z; + r3=z*C[2];r3=r3+C[1];z3=z2*z1; + r=z3*r1+z2*r2+z*r3; +#endif + if(ix < 0x3FD33333) /* if |x| < 0.3 */ + return C[0] - (0.5*z - (z*r - x*y)); else { if(ix > 0x3fe90000) { /* x > 0.78125 */ qx = 0.28125; @@ -90,7 +101,7 @@ C6 = -1.13596475577881948265e-11; /* 0xBDA8FAE9, 0xBE8838D4 */ INSERT_WORDS(qx,ix-0x00200000,0); /* x/4 */ } hz = 0.5*z-qx; - a = one-qx; + a = C[0]-qx; return a - (hz - (z*r-x*y)); } } |