diff options
Diffstat (limited to 'sysdeps/libm-ieee754/e_acos.c')
| -rw-r--r-- | sysdeps/libm-ieee754/e_acos.c | 67 |
1 files changed, 50 insertions, 17 deletions
diff --git a/sysdeps/libm-ieee754/e_acos.c b/sysdeps/libm-ieee754/e_acos.c index 78bdae9..fa858de 100644 --- a/sysdeps/libm-ieee754/e_acos.c +++ b/sysdeps/libm-ieee754/e_acos.c @@ -5,24 +5,27 @@ * * 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: e_acos.c,v 1.9 1995/05/12 04:57:13 jtc Exp $"; #endif /* __ieee754_acos(x) - * Method : + * Method : * acos(x) = pi/2 - asin(x) * acos(-x) = pi/2 + asin(x) * For |x|<=0.5 * acos(x) = pi/2 - (x + x*x^2*R(x^2)) (see asin.c) * For x>0.5 * acos(x) = pi/2 - (pi/2 - 2asin(sqrt((1-x)/2))) - * = 2asin(sqrt((1-x)/2)) + * = 2asin(sqrt((1-x)/2)) * = 2s + 2s*z*R(z) ...z=(1-x)/2, s=sqrt(z) * = 2f + (2c + 2s*z*R(z)) * where f=hi part of s, and c = (z-f*f)/(s+f) is the correction term @@ -40,26 +43,26 @@ static char rcsid[] = "$NetBSD: e_acos.c,v 1.9 1995/05/12 04:57:13 jtc Exp $"; #include "math.h" #include "math_private.h" +#define one qS[0] #ifdef __STDC__ -static const double +static const double #else -static double +static double #endif -one= 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ pi = 3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */ pio2_hi = 1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */ pio2_lo = 6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */ -pS0 = 1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */ -pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */ -pS2 = 2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */ -pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */ -pS4 = 7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */ -pS5 = 3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */ -qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */ -qS2 = 2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */ -qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */ -qS4 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */ +pS[] = {1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */ + -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */ + 2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */ + -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */ + 7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */ + 3.47933107596021167570e-05}, /* 0x3F023DE1, 0x0DFDF709 */ +qS[] ={1.0, -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */ + 2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */ + -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */ + 7.70381505559019352791e-02}; /* 0x3FB3B8C5, 0xB12E9282 */ #ifdef __STDC__ double __ieee754_acos(double x) @@ -68,7 +71,7 @@ qS4 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */ double x; #endif { - double z,p,q,r,w,s,c,df; + double z,p,q,r,w,s,c,df,p1,p2,p3,q1,q2,q3,z2,z4,z6; int32_t hx,ix; GET_HIGH_WORD(hx,x); ix = hx&0x7fffffff; @@ -84,14 +87,34 @@ qS4 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */ if(ix<0x3fe00000) { /* |x| < 0.5 */ if(ix<=0x3c600000) return pio2_hi+pio2_lo;/*if|x|<2**-57*/ z = x*x; +#ifdef DO_NOT_USE_THIS p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5))))); q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4))); +#else + p1 = z*pS[0]; z2=z*z; + p2 = pS[1]+z*pS[2]; z4=z2*z2; + p3 = pS[3]+z*pS[4]; z6=z4*z2; + q1 = one+z*qS[1]; + q2 = qS[2]+z*qS[3]; + p = p1 + z2*p2 + z4*p3 + z6*pS[5]; + q = q1 + z2*q2 + z4*qS[4]; +#endif r = p/q; return pio2_hi - (x - (pio2_lo-x*r)); } else if (hx<0) { /* x < -0.5 */ z = (one+x)*0.5; +#ifdef DO_NOT_USE_THIS p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5))))); q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4))); +#else + p1 = z*pS[0]; z2=z*z; + p2 = pS[1]+z*pS[2]; z4=z2*z2; + p3 = pS[3]+z*pS[4]; z6=z4*z2; + q1 = one+z*qS[1]; + q2 = qS[2]+z*qS[3]; + p = p1 + z2*p2 + z4*p3 + z6*pS[5]; + q = q1 + z2*q2 + z4*qS[4]; +#endif s = __ieee754_sqrt(z); r = p/q; w = r*s-pio2_lo; @@ -102,8 +125,18 @@ qS4 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */ df = s; SET_LOW_WORD(df,0); c = (z-df*df)/(s+df); +#ifdef DO_NOT_USE_THIS p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5))))); q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4))); +#else + p1 = z*pS[0]; z2=z*z; + p2 = pS[1]+z*pS[2]; z4=z2*z2; + p3 = pS[3]+z*pS[4]; z6=z4*z2; + q1 = one+z*qS[1]; + q2 = qS[2]+z*qS[3]; + p = p1 + z2*p2 + z4*p3 + z6*pS[5]; + q = q1 + z2*q2 + z4*qS[4]; +#endif r = p/q; w = r*s+c; return 2.0*(df+w); |