diff options
Diffstat (limited to 'sysdeps/ieee754/flt-32/e_asinf.c')
| -rw-r--r-- | sysdeps/ieee754/flt-32/e_asinf.c | 51 |
1 files changed, 26 insertions, 25 deletions
diff --git a/sysdeps/ieee754/flt-32/e_asinf.c b/sysdeps/ieee754/flt-32/e_asinf.c index 5270f31144..5c3f0d500f 100644 --- a/sysdeps/ieee754/flt-32/e_asinf.c +++ b/sysdeps/ieee754/flt-32/e_asinf.c @@ -13,6 +13,12 @@ * ==================================================== */ +/* + Single precision expansion contributed by + Stephen L. Moshier <moshier@na-net.ornl.gov> +*/ + + #if defined(LIBM_SCCS) && !defined(lint) static char rcsid[] = "$NetBSD: e_asinf.c,v 1.5 1995/05/12 04:57:25 jtc Exp $"; #endif @@ -27,20 +33,19 @@ static float #endif one = 1.0000000000e+00, /* 0x3F800000 */ huge = 1.000e+30, -pio2_hi = 1.5707962513e+00, /* 0x3fc90fda */ -pio2_lo = 7.5497894159e-08, /* 0x33a22168 */ -pio4_hi = 7.8539818525e-01, /* 0x3f490fdb */ - /* coefficient for R(x^2) */ -pS0 = 1.6666667163e-01, /* 0x3e2aaaab */ -pS1 = -3.2556581497e-01, /* 0xbea6b090 */ -pS2 = 2.0121252537e-01, /* 0x3e4e0aa8 */ -pS3 = -4.0055535734e-02, /* 0xbd241146 */ -pS4 = 7.9153501429e-04, /* 0x3a4f7f04 */ -pS5 = 3.4793309169e-05, /* 0x3811ef08 */ -qS1 = -2.4033949375e+00, /* 0xc019d139 */ -qS2 = 2.0209457874e+00, /* 0x4001572d */ -qS3 = -6.8828397989e-01, /* 0xbf303361 */ -qS4 = 7.7038154006e-02; /* 0x3d9dc62e */ + +pio2_hi = 1.57079637050628662109375f, +pio2_lo = -4.37113900018624283e-8f, +pio4_hi = 0.785398185253143310546875f, + +/* asin x = x + x^3 p(x^2) + -0.5 <= x <= 0.5; + Peak relative error 4.8e-9 */ +p0 = 1.666675248e-1f, +p1 = 7.495297643e-2f, +p2 = 4.547037598e-2f, +p3 = 2.417951451e-2f, +p4 = 4.216630880e-2f; #ifdef __STDC__ float __ieee754_asinf(float x) @@ -63,30 +68,26 @@ qS4 = 7.7038154006e-02; /* 0x3d9dc62e */ if(huge+x>one) return x;/* return x with inexact if x!=0*/ } else { t = x*x; - p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5))))); - q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4))); - w = p/q; + w = t * (p0 + t * (p1 + t * (p2 + t * (p3 + t * p4)))); return x+x*w; } } /* 1> |x|>= 0.5 */ w = one-fabsf(x); - t = w*(float)0.5; - p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5))))); - q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4))); + t = w*0.5f; + p = t * (p0 + t * (p1 + t * (p2 + t * (p3 + t * p4)))); s = __ieee754_sqrtf(t); if(ix>=0x3F79999A) { /* if |x| > 0.975 */ - w = p/q; - t = pio2_hi-((float)2.0*(s+s*w)-pio2_lo); + t = pio2_hi-(2.0f*(s+s*p)-pio2_lo); } else { int32_t iw; w = s; GET_FLOAT_WORD(iw,w); SET_FLOAT_WORD(w,iw&0xfffff000); c = (t-w*w)/(s+w); - r = p/q; - p = (float)2.0*s*r-(pio2_lo-(float)2.0*c); - q = pio4_hi-(float)2.0*w; + r = p; + p = 2.0f*s*r-(pio2_lo-2.0f*c); + q = pio4_hi-2.0f*w; t = pio4_hi-(p-q); } if(hx>0) return t; else return -t; |