diff options
Diffstat (limited to 'src/math/asin.c')
| -rw-r--r-- | src/math/asin.c | 71 |
1 files changed, 36 insertions, 35 deletions
diff --git a/src/math/asin.c b/src/math/asin.c index e3d8b250..a1906b08 100644 --- a/src/math/asin.c +++ b/src/math/asin.c @@ -42,10 +42,8 @@ #include "libm.h" static const double -huge = 1.000e+300, pio2_hi = 1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */ pio2_lo = 6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */ -pio4_hi = 7.85398163397448278999e-01, /* 0x3FE921FB, 0x54442D18 */ /* coefficients for R(x^2) */ pS0 = 1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */ pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */ @@ -58,51 +56,54 @@ qS2 = 2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */ qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */ qS4 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */ +static double R(double z) +{ + double p, q; + p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5))))); + q = 1.0+z*(qS1+z*(qS2+z*(qS3+z*qS4))); + return p/q; +} + double asin(double x) { - double t=0.0,w,p,q,c,r,s; - int32_t hx,ix; + double z,r,s; + uint32_t hx,ix; GET_HIGH_WORD(hx, x); ix = hx & 0x7fffffff; - if (ix >= 0x3ff00000) { /* |x|>= 1 */ + /* |x| >= 1 or nan */ + if (ix >= 0x3ff00000) { uint32_t lx; - GET_LOW_WORD(lx, x); if ((ix-0x3ff00000 | lx) == 0) /* asin(1) = +-pi/2 with inexact */ - return x*pio2_hi + x*pio2_lo; - return (x-x)/(x-x); /* asin(|x|>1) is NaN */ - } else if (ix < 0x3fe00000) { /* |x|<0.5 */ - if (ix < 0x3e500000) { /* if |x| < 2**-26 */ - if (huge+x > 1.0) - return x; /* return x with inexact if x!=0*/ + return x*pio2_hi + 0x1p-1000; + return 0/(x-x); + } + /* |x| < 0.5 */ + if (ix < 0x3fe00000) { + if (ix < 0x3e500000) { + /* |x|<0x1p-26, return x with inexact if x!=0*/ + FORCE_EVAL(x + 0x1p1000); + return x; } - t = x*x; - p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5))))); - q = 1.0+t*(qS1+t*(qS2+t*(qS3+t*qS4))); - w = p/q; - return x + x*w; + return x + x*R(x*x); } /* 1 > |x| >= 0.5 */ - w = 1.0 - fabs(x); - t = w*0.5; - p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5))))); - q = 1.0+t*(qS1+t*(qS2+t*(qS3+t*qS4))); - s = sqrt(t); - if (ix >= 0x3FEF3333) { /* if |x| > 0.975 */ - w = p/q; - t = pio2_hi-(2.0*(s+s*w)-pio2_lo); + z = (1 - fabs(x))*0.5; + s = sqrt(z); + r = R(z); + if (ix >= 0x3fef3333) { /* if |x| > 0.975 */ + x = pio2_hi-(2*(s+s*r)-pio2_lo); } else { - w = s; - SET_LOW_WORD(w,0); - c = (t-w*w)/(s+w); - r = p/q; - p = 2.0*s*r-(pio2_lo-2.0*c); - q = pio4_hi - 2.0*w; - t = pio4_hi - (p-q); + double f,c; + /* f+c = sqrt(z) */ + f = s; + SET_LOW_WORD(f,0); + c = (z-f*f)/(s+f); + x = 0.5*pio2_hi - (2*s*r - (pio2_lo-2*c) - (0.5*pio2_hi-2*f)); } - if (hx > 0) - return t; - return -t; + if (hx >> 31) + return -x; + return x; } |