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authorSzabolcs Nagy <nsz@port70.net>2012-12-11 23:56:59 +0100
committerSzabolcs Nagy <nsz@port70.net>2012-12-11 23:56:59 +0100
commitb12a73d5bf595b7fbb73db30c6bb144078e86ef5 (patch)
tree547edc4ee13453230bb1c154015150b9fc88c766 /src/math/asin.c
parent482ccd2f7497a79ca83e998f54e823e7cedaaa6e (diff)
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math: clean up inverse trigonometric functions
modifications: * avoid unsigned->signed conversions * removed various volatile hacks * use FORCE_EVAL when evaluating only for side-effects * factor out R() rational approximation instead of manual inline * __invtrigl.h now only provides __invtrigl_R, __pio2_hi and __pio2_lo * use 2*pio2_hi, 2*pio2_lo instead of pi_hi, pi_lo otherwise the logic is not changed, long double versions will need a revisit when a genaral long double cleanup happens
Diffstat (limited to 'src/math/asin.c')
-rw-r--r--src/math/asin.c71
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;
}