summaryrefslogtreecommitdiff
path: root/src/math/acos.c
diff options
context:
space:
mode:
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/acos.c
parent482ccd2f7497a79ca83e998f54e823e7cedaaa6e (diff)
downloadmusl-b12a73d5bf595b7fbb73db30c6bb144078e86ef5.tar.gz
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/acos.c')
-rw-r--r--src/math/acos.c74
1 files changed, 37 insertions, 37 deletions
diff --git a/src/math/acos.c b/src/math/acos.c
index 0eb15bed..be95d25e 100644
--- a/src/math/acos.c
+++ b/src/math/acos.c
@@ -36,12 +36,8 @@
#include "libm.h"
static const double
-pi = 3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */
-pio2_hi = 1.57079632679489655800e+00; /* 0x3FF921FB, 0x54442D18 */
-// FIXME
-static const volatile double
-pio2_lo = 6.12323399573676603587e-17; /* 0x3C91A626, 0x33145C07 */
-static const double
+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 */
@@ -53,49 +49,53 @@ 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 acos(double x)
{
- double z,p,q,r,w,s,c,df;
- int32_t hx,ix;
+ double z,w,s,c,df;
+ 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) { /* |x|==1 */
- if (hx > 0) return 0.0; /* acos(1) = 0 */
- return pi + 2.0*pio2_lo; /* acos(-1)= pi */
+ if ((ix-0x3ff00000 | lx) == 0) {
+ /* acos(1)=0, acos(-1)=pi */
+ if (hx >> 31)
+ return 2*pio2_hi + 0x1p-1000;
+ return 0;
}
- return (x-x)/(x-x); /* acos(|x|>1) is NaN */
+ return 0/(x-x);
}
- if (ix < 0x3fe00000) { /* |x| < 0.5 */
+ /* |x| < 0.5 */
+ if (ix < 0x3fe00000) {
if (ix <= 0x3c600000) /* |x| < 2**-57 */
- return pio2_hi + pio2_lo;
- z = x*x;
- p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
- q = 1.0+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
- r = p/q;
- return pio2_hi - (x - (pio2_lo-x*r));
- } else if (hx < 0) { /* x < -0.5 */
+ return pio2_hi + 0x1p-1000;
+ return pio2_hi - (x - (pio2_lo-x*R(x*x)));
+ }
+ /* x < -0.5 */
+ if (hx >> 31) {
z = (1.0+x)*0.5;
- p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
- q = 1.0+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
- s = sqrt(z);
- r = p/q;
- w = r*s-pio2_lo;
- return pi - 2.0*(s+w);
- } else { /* x > 0.5 */
- z = (1.0-x)*0.5;
s = sqrt(z);
- df = s;
- SET_LOW_WORD(df,0);
- c = (z-df*df)/(s+df);
- p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
- q = 1.0+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
- r = p/q;
- w = r*s+c;
- return 2.0*(df+w);
+ w = R(z)*s-pio2_lo;
+ return 2*(pio2_hi - (s+w));
}
+ /* x > 0.5 */
+ z = (1.0-x)*0.5;
+ s = sqrt(z);
+ df = s;
+ SET_LOW_WORD(df,0);
+ c = (z-df*df)/(s+df);
+ w = R(z)*s+c;
+ return 2*(df+w);
}