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

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);
 }