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, 25 insertions, 26 deletions

diff --git a/src/math/asinf.c b/src/math/asinf.c
index c1c42c7b..462bf043 100644
--- a/src/math/asinf.c
+++ b/src/math/asinf.c
@@ -12,52 +12,51 @@
  * is preserved.
  * ====================================================
  */
-
 #include "libm.h"
 
+static const double
+pio2 = 1.570796326794896558e+00;
+
 static const float
-huge = 1.000e+30,
 /* coefficients for R(x^2) */
 pS0 =  1.6666586697e-01,
 pS1 = -4.2743422091e-02,
 pS2 = -8.6563630030e-03,
 qS1 = -7.0662963390e-01;
 
-static const double
-pio2 = 1.570796326794896558e+00;
+static float R(float z)
+{
+	float p, q;
+	p = z*(pS0+z*(pS1+z*pS2));
+	q = 1.0f+z*qS1;
+	return p/q;
+}
 
 float asinf(float x)
 {
 	double s;
-	float t,w,p,q;
-	int32_t hx,ix;
+	float z;
+	uint32_t hx,ix;
 
 	GET_FLOAT_WORD(hx, x);
 	ix = hx & 0x7fffffff;
 	if (ix >= 0x3f800000) {  /* |x| >= 1 */
 		if (ix == 0x3f800000)  /* |x| == 1 */
-			return x*pio2;  /* asin(+-1) = +-pi/2 with inexact */
-		return (x-x)/(x-x);  /* asin(|x|>1) is NaN */
-	} else if (ix < 0x3f000000) {  /* |x|<0.5 */
+			return x*pio2 + 0x1p-120f;  /* asin(+-1) = +-pi/2 with inexact */
+		return 0/(x-x);  /* asin(|x|>1) is NaN */
+	}
+	if (ix < 0x3f000000) {  /* |x| < 0.5 */
 		if (ix < 0x39800000) {  /* |x| < 2**-12 */
-			if (huge+x > 1.0f)
-				return x; /* return x with inexact if x!=0 */
+			FORCE_EVAL(x + 0x1p120f);
+			return x; /* return x with inexact if x!=0 */
 		}
-		t = x*x;
-		p = t*(pS0+t*(pS1+t*pS2));
-		q = 1.0f+t*qS1;
-		w = p/q;
-		return x + x*w;
+		return x + x*R(x*x);
 	}
 	/* 1 > |x| >= 0.5 */
-	w = 1.0f - fabsf(x);
-	t = w*0.5f;
-	p = t*(pS0+t*(pS1+t*pS2));
-	q = 1.0f+t*qS1;
-	s = sqrt(t);
-	w = p/q;
-	t = pio2-2.0*(s+s*w);
-	if (hx > 0)
-		return t;
-	return -t;
+	z = (1 - fabsf(x))*0.5f;
+	s = sqrt(z);
+	x = pio2 - 2*(s+s*R(z));
+	if (hx >> 31)
+		return -x;
+	return x;
 }