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, 19 insertions, 21 deletions

diff --git a/src/math/atan2l.c b/src/math/atan2l.c
index 45cbfcc1..e86dbffb 100644
--- a/src/math/atan2l.c
+++ b/src/math/atan2l.c
@@ -24,8 +24,6 @@ long double atan2l(long double y, long double x)
 }
 #elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384
 #include "__invtrigl.h"
-// FIXME:
-static const volatile long double tiny = 1.0e-300;
 
 long double atan2l(long double y, long double x)
 {
@@ -40,12 +38,12 @@ long double atan2l(long double y, long double x)
 	ux.e = x;
 	expsignx = ux.xbits.expsign;
 	exptx = expsignx & 0x7fff;
-	if ((exptx==BIAS+LDBL_MAX_EXP &&
+	if ((exptx==0x7fff &&
 	     ((ux.bits.manh&~LDBL_NBIT)|ux.bits.manl)!=0) || /* x is NaN */
-	    (expty==BIAS+LDBL_MAX_EXP &&
+	    (expty==0x7fff &&
 	     ((uy.bits.manh&~LDBL_NBIT)|uy.bits.manl)!=0))   /* y is NaN */
 		return x+y;
-	if (expsignx==BIAS && ((ux.bits.manh&~LDBL_NBIT)|ux.bits.manl)==0) /* x=1.0 */
+	if (expsignx==0x3fff && ((ux.bits.manh&~LDBL_NBIT)|ux.bits.manl)==0) /* x=1.0 */
 		return atanl(y);
 	m = ((expsigny>>15)&1) | ((expsignx>>14)&2);  /* 2*sign(x)+sign(y) */
 
@@ -54,39 +52,39 @@ long double atan2l(long double y, long double x)
 		switch(m) {
 		case 0:
 		case 1: return y;           /* atan(+-0,+anything)=+-0 */
-		case 2: return  pi_hi+tiny; /* atan(+0,-anything) = pi */
-		case 3: return -pi_hi-tiny; /* atan(-0,-anything) =-pi */
+		case 2: return  2*pio2_hi+0x1p-1000; /* atan(+0,-anything) = pi */
+		case 3: return -2*pio2_hi-0x1p-1000; /* atan(-0,-anything) =-pi */
 		}
 	}
 	/* when x = 0 */
 	if (exptx==0 && ((ux.bits.manh&~LDBL_NBIT)|ux.bits.manl)==0)
-		return expsigny < 0 ? -pio2_hi-tiny : pio2_hi+tiny;
+		return expsigny < 0 ? -pio2_hi-0x1p-1000 : pio2_hi+0x1p-1000;
 	/* when x is INF */
-	if (exptx == BIAS+LDBL_MAX_EXP) {
-		if (expty == BIAS+LDBL_MAX_EXP) {
+	if (exptx == 0x7fff) {
+		if (expty == 0x7fff) {
 			switch(m) {
-			case 0: return  pio2_hi*0.5+tiny; /* atan(+INF,+INF) */
-			case 1: return -pio2_hi*0.5-tiny; /* atan(-INF,+INF) */
-			case 2: return  1.5*pio2_hi+tiny; /* atan(+INF,-INF) */
-			case 3: return -1.5*pio2_hi-tiny; /* atan(-INF,-INF) */
+			case 0: return  pio2_hi*0.5+0x1p-1000; /* atan(+INF,+INF) */
+			case 1: return -pio2_hi*0.5-0x1p-1000; /* atan(-INF,+INF) */
+			case 2: return  1.5*pio2_hi+0x1p-1000; /* atan(+INF,-INF) */
+			case 3: return -1.5*pio2_hi-0x1p-1000; /* atan(-INF,-INF) */
 			}
 		} else {
 			switch(m) {
 			case 0: return  0.0;        /* atan(+...,+INF) */
 			case 1: return -0.0;        /* atan(-...,+INF) */
-			case 2: return  pi_hi+tiny; /* atan(+...,-INF) */
-			case 3: return -pi_hi-tiny; /* atan(-...,-INF) */
+			case 2: return  2*pio2_hi+0x1p-1000; /* atan(+...,-INF) */
+			case 3: return -2*pio2_hi-0x1p-1000; /* atan(-...,-INF) */
 			}
 		}
 	}
 	/* when y is INF */
-	if (expty == BIAS+LDBL_MAX_EXP)
-		return expsigny < 0 ? -pio2_hi-tiny : pio2_hi+tiny;
+	if (expty == 0x7fff)
+		return expsigny < 0 ? -pio2_hi-0x1p-1000 : pio2_hi+0x1p-1000;
 
 	/* compute y/x */
 	k = expty-exptx;
 	if(k > LDBL_MANT_DIG+2) { /* |y/x| huge */
-		z = pio2_hi+pio2_lo;
+		z = pio2_hi+0x1p-1000;
 		m &= 1;
 	} else if (expsignx < 0 && k < -LDBL_MANT_DIG-2) /* |y/x| tiny, x<0 */
 		z = 0.0;
@@ -95,9 +93,9 @@ long double atan2l(long double y, long double x)
 	switch (m) {
 	case 0: return z;               /* atan(+,+) */
 	case 1: return -z;              /* atan(-,+) */
-	case 2: return pi_hi-(z-pi_lo); /* atan(+,-) */
+	case 2: return 2*pio2_hi-(z-2*pio2_lo); /* atan(+,-) */
 	default: /* case 3 */
-		return (z-pi_lo)-pi_hi; /* atan(-,-) */
+		return (z-2*pio2_lo)-2*pio2_hi; /* atan(-,-) */
 	}
 }
 #endif