From c6383b7b10303457306932584fc23f24b5153a81 Mon Sep 17 00:00:00 2001
From: Szabolcs Nagy <nsz@port70.net>
Date: Sun, 16 Dec 2012 20:28:43 +0100
Subject: [PATCH] math: use 0x1p-120f and 0x1p120f for tiny and huge values

previously 0x1p-1000 and 0x1p1000 was used for raising inexact
exception like x+tiny (when x is big) or x+huge (when x is small)

the rational is that these float consts are large enough
(0x1p-120 + 1 raises inexact even on ld128 which has 113 mant bits)
and float consts maybe smaller or easier to load on some platforms
(on i386 this reduced the object file size by 4bytes in some cases)
---
 src/math/acos.c   |  4 ++--
 src/math/acosl.c  |  4 ++--
 src/math/asin.c   |  4 ++--
 src/math/asinh.c  |  2 +-
 src/math/asinhl.c |  2 +-
 src/math/asinl.c  |  4 ++--
 src/math/atan.c   |  4 ++--
 src/math/atan2l.c | 22 +++++++++++-----------
 src/math/atanl.c  |  4 ++--
 src/math/exp2f.c  |  4 ++--
 10 files changed, 27 insertions(+), 27 deletions(-)

diff --git a/src/math/acos.c b/src/math/acos.c
index be95d25e..cd5d06a6 100644
--- a/src/math/acos.c
+++ b/src/math/acos.c
@@ -72,7 +72,7 @@ double acos(double x)
 		if ((ix-0x3ff00000 | lx) == 0) {
 			/* acos(1)=0, acos(-1)=pi */
 			if (hx >> 31)
-				return 2*pio2_hi + 0x1p-1000;
+				return 2*pio2_hi + 0x1p-120f;
 			return 0;
 		}
 		return 0/(x-x);
@@ -80,7 +80,7 @@ double acos(double x)
 	/* |x| < 0.5 */
 	if (ix < 0x3fe00000) {
 		if (ix <= 0x3c600000)  /* |x| < 2**-57 */
-			return pio2_hi + 0x1p-1000;
+			return pio2_hi + 0x1p-120f;
 		return pio2_hi - (x - (pio2_lo-x*R(x*x)));
 	}
 	/* x < -0.5 */
diff --git a/src/math/acosl.c b/src/math/acosl.c
index 9e9b01e4..9e7b7fb3 100644
--- a/src/math/acosl.c
+++ b/src/math/acosl.c
@@ -38,14 +38,14 @@ long double acosl(long double x)
 			((u.bits.manh & ~LDBL_NBIT) | u.bits.manl) == 0) {
 			if (expsign > 0)
 				return 0;  /* acos(1) = 0 */
-			return 2*pio2_hi + 0x1p-1000;  /* acos(-1)= pi */
+			return 2*pio2_hi + 0x1p-120f;  /* acos(-1)= pi */
 		}
 		return 0/(x-x);  /* acos(|x|>1) is NaN */
 	}
 	/* |x| < 0.5 */
 	if (expt < 0x3fff - 1) {
 		if (expt < 0x3fff - 65)
-			return pio2_hi + 0x1p-1000;  /* x < 0x1p-65: acosl(x)=pi/2 */
+			return pio2_hi + 0x1p-120f;  /* x < 0x1p-65: acosl(x)=pi/2 */
 		return pio2_hi - (x - (pio2_lo - x * __invtrigl_R(x*x)));
 	}
 	/* x < -0.5 */
diff --git a/src/math/asin.c b/src/math/asin.c
index a1906b08..d61c04b4 100644
--- a/src/math/asin.c
+++ b/src/math/asin.c
@@ -77,14 +77,14 @@ double asin(double x)
 		GET_LOW_WORD(lx, x);
 		if ((ix-0x3ff00000 | lx) == 0)
 			/* asin(1) = +-pi/2 with inexact */
-			return x*pio2_hi + 0x1p-1000;
+			return x*pio2_hi + 0x1p-120f;
 		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);
+			FORCE_EVAL(x + 0x1p120f);
 			return x;
 		}
 		return x + x*R(x*x);
diff --git a/src/math/asinh.c b/src/math/asinh.c
index 4152dc39..0829f228 100644
--- a/src/math/asinh.c
+++ b/src/math/asinh.c
@@ -22,7 +22,7 @@ double asinh(double x)
 		x = log1p(x + x*x/(sqrt(x*x+1)+1));
 	} else {
 		/* |x| < 0x1p-26, raise inexact if x != 0 */
-		FORCE_EVAL(x + 0x1p1000);
+		FORCE_EVAL(x + 0x1p120f);
 	}
 	return s ? -x : x;
 }
diff --git a/src/math/asinhl.c b/src/math/asinhl.c
index db966246..3ea88745 100644
--- a/src/math/asinhl.c
+++ b/src/math/asinhl.c
@@ -31,7 +31,7 @@ long double asinhl(long double x)
 		x = log1pl(x + x*x/(sqrtl(x*x+1)+1));
 	} else {
 		/* |x| < 0x1p-32, raise inexact if x!=0 */
-		FORCE_EVAL(x + 0x1p1000);
+		FORCE_EVAL(x + 0x1p120f);
 	}
 	return s ? -x : x;
 }
diff --git a/src/math/asinl.c b/src/math/asinl.c
index 0ef9853b..8799341d 100644
--- a/src/math/asinl.c
+++ b/src/math/asinl.c
@@ -39,13 +39,13 @@ long double asinl(long double x)
 		if (expt == 0x3fff &&
 		    ((u.bits.manh&~LDBL_NBIT)|u.bits.manl) == 0)
 			/* asin(+-1)=+-pi/2 with inexact */
-			return x*pio2_hi + 0x1p-1000;
+			return x*pio2_hi + 0x1p-120f;
 		return 0/(x-x);
 	}
 	if (expt < 0x3fff - 1) {  /* |x| < 0.5 */
 		if (expt < 0x3fff - 32) {  /* |x|<0x1p-32, asinl(x)=x */
 			/* return x with inexact if x!=0 */
-			FORCE_EVAL(x + 0x1p1000);
+			FORCE_EVAL(x + 0x1p120f);
 			return x;
 		}
 		return x + x*__invtrigl_R(x*x);
diff --git a/src/math/atan.c b/src/math/atan.c
index 7fd8a3b8..3c9a59ff 100644
--- a/src/math/atan.c
+++ b/src/math/atan.c
@@ -72,13 +72,13 @@ double atan(double x)
 	if (ix >= 0x44100000) {   /* if |x| >= 2^66 */
 		if (isnan(x))
 			return x;
-		z = atanhi[3] + 0x1p-1000;
+		z = atanhi[3] + 0x1p-120f;
 		return sign ? -z : z;
 	}
 	if (ix < 0x3fdc0000) {    /* |x| < 0.4375 */
 		if (ix < 0x3e400000) {  /* |x| < 2^-27 */
 			/* raise inexact if x!=0 */
-			FORCE_EVAL(x + 0x1p1000);
+			FORCE_EVAL(x + 0x1p120f);
 			return x;
 		}
 		id = -1;
diff --git a/src/math/atan2l.c b/src/math/atan2l.c
index e86dbffb..7cb42c2f 100644
--- a/src/math/atan2l.c
+++ b/src/math/atan2l.c
@@ -52,39 +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  2*pio2_hi+0x1p-1000; /* atan(+0,-anything) = pi */
-		case 3: return -2*pio2_hi-0x1p-1000; /* atan(-0,-anything) =-pi */
+		case 2: return  2*pio2_hi+0x1p-120f; /* atan(+0,-anything) = pi */
+		case 3: return -2*pio2_hi-0x1p-120f; /* atan(-0,-anything) =-pi */
 		}
 	}
 	/* when x = 0 */
 	if (exptx==0 && ((ux.bits.manh&~LDBL_NBIT)|ux.bits.manl)==0)
-		return expsigny < 0 ? -pio2_hi-0x1p-1000 : pio2_hi+0x1p-1000;
+		return expsigny < 0 ? -pio2_hi-0x1p-120f : pio2_hi+0x1p-120f;
 	/* when x is INF */
 	if (exptx == 0x7fff) {
 		if (expty == 0x7fff) {
 			switch(m) {
-			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) */
+			case 0: return  pio2_hi*0.5+0x1p-120f; /* atan(+INF,+INF) */
+			case 1: return -pio2_hi*0.5-0x1p-120f; /* atan(-INF,+INF) */
+			case 2: return  1.5*pio2_hi+0x1p-120f; /* atan(+INF,-INF) */
+			case 3: return -1.5*pio2_hi-0x1p-120f; /* atan(-INF,-INF) */
 			}
 		} else {
 			switch(m) {
 			case 0: return  0.0;        /* atan(+...,+INF) */
 			case 1: return -0.0;        /* atan(-...,+INF) */
-			case 2: return  2*pio2_hi+0x1p-1000; /* atan(+...,-INF) */
-			case 3: return -2*pio2_hi-0x1p-1000; /* atan(-...,-INF) */
+			case 2: return  2*pio2_hi+0x1p-120f; /* atan(+...,-INF) */
+			case 3: return -2*pio2_hi-0x1p-120f; /* atan(-...,-INF) */
 			}
 		}
 	}
 	/* when y is INF */
 	if (expty == 0x7fff)
-		return expsigny < 0 ? -pio2_hi-0x1p-1000 : pio2_hi+0x1p-1000;
+		return expsigny < 0 ? -pio2_hi-0x1p-120f : pio2_hi+0x1p-120f;
 
 	/* compute y/x */
 	k = expty-exptx;
 	if(k > LDBL_MANT_DIG+2) { /* |y/x| huge */
-		z = pio2_hi+0x1p-1000;
+		z = pio2_hi+0x1p-120f;
 		m &= 1;
 	} else if (expsignx < 0 && k < -LDBL_MANT_DIG-2) /* |y/x| tiny, x<0 */
 		z = 0.0;
diff --git a/src/math/atanl.c b/src/math/atanl.c
index 6a480a7a..e76693e4 100644
--- a/src/math/atanl.c
+++ b/src/math/atanl.c
@@ -80,7 +80,7 @@ long double atanl(long double x)
 		if (expt == 0x7fff &&
 		    ((u.bits.manh&~LDBL_NBIT)|u.bits.manl)!=0)  /* NaN */
 			return x+x;
-		z = atanhi[3] + 0x1p-1000;
+		z = atanhi[3] + 0x1p-120f;
 		return expsign < 0 ? -z : z;
 	}
 	/* Extract the exponent and the first few bits of the mantissa. */
@@ -89,7 +89,7 @@ long double atanl(long double x)
 	if (expman < ((0x3fff - 2) << 8) + 0xc0) {  /* |x| < 0.4375 */
 		if (expt < 0x3fff - 32) {   /* if |x| is small, atanl(x)~=x */
 			/* raise inexact if x!=0 */
-			FORCE_EVAL(x + 0x1p1000);
+			FORCE_EVAL(x + 0x1p120f);
 			return x;
 		}
 		id = -1;
diff --git a/src/math/exp2f.c b/src/math/exp2f.c
index 279f32de..ea50db4a 100644
--- a/src/math/exp2f.c
+++ b/src/math/exp2f.c
@@ -97,11 +97,11 @@ float exp2f(float x)
 			return x;
 		}
 		if (x >= 128) {
-			STRICT_ASSIGN(float, x, x * 0x1p127);
+			STRICT_ASSIGN(float, x, x * 0x1p127f);
 			return x;
 		}
 		if (x <= -150) {
-			STRICT_ASSIGN(float, x, 0x1p-100*0x1p-100);
+			STRICT_ASSIGN(float, x, 0x1p-100f*0x1p-100f);
 			return x;
 		}
 	} else if (ix <= 0x33000000) {  /* |x| <= 0x1p-25 */
-- 
2.25.1