* libc/include/machine/ieeefp.h: Comment about new configuration

	macros _FLT_LARGEST_EXPONENT_IS_NORMAL and _FLT_NO_DENORMALS.
	* libm/common/fdlib.h: Define new macros for testing floats.
	* libm/common/sf_*: Use them.
	* libm/math/ef_*: Likewise.
	* libm/math/sf_*: Likewise.

41 files changed, 306 insertions, 166 deletions

diff --git a/newlib/ChangeLog b/newlib/ChangeLog
index 77426d3cb..46746a42f 100644
--- a/newlib/ChangeLog
+++ b/newlib/ChangeLog
@@ -1,3 +1,12 @@
+2001-04-04  Richard Sandiford  <rsandifo@redhat.com>
+
+	* libc/include/machine/ieeefp.h: Comment about new configuration
+	macros _FLT_LARGEST_EXPONENT_IS_NORMAL and _FLT_NO_DENORMALS.
+	* libm/common/fdlib.h: Define new macros for testing floats.
+	* libm/common/sf_*: Use them.
+	* libm/math/ef_*: Likewise.
+	* libm/math/sf_*: Likewise.
+
 2001-03-29  Jeff Johnston  <jjohnstn@redhat.com>
 
 	* libc/sys/arm/setjmp.S: Added .code 16 specifier for thumb-mode
diff --git a/newlib/libc/include/machine/ieeefp.h b/newlib/libc/include/machine/ieeefp.h
index 570db14ef..b96f91274 100644
--- a/newlib/libc/include/machine/ieeefp.h
+++ b/newlib/libc/include/machine/ieeefp.h
@@ -1,6 +1,24 @@
 #ifndef __IEEE_BIG_ENDIAN
 #ifndef __IEEE_LITTLE_ENDIAN
 
+/* This file can define macros to choose variations of the IEEE float
+   format:
+
+   _FLT_LARGEST_EXPONENT_IS_NORMAL
+
+	Defined if the float format uses the largest exponent for finite
+	numbers rather than NaN and infinity representations.  Such a
+	format cannot represent NaNs or infinities at all, but it's FLT_MAX
+	is twice the IEEE value.
+
+   _FLT_NO_DENORMALS
+
+	Defined if the float format does not support IEEE denormals.  Every
+	float with a zero exponent is taken to be a zero representation.
+
+   ??? At the moment, there are no equivalent macros for doubles and
+   the macros are not fully supported by --enable-newlib-hw-fp.  */
+
 #if defined(__arm__) || defined(__thumb__)
 /* ARM always has big-endian words.  Within those words the byte ordering
    appears to be big or little endian.  Newlib doesn't seem to care about
diff --git a/newlib/libm/common/fdlibm.h b/newlib/libm/common/fdlibm.h
index 752d24246..5ca1a917b 100644
--- a/newlib/libm/common/fdlibm.h
+++ b/newlib/libm/common/fdlibm.h
@@ -18,14 +18,116 @@
 /* CYGNUS LOCAL: Default to XOPEN_MODE.  */
 #define _XOPEN_MODE
 
+/* Most routines need to check whether a float is finite, infinite, or not a
+   number, and many need to know whether the result of an operation will
+   overflow.  These conditions depend on whether the largest exponent is
+   used for NaNs & infinities, or whether it's used for finite numbers.  The
+   macros below wrap up that kind of information:
+
+   FLT_UWORD_IS_FINITE(X)
+	True if a positive float with bitmask X is finite.
+
+   FLT_UWORD_IS_NAN(X)
+	True if a positive float with bitmask X is not a number.
+
+   FLT_UWORD_IS_INFINITE(X)
+	True if a positive float with bitmask X is +infinity.
+
+   FLT_UWORD_MAX
+	The bitmask of FLT_MAX.
+
+   FLT_UWORD_HALF_MAX
+	The bitmask of FLT_MAX/2.
+
+   FLT_UWORD_EXP_MAX
+	The bitmask of the largest finite exponent (129 if the largest
+	exponent is used for finite numbers, 128 otherwise).
+
+   FLT_UWORD_LOG_MAX
+	The bitmask of log(FLT_MAX), rounded down.  This value is the largest
+	input that can be passed to exp() without producing overflow.
+
+   FLT_UWORD_LOG_2MAX
+	The bitmask of log(2*FLT_MAX), rounded down.  This value is the
+	largest input than can be passed to cosh() without producing
+	overflow.
+
+   FLT_LARGEST_EXP
+	The largest biased exponent that can be used for finite numbers
+	(255 if the largest exponent is used for finite numbers, 254
+	otherwise) */
+
+#ifdef _FLT_LARGEST_EXPONENT_IS_NORMAL
+#define FLT_UWORD_IS_FINITE(x) 1
+#define FLT_UWORD_IS_NAN(x) 0
+#define FLT_UWORD_IS_INFINITE(x) 0
+#define FLT_UWORD_MAX 0x7fffffff
+#define FLT_UWORD_EXP_MAX 0x43010000
+#define FLT_UWORD_LOG_MAX 0x42b2d4fc
+#define FLT_UWORD_LOG_2MAX 0x42b437e0
+#define HUGE ((float)0X1.FFFFFEP128)
+#else
+#define FLT_UWORD_IS_FINITE(x) ((x)<0x7f800000L)
+#define FLT_UWORD_IS_NAN(x) ((x)>0x7f800000L)
+#define FLT_UWORD_IS_INFINITE(x) ((x)==0x7f800000L)
+#define FLT_UWORD_MAX 0x7f7fffff
+#define FLT_UWORD_EXP_MAX 0x43000000
+#define FLT_UWORD_LOG_MAX 0x42b17217
+#define FLT_UWORD_LOG_2MAX 0x42b2d4fc
+#define HUGE ((float)3.40282346638528860e+38)
+#endif
+#define FLT_UWORD_HALF_MAX (FLT_UWORD_MAX-(1<<23))
+#define FLT_LARGEST_EXP (FLT_UWORD_MAX>>23)
+
+/* Many routines check for zero and subnormal numbers.  Such things depend
+   on whether the target supports denormals or not:
+
+   FLT_UWORD_IS_ZERO(X)
+	True if a positive float with bitmask X is +0.	Without denormals,
+	any float with a zero exponent is a +0 representation.	With
+	denormals, the only +0 representation is a 0 bitmask.
+
+   FLT_UWORD_IS_SUBNORMAL(X)
+	True if a non-zero positive float with bitmask X is subnormal.
+	(Routines should check for zeros first.)
+
+   FLT_UWORD_MIN
+	The bitmask of the smallest float above +0.  Call this number
+	REAL_FLT_MIN...
+
+   FLT_UWORD_EXP_MIN
+	The bitmask of the float representation of REAL_FLT_MIN's exponent.
+
+   FLT_UWORD_LOG_MIN
+	The bitmask of |log(REAL_FLT_MIN)|, rounding down.
+
+   FLT_SMALLEST_EXP
+	REAL_FLT_MIN's exponent - EXP_BIAS (1 if denormals are not supported,
+	-22 if they are).
+*/
+
+#ifdef _FLT_NO_DENORMALS
+#define FLT_UWORD_IS_ZERO(x) ((x)<0x00800000L)
+#define FLT_UWORD_IS_SUBNORMAL(x) 0
+#define FLT_UWORD_MIN 0x00800000
+#define FLT_UWORD_EXP_MIN 0x42fc0000
+#define FLT_UWORD_LOG_MIN 0x42aeac50
+#define FLT_SMALLEST_EXP 1
+#else
+#define FLT_UWORD_IS_ZERO(x) ((x)==0)
+#define FLT_UWORD_IS_SUBNORMAL(x) ((x)<0x00800000L)
+#define FLT_UWORD_MIN 0x00000001
+#define FLT_UWORD_EXP_MIN 0x43160000
+#define FLT_UWORD_LOG_MIN 0x42cff1b5
+#define FLT_SMALLEST_EXP -22
+#endif
+
 #ifdef __STDC__
 #define	__P(p)	p
 #else
 #define	__P(p)	()
 #endif
 
-#define	HUGE	((float)3.40282346638528860e+38)
-
 /* 
  * set X_TLOSS = pi*2**52, which is possibly defined in <values.h>
  * (one may replace the following line by "#include <values.h>")
diff --git a/newlib/libm/common/sf_cbrt.c b/newlib/libm/common/sf_cbrt.c
index c053d9548..fe632f0a8 100644
--- a/newlib/libm/common/sf_cbrt.c
+++ b/newlib/libm/common/sf_cbrt.c
@@ -53,13 +53,14 @@ G =  3.5714286566e-01; /* 5/14      = 0x3eb6db6e */
 	GET_FLOAT_WORD(hx,x);
 	sign=hx&0x80000000; 		/* sign= sign(x) */
 	hx  ^=sign;
-	if(hx>=0x7f800000) return(x+x); /* cbrt(NaN,INF) is itself */
-	if(hx==0) 
-	    return(x);		/* cbrt(0) is itself */
+	if(!FLT_UWORD_IS_FINITE(hx))
+	    return(x+x);		/* cbrt(NaN,INF) is itself */
+	if(FLT_UWORD_IS_ZERO(hx))
+	    return(x);			/* cbrt(0) is itself */
 
 	SET_FLOAT_WORD(x,hx);	/* x <- |x| */
     /* rough cbrt to 5 bits */
-	if(hx<0x00800000) 		/* subnormal number */
+	if(FLT_UWORD_IS_SUBNORMAL(hx)) 		/* subnormal number */
 	  {SET_FLOAT_WORD(t,0x4b800000); /* set t= 2**24 */
 	   t*=x; GET_FLOAT_WORD(high,t); SET_FLOAT_WORD(t,high/3+B2);
 	  }
diff --git a/newlib/libm/common/sf_expm1.c b/newlib/libm/common/sf_expm1.c
index e9108b7b8..4ba3b815a 100644
--- a/newlib/libm/common/sf_expm1.c
+++ b/newlib/libm/common/sf_expm1.c
@@ -27,7 +27,6 @@ static float
 one		= 1.0,
 huge		= 1.0e+30,
 tiny		= 1.0e-30,
-o_threshold	= 8.8721679688e+01,/* 0x42b17180 */
 ln2_hi		= 6.9313812256e-01,/* 0x3f317180 */
 ln2_lo		= 9.0580006145e-06,/* 0x3717f7d1 */
 invln2		= 1.4426950216e+00,/* 0x3fb8aa3b */
@@ -56,13 +55,12 @@ Q5  =  -2.0109921195e-07; /* 0xb457edbb */
 
     /* filter out huge and non-finite argument */
 	if(hx >= 0x4195b844) {			/* if |x|>=27*ln2 */
-	    if(hx >= 0x42b17218) {		/* if |x|>=88.721... */
-                if(hx>0x7f800000)
-		    return x+x; 	 /* NaN */
-		if(hx==0x7f800000)
-		    return (xsb==0)? x:-1.0;/* exp(+-inf)={inf,-1} */
-	        if(x > o_threshold) return huge*huge; /* overflow */
-	    }
+	    if(FLT_UWORD_IS_NAN(hx))
+	        return x+x;
+	    if(FLT_UWORD_IS_INFINITE(hx))
+		return (xsb==0)? x:-1.0;/* exp(+-inf)={inf,-1} */
+	    if(xsb == 0 && hx > FLT_UWORD_LOG_MAX) /* if x>=o_threshold */
+		return huge*huge; /* overflow */
 	    if(xsb!=0) { /* x < -27*ln2, return -1.0 with inexact */
 		if(x+tiny<(float)0.0)	/* raise inexact */
 		return tiny-one;	/* return -1 */
diff --git a/newlib/libm/common/sf_finite.c b/newlib/libm/common/sf_finite.c
index 4c48f400f..cb7026fbd 100644
--- a/newlib/libm/common/sf_finite.c
+++ b/newlib/libm/common/sf_finite.c
@@ -29,7 +29,8 @@
 {
 	__int32_t ix;
 	GET_FLOAT_WORD(ix,x);
-	return  (int)((__uint32_t)((ix&0x7fffffff)-0x7f800000)>>31);
+	ix &= 0x7fffffff;
+	return (FLT_UWORD_IS_FINITE(ix));
 }
 
 #ifdef _DOUBLE_IS_32BITS
diff --git a/newlib/libm/common/sf_ilogb.c b/newlib/libm/common/sf_ilogb.c
index ee65594b1..ec59406e1 100644
--- a/newlib/libm/common/sf_ilogb.c
+++ b/newlib/libm/common/sf_ilogb.c
@@ -27,15 +27,14 @@
 
 	GET_FLOAT_WORD(hx,x);
 	hx &= 0x7fffffff;
-	if(hx<0x00800000) {
-	    if(hx==0) 
-		return - INT_MAX;	/* ilogb(0) = 0x80000001 */
-	    else			/* subnormal x */
-	        for (ix = -126,hx<<=8; hx>0; hx<<=1) ix -=1;
+	if(FLT_UWORD_IS_ZERO(hx))
+	    return - INT_MAX;	/* ilogb(0) = 0x80000001 */
+	if(FLT_UWORD_IS_SUBNORMAL(hx)) {
+	    for (ix = -126,hx<<=8; hx>0; hx<<=1) ix -=1;
 	    return ix;
 	}
-	else if (hx<0x7f800000) return (hx>>23)-127;
-	else return INT_MAX;
+	else if (!FLT_UWORD_IS_FINITE(hx)) return INT_MAX;
+	else return (hx>>23)-127;
 }
 
 #ifdef _DOUBLE_IS_32BITS
diff --git a/newlib/libm/common/sf_log1p.c b/newlib/libm/common/sf_log1p.c
index 5ae7fb936..e09170f3e 100644
--- a/newlib/libm/common/sf_log1p.c
+++ b/newlib/libm/common/sf_log1p.c
@@ -51,6 +51,7 @@ static float zero = 0.0;
 	ax = hx&0x7fffffff;
 
 	k = 1;
+	if (!FLT_UWORD_IS_FINITE(hx)) return x+x;
 	if (hx < 0x3ed413d7) {			/* x < 0.41422  */
 	    if(ax>=0x3f800000) {		/* x <= -1.0 */
 		if(x==(float)-1.0) return -two25/zero; /* log1p(-1)=+inf */
@@ -65,8 +66,7 @@ static float zero = 0.0;
 	    }
 	    if(hx>0||hx<=((__int32_t)0xbe95f61f)) {
 		k=0;f=x;hu=1;}	/* -0.2929<x<0.41422 */
-	} 
-	if (hx >= 0x7f800000) return x+x;
+	}
 	if(k!=0) {
 	    if(hx<0x5a000000) {
 		u  = (float)1.0+x; 
diff --git a/newlib/libm/common/sf_logb.c b/newlib/libm/common/sf_logb.c
index 6e67637fe..f193f91f6 100644
--- a/newlib/libm/common/sf_logb.c
+++ b/newlib/libm/common/sf_logb.c
@@ -25,8 +25,8 @@
 	__int32_t ix;
 	GET_FLOAT_WORD(ix,x);
 	ix &= 0x7fffffff;			/* high |x| */
-	if(ix==0) return (float)-1.0/fabsf(x);
-	if(ix>=0x7f800000) return x*x;
+	if(FLT_UWORD_IS_ZERO(ix)) return (float)-1.0/fabsf(x);
+	if(!FLT_UWORD_IS_FINITE(ix)) return x*x;
 	if((ix>>=23)==0) 			/* IEEE 754 logb */
 		return -126.0; 
 	else
diff --git a/newlib/libm/common/sf_nan.c b/newlib/libm/common/sf_nan.c
index cb3e1cd03..c8d7027f8 100644
--- a/newlib/libm/common/sf_nan.c
+++ b/newlib/libm/common/sf_nan.c
@@ -21,3 +21,4 @@
 }
 
 #endif /* defined(_DOUBLE_IS_32BITS) */
+
diff --git a/newlib/libm/common/sf_nextafter.c b/newlib/libm/common/sf_nextafter.c
index cd938d339..cea4da58d 100644
--- a/newlib/libm/common/sf_nextafter.c
+++ b/newlib/libm/common/sf_nextafter.c
@@ -29,15 +29,15 @@
 	ix = hx&0x7fffffff;		/* |x| */
 	iy = hy&0x7fffffff;		/* |y| */
 
-	if((ix>0x7f800000) ||   /* x is nan */ 
-	   (iy>0x7f800000))     /* y is nan */ 
-	   return x+y;				
+	if(FLT_UWORD_IS_NAN(ix) ||
+	   FLT_UWORD_IS_NAN(iy))
+	   return x+y;
 	if(x==y) return x;		/* x=y, return x */
-	if(ix==0) {				/* x == 0 */
-	    SET_FLOAT_WORD(x,(hy&0x80000000)|1);/* return +-minsubnormal */
+	if(FLT_UWORD_IS_ZERO(ix)) {		/* x == 0 */
+	    SET_FLOAT_WORD(x,(hy&0x80000000)|FLT_UWORD_MIN);
 	    y = x*x;
 	    if(y==x) return y; else return x;	/* raise underflow flag */
-	} 
+	}
 	if(hx>=0) {				/* x > 0 */
 	    if(hx>hy) {				/* x > y, x -= ulp */
 		hx -= 1;
@@ -52,7 +52,7 @@
 	    }
 	}
 	hy = hx&0x7f800000;
-	if(hy>=0x7f800000) return x+x;	/* overflow  */
+	if(hy>FLT_UWORD_MAX) return x+x;	/* overflow  */
 	if(hy<0x00800000) {		/* underflow */
 	    y = x*x;
 	    if(y!=x) {		/* raise underflow flag */
diff --git a/newlib/libm/common/sf_rint.c b/newlib/libm/common/sf_rint.c
index d38080a5d..6459b7a4c 100644
--- a/newlib/libm/common/sf_rint.c
+++ b/newlib/libm/common/sf_rint.c
@@ -33,15 +33,17 @@ TWO23[2]={
 #endif
 {
 	__int32_t i0,j0,sx;
-	__uint32_t i,i1;
+	__uint32_t i,i1,ix;
 	float t;
 	volatile float w;
 	GET_FLOAT_WORD(i0,x);
 	sx = (i0>>31)&1;
-	j0 = ((i0>>23)&0xff)-0x7f;
+	ix = (i0&0x7fffffff);
+	j0 = (ix>>23)-0x7f;
 	if(j0<23) {
-	    if(j0<0) { 	
-		if((i0&0x7fffffff)==0) return x;
+	    if(FLT_UWORD_IS_ZERO(ix))
+	        return x;
+	    if(j0<0) {
 		i1 = (i0&0x07fffff);
 		i0 &= 0xfff00000;
 		i0 |= ((i1|-i1)>>9)&0x400000;
@@ -58,8 +60,9 @@ TWO23[2]={
 		if((i0&i)!=0) i0 = (i0&(~i))|((0x100000)>>j0);
 	    }
 	} else {
-	    if(j0==0x80) return x+x;	/* inf or NaN */
-	    else return x;		/* x is integral */
+	    if(!FLT_UWORD_IS_FINITE(ix)) return x+x; /* inf or NaN */
+	    else
+	      return x;		/* x is integral */
 	}
 	SET_FLOAT_WORD(x,i0);
 	w = TWO23[sx]+x;
diff --git a/newlib/libm/common/sf_scalbn.c b/newlib/libm/common/sf_scalbn.c
index fb67c7816..700060010 100644
--- a/newlib/libm/common/sf_scalbn.c
+++ b/newlib/libm/common/sf_scalbn.c
@@ -15,6 +15,7 @@
 
 #include "fdlibm.h"
 #include <limits.h>
+#include <float.h>
 
 #if INT_MAX > 50000
 #define OVERFLOW_INT 50000
@@ -40,25 +41,30 @@ tiny   = 1.0e-30;
 #endif
 {
 	__int32_t  k,ix;
+	__uint32_t hx;
+
 	GET_FLOAT_WORD(ix,x);
-        k = (ix&0x7f800000)>>23;		/* extract exponent */
-        if (k==0) {				/* 0 or subnormal x */
-            if ((ix&0x7fffffff)==0) return x; /* +-0 */
+	hx = ix&0x7fffffff;
+        k = hx>>23;		/* extract exponent */
+	if (FLT_UWORD_IS_ZERO(hx))
+	    return x;
+        if (!FLT_UWORD_IS_FINITE(hx))
+	    return x+x;		/* NaN or Inf */
+        if (FLT_UWORD_IS_SUBNORMAL(hx)) {
 	    x *= two25;
 	    GET_FLOAT_WORD(ix,x);
 	    k = ((ix&0x7f800000)>>23) - 25; 
             if (n< -50000) return tiny*x; 	/*underflow*/
-	    }
-        if (k==0xff) return x+x;		/* NaN or Inf */
+        }
         k = k+n; 
-        if (k >  0xfe) return huge*copysignf(huge,x); /* overflow  */
+        if (k > FLT_LARGEST_EXP) return huge*copysignf(huge,x); /* overflow  */
         if (k > 0) 				/* normal result */
 	    {SET_FLOAT_WORD(x,(ix&0x807fffff)|(k<<23)); return x;}
-        if (k <= -25) {
+        if (k < FLT_SMALLEST_EXP) {
             if (n > OVERFLOW_INT) 	/* in case integer overflow in n+k */
 		return huge*copysignf(huge,x);	/*overflow*/
 	    else return tiny*copysignf(tiny,x);	/*underflow*/
-       }
+        }
         k += 25;				/* subnormal result */
 	SET_FLOAT_WORD(x,(ix&0x807fffff)|(k<<23));
         return x*twom25;
diff --git a/newlib/libm/math/ef_acosh.c b/newlib/libm/math/ef_acosh.c
index 37c788576..1119c2c86 100644
--- a/newlib/libm/math/ef_acosh.c
+++ b/newlib/libm/math/ef_acosh.c
@@ -37,7 +37,7 @@ ln2	= 6.9314718246e-01;  /* 0x3f317218 */
 	if(hx<0x3f800000) {		/* x < 1 */
 	    return (x-x)/(x-x);
 	} else if(hx >=0x4d800000) {	/* x > 2**28 */
-	    if(hx >=0x7f800000) {	/* x is inf of NaN */
+	    if(!FLT_UWORD_IS_FINITE(hx)) {	/* x is inf of NaN */
 	        return x+x;
 	    } else 
 		return __ieee754_logf(x)+ln2;	/* acosh(huge)=log(2x) */
diff --git a/newlib/libm/math/ef_atan2.c b/newlib/libm/math/ef_atan2.c
index 25e86b374..45b5acb0c 100644
--- a/newlib/libm/math/ef_atan2.c
+++ b/newlib/libm/math/ef_atan2.c
@@ -42,14 +42,14 @@ pi_lo   = 1.5099578832e-07; /* 0x34222168 */
 	ix = hx&0x7fffffff;
 	GET_FLOAT_WORD(hy,y);
 	iy = hy&0x7fffffff;
-	if((ix>0x7f800000)||
-	   (iy>0x7f800000))	/* x or y is NaN */
+	if(FLT_UWORD_IS_NAN(ix)||
+	   FLT_UWORD_IS_NAN(iy))	/* x or y is NaN */
 	   return x+y;
 	if(hx==0x3f800000) return atanf(y);   /* x=1.0 */
 	m = ((hy>>31)&1)|((hx>>30)&2);	/* 2*sign(x)+sign(y) */
 
     /* when y = 0 */
-	if(iy==0) {
+	if(FLT_UWORD_IS_ZERO(iy)) {
 	    switch(m) {
 		case 0: 
 		case 1: return y; 	/* atan(+-0,+anything)=+-0 */
@@ -58,11 +58,11 @@ pi_lo   = 1.5099578832e-07; /* 0x34222168 */
 	    }
 	}
     /* when x = 0 */
-	if(ix==0) return (hy<0)?  -pi_o_2-tiny: pi_o_2+tiny;
+	if(FLT_UWORD_IS_ZERO(ix)) return (hy<0)?  -pi_o_2-tiny: pi_o_2+tiny;
 	    
     /* when x is INF */
-	if(ix==0x7f800000) {
-	    if(iy==0x7f800000) {
+	if(FLT_UWORD_IS_INFINITE(ix)) {
+	    if(FLT_UWORD_IS_INFINITE(iy)) {
 		switch(m) {
 		    case 0: return  pi_o_4+tiny;/* atan(+INF,+INF) */
 		    case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */
@@ -79,7 +79,7 @@ pi_lo   = 1.5099578832e-07; /* 0x34222168 */
 	    }
 	}
     /* when y is INF */
-	if(iy==0x7f800000) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
+	if(FLT_UWORD_IS_INFINITE(iy)) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
 
     /* compute y/x */
 	k = (iy-ix)>>23;
diff --git a/newlib/libm/math/ef_cosh.c b/newlib/libm/math/ef_cosh.c
index 68e59f886..bdce61a00 100644
--- a/newlib/libm/math/ef_cosh.c
+++ b/newlib/libm/math/ef_cosh.c
@@ -39,7 +39,7 @@ static float one = 1.0, half=0.5, huge = 1.0e30;
 	ix &= 0x7fffffff;
 
     /* x is INF or NaN */
-	if(ix>=0x7f800000) return x*x;	
+	if(!FLT_UWORD_IS_FINITE(ix)) return x*x;	
 
     /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */
 	if(ix<0x3eb17218) {
@@ -56,10 +56,11 @@ static float one = 1.0, half=0.5, huge = 1.0e30;
 	}
 
     /* |x| in [22, log(maxdouble)] return half*exp(|x|) */
-	if (ix < 0x42b17180)  return half*__ieee754_expf(fabsf(x));
+	if (ix <= FLT_UWORD_LOG_MAX)
+	  return half*__ieee754_expf(fabsf(x));
 
     /* |x| in [log(maxdouble), overflowthresold] */
-	if (ix<=0x42b2d4fc) {
+	if (ix <= FLT_UWORD_LOG_2MAX) {
 	    w = __ieee754_expf(half*fabsf(x));
 	    t = half*w;
 	    return t*w;
diff --git a/newlib/libm/math/ef_exp.c b/newlib/libm/math/ef_exp.c
index 04331a52a..19c570cfd 100644
--- a/newlib/libm/math/ef_exp.c
+++ b/newlib/libm/math/ef_exp.c
@@ -28,8 +28,6 @@ one	= 1.0,
 halF[2]	= {0.5,-0.5,},
 huge	= 1.0e+30,
 twom100 = 7.8886090522e-31,      /* 2**-100=0x0d800000 */
-o_threshold=  8.8721679688e+01,  /* 0x42b17180 */
-u_threshold= -1.0397208405e+02,  /* 0xc2cff1b5 */
 ln2HI[2]   ={ 6.9313812256e-01,		/* 0x3f317180 */
 	     -6.9313812256e-01,},	/* 0xbf317180 */
 ln2LO[2]   ={ 9.0580006145e-06,  	/* 0x3717f7d1 */
@@ -49,23 +47,23 @@ P5   =  4.1381369442e-08; /* 0x3331bb4c */
 #endif
 {
 	float y,hi,lo,c,t;
-	__int32_t k,xsb;
+	__int32_t k,xsb,sx;
 	__uint32_t hx;
 
-	GET_FLOAT_WORD(hx,x);
-	xsb = (hx>>31)&1;		/* sign bit of x */
-	hx &= 0x7fffffff;		/* high word of |x| */
+	GET_FLOAT_WORD(sx,x);
+	xsb = (sx>>31)&1;		/* sign bit of x */
+	hx = sx & 0x7fffffff;		/* high word of |x| */
 
     /* filter out non-finite argument */
-	if(hx >= 0x42b17218) {			/* if |x|>=88.721... */
-	    if(hx>0x7f800000)
-		 return x+x;	 		/* NaN */
-            if(hx==0x7f800000)
-		return (xsb==0)? x:0.0;		/* exp(+-inf)={inf,0} */
-	    if(x > o_threshold) return huge*huge; /* overflow */
-	    if(x < u_threshold) return twom100*twom100; /* underflow */
-	}
-
+        if(FLT_UWORD_IS_NAN(hx))
+            return x+x;	 	/* NaN */
+        if(FLT_UWORD_IS_INFINITE(hx))
+	    return (xsb==0)? x:0.0;		/* exp(+-inf)={inf,0} */
+	if(sx > FLT_UWORD_LOG_MAX)
+	    return huge*huge; /* overflow */
+	if(sx < 0 && hx > FLT_UWORD_LOG_MIN)
+	    return twom100*twom100; /* underflow */
+	
     /* argument reduction */
 	if(hx > 0x3eb17218) {		/* if  |x| > 0.5 ln2 */ 
 	    if(hx < 0x3F851592) {	/* and |x| < 1.5 ln2 */
diff --git a/newlib/libm/math/ef_fmod.c b/newlib/libm/math/ef_fmod.c
index d5d28e08e..53c1ba280 100644
--- a/newlib/libm/math/ef_fmod.c
+++ b/newlib/libm/math/ef_fmod.c
@@ -43,20 +43,23 @@ static float one = 1.0, Zero[] = {0.0, -0.0,};
 	hy &= 0x7fffffff;	/* |y| */
 
     /* purge off exception values */
-	if(hy==0||(hx>=0x7f800000)||		/* y=0,or x not finite */
-	   (hy>0x7f800000))			/* or y is NaN */
+	if(FLT_UWORD_IS_ZERO(hy)||
+	   !FLT_UWORD_IS_FINITE(hx)||
+	   FLT_UWORD_IS_NAN(hy))
 	    return (x*y)/(x*y);
 	if(hx<hy) return x;			/* |x|<|y| return x */
 	if(hx==hy)
 	    return Zero[(__uint32_t)sx>>31];	/* |x|=|y| return x*0*/
 
+    /* Note: y cannot be zero if we reach here. */
+
     /* determine ix = ilogb(x) */
-	if(hx<0x00800000) {	/* subnormal x */
+	if(FLT_UWORD_IS_SUBNORMAL(hx)) {	/* subnormal x */
 	    for (ix = -126,i=(hx<<8); i>0; i<<=1) ix -=1;
 	} else ix = (hx>>23)-127;
 
     /* determine iy = ilogb(y) */
-	if(hy<0x00800000) {	/* subnormal y */
+	if(FLT_UWORD_IS_SUBNORMAL(hy)) {	/* subnormal y */
 	    for (iy = -126,i=(hy<<8); i>=0; i<<=1) iy -=1;
 	} else iy = (hy>>23)-127;
 
@@ -99,6 +102,8 @@ static float one = 1.0, Zero[] = {0.0, -0.0,};
 	    hx = ((hx-0x00800000)|((iy+127)<<23));
 	    SET_FLOAT_WORD(x,hx|sx);
 	} else {		/* subnormal output */
+	    /* If denormals are not supported, this code will generate a
+	       zero representation.  */
 	    n = -126 - iy;
 	    hx >>= n;
 	    SET_FLOAT_WORD(x,hx|sx);
diff --git a/newlib/libm/math/ef_hypot.c b/newlib/libm/math/ef_hypot.c
index a87fa489e..9f6d40c9c 100644
--- a/newlib/libm/math/ef_hypot.c
+++ b/newlib/libm/math/ef_hypot.c
@@ -35,10 +35,10 @@
 	if((ha-hb)>0xf000000L) {return a+b;} /* x/y > 2**30 */
 	k=0;
 	if(ha > 0x58800000L) {	/* a>2**50 */
-	   if(ha >= 0x7f800000L) {	/* Inf or NaN */
+	   if(!FLT_UWORD_IS_FINITE(ha)) {	/* Inf or NaN */
 	       w = a+b;			/* for sNaN */
-	       if(ha == 0x7f800000L) w = a;
-	       if(hb == 0x7f800000L) w = b;
+	       if(FLT_UWORD_IS_INFINITE(ha)) w = a;
+	       if(FLT_UWORD_IS_INFINITE(hb)) w = b;
 	       return w;
 	   }
 	   /* scale a and b by 2**-60 */
@@ -47,8 +47,9 @@
 	   SET_FLOAT_WORD(b,hb);
 	}
 	if(hb < 0x26800000L) {	/* b < 2**-50 */
-	    if(hb <= 0x007fffffL) {	/* subnormal b or 0 */	
-	        if(hb==0) return a;
+	    if(FLT_UWORD_IS_ZERO(hb)) {
+	        return a;
+	    } else if(FLT_UWORD_IS_SUBNORMAL(hb)) {
 		SET_FLOAT_WORD(t1,0x3f000000L);	/* t1=2^126 */
 		b *= t1;
 		a *= t1;
diff --git a/newlib/libm/math/ef_j0.c b/newlib/libm/math/ef_j0.c
index e7ee6e748..866cfcf96 100644
--- a/newlib/libm/math/ef_j0.c
+++ b/newlib/libm/math/ef_j0.c
@@ -58,14 +58,14 @@ static float zero = 0.0;
 
 	GET_FLOAT_WORD(hx,x);
 	ix = hx&0x7fffffff;
-	if(ix>=0x7f800000) return one/(x*x);
+	if(!FLT_UWORD_IS_FINITE(ix)) return one/(x*x);
 	x = fabsf(x);
 	if(ix >= 0x40000000) {	/* |x| >= 2.0 */
 		s = sinf(x);
 		c = cosf(x);
 		ss = s-c;
 		cc = s+c;
-		if(ix<0x7f000000) {  /* make sure x+x not overflow */
+		if(ix<=FLT_UWORD_HALF_MAX) {  /* make sure x+x not overflow */
 		    z = -cosf(x+x);
 		    if ((s*c)<zero) cc = z/ss;
 		    else 	    ss = z/cc;
@@ -128,8 +128,8 @@ v04  =  4.4111031494e-10; /* 0x2ff280c2 */
 	GET_FLOAT_WORD(hx,x);
         ix = 0x7fffffff&hx;
     /* Y0(NaN) is NaN, y0(-inf) is Nan, y0(inf) is 0  */
-	if(ix>=0x7f800000) return  one/(x+x*x); 
-        if(ix==0) return -one/zero;
+	if(!FLT_UWORD_IS_FINITE(ix)) return  one/(x+x*x); 
+        if(FLT_UWORD_IS_ZERO(ix)) return -one/zero;
         if(hx<0) return zero/zero;
         if(ix >= 0x40000000) {  /* |x| >= 2.0 */
         /* y0(x) = sqrt(2/(pi*x))*(p0(x)*sin(x0)+q0(x)*cos(x0))
@@ -151,7 +151,7 @@ v04  =  4.4111031494e-10; /* 0x2ff280c2 */
 	 * j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x)
 	 * y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x)
 	 */
-                if(ix<0x7f000000) {  /* make sure x+x not overflow */
+                if(ix<=FLT_UWORD_HALF_MAX) {  /* make sure x+x not overflow */
                     z = -cosf(x+x);
                     if ((s*c)<zero) cc = z/ss;
                     else            ss = z/cc;
diff --git a/newlib/libm/math/ef_j1.c b/newlib/libm/math/ef_j1.c
index e11cf1fba..01bd24cf1 100644
--- a/newlib/libm/math/ef_j1.c
+++ b/newlib/libm/math/ef_j1.c
@@ -59,14 +59,14 @@ static float zero    = 0.0;
 
 	GET_FLOAT_WORD(hx,x);
 	ix = hx&0x7fffffff;
-	if(ix>=0x7f800000) return one/x;
+	if(!FLT_UWORD_IS_FINITE(ix)) return one/x;
 	y = fabsf(x);
 	if(ix >= 0x40000000) {	/* |x| >= 2.0 */
 		s = sinf(y);
 		c = cosf(y);
 		ss = -s-c;
 		cc = s-c;
-		if(ix<0x7f000000) {  /* make sure y+y not overflow */
+		if(ix<=FLT_UWORD_HALF_MAX) {  /* make sure y+y not overflow */
 		    z = cosf(y+y);
 		    if ((s*c)>zero) cc = z/ss;
 		    else 	    ss = z/cc;
@@ -129,15 +129,15 @@ static float V0[5] = {
 	GET_FLOAT_WORD(hx,x);
         ix = 0x7fffffff&hx;
     /* if Y1(NaN) is NaN, Y1(-inf) is NaN, Y1(inf) is 0 */
-	if(ix>=0x7f800000) return  one/(x+x*x); 
-        if(ix==0) return -one/zero;
+	if(!FLT_UWORD_IS_FINITE(ix)) return one/(x+x*x); 
+        if(FLT_UWORD_IS_ZERO(ix)) return -one/zero;
         if(hx<0) return zero/zero;
         if(ix >= 0x40000000) {  /* |x| >= 2.0 */
                 s = sinf(x);
                 c = cosf(x);
                 ss = -s-c;
                 cc = s-c;
-                if(ix<0x7f000000) {  /* make sure x+x not overflow */
+                if(ix<=FLT_UWORD_HALF_MAX) {  /* make sure x+x not overflow */
                     z = cosf(x+x);
                     if ((s*c)>zero) cc = z/ss;
                     else            ss = z/cc;
diff --git a/newlib/libm/math/ef_jn.c b/newlib/libm/math/ef_jn.c
index 04a93b685..bedfb3ed5 100644
--- a/newlib/libm/math/ef_jn.c
+++ b/newlib/libm/math/ef_jn.c
@@ -47,7 +47,7 @@ static float zero  =  0.0000000000e+00;
 	GET_FLOAT_WORD(hx,x);
 	ix = 0x7fffffff&hx;
     /* if J(n,NaN) is NaN */
-	if(ix>0x7f800000) return x+x;
+	if(FLT_UWORD_IS_NAN(ix)) return x+x;
 	if(n<0){		
 		n = -n;
 		x = -x;
@@ -57,7 +57,7 @@ static float zero  =  0.0000000000e+00;
 	if(n==1) return(__ieee754_j1f(x));
 	sgn = (n&1)&(hx>>31);	/* even n -- 0, odd n -- sign(x) */
 	x = fabsf(x);
-	if(ix==0||ix>=0x7f800000) 	/* if x is 0 or inf */
+	if(FLT_UWORD_IS_ZERO(ix)||FLT_UWORD_IS_INFINITE(ix))
 	    b = zero;
 	else if((float)n<=x) {   
 		/* Safe to use J(n+1,x)=2n/x *J(n,x)-J(n-1,x) */
@@ -181,8 +181,8 @@ static float zero  =  0.0000000000e+00;
 	GET_FLOAT_WORD(hx,x);
 	ix = 0x7fffffff&hx;
     /* if Y(n,NaN) is NaN */
-	if(ix>0x7f800000) return x+x;
-	if(ix==0) return -one/zero;
+	if(FLT_UWORD_IS_NAN(ix)) return x+x;
+	if(FLT_UWORD_IS_ZERO(ix)) return -one/zero;
 	if(hx<0) return zero/zero;
 	sign = 1;
 	if(n<0){
@@ -191,7 +191,7 @@ static float zero  =  0.0000000000e+00;
 	}
 	if(n==0) return(__ieee754_y0f(x));
 	if(n==1) return(sign*__ieee754_y1f(x));
-	if(ix==0x7f800000) return zero;
+	if(FLT_UWORD_IS_INFINITE(ix)) return zero;
 
 	a = __ieee754_y0f(x);
 	b = __ieee754_y1f(x);
diff --git a/newlib/libm/math/ef_log.c b/newlib/libm/math/ef_log.c
index 87d6af2c5..619fe9090 100644
--- a/newlib/libm/math/ef_log.c
+++ b/newlib/libm/math/ef_log.c
@@ -50,14 +50,14 @@ static float zero   =  0.0;
 	GET_FLOAT_WORD(ix,x);
 
 	k=0;
-	if (ix < 0x00800000) {			/* x < 2**-126  */
-	    if ((ix&0x7fffffff)==0) 
-		return -two25/zero;		/* log(+-0)=-inf */
-	    if (ix<0) return (x-x)/zero;	/* log(-#) = NaN */
+	if (FLT_UWORD_IS_ZERO(ix&0x7fffffff))
+	    return -two25/zero;		/* log(+-0)=-inf */
+        if (ix<0) return (x-x)/zero;	/* log(-#) = NaN */
+	if (!FLT_UWORD_IS_FINITE(ix)) return x+x;
+	if (FLT_UWORD_IS_SUBNORMAL(ix)) {
 	    k -= 25; x *= two25; /* subnormal number, scale up x */
 	    GET_FLOAT_WORD(ix,x);
 	} 
-	if (ix >= 0x7f800000) return x+x;
 	k += (ix>>23)-127;
 	ix &= 0x007fffff;
 	i = (ix+(0x95f64<<3))&0x800000;
diff --git a/newlib/libm/math/ef_log10.c b/newlib/libm/math/ef_log10.c
index 63fee9b9d..5ab23c43f 100644
--- a/newlib/libm/math/ef_log10.c
+++ b/newlib/libm/math/ef_log10.c
@@ -44,14 +44,14 @@ static float zero   =  0.0;
 	GET_FLOAT_WORD(hx,x);
 
         k=0;
-        if (hx < 0x00800000) {                  /* x < 2**-126  */
-            if ((hx&0x7fffffff)==0)
-                return -two25/zero;             /* log(+-0)=-inf */
-            if (hx<0) return (x-x)/zero;        /* log(-#) = NaN */
+        if (FLT_UWORD_IS_ZERO(hx&0x7fffffff))
+            return -two25/zero;             /* log(+-0)=-inf */
+        if (hx<0) return (x-x)/zero;        /* log(-#) = NaN */
+	if (!FLT_UWORD_IS_FINITE(hx)) return x+x;
+        if (FLT_UWORD_IS_SUBNORMAL(hx)) {
             k -= 25; x *= two25; /* subnormal number, scale up x */
 	    GET_FLOAT_WORD(hx,x);
         }
-	if (hx >= 0x7f800000) return x+x;
 	k += (hx>>23)-127;
 	i  = ((__uint32_t)k&0x80000000)>>31;
         hx = (hx&0x007fffff)|((0x7f-i)<<23);
diff --git a/newlib/libm/math/ef_pow.c b/newlib/libm/math/ef_pow.c
index 40b679d6e..e50cc58b3 100644
--- a/newlib/libm/math/ef_pow.c
+++ b/newlib/libm/math/ef_pow.c
@@ -73,11 +73,11 @@ ivln2_l  =  7.0526075433e-06; /* 0x36eca570 =1/ln2 tail*/
 	ix = hx&0x7fffffff;  iy = hy&0x7fffffff;
 
     /* y==zero: x**0 = 1 */
-	if(iy==0) return one; 	
+	if(FLT_UWORD_IS_ZERO(iy)) return one; 	
 
     /* +-NaN return x+y */
-	if(ix > 0x7f800000 ||
-	   iy > 0x7f800000)
+	if(FLT_UWORD_IS_NAN(ix) ||
+	   FLT_UWORD_IS_NAN(iy))
 		return x+y;	
 
     /* determine if y is an odd int when x < 0
@@ -96,7 +96,7 @@ ivln2_l  =  7.0526075433e-06; /* 0x36eca570 =1/ln2 tail*/
 	} 
 
     /* special value of y */
-	if (iy==0x7f800000) {	/* y is +-inf */
+	if (FLT_UWORD_IS_INFINITE(iy)) {	/* y is +-inf */
 	    if (ix==0x3f800000)
 	        return  y - y;	/* inf**+-1 is NaN */
 	    else if (ix > 0x3f800000)/* (|x|>1)**+-inf = inf,0 */
@@ -115,7 +115,7 @@ ivln2_l  =  7.0526075433e-06; /* 0x36eca570 =1/ln2 tail*/
 
 	ax   = fabsf(x);
     /* special value of x */
-	if(ix==0x7f800000||ix==0||ix==0x3f800000){
+	if(FLT_UWORD_IS_INFINITE(ix)||FLT_UWORD_IS_ZERO(ix)||ix==0x3f800000){
 	    z = ax;			/*x is +-0,+-inf,+-1*/
 	    if(hy<0) z = one/z;	/* z = (1/|x|) */
 	    if(hx<0) {
@@ -149,7 +149,7 @@ ivln2_l  =  7.0526075433e-06; /* 0x36eca570 =1/ln2 tail*/
 	    float s2,s_h,s_l,t_h,t_l;
 	    n = 0;
 	/* take care subnormal number */
-	    if(ix<0x00800000)
+	    if(FLT_UWORD_IS_SUBNORMAL(ix))
 		{ax *= two24; n -= 24; GET_FLOAT_WORD(ix,ax); }
 	    n  += ((ix)>>23)-0x7f;
 	    j  = ix&0x007fffff;
@@ -209,20 +209,21 @@ ivln2_l  =  7.0526075433e-06; /* 0x36eca570 =1/ln2 tail*/
 	p_h = y1*t1;
 	z = p_l+p_h;
 	GET_FLOAT_WORD(j,z);
-	if (j>0x43000000)				/* if z > 128 */
-	    return s*huge*huge;				/* overflow */
-	else if (j==0x43000000) {			/* if z == 128 */
-	    if(p_l+ovt>z-p_h) return s*huge*huge;	/* overflow */
-	}
-	else if ((j&0x7fffffff)>0x43160000)		/* z <= -150 */
-	    return s*tiny*tiny;				/* underflow */
-	else if (j==0xc3160000){			/* z == -150 */
-	    if(p_l<=z-p_h) return s*tiny*tiny;		/* underflow */
+	i = j&0x7fffffff;
+	if (j>0) {
+	    if (i>FLT_UWORD_EXP_MAX)
+	        return s*huge*huge;			/* overflow */
+	    else if (i==FLT_UWORD_EXP_MAX)
+	        if(p_l+ovt>z-p_h) return s*huge*huge;	/* overflow */
+        } else {
+	    if (i>FLT_UWORD_EXP_MIN)
+	        return s*tiny*tiny;			/* underflow */
+	    else if (i==FLT_UWORD_EXP_MIN)
+	        if(p_l<=z-p_h) return s*tiny*tiny;	/* underflow */
 	}
     /*
      * compute 2**(p_h+p_l)
      */
-	i = j&0x7fffffff;
 	k = (i>>23)-0x7f;
 	n = 0;
 	if(i>0x3f000000) {		/* if |z| > 0.5, set n = [z+0.5] */
diff --git a/newlib/libm/math/ef_rem_pio2.c b/newlib/libm/math/ef_rem_pio2.c
index e91aa47f3..f1191d09f 100644
--- a/newlib/libm/math/ef_rem_pio2.c
+++ b/newlib/libm/math/ef_rem_pio2.c
@@ -174,7 +174,7 @@ pio2_3t =  6.1232342629e-17; /* 0x248d3132 */
     /* 
      * all other (large) arguments
      */
-	if(ix>=0x7f800000) {		/* x is inf or NaN */
+	if(!FLT_UWORD_IS_FINITE(ix)) {
 	    y[0]=y[1]=x-x; return 0;
 	}
     /* set z = scalbn(|x|,ilogb(x)-7) */
diff --git a/newlib/libm/math/ef_remainder.c b/newlib/libm/math/ef_remainder.c
index 8ce7fac99..23d29d05a 100644
--- a/newlib/libm/math/ef_remainder.c
+++ b/newlib/libm/math/ef_remainder.c
@@ -40,13 +40,13 @@ static float zero = 0.0;
 	hx &= 0x7fffffff;
 
     /* purge off exception values */
-	if(hp==0) return (x*p)/(x*p);	 	/* p = 0 */
-	if((hx>=0x7f800000)||			/* x not finite */
-	  ((hp>0x7f800000)))			/* p is NaN */
+	if(FLT_UWORD_IS_ZERO(hp)||
+	   !FLT_UWORD_IS_FINITE(hx)||
+	   FLT_UWORD_IS_NAN(hp))
 	    return (x*p)/(x*p);
 
 
-	if (hp<=0x7effffff) x = __ieee754_fmodf(x,p+p);	/* now x < 2p */
+	if (hp<=FLT_UWORD_HALF_MAX) x = __ieee754_fmodf(x,p+p); /* now x < 2p */
 	if ((hx-hp)==0) return zero*x;
 	x  = fabsf(x);
 	p  = fabsf(p);
diff --git a/newlib/libm/math/ef_sinh.c b/newlib/libm/math/ef_sinh.c
index 375198344..a61b17294 100644
--- a/newlib/libm/math/ef_sinh.c
+++ b/newlib/libm/math/ef_sinh.c
@@ -35,7 +35,7 @@ static float one = 1.0, shuge = 1.0e37;
 	ix = jx&0x7fffffff;
 
     /* x is INF or NaN */
-	if(ix>=0x7f800000) return x+x;	
+	if(!FLT_UWORD_IS_FINITE(ix)) return x+x;	
 
 	h = 0.5;
 	if (jx<0) h = -h;
@@ -49,10 +49,10 @@ static float one = 1.0, shuge = 1.0e37;
 	}
 
     /* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */
-	if (ix < 0x42b17180)  return h*__ieee754_expf(fabsf(x));
+	if (ix<=FLT_UWORD_LOG_MAX)  return h*__ieee754_expf(fabsf(x));
 
     /* |x| in [log(maxdouble), overflowthresold] */
-	if (ix<=0x42b2d4fc) {
+	if (ix<=FLT_UWORD_LOG_2MAX) {
 	    w = __ieee754_expf((float)0.5*fabsf(x));
 	    t = h*w;
 	    return t*w;
diff --git a/newlib/libm/math/ef_sqrt.c b/newlib/libm/math/ef_sqrt.c
index aabbc51ce..17dab9311 100644
--- a/newlib/libm/math/ef_sqrt.c
+++ b/newlib/libm/math/ef_sqrt.c
@@ -30,25 +30,23 @@ static	float	one	= 1.0, tiny=1.0e-30;
 {
 	float z;
 	__int32_t 	sign = (__int32_t)0x80000000; 
-	__uint32_t r;
+	__uint32_t r,hx;
 	__int32_t ix,s,q,m,t,i;
 
 	GET_FLOAT_WORD(ix,x);
+	hx = ix&0x7fffffff;
 
     /* take care of Inf and NaN */
-	if((ix&0x7f800000L)==0x7f800000L) {			
+	if(!FLT_UWORD_IS_FINITE(hx))
 	    return x*x+x;		/* sqrt(NaN)=NaN, sqrt(+inf)=+inf
 					   sqrt(-inf)=sNaN */
-	} 
-    /* take care of zero */
-	if(ix<=0) {
-	    if((ix&(~sign))==0) return x;/* sqrt(+-0) = +-0 */
-	    else if(ix<0)
-		return (x-x)/(x-x);		/* sqrt(-ve) = sNaN */
-	}
+    /* take care of zero and -ves */
+	if(FLT_UWORD_IS_ZERO(hx)) return x;/* sqrt(+-0) = +-0 */
+	if(ix<0) return (x-x)/(x-x);		/* sqrt(-ve) = sNaN */
+
     /* normalize x */
 	m = (ix>>23);
-	if(m==0) {				/* subnormal x */
+	if(FLT_UWORD_IS_SUBNORMAL(hx)) {		/* subnormal x */
 	    for(i=0;(ix&0x00800000L)==0;i++) ix<<=1;
 	    m -= i-1;
 	}
diff --git a/newlib/libm/math/sf_asinh.c b/newlib/libm/math/sf_asinh.c
index d5dfef811..4688ea8c1 100644
--- a/newlib/libm/math/sf_asinh.c
+++ b/newlib/libm/math/sf_asinh.c
@@ -35,7 +35,7 @@ huge=  1.0000000000e+30;
 	__int32_t hx,ix;
 	GET_FLOAT_WORD(hx,x);
 	ix = hx&0x7fffffff;
-	if(ix>=0x7f800000) return x+x;	/* x is inf or NaN */
+	if(!FLT_UWORD_IS_FINITE(ix)) return x+x;	/* x is inf or NaN */
 	if(ix< 0x31800000) {	/* |x|<2**-28 */
 	    if(huge+x>one) return x;	/* return x inexact except 0 */
 	} 
diff --git a/newlib/libm/math/sf_atan.c b/newlib/libm/math/sf_atan.c
index 7ea664f23..6edf05fe5 100644
--- a/newlib/libm/math/sf_atan.c
+++ b/newlib/libm/math/sf_atan.c
@@ -77,7 +77,7 @@ huge   = 1.0e30;
 	GET_FLOAT_WORD(hx,x);
 	ix = hx&0x7fffffff;
 	if(ix>=0x50800000) {	/* if |x| >= 2^34 */
-	    if(ix>0x7f800000)
+	    if(FLT_UWORD_IS_NAN(ix))
 		return x+x;		/* NaN */
 	    if(hx>0) return  atanhi[3]+atanlo[3];
 	    else     return -atanhi[3]-atanlo[3];
diff --git a/newlib/libm/math/sf_ceil.c b/newlib/libm/math/sf_ceil.c
index 85f0e9714..8a8edac14 100644
--- a/newlib/libm/math/sf_ceil.c
+++ b/newlib/libm/math/sf_ceil.c
@@ -29,14 +29,15 @@ static float huge = 1.0e30;
 #endif
 {
 	__int32_t i0,j0;
-	__uint32_t i;
+	__uint32_t i,ix;
 	GET_FLOAT_WORD(i0,x);
-	j0 = ((i0>>23)&0xff)-0x7f;
+	ix = (i0&0x7fffffff);
+	j0 = (ix>>23)-0x7f;
 	if(j0<23) {
 	    if(j0<0) { 	/* raise inexact if x != 0 */
 		if(huge+x>(float)0.0) {/* return 0*sign(x) if |x|<1 */
 		    if(i0<0) {i0=0x80000000;} 
-		    else if(i0!=0) { i0=0x3f800000;}
+		    else if(!FLT_UWORD_IS_ZERO(ix)) { i0=0x3f800000;}
 		}
 	    } else {
 		i = (0x007fffff)>>j0;
@@ -47,7 +48,7 @@ static float huge = 1.0e30;
 		}
 	    }
 	} else {
-	    if(j0==0x80) return x+x;	/* inf or NaN */
+	    if(!FLT_UWORD_IS_FINITE(ix)) return x+x; /* inf or NaN */
 	    else return x;		/* x is integral */
 	}
 	SET_FLOAT_WORD(x,i0);
diff --git a/newlib/libm/math/sf_cos.c b/newlib/libm/math/sf_cos.c
index 8f3a8af01..4c0a9a535 100644
--- a/newlib/libm/math/sf_cos.c
+++ b/newlib/libm/math/sf_cos.c
@@ -38,7 +38,7 @@ static float one=1.0;
 	if(ix <= 0x3f490fd8) return __kernel_cosf(x,z);
 
     /* cos(Inf or NaN) is NaN */
-	else if (ix>=0x7f800000) return x-x;
+	else if (!FLT_UWORD_IS_FINITE(ix)) return x-x;
 
     /* argument reduction needed */
 	else {
diff --git a/newlib/libm/math/sf_erf.c b/newlib/libm/math/sf_erf.c
index 1a9fa8d01..0329c60fa 100644
--- a/newlib/libm/math/sf_erf.c
+++ b/newlib/libm/math/sf_erf.c
@@ -109,7 +109,7 @@ sb7  = -2.2440952301e+01; /* 0xc1b38712 */
 	float R,S,P,Q,s,y,z,r;
 	GET_FLOAT_WORD(hx,x);
 	ix = hx&0x7fffffff;
-	if(ix>=0x7f800000) {		/* erf(nan)=nan */
+	if(!FLT_UWORD_IS_FINITE(ix)) {		/* erf(nan)=nan */
 	    i = ((__uint32_t)hx>>31)<<1;
 	    return (float)(1-i)+one/x;	/* erf(+-inf)=+-1 */
 	}
@@ -166,7 +166,7 @@ sb7  = -2.2440952301e+01; /* 0xc1b38712 */
 	float R,S,P,Q,s,y,z,r;
 	GET_FLOAT_WORD(hx,x);
 	ix = hx&0x7fffffff;
-	if(ix>=0x7f800000) {			/* erfc(nan)=nan */
+	if(!FLT_UWORD_IS_FINITE(ix)) {			/* erfc(nan)=nan */
 						/* erfc(+-inf)=0,2 */
 	    return (float)(((__uint32_t)hx>>31)<<1)+one/x;
 	}
diff --git a/newlib/libm/math/sf_floor.c b/newlib/libm/math/sf_floor.c
index 787f2fdf0..9264d81e9 100644
--- a/newlib/libm/math/sf_floor.c
+++ b/newlib/libm/math/sf_floor.c
@@ -38,14 +38,15 @@ static float huge = 1.0e30;
 #endif
 {
 	__int32_t i0,j0;
-	__uint32_t i;
+	__uint32_t i,ix;
 	GET_FLOAT_WORD(i0,x);
-	j0 = ((i0>>23)&0xff)-0x7f;
+	ix = (i0&0x7fffffff);
+	j0 = (ix>>23)-0x7f;
 	if(j0<23) {
 	    if(j0<0) { 	/* raise inexact if x != 0 */
 		if(huge+x>(float)0.0) {/* return 0*sign(x) if |x|<1 */
 		    if(i0>=0) {i0=0;} 
-		    else if((i0&0x7fffffff)!=0)
+		    else if(!FLT_UWORD_IS_ZERO(ix))
 			{ i0=0xbf800000;}
 		}
 	    } else {
@@ -57,7 +58,7 @@ static float huge = 1.0e30;
 		}
 	    }
 	} else {
-	    if(j0==0x80) return x+x;	/* inf or NaN */
+	    if(!FLT_UWORD_IS_FINITE(ix)) return x+x;	/* inf or NaN */
 	    else return x;		/* x is integral */
 	}
 	SET_FLOAT_WORD(x,i0);
diff --git a/newlib/libm/math/sf_frexp.c b/newlib/libm/math/sf_frexp.c
index 271fb9dca..8dd8a9767 100644
--- a/newlib/libm/math/sf_frexp.c
+++ b/newlib/libm/math/sf_frexp.c
@@ -33,8 +33,8 @@ two25 =  3.3554432000e+07; /* 0x4c000000 */
 	GET_FLOAT_WORD(hx,x);
 	ix = 0x7fffffff&hx;
 	*eptr = 0;
-	if(ix>=0x7f800000||(ix==0)) return x;	/* 0,inf,nan */
-	if (ix<0x00800000) {		/* subnormal */
+	if(!FLT_UWORD_IS_FINITE(ix)||FLT_UWORD_IS_ZERO(ix)) return x;	/* 0,inf,nan */
+	if (FLT_UWORD_IS_SUBNORMAL(ix)) {		/* subnormal */
 	    x *= two25;
 	    GET_FLOAT_WORD(hx,x);
 	    ix = hx&0x7fffffff;
diff --git a/newlib/libm/math/sf_isinf.c b/newlib/libm/math/sf_isinf.c
index 1af4aab2a..43a8abdf2 100644
--- a/newlib/libm/math/sf_isinf.c
+++ b/newlib/libm/math/sf_isinf.c
@@ -1,6 +1,5 @@
 /*
- * isinff(x) returns 1 if x is infinity, else 0;
- * no branching!
+ * isinff(x) returns 1 if x is +-infinity, else 0;
  * Added by Cygnus Support.
  */
 
@@ -16,8 +15,7 @@
 	__int32_t ix;
 	GET_FLOAT_WORD(ix,x);
 	ix &= 0x7fffffff;
-	ix = 0x7f800000 - ix;
-	return 1 - (int)((__uint32_t)(ix|(-ix))>>31);
+	return FLT_UWORD_IS_INFINITE(ix);
 }
 
 #ifdef _DOUBLE_IS_32BITS
diff --git a/newlib/libm/math/sf_isnan.c b/newlib/libm/math/sf_isnan.c
index 8fdb6adf2..0b4be3e9c 100644
--- a/newlib/libm/math/sf_isnan.c
+++ b/newlib/libm/math/sf_isnan.c
@@ -15,7 +15,6 @@
 
 /*
  * isnanf(x) returns 1 is x is nan, else 0;
- * no branching!
  */
 
 #include "fdlibm.h"
@@ -30,8 +29,7 @@
 	__int32_t ix;
 	GET_FLOAT_WORD(ix,x);
 	ix &= 0x7fffffff;
-	ix = 0x7f800000 - ix;
-	return (int)(((__uint32_t)(ix))>>31);
+	return FLT_UWORD_IS_NAN(ix);
 }
 
 #ifdef _DOUBLE_IS_32BITS
diff --git a/newlib/libm/math/sf_sin.c b/newlib/libm/math/sf_sin.c
index 315d4b4ba..da81845d9 100644
--- a/newlib/libm/math/sf_sin.c
+++ b/newlib/libm/math/sf_sin.c
@@ -32,7 +32,7 @@
 	if(ix <= 0x3f490fd8) return __kernel_sinf(x,z,0);
 
     /* sin(Inf or NaN) is NaN */
-	else if (ix>=0x7f800000) return x-x;
+	else if (!FLT_UWORD_IS_FINITE(ix)) return x-x;
 
     /* argument reduction needed */
 	else {
diff --git a/newlib/libm/math/sf_tan.c b/newlib/libm/math/sf_tan.c
index ade1cb216..18c47a454 100644
--- a/newlib/libm/math/sf_tan.c
+++ b/newlib/libm/math/sf_tan.c
@@ -32,7 +32,7 @@
 	if(ix <= 0x3f490fda) return __kernel_tanf(x,z,1);
 
     /* tan(Inf or NaN) is NaN */
-	else if (ix>=0x7f800000) return x-x;		/* NaN */
+	else if (!FLT_UWORD_IS_FINITE(ix)) return x-x;		/* NaN */
 
     /* argument reduction needed */
 	else {
diff --git a/newlib/libm/math/sf_tanh.c b/newlib/libm/math/sf_tanh.c
index ba9edf5c0..1eb44a2ff 100644
--- a/newlib/libm/math/sf_tanh.c
+++ b/newlib/libm/math/sf_tanh.c
@@ -35,7 +35,7 @@ static float one=1.0, two=2.0, tiny = 1.0e-30;
 	ix = jx&0x7fffffff;
 
     /* x is INF or NaN */
-	if(ix>=0x7f800000) { 
+	if(!FLT_UWORD_IS_FINITE(ix)) {
 	    if (jx>=0) return one/x+one;    /* tanh(+-inf)=+-1 */
 	    else       return one/x-one;    /* tanh(NaN) = NaN */
 	}