math: nextafter and nexttoward cleanup

make nexttoward, nexttowardf independent of long double representation.
fix nextafterl: it did not raise underflow flag when the result was 0.

src/math/nextafter.c

@@ -1,79 +1,36 @@
-/* origin: FreeBSD /usr/src/lib/msun/src/s_nextafter.c */
-/*
- * ====================================================
- * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
- *
- * Developed at SunPro, a Sun Microsystems, Inc. business.
- * Permission to use, copy, modify, and distribute this
- * software is freely granted, provided that this notice
- * is preserved.
- * ====================================================
- */
-/* IEEE functions
- *      nextafter(x,y)
- *      return the next machine floating-point number of x in the
- *      direction toward y.
- *   Special cases:
- */
-
 #include "libm.h"
 
+#define SIGN ((uint64_t)1<<63)
+
 double nextafter(double x, double y)
 {
-	volatile double t;
+	union dshape ux, uy;
-	int32_t hx,hy,ix,iy;
+	uint64_t ax, ay;
-	uint32_t lx,ly;
+	int e;
-
-	EXTRACT_WORDS(hx, lx, x);
-	EXTRACT_WORDS(hy, ly, y);
-	ix = hx & 0x7fffffff;  /* |x| */
-	iy = hy & 0x7fffffff;  /* |y| */
 
-	if ((ix >= 0x7ff00000 && (ix-0x7ff00000)|lx) != 0 ||   /* x is nan */
+	if (isnan(x) || isnan(y))
-	    (iy >= 0x7ff00000 && (iy-0x7ff00000)|ly) != 0)     /* y is nan */
+		return x + y;
-		return x+y;
+	ux.value = x;
-	if (x == y)          /* x == y */
+	uy.value = y;
+	if (ux.bits == uy.bits)
 		return y;
-	if ((ix|lx) == 0) {  /* x == 0 */
+	ax = ux.bits & ~SIGN;
-		INSERT_WORDS(x, hy&0x80000000, 1);  /* return +-minsubnormal */
+	ay = uy.bits & ~SIGN;
-		/* raise underflow flag */
+	if (ax == 0) {
-		t = x*x;
+		if (ay == 0)
-		if (t == x)
-			return t;
-		return x;
-	}
-	if (hx >= 0) {  /* x > 0 */
-		if (hx > hy || (hx == hy && lx > ly)) {  /* x > y, x -= ulp */
-			if (lx == 0)
-				hx--;
-			lx--;
-		} else {                                 /* x < y, x += ulp */
-			lx++;
-			if (lx == 0)
-				hx++;
-		}
-	} else {        /* x < 0 */
-		if (hy >= 0 || hx > hy || (hx == hy && lx > ly)) { /* x < y, x -= ulp */
-			if (lx == 0)
-				hx--;
-			lx--;
-		} else {                                 /* x > y, x += ulp */
-			lx++;
-			if (lx == 0)
-				hx++;
-		}
-	}
-	hy = hx & 0x7ff00000;
-	if (hy >= 0x7ff00000)  /* overflow  */
-		return x+x;
-	if (hy < 0x00100000) { /* underflow */
-		/* raise underflow flag */
-		t = x*x;
-		if (t != x) {
-			INSERT_WORDS(y, hx, lx);
 			return y;
-		}
+		ux.bits = (uy.bits & SIGN) | 1;
+	} else if (ax > ay || ((ux.bits ^ uy.bits) & SIGN))
+		ux.bits--;
+	else
+		ux.bits++;
+	e = ux.bits >> 52 & 0x7ff;
+	/* raise overflow if ux.value is infinite and x is finite */
+	if (e == 0x7ff)
+		return x + x;
+	/* raise underflow if ux.value is subnormal or zero */
+	if (e == 0) {
+		volatile double z = x*x + ux.value*ux.value;
 	}
-	INSERT_WORDS(x, hx, lx);
+	return ux.value;
-	return x;
 }

src/math/nextafterf.c

@@ -1,67 +1,35 @@
-/* origin: FreeBSD /usr/src/lib/msun/src/s_nextafterf.c */
-/*
- * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
- */
-/*
- * ====================================================
- * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
- *
- * Developed at SunPro, a Sun Microsystems, Inc. business.
- * Permission to use, copy, modify, and distribute this
- * software is freely granted, provided that this notice
- * is preserved.
- * ====================================================
- */
-
 #include "libm.h"
 
+#define SIGN 0x80000000
+
 float nextafterf(float x, float y)
 {
-	volatile float t;
+	union fshape ux, uy;
-	int32_t hx,hy,ix,iy;
+	uint32_t ax, ay, e;
-
-	GET_FLOAT_WORD(hx, x);
-	GET_FLOAT_WORD(hy, y);
-	ix = hx & 0x7fffffff;  /* |x| */
-	iy = hy & 0x7fffffff;  /* |y| */
 
-	if (ix > 0x7f800000 || /* x is nan */
+	if (isnan(x) || isnan(y))
-	    iy > 0x7f800000)   /* y is nan */
+		return x + y;
-		return x+y;
+	ux.value = x;
-	if (x == y)            /* x == y */
+	uy.value = y;
+	if (ux.bits == uy.bits)
 		return y;
-	if (ix == 0) {         /* x == 0 */
+	ax = ux.bits & ~SIGN;
-		SET_FLOAT_WORD(x, (hy&0x80000000)|1); /* return +-minsubnormal */
+	ay = uy.bits & ~SIGN;
-		/* raise underflow flag */
+	if (ax == 0) {
-		t = x*x;
+		if (ay == 0)
-		if (t == x)
-			return t;
-		return x;
-	}
-	if (hx >= 0) {         /* x > 0 */
-		if (hx > hy) {             /* x > y, x -= ulp */
-			hx--;
-		} else {                   /* x < y, x += ulp */
-			hx++;
-		}
-	} else {               /* x < 0 */
-		if (hy >= 0 || hx > hy) {  /* x < y, x -= ulp */
-			hx--;
-		} else {                   /* x > y, x += ulp */
-			hx++;
-		}
-	}
-	hy = hx & 0x7f800000;
-	if (hy >= 0x7f800000)  /* overflow */
-		return x+x;
-	if (hy < 0x00800000) { /* underflow */
-		/* raise underflow flag */
-		t = x*x;
-		if (t != x) {
-			SET_FLOAT_WORD(y, hx);
 			return y;
-		}
+		ux.bits = (uy.bits & SIGN) | 1;
+	} else if (ax > ay || ((ux.bits ^ uy.bits) & SIGN))
+		ux.bits--;
+	else
+		ux.bits++;
+	e = ux.bits & 0x7f800000;
+	/* raise overflow if ux.value is infinite and x is finite */
+	if (e == 0x7f800000)
+		return x + x;
+	/* raise underflow if ux.value is subnormal or zero */
+	if (e == 0) {
+		volatile float z = x*x + ux.value*ux.value;
 	}
-	SET_FLOAT_WORD(x, hx);
+	return ux.value;
-	return x;
 }

src/math/nextafterl.c

@@ -1,21 +1,3 @@
-/* origin: FreeBSD /usr/src/lib/msun/src/s_nextafterl.c */
-/*
- * ====================================================
- * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
- *
- * Developed at SunPro, a Sun Microsystems, Inc. business.
- * Permission to use, copy, modify, and distribute this
- * software is freely granted, provided that this notice
- * is preserved.
- * ====================================================
- */
-/* IEEE functions
- *      nextafter(x,y)
- *      return the next machine floating-point number of x in the
- *      direction toward y.
- *   Special cases:
- */
-
 #include "libm.h"
 
 #if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
@@ -23,55 +5,80 @@ long double nextafterl(long double x, long double y)
 {
 	return nextafter(x, y);
 }
-#elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384
+#elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384
+#define MSB ((uint64_t)1<<63)
 long double nextafterl(long double x, long double y)
 {
-	volatile long double t;
+	union ldshape ux, uy;
-	union IEEEl2bits ux, uy;
-
-	ux.e = x;
-	uy.e = y;
 
-	if ((ux.bits.exp == 0x7fff && ((ux.bits.manh&~LDBL_NBIT)|ux.bits.manl) != 0) ||
+	if (isnan(x) || isnan(y))
-	    (uy.bits.exp == 0x7fff && ((uy.bits.manh&~LDBL_NBIT)|uy.bits.manl) != 0))
+		return x + y;
-		return x+y;  /* x or y is nan */
 	if (x == y)
-		return y;    /* x=y, return y */
+		return y;
-	if (x == 0.0) {
+	ux.value = x;
-		/* return +-minsubnormal */
+	if (x == 0) {
-		ux.bits.manh = 0;
+		uy.value = y;
-		ux.bits.manl = 1;
+		ux.bits.m = 1;
 		ux.bits.sign = uy.bits.sign;
-		/* raise underflow flag */
+	} else if (x < y ^ ux.bits.sign) {
-		t = ux.e*ux.e;
+		ux.bits.m++;
-		if (t == ux.e)
+		if ((ux.bits.m & ~MSB) == 0) {
-			return t;
+			ux.bits.m = MSB;
-		return ux.e;
+			ux.bits.exp++;
-	}
-	if(x > 0.0 ^ x < y) {  /* x -= ulp */
-		if (ux.bits.manl == 0) {
-			if ((ux.bits.manh&~LDBL_NBIT) == 0)
-				ux.bits.exp--;
-			ux.bits.manh = (ux.bits.manh - 1) | (ux.bits.manh & LDBL_NBIT);
 		}
-		ux.bits.manl--;
+	} else {
-	} else {               /* x += ulp */
+		if ((ux.bits.m & ~MSB) == 0) {
-		ux.bits.manl++;
+			ux.bits.exp--;
-		if (ux.bits.manl == 0) {
+			if (ux.bits.exp)
-			ux.bits.manh = (ux.bits.manh + 1) | (ux.bits.manh & LDBL_NBIT);
+				ux.bits.m = 0;
-			if ((ux.bits.manh&~LDBL_NBIT)==0)
+		}
+		ux.bits.m--;
+	}
+	/* raise overflow if ux.value is infinite and x is finite */
+	if (ux.bits.exp == 0x7fff)
+		return x + x;
+	/* raise underflow if ux.value is subnormal or zero */
+	if (ux.bits.exp == 0) {
+		volatile float z = x*x + ux.value*ux.value;
+	}
+	return ux.value;
+}
+#elif LDBL_MANT_DIG == 113 && LDBL_MAX_EXP == 16384
+long double nextafterl(long double x, long double y)
+{
+	union ldshape ux, uy;
+
+	if (isnan(x) || isnan(y))
+		return x + y;
+	if (x == y)
+		return y;
+	ux.value = x;
+	if (x == 0) {
+		uy.value = y;
+		ux.bits.mlo = 1;
+		ux.bits.sign = uy.bits.sign;
+	} else if (x < y ^ ux.bits.sign) {
+		ux.bits.mlo++;
+		if (ux.bits.mlo == 0) {
+			ux.bits.mhi++;
+			if (ux.bits.mhi == 0)
 				ux.bits.exp++;
 		}
+	} else {
+		if (ux.bits.mlo == 0) {
+			if (ux.bits.mhi == 0)
+				ux.bits.exp--;
+			ux.bits.mhi--;
+		}
+		ux.bits.mlo--;
 	}
-	if (ux.bits.exp == 0x7fff)  /* overflow  */
+	/* raise overflow if ux.value is infinite and x is finite */
-		return x+x;
+	if (ux.bits.exp == 0x7fff)
-	if (ux.bits.exp == 0) {     /* underflow */
+		return x + x;
-		mask_nbit_l(ux);
+	/* raise underflow if ux.value is subnormal or zero */
-		/* raise underflow flag */
+	if (ux.bits.exp == 0) {
-		t = ux.e * ux.e;
+		volatile float z = x*x + ux.value*ux.value;
-		if (t != ux.e)
-			return ux.e;
 	}
-	return ux.e;
+	return ux.value;
 }
 #endif

src/math/nexttoward.c

@@ -1,15 +1,3 @@
-/* origin: FreeBSD /usr/src/lib/msun/src/s_nexttoward.c */
-/*
- * ====================================================
- * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
- *
- * Developed at SunPro, a Sun Microsystems, Inc. business.
- * Permission to use, copy, modify, and distribute this
- * software is freely granted, provided that this notice
- * is preserved.
- * ====================================================
- */
-
 #include "libm.h"
 
 #if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
@@ -17,52 +5,42 @@ double nexttoward(double x, long double y)
 {
 	return nextafter(x, y);
 }
-#elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384
+#else
+#define SIGN ((uint64_t)1<<63)
+
 double nexttoward(double x, long double y)
 {
-	union IEEEl2bits uy;
+	union dshape ux;
-	volatile double t;
+	int e;
-	int32_t hx,ix;
-	uint32_t lx;
 
-	EXTRACT_WORDS(hx, lx, x);
+	if (isnan(x) || isnan(y))
-	ix = hx & 0x7fffffff;
+		return x + y;
-	uy.e = y;
-
-	if ((ix >= 0x7ff00000 && ((ix-0x7ff00000)|lx) != 0) ||
-	    (uy.bits.exp == 0x7fff && ((uy.bits.manh&~LDBL_NBIT)|uy.bits.manl) != 0))
-		return x + y;  /* x or y is nan */
 	if (x == y)
-		return (double)y;
+		return y;
-	if (x == 0.0) {
+	ux.value = x;
-		INSERT_WORDS(x, uy.bits.sign<<31, 1);  /* return +-minsubnormal */
+	if (x == 0) {
-		/* raise underflow */
+		ux.bits = 1;
-		t = x * x;
+		if (signbit(y))
-		if (t == x)
+			ux.bits |= SIGN;
-			return t;
+	} else if (x < y) {
-		return x;
+		if (signbit(x))
-	}
+			ux.bits--;
-	if (hx > 0.0 ^ x < y) {  /* x -= ulp */
+		else
-		if (lx == 0)
+			ux.bits++;
-			hx--;
+	} else {
-		lx--;
+		if (signbit(x))
-	} else {                 /* x += ulp */
+			ux.bits++;
-		lx++;
+		else
-		if (lx == 0)
+			ux.bits--;
-			hx++;
 	}
-	ix = hx & 0x7ff00000;
+	e = ux.bits>>52 & 0x7ff;
-	if (ix >= 0x7ff00000)   /* overflow  */
+	/* raise overflow if ux.value is infinite and x is finite */
+	if (e == 0x7ff)
 		return x + x;
-	if (ix < 0x00100000) {  /* underflow */
+	/* raise underflow if ux.value is subnormal or zero */
-		/* raise underflow flag */
+	if (e == 0) {
-		t = x * x;
+		volatile float z = x*x + ux.value*ux.value;
-		if (t != x) {
-			INSERT_WORDS(x, hx, lx);
-			return x;
-		}
 	}
-	INSERT_WORDS(x, hx, lx);
+	return ux.value;
-	return x;
 }
 #endif

src/math/nexttowardf.c

@@ -1,62 +1,37 @@
-/* origin: FreeBSD /usr/src/lib/msun/src/s_nexttowardf.c */
-/*
- * ====================================================
- * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
- *
- * Developed at SunPro, a Sun Microsystems, Inc. business.
- * Permission to use, copy, modify, and distribute this
- * software is freely granted, provided that this notice
- * is preserved.
- * ====================================================
- */
-
 #include "libm.h"
 
-#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
-// FIXME
-#elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384
-#define LDBL_INFNAN_EXP (LDBL_MAX_EXP * 2 - 1)
-
 float nexttowardf(float x, long double y)
 {
-	union IEEEl2bits uy;
+	union fshape ux;
-	volatile float t;
+	uint32_t e;
-	int32_t hx,ix;
-
-	GET_FLOAT_WORD(hx, x);
-	ix = hx & 0x7fffffff;  /* |x| */
-	uy.e = y;
 
-	if (ix > 0x7f800000 ||
+	if (isnan(x) || isnan(y))
-	    (uy.bits.exp == LDBL_INFNAN_EXP &&
+		return x + y;
-	     ((uy.bits.manh&~LDBL_NBIT)|uy.bits.manl) != 0))
-		return x + y;  /* x or y is nan */
 	if (x == y)
-		return (float)y;  /* x=y, return y */
+		return y;
-	if (ix == 0) {   /* x == 0 */
+	ux.value = x;
-		SET_FLOAT_WORD(x, (uy.bits.sign<<31)|1); /* return +-minsubnormal */
+	if (x == 0) {
-		/* raise underflow flag */
+		ux.bits = 1;
-		t = x*x;
+		if (signbit(y))
-		if (t == x)
+			ux.bits |= 0x80000000;
-			return t;
+	} else if (x < y) {
-		return x;
+		if (signbit(x))
+			ux.bits--;
+		else
+			ux.bits++;
+	} else {
+		if (signbit(x))
+			ux.bits++;
+		else
+			ux.bits--;
 	}
-	if (hx >= 0 ^ x < y)  /* x -= ulp */
+	e = ux.bits & 0x7f800000;
-		hx--;
+	/* raise overflow if ux.value is infinite and x is finite */
-	else                  /* x += ulp */
+	if (e == 0x7f800000)
-		hx++;
+		return x + x;
-	ix = hx & 0x7f800000;
+	/* raise underflow if ux.value is subnormal or zero */
-	if (ix >= 0x7f800000)  /* overflow  */
+	if (e == 0) {
-		return x+x;
+		volatile float z = x*x + ux.value*ux.value;
-	if (ix < 0x00800000) { /* underflow */
-		/* raise underflow flag */
-		t = x*x;
-		if (t != x) {
-			SET_FLOAT_WORD(x, hx);
-			return x;
-		}
 	}
-	SET_FLOAT_WORD(x, hx);
+	return ux.value;
-	return x;
 }
-#endif