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.
diff --git a/src/math/nextafter.c b/src/math/nextafter.c
index 5e53654..d9e2923 100644
--- a/src/math/nextafter.c
+++ b/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;
- int32_t hx,hy,ix,iy;
- uint32_t lx,ly;
+ union dshape ux, uy;
+ uint64_t ax, ay;
+ 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 */
- (iy >= 0x7ff00000 && (iy-0x7ff00000)|ly) != 0) /* y is nan */
- return x+y;
- if (x == y) /* x == y */
+ if (isnan(x) || isnan(y))
+ return x + y;
+ ux.value = x;
+ uy.value = y;
+ if (ux.bits == uy.bits)
return y;
- if ((ix|lx) == 0) { /* x == 0 */
- INSERT_WORDS(x, hy&0x80000000, 1); /* return +-minsubnormal */
- /* raise underflow flag */
- t = x*x;
- 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);
+ ax = ux.bits & ~SIGN;
+ ay = uy.bits & ~SIGN;
+ if (ax == 0) {
+ if (ay == 0)
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 x;
+ return ux.value;
}
diff --git a/src/math/nextafterf.c b/src/math/nextafterf.c
index bdc88ca..4727f7b 100644
--- a/src/math/nextafterf.c
+++ b/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;
- int32_t hx,hy,ix,iy;
+ union fshape ux, uy;
+ 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 */
- iy > 0x7f800000) /* y is nan */
- return x+y;
- if (x == y) /* x == y */
+ if (isnan(x) || isnan(y))
+ return x + y;
+ ux.value = x;
+ uy.value = y;
+ if (ux.bits == uy.bits)
return y;
- if (ix == 0) { /* x == 0 */
- SET_FLOAT_WORD(x, (hy&0x80000000)|1); /* return +-minsubnormal */
- /* raise underflow flag */
- t = x*x;
- 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);
+ ax = ux.bits & ~SIGN;
+ ay = uy.bits & ~SIGN;
+ if (ax == 0) {
+ if (ay == 0)
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 x;
+ return ux.value;
}
diff --git a/src/math/nextafterl.c b/src/math/nextafterl.c
index aec8ab4..611ea53 100644
--- a/src/math/nextafterl.c
+++ b/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 @@
{
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 IEEEl2bits ux, uy;
+ union ldshape ux, uy;
- ux.e = x;
- uy.e = y;
-
- if ((ux.bits.exp == 0x7fff && ((ux.bits.manh&~LDBL_NBIT)|ux.bits.manl) != 0) ||
- (uy.bits.exp == 0x7fff && ((uy.bits.manh&~LDBL_NBIT)|uy.bits.manl) != 0))
- return x+y; /* x or y is nan */
+ if (isnan(x) || isnan(y))
+ return x + y;
if (x == y)
- return y; /* x=y, return y */
- if (x == 0.0) {
- /* return +-minsubnormal */
- ux.bits.manh = 0;
- ux.bits.manl = 1;
+ return y;
+ ux.value = x;
+ if (x == 0) {
+ uy.value = y;
+ ux.bits.m = 1;
ux.bits.sign = uy.bits.sign;
- /* raise underflow flag */
- t = ux.e*ux.e;
- if (t == ux.e)
- return t;
- return ux.e;
- }
- 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);
+ } else if (x < y ^ ux.bits.sign) {
+ ux.bits.m++;
+ if ((ux.bits.m & ~MSB) == 0) {
+ ux.bits.m = MSB;
+ ux.bits.exp++;
}
- ux.bits.manl--;
- } else { /* x += ulp */
- ux.bits.manl++;
- if (ux.bits.manl == 0) {
- ux.bits.manh = (ux.bits.manh + 1) | (ux.bits.manh & LDBL_NBIT);
- if ((ux.bits.manh&~LDBL_NBIT)==0)
+ } else {
+ if ((ux.bits.m & ~MSB) == 0) {
+ ux.bits.exp--;
+ if (ux.bits.exp)
+ ux.bits.m = 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 */
- return x+x;
- if (ux.bits.exp == 0) { /* underflow */
- mask_nbit_l(ux);
- /* raise underflow flag */
- t = ux.e * ux.e;
- if (t != ux.e)
- return ux.e;
+ /* 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.e;
+ return ux.value;
}
#endif
diff --git a/src/math/nexttoward.c b/src/math/nexttoward.c
index e150eaa..741b6b5 100644
--- a/src/math/nexttoward.c
+++ b/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 @@
{
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;
- volatile double t;
- int32_t hx,ix;
- uint32_t lx;
+ union dshape ux;
+ int e;
- EXTRACT_WORDS(hx, lx, x);
- ix = hx & 0x7fffffff;
- 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 (isnan(x) || isnan(y))
+ return x + y;
if (x == y)
- return (double)y;
- if (x == 0.0) {
- INSERT_WORDS(x, uy.bits.sign<<31, 1); /* return +-minsubnormal */
- /* raise underflow */
- t = x * x;
- if (t == x)
- return t;
- return x;
+ return y;
+ ux.value = x;
+ if (x == 0) {
+ ux.bits = 1;
+ if (signbit(y))
+ ux.bits |= SIGN;
+ } else if (x < y) {
+ if (signbit(x))
+ ux.bits--;
+ else
+ ux.bits++;
+ } else {
+ if (signbit(x))
+ ux.bits++;
+ else
+ ux.bits--;
}
- if (hx > 0.0 ^ x < y) { /* x -= ulp */
- if (lx == 0)
- hx--;
- lx--;
- } else { /* x += ulp */
- lx++;
- if (lx == 0)
- hx++;
- }
- ix = hx & 0x7ff00000;
- if (ix >= 0x7ff00000) /* overflow */
+ e = ux.bits>>52 & 0x7ff;
+ /* raise overflow if ux.value is infinite and x is finite */
+ if (e == 0x7ff)
return x + x;
- if (ix < 0x00100000) { /* underflow */
- /* raise underflow flag */
- t = x * x;
- if (t != x) {
- INSERT_WORDS(x, hx, lx);
- return x;
- }
+ /* raise underflow if ux.value is subnormal or zero */
+ if (e == 0) {
+ volatile float z = x*x + ux.value*ux.value;
}
- INSERT_WORDS(x, hx, lx);
- return x;
+ return ux.value;
}
#endif
diff --git a/src/math/nexttowardf.c b/src/math/nexttowardf.c
index c52ef3a..821f72a 100644
--- a/src/math/nexttowardf.c
+++ b/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;
- volatile float t;
- int32_t hx,ix;
+ union fshape ux;
+ uint32_t e;
- GET_FLOAT_WORD(hx, x);
- ix = hx & 0x7fffffff; /* |x| */
- uy.e = y;
-
- if (ix > 0x7f800000 ||
- (uy.bits.exp == LDBL_INFNAN_EXP &&
- ((uy.bits.manh&~LDBL_NBIT)|uy.bits.manl) != 0))
- return x + y; /* x or y is nan */
+ if (isnan(x) || isnan(y))
+ return x + y;
if (x == y)
- return (float)y; /* x=y, return y */
- if (ix == 0) { /* x == 0 */
- SET_FLOAT_WORD(x, (uy.bits.sign<<31)|1); /* return +-minsubnormal */
- /* raise underflow flag */
- t = x*x;
- if (t == x)
- return t;
- return x;
+ return y;
+ ux.value = x;
+ if (x == 0) {
+ ux.bits = 1;
+ if (signbit(y))
+ ux.bits |= 0x80000000;
+ } else if (x < y) {
+ if (signbit(x))
+ ux.bits--;
+ else
+ ux.bits++;
+ } else {
+ if (signbit(x))
+ ux.bits++;
+ else
+ ux.bits--;
}
- if (hx >= 0 ^ x < y) /* x -= ulp */
- hx--;
- else /* x += ulp */
- hx++;
- ix = hx & 0x7f800000;
- if (ix >= 0x7f800000) /* overflow */
- return x+x;
- if (ix < 0x00800000) { /* underflow */
- /* raise underflow flag */
- t = x*x;
- if (t != x) {
- SET_FLOAT_WORD(x, hx);
- return x;
- }
+ 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 x;
+ return ux.value;
}
-#endif