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math: nextafter and nexttoward cleanup

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make nexttoward, nexttowardf independent of long double representation.
fix nextafterl: it did not raise underflow flag when the result was 0.
This commit is contained in:
nsz 2012-05-06 13:08:59 +02:00
parent 98c9af5001
commit 6cf865dba6
5 changed files with 176 additions and 291 deletions
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97
src/math/nextafter.c
View File

@ -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;
}

84
src/math/nextafterf.c
View File

@ -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;
}

123
src/math/nextafterl.c
View File

@ -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 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

82
src/math/nexttoward.c
View File

@ -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;
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

81
src/math/nexttowardf.c
View File

@ -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