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math: rewrite rounding functions (ceil, floor, trunc, round, rint)

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* faster, smaller, cleaner implementation than the bit hacks of fdlibm
* use arithmetics like y=(double)(x+0x1p52)-0x1p52, which is an integer
neighbor of x in all rounding modes (0<=x<0x1p52) and only use bithacks
when that's faster and smaller (for float it usually is)
* the code assumes standard excess precision handling for casts
* long double code supports both ld80 and ld128
* nearbyint is not changed (it is a wrapper around rint)
This commit is contained in:
Szabolcs Nagy
2013-09-03 03:27:02 +00:00
parent 98be442ee8
commit d1a2ead878
15 changed files with 273 additions and 904 deletions
Download Patch File Download Diff File Expand all files Collapse all files

90
src/math/ceil.c
View File

@ -1,82 +1,24 @@
/* origin: FreeBSD /usr/src/lib/msun/src/s_ceil.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.
* ====================================================
*/
/*
* ceil(x)
* Return x rounded toward -inf to integral value
* Method:
* Bit twiddling.
* Exception:
* Inexact flag raised if x not equal to ceil(x).
*/
#include "libm.h" #include "libm.h"
static const double huge = 1.0e300;
double ceil(double x) double ceil(double x)
{ {
int32_t i0,i1,j0; union {double f; uint64_t i;} u = {x};
uint32_t i,j; int e = u.i >> 52 & 0x7ff;
double_t y;
EXTRACT_WORDS(i0, i1, x); if (e >= 0x3ff+52 || x == 0)
// FIXME signed shift
j0 = ((i0>>20)&0x7ff) - 0x3ff;
if (j0 < 20) {
if (j0 < 0) {
/* raise inexact if x != 0 */
if (huge+x > 0.0) {
if (i0 < 0) {
i0 = 0x80000000;
i1=0;
} else if ((i0|i1) != 0) {
i0=0x3ff00000;
i1=0;
}
}
} else {
i = 0x000fffff>>j0;
if (((i0&i)|i1) == 0) /* x is integral */
return x; return x;
/* raise inexact flag */ /* y = int(x) - x, where int(x) is an integer neighbor of x */
if (huge+x > 0.0) { if (u.i >> 63)
if (i0 > 0) y = (double)(x - 0x1p52) + 0x1p52 - x;
i0 += 0x00100000>>j0; else
i0 &= ~i; y = (double)(x + 0x1p52) - 0x1p52 - x;
i1 = 0; /* special case because of non-nearest rounding modes */
if (e <= 0x3ff-1) {
FORCE_EVAL(y);
return u.i >> 63 ? -0.0 : 1;
} }
} if (y < 0)
} else if (j0 > 51) { return x + y + 1;
if (j0 == 0x400) /* inf or NaN */ return x + y;
return x+x;
return x; /* x is integral */
} else {
i = (uint32_t)0xffffffff>>(j0-20);
if ((i1&i) == 0)
return x; /* x is integral */
/* raise inexact flag */
if (huge+x > 0.0) {
if (i0 > 0) {
if (j0 == 20)
i0 += 1;
else {
j = i1 + (1<<(52-j0));
if (j < i1) /* got a carry */
i0 += 1;
i1 = j;
}
}
i1 &= ~i;
}
}
INSERT_WORDS(x, i0, i1);
return x;
} }

67
src/math/ceilf.c
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@ -1,54 +1,27 @@
/* origin: FreeBSD /usr/src/lib/msun/src/s_ceilf.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" #include "libm.h"
static const float huge = 1.0e30;
float ceilf(float x) float ceilf(float x)
{ {
int32_t i0,j0; union {float f; uint32_t i;} u = {x};
uint32_t i; int e = (int)(u.i >> 23 & 0xff) - 0x7f;
uint32_t m;
GET_FLOAT_WORD(i0, x); if (e >= 23)
j0 = ((i0>>23)&0xff) - 0x7f;
if (j0 < 23) {
if (j0 < 0) {
/* raise inexact if x != 0 */
if (huge+x > 0.0f) {
if (i0 < 0)
i0 = 0x80000000;
else if(i0 != 0)
i0 = 0x3f800000;
}
} else {
i = 0x007fffff>>j0;
if ((i0&i) == 0)
return x; /* x is integral */
/* raise inexact flag */
if (huge+x > 0.0f) {
if (i0 > 0)
i0 += 0x00800000>>j0;
i0 &= ~i;
}
}
} else {
if (j0 == 0x80) /* inf or NaN */
return x+x;
return x; /* x is integral */
}
SET_FLOAT_WORD(x, i0);
return x; return x;
if (e >= 0) {
m = 0x007fffff >> e;
if ((u.i & m) == 0)
return x;
FORCE_EVAL(x + 0x1p120f);
if (u.i >> 31 == 0)
u.i += m;
u.i &= ~m;
} else {
FORCE_EVAL(x + 0x1p120f);
if (u.i >> 31)
u.f = -0.0;
else if (u.i << 1)
u.f = 1.0;
}
return u.f;
} }

106
src/math/ceill.c
View File

@ -1,23 +1,3 @@
/* origin: FreeBSD /usr/src/lib/msun/src/s_ceill.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.
* ====================================================
*/
/*
* ceill(x)
* Return x rounded toward -inf to integral value
* Method:
* Bit twiddling.
* Exception:
* Inexact flag raised if x not equal to ceill(x).
*/
#include "libm.h" #include "libm.h"
#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 #if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
@ -26,77 +6,31 @@ long double ceill(long double x)
return ceil(x); return ceil(x);
} }
#elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384 #elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384
#if LDBL_MANT_DIG == 64
#ifdef LDBL_IMPLICIT_NBIT #define TOINT 0x1p63
#define MANH_SIZE (LDBL_MANH_SIZE + 1) #elif LDBL_MANT_DIG == 113
#define INC_MANH(u, c) do { \ #define TOINT 0x1p112
uint64_t o = u.bits.manh; \
u.bits.manh += (c); \
if (u.bits.manh < o) \
u.bits.exp++; \
} while (0)
#else
#define MANH_SIZE LDBL_MANH_SIZE
#define INC_MANH(u, c) do { \
uint64_t o = u.bits.manh; \
u.bits.manh += (c); \
if (u.bits.manh < o) { \
u.bits.exp++; \
u.bits.manh |= 1llu << (LDBL_MANH_SIZE - 1); \
} \
} while (0)
#endif #endif
static const long double huge = 1.0e300;
long double ceill(long double x) long double ceill(long double x)
{ {
union IEEEl2bits u = { .e = x }; union ldshape u = {x};
int e = u.bits.exp - LDBL_MAX_EXP + 1; int e = u.i.se & 0x7fff;
long double y;
if (e < MANH_SIZE - 1) { if (e >= 0x3fff+LDBL_MANT_DIG-1 || x == 0)
if (e < 0) { return x;
/* raise inexact if x != 0 */ /* y = int(x) - x, where int(x) is an integer neighbor of x */
if (huge + x > 0.0) if (u.i.se >> 15)
if (u.bits.exp > 0 || y = x - TOINT + TOINT - x;
(u.bits.manh | u.bits.manl) != 0)
u.e = u.bits.sign ? -0.0 : 1.0;
} else {
uint64_t m = ((1llu << MANH_SIZE) - 1) >> (e + 1);
if (((u.bits.manh & m) | u.bits.manl) == 0)
return x; /* x is integral */
if (!u.bits.sign) {
#ifdef LDBL_IMPLICIT_NBIT
if (e == 0)
u.bits.exp++;
else else
#endif y = x + TOINT - TOINT - x;
INC_MANH(u, 1llu << (MANH_SIZE - e - 1)); /* special case because of non-nearest rounding modes */
if (e <= 0x3fff-1) {
FORCE_EVAL(y);
return u.i.se >> 15 ? -0.0 : 1;
} }
/* raise inexact flag */ if (y < 0)
if (huge + x > 0.0) { return x + y + 1;
u.bits.manh &= ~m; return x + y;
u.bits.manl = 0;
}
}
} else if (e < LDBL_MANT_DIG - 1) {
uint64_t m = (uint64_t)-1 >> (64 - LDBL_MANT_DIG + e + 1);
if ((u.bits.manl & m) == 0)
return x; /* x is integral */
if (!u.bits.sign) {
if (e == MANH_SIZE - 1)
INC_MANH(u, 1);
else {
uint64_t o = u.bits.manl;
u.bits.manl += 1llu << (LDBL_MANT_DIG - e - 1);
if (u.bits.manl < o) /* got a carry */
INC_MANH(u, 1);
}
}
/* raise inexact flag */
if (huge + x > 0.0)
u.bits.manl &= ~m;
}
return u.e;
} }
#endif #endif

92
src/math/floor.c
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@ -1,82 +1,24 @@
/* origin: FreeBSD /usr/src/lib/msun/src/s_floor.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.
* ====================================================
*/
/*
* floor(x)
* Return x rounded toward -inf to integral value
* Method:
* Bit twiddling.
* Exception:
* Inexact flag raised if x not equal to floor(x).
*/
#include "libm.h" #include "libm.h"
static const double huge = 1.0e300;
double floor(double x) double floor(double x)
{ {
int32_t i0,i1,j0; union {double f; uint64_t i;} u = {x};
uint32_t i,j; int e = u.i >> 52 & 0x7ff;
double_t y;
EXTRACT_WORDS(i0, i1, x); if (e >= 0x3ff+52 || x == 0)
// FIXME: signed shift
j0 = ((i0>>20)&0x7ff) - 0x3ff;
if (j0 < 20) {
if (j0 < 0) { /* |x| < 1 */
/* raise inexact if x != 0 */
if (huge+x > 0.0) {
if (i0 >= 0) { /* x >= 0 */
i0 = i1 = 0;
} else if (((i0&0x7fffffff)|i1) != 0) {
i0 = 0xbff00000;
i1 = 0;
}
}
} else {
i = 0x000fffff>>j0;
if (((i0&i)|i1) == 0)
return x; /* x is integral */
/* raise inexact flag */
if (huge+x > 0.0) {
if (i0 < 0)
i0 += 0x00100000>>j0;
i0 &= ~i;
i1 = 0;
}
}
} else if (j0 > 51) {
if (j0 == 0x400)
return x+x; /* inf or NaN */
else
return x; /* x is integral */
} else {
i = (uint32_t)0xffffffff>>(j0-20);
if ((i1&i) == 0)
return x; /* x is integral */
/* raise inexact flag */
if (huge+x > 0.0) {
if (i0 < 0) {
if (j0 == 20)
i0++;
else {
j = i1+(1<<(52-j0));
if (j < i1)
i0++; /* got a carry */
i1 = j;
}
}
i1 &= ~i;
}
}
INSERT_WORDS(x, i0, i1);
return x; return x;
/* y = int(x) - x, where int(x) is an integer neighbor of x */
if (u.i >> 63)
y = (double)(x - 0x1p52) + 0x1p52 - x;
else
y = (double)(x + 0x1p52) - 0x1p52 - x;
/* special case because of non-nearest rounding modes */
if (e <= 0x3ff-1) {
FORCE_EVAL(y);
return u.i >> 63 ? -1 : 0;
}
if (y > 0)
return x + y - 1;
return x + y;
} }

77
src/math/floorf.c
View File

@ -1,64 +1,27 @@
/* origin: FreeBSD /usr/src/lib/msun/src/s_floorf.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.
* ====================================================
*/
/*
* floorf(x)
* Return x rounded toward -inf to integral value
* Method:
* Bit twiddling.
* Exception:
* Inexact flag raised if x not equal to floorf(x).
*/
#include "libm.h" #include "libm.h"
static const float huge = 1.0e30;
float floorf(float x) float floorf(float x)
{ {
int32_t i0,j0; union {float f; uint32_t i;} u = {x};
uint32_t i; int e = (int)(u.i >> 23 & 0xff) - 0x7f;
uint32_t m;
GET_FLOAT_WORD(i0, x); if (e >= 23)
// FIXME: signed shift
j0 = ((i0>>23)&0xff) - 0x7f;
if (j0 < 23) {
if (j0 < 0) { /* |x| < 1 */
/* raise inexact if x != 0 */
if (huge+x > 0.0f) {
if (i0 >= 0) /* x >= 0 */
i0 = 0;
else if ((i0&0x7fffffff) != 0)
i0 = 0xbf800000;
}
} else {
i = 0x007fffff>>j0;
if ((i0&i) == 0)
return x; /* x is integral */
/* raise inexact flag */
if (huge+x > 0.0f) {
if (i0 < 0)
i0 += 0x00800000>>j0;
i0 &= ~i;
}
}
} else {
if (j0 == 0x80) /* inf or NaN */
return x+x;
else
return x; /* x is integral */
}
SET_FLOAT_WORD(x, i0);
return x; return x;
if (e >= 0) {
m = 0x007fffff >> e;
if ((u.i & m) == 0)
return x;
FORCE_EVAL(x + 0x1p120f);
if (u.i >> 31)
u.i += m;
u.i &= ~m;
} else {
FORCE_EVAL(x + 0x1p120f);
if (u.i >> 31 == 0)
u.i = 0;
else if (u.i << 1)
u.f = -1.0;
}
return u.f;
} }

106
src/math/floorl.c
View File

@ -1,23 +1,3 @@
/* origin: FreeBSD /usr/src/lib/msun/src/s_floorl.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.
* ====================================================
*/
/*
* floorl(x)
* Return x rounded toward -inf to integral value
* Method:
* Bit twiddling.
* Exception:
* Inexact flag raised if x not equal to floorl(x).
*/
#include "libm.h" #include "libm.h"
#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 #if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
@ -26,77 +6,31 @@ long double floorl(long double x)
return floor(x); return floor(x);
} }
#elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384 #elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384
#if LDBL_MANT_DIG == 64
#ifdef LDBL_IMPLICIT_NBIT #define TOINT 0x1p63
#define MANH_SIZE (LDBL_MANH_SIZE + 1) #elif LDBL_MANT_DIG == 113
#define INC_MANH(u, c) do { \ #define TOINT 0x1p112
uint64_t o = u.bits.manh; \
u.bits.manh += (c); \
if (u.bits.manh < o) \
u.bits.exp++; \
} while (0)
#else
#define MANH_SIZE LDBL_MANH_SIZE
#define INC_MANH(u, c) do { \
uint64_t o = u.bits.manh; \
u.bits.manh += (c); \
if (u.bits.manh < o) { \
u.bits.exp++; \
u.bits.manh |= 1llu << (LDBL_MANH_SIZE - 1); \
} \
} while (0)
#endif #endif
static const long double huge = 1.0e300;
long double floorl(long double x) long double floorl(long double x)
{ {
union IEEEl2bits u = { .e = x }; union ldshape u = {x};
int e = u.bits.exp - LDBL_MAX_EXP + 1; int e = u.i.se & 0x7fff;
long double y;
if (e < MANH_SIZE - 1) { if (e >= 0x3fff+LDBL_MANT_DIG-1 || x == 0)
if (e < 0) { return x;
/* raise inexact if x != 0 */ /* y = int(x) - x, where int(x) is an integer neighbor of x */
if (huge + x > 0.0) if (u.i.se >> 15)
if (u.bits.exp > 0 || y = x - TOINT + TOINT - x;
(u.bits.manh | u.bits.manl) != 0)
u.e = u.bits.sign ? -1.0 : 0.0;
} else {
uint64_t m = ((1llu << MANH_SIZE) - 1) >> (e + 1);
if (((u.bits.manh & m) | u.bits.manl) == 0)
return x; /* x is integral */
if (u.bits.sign) {
#ifdef LDBL_IMPLICIT_NBIT
if (e == 0)
u.bits.exp++;
else else
#endif y = x + TOINT - TOINT - x;
INC_MANH(u, 1llu << (MANH_SIZE - e - 1)); /* special case because of non-nearest rounding modes */
if (e <= 0x3fff-1) {
FORCE_EVAL(y);
return u.i.se >> 15 ? -1 : 0;
} }
/* raise inexact flag */ if (y > 0)
if (huge + x > 0.0) { return x + y - 1;
u.bits.manh &= ~m; return x + y;
u.bits.manl = 0;
}
}
} else if (e < LDBL_MANT_DIG - 1) {
uint64_t m = (uint64_t)-1 >> (64 - LDBL_MANT_DIG + e + 1);
if ((u.bits.manl & m) == 0)
return x; /* x is integral */
if (u.bits.sign) {
if (e == MANH_SIZE - 1)
INC_MANH(u, 1);
else {
uint64_t o = u.bits.manl;
u.bits.manl += 1llu << (LDBL_MANT_DIG - e - 1);
if (u.bits.manl < o) /* got a carry */
INC_MANH(u, 1);
}
}
/* raise inexact flag */
if (huge + x > 0.0)
u.bits.manl &= ~m;
}
return u.e;
} }
#endif #endif

96
src/math/rint.c
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@ -1,90 +1,20 @@
/* origin: FreeBSD /usr/src/lib/msun/src/s_rint.c */ #include <math.h>
/* #include <stdint.h>
* ====================================================
* 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.
* ====================================================
*/
/*
* rint(x)
* Return x rounded to integral value according to the prevailing
* rounding mode.
* Method:
* Using floating addition.
* Exception:
* Inexact flag raised if x not equal to rint(x).
*/
#include "libm.h"
static const double
TWO52[2] = {
4.50359962737049600000e+15, /* 0x43300000, 0x00000000 */
-4.50359962737049600000e+15, /* 0xC3300000, 0x00000000 */
};
double rint(double x) double rint(double x)
{ {
int32_t i0,j0,sx; union {double f; uint64_t i;} u = {x};
uint32_t i,i1; int e = u.i>>52 & 0x7ff;
double w,t; int s = u.i>>63;
double_t y;
EXTRACT_WORDS(i0, i1, x); if (e >= 0x3ff+52)
// FIXME: signed shift
sx = (i0>>31) & 1;
j0 = ((i0>>20)&0x7ff) - 0x3ff;
if (j0 < 20) {
if (j0 < 0) {
if (((i0&0x7fffffff)|i1) == 0)
return x; return x;
i1 |= i0 & 0x0fffff; if (s)
i0 &= 0xfffe0000; y = (double)(x - 0x1p52) + 0x1p52;
i0 |= ((i1|-i1)>>12) & 0x80000;
SET_HIGH_WORD(x, i0);
STRICT_ASSIGN(double, w, TWO52[sx] + x);
t = w - TWO52[sx];
GET_HIGH_WORD(i0, t);
SET_HIGH_WORD(t, (i0&0x7fffffff)|(sx<<31));
return t;
} else {
i = 0x000fffff>>j0;
if (((i0&i)|i1) == 0)
return x; /* x is integral */
i >>= 1;
if (((i0&i)|i1) != 0) {
/*
* Some bit is set after the 0.5 bit. To avoid the
* possibility of errors from double rounding in
* w = TWO52[sx]+x, adjust the 0.25 bit to a lower
* guard bit. We do this for all j0<=51. The
* adjustment is trickiest for j0==18 and j0==19
* since then it spans the word boundary.
*/
if (j0 == 19)
i1 = 0x40000000;
else if (j0 == 18)
i1 = 0x80000000;
else else
i0 = (i0 & ~i)|(0x20000>>j0); y = (double)(x + 0x1p52) - 0x1p52;
} if (y == 0)
} return s ? -0.0 : 0;
} else if (j0 > 51) { return y;
if (j0 == 0x400)
return x+x; /* inf or NaN */
return x; /* x is integral */
} else {
i = (uint32_t)0xffffffff>>(j0-20);
if ((i1&i) == 0)
return x; /* x is integral */
i >>= 1;
if ((i1&i) != 0)
i1 = (i1 & ~i)|(0x40000000>>(j0-20));
}
INSERT_WORDS(x, i0, i1);
STRICT_ASSIGN(double, w, TWO52[sx] + x);
return w - TWO52[sx];
} }

56
src/math/rintf.c
View File

@ -1,48 +1,20 @@
/* origin: FreeBSD /usr/src/lib/msun/src/s_rintf.c */ #include <math.h>
/* #include <stdint.h>
* 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"
static const float
TWO23[2] = {
8.3886080000e+06, /* 0x4b000000 */
-8.3886080000e+06, /* 0xcb000000 */
};
float rintf(float x) float rintf(float x)
{ {
int32_t i0,j0,sx; union {float f; uint32_t i;} u = {x};
float w,t; int e = u.i>>23 & 0xff;
int s = u.i>>31;
float_t y;
GET_FLOAT_WORD(i0, x); if (e >= 0x7f+23)
sx = (i0>>31) & 1;
j0 = ((i0>>23)&0xff) - 0x7f;
if (j0 < 23) {
if (j0 < 0) {
if ((i0&0x7fffffff) == 0)
return x; return x;
STRICT_ASSIGN(float, w, TWO23[sx] + x); if (s)
t = w - TWO23[sx]; y = (float)(x - 0x1p23f) + 0x1p23f;
GET_FLOAT_WORD(i0, t); else
SET_FLOAT_WORD(t, (i0&0x7fffffff)|(sx<<31)); y = (float)(x + 0x1p23f) - 0x1p23f;
return t; if (y == 0)
} return s ? -0.0f : 0.0f;
STRICT_ASSIGN(float, w, TWO23[sx] + x); return y;
return w - TWO23[sx];
}
if (j0 == 0x80)
return x+x; /* inf or NaN */
return x; /* x is integral */
} }

82
src/math/rintl.c
View File

@ -1,30 +1,3 @@
/* origin: FreeBSD /usr/src/lib/msun/src/s_rintl.c */
/*-
* Copyright (c) 2008 David Schultz <das@FreeBSD.ORG>
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
* 1. Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
*
* THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
* ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
* SUCH DAMAGE.
*/
#include "libm.h" #include "libm.h"
#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 #if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
@ -33,53 +6,26 @@ long double rintl(long double x)
return rint(x); return rint(x);
} }
#elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384 #elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384
#define BIAS (LDBL_MAX_EXP - 1)
static const float
shift[2] = {
#if LDBL_MANT_DIG == 64 #if LDBL_MANT_DIG == 64
0x1.0p63, -0x1.0p63 #define TOINT 0x1p63
#elif LDBL_MANT_DIG == 113 #elif LDBL_MANT_DIG == 113
0x1.0p112, -0x1.0p112 #define TOINT 0x1p112
#endif #endif
};
static const float zero[2] = { 0.0, -0.0 };
long double rintl(long double x) long double rintl(long double x)
{ {
union IEEEl2bits u; union ldshape u = {x};
uint32_t expsign; int e = u.i.se & 0x7fff;
int ex, sign; int s = u.i.se >> 15;
long double y;
u.e = x;
expsign = u.xbits.expsign;
ex = expsign & 0x7fff;
if (ex >= BIAS + LDBL_MANT_DIG - 1) {
if (ex == BIAS + LDBL_MAX_EXP)
return x + x; /* Inf, NaN, or unsupported format */
return x; /* finite and already an integer */
}
sign = expsign >> 15;
/*
* The following code assumes that intermediate results are
* evaluated in long double precision. If they are evaluated in
* greater precision, double rounding may occur, and if they are
* evaluated in less precision (as on i386), results will be
* wildly incorrect.
*/
x += shift[sign];
x -= shift[sign];
/*
* If the result is +-0, then it must have the same sign as x, but
* the above calculation doesn't always give this. Fix up the sign.
*/
if (ex < BIAS && x == 0.0)
return zero[sign];
if (e >= 0x3fff+LDBL_MANT_DIG-1)
return x; return x;
if (s)
y = x - TOINT + TOINT;
else
y = x + TOINT - TOINT;
if (y == 0)
return 0*x;
return y;
} }
#endif #endif

62
src/math/round.c
View File

@ -1,48 +1,28 @@
/* origin: FreeBSD /usr/src/lib/msun/src/s_round.c */ #include "libm.h"
/*-
* Copyright (c) 2003, Steven G. Kargl
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
* 1. Redistributions of source code must retain the above copyright
* notice unmodified, this list of conditions, and the following
* disclaimer.
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
*
* THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
* IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
* OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
* IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
* NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
* DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
* THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
* THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*/
#include <math.h>
double round(double x) double round(double x)
{ {
double t; union {double f; uint64_t i;} u = {x};
int e = u.i >> 52 & 0x7ff;
double_t y;
if (!isfinite(x)) if (e >= 0x3ff+52)
return x; return x;
if (u.i >> 63)
if (x >= 0.0) { x = -x;
t = floor(x); if (e < 0x3ff-1) {
if (t - x <= -0.5) /* raise inexact if x!=0 */
t += 1.0; FORCE_EVAL(x + 0x1p52);
return t; return 0*u.f;
} else {
t = floor(-x);
if (t + x <= -0.5)
t += 1.0;
return -t;
} }
y = (double)(x + 0x1p52) - 0x1p52 - x;
if (y > 0.5)
y = y + x - 1;
else if (y <= -0.5)
y = y + x + 1;
else
y = y + x;
if (u.i >> 63)
y = -y;
return y;
} }

61
src/math/roundf.c
View File

@ -1,48 +1,27 @@
/* origin: FreeBSD /usr/src/lib/msun/src/s_roundf.c */ #include "libm.h"
/*-
* Copyright (c) 2003, Steven G. Kargl
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
* 1. Redistributions of source code must retain the above copyright
* notice unmodified, this list of conditions, and the following
* disclaimer.
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
*
* THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
* IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
* OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
* IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
* NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
* DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
* THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
* THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*/
#include <math.h>
float roundf(float x) float roundf(float x)
{ {
float t; union {float f; uint32_t i;} u = {x};
int e = u.i >> 23 & 0xff;
float_t y;
if (!isfinite(x)) if (e >= 0x7f+23)
return x; return x;
if (u.i >> 31)
if (x >= 0.0) { x = -x;
t = floorf(x); if (e < 0x7f-1) {
if (t - x <= -0.5) FORCE_EVAL(x + 0x1p23f);
t += 1.0; return 0*u.f;
return t;
} else {
t = floorf(-x);
if (t + x <= -0.5)
t += 1.0;
return -t;
} }
y = (float)(x + 0x1p23f) - 0x1p23f - x;
if (y > 0.5f)
y = y + x - 1;
else if (y <= -0.5f)
y = y + x + 1;
else
y = y + x;
if (u.i >> 31)
y = -y;
return y;
} }

69
src/math/roundl.c
View File

@ -1,56 +1,39 @@
/* origin: FreeBSD /usr/src/lib/msun/src/s_roundl.c */ #include "libm.h"
/*-
* Copyright (c) 2003, Steven G. Kargl
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
* 1. Redistributions of source code must retain the above copyright
* notice unmodified, this list of conditions, and the following
* disclaimer.
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
*
* THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
* IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
* OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
* IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
* NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
* DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
* THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
* THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*/
#include <math.h>
#include <float.h>
#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 #if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
long double roundl(long double x) long double roundl(long double x)
{ {
return round(x); return round(x);
} }
#else #elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384
#if LDBL_MANT_DIG == 64
#define TOINT 0x1p63
#elif LDBL_MANT_DIG == 113
#define TOINT 0x1p112
#endif
long double roundl(long double x) long double roundl(long double x)
{ {
long double t; union ldshape u = {x};
int e = u.i.se & 0x7fff;
long double y;
if (!isfinite(x)) if (e >= 0x3fff+LDBL_MANT_DIG-1)
return x; return x;
if (u.i.se >> 15)
if (x >= 0.0) { x = -x;
t = floorl(x); if (e < 0x3fff-1) {
if (t - x <= -0.5) FORCE_EVAL(x + TOINT);
t += 1.0; return 0*u.f;
return t;
} else {
t = floorl(-x);
if (t + x <= -0.5)
t += 1.0;
return -t;
} }
y = x + TOINT - TOINT - x;
if (y > 0.5)
y = y + x - 1;
else if (y <= -0.5)
y = y + x + 1;
else
y = y + x;
if (u.i.se >> 15)
y = -y;
return y;
} }
#endif #endif

68
src/math/trunc.c
View File

@ -1,63 +1,19 @@
/* origin: FreeBSD /usr/src/lib/msun/src/s_trunc.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.
* ====================================================
*/
/*
* trunc(x)
* Return x rounded toward 0 to integral value
* Method:
* Bit twiddling.
* Exception:
* Inexact flag raised if x not equal to trunc(x).
*/
#include "libm.h" #include "libm.h"
static const double huge = 1.0e300;
double trunc(double x) double trunc(double x)
{ {
int32_t i0,i1,j0; union {double f; uint64_t i;} u = {x};
uint32_t i; int e = (int)(u.i >> 52 & 0x7ff) - 0x3ff + 12;
uint64_t m;
EXTRACT_WORDS(i0, i1, x); if (e >= 52 + 12)
j0 = ((i0>>20)&0x7ff) - 0x3ff;
if (j0 < 20) {
if (j0 < 0) { /* |x|<1, return 0*sign(x) */
/* raise inexact if x != 0 */
if (huge+x > 0.0) {
i0 &= 0x80000000U;
i1 = 0;
}
} else {
i = 0x000fffff>>j0;
if (((i0&i)|i1) == 0)
return x; /* x is integral */
/* raise inexact */
if (huge+x > 0.0) {
i0 &= ~i;
i1 = 0;
}
}
} else if (j0 > 51) {
if (j0 == 0x400)
return x + x; /* inf or NaN */
return x; /* x is integral */
} else {
i = (uint32_t)0xffffffff>>(j0-20);
if ((i1&i) == 0)
return x; /* x is integral */
/* raise inexact */
if (huge+x > 0.0)
i1 &= ~i;
}
INSERT_WORDS(x, i0, i1);
return x; return x;
if (e < 12)
e = 1;
m = -1ULL >> e;
if ((u.i & m) == 0)
return x;
FORCE_EVAL(x + 0x1p120f);
u.i &= ~m;
return u.f;
} }

57
src/math/truncf.c
View File

@ -1,52 +1,19 @@
/* origin: FreeBSD /usr/src/lib/msun/src/s_truncf.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.
* ====================================================
*/
/*
* truncf(x)
* Return x rounded toward 0 to integral value
* Method:
* Bit twiddling.
* Exception:
* Inexact flag raised if x not equal to truncf(x).
*/
#include "libm.h" #include "libm.h"
static const float huge = 1.0e30f;
float truncf(float x) float truncf(float x)
{ {
int32_t i0,j0; union {float f; uint32_t i;} u = {x};
uint32_t i; int e = (int)(u.i >> 23 & 0xff) - 0x7f + 9;
uint32_t m;
GET_FLOAT_WORD(i0, x); if (e >= 23 + 9)
j0 = ((i0>>23)&0xff) - 0x7f;
if (j0 < 23) {
if (j0 < 0) { /* |x|<1, return 0*sign(x) */
/* raise inexact if x != 0 */
if (huge+x > 0.0f)
i0 &= 0x80000000;
} else {
i = 0x007fffff>>j0;
if ((i0&i) == 0)
return x; /* x is integral */
/* raise inexact */
if (huge+x > 0.0f)
i0 &= ~i;
}
} else {
if (j0 == 0x80)
return x + x; /* inf or NaN */
return x; /* x is integral */
}
SET_FLOAT_WORD(x, i0);
return x; return x;
if (e < 9)
e = 1;
m = -1U >> e;
if ((u.i & m) == 0)
return x;
FORCE_EVAL(x + 0x1p120f);
u.i &= ~m;
return u.f;
} }

74
src/math/truncl.c
View File

@ -1,23 +1,3 @@
/* origin: FreeBSD /usr/src/lib/msun/src/s_truncl.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.
* ====================================================
*/
/*
* truncl(x)
* Return x rounded toward 0 to integral value
* Method:
* Bit twiddling.
* Exception:
* Inexact flag raised if x not equal to truncl(x).
*/
#include "libm.h" #include "libm.h"
#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 #if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
@ -26,43 +6,31 @@ long double truncl(long double x)
return trunc(x); return trunc(x);
} }
#elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384 #elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384
#ifdef LDBL_IMPLICIT_NBIT #if LDBL_MANT_DIG == 64
#define MANH_SIZE (LDBL_MANH_SIZE + 1) #define TOINT 0x1p63
#else #elif LDBL_MANT_DIG == 113
#define MANH_SIZE LDBL_MANH_SIZE #define TOINT 0x1p112
#endif #endif
static const long double huge = 1.0e300;
static const float zero[] = { 0.0, -0.0 };
long double truncl(long double x) long double truncl(long double x)
{ {
union IEEEl2bits u = { .e = x }; union ldshape u = {x};
int e = u.bits.exp - LDBL_MAX_EXP + 1; int e = u.i.se & 0x7fff;
int s = u.i.se >> 15;
long double y;
if (e < MANH_SIZE - 1) { if (e >= 0x3fff+LDBL_MANT_DIG-1)
if (e < 0) { return x;
/* raise inexact if x != 0 */ if (e <= 0x3fff-1) {
if (huge + x > 0.0) FORCE_EVAL(x + 0x1p120f);
u.e = zero[u.bits.sign]; return x*0;
} else {
uint64_t m = ((1llu << MANH_SIZE) - 1) >> (e + 1);
if (((u.bits.manh & m) | u.bits.manl) == 0)
return x; /* x is integral */
/* raise inexact */
if (huge + x > 0.0) {
u.bits.manh &= ~m;
u.bits.manl = 0;
} }
} /* y = int(|x|) - |x|, where int(|x|) is an integer neighbor of |x| */
} else if (e < LDBL_MANT_DIG - 1) { if (s)
uint64_t m = (uint64_t)-1 >> (64 - LDBL_MANT_DIG + e + 1); x = -x;
if ((u.bits.manl & m) == 0) y = x + TOINT - TOINT - x;
return x; /* x is integral */ if (y > 0)
/* raise inexact */ y -= 1;
if (huge + x > 0.0) x += y;
u.bits.manl &= ~m; return s ? -x : x;
}
return u.e;
} }
#endif #endif