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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
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75
src/math/floorf.c
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@ -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"
static const float huge = 1.0e30;
float floorf(float x)
{
int32_t i0,j0;
uint32_t i;
union {float f; uint32_t i;} u = {x};
int e = (int)(u.i >> 23 & 0xff) - 0x7f;
uint32_t m;
GET_FLOAT_WORD(i0, x);
// 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;
}
}
if (e >= 23)
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 {
if (j0 == 0x80) /* inf or NaN */
return x+x;
else
return x; /* x is integral */
FORCE_EVAL(x + 0x1p120f);
if (u.i >> 31 == 0)
u.i = 0;
else if (u.i << 1)
u.f = -1.0;
}
SET_FLOAT_WORD(x, i0);
return x;
return u.f;
}