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/* @(#)s_rint.c 5.1 93/09/24 */
/*
* ====================================================
* 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.
* ====================================================
*/
/*
FUNCTION
<<rint>>, <<rintf>>---round to integer
INDEX
rint
INDEX
rintf
SYNOPSIS
#include <math.h>
double rint(double <[x]>);
float rintf(float <[x]>);
DESCRIPTION
The <<rint>> functions round their argument to an integer value in
floating-point format, using the current rounding direction. They
raise the "inexact" floating-point exception if the result differs
in value from the argument. See the <<nearbyint>> functions for the
same function with the "inexact" floating-point exception never being
raised. Newlib does not directly support floating-point exceptions.
The <<rint>> functions are written so that the "inexact" exception is
raised in hardware implementations that support it, even though Newlib
does not provide access.
RETURNS
<[x]> rounded to an integral value, using the current rounding direction.
PORTABILITY
ANSI C, POSIX
SEEALSO
<<nearbyint>>, <<round>>
*/
/*
* rint(x)
* Return x rounded to integral value according to the prevailing
* rounding mode.
* Method:
* Using floating addition.
* Whenever a fraction is present, if the second or any following bit after
* the radix point is set, limit to the second radix point to avoid
* possible double rounding in the TWO52 +- steps (in case guard bits are
* used). Specifically, if have any, chop off bits past the 2nd place and
* set the second place.
* (e.g. 2.0625=0b10.0001 => 0b10.01=2.25;
* 2.3125=0b10.011 => 0b10.01=2.25;
* 1.5625= 0b1.1001 => 0b1.11=1.75;
* 1.9375= 0b1.1111 => 0b1.11=1.75.
* Pseudo-code: if(x.frac & ~0b0.10) x.frac = (x.frac & 0b0.11) | 0b0.01;).
* Exception:
* Inexact flag raised if x not equal to rint(x).
*/
#include "fdlibm.h"
#ifndef _DOUBLE_IS_32BITS
static const double
TWO52[2]={
4.50359962737049600000e+15, /* 0x43300000, 0x00000000 */
-4.50359962737049600000e+15, /* 0xC3300000, 0x00000000 */
};
double rint(double x)
{
__int32_t i0,j0,sx;
__uint32_t i,i1;
double t;
volatile double w;
EXTRACT_WORDS(i0,i1,x);
sx = (i0>>31)&1; /* sign */
j0 = ((i0>>20)&0x7ff)-0x3ff; /* exponent */
if(j0<20) { /* no integral bits in LS part */
if(j0<0) { /* x is fractional or 0 */
if(((i0&0x7fffffff)|i1)==0) return x; /* x == 0 */
i1 |= (i0&0x0fffff);
i0 &= 0xfffe0000;
i0 |= ((i1|-i1)>>12)&0x80000;
SET_HIGH_WORD(x,i0);
w = TWO52[sx]+x;
t = w-TWO52[sx];
GET_HIGH_WORD(i0,t);
SET_HIGH_WORD(t,(i0&0x7fffffff)|(sx<<31));
return t;
} else { /* x has integer and maybe fraction */
i = (0x000fffff)>>j0;
if(((i0&i)|i1)==0) return x; /* x is integral */
i>>=1;
if(((i0&i)|i1)!=0) {
/* 2nd or any later bit after radix is set */
if(j0==19) i1 = 0x80000000; else i1 = 0;
i0 = (i0&(~i))|((0x40000)>>j0);
}
}
} 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 */
i>>=1;
if((i1&i)!=0) i1 = (i1&(~i))|((0x40000000)>>(j0-20));
}
INSERT_WORDS(x,i0,i1);
w = TWO52[sx]+x;
return w-TWO52[sx];
}
#endif /* _DOUBLE_IS_32BITS */
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