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/* Round to nearest integer value, rounding halfway cases to even.
dbl-64 version.
Copyright (C) 2016-2021 Free Software Foundation, Inc.
This file is part of the GNU C Library.
The GNU C Library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
License as published by the Free Software Foundation; either
version 2.1 of the License, or (at your option) any later version.
The GNU C Library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with the GNU C Library; if not, see
<https://www.gnu.org/licenses/>. */
#include <math.h>
#include <math_private.h>
#include <libm-alias-double.h>
#include <stdint.h>
#define BIAS 0x3ff
#define MANT_DIG 53
#define MAX_EXP (2 * BIAS + 1)
double
__roundeven (double x)
{
uint32_t hx, lx, uhx;
EXTRACT_WORDS (hx, lx, x);
uhx = hx & 0x7fffffff;
int exponent = uhx >> (MANT_DIG - 1 - 32);
if (exponent >= BIAS + MANT_DIG - 1)
{
/* Integer, infinity or NaN. */
if (exponent == MAX_EXP)
/* Infinity or NaN; quiet signaling NaNs. */
return x + x;
else
return x;
}
else if (exponent >= BIAS + MANT_DIG - 32)
{
/* Not necessarily an integer; integer bit is in low word.
Locate the bits with exponents 0 and -1. */
int int_pos = (BIAS + MANT_DIG - 1) - exponent;
int half_pos = int_pos - 1;
uint32_t half_bit = 1U << half_pos;
uint32_t int_bit = 1U << int_pos;
if ((lx & (int_bit | (half_bit - 1))) != 0)
{
/* Carry into the exponent works correctly. No need to test
whether HALF_BIT is set. */
lx += half_bit;
hx += lx < half_bit;
}
lx &= ~(int_bit - 1);
}
else if (exponent == BIAS + MANT_DIG - 33)
{
/* Not necessarily an integer; integer bit is bottom of high
word, half bit is top of low word. */
if (((hx & 1) | (lx & 0x7fffffff)) != 0)
{
lx += 0x80000000;
hx += lx < 0x80000000;
}
lx = 0;
}
else if (exponent >= BIAS)
{
/* At least 1; not necessarily an integer, integer bit and half
bit are in the high word. Locate the bits with exponents 0
and -1 (when the unbiased exponent is 0, the bit with
exponent 0 is implicit, but as the bias is odd it is OK to
take it from the low bit of the exponent). */
int int_pos = (BIAS + MANT_DIG - 33) - exponent;
int half_pos = int_pos - 1;
uint32_t half_bit = 1U << half_pos;
uint32_t int_bit = 1U << int_pos;
if (((hx & (int_bit | (half_bit - 1))) | lx) != 0)
hx += half_bit;
hx &= ~(int_bit - 1);
lx = 0;
}
else if (exponent == BIAS - 1 && (uhx > 0x3fe00000 || lx != 0))
{
/* Interval (0.5, 1). */
hx = (hx & 0x80000000) | 0x3ff00000;
lx = 0;
}
else
{
/* Rounds to 0. */
hx &= 0x80000000;
lx = 0;
}
INSERT_WORDS (x, hx, lx);
return x;
}
hidden_def (__roundeven)
libm_alias_double (__roundeven, roundeven)
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