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/* Round to integer type. Common helper functions.
Copyright (C) 2016-2025 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 <errno.h>
#include <fenv.h>
#include <float.h>
#include <math.h>
#include <math-barriers.h>
#include <stdbool.h>
#include <stdint.h>
/* The including file should have defined UNSIGNED to 0 (signed return
type) or 1 (unsigned return type), INEXACT to 0 (no inexact
exceptions) or 1 (raise inexact exceptions) and RET_TYPE to the
return type (intmax_t or uintmax_t). */
/* Return the maximum unbiased exponent for an argument (negative if
NEGATIVE is set) that might be in range for a call to a fromfp
function with width WIDTH (greater than 0, and not exceeding that
of intmax_t). The truncated argument may still be out of range in
the case of negative arguments, and if not out of range it may
become out of range as a result of rounding. */
static int
fromfp_max_exponent (bool negative, int width)
{
if (UNSIGNED)
return negative ? -1 : width - 1;
else
return negative ? width - 1 : width - 2;
}
/* Return the result of rounding an integer value X (passed as the
absolute value; NEGATIVE is true if the value is negative), where
HALF_BIT is true if the bit with value 0.5 is set and MORE_BITS is
true if any lower bits are set, in the rounding direction
ROUND. */
static uintmax_t
fromfp_round (bool negative, uintmax_t x, bool half_bit, bool more_bits,
int round)
{
switch (round)
{
case FP_INT_UPWARD:
return x + (!negative && (half_bit || more_bits));
case FP_INT_DOWNWARD:
return x + (negative && (half_bit || more_bits));
case FP_INT_TOWARDZERO:
default:
/* Unknown rounding directions are defined to mean unspecified
rounding; treat this as truncation. */
return x;
case FP_INT_TONEARESTFROMZERO:
return x + half_bit;
case FP_INT_TONEAREST:
return x + (half_bit && ((x & 1) || more_bits));
}
}
/* Integer rounding, of a value whose exponent EXPONENT did not exceed
the maximum exponent MAX_EXPONENT and so did not necessarily
overflow, has produced X (possibly wrapping to 0); the sign is
negative if NEGATIVE is true. Return whether this overflowed the
allowed width. */
static bool
fromfp_overflowed (bool negative, uintmax_t x, int exponent, int max_exponent)
{
if (UNSIGNED)
{
if (negative)
return x != 0;
else if (max_exponent == INTMAX_WIDTH - 1)
return exponent == INTMAX_WIDTH - 1 && x == 0;
else
return x == (1ULL << (max_exponent + 1));
}
else
{
if (negative)
return exponent == max_exponent && x != (1ULL << max_exponent);
else
return x == (1ULL << (max_exponent + 1));
}
}
/* Handle a domain error for a call to a fromfp function with an
argument which is negative if NEGATIVE is set, and specified width
(not exceeding that of intmax_t) WIDTH. The return value is
unspecified (with it being unclear if the result needs to fit
within WIDTH bits in this case); we choose to saturate to the given
number of bits (treating NaNs like any other value). */
static RET_TYPE
fromfp_domain_error (bool negative, unsigned int width)
{
feraiseexcept (FE_INVALID);
__set_errno (EDOM);
/* The return value is unspecified; we choose to saturate to the
given number of bits (treating NaNs like any other value). */
if (UNSIGNED)
{
if (negative)
return 0;
else if (width == INTMAX_WIDTH)
return -1;
else
return (1ULL << width) - 1;
}
else
{
if (width == 0)
return 0;
else if (negative)
return -(1ULL << (width - 1));
else
return (1ULL << (width - 1)) - 1;
}
}
/* Given X, the absolute value of a floating-point number (negative if
NEGATIVE is set) truncated towards zero, where HALF_BIT is true if
the bit with value 0.5 is set and MORE_BITS is true if any lower
bits are set, round it in the rounding direction ROUND, handle
errors and exceptions and return the appropriate return value for a
fromfp function. X originally had floating-point exponent
EXPONENT, which does not exceed MAX_EXPONENT, the return value from
fromfp_max_exponent with width WIDTH. */
static RET_TYPE
fromfp_round_and_return (bool negative, uintmax_t x, bool half_bit,
bool more_bits, int round, int exponent,
int max_exponent, unsigned int width)
{
uintmax_t uret = fromfp_round (negative, x, half_bit, more_bits, round);
if (fromfp_overflowed (negative, uret, exponent, max_exponent))
return fromfp_domain_error (negative, width);
if (INEXACT && (half_bit || more_bits))
{
/* There is no need for this to use the specific floating-point
type for which this header is included, and there is no need
for this header to know that type at all, so just use float
here. */
float force_inexact = 1.0f + FLT_MIN;
math_force_eval (force_inexact);
}
if (UNSIGNED)
/* A negative argument not rounding to zero will already have
produced a domain error. */
return uret;
else
return negative ? -uret : uret;
}
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