source: mainline/uspace/lib/math/generic/nearbyint.c

/*
 * Copyright (c) 2018 CZ.NIC, z.s.p.o.
 * All rights reserved.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions
 * are met:
 *
 * - Redistributions of source code must retain the above copyright
 *   notice, this list of conditions and the following disclaimer.
 * - 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.
 * - The name of the author may not be used to endorse or promote products
 *   derived from this software without specific prior written permission.
 *
 * 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.
 */

/** @addtogroup libmath
 * @{
 */
/** @file
 */

#include <assert.h>
#include <math.h>
#include <fenv.h>
#include <float.h>
#include <stdbool.h>
#include <stdint.h>

static float _roundf_even(float val)
{
        assert(!signbit(val));

        /* Get some special cases out of the way first. */

        if (islessequal(val, 0.5f))
                return 0.0f;

        if (isless(val, 1.5f))
                return 1.0f;

        if (islessequal(val, 2.5f))
                return 2.0f;

        const int exp_bias = FLT_MAX_EXP - 1;
        const int mant_bits = FLT_MANT_DIG - 1;
        const uint32_t mant_mask = (UINT32_C(1) << mant_bits) - 1;

        union {
                float f;
                uint32_t i;
        } u = { .f = val };

        int exp = (u.i >> mant_bits) - exp_bias;
        assert(exp > 0);

        /* Mantissa has no fractional places. */
        if (exp >= mant_bits)
                return val;

        /* Check whether we are rounding up or down. */
        uint32_t first = (UINT32_C(1) << (mant_bits - exp));
        uint32_t midpoint = first >> 1;
        uint32_t frac = u.i & (mant_mask >> exp);

        bool up;
        if (frac == midpoint) {
                up = (u.i & first);
        } else {
                up = (frac > midpoint);
        }

        u.i &= ~(mant_mask >> exp);
        if (up) {
                u.i += first;
        }
        return copysignf(u.f, val);
}

static float _round_even(float val)
{
        assert(!signbit(val));

        /* Get some special cases out of the way first. */

        if (islessequal(val, 0.5))
                return 0.0;

        if (isless(val, 1.5))
                return 1.0;

        if (islessequal(val, 2.5))
                return 2.0;

        const int exp_bias = DBL_MAX_EXP - 1;
        const int mant_bits = DBL_MANT_DIG - 1;
        const uint64_t mant_mask = (UINT64_C(1) << mant_bits) - 1;

        union {
                double f;
                uint64_t i;
        } u = { .f = val };

        int exp = (u.i >> mant_bits) - exp_bias;
        assert(exp > 0);

        /* Mantissa has no fractional places. */
        if (exp >= mant_bits)
                return val;

        /* Check whether we are rounding up or down. */
        uint64_t first = (UINT64_C(1) << (mant_bits - exp));
        uint64_t midpoint = first >> 1;
        uint64_t frac = u.i & (mant_mask >> exp);

        bool up;
        if (frac == midpoint) {
                up = (u.i & first);
        } else {
                up = (frac > midpoint);
        }

        u.i &= ~(mant_mask >> exp);
        if (up) {
                u.i += first;
        }
        return copysignf(u.f, val);
}

/**
 * Rounds its argument to the nearest integer value in floating-point format,
 * using the current rounding direction and without raising the inexact
 * floating-point exception.
 */
float nearbyintf(float val)
{
        switch (fegetround()) {
        case FE_DOWNWARD:
                return floorf(val);
        case FE_UPWARD:
                return ceilf(val);
        case FE_TOWARDZERO:
                return truncf(val);
        case FE_TONEAREST:
                return copysignf(_roundf_even(fabsf(val)), val);
        }

        assert(false);
}

/**
 * Rounds its argument to the nearest integer value in floating-point format,
 * using the current rounding direction and without raising the inexact
 * floating-point exception.
 */
double nearbyint(double val)
{
        switch (fegetround()) {
        case FE_DOWNWARD:
                return floor(val);
        case FE_UPWARD:
                return ceil(val);
        case FE_TOWARDZERO:
                return trunc(val);
        case FE_TONEAREST:
                return copysign(_round_even(fabs(val)), val);
        }

        assert(false);
}

/** @}
 */