/*
* Copyright (c) 2012 Adam Hraska
* 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.
*/
#include <ieee_double.h>
#include <assert.h>
/** Returns an easily processible description of the double val.
*/
ieee_double_t extract_ieee_double(double val)
{
const uint64_t significand_mask = 0xfffffffffffffULL;
const uint64_t exponent_mask = 0x7ff0000000000000ULL;
const int exponent_shift = 64 - 11 - 1;
const uint64_t sign_mask = 0x8000000000000000ULL;
const int special_exponent = 0x7ff;
const int denormal_exponent = 0;
const uint64_t hidden_bit = (1ULL << 52);
const int exponent_bias = 1075;
static_assert(sizeof(val) == sizeof(uint64_t), "");
union {
uint64_t num;
double val;
} bits;
bits.val = val;
/*
* Extract the binary ieee representation of the double.
* Relies on integers having the same endianness as doubles.
*/
uint64_t num = bits.num;
ieee_double_t ret;
/* Determine the sign. */
ret.is_negative = ((num & sign_mask) != 0);
/* Extract the exponent. */
int raw_exponent = (num & exponent_mask) >> exponent_shift;
/* The extracted raw significand may not contain the hidden bit */
uint64_t raw_significand = num & significand_mask;
ret.is_special = (raw_exponent == special_exponent);
/* NaN or infinity */
if (ret.is_special) {
ret.is_infinity = (raw_significand == 0);
ret.is_nan = (raw_significand != 0);
/* These are not valid for special numbers but init them anyway. */
ret.is_denormal = true;
ret.is_accuracy_step = false;
ret.pos_val.significand = 0;
ret.pos_val.exponent = 0;
} else {
ret.is_infinity = false;
ret.is_nan = false;
ret.is_denormal = (raw_exponent == denormal_exponent);
/* Denormal or zero. */
if (ret.is_denormal) {
ret.pos_val.significand = raw_significand;
ret.pos_val.exponent = 1 - exponent_bias;
ret.is_accuracy_step = false;
} else {
ret.pos_val.significand = raw_significand + hidden_bit;
ret.pos_val.exponent = raw_exponent - exponent_bias;
/*
* The predecessor is closer to val than the successor
* if val is a normal value of the form 2^k (hence
* raw_significand == 0) with the only exception being
* the smallest normal (raw_exponent == 1). The smallest
* normal's predecessor is the largest denormal and denormals
* do not get an extra bit of precision because their exponent
* stays the same (ie it does not decrease from k to k-1).
*/
ret.is_accuracy_step = (raw_significand == 0) && (raw_exponent != 1);
}
}
return ret;
}