/* * 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; }