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/*
* Copyright (C) 2005 Josef Cejka
* 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<sftypes.h>
#include<common.h>
/* Table for fast leading zeroes counting */
char zeroTable[256] = {
8, 7, 7, 6, 6, 6, 6, 4, 4, 4, 4, 4, 4, 4, 4, \
3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, \
2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, \
2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, \
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, \
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, \
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, \
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, \
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
};
/** Take fraction shifted by 10 bits to left, round it, normalize it and detect exceptions
* @param cexp exponent with bias
* @param cfrac fraction shifted 10 places left with added hidden bit
* @param sign
* @return valied float64
*/
float64 finishFloat64(int32_t cexp, uint64_t cfrac, char sign)
{
float64 result;
result.parts.sign = sign;
/* find first nonzero digit and shift result and detect possibly underflow */
while ((cexp > 0) && (cfrac) && (!(cfrac & (FLOAT64_HIDDEN_BIT_MASK << (64 - FLOAT64_FRACTION_SIZE - 1 ) )))) {
cexp--;
cfrac <<= 1;
/* TODO: fix underflow */
};
if ((cexp < 0) || ( cexp == 0 && (!(cfrac & (FLOAT64_HIDDEN_BIT_MASK << (64 - FLOAT64_FRACTION_SIZE - 1)))))) {
/* FIXME: underflow */
result.parts.exp = 0;
if ((cexp + FLOAT64_FRACTION_SIZE + 1) < 0) { /* +1 is place for rounding */
result.parts.fraction = 0;
return result;
}
while (cexp < 0) {
cexp++;
cfrac >>= 1;
}
cfrac += (0x1 << (64 - FLOAT64_FRACTION_SIZE - 3));
if (!(cfrac & (FLOAT64_HIDDEN_BIT_MASK << (64 - FLOAT64_FRACTION_SIZE - 1)))) {
result.parts.fraction = ((cfrac >>(64 - FLOAT64_FRACTION_SIZE - 2) ) & (~FLOAT64_HIDDEN_BIT_MASK));
return result;
}
} else {
cfrac += (0x1 << (64 - FLOAT64_FRACTION_SIZE - 3));
}
++cexp;
if (cfrac & (FLOAT64_HIDDEN_BIT_MASK << (64 - FLOAT64_FRACTION_SIZE - 1 ))) {
++cexp;
cfrac >>= 1;
}
/* check overflow */
if (cexp >= FLOAT64_MAX_EXPONENT ) {
/* FIXME: overflow, return infinity */
result.parts.exp = FLOAT64_MAX_EXPONENT;
result.parts.fraction = 0;
return result;
}
result.parts.exp = (uint32_t)cexp;
result.parts.fraction = ((cfrac >>(64 - FLOAT64_FRACTION_SIZE - 2 ) ) & (~FLOAT64_HIDDEN_BIT_MASK));
return result;
}
/** Counts leading zeroes in 64bit unsigned integer
* @param i
*/
int countZeroes64(uint64_t i)
{
int j;
for (j =0; j < 64; j += 8) {
if ( i & (0xFFll << (56 - j))) {
return (j + countZeroes8(i >> (56 - j)));
}
}
return 64;
}
/** Counts leading zeroes in 32bit unsigned integer
* @param i
*/
int countZeroes32(uint32_t i)
{
int j;
for (j =0; j < 32; j += 8) {
if ( i & (0xFF << (24 - j))) {
return (j + countZeroes8(i >> (24 - j)));
}
}
return 32;
}
/** Counts leading zeroes in byte
* @param i
*/
int countZeroes8(uint8_t i)
{
return zeroTable[i];
}
/** Round and normalize number expressed by exponent and fraction with first bit (equal to hidden bit) at 30. bit
* @param exp exponent
* @param fraction part with hidden bit shifted to 30. bit
*/
void roundFloat32(int32_t *exp, uint32_t *fraction)
{
/* rounding - if first bit after fraction is set then round up */
(*fraction) += (0x1 << 6);
if ((*fraction) & (FLOAT32_HIDDEN_BIT_MASK << 8)) {
/* rounding overflow */
++(*exp);
(*fraction) >>= 1;
};
if (((*exp) >= FLOAT32_MAX_EXPONENT ) || ((*exp) < 0)) {
/* overflow - set infinity as result */
(*exp) = FLOAT32_MAX_EXPONENT;
(*fraction) = 0;
return;
}
return;
}
/** Round and normalize number expressed by exponent and fraction with first bit (equal to hidden bit) at 62. bit
* @param exp exponent
* @param fraction part with hidden bit shifted to 62. bit
*/
void roundFloat64(int32_t *exp, uint64_t *fraction)
{
/* rounding - if first bit after fraction is set then round up */
(*fraction) += (0x1 << 9);
if ((*fraction) & (FLOAT64_HIDDEN_BIT_MASK << 11)) {
/* rounding overflow */
++(*exp);
(*fraction) >>= 1;
};
if (((*exp) >= FLOAT64_MAX_EXPONENT ) || ((*exp) < 0)) {
/* overflow - set infinity as result */
(*exp) = FLOAT64_MAX_EXPONENT;
(*fraction) = 0;
return;
}
return;
}