0,0 → 1,287 |
/* |
* 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<mul.h> |
#include<comparison.h> |
#include<common.h> |
|
/** Multiply two 32 bit float numbers |
* |
*/ |
float32 mulFloat32(float32 a, float32 b) |
{ |
float32 result; |
uint64_t frac1, frac2; |
int32_t exp; |
|
result.parts.sign = a.parts.sign ^ b.parts.sign; |
|
if (isFloat32NaN(a) || isFloat32NaN(b) ) { |
/* TODO: fix SigNaNs */ |
if (isFloat32SigNaN(a)) { |
result.parts.fraction = a.parts.fraction; |
result.parts.exp = a.parts.exp; |
return result; |
}; |
if (isFloat32SigNaN(b)) { /* TODO: fix SigNaN */ |
result.parts.fraction = b.parts.fraction; |
result.parts.exp = b.parts.exp; |
return result; |
}; |
/* set NaN as result */ |
result.binary = FLOAT32_NAN; |
return result; |
}; |
|
if (isFloat32Infinity(a)) { |
if (isFloat32Zero(b)) { |
/* FIXME: zero * infinity */ |
result.binary = FLOAT32_NAN; |
return result; |
} |
result.parts.fraction = a.parts.fraction; |
result.parts.exp = a.parts.exp; |
return result; |
} |
|
if (isFloat32Infinity(b)) { |
if (isFloat32Zero(a)) { |
/* FIXME: zero * infinity */ |
result.binary = FLOAT32_NAN; |
return result; |
} |
result.parts.fraction = b.parts.fraction; |
result.parts.exp = b.parts.exp; |
return result; |
} |
|
/* exp is signed so we can easy detect underflow */ |
exp = a.parts.exp + b.parts.exp; |
exp -= FLOAT32_BIAS; |
|
if (exp >= FLOAT32_MAX_EXPONENT) { |
/* FIXME: overflow */ |
/* set infinity as result */ |
result.binary = FLOAT32_INF; |
result.parts.sign = a.parts.sign ^ b.parts.sign; |
return result; |
}; |
|
if (exp < 0) { |
/* FIXME: underflow */ |
/* return signed zero */ |
result.parts.fraction = 0x0; |
result.parts.exp = 0x0; |
return result; |
}; |
|
frac1 = a.parts.fraction; |
if (a.parts.exp > 0) { |
frac1 |= FLOAT32_HIDDEN_BIT_MASK; |
} else { |
++exp; |
}; |
|
frac2 = b.parts.fraction; |
|
if (b.parts.exp > 0) { |
frac2 |= FLOAT32_HIDDEN_BIT_MASK; |
} else { |
++exp; |
}; |
|
frac1 <<= 1; /* one bit space for rounding */ |
|
frac1 = frac1 * frac2; |
/* round and return */ |
|
while ((exp < FLOAT32_MAX_EXPONENT) && (frac1 >= ( 1 << (FLOAT32_FRACTION_SIZE + 2)))) { |
/* 23 bits of fraction + one more for hidden bit (all shifted 1 bit left)*/ |
++exp; |
frac1 >>= 1; |
}; |
|
/* rounding */ |
/* ++frac1; FIXME: not works - without it is ok */ |
frac1 >>= 1; /* shift off rounding space */ |
|
if ((exp < FLOAT32_MAX_EXPONENT) && (frac1 >= (1 << (FLOAT32_FRACTION_SIZE + 1)))) { |
++exp; |
frac1 >>= 1; |
}; |
|
if (exp >= FLOAT32_MAX_EXPONENT ) { |
/* TODO: fix overflow */ |
/* return infinity*/ |
result.parts.exp = FLOAT32_MAX_EXPONENT; |
result.parts.fraction = 0x0; |
return result; |
} |
|
exp -= FLOAT32_FRACTION_SIZE; |
|
if (exp <= FLOAT32_FRACTION_SIZE) { |
/* denormalized number */ |
frac1 >>= 1; /* denormalize */ |
while ((frac1 > 0) && (exp < 0)) { |
frac1 >>= 1; |
++exp; |
}; |
if (frac1 == 0) { |
/* FIXME : underflow */ |
result.parts.exp = 0; |
result.parts.fraction = 0; |
return result; |
}; |
}; |
result.parts.exp = exp; |
result.parts.fraction = frac1 & ( (1 << FLOAT32_FRACTION_SIZE) - 1); |
|
return result; |
|
} |
|
/** Multiply two 64 bit float numbers |
* |
*/ |
float64 mulFloat64(float64 a, float64 b) |
{ |
float64 result; |
uint64_t frac1, frac2; |
int32_t exp; |
|
result.parts.sign = a.parts.sign ^ b.parts.sign; |
|
if (isFloat64NaN(a) || isFloat64NaN(b) ) { |
/* TODO: fix SigNaNs */ |
if (isFloat64SigNaN(a)) { |
result.parts.fraction = a.parts.fraction; |
result.parts.exp = a.parts.exp; |
return result; |
}; |
if (isFloat64SigNaN(b)) { /* TODO: fix SigNaN */ |
result.parts.fraction = b.parts.fraction; |
result.parts.exp = b.parts.exp; |
return result; |
}; |
/* set NaN as result */ |
result.binary = FLOAT64_NAN; |
return result; |
}; |
|
if (isFloat64Infinity(a)) { |
if (isFloat64Zero(b)) { |
/* FIXME: zero * infinity */ |
result.binary = FLOAT64_NAN; |
return result; |
} |
result.parts.fraction = a.parts.fraction; |
result.parts.exp = a.parts.exp; |
return result; |
} |
|
if (isFloat64Infinity(b)) { |
if (isFloat64Zero(a)) { |
/* FIXME: zero * infinity */ |
result.binary = FLOAT64_NAN; |
return result; |
} |
result.parts.fraction = b.parts.fraction; |
result.parts.exp = b.parts.exp; |
return result; |
} |
|
/* exp is signed so we can easy detect underflow */ |
exp = a.parts.exp + b.parts.exp - FLOAT64_BIAS; |
|
frac1 = a.parts.fraction; |
|
if (a.parts.exp > 0) { |
frac1 |= FLOAT64_HIDDEN_BIT_MASK; |
} else { |
++exp; |
}; |
|
frac2 = b.parts.fraction; |
|
if (b.parts.exp > 0) { |
frac2 |= FLOAT64_HIDDEN_BIT_MASK; |
} else { |
++exp; |
}; |
|
frac1 <<= (64 - FLOAT64_FRACTION_SIZE - 1); |
frac2 <<= (64 - FLOAT64_FRACTION_SIZE - 2); |
|
mul64integers(frac1, frac2, &frac1, &frac2); |
|
frac2 |= (frac1 != 0); |
if (frac2 & (0x1ll << 62)) { |
frac2 <<= 1; |
exp--; |
} |
|
result = finishFloat64(exp, frac2, result.parts.sign); |
return result; |
} |
|
/** Multiply two 64 bit numbers and return result in two parts |
* @param a first operand |
* @param b second operand |
* @param lo lower part from result |
* @param hi higher part of result |
*/ |
void mul64integers(uint64_t a,uint64_t b, uint64_t *lo, uint64_t *hi) |
{ |
uint64_t low, high, middle1, middle2; |
uint32_t alow, blow; |
|
alow = a & 0xFFFFFFFF; |
blow = b & 0xFFFFFFFF; |
|
a >>= 32; |
b >>= 32; |
|
low = ((uint64_t)alow) * blow; |
middle1 = a * blow; |
middle2 = alow * b; |
high = a * b; |
|
middle1 += middle2; |
high += (((uint64_t)(middle1 < middle2)) << 32) + (middle1 >> 32); |
middle1 <<= 32; |
low += middle1; |
high += (low < middle1); |
*lo = low; |
*hi = high; |
|
return; |
} |
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