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/*
** Copyright (C) 2018 Martin Brain
**
** See the file LICENSE for licensing information.
*/
/*
** fma.h
**
** Martin Brain
** martin.brain@cs.ox.ac.uk
** 20/05/15
**
** Fused multiply and add :
** fma(R,A,B,C) = round(R, A * B + C)
**
*/
#include "symfpu/core/unpackedFloat.h"
#include "symfpu/core/ite.h"
#include "symfpu/core/rounder.h"
#include "symfpu/core/multiply.h"
#include "symfpu/core/convert.h"
#include "symfpu/core/add.h"
#ifndef SYMFPU_FMA
#define SYMFPU_FMA
namespace symfpu {
template <class t>
unpackedFloat<t> fma (const typename t::fpt &format,
const typename t::rm &roundingMode,
const unpackedFloat<t> &leftMultiply,
const unpackedFloat<t> &rightMultiply,
const unpackedFloat<t> &addArgument) {
// typedef typename t::bwt bwt;
typedef typename t::prop prop;
//typedef typename t::ubv ubv;
//typedef typename t::sbv sbv;
typedef typename t::fpt fpt;
PRECONDITION(leftMultiply.valid(format));
PRECONDITION(rightMultiply.valid(format));
PRECONDITION(addArgument.valid(format));
/* First multiply */
unpackedFloat<t> arithmeticMultiplyResult(arithmeticMultiply(format, leftMultiply, rightMultiply));
fpt extendedFormat(format.exponentWidth() + 1, format.significandWidth() * 2);
INVARIANT(arithmeticMultiplyResult.valid(extendedFormat));
/* Then add */
// Rounding mode doesn't matter as this is a strict extension
unpackedFloat<t> extendedAddArgument(convertFloatToFloat(format, extendedFormat, t::RTZ(), addArgument));
prop knownInCorrectOrder(false);
exponentCompareInfo<t> ec(addExponentCompare<t>(arithmeticMultiplyResult.getExponent().getWidth() + 1,
arithmeticMultiplyResult.getSignificand().getWidth(),
arithmeticMultiplyResult.getExponent(),
extendedAddArgument.getExponent(),
knownInCorrectOrder));
unpackedFloat<t> additionResult(arithmeticAdd(extendedFormat, roundingMode, arithmeticMultiplyResult, extendedAddArgument, prop(true), knownInCorrectOrder, ec).uf);
// Custom rounder flags are ignored as they are not applicable in this case
fpt evenMoreExtendedFormat(extendedFormat.exponentWidth() + 1, extendedFormat.significandWidth() + 2);
INVARIANT(additionResult.valid(evenMoreExtendedFormat));
/* Then round */
unpackedFloat<t> roundedResult(rounder(format, roundingMode, additionResult));
INVARIANT(roundedResult.valid(format));
// This result is correct as long as neither of multiplyResult or extendedAddArgument is
// 0, Inf or NaN. Note that roundedResult may be zero from cancelation or underflow
// or infinity due to rounding. If it is, it has the correct sign.
/* Finally, the special cases */
// One disadvantage to having a flag for zero and default exponents and significands for zero
// that are not (min, 0) is that the x + (+/-)0 case has to be handled by the addition special cases.
// This means that you need the value of x, rounded to the correct format.
// arithmeticMultiplyResult is in extended format, thus we have to use a second rounder just for this case.
// It is not zero, inf or NaN so it only matters when addArgument is zero when it would be returned.
unpackedFloat<t> roundedMultiplyResult(rounder(format, roundingMode, arithmeticMultiplyResult));
unpackedFloat<t> fullMultiplyResult(addMultiplySpecialCases(format, leftMultiply, rightMultiply, roundedMultiplyResult.getSign(), roundedMultiplyResult));
// We need the flags from the multiply special cases, determined on the arithemtic result,
// i.e. handling special values and not the underflow / overflow of the result.
// But we will use roundedMultiplyResult instead of the value so ...
unpackedFloat<t> dummyZero(unpackedFloat<t>::makeZero(format, prop(false)));
unpackedFloat<t> dummyValue(dummyZero.getSign(), dummyZero.getExponent(), dummyZero.getSignificand());
unpackedFloat<t> multiplyResultWithSpecialCases(addMultiplySpecialCases(format, leftMultiply, rightMultiply, arithmeticMultiplyResult.getSign(), dummyValue));
unpackedFloat<t> result(addAdditionSpecialCasesWithID(format,
roundingMode,
multiplyResultWithSpecialCases,
fullMultiplyResult, // for the identity case
addArgument,
roundedResult,
prop(true)));
POSTCONDITION(result.valid(format));
return result;
}
/*
* BUGS :
* 1. sign of zero different for exact 0 and underflow
* 2. large * -large + inf = inf not NaN
* 3. rounder decision bugs : one looks like an issue with too-eager overflow,
* one looks like a misplaced decision on highest subnormal exponent
*/
template <class t>
unpackedFloat<t> fmaBroken (const typename t::fpt &format,
const typename t::rm &roundingMode,
const unpackedFloat<t> &leftMultiply,
const unpackedFloat<t> &rightMultiply,
const unpackedFloat<t> &addArgument) {
// typedef typename t::bwt bwt;
typedef typename t::prop prop;
//typedef typename t::ubv ubv;
//typedef typename t::sbv sbv;
typedef typename t::fpt fpt;
PRECONDITION(leftMultiply.valid(format));
PRECONDITION(rightMultiply.valid(format));
PRECONDITION(addArgument.valid(format));
unpackedFloat<t> multiplyResult(arithmeticMultiply(format, leftMultiply, rightMultiply));
fpt extendedFormat(format.exponentWidth() + 1, format.significandWidth() * 2);
INVARIANT(multiplyResult.valid(extendedFormat));
// Rounding mode doesn't matter as this is a strict extension
unpackedFloat<t> extendedAddArgument(convertFloatToFloat(format, extendedFormat, t::RTZ(), addArgument));
unpackedFloat<t> additionResult(arithmeticAdd(extendedFormat, roundingMode, multiplyResult, extendedAddArgument, prop(true), prop(false)).uf);
// Custom rounder flags are ignored as they are not applicable in this case
unpackedFloat<t> roundedResult(rounder(format, roundingMode, additionResult));
// Note that multiplyResult.getSign() != roundedResult.getSign() in rare cases
// the multiply special cases use the sign for zeros and infinities, thus the sign of the
// result of the multiplication is needed (i.e. the xor of the sign of left and right multiply)
// (-small, +inf, large) should trigger this as the desired result is -inf
// but roundedResult.getSign() is positive.
unpackedFloat<t> roundedResultWithMultiplyCases(addMultiplySpecialCases(format,
leftMultiply,
rightMultiply,
multiplyResult.getSign(),
roundedResult));
// One disadvantage to having a flag for zero and default exponents and significands for zero
// that are not (min, 0) is that the x + 0 case has to be handled by the addition special cases.
// This means that you need the value of x, rounded to the correct format.
// multiplyResult is in extended format, thus we have to use a second rounder just for this case.
// It is not zero, inf or NaN so it only matters when addArgument is zero when it would be returned.
unpackedFloat<t> roundedMultiplyResult(rounder(format, roundingMode, multiplyResult));
// Optimisation : Try ITE before rounding so that only one rounder is needed
// To make matters more awkward, we also need to apply the multiplicative special cases so that
// (x*0) + y is correctly handled by the addition special cases. Without applying the
// multiplicative ones, (x*0) would not be correctly flagged as 0.
unpackedFloat<t> roundedMultiplyResultWithMultiplyCases(addMultiplySpecialCases(format,
leftMultiply,
rightMultiply,
multiplyResult.getSign(),
roundedMultiplyResult));
// Optimisation : consolidate the special cases and verify against this
unpackedFloat<t> result(addAdditionSpecialCases(format,
roundingMode,
roundedMultiplyResultWithMultiplyCases,
addArgument,
roundedResultWithMultiplyCases,
prop(true)));
POSTCONDITION(result.valid(format));
return result;
}
}
#endif
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