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/* |
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** Copyright (C) 2018 Martin Brain |
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** |
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** See the file LICENSE for licensing information. |
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*/ |
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/* |
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** multiply.h |
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** |
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** Martin Brain |
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** martin.brain@cs.ox.ac.uk |
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** 25/08/14 |
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** |
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** Multiplication of arbitrary precision floats |
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** |
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*/ |
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#include "symfpu/core/unpackedFloat.h" |
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#include "symfpu/core/ite.h" |
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#include "symfpu/core/rounder.h" |
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#include "symfpu/core/operations.h" |
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#ifndef SYMFPU_MULTIPLY |
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#define SYMFPU_MULTIPLY |
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namespace symfpu { |
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// sign == multiplyResult.getSign() normally but not for FMA, thus an argument is needed |
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template <class t> |
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unpackedFloat<t> addMultiplySpecialCases (const typename t::fpt &format, |
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const unpackedFloat<t> &left, |
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const unpackedFloat<t> &right, |
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const typename t::prop &sign, |
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const unpackedFloat<t> &multiplyResult) { |
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typedef typename t::prop prop; |
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prop eitherArgumentNan(left.getNaN() || right.getNaN()); |
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prop generateNan((left.getInf() && right.getZero()) || |
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(left.getZero() && right.getInf())); |
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prop isNan(eitherArgumentNan || generateNan); |
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prop isInf(left.getInf() || right.getInf()); |
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prop isZero(left.getZero() || right.getZero()); |
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return ITE(isNan, |
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unpackedFloat<t>::makeNaN(format), |
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ITE(isInf, |
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unpackedFloat<t>::makeInf(format, sign), |
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ITE(isZero, |
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unpackedFloat<t>::makeZero(format, sign), |
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multiplyResult))); |
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} |
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template <class t> |
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unpackedFloat<t> arithmeticMultiply (const typename t::fpt &format, |
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const unpackedFloat<t> &left, |
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const unpackedFloat<t> &right) { |
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typedef typename t::bwt bwt; |
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typedef typename t::prop prop; |
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typedef typename t::ubv ubv; |
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typedef typename t::sbv sbv; |
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typedef typename t::fpt fpt; |
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PRECONDITION(left.valid(format)); |
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PRECONDITION(right.valid(format)); |
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// Compute sign |
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prop multiplySign(left.getSign() ^ right.getSign()); |
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// Multiply the significands |
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ubv significandProduct(expandingMultiply<t>(left.getSignificand(), right.getSignificand())); |
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// Optimisation : low bits are not needed apart from the guard and sticky bits |
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// Optimisation : top bits accurately predict whether re-alignment is needed |
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bwt spWidth(significandProduct.getWidth()); |
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ubv topBit(significandProduct.extract(spWidth - 1, spWidth - 1)); |
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ubv nextBit(significandProduct.extract(spWidth - 2, spWidth - 2)); |
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// Alignment of inputs means at least one of the two MSB is 1 |
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// i.e. [1,2) * [1,2) = [1,4) |
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// topBitSet is the likely case |
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prop topBitSet(topBit.isAllOnes()); |
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INVARIANT(topBitSet || nextBit.isAllOnes()); |
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probabilityAnnotation<t>(topBitSet, LIKELY); |
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// Re-align |
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ubv alignedSignificand(conditionalLeftShiftOne<t>(!topBitSet, significandProduct)); // Will not loose information |
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// Add up exponents |
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#if 0 |
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sbv exponentSum(expandingAdd<t>(left.getExponent(),right.getExponent())); |
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sbv min(unpackedFloat<t>::minSubnormalExponent(format)); |
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sbv max(unpackedFloat<t>::maxNormalExponent(format)); |
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INVARIANT(expandingAdd<t>(min,min) <= exponentSum); |
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INVARIANT(exponentSum <= expandingAdd<t>(max, max)); |
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// Optimisation : use the if-then-lazy-else to avoid multiplying for underflow and overflow |
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// subnormal * subnormal does not need to be evaluated |
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// may be best done in the rounder along with underflow |
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#endif |
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sbv alignedExponent(expandingAddWithCarryIn<t>(left.getExponent(),right.getExponent(), topBitSet)); |
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// Put back together |
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fpt extendedFormat(format.exponentWidth() + 1, format.significandWidth() * 2); |
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unpackedFloat<t> multiplyResult(extendedFormat, multiplySign, alignedExponent, alignedSignificand); |
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POSTCONDITION(multiplyResult.valid(extendedFormat)); |
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return multiplyResult; |
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} |
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// Put it all together... |
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template <class t> |
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unpackedFloat<t> multiply (const typename t::fpt &format, |
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const typename t::rm &roundingMode, |
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const unpackedFloat<t> &left, |
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const unpackedFloat<t> &right) { |
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//typedef typename t::bwt bwt; |
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//typedef typename t::prop prop; |
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//typedef typename t::ubv ubv; |
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//typedef typename t::sbv sbv; |
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PRECONDITION(left.valid(format)); |
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PRECONDITION(right.valid(format)); |
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unpackedFloat<t> multiplyResult(arithmeticMultiply(format, left, right)); |
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unpackedFloat<t> roundedMultiplyResult(rounder(format, roundingMode, multiplyResult)); |
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unpackedFloat<t> result(addMultiplySpecialCases(format, left, right, roundedMultiplyResult.getSign(), roundedMultiplyResult)); |
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POSTCONDITION(result.valid(format)); |
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return result; |
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} |
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} |
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#endif |
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