FPge_expr::FPge_expr(Target* _target, int wE, int wF) :
Operator(_target) {
ostringstream name;
name<<"FPge_expr_" <<wE<<"_"<<wF;
setName(name.str());
setCopyrightString("Fabrizio Ferrandi (2011-2017)");
/* Set up the IO signals */
addFPInput ("X", wE,wF);
addFPInput ("Y", wE,wF);
addOutput ("R", 1);
/* VHDL code description */
manageCriticalPath(_target->localWireDelay() + _target->lutDelay());
vhdl << tab << declare("nY",wE+wF+3) << " <= Y"<< range(wE+wF+2,wE+wF+1) << " & not(Y"<< of(wE+wF) << ") & Y" << range(wE+wF-1,0) << ";" << endl;
FPAdderSinglePath * value_difference = new FPAdderSinglePath(_target, wE, wF, wE, wF, wE, wF);
value_difference->changeName(getName()+"value_difference");
oplist.push_back(value_difference);
inPortMap (value_difference, "X", "X");
inPortMap (value_difference, "Y", "nY");
outPortMap (value_difference, "R","valueDiff");
vhdl << instance(value_difference, "value_difference");
syncCycleFromSignal("valueDiff");
setCriticalPath(value_difference->getOutputDelay("R"));
manageCriticalPath(_target->localWireDelay() + _target->lutDelay());
vhdl << tab << "R(0) <= '1' when (valueDiff" << of(wE+wF) << "='0' or (valueDiff" << range(wE+wF+2,wE+wF+1) << " = \"00\")) else '0';" << endl;
}
FPSumOf3Squares::FPSumOf3Squares(Target* target, int wE, int wF, int optimize)
: Operator(target), wE(wE), wF(wF)
{
setCopyrightString("F. de Dinechin, Bogdan Pasca (2011)");
srcFileName="FPSumOf3Squares";
ostringstream o;
o << "FPSumOf3Squares_" << wE << "_" << wF;
if(!optimize)
o << "_FP";
setName(o.str());
addFPInput("X", wE, wF);
addFPInput("Y", wE, wF);
addFPInput("Z", wE, wF);
addFPOutput("R", wE, wF, 2); // This 2 means: we will allow two possible inputs (faithful rounding)
if(!optimize) {
//////////////////////////////////////////////////////////////////:
// A version that assembles FP operators //
//////////////////////////////////////////////////////////////////:
FPMult* mult = new FPMult(target, wE, wF, wE, wF, wE, wF, 1);
oplist.push_back(mult);
FPAddSinglePath* add = new FPAddSinglePath(target, wE, wF, wE, wF, wE, wF);
oplist.push_back(add);
inPortMap (mult, "X", "X");
inPortMap (mult, "Y", "X");
outPortMap(mult, "R", "X2");
vhdl << instance(mult, "multx");
inPortMap (mult, "X", "Y");
inPortMap (mult, "Y", "Y");
outPortMap(mult, "R", "Y2");
vhdl << instance(mult, "multy");
inPortMap (mult, "X", "Z");
inPortMap (mult, "Y", "Z");
outPortMap(mult, "R", "Z2");
vhdl << instance(mult, "multz");
syncCycleFromSignal("Z2", false);
nextCycle();
inPortMap (add, "X", "X2");
inPortMap (add, "Y", "Y2");
outPortMap(add, "R", "X2PY2");
vhdl << instance(add, "add1");
syncCycleFromSignal("X2PY2", false);
nextCycle();
inPortMap (add, "X", "X2PY2");
inPortMap (add, "Y", "Z2");
outPortMap(add, "R", "X2PY2PZ2");
vhdl << instance(add, "add2");
syncCycleFromSignal("X2PY2PZ2", false);
setCriticalPath(add->getOutputDelay("R"));
vhdl << tab << "R <= X2PY2PZ2;"<<endl;
outDelayMap["R"]=getCriticalPath();
}
else { ////////////////// here comes the FloPoCo version //////////////////////////:
// Error analysis
// 3 ulps(wF+g) in the multiplier truncation
// Again 2 ulps(wF+g) in the shifter output truncation
// Normalisation truncation: either 0 (total 5), or 1 ulp(wF+g) but dividing the previous by 2 (total 3.5)
// Total max 5 ulps, we're safe with 3 guard bits
// guard bits for a faithful result
int g=3;
// The exponent datapath
// setCriticalPath( getMaxInputDelays(inputDelays) + target->localWireDelay());
setCriticalPath(0);
manageCriticalPath( target->adderDelay(wE+1) // subtractions
+ target->localWireDelay(wE) // fanout of XltY etc
+ target->lutDelay() // & and mux
);
//---------------------------------------------------------------------
// extract the three biased exponents.
vhdl << tab << declare("EX", wE) << " <= X" << range(wE+wF-1, wF) << ";" << endl;
vhdl << tab << declare("EY", wE) << " <= Y" << range(wE+wF-1, wF) << ";" << endl;
vhdl << tab << declare("EZ", wE) << " <= Z" << range(wE+wF-1, wF) << ";" << endl;
// determine the max of the exponents
vhdl << tab << declare("DEXY", wE+1) << " <= ('0' & EX) - ('0' & EY);" << endl;
vhdl << tab << declare("DEYZ", wE+1) << " <= ('0' & EY) - ('0' & EZ);" << endl;
vhdl << tab << declare("DEXZ", wE+1) << " <= ('0' & EX) - ('0' & EZ);" << endl;
vhdl << tab << declare("XltY") << " <= DEXY("<< wE<<");" << endl;
vhdl << tab << declare("YltZ") << " <= DEYZ("<< wE<<");" << endl;
vhdl << tab << declare("XltZ") << " <= DEXZ("<< wE<<");" << endl;
// rename the exponents to A,B,C with A>=(B,C)
vhdl << tab << declare("EA", wE) << " <= " << endl
<< tab << tab << "EZ when (XltZ='1') and (YltZ='1') else " << endl
<< tab << tab << "EY when (XltY='1') and (YltZ='0') else " << endl
<< tab << tab << "EX; " << endl;
vhdl << tab << declare("EB", wE) << " <= " << endl
<< tab << tab << "EX when (XltZ='1') and (YltZ='1') else " << endl
<< tab << tab << "EZ when (XltY='1') and (YltZ='0') else " << endl
<< tab << tab << "EY; " << endl;
vhdl << tab << declare("EC", wE) << " <= " << endl
<< tab << tab << "EY when (XltZ='1') and (YltZ='1') else " << endl
<< tab << tab << "EX when (XltY='1') and (YltZ='0') else " << endl
<< tab << tab << "EZ; " << endl;
//---------------------------------------------------------------------
// Now recompute our two shift values -- they were already computed at cycle 0 but it is cheaper this way, otherwise we have to register, negate and mux them.
manageCriticalPath( target->adderDelay(wE-1) );
vhdl << tab << declare("fullShiftValB", wE) << " <= (EA" << range(wE-2,0) << " - EB" << range(wE-2,0) << ") & '0' ; -- positive result, no overflow " << endl;
vhdl << tab << declare("fullShiftValC", wE) << " <= (EA" << range(wE-2,0) << " - EC" << range(wE-2,0) << ") & '0' ; -- positive result, no overflow " << endl;
double cpfullShiftValC = getCriticalPath();
//---------------------------------------------------------------------
Shifter* rightShifterDummy = new Shifter(target,wF+g+2, wF+g+2, Shifter::Right);
int sizeRightShift = rightShifterDummy->getShiftInWidth();
//-- Manage the shift value of the mantissa of B --------
manageCriticalPath( target->localWireDelay() + target->lutDelay());
vhdl<<tab<<declare("shiftedOutB") << " <= ";
if (wE>sizeRightShift){
for (int i=wE-1;i>=sizeRightShift;i--) {
vhdl<< "fullShiftValB("<<i<<")";
if (i>sizeRightShift)
vhdl<< " or ";
}
vhdl<<";"<<endl;
}
else
vhdl<<tab<<"'0';"<<endl;
if (wE>sizeRightShift) {
manageCriticalPath( target->localWireDelay() + target->lutDelay());
vhdl<<tab<<declare("shiftValB",sizeRightShift) << " <= fullShiftValB("<< sizeRightShift-1<<" downto 0)"
<< " when shiftedOutB='0'"<<endl
<<tab << tab << " else CONV_STD_LOGIC_VECTOR("<<wF+g+1<<","<<sizeRightShift<<") ;" << endl;
}else if (wE==sizeRightShift) {
vhdl<<tab<<declare("shiftValB",sizeRightShift) << " <= fullShiftValB;" << endl ;
}else { // wE< sizeRightShift
vhdl<<tab<<declare("shiftValB",sizeRightShift) << " <= CONV_STD_LOGIC_VECTOR(0,"<<sizeRightShift-wE <<") & fullShiftValB;" << endl;
}
double cpshiftValB = getCriticalPath();
//-- Manage the shift value of the mantissa of C --------
manageCriticalPath( target->localWireDelay() + target->lutDelay());
//FIXME possible fixme needed when or does not fit on lut
vhdl<<tab<<declare("shiftedOutC") << " <= ";
if (wE>sizeRightShift){
for (int i=wE-1;i>=sizeRightShift;i--) {
vhdl<< "fullShiftValC("<<i<<")";
if (i>sizeRightShift)
vhdl<< " or ";
}
vhdl<<";"<<endl;
}
else
vhdl<<tab<<"'0';"<<endl;
setCycleFromSignal("fullShiftValC",cpfullShiftValC);
if (wE>sizeRightShift) {
manageCriticalPath( target->localWireDelay() + target->lutDelay());//the mux delay
vhdl<<tab<<declare("shiftValC",sizeRightShift) << " <= fullShiftValC("<< sizeRightShift-1<<" downto 0)"
<< " when shiftedOutC='0'"<<endl
<<tab << tab << " else CONV_STD_LOGIC_VECTOR("<<wF+g+1<<","<<sizeRightShift<<") ;" << endl;
} else if (wE==sizeRightShift) {
vhdl<<tab<<declare("shiftValC",sizeRightShift) << " <= fullShiftValC;" << endl ;
} else { // wE< sizeRightShift
vhdl<<tab<<declare("shiftValC",sizeRightShift) << " <= CONV_STD_LOGIC_VECTOR(0,"<<sizeRightShift-wE <<") & fullShiftValC;" << endl;
}
// Back to cycle 0 for the significand datapath
setCycle(0);
//FIXME add inDelayMap for use within hierarchies of components
// Square the significands
#define USE_SQUARER 1
#if USE_SQUARER
IntSquarer* mult = new IntSquarer(target, 1+ wF);
#else
IntMultiplier* mult = new IntMultiplier(target, 1+ wF, 1+ wF);
#endif
oplist.push_back(mult);
vhdl << tab << declare("mX", wF+1) << " <= '1' & X" << range(wF-1, 0) << "; " << endl;
inPortMap (mult, "X", "mX");
#if !USE_SQUARER
inPortMap (mult, "Y", "mX");
#endif
outPortMap(mult, "R", "mX2");
vhdl << instance(mult, "multx");
vhdl << tab << declare("mY", wF+1) << " <= '1' & Y" << range(wF-1, 0) << "; " << endl;
inPortMap (mult, "X", "mY");
#if !USE_SQUARER
inPortMap (mult, "Y", "mY");
#endif
outPortMap(mult, "R", "mY2");
vhdl << instance(mult, "multy");
vhdl << tab << declare("mZ", wF+1) << " <= '1' & Z" << range(wF-1, 0) << "; " << endl;
inPortMap (mult, "X", "mZ");
#if !USE_SQUARER
inPortMap (mult, "Y", "mZ");
#endif
outPortMap(mult, "R", "mZ2");
vhdl << instance(mult, "multz");
syncCycleFromSignal("mZ2", false);
setCriticalPath(mult->getOutputDelay("R"));
// truncate the three results to wF+g+2
int prodsize = 2+2*wF;
vhdl << tab << declare("X2t", wF+g+2) << " <= mX2" << range(prodsize-1, prodsize - wF-g-2) << "; " << endl;
vhdl << tab << declare("Y2t", wF+g+2) << " <= mY2" << range(prodsize-1, prodsize - wF-g-2) << "; " << endl;
vhdl << tab << declare("Z2t", wF+g+2) << " <= mZ2" << range(prodsize-1, prodsize - wF-g-2) << "; " << endl;
// Now we have our three FP squares, we rename them to A,B,C with A>=(B,C)
// only 3 3-muxes
manageCriticalPath(target->localWireDelay(wF) + target->lutDelay());
vhdl << tab << declare("MA", wF+g+2) << " <= " << endl
<< tab << tab << "Z2t when (XltZ='1') and (YltZ='1') else " << endl
<< tab << tab << "Y2t when (XltY='1') and (YltZ='0') else " << endl
<< tab << tab << "X2t; " << endl;
vhdl << tab << declare("MB", wF+g+2) << " <= " << endl
<< tab << tab << "X2t when (XltZ='1') and (YltZ='1') else " << endl
<< tab << tab << "Z2t when (XltY='1') and (YltZ='0') else " << endl
<< tab << tab << "Y2t; " << endl;
vhdl << tab << declare("MC", wF+g+2) << " <= " << endl
<< tab << tab << "Y2t when (XltZ='1') and (YltZ='1') else " << endl
<< tab << tab << "X2t when (XltY='1') and (YltZ='0') else " << endl
<< tab << tab << "Z2t; " << endl;
//Synchronize exponent and significand datapath
syncCycleFromSignal("shiftValB", cpshiftValB, false);
// B and C right shifters are the same
Shifter* rightShifter = new Shifter(target,wF+g+2, wF+g+2, Shifter::Right, inDelayMap("X",target->localWireDelay()+getCriticalPath()));
oplist.push_back(rightShifter);
inPortMap (rightShifter, "X", "MB");
inPortMap (rightShifter, "S", "shiftValB");
outPortMap (rightShifter, "R","shiftedB");
vhdl << instance(rightShifter, "ShifterForB");
inPortMap (rightShifter, "X", "MC");
inPortMap (rightShifter, "S", "shiftValC");
outPortMap (rightShifter, "R","shiftedC");
vhdl << instance(rightShifter, "ShifterForC");
// superbly ignore the bits that are shifted out
syncCycleFromSignal("shiftedB", false);
setCriticalPath( rightShifter->getOutputDelay("R"));
int shiftedB_size = getSignalByName("shiftedB")->width();
vhdl << tab << declare("alignedB", wF+g+2) << " <= shiftedB" << range(shiftedB_size-1, shiftedB_size -(wF+g+2)) << "; " << endl;
vhdl << tab << declare("alignedC", wF+g+2) << " <= shiftedC" << range(shiftedB_size-1, shiftedB_size -(wF+g+2)) << "; " << endl;
vhdl << tab << declare("paddedA", wF+g+4) << " <= \"00\" & MA; " << endl;
vhdl << tab << declare("paddedB", wF+g+4) << " <= \"00\" & alignedB; " << endl;
vhdl << tab << declare("paddedC", wF+g+4) << " <= \"00\" & alignedC; " << endl;
IntMultiAdder* adder = new IntMultiAdder(target,wF+g+4, 3, inDelayMap("X0", target->localWireDelay() + getCriticalPath() ));
oplist.push_back(adder);
inPortMap (adder, "X0", "paddedA");
inPortMap (adder, "X1", "paddedB");
inPortMap (adder, "X2", "paddedC");
inPortMapCst(adder, "Cin", "'0'"); // a 1 would compensate the two truncations in the worst case -- to explore
outPortMap (adder, "R","sum");
vhdl << instance(adder, "adder1");
syncCycleFromSignal("sum", false);
setCriticalPath(adder->getOutputDelay("R"));
manageCriticalPath(target->localWireDelay() + target->lutDelay());
// Possible 3-bit normalisation, with a truncation
vhdl << tab << declare("finalFraction", wF+g) << " <= " << endl
<< tab << tab << "sum" << range(wF+g+2,3) << " when sum(" << wF+g+3 << ")='1' else " << endl
<< tab << tab << "sum" << range(wF+g+1, 2) << " when (sum" << range(wF+g+3, wF+g+2) << "=\"01\") else " << endl
<< tab << tab << "sum" << range(wF+g, 1) << " when (sum" << range(wF+g+3, wF+g+1) << "=\"001\") else " << endl
<< tab << tab << "sum" << range(wF+g-1, 0) << "; " << endl;
// Exponent datapath. We have to compute 2*EA - bias + an update corresponding to the normalisatiobn
// since (1.m)*(1.m) = xx.xxxxxx sum is xxxx.xxxxxx
// All the following ignores overflows, infinities, zeroes, etc for the sake of simplicity.
manageCriticalPath(target->localWireDelay() + target->lutDelay());
int bias = (1<<(wE-1))-1;
vhdl << tab << declare("exponentUpdate", wE+1) << " <= " << endl
<< tab << tab << "CONV_STD_LOGIC_VECTOR(" << bias-3 << ", "<< wE+1 <<") when sum(" << wF+g+3 << ")='1' else " << endl
<< tab << tab << "CONV_STD_LOGIC_VECTOR(" << bias-2 << ", "<< wE+1 <<") when (sum" << range(wF+g+3, wF+g+2) << "=\"01\") else " << endl
<< tab << tab << "CONV_STD_LOGIC_VECTOR(" << bias-1 << ", "<< wE+1 <<") when (sum" << range(wF+g+3, wF+g+1) << "=\"001\") else " << endl
<< tab << tab << "CONV_STD_LOGIC_VECTOR(" << bias << ", "<< wE+1 <<") ; " << endl;
manageCriticalPath( target->localWireDelay() + target->adderDelay(wE+1));
vhdl << tab << declare("finalExp", wE+1) << " <= (EA & '0') - exponentUpdate ; " << endl;
IntAdder *roundingAdder = new IntAdder(target, wE +1 + wF);
oplist.push_back(roundingAdder);
vhdl << tab << declare("roundingOp",wE+1 + wF) << "<= finalExp & finalFraction"<<range(wF+g-1,g)<<";"<<endl;
inPortMap ( roundingAdder, "X", "roundingOp");
inPortMapCst ( roundingAdder, "Y", zg(wE+1+wF));
inPortMapCst ( roundingAdder, "Cin", "'1'");
outPortMap ( roundingAdder, "R", "expFrac");
vhdl << tab << instance( roundingAdder, "RoundingAdder");
syncCycleFromSignal("expFrac");
setCriticalPath( roundingAdder->getOutputDelay("R"));
//TODO
vhdl << tab << declare("rExc",2) << " <= \"01\" when expFrac"<<of(wE+wF)<<"='0' else \"10\";"<<endl;
vhdl << tab << "R <= rExc & '0' & expFrac"<<range(wE+1 + wF-2,0)<<";"<<endl;
}
}
