cvw/pipelined/src/fpu/fma.sv
2022-07-07 16:01:33 -07:00

296 lines
12 KiB
Systemverilog

///////////////////////////////////////////
//
// Written: me@KatherineParry.com, David Harris
// Modified: 6/23/2021
//
// Purpose: Floating point multiply-accumulate of configurable size
//
// A component of the Wally configurable RISC-V project.
//
// Copyright (C) 2021 Harvey Mudd College & Oklahoma State University
//
// MIT LICENSE
// Permission is hereby granted, free of charge, to any person obtaining a copy of this
// software and associated documentation files (the "Software"), to deal in the Software
// without restriction, including without limitation the rights to use, copy, modify, merge,
// publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons
// to whom the Software is furnished to do so, subject to the following conditions:
//
// The above copyright notice and this permission notice shall be included in all copies or
// substantial portions of the Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED,
// INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR
// PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS
// BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,
// TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE
// OR OTHER DEALINGS IN THE SOFTWARE.
////////////////////////////////////////////////////////////////////////////////////////////////
`include "wally-config.vh"
module fma(
input logic Xs, Ys, Zs, // input's signs
input logic [`NE-1:0] Xe, Ye, Ze, // input's biased exponents in B(NE.0) format
input logic [`NF:0] Xm, Ym, Zm, // input's significands in U(0.NF) format
input logic XZero, YZero, ZZero, // is the input zero
input logic [2:0] FOpCtrl, // 000 = fmadd (X*Y)+Z, 001 = fmsub (X*Y)-Z, 010 = fnmsub -(X*Y)+Z, 011 = fnmadd -(X*Y)-Z, 100 = fmul (X*Y)
input logic [`FMTBITS-1:0] Fmt, // format of the result single double half or quad
output logic [`NE+1:0] Pe, // the product's exponent B(NE+2.0) format; adds 2 bits to allow for size of number and negative sign
output logic ZmSticky, // sticky bit that is calculated during alignment
output logic KillProd, // set the product to zero before addition if the product is too small to matter
output logic [3*`NF+5:0] Sm, // the positive sum's significand
output logic NegSum, // was the sum negitive
output logic InvA, // Was A inverted for effective subtraction (P-A or -P+A)
output logic As, // the aligned addend's sign (modified Z sign for other opperations)
output logic Ps, // the product's sign
output logic [$clog2(3*`NF+7)-1:0] NCnt // normalization shift count
);
logic [2*`NF+1:0] Pm; // the product's significand in U(2.2Nf) format
logic [3*`NF+5:0] Am; // addend aligned's mantissa for addition in U(NF+5.2NF+1)
logic [3*`NF+6:0] AmInv; // aligned addend's mantissa possibly inverted
logic [2*`NF+1:0] PmKilled; // the product's mantissa possibly killed
logic [3*`NF+6:0] PreSum, NegPreSum; // positive and negitve versions of the sum
///////////////////////////////////////////////////////////////////////////////
// Calculate the product
// - When multipliying two fp numbers, add the exponents
// - Subtract the bias (XExp + YExp has two biases, one from each exponent)
// - If the product is zero then kill the exponent
// - Multiply the mantissas
///////////////////////////////////////////////////////////////////////////////
// calculate the product's exponent
expadd expadd(.Fmt, .Xe, .Ye, .XZero, .YZero, .Pe);
// multiplication of the mantissa's
mult mult(.Xm, .Ym, .Pm);
///////////////////////////////////////////////////////////////////////////////
// Alignment shifter
///////////////////////////////////////////////////////////////////////////////
align align(.Ze, .Zm, .XZero, .YZero, .ZZero, .Xe, .Ye,
.Am, .ZmSticky, .KillProd);
// calculate the signs and take the opperation into account
sign sign(.FOpCtrl, .Xs, .Ys, .Zs, .Ps, .As);
// ///////////////////////////////////////////////////////////////////////////////
// // Addition/LZA
// ///////////////////////////////////////////////////////////////////////////////
add add(.Am, .Pm, .Ps, .As, .KillProd, .AmInv, .PmKilled, .NegSum, .PreSum, .NegPreSum, .InvA, .XZero, .YZero, .Sm);
loa loa(.A(AmInv+{(3*`NF+6)'(0),InvA}), .P(PmKilled), .NCnt);
endmodule
module expadd(
input logic [`FMTBITS-1:0] Fmt, // format of the output: single double half quad
input logic [`NE-1:0] Xe, Ye, // input's exponents
input logic XZero, YZero, // are the inputs zero
output logic [`NE+1:0] Pe // product's exponent B^(1023)NE+2
);
// kill the exponent if the product is zero - either X or Y is 0
assign Pe = ({2'b0, Xe} + {2'b0, Ye} - {2'b0, (`NE)'(`BIAS)})&{`NE+2{~(XZero|YZero)}};
endmodule
module mult(
input logic [`NF:0] Xm, Ym,
output logic [2*`NF+1:0] Pm
);
assign Pm = Xm * Ym;
endmodule
module sign(
input logic [2:0] FOpCtrl, // opperation contol
input logic Xs, Ys, Zs, // sign of the inputs
output logic Ps, // the product's sign - takes opperation into account
output logic As // aligned addend sign used in fma - takes opperation into account
);
// Calculate the product's sign
// Negate product's sign if FNMADD or FNMSUB
// flip is negation opperation
assign Ps = Xs ^ Ys ^ (FOpCtrl[1]&~FOpCtrl[2]);
// flip if subtraction
assign As = Zs^FOpCtrl[0];
endmodule
module align(
input logic [`NE-1:0] Xe, Ye, Ze, // biased exponents in B(NE.0) format
input logic [`NF:0] Zm, // significand in U(0.NF) format]
input logic XZero, YZero, ZZero, // is the input zero
output logic [3*`NF+5:0] Am, // addend aligned for addition in U(NF+5.2NF+1)
output logic ZmSticky, // Sticky bit calculated from the aliged addend
output logic KillProd // should the product be set to zero
);
logic [`NE+1:0] ACnt; // how far to shift the addend to align with the product in Q(NE+2.0) format
logic [4*`NF+5:0] ZmShifted; // output of the alignment shifter including sticky bits U(NF+5.3NF+1)
logic [4*`NF+5:0] ZmPreshifted; // input to the alignment shifter U(NF+5.3NF+1)
logic KillZ;
///////////////////////////////////////////////////////////////////////////////
// Alignment shifter
///////////////////////////////////////////////////////////////////////////////
// determine the shift count for alignment
// - negitive means Z is larger, so shift Z left
// - positive means the product is larger, so shift Z right
// This could have been done using Pe, but ACnt is on the critical path so we replicate logic for speed
assign ACnt = {2'b0, Xe} + {2'b0, Ye} - {2'b0, (`NE)'(`BIAS)} + (`NE+2)'(`NF+3) - {2'b0, Ze};
// Defualt Addition without shifting
// | 54'b0 | 106'b(product) | 2'b0 |
// | addnend |
// the 1'b0 before the added is because the product's mantissa has two bits before the binary point (xx.xxxxxxxxxx...)
assign ZmPreshifted = {Zm,(3*`NF+5)'(0)};
assign KillProd = ACnt[`NE+1]|XZero|YZero;
assign KillZ = $signed(ACnt)>$signed((`NE+2)'(3)*(`NE+2)'(`NF)+(`NE+2)'(5));
always_comb
begin
// If the product is too small to effect the sum, kill the product
// | 54'b0 | 106'b(product) | 2'b0 |
// | addnend |
if (KillProd) begin
ZmShifted = ZmPreshifted;
ZmSticky = ~(XZero|YZero);
// If the addend is too small to effect the addition
// - The addend has to shift two past the end of the addend to be considered too small
// - The 2 extra bits are needed for rounding
// | 54'b0 | 106'b(product) | 2'b0 |
// | addnend |
end else if (KillZ) begin
ZmShifted = 0;
ZmSticky = ~ZZero;
// If the Addend is shifted right
// | 54'b0 | 106'b(product) | 2'b0 |
// | addnend |
end else begin
ZmShifted = ZmPreshifted >> ACnt;
ZmSticky = |(ZmShifted[`NF-1:0]);
end
end
assign Am = ZmShifted[4*`NF+5:`NF];
endmodule
module add(
input logic [3*`NF+5:0] Am, // aligned addend's mantissa for addition in U(NF+5.2NF+1)
input logic [2*`NF+1:0] Pm, // the product's mantissa
input logic Ps, As,// the product sign and the alligend addeded's sign (Modified Z sign for other opperations)
input logic KillProd, // should the product be set to 0
input logic XZero, YZero, // is the input zero
output logic [3*`NF+6:0] AmInv, // aligned addend possibly inverted
output logic [2*`NF+1:0] PmKilled, // the product's mantissa possibly killed
output logic NegSum, // was the sum negitive
output logic InvA, // do you invert the aligned addend
output logic [3*`NF+5:0] Sm, // the positive sum
output logic [3*`NF+6:0] PreSum, NegPreSum// possibly negitive sum
);
///////////////////////////////////////////////////////////////////////////////
// Addition
///////////////////////////////////////////////////////////////////////////////
// Negate Z when doing one of the following opperations:
// -prod + Z
// prod - Z
assign InvA = As ^ Ps;
// Choose an inverted or non-inverted addend - the one has to be added now for the LZA
assign AmInv = InvA ? {1'b1, ~Am} : {1'b0, Am};
// Kill the product if the product is too small to effect the addition (determined in fma1.sv)
assign PmKilled = Pm&{2*`NF+2{~KillProd}};
// Do the addition
// - calculate a positive and negitive sum in parallel
assign PreSum = {{`NF+3{1'b0}}, PmKilled, 2'b0} + AmInv + {{3*`NF+6{1'b0}}, InvA};
assign NegPreSum = {1'b0, Am} + {{`NF+3{1'b1}}, ~PmKilled, 2'b0} + {(3*`NF+7)'(4)};
// Is the sum negitive
assign NegSum = PreSum[3*`NF+6];
// Choose the positive sum and accompanying LZA result.
assign Sm = NegSum ? NegPreSum[3*`NF+5:0] : PreSum[3*`NF+5:0];
endmodule
module loa( // [Schmookler & Nowka, Leading zero anticipation and detection, IEEE Sym. Computer Arithmetic, 2001]
input logic [3*`NF+6:0] A, // addend
input logic [2*`NF+1:0] P, // product
output logic [$clog2(3*`NF+7)-1:0] NCnt // normalization shift count for the positive result
);
logic [3*`NF+6:0] T;
logic [3*`NF+6:0] G;
logic [3*`NF+6:0] Z;
logic [3*`NF+6:0] f;
assign T[3*`NF+6:2*`NF+4] = A[3*`NF+6:2*`NF+4];
assign G[3*`NF+6:2*`NF+4] = 0;
assign Z[3*`NF+6:2*`NF+4] = ~A[3*`NF+6:2*`NF+4];
assign T[2*`NF+3:2] = A[2*`NF+3:2]^P;
assign G[2*`NF+3:2] = A[2*`NF+3:2]&P;
assign Z[2*`NF+3:2] = ~A[2*`NF+3:2]&~P;
assign T[1:0] = A[1:0];
assign G[1:0] = 0;
assign Z[1:0] = ~A[1:0];
// Apply function to determine Leading pattern
// - note: the paper linked above uses the numbering system where 0 is the most significant bit
//f[n] = ~T[n]&T[n-1] note: n is the MSB
//f[i] = (T[i+1]&(G[i]&~Z[i-1] | Z[i]&~G[i-1])) | (~T[i+1]&(Z[i]&~Z[i-1] | G[i]&~G[i-1]))
assign f[3*`NF+6] = ~T[3*`NF+6]&T[3*`NF+5];
assign f[3*`NF+5:0] = (T[3*`NF+6:1]&(G[3*`NF+5:0]&{~Z[3*`NF+4:0], 1'b0} | Z[3*`NF+5:0]&{~G[3*`NF+4:0], 1'b1})) | (~T[3*`NF+6:1]&(Z[3*`NF+5:0]&{~Z[3*`NF+4:0], 1'b0} | G[3*`NF+5:0]&{~G[3*`NF+4:0], 1'b1}));
lzc #(3*`NF+7) lzc (.num(f), .ZeroCnt(NCnt));
endmodule