Results – Complex Multipliers Six types of multipliers, including Booth multipliers btor : generated by Boolector; abc: generated by abc; AOKI mults: sp – standard partial products; bp - booth partial products ar - array based adder chain; rc - ripple carry based adder chain # bits 128 Designs Yu’16 Ahmed’16 Ritirc’17 Ritirc’18 This work (sec) btor; btor-resyn3; abc; abc-resyn3; CSA; CSA-resyn3; MO TO ES ES 1.5 abc-booth; abc-booth-resyn3 MO TO ES ES 0.5 sp-ar-rc [AOKI] - TO ES ES 1.5 - TO ES ES MO TO ES ES bp-ar-rc-dc2; bp-ar-rc-resyn3; sp-ar-rc-dc2; sp-ar-rc-resyn3; 256 abc; abc-resyn3; abc-booth; abc-booth-resyn3 abc; abc-resyn3; abc-booth; 1024 abc-booth; abc-booth-resyn3 UAT 14 3.5 - - - - 9482 139 UAT = Unstructured adder trees; TO = time out of 3 hours; MO = memory out of 8 GB; ES = error state 22
Heuristic 2-level logic minimization (espresso) Consider F(a,b,c) initially specified as: f = {abc, abc, abc} (on-set), and d ={abc, abc} (don’t care set) F1= abc + abc+ abc Expand abca on off don’t care F2= a+abc + abc abc is redundant a is prime F3= a+abc Expand abc bc c b a F4= a+bc Intro to Logic Synthesis 21
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