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Add a multiplier using CSA and booth coding (#418)
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‎python/ci-tests/test_csamul.py‎

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from assassyn.frontend import *
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from assassyn.test import run_test
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import random
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# Stage 3: full adder
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class FinalAdder(Module):
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def __init__(self):
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super().__init__(ports={
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'a': Port(Int(32)),
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'b': Port(Int(32)),
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'cnt': Port(Int(32)),
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's': Port(Int(64)),
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'carry': Port(Int(64)),
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}
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)
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@module.combinational
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def build(self):
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a, b, cnt, s, carry = self.pop_all_ports(True)
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result = s + carry
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log("Final result {:?} * {:?} = {:?}", a, b, result)
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# MulStage 2: CSA + Pseudo-Wallace Tree
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class CSATree(Module):
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def __init__(self):
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super().__init__(
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ports={
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'a': Port(Int(32)),
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'b': Port(Int(32)),
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'cnt': Port(Int(32)),
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'booth0': Port(Int(64)),
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'booth1': Port(Int(64)),
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'booth2': Port(Int(64)),
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'booth3': Port(Int(64)),
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'booth4': Port(Int(64)),
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'booth5': Port(Int(64)),
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'booth6': Port(Int(64)),
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'booth7': Port(Int(64)),
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'booth8': Port(Int(64)),
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'booth9': Port(Int(64)),
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'booth10': Port(Int(64)),
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'booth11': Port(Int(64)),
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'booth12': Port(Int(64)),
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'booth13': Port(Int(64)),
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'booth14': Port(Int(64)),
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'booth15': Port(Int(64)),
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}
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)
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@module.combinational
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def build(self, finaladder: FinalAdder):
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a, b, cnt, booth0, booth1, booth2, booth3, booth4, booth5, booth6, booth7, \
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booth8, booth9, booth10, booth11, booth12, booth13, booth14, booth15 = self.pop_all_ports(True)
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def csa(x1, x2, x3):
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x1_b = x1.bitcast(Bits(64))
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x2_b = x2.bitcast(Bits(64))
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x3_b = x3.bitcast(Bits(64))
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s_b = (x1_b ^ x2_b) ^ x3_b
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c_b = ((x1_b & x2_b) | (x2_b & x3_b) | (x3_b & x1_b)) << Bits(64)(1)
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return s_b.bitcast(Int(64)), c_b.bitcast(Int(64))
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current_pps = []
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current_pps.append(booth0)
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current_pps.append(booth1)
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current_pps.append(booth2)
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current_pps.append(booth3)
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current_pps.append(booth4)
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current_pps.append(booth5)
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current_pps.append(booth6)
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current_pps.append(booth7)
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current_pps.append(booth8)
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current_pps.append(booth9)
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current_pps.append(booth10)
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current_pps.append(booth11)
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current_pps.append(booth12)
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current_pps.append(booth13)
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current_pps.append(booth14)
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current_pps.append(booth15)
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while len(current_pps) > 2:
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next_pps = []
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num_inputs = len(current_pps)
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i = 0
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while (i + 2 < num_inputs):
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in1 = current_pps[i]
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in2 = current_pps[i + 1]
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in3 = current_pps[i + 2]
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s, c = csa(in1, in2, in3)
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next_pps.append(s)
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next_pps.append(c)
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i += 3
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while i < num_inputs:
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next_pps.append(current_pps[i])
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i += 1
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current_pps = next_pps
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final_s = current_pps[0]
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final_carry = current_pps[1]
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log("CSATree: sum = {:?}, carry = {:?}",final_s,final_carry)
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finaladder.async_called(a=a, b=b, cnt=cnt, s=final_s, carry=final_carry)
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# MulStage 1: radix-4 booth encoding
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class BoothEncoder(Module):
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def __init__(self):
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super().__init__(
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ports={
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'a': Port(Int(32)),
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'b': Port(Int(32)),
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'cnt': Port(Int(32)),
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}
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)
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@module.combinational
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def build(self, csatree: CSATree):
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a, b, cnt = self.pop_all_ports(True)
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b_unsigned = b.bitcast(Bits(32))
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#calculate the complement of -2a
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a_comp = ((Int(32)(-1)*a) << Int(32)(1)).bitcast(Int(32))
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#bit 0-5
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b01 = Int(32)(0)
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b0 = (b_unsigned & Bits(32)(1)).bitcast(Int(32))
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b1 = ((b_unsigned >> Bits(32)(1)) & Bits(32)(1)).bitcast(Int(32))
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b2 = ((b_unsigned >> Bits(32)(2)) & Bits(32)(1)).bitcast(Int(32))
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b3 = ((b_unsigned >> Bits(32)(3)) & Bits(32)(1)).bitcast(Int(32))
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b4 = ((b_unsigned >> Bits(32)(4)) & Bits(32)(1)).bitcast(Int(32))
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b5 = ((b_unsigned >> Bits(32)(5)) & Bits(32)(1)).bitcast(Int(32))
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booth0 = ((b01 + b0) * a + b1 * a_comp).bitcast(Int(64))
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booth1 = (((b1 + b2) * a + b3 * a_comp) << Int(32)(2)).bitcast(Int(64))
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booth2 = (((b3 + b4) * a + b5 * a_comp) << Int(32)(4)).bitcast(Int(64))
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#bit 6-11
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b_shift_unsigned = ((b_unsigned >> Bits(32)(6)) & Bits(32)(31)) #
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b0 = (b_shift_unsigned & Bits(32)(1)).bitcast(Int(32))
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b1 = ((b_shift_unsigned >> Bits(32)(1)) & Bits(32)(1)).bitcast(Int(32))
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b2 = ((b_shift_unsigned >> Bits(32)(2)) & Bits(32)(1)).bitcast(Int(32))
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b3 = ((b_shift_unsigned >> Bits(32)(3)) & Bits(32)(1)).bitcast(Int(32))
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b4 = ((b_shift_unsigned >> Bits(32)(4)) & Bits(32)(1)).bitcast(Int(32))
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booth3 = (((b5 + b0) * a + b1 * a_comp) << Int(32)(6)).bitcast(Int(64))
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booth4 = (((b1 + b2) * a + b3 * a_comp) << Int(32)(8)).bitcast(Int(64))
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b5 = ((b_shift_unsigned >> Bits(32)(5)) & Bits(32)(1)).bitcast(Int(32))
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booth5 = (((b3 + b4) * a + b5 * a_comp) << Int(32)(10)).bitcast(Int(64))
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#bit 12-17
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b_shift_unsigned = ((b_shift_unsigned >> Bits(32)(6)) & Bits(32)(31))
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b0 = (b_shift_unsigned & Bits(32)(1)).bitcast(Int(32))
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b1 = ((b_shift_unsigned >> Bits(32)(1)) & Bits(32)(1)).bitcast(Int(32))
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b2 = ((b_shift_unsigned >> Bits(32)(2)) & Bits(32)(1)).bitcast(Int(32))
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b3 = ((b_shift_unsigned >> Bits(32)(3)) & Bits(32)(1)).bitcast(Int(32))
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b4 = ((b_shift_unsigned >> Bits(32)(4)) & Bits(32)(1)).bitcast(Int(32))
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booth6 = (((b5 + b0) * a + b1 * a_comp) << Int(32)(12)).bitcast(Int(64))
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booth7 = (((b1 + b2) * a + b3 * a_comp) << Int(32)(14)).bitcast(Int(64))
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b5 = ((b_shift_unsigned >> Bits(32)(5)) & Bits(32)(1)).bitcast(Int(32))
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booth8 = (((b3 + b4) * a + b5 * a_comp) << Int(32)(16)).bitcast(Int(64))
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#bit 18-23
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b_shift_unsigned = ((b_shift_unsigned >> Bits(32)(6)) & Bits(32)(31))
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b0 = (b_shift_unsigned & Bits(32)(1)).bitcast(Int(32))
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b1 = ((b_shift_unsigned >> Bits(32)(1)) & Bits(32)(1)).bitcast(Int(32))
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b2 = ((b_shift_unsigned >> Bits(32)(2)) & Bits(32)(1)).bitcast(Int(32))
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b3 = ((b_shift_unsigned >> Bits(32)(3)) & Bits(32)(1)).bitcast(Int(32))
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b4 = ((b_shift_unsigned >> Bits(32)(4)) & Bits(32)(1)).bitcast(Int(32))
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booth9 = (((b5 + b0) * a + b1 * a_comp) << Int(32)(18)).bitcast(Int(64))
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booth10 = (((b1 + b2) * a + b3 * a_comp) << Int(32)(20)).bitcast(Int(64))
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b5 = ((b_shift_unsigned >> Bits(32)(5)) & Bits(32)(1)).bitcast(Int(32))
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booth11 = (((b3 + b4) * a + b5 * a_comp) << Int(32)(22)).bitcast(Int(64))
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#bit 24-29
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b_shift_unsigned = ((b_shift_unsigned >> Bits(32)(6)) & Bits(32)(31))
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b0 = (b_shift_unsigned & Bits(32)(1)).bitcast(Int(32))
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b1 = ((b_shift_unsigned >> Bits(32)(1)) & Bits(32)(1)).bitcast(Int(32))
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b2 = ((b_shift_unsigned >> Bits(32)(2)) & Bits(32)(1)).bitcast(Int(32))
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b3 = ((b_shift_unsigned >> Bits(32)(3)) & Bits(32)(1)).bitcast(Int(32))
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b4 = ((b_shift_unsigned >> Bits(32)(4)) & Bits(32)(1)).bitcast(Int(32))
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booth12 = (((b5 + b0) * a + b1 * a_comp) << Int(32)(24)).bitcast(Int(64))
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booth13 = (((b1 + b2) * a + b3 * a_comp) << Int(32)(26)).bitcast(Int(64))
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b5 = ((b_shift_unsigned >> Bits(32)(5)) & Bits(32)(1)).bitcast(Int(32))
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booth14 = (((b3 + b4) * a + b5 * a_comp) << Int(32)(28)).bitcast(Int(64))
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#bit 30-31
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b_shift_unsigned = ((b_shift_unsigned >> Bits(32)(6)) & Bits(32)(31))
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b0 = (b_shift_unsigned & Bits(32)(1)).bitcast(Int(32))
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b1 = ((b_shift_unsigned >> Bits(32)(1)) & Bits(32)(1)).bitcast(Int(32))
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booth15 = (((b5 + b0) * a + b1 * a_comp) << Int(32)(30)).bitcast(Int(64))
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log("BoothEncoder: DONE booth coding for {:?} * {:?}", a, b)
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csatree.async_called(a=a, b=b, cnt=cnt, booth0=booth0, booth1=booth1, booth2=booth2, booth3=booth3, booth4=booth4, booth5=booth5,
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booth6=booth6, booth7=booth7, booth8=booth8, booth9=booth9, booth10=booth10, booth11=booth11, booth12=booth12, booth13=booth13,
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booth14=booth14, booth15=booth15,)
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class Driver(Module):
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def __init__(self):
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super().__init__(ports={})
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@module.combinational
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def build(self, boothencoder: BoothEncoder):
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cnt = RegArray(Int(32), 1)
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(cnt & self)[0] <= cnt[0] + Int(32)(1)
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cond = cnt[0] < Int(32)(95)
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# test input from 0 to 94
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input_a = RegArray(Int(32),1)
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input_b = RegArray(Int(32),1)
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(input_a & self)[0] <= input_a[0] + Int(32)(1)
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(input_b & self)[0] <= input_b[0] + Int(32)(1)
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with Condition(cond):
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boothencoder.async_called(a=input_a[0], b=input_b[0], cnt=cnt[0])
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def build_system():
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finaladder = FinalAdder()
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finaladder.build()
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csatree = CSATree()
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csatree.build(finaladder)
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boothencoder = BoothEncoder()
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boothencoder.build(csatree)
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driver = Driver()
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driver.build(boothencoder)
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def check_raw(raw):
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cnt = 0
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for i in raw.split('\n'):
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if 'Final result' in i:
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line_toks = i.split()
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c = line_toks[-1]
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b = line_toks[-3]
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a = line_toks[-5]
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assert int(a) * int(b) == int(c)
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cnt += 1
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def test_multiplier():
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run_test('multiplier_test', build_system, check_raw)
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if __name__ == '__main__':
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test_multiplier()

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