66 lines
1.8 KiB
Python
66 lines
1.8 KiB
Python
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#!/usr/bin/env python3
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# Quick reference model for sequential unsigned multiply/divide/modulo
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def div_step(w, accum, divisor):
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sub_tmp = accum - (divisor << (w - 1))
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underflow = sub_tmp < 0
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if not underflow:
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accum = sub_tmp
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accum = (accum << 1) | (not underflow)
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return accum
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def divmod(w, dividend, divisor, debug=True):
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accum = dividend
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for i in range(w):
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accum_prev = accum
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accum = div_step(w, accum, divisor)
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if debug:
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print("Step {:02d}: accum {:0{}x} -> {:0{}x}".format(
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i, accum_prev, int(w / 2), accum, int(w / 2)))
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return (accum >> w, accum & ((1 << w) - 1))
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def mul_step(w, accum, multiplicand):
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add_en = accum & 1
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accum = accum >> 1
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if add_en:
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accum += (multiplicand << (w - 1))
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return accum
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def mul(w, multiplicand, multiplier, debug=True):
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accum = multiplier
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for i in range(w):
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accum_prev = accum
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accum = mul_step(w, accum, multiplicand)
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if debug:
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print("Step {:02d}: accum {:0{}x} -> {:0{}x}".format(
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i, accum_prev, int(w / 2), accum, int(w / 2)))
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return (accum >> w, accum & ((1 << w) - 1))
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def divtest(w=4):
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for i in range(2 ** w):
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for j in range(1, 2 ** w):
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gatemod, gatediv = divmod(w, i, j, debug=False)
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goldmod, golddiv = (i % j, i // j)
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print("{:02d} % {:02d} = {:02d} (gold {:02d}); ./. = {:02d} (gold {:02d})"
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.format(i, j, gatemod, goldmod, gatediv, golddiv))
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assert(gatemod == goldmod)
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assert(gatediv == golddiv)
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def multest(w=4):
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for i in range(2 ** w):
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for j in range(2 ** w):
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gateh, gatel = mul(w, i, j, debug=False)
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gold = i * j
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goldl, goldh = (gold & ((1 << w) - 1), gold >> w)
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print("{:02d} * {:02d} = ({:02d} (gold {:02d}), {:02d} (gold {:02d})"
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.format(i, j, gateh, goldh, gatel, goldl))
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assert(gatel == goldl)
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assert(gateh == goldh)
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if __name__ == "__main__":
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print("Test division:")
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divtest()
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print("Test multiplication:")
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multest()
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