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51 lines
1.3 KiB
Plaintext
51 lines
1.3 KiB
Plaintext
module Karatsuba where
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kmult : {limb,n} (fin n, fin limb, limb >= 6, n>=1) => [n] -> [n] -> [2*n]
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kmult x y =
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if `n <= (demote`{limb, max (width limb) (width n)}) then
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(zero#x)*(zero#y)
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else
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take (splitmult`{limb} (make_atleast`{limb} x) (make_atleast`{limb} y))
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make_atleast : {n, m, a} (fin n, fin m, Zero a) => [m]a -> [max n m]a
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make_atleast x = zero#x
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splitmult : {limb,n} (fin n, fin limb, limb >= 6, n>=6)
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=> [n] -> [n] -> [2*n]
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splitmult x y = (ac # bd) + (zero # ad_bc # (zero:[low]))
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where
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type hi = n/2
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type low = n - hi
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(a,b) = splitAt`{hi} x
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(c,d) = splitAt`{hi} y
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ac : [2*hi]
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ac = kmult`{limb,hi} a c
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bd : [2*low]
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bd = kmult`{limb,low} b d
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a_b = (zext a) + (zext b)
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c_d = (zext c) + (zext d)
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ad_bc : [2*(low+1)]
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ad_bc = (kmult`{limb,low+1} a_b c_d) - (zext ac) - (zext bd)
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property splitmult_correct_tiny (x:[9]) (y:[9]) =
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zext x * zext y == splitmult`{limb=7} x y
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property splitmult_correct_small (x:[11]) (y:[11]) =
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zext x * zext y == splitmult`{limb=7} x y
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property splitmult_correct_medium(x:[17]) (y:[17]) =
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zext x * zext y == splitmult`{limb=7} x y
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property splitmult_correct_large (x:[59]) (y:[59]) =
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zext x * zext y == splitmult`{limb=7} x y
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property splitmult_correct_huge (x:[511]) (y:[511]) =
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zext x * zext y == splitmult`{limb=63} x y
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