Author: Carl Friedrich Bolz <[email protected]>
Branch:
Changeset: r68714:84ab6e698cac
Date: 2014-01-17 13:23 +0100
http://bitbucket.org/pypy/pypy/changeset/84ab6e698cac/
Log: issue892 testing
integrate Mario Pernici's patch to speed up the naive multiplication
algorithm Thanks!
diff --git a/rpython/rlib/rbigint.py b/rpython/rlib/rbigint.py
--- a/rpython/rlib/rbigint.py
+++ b/rpython/rlib/rbigint.py
@@ -1290,26 +1290,58 @@
# Even if it's not power of two it can still be useful.
return _muladd1(b, digit)
+ # a is not b
+ # use the following identity to reduce the number of operations
+ # a * b = a_0*b_0 + sum_{i=1}^n(a_0*b_i + a_1*b_{i-1}) + a_1*b_n
z = rbigint([NULLDIGIT] * (size_a + size_b), 1)
- # gradeschool long mult
i = UDIGIT_TYPE(0)
- while i < size_a:
- carry = 0
- f = a.widedigit(i)
+ size_a1 = UDIGIT_TYPE(size_a - 1)
+ size_b1 = UDIGIT_TYPE(size_b - 1)
+ while i < size_a1:
+ f0 = a.widedigit(i)
+ f1 = a.widedigit(i + 1)
pz = i
+ carry = z.widedigit(pz) + b.widedigit(0) * f0
+ z.setdigit(pz, carry)
+ pz += 1
+ carry >>= SHIFT
+ j = UDIGIT_TYPE(0)
+ while j < size_b1:
+ # this operation does not overflow using
+ # SHIFT = (LONG_BIT // 2) - 1 = B - 1; in fact before it
+ # carry and z.widedigit(pz) are less than 2**(B - 1);
+ # b.widedigit(j + 1) * f0 < (2**(B-1) - 1)**2; so
+ # carry + z.widedigit(pz) + b.widedigit(j + 1) * f0 +
+ # b.widedigit(j) * f1 < 2**(2*B - 1) - 2**B < 2**LONG)BIT - 1
+ carry += z.widedigit(pz) + b.widedigit(j + 1) * f0 + \
+ b.widedigit(j) * f1
+ z.setdigit(pz, carry)
+ pz += 1
+ carry >>= SHIFT
+ j += 1
+ # carry < 2**(B + 1) - 2
+ carry += z.widedigit(pz) + b.widedigit(size_b1) * f1
+ z.setdigit(pz, carry)
+ pz += 1
+ carry >>= SHIFT
+ # carry < 4
+ if carry:
+ z.setdigit(pz, carry)
+ assert (carry >> SHIFT) == 0
+ i += 2
+ if size_a & 1:
+ pz = size_a1
+ f = a.widedigit(pz)
pb = 0
+ carry = _widen_digit(0)
while pb < size_b:
carry += z.widedigit(pz) + b.widedigit(pb) * f
pb += 1
z.setdigit(pz, carry)
pz += 1
carry >>= SHIFT
- assert carry <= MASK
if carry:
- assert pz >= 0
z.setdigit(pz, z.widedigit(pz) + carry)
- assert (carry >> SHIFT) == 0
- i += 1
z._normalize()
return z
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