[issue43053] Speed up math.isqrt, again
Mark Dickinson
report at bugs.python.org
Thu Jan 28 12:57:58 EST 2021
Mark Dickinson <dickinsm at gmail.com> added the comment:
Translation of the proposal to the iterative version described here: https://github.com/python/cpython/blob/64fc105b2d2faaeadd1026d2417b83915af6622f/Modules/mathmodule.c#L1591-L1611
The main loop:
c = (n.bit_length() - 1) // 2
a = 1
d = 0
for s in reversed(range(c.bit_length())):
# Loop invariant: (a-1)**2 < (n >> 2*(c - d)) < (a+1)**2
e = d
d = c >> s
a = (a << d - e - 1) + (n >> 2*c - e - d + 1) // a
becomes (again identical except for the last line):
c = (n.bit_length() - 1) // 2
a = 1
d = 0
for s in reversed(range(c.bit_length())):
# Loop invariant: (a-1)**2 < (n >> 2*(c - d)) < (a+1)**2
e = d
d = c >> s
a = (a << d - e) + ((n >> 2*c - e - d + 1) - (a*a << d - e - 1)) // a
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<https://bugs.python.org/issue43053>
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