I'm experimenting with various implementations of product(values). Here's a
naive version that easily suffers from overflow:
from functools import reduce
from operator import mul
def product_naive(values):
return reduce(mul, values)
py> product_naive([2, 4, 5])
40
py> product_naive([1e200, 1e200, 1e200])
inf
So I started experimenting with math.frexp, but I'm having trouble
understanding what I'm doing wrong here.
Help on built-in function frexp in module math:
frexp(...)
frexp(x)
Return the mantissa and exponent of x, as pair (m, e).
m is a float and e is an int, such that x = m * 2.**e.
If x is 0, m and e are both 0. Else 0.5 <= abs(m) < 1.0.
If x and y are both floats, then given:
m1, e1 = math.frexp(x)
m2, e2 = math.frexp(y)
Then x*y = m1*m2 * 2.0**(e1 + e2). We can test that:
py> from math import frexp
py> x = 2.5
py> y = 3.5
py> x*y
8.75
py> m1, e1 = math.frexp(x)
py> m2, e2 = math.frexp(y)
py> m1*m2 * 2.0**(e1 + e2)
8.75
Looks good to me. So let's try a less naive version of product():
def product_scaled(values):
scale = 0
prod = 1.0
for a in values:
m1, e1 = math.frexp(a)
m2, e2 = math.frexp(prod)
scale += (e1 + e2)
prod *= (m1*m2)
return (prod * 2.0**scale)
py> product_scaled([2.5, 3.5]) # expected 8.75
2.734375
What am I doing wrong?
--
Steven
“Cheer up,” they said, “things could be worse.” So I cheered up, and sure
enough, things got worse.
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