from math import isinf from sys import float_info twopow = 2.0**(float_info.max_exp-1) def msum(iterable): # assumes no infinities and nans in the input def add_to_partials(x): i = 1 for y in partials[1:]: if abs(x) < abs(y): x, y = y, x hi = x+y # if hi overflows, adjust x by +-2**max_exp, adjust # partials[0] accordingly, and recompute if isinf(hi): if x > 0: x = x-twopow-twopow partials[0] += 1.0 else: x = x+twopow+twopow partials[0] -= 1.0 hi = x+y x, lo = hi, y - (hi - x) if lo: partials[i] = lo i += 1 partials[i:] = [x] if x else [] partials = [0.0] for x in iterable: add_to_partials(x) psum = sum(partials[1:], 0.0) if not partials[0]: # usual case return psum elif partials[0] == 1.0 and psum < 0.0: partials[0] -= 1.0 add_to_partials(twopow) add_to_partials(twopow) if partials[0] == 0.0: return sum(partials[1:], 0.0) elif partials[0] == -1.0 and psum > 0.0: partials[0] += 1.0 add_to_partials(-twopow) add_to_partials(-twopow) if partials[0] == 0.0: return sum(partials[1:], 0.0) if partials[0] > 0: return float('inf') else: return float('-inf') test_values = [ ([], 0.0), ([0.0], 0.0), ([1e100, 1.0, -1e100, 1e-100, 1e50, -1.0, -1e50], 1e-100), ([1e308, 1e308, -1e308], 1e308), ([-1e308, 1e308, 1e308], 1e308), ([1e308, -1e308, 1e308], 1e308), ([2.0**1023, 2.0**1023], float('inf')), ([2.0**1023, 2.0**1023, -1.0], float('inf')), ([2.0**1023, 2.0**1023, -2.0**1000], 1.7976930277114552e+308), ([twopow, twopow, twopow, twopow, -twopow, -twopow], float('inf')), ([twopow, twopow, twopow, twopow, -twopow, -twopow, -twopow], 8.9884656743115795e+307), ([2.0**53, -0.5, -2.0**-54], 2.0**53-1.0), ([2.0**1023-2.0**970, -1.0, 2.0**1023], 1.7976931348623157e+308), ([2.0**1023-2.0**970, 0.0, 2.0**1023], float('inf')), ([2.0**1023-2.0**970, 1.0, 2.0**1023], float('inf')), ] for i, (vals, s) in enumerate(test_values): assert msum(vals) == s, "Test %d failed." % i