I use up-to-date Debian testing (wheezy), amd64 architecture. From the docs for numpy.MachAr: maxexp int Smallest (positive) power of ibeta that causes overflow. On my machine, ibeta = 2 and maxexp = 16384. For float64, float32, and float16 things behave as expected. For float128, I get the message about overflow for exponent 8192 (and greater) but the correct answer is printed. What is the problem? #! /usr/bin/env python3.2 import numpy print('float128') fi = numpy.finfo(numpy.float128) print('ibeta:', fi.machar.ibeta) # 2 print('maxexp:', fi.machar.maxexp) # 16384 print('xmax:', fi.machar.xmax) # 1.18973149536e+4932 two = numpy.float128(2) big = numpy.float128(8191) x = numpy.power(two, big) print('2**8191:', x) # 5.4537406781e+2465 big = numpy.float128(8192) # RuntimeWarning: overflow encountered in power x = numpy.power(two, big) print('2**8192:', x) # 1.09074813562e+2466