Method testFsum

Lib/test/test_math.py:647–756

(self)

    @unittest.skipIf(HAVE_DOUBLE_ROUNDING,
                         "fsum is not exact on machines with double rounding")
    def testFsum(self):
        # math.fsum relies on exact rounding for correct operation.
        # There's a known problem with IA32 floating-point that causes
        # inexact rounding in some situations, and will cause the
        # math.fsum tests below to fail; see issue #2937.  On non IEEE
        # 754 platforms, and on IEEE 754 platforms that exhibit the
        # problem described in issue #2937, we simply skip the whole
        # test.

        # Python version of math.fsum, for comparison.  Uses a
        # different algorithm based on frexp, ldexp and integer
        # arithmetic.
        from sys import float_info
        mant_dig = float_info.mant_dig
        etiny = float_info.min_exp - mant_dig

        def msum(iterable):
            """Full precision summation.  Compute sum(iterable) without any
            intermediate accumulation of error.  Based on the 'lsum' function
            at https://code.activestate.com/recipes/393090-binary-floating-point-summation-accurate-to-full-p/

            """
            tmant, texp = 0, 0
            for x in iterable:
                mant, exp = math.frexp(x)
                mant, exp = int(math.ldexp(mant, mant_dig)), exp - mant_dig
                if texp > exp:
                    tmant <<= texp-exp
                    texp = exp
                else:
                    mant <<= exp-texp
                tmant += mant
            # Round tmant * 2**texp to a float.  The original recipe
            # used float(str(tmant)) * 2.0**texp for this, but that's
            # a little unsafe because str -> float conversion can't be
            # relied upon to do correct rounding on all platforms.
            tail = max(len(bin(abs(tmant)))-2 - mant_dig, etiny - texp)
            if tail > 0:
                h = 1 << (tail-1)
                tmant = tmant // (2*h) + bool(tmant & h and tmant & 3*h-1)
                texp += tail
            return math.ldexp(tmant, texp)

        test_values = [
            ([], 0.0),
            ([0.0], 0.0),
            ([1e100, 1.0, -1e100, 1e-100, 1e50, -1.0, -1e50], 1e-100),
            ([1e100, 1.0, -1e100, 1e-100, 1e50, -1, -1e50], 1e-100),
            ([2.0**53, -0.5, -2.0**-54], 2.0**53-1.0),
            ([2.0**53, 1.0, 2.0**-100], 2.0**53+2.0),
            ([2.0**53+10.0, 1.0, 2.0**-100], 2.0**53+12.0),
            ([2.0**53-4.0, 0.5, 2.0**-54], 2.0**53-3.0),
            ([1./n for n in range(1, 1001)],
             float.fromhex('0x1.df11f45f4e61ap+2')),
            ([(-1.)**n/n for n in range(1, 1001)],
             float.fromhex('-0x1.62a2af1bd3624p-1')),
            ([1e16, 1., 1e-16], 10000000000000002.0),
            ([1e16-2., 1.-2.**-53, -(1e16-2.), -(1.-2.**-53)], 0.0),