Python numpy.nextafter() Examples

def test_spacing_nextafter(self):
        """Test np.spacing and np.nextafter"""
        # All non-negative finite #'s
        a = np.arange(0x7c00, dtype=uint16)
        hinf = np.array((np.inf,), dtype=float16)
        a_f16 = a.view(dtype=float16)

        assert_equal(np.spacing(a_f16[:-1]), a_f16[1:]-a_f16[:-1])

        assert_equal(np.nextafter(a_f16[:-1], hinf), a_f16[1:])
        assert_equal(np.nextafter(a_f16[0], -hinf), -a_f16[1])
        assert_equal(np.nextafter(a_f16[1:], -hinf), a_f16[:-1])

        # switch to negatives
        a |= 0x8000

        assert_equal(np.spacing(a_f16[0]), np.spacing(a_f16[1]))
        assert_equal(np.spacing(a_f16[1:]), a_f16[:-1]-a_f16[1:])

        assert_equal(np.nextafter(a_f16[0], hinf), -a_f16[1])
        assert_equal(np.nextafter(a_f16[1:], hinf), a_f16[:-1])
        assert_equal(np.nextafter(a_f16[:-1], -hinf), a_f16[1:]) 

def _sample(self, n_samples):
        # samples must be sampled from (-1, 1) rather than [-1, 1)
        loc, scale = self.loc, self.scale
        if not self.is_reparameterized:
            loc = tf.stop_gradient(loc)
            scale = tf.stop_gradient(scale)
        shape = tf.concat([[n_samples], self.batch_shape], 0)
        uniform_samples = tf.random_uniform(
            shape=shape,
            minval=np.nextafter(self.dtype.as_numpy_dtype(-1.),
                                self.dtype.as_numpy_dtype(0.)),
            maxval=1.,
            dtype=self.dtype)
        samples = loc - scale * tf.sign(uniform_samples) * \
            tf.log1p(-tf.abs(uniform_samples))
        static_n_samples = n_samples if isinstance(n_samples, int) else None
        samples.set_shape(
            tf.TensorShape([static_n_samples]).concatenate(
                self.get_batch_shape()))
        return samples 

def make_strictly_feasible(x, lb, ub, rstep=1e-10):
    """Shift a point to the interior of a feasible region.
    
    Each element of the returned vector is at least at a relative distance
    `rstep` from the closest bound. If ``rstep=0`` then `np.nextafter` is used.
    """
    x_new = x.copy()

    active = find_active_constraints(x, lb, ub, rstep)
    lower_mask = np.equal(active, -1)
    upper_mask = np.equal(active, 1)

    if rstep == 0:
        x_new[lower_mask] = np.nextafter(lb[lower_mask], ub[lower_mask])
        x_new[upper_mask] = np.nextafter(ub[upper_mask], lb[upper_mask])
    else:
        x_new[lower_mask] = (lb[lower_mask] +
                             rstep * np.maximum(1, np.abs(lb[lower_mask])))
        x_new[upper_mask] = (ub[upper_mask] -
                             rstep * np.maximum(1, np.abs(ub[upper_mask])))

    tight_bounds = (x_new < lb) | (x_new > ub)
    x_new[tight_bounds] = 0.5 * (lb[tight_bounds] + ub[tight_bounds])

    return x_new 

def _sample_n(self, n, seed=None):
    shape = array_ops.concat([[n], array_ops.shape(self._rate)], 0)
    # Uniform variates must be sampled from the open-interval `(0, 1)` rather
    # than `[0, 1)`. To do so, we use `np.finfo(self.dtype.as_numpy_dtype).tiny`
    # because it is the smallest, positive, "normal" number. A "normal" number
    # is such that the mantissa has an implicit leading 1. Normal, positive
    # numbers x, y have the reasonable property that, `x + y >= max(x, y)`. In
    # this case, a subnormal number (i.e., np.nextafter) can cause us to sample
    # 0.
    sampled = random_ops.random_uniform(
        shape,
        minval=np.finfo(self.dtype.as_numpy_dtype).tiny,
        maxval=1.,
        seed=seed,
        dtype=self.dtype)
    return -math_ops.log(sampled) / self._rate 

def _sample_n(self, n, seed=None):
    shape = array_ops.concat([[n], self.batch_shape_tensor()], 0)
    # Uniform variates must be sampled from the open-interval `(-1, 1)` rather
    # than `[-1, 1)`. In the case of `(0, 1)` we'd use
    # `np.finfo(self.dtype.as_numpy_dtype).tiny` because it is the smallest,
    # positive, "normal" number. However, the concept of subnormality exists
    # only at zero; here we need the smallest usable number larger than -1,
    # i.e., `-1 + eps/2`.
    uniform_samples = random_ops.random_uniform(
        shape=shape,
        minval=np.nextafter(self.dtype.as_numpy_dtype(-1.),
                            self.dtype.as_numpy_dtype(0.)),
        maxval=1.,
        dtype=self.dtype,
        seed=seed)
    return (self.loc - self.scale * math_ops.sign(uniform_samples) *
            math_ops.log1p(-math_ops.abs(uniform_samples))) 

def _sample_n(self, n, seed=None):
    # Uniform variates must be sampled from the open-interval `(0, 1)` rather
    # than `[0, 1)`. To do so, we use `np.finfo(self.dtype.as_numpy_dtype).tiny`
    # because it is the smallest, positive, "normal" number. A "normal" number
    # is such that the mantissa has an implicit leading 1. Normal, positive
    # numbers x, y have the reasonable property that, `x + y >= max(x, y)`. In
    # this case, a subnormal number (i.e., np.nextafter) can cause us to sample
    # 0.
    uniform = random_ops.random_uniform(
        shape=array_ops.concat([[n], self.batch_shape_tensor()], 0),
        minval=np.finfo(self.dtype.as_numpy_dtype).tiny,
        maxval=1.,
        dtype=self.dtype,
        seed=seed)
    sampled = math_ops.log(uniform) - math_ops.log1p(-1. * uniform)
    return sampled * self.scale + self.loc 

def _sample_n(self, n, seed=None):
    # Uniform variates must be sampled from the open-interval `(0, 1)` rather
    # than `[0, 1)`. To do so, we use `np.finfo(self.dtype.as_numpy_dtype).tiny`
    # because it is the smallest, positive, "normal" number. A "normal" number
    # is such that the mantissa has an implicit leading 1. Normal, positive
    # numbers x, y have the reasonable property that, `x + y >= max(x, y)`. In
    # this case, a subnormal number (i.e., np.nextafter) can cause us to sample
    # 0.
    uniform = random_ops.random_uniform(
        shape=array_ops.concat([[n], self.batch_shape_tensor()], 0),
        minval=np.finfo(self.dtype.as_numpy_dtype).tiny,
        maxval=1.,
        dtype=self.dtype,
        seed=seed)
    sampled = -math_ops.log(-math_ops.log(uniform))
    return sampled * self.scale + self.loc 

def _sample_n(self, n, seed=None):
    sample_shape = array_ops.concat([[n], array_ops.shape(self.logits)], 0)
    logits = self.logits * array_ops.ones(sample_shape)
    logits_2d = array_ops.reshape(logits, [-1, self.event_size])
    # Uniform variates must be sampled from the open-interval `(0, 1)` rather
    # than `[0, 1)`. To do so, we use `np.finfo(self.dtype.as_numpy_dtype).tiny`
    # because it is the smallest, positive, "normal" number. A "normal" number
    # is such that the mantissa has an implicit leading 1. Normal, positive
    # numbers x, y have the reasonable property that, `x + y >= max(x, y)`. In
    # this case, a subnormal number (i.e., np.nextafter) can cause us to sample
    # 0.
    uniform = random_ops.random_uniform(
        shape=array_ops.shape(logits_2d),
        minval=np.finfo(self.dtype.as_numpy_dtype).tiny,
        maxval=1.,
        dtype=self.dtype,
        seed=seed)
    gumbel = -math_ops.log(-math_ops.log(uniform))
    noisy_logits = math_ops.div(gumbel + logits_2d, self._temperature_2d)
    samples = nn_ops.log_softmax(noisy_logits)
    ret = array_ops.reshape(samples, sample_shape)
    return ret 

def test_spacing_nextafter(self):
        """Test np.spacing and np.nextafter"""
        # All non-negative finite #'s
        a = np.arange(0x7c00, dtype=uint16)
        hinf = np.array((np.inf,), dtype=float16)
        a_f16 = a.view(dtype=float16)

        assert_equal(np.spacing(a_f16[:-1]), a_f16[1:]-a_f16[:-1])

        assert_equal(np.nextafter(a_f16[:-1], hinf), a_f16[1:])
        assert_equal(np.nextafter(a_f16[0], -hinf), -a_f16[1])
        assert_equal(np.nextafter(a_f16[1:], -hinf), a_f16[:-1])

        # switch to negatives
        a |= 0x8000

        assert_equal(np.spacing(a_f16[0]), np.spacing(a_f16[1]))
        assert_equal(np.spacing(a_f16[1:]), a_f16[:-1]-a_f16[1:])

        assert_equal(np.nextafter(a_f16[0], hinf), -a_f16[1])
        assert_equal(np.nextafter(a_f16[1:], hinf), a_f16[:-1])
        assert_equal(np.nextafter(a_f16[:-1], -hinf), a_f16[1:]) 

def _sample_n(self, n, seed=None):
    sample_shape = array_ops.concat(([n], array_ops.shape(self.logits)), 0)
    logits = self.logits * array_ops.ones(sample_shape)
    if logits.get_shape().ndims == 2:
      logits_2d = logits
    else:
      logits_2d = array_ops.reshape(logits, [-1, self.num_classes])
    np_dtype = self.dtype.as_numpy_dtype()
    minval = np.nextafter(np_dtype(0), np_dtype(1))
    uniform = random_ops.random_uniform(shape=array_ops.shape(logits_2d),
                                        minval=minval,
                                        maxval=1,
                                        dtype=self.dtype,
                                        seed=seed)
    gumbel = - math_ops.log(- math_ops.log(uniform))
    noisy_logits = math_ops.div(gumbel + logits_2d, self.temperature)
    samples = nn_ops.log_softmax(noisy_logits)
    ret = array_ops.reshape(samples, sample_shape)
    return ret 

def test_spacing_nextafter(self):
        """Test np.spacing and np.nextafter"""
        # All non-negative finite #'s
        a = np.arange(0x7c00, dtype=uint16)
        hinf = np.array((np.inf,), dtype=float16)
        a_f16 = a.view(dtype=float16)

        assert_equal(np.spacing(a_f16[:-1]), a_f16[1:]-a_f16[:-1])

        assert_equal(np.nextafter(a_f16[:-1], hinf), a_f16[1:])
        assert_equal(np.nextafter(a_f16[0], -hinf), -a_f16[1])
        assert_equal(np.nextafter(a_f16[1:], -hinf), a_f16[:-1])

        # switch to negatives
        a |= 0x8000

        assert_equal(np.spacing(a_f16[0]), np.spacing(a_f16[1]))
        assert_equal(np.spacing(a_f16[1:]), a_f16[:-1]-a_f16[1:])

        assert_equal(np.nextafter(a_f16[0], hinf), -a_f16[1])
        assert_equal(np.nextafter(a_f16[1:], hinf), a_f16[:-1])
        assert_equal(np.nextafter(a_f16[:-1], -hinf), a_f16[1:]) 

def _predict_prob(self, params, exog, exog_infl, exposure, offset):
        params_infl = params[:self.k_inflate]
        params_main = params[self.k_inflate:]

        p = self.model_main.parameterization
        counts = np.atleast_2d(np.arange(0, np.max(self.endog)+1))

        if len(exog_infl.shape) < 2:
            transform = True
            w = np.atleast_2d(
                self.model_infl.predict(params_infl, exog_infl))[:, None]
        else:
            transform = False
            w = self.model_infl.predict(params_infl, exog_infl)[:, None]

        w[w == 1.] = np.nextafter(1, 0)
        mu = self.model_main.predict(params_main, exog,
            exposure=exposure, offset=offset)[:, None]
        result = self.distribution.pmf(counts, mu, params_main[-1], p, w)
        return result[0] if transform else result 

def test_spacing_nextafter(self):
        """Test np.spacing and np.nextafter"""
        # All non-negative finite #'s
        a = np.arange(0x7c00, dtype=uint16)
        hinf = np.array((np.inf,), dtype=float16)
        a_f16 = a.view(dtype=float16)

        assert_equal(np.spacing(a_f16[:-1]), a_f16[1:]-a_f16[:-1])

        assert_equal(np.nextafter(a_f16[:-1], hinf), a_f16[1:])
        assert_equal(np.nextafter(a_f16[0], -hinf), -a_f16[1])
        assert_equal(np.nextafter(a_f16[1:], -hinf), a_f16[:-1])

        # switch to negatives
        a |= 0x8000

        assert_equal(np.spacing(a_f16[0]), np.spacing(a_f16[1]))
        assert_equal(np.spacing(a_f16[1:]), a_f16[:-1]-a_f16[1:])

        assert_equal(np.nextafter(a_f16[0], hinf), -a_f16[1])
        assert_equal(np.nextafter(a_f16[1:], hinf), a_f16[:-1])
        assert_equal(np.nextafter(a_f16[:-1], -hinf), a_f16[1:]) 

def test_spacing_nextafter(self):
        """Test np.spacing and np.nextafter"""
        # All non-negative finite #'s
        a = np.arange(0x7c00, dtype=uint16)
        hinf = np.array((np.inf,), dtype=float16)
        a_f16 = a.view(dtype=float16)

        assert_equal(np.spacing(a_f16[:-1]), a_f16[1:]-a_f16[:-1])

        assert_equal(np.nextafter(a_f16[:-1], hinf), a_f16[1:])
        assert_equal(np.nextafter(a_f16[0], -hinf), -a_f16[1])
        assert_equal(np.nextafter(a_f16[1:], -hinf), a_f16[:-1])

        # switch to negatives
        a |= 0x8000

        assert_equal(np.spacing(a_f16[0]), np.spacing(a_f16[1]))
        assert_equal(np.spacing(a_f16[1:]), a_f16[:-1]-a_f16[1:])

        assert_equal(np.nextafter(a_f16[0], hinf), -a_f16[1])
        assert_equal(np.nextafter(a_f16[1:], hinf), a_f16[:-1])
        assert_equal(np.nextafter(a_f16[:-1], -hinf), a_f16[1:]) 

def test_spacing_nextafter(self):
        """Test np.spacing and np.nextafter"""
        # All non-negative finite #'s
        a = np.arange(0x7c00, dtype=uint16)
        hinf = np.array((np.inf,), dtype=float16)
        a_f16 = a.view(dtype=float16)

        assert_equal(np.spacing(a_f16[:-1]), a_f16[1:]-a_f16[:-1])

        assert_equal(np.nextafter(a_f16[:-1], hinf), a_f16[1:])
        assert_equal(np.nextafter(a_f16[0], -hinf), -a_f16[1])
        assert_equal(np.nextafter(a_f16[1:], -hinf), a_f16[:-1])

        # switch to negatives
        a |= 0x8000

        assert_equal(np.spacing(a_f16[0]), np.spacing(a_f16[1]))
        assert_equal(np.spacing(a_f16[1:]), a_f16[:-1]-a_f16[1:])

        assert_equal(np.nextafter(a_f16[0], hinf), -a_f16[1])
        assert_equal(np.nextafter(a_f16[1:], hinf), a_f16[:-1])
        assert_equal(np.nextafter(a_f16[:-1], -hinf), a_f16[1:]) 

def test_wrightomega_branch():
    x = -np.logspace(10, 0, 25)
    picut_above = [np.nextafter(np.pi, np.inf)]
    picut_below = [np.nextafter(np.pi, -np.inf)]
    npicut_above = [np.nextafter(-np.pi, np.inf)]
    npicut_below = [np.nextafter(-np.pi, -np.inf)]
    for i in range(50):
        picut_above.append(np.nextafter(picut_above[-1], np.inf))
        picut_below.append(np.nextafter(picut_below[-1], -np.inf))
        npicut_above.append(np.nextafter(npicut_above[-1], np.inf))
        npicut_below.append(np.nextafter(npicut_below[-1], -np.inf))
    y = np.hstack((picut_above, picut_below, npicut_above, npicut_below))
    x, y = np.meshgrid(x, y)
    z = (x + 1j*y).flatten()

    dataset = []
    for z0 in z:
        dataset.append((z0, complex(_mpmath_wrightomega(z0, 25))))
    dataset = np.asarray(dataset)

    FuncData(sc.wrightomega, dataset, 0, 1, rtol=1e-8).check() 

def test_spacing_nextafter(self):
        """Test np.spacing and np.nextafter"""
        # All non-negative finite #'s
        a = np.arange(0x7c00, dtype=uint16)
        hinf = np.array((np.inf,), dtype=float16)
        a_f16 = a.view(dtype=float16)

        assert_equal(np.spacing(a_f16[:-1]), a_f16[1:]-a_f16[:-1])

        assert_equal(np.nextafter(a_f16[:-1], hinf), a_f16[1:])
        assert_equal(np.nextafter(a_f16[0], -hinf), -a_f16[1])
        assert_equal(np.nextafter(a_f16[1:], -hinf), a_f16[:-1])

        # switch to negatives
        a |= 0x8000

        assert_equal(np.spacing(a_f16[0]), np.spacing(a_f16[1]))
        assert_equal(np.spacing(a_f16[1:]), a_f16[:-1]-a_f16[1:])

        assert_equal(np.nextafter(a_f16[0], hinf), -a_f16[1])
        assert_equal(np.nextafter(a_f16[1:], hinf), a_f16[:-1])
        assert_equal(np.nextafter(a_f16[:-1], -hinf), a_f16[1:]) 

def test_uniform_range_bounds(self):
        fmin = np.finfo('float').min
        fmax = np.finfo('float').max

        func = np.random.uniform
        assert_raises(OverflowError, func, -np.inf, 0)
        assert_raises(OverflowError, func,  0,      np.inf)
        assert_raises(OverflowError, func,  fmin,   fmax)
        assert_raises(OverflowError, func, [-np.inf], [0])
        assert_raises(OverflowError, func, [0], [np.inf])

        # (fmax / 1e17) - fmin is within range, so this should not throw
        # account for i386 extended precision DBL_MAX / 1e17 + DBL_MAX >
        # DBL_MAX by increasing fmin a bit
        np.random.uniform(low=np.nextafter(fmin, 1), high=fmax / 1e17) 

def test_float_remainder_corner_cases(self):
        # Check remainder magnitude.
        for dt in np.typecodes['Float']:
            b = np.array(1.0, dtype=dt)
            a = np.nextafter(np.array(0.0, dtype=dt), -b)
            rem = np.remainder(a, b)
            assert_(rem <= b, 'dt: %s' % dt)
            rem = np.remainder(-a, -b)
            assert_(rem >= -b, 'dt: %s' % dt)

        # Check nans, inf
        with suppress_warnings() as sup:
            sup.filter(RuntimeWarning, "invalid value encountered in remainder")
            for dt in np.typecodes['Float']:
                fone = np.array(1.0, dtype=dt)
                fzer = np.array(0.0, dtype=dt)
                finf = np.array(np.inf, dtype=dt)
                fnan = np.array(np.nan, dtype=dt)
                rem = np.remainder(fone, fzer)
                assert_(np.isnan(rem), 'dt: %s, rem: %s' % (dt, rem))
                # MSVC 2008 returns NaN here, so disable the check.
                #rem = np.remainder(fone, finf)
                #assert_(rem == fone, 'dt: %s, rem: %s' % (dt, rem))
                rem = np.remainder(fone, fnan)
                assert_(np.isnan(rem), 'dt: %s, rem: %s' % (dt, rem))
                rem = np.remainder(finf, fone)
                assert_(np.isnan(rem), 'dt: %s, rem: %s' % (dt, rem)) 

def _test_nextafter(t):
    one = t(1)
    two = t(2)
    zero = t(0)
    eps = np.finfo(t).eps
    assert_(np.nextafter(one, two) - one == eps)
    assert_(np.nextafter(one, zero) - one < 0)
    assert_(np.isnan(np.nextafter(np.nan, one)))
    assert_(np.isnan(np.nextafter(one, np.nan)))
    assert_(np.nextafter(one, one) == one) 

def test_nextafter_vs_spacing():
    # XXX: spacing does not handle long double yet
    for t in [np.float32, np.float64]:
        for _f in [1, 1e-5, 1000]:
            f = t(_f)
            f1 = t(_f + 1)
            assert_(np.nextafter(f, f1) - f == np.spacing(f)) 

def test_float_modulus_corner_cases(self):
        # Check remainder magnitude.
        for dt in np.typecodes['Float']:
            b = np.array(1.0, dtype=dt)
            a = np.nextafter(np.array(0.0, dtype=dt), -b)
            rem = operator.mod(a, b)
            assert_(rem <= b, 'dt: %s' % dt)
            rem = operator.mod(-a, -b)
            assert_(rem >= -b, 'dt: %s' % dt)

        # Check nans, inf
        with suppress_warnings() as sup:
            sup.filter(RuntimeWarning, "invalid value encountered in remainder")
            for dt in np.typecodes['Float']:
                fone = np.array(1.0, dtype=dt)
                fzer = np.array(0.0, dtype=dt)
                finf = np.array(np.inf, dtype=dt)
                fnan = np.array(np.nan, dtype=dt)
                rem = operator.mod(fone, fzer)
                assert_(np.isnan(rem), 'dt: %s' % dt)
                # MSVC 2008 returns NaN here, so disable the check.
                #rem = operator.mod(fone, finf)
                #assert_(rem == fone, 'dt: %s' % dt)
                rem = operator.mod(fone, fnan)
                assert_(np.isnan(rem), 'dt: %s' % dt)
                rem = operator.mod(finf, fone)
                assert_(np.isnan(rem), 'dt: %s' % dt) 

def test_boundary_float(self, nselect_method, float_dtype):
        # GH 21426
        dtype_info = np.finfo(float_dtype)
        min_val, max_val = dtype_info.min, dtype_info.max
        min_2nd, max_2nd = np.nextafter(
            [min_val, max_val], 0, dtype=float_dtype)
        vals = [min_val, min_2nd, max_2nd, max_val]
        assert_check_nselect_boundary(vals, float_dtype, nselect_method) 

def _get_next_label(label):
    dtype = getattr(label, 'dtype', type(label))
    if isinstance(label, (Timestamp, Timedelta)):
        dtype = 'datetime64'
    if is_datetime_or_timedelta_dtype(dtype) or is_datetime64tz_dtype(dtype):
        return label + np.timedelta64(1, 'ns')
    elif is_integer_dtype(dtype):
        return label + 1
    elif is_float_dtype(dtype):
        return np.nextafter(label, np.infty)
    else:
        raise TypeError('cannot determine next label for type {typ!r}'
                        .format(typ=type(label))) 

def _get_prev_label(label):
    dtype = getattr(label, 'dtype', type(label))
    if isinstance(label, (Timestamp, Timedelta)):
        dtype = 'datetime64'
    if is_datetime_or_timedelta_dtype(dtype) or is_datetime64tz_dtype(dtype):
        return label - np.timedelta64(1, 'ns')
    elif is_integer_dtype(dtype):
        return label - 1
    elif is_float_dtype(dtype):
        return np.nextafter(label, -np.infty)
    else:
        raise TypeError('cannot determine next label for type {typ!r}'
                        .format(typ=type(label))) 

def nextafter(x1, x2, out=None, where=None, **kwargs):
    """
    Return the next floating-point value after x1 towards x2, element-wise.

    Parameters
    ----------
    x1 : array_like
        Values to find the next representable value of.
    x2 : array_like
        The direction where to look for the next representable value of `x1`.
    out : Tensor, None, or tuple of Tensor and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or `None`,
        a freshly-allocated tensor is returned. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.
    where : array_like, optional
        Values of True indicate to calculate the ufunc at that position, values
        of False indicate to leave the value in the output alone.
    **kwargs

    Returns
    -------
    out : array_like
        The next representable values of `x1` in the direction of `x2`.

    Examples
    --------
    >>> import mars.tensor as mt

    >>> eps = mt.finfo(mt.float64).eps
    >>> (mt.nextafter(1, 2) == eps + 1).execute()
    True
    >>> (mt.nextafter([1, 2], [2, 1]) == [eps + 1, 2 - eps]).execute()
    array([ True,  True])
    """
    op = TensorNextafter(**kwargs)
    return op(x1, x2, out=out, where=where) 

def test_float_remainder_corner_cases(self):
        # Check remainder magnitude.
        for dt in np.typecodes['Float']:
            b = np.array(1.0, dtype=dt)
            a = np.nextafter(np.array(0.0, dtype=dt), -b)
            rem = np.remainder(a, b)
            assert_(rem <= b, 'dt: %s' % dt)
            rem = np.remainder(-a, -b)
            assert_(rem >= -b, 'dt: %s' % dt)

        # Check nans, inf
        with warnings.catch_warnings():
            warnings.simplefilter('always')
            warnings.simplefilter('ignore', RuntimeWarning)
            for dt in np.typecodes['Float']:
                fone = np.array(1.0, dtype=dt)
                fzer = np.array(0.0, dtype=dt)
                finf = np.array(np.inf, dtype=dt)
                fnan = np.array(np.nan, dtype=dt)
                rem = np.remainder(fone, fzer)
                assert_(np.isnan(rem), 'dt: %s, rem: %s' % (dt, rem))
                # MSVC 2008 returns NaN here, so disable the check.
                #rem = np.remainder(fone, finf)
                #assert_(rem == fone, 'dt: %s, rem: %s' % (dt, rem))
                rem = np.remainder(fone, fnan)
                assert_(np.isnan(rem), 'dt: %s, rem: %s' % (dt, rem))
                rem = np.remainder(finf, fone)
                assert_(np.isnan(rem), 'dt: %s, rem: %s' % (dt, rem)) 

def _test_nextafter(t):
    one = t(1)
    two = t(2)
    zero = t(0)
    eps = np.finfo(t).eps
    assert_(np.nextafter(one, two) - one == eps)
    assert_(np.nextafter(one, zero) - one < 0)
    assert_(np.isnan(np.nextafter(np.nan, one)))
    assert_(np.isnan(np.nextafter(one, np.nan)))
    assert_(np.nextafter(one, one) == one) 

def test_nextafter_vs_spacing():
    # XXX: spacing does not handle long double yet
    for t in [np.float32, np.float64]:
        for _f in [1, 1e-5, 1000]:
            f = t(_f)
            f1 = t(_f + 1)
            assert_(np.nextafter(f, f1) - f == np.spacing(f)) 

def test_float_modulus_corner_cases(self):
        # Check remainder magnitude.
        for dt in np.typecodes['Float']:
            b = np.array(1.0, dtype=dt)
            a = np.nextafter(np.array(0.0, dtype=dt), -b)
            rem = self.mod(a, b)
            assert_(rem <= b, 'dt: %s' % dt)
            rem = self.mod(-a, -b)
            assert_(rem >= -b, 'dt: %s' % dt)

        # Check nans, inf
        with warnings.catch_warnings():
            warnings.simplefilter('always')
            warnings.simplefilter('ignore', RuntimeWarning)
            for dt in np.typecodes['Float']:
                fone = np.array(1.0, dtype=dt)
                fzer = np.array(0.0, dtype=dt)
                finf = np.array(np.inf, dtype=dt)
                fnan = np.array(np.nan, dtype=dt)
                rem = self.mod(fone, fzer)
                assert_(np.isnan(rem), 'dt: %s' % dt)
                # MSVC 2008 returns NaN here, so disable the check.
                #rem = self.mod(fone, finf)
                #assert_(rem == fone, 'dt: %s' % dt)
                rem = self.mod(fone, fnan)
                assert_(np.isnan(rem), 'dt: %s' % dt)
                rem = self.mod(finf, fone)
                assert_(np.isnan(rem), 'dt: %s' % dt)