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import platform
import pytest
import numpy as np
from numpy import uint16, float16, float32, float64
from numpy.testing import assert_, assert_equal, _OLD_PROMOTION, IS_WASM
def assert_raises_fpe(strmatch, callable, *args, **kwargs):
try:
callable(*args, **kwargs)
except FloatingPointError as exc:
assert_(str(exc).find(strmatch) >= 0,
"Did not raise floating point %s error" % strmatch)
else:
assert_(False,
"Did not raise floating point %s error" % strmatch)
class TestHalf:
def setup_method(self):
# An array of all possible float16 values
self.all_f16 = np.arange(0x10000, dtype=uint16)
self.all_f16.dtype = float16
self.all_f32 = np.array(self.all_f16, dtype=float32)
self.all_f64 = np.array(self.all_f16, dtype=float64)
# An array of all non-NaN float16 values, in sorted order
self.nonan_f16 = np.concatenate(
(np.arange(0xfc00, 0x7fff, -1, dtype=uint16),
np.arange(0x0000, 0x7c01, 1, dtype=uint16)))
self.nonan_f16.dtype = float16
self.nonan_f32 = np.array(self.nonan_f16, dtype=float32)
self.nonan_f64 = np.array(self.nonan_f16, dtype=float64)
# An array of all finite float16 values, in sorted order
self.finite_f16 = self.nonan_f16[1:-1]
self.finite_f32 = self.nonan_f32[1:-1]
self.finite_f64 = self.nonan_f64[1:-1]
def test_half_conversions(self):
"""Checks that all 16-bit values survive conversion
to/from 32-bit and 64-bit float"""
# Because the underlying routines preserve the NaN bits, every
# value is preserved when converting to/from other floats.
# Convert from float32 back to float16
b = np.array(self.all_f32, dtype=float16)
assert_equal(self.all_f16.view(dtype=uint16),
b.view(dtype=uint16))
# Convert from float64 back to float16
b = np.array(self.all_f64, dtype=float16)
assert_equal(self.all_f16.view(dtype=uint16),
b.view(dtype=uint16))
# Convert float16 to longdouble and back
# This doesn't necessarily preserve the extra NaN bits,
# so exclude NaNs.
a_ld = np.array(self.nonan_f16, dtype=np.longdouble)
b = np.array(a_ld, dtype=float16)
assert_equal(self.nonan_f16.view(dtype=uint16),
b.view(dtype=uint16))
# Check the range for which all integers can be represented
i_int = np.arange(-2048, 2049)
i_f16 = np.array(i_int, dtype=float16)
j = np.array(i_f16, dtype=int)
assert_equal(i_int, j)
@pytest.mark.parametrize("string_dt", ["S", "U"])
def test_half_conversion_to_string(self, string_dt):
# Currently uses S/U32 (which is sufficient for float32)
expected_dt = np.dtype(f"{string_dt}32")
assert np.promote_types(np.float16, string_dt) == expected_dt
assert np.promote_types(string_dt, np.float16) == expected_dt
arr = np.ones(3, dtype=np.float16).astype(string_dt)
assert arr.dtype == expected_dt
@pytest.mark.parametrize("string_dt", ["S", "U"])
def test_half_conversion_from_string(self, string_dt):
string = np.array("3.1416", dtype=string_dt)
assert string.astype(np.float16) == np.array(3.1416, dtype=np.float16)
@pytest.mark.parametrize("offset", [None, "up", "down"])
@pytest.mark.parametrize("shift", [None, "up", "down"])
@pytest.mark.parametrize("float_t", [np.float32, np.float64])
@np._no_nep50_warning()
def test_half_conversion_rounding(self, float_t, shift, offset):
# Assumes that round to even is used during casting.
max_pattern = np.float16(np.finfo(np.float16).max).view(np.uint16)
# Test all (positive) finite numbers, denormals are most interesting
# however:
f16s_patterns = np.arange(0, max_pattern+1, dtype=np.uint16)
f16s_float = f16s_patterns.view(np.float16).astype(float_t)
# Shift the values by half a bit up or a down (or do not shift),
if shift == "up":
f16s_float = 0.5 * (f16s_float[:-1] + f16s_float[1:])[1:]
elif shift == "down":
f16s_float = 0.5 * (f16s_float[:-1] + f16s_float[1:])[:-1]
else:
f16s_float = f16s_float[1:-1]
# Increase the float by a minimal value:
if offset == "up":
f16s_float = np.nextafter(f16s_float, float_t(np.inf))
elif offset == "down":
f16s_float = np.nextafter(f16s_float, float_t(-np.inf))
# Convert back to float16 and its bit pattern:
res_patterns = f16s_float.astype(np.float16).view(np.uint16)
# The above calculations tries the original values, or the exact
# mid points between the float16 values. It then further offsets them
# by as little as possible. If no offset occurs, "round to even"
# logic will be necessary, an arbitrarily small offset should cause
# normal up/down rounding always.
# Calculate the expected pattern:
cmp_patterns = f16s_patterns[1:-1].copy()
if shift == "down" and offset != "up":
shift_pattern = -1
elif shift == "up" and offset != "down":
shift_pattern = 1
else:
# There cannot be a shift, either shift is None, so all rounding
# will go back to original, or shift is reduced by offset too much.
shift_pattern = 0
# If rounding occurs, is it normal rounding or round to even?
if offset is None:
# Round to even occurs, modify only non-even, cast to allow + (-1)
cmp_patterns[0::2].view(np.int16)[...] += shift_pattern
else:
cmp_patterns.view(np.int16)[...] += shift_pattern
assert_equal(res_patterns, cmp_patterns)
@pytest.mark.parametrize(["float_t", "uint_t", "bits"],
[(np.float32, np.uint32, 23),
(np.float64, np.uint64, 52)])
def test_half_conversion_denormal_round_even(self, float_t, uint_t, bits):
# Test specifically that all bits are considered when deciding
# whether round to even should occur (i.e. no bits are lost at the
# end. Compare also gh-12721. The most bits can get lost for the
# smallest denormal:
smallest_value = np.uint16(1).view(np.float16).astype(float_t)
assert smallest_value == 2**-24
# Will be rounded to zero based on round to even rule:
rounded_to_zero = smallest_value / float_t(2)
assert rounded_to_zero.astype(np.float16) == 0
# The significand will be all 0 for the float_t, test that we do not
# lose the lower ones of these:
for i in range(bits):
# slightly increasing the value should make it round up:
larger_pattern = rounded_to_zero.view(uint_t) | uint_t(1 << i)
larger_value = larger_pattern.view(float_t)
assert larger_value.astype(np.float16) == smallest_value
def test_nans_infs(self):
with np.errstate(all='ignore'):
# Check some of the ufuncs
assert_equal(np.isnan(self.all_f16), np.isnan(self.all_f32))
assert_equal(np.isinf(self.all_f16), np.isinf(self.all_f32))
assert_equal(np.isfinite(self.all_f16), np.isfinite(self.all_f32))
assert_equal(np.signbit(self.all_f16), np.signbit(self.all_f32))
assert_equal(np.spacing(float16(65504)), np.inf)
# Check comparisons of all values with NaN
nan = float16(np.nan)
assert_(not (self.all_f16 == nan).any())
assert_(not (nan == self.all_f16).any())
assert_((self.all_f16 != nan).all())
assert_((nan != self.all_f16).all())
assert_(not (self.all_f16 < nan).any())
assert_(not (nan < self.all_f16).any())
assert_(not (self.all_f16 <= nan).any())
assert_(not (nan <= self.all_f16).any())
assert_(not (self.all_f16 > nan).any())
assert_(not (nan > self.all_f16).any())
assert_(not (self.all_f16 >= nan).any())
assert_(not (nan >= self.all_f16).any())
def test_half_values(self):
"""Confirms a small number of known half values"""
a = np.array([1.0, -1.0,
2.0, -2.0,
0.0999755859375, 0.333251953125, # 1/10, 1/3
65504, -65504, # Maximum magnitude
2.0**(-14), -2.0**(-14), # Minimum normal
2.0**(-24), -2.0**(-24), # Minimum subnormal
0, -1/1e1000, # Signed zeros
np.inf, -np.inf])
b = np.array([0x3c00, 0xbc00,
0x4000, 0xc000,
0x2e66, 0x3555,
0x7bff, 0xfbff,
0x0400, 0x8400,
0x0001, 0x8001,
0x0000, 0x8000,
0x7c00, 0xfc00], dtype=uint16)
b.dtype = float16
assert_equal(a, b)
def test_half_rounding(self):
"""Checks that rounding when converting to half is correct"""
a = np.array([2.0**-25 + 2.0**-35, # Rounds to minimum subnormal
2.0**-25, # Underflows to zero (nearest even mode)
2.0**-26, # Underflows to zero
1.0+2.0**-11 + 2.0**-16, # rounds to 1.0+2**(-10)
1.0+2.0**-11, # rounds to 1.0 (nearest even mode)
1.0+2.0**-12, # rounds to 1.0
65519, # rounds to 65504
65520], # rounds to inf
dtype=float64)
rounded = [2.0**-24,
0.0,
0.0,
1.0+2.0**(-10),
1.0,
1.0,
65504,
np.inf]
# Check float64->float16 rounding
with np.errstate(over="ignore"):
b = np.array(a, dtype=float16)
assert_equal(b, rounded)
# Check float32->float16 rounding
a = np.array(a, dtype=float32)
with np.errstate(over="ignore"):
b = np.array(a, dtype=float16)
assert_equal(b, rounded)
def test_half_correctness(self):
"""Take every finite float16, and check the casting functions with
a manual conversion."""
# Create an array of all finite float16s
a_bits = self.finite_f16.view(dtype=uint16)
# Convert to 64-bit float manually
a_sgn = (-1.0)**((a_bits & 0x8000) >> 15)
a_exp = np.array((a_bits & 0x7c00) >> 10, dtype=np.int32) - 15
a_man = (a_bits & 0x03ff) * 2.0**(-10)
# Implicit bit of normalized floats
a_man[a_exp != -15] += 1
# Denormalized exponent is -14
a_exp[a_exp == -15] = -14
a_manual = a_sgn * a_man * 2.0**a_exp
a32_fail = np.nonzero(self.finite_f32 != a_manual)[0]
if len(a32_fail) != 0:
bad_index = a32_fail[0]
assert_equal(self.finite_f32, a_manual,
"First non-equal is half value %x -> %g != %g" %
(self.finite_f16[bad_index],
self.finite_f32[bad_index],
a_manual[bad_index]))
a64_fail = np.nonzero(self.finite_f64 != a_manual)[0]
if len(a64_fail) != 0:
bad_index = a64_fail[0]
assert_equal(self.finite_f64, a_manual,
"First non-equal is half value %x -> %g != %g" %
(self.finite_f16[bad_index],
self.finite_f64[bad_index],
a_manual[bad_index]))
def test_half_ordering(self):
"""Make sure comparisons are working right"""
# All non-NaN float16 values in reverse order
a = self.nonan_f16[::-1].copy()
# 32-bit float copy
b = np.array(a, dtype=float32)
# Should sort the same
a.sort()
b.sort()
assert_equal(a, b)
# Comparisons should work
assert_((a[:-1] <= a[1:]).all())
assert_(not (a[:-1] > a[1:]).any())
assert_((a[1:] >= a[:-1]).all())
assert_(not (a[1:] < a[:-1]).any())
# All != except for +/-0
assert_equal(np.nonzero(a[:-1] < a[1:])[0].size, a.size-2)
assert_equal(np.nonzero(a[1:] > a[:-1])[0].size, a.size-2)
def test_half_funcs(self):
"""Test the various ArrFuncs"""
# fill
assert_equal(np.arange(10, dtype=float16),
np.arange(10, dtype=float32))
# fillwithscalar
a = np.zeros((5,), dtype=float16)
a.fill(1)
assert_equal(a, np.ones((5,), dtype=float16))
# nonzero and copyswap
a = np.array([0, 0, -1, -1/1e20, 0, 2.0**-24, 7.629e-6], dtype=float16)
assert_equal(a.nonzero()[0],
[2, 5, 6])
a = a.byteswap().newbyteorder()
assert_equal(a.nonzero()[0],
[2, 5, 6])
# dot
a = np.arange(0, 10, 0.5, dtype=float16)
b = np.ones((20,), dtype=float16)
assert_equal(np.dot(a, b),
95)
# argmax
a = np.array([0, -np.inf, -2, 0.5, 12.55, 7.3, 2.1, 12.4], dtype=float16)
assert_equal(a.argmax(),
4)
a = np.array([0, -np.inf, -2, np.inf, 12.55, np.nan, 2.1, 12.4], dtype=float16)
assert_equal(a.argmax(),
5)
# getitem
a = np.arange(10, dtype=float16)
for i in range(10):
assert_equal(a.item(i), i)
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)
hnan = np.array((np.nan,), 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])
assert_equal(np.nextafter(hinf, a_f16), a_f16[-1])
assert_equal(np.nextafter(-hinf, a_f16), -a_f16[-1])
assert_equal(np.nextafter(hinf, hinf), hinf)
assert_equal(np.nextafter(hinf, -hinf), a_f16[-1])
assert_equal(np.nextafter(-hinf, hinf), -a_f16[-1])
assert_equal(np.nextafter(-hinf, -hinf), -hinf)
assert_equal(np.nextafter(a_f16, hnan), hnan[0])
assert_equal(np.nextafter(hnan, a_f16), hnan[0])
assert_equal(np.nextafter(hnan, hnan), hnan)
assert_equal(np.nextafter(hinf, hnan), hnan)
assert_equal(np.nextafter(hnan, hinf), hnan)
# 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:])
assert_equal(np.nextafter(hinf, a_f16), -a_f16[-1])
assert_equal(np.nextafter(-hinf, a_f16), a_f16[-1])
assert_equal(np.nextafter(a_f16, hnan), hnan[0])
assert_equal(np.nextafter(hnan, a_f16), hnan[0])
def test_half_ufuncs(self):
"""Test the various ufuncs"""
a = np.array([0, 1, 2, 4, 2], dtype=float16)
b = np.array([-2, 5, 1, 4, 3], dtype=float16)
c = np.array([0, -1, -np.inf, np.nan, 6], dtype=float16)
assert_equal(np.add(a, b), [-2, 6, 3, 8, 5])
assert_equal(np.subtract(a, b), [2, -4, 1, 0, -1])
assert_equal(np.multiply(a, b), [0, 5, 2, 16, 6])
assert_equal(np.divide(a, b), [0, 0.199951171875, 2, 1, 0.66650390625])
assert_equal(np.equal(a, b), [False, False, False, True, False])
assert_equal(np.not_equal(a, b), [True, True, True, False, True])
assert_equal(np.less(a, b), [False, True, False, False, True])
assert_equal(np.less_equal(a, b), [False, True, False, True, True])
assert_equal(np.greater(a, b), [True, False, True, False, False])
assert_equal(np.greater_equal(a, b), [True, False, True, True, False])
assert_equal(np.logical_and(a, b), [False, True, True, True, True])
assert_equal(np.logical_or(a, b), [True, True, True, True, True])
assert_equal(np.logical_xor(a, b), [True, False, False, False, False])
assert_equal(np.logical_not(a), [True, False, False, False, False])
assert_equal(np.isnan(c), [False, False, False, True, False])
assert_equal(np.isinf(c), [False, False, True, False, False])
assert_equal(np.isfinite(c), [True, True, False, False, True])
assert_equal(np.signbit(b), [True, False, False, False, False])
assert_equal(np.copysign(b, a), [2, 5, 1, 4, 3])
assert_equal(np.maximum(a, b), [0, 5, 2, 4, 3])
x = np.maximum(b, c)
assert_(np.isnan(x[3]))
x[3] = 0
assert_equal(x, [0, 5, 1, 0, 6])
assert_equal(np.minimum(a, b), [-2, 1, 1, 4, 2])
x = np.minimum(b, c)
assert_(np.isnan(x[3]))
x[3] = 0
assert_equal(x, [-2, -1, -np.inf, 0, 3])
assert_equal(np.fmax(a, b), [0, 5, 2, 4, 3])
assert_equal(np.fmax(b, c), [0, 5, 1, 4, 6])
assert_equal(np.fmin(a, b), [-2, 1, 1, 4, 2])
assert_equal(np.fmin(b, c), [-2, -1, -np.inf, 4, 3])
assert_equal(np.floor_divide(a, b), [0, 0, 2, 1, 0])
assert_equal(np.remainder(a, b), [0, 1, 0, 0, 2])
assert_equal(np.divmod(a, b), ([0, 0, 2, 1, 0], [0, 1, 0, 0, 2]))
assert_equal(np.square(b), [4, 25, 1, 16, 9])
assert_equal(np.reciprocal(b), [-0.5, 0.199951171875, 1, 0.25, 0.333251953125])
assert_equal(np.ones_like(b), [1, 1, 1, 1, 1])
assert_equal(np.conjugate(b), b)
assert_equal(np.absolute(b), [2, 5, 1, 4, 3])
assert_equal(np.negative(b), [2, -5, -1, -4, -3])
assert_equal(np.positive(b), b)
assert_equal(np.sign(b), [-1, 1, 1, 1, 1])
assert_equal(np.modf(b), ([0, 0, 0, 0, 0], b))
assert_equal(np.frexp(b), ([-0.5, 0.625, 0.5, 0.5, 0.75], [2, 3, 1, 3, 2]))
assert_equal(np.ldexp(b, [0, 1, 2, 4, 2]), [-2, 10, 4, 64, 12])
@np._no_nep50_warning()
def test_half_coercion(self, weak_promotion):
"""Test that half gets coerced properly with the other types"""
a16 = np.array((1,), dtype=float16)
a32 = np.array((1,), dtype=float32)
b16 = float16(1)
b32 = float32(1)
assert np.power(a16, 2).dtype == float16
assert np.power(a16, 2.0).dtype == float16
assert np.power(a16, b16).dtype == float16
expected_dt = float32 if weak_promotion else float16
assert np.power(a16, b32).dtype == expected_dt
assert np.power(a16, a16).dtype == float16
assert np.power(a16, a32).dtype == float32
expected_dt = float16 if weak_promotion else float64
assert np.power(b16, 2).dtype == expected_dt
assert np.power(b16, 2.0).dtype == expected_dt
assert np.power(b16, b16).dtype, float16
assert np.power(b16, b32).dtype, float32
assert np.power(b16, a16).dtype, float16
assert np.power(b16, a32).dtype, float32
assert np.power(a32, a16).dtype == float32
assert np.power(a32, b16).dtype == float32
expected_dt = float32 if weak_promotion else float16
assert np.power(b32, a16).dtype == expected_dt
assert np.power(b32, b16).dtype == float32
@pytest.mark.skipif(platform.machine() == "armv5tel",
reason="See gh-413.")
@pytest.mark.skipif(IS_WASM,
reason="fp exceptions don't work in wasm.")
def test_half_fpe(self):
with np.errstate(all='raise'):
sx16 = np.array((1e-4,), dtype=float16)
bx16 = np.array((1e4,), dtype=float16)
sy16 = float16(1e-4)
by16 = float16(1e4)
# Underflow errors
assert_raises_fpe('underflow', lambda a, b:a*b, sx16, sx16)
assert_raises_fpe('underflow', lambda a, b:a*b, sx16, sy16)
assert_raises_fpe('underflow', lambda a, b:a*b, sy16, sx16)
assert_raises_fpe('underflow', lambda a, b:a*b, sy16, sy16)
assert_raises_fpe('underflow', lambda a, b:a/b, sx16, bx16)
assert_raises_fpe('underflow', lambda a, b:a/b, sx16, by16)
assert_raises_fpe('underflow', lambda a, b:a/b, sy16, bx16)
assert_raises_fpe('underflow', lambda a, b:a/b, sy16, by16)
assert_raises_fpe('underflow', lambda a, b:a/b,
float16(2.**-14), float16(2**11))
assert_raises_fpe('underflow', lambda a, b:a/b,
float16(-2.**-14), float16(2**11))
assert_raises_fpe('underflow', lambda a, b:a/b,
float16(2.**-14+2**-24), float16(2))
assert_raises_fpe('underflow', lambda a, b:a/b,
float16(-2.**-14-2**-24), float16(2))
assert_raises_fpe('underflow', lambda a, b:a/b,
float16(2.**-14+2**-23), float16(4))
# Overflow errors
assert_raises_fpe('overflow', lambda a, b:a*b, bx16, bx16)
assert_raises_fpe('overflow', lambda a, b:a*b, bx16, by16)
assert_raises_fpe('overflow', lambda a, b:a*b, by16, bx16)
assert_raises_fpe('overflow', lambda a, b:a*b, by16, by16)
assert_raises_fpe('overflow', lambda a, b:a/b, bx16, sx16)
assert_raises_fpe('overflow', lambda a, b:a/b, bx16, sy16)
assert_raises_fpe('overflow', lambda a, b:a/b, by16, sx16)
assert_raises_fpe('overflow', lambda a, b:a/b, by16, sy16)
assert_raises_fpe('overflow', lambda a, b:a+b,
float16(65504), float16(17))
assert_raises_fpe('overflow', lambda a, b:a-b,
float16(-65504), float16(17))
assert_raises_fpe('overflow', np.nextafter, float16(65504), float16(np.inf))
assert_raises_fpe('overflow', np.nextafter, float16(-65504), float16(-np.inf))
assert_raises_fpe('overflow', np.spacing, float16(65504))
# Invalid value errors
assert_raises_fpe('invalid', np.divide, float16(np.inf), float16(np.inf))
assert_raises_fpe('invalid', np.spacing, float16(np.inf))
assert_raises_fpe('invalid', np.spacing, float16(np.nan))
# These should not raise
float16(65472)+float16(32)
float16(2**-13)/float16(2)
float16(2**-14)/float16(2**10)
np.spacing(float16(-65504))
np.nextafter(float16(65504), float16(-np.inf))
np.nextafter(float16(-65504), float16(np.inf))
np.nextafter(float16(np.inf), float16(0))
np.nextafter(float16(-np.inf), float16(0))
np.nextafter(float16(0), float16(np.nan))
np.nextafter(float16(np.nan), float16(0))
float16(2**-14)/float16(2**10)
float16(-2**-14)/float16(2**10)
float16(2**-14+2**-23)/float16(2)
float16(-2**-14-2**-23)/float16(2)
def test_half_array_interface(self):
"""Test that half is compatible with __array_interface__"""
class Dummy:
pass
a = np.ones((1,), dtype=float16)
b = Dummy()
b.__array_interface__ = a.__array_interface__
c = np.array(b)
assert_(c.dtype == float16)
assert_equal(a, c)
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