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test_half.py
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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