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# Copyright (c) 2024 Graphcore Ltd. All rights reserved.
from typing import Type
import ml_dtypes
import numpy as np
import pytest
from gfloat import RoundMode, decode_float, round_float
from gfloat.formats import *
def test_round_p3109() -> None:
fi = format_info_p3109(4)
assert round_float(fi, 0.0068359375) == 0.0068359375
assert round_float(fi, 0.0029296875) == 0.0029296875
assert round_float(fi, 0.0078125) == 0.0078125
assert round_float(fi, 0.017578125) == 0.017578125
assert round_float(fi, 224.0) == 224.0
assert round_float(fi, 240.0) == np.inf
assert round_float(fi, 224.1, RoundMode.TowardPositive) == np.inf
assert round_float(fi, 232.0) == 224.0
assert round_float(fi, 232.0, RoundMode.TiesToAway) == np.inf
assert round_float(fi, 232.0, RoundMode.TowardZero) == 224.0
assert round_float(fi, 232.0, RoundMode.TowardNegative) == 224.0
assert round_float(fi, 232.0, RoundMode.TowardPositive) == np.inf
assert round_float(fi, -232.0) == -224.0
assert round_float(fi, -232.0, RoundMode.TiesToAway) == -np.inf
assert round_float(fi, -232.0, RoundMode.TowardZero) == -224.0
assert round_float(fi, -232.0, RoundMode.TowardNegative) == -np.inf
assert round_float(fi, -232.0, RoundMode.TowardPositive) == -224.0
assert round_float(fi, 232.1) == np.inf
p4min = 2**-10 # smallest subnormal in p4
@pytest.mark.parametrize(
"mode, vals",
(
(
RoundMode.TowardZero,
(
(p4min, p4min),
(p4min / 4, 0.0),
(p4min / 2, 0.0),
(-p4min, -p4min),
(-p4min / 4, 0.0),
(-p4min / 2, 0.0),
(64.0, 64.0),
(63.0, 60.0),
(62.0, 60.0),
(-64.0, -64.0),
(-63.0, -60.0),
(-62.0, -60.0),
),
),
(
RoundMode.TowardPositive,
(
(p4min, p4min),
(p4min / 4, p4min),
(p4min / 2, p4min),
(-p4min, -p4min),
(-p4min / 4, 0.0),
(-p4min / 2, 0.0),
(64.0, 64.0),
(63.0, 64.0),
(62.0, 64.0),
(-64.0, -64.0),
(-63.0, -60.0),
(-62.0, -60.0),
),
),
(
RoundMode.TowardNegative,
(
(p4min, p4min),
(p4min / 4, 0.0),
(p4min / 2, 0.0),
(-p4min, -p4min),
(-p4min / 4, -p4min),
(-p4min / 2, -p4min),
(64.0, 64.0),
(63.0, 60.0),
(62.0, 60.0),
(-64.0, -64.0),
(-63.0, -64.0),
(-62.0, -64.0),
),
),
(
RoundMode.TiesToEven,
(
(p4min, p4min),
(p4min / 4, 0.0),
(p4min / 2, 0.0),
(-p4min, -p4min),
(-p4min / 4, 0.0),
(-p4min / 2, 0.0),
(64.0, 64.0),
(63.0, 64.0),
(62.0, 64.0),
(61.0, 60.0),
(-64.0, -64.0),
(-63.0, -64.0),
(-62.0, -64.0),
(-61.0, -60.0),
(-58.0, -56.0),
),
),
(
RoundMode.TiesToAway,
(
(p4min, p4min),
(p4min / 4, 0.0),
(p4min / 2, p4min),
(-p4min, -p4min),
(-p4min / 4, 0.0),
(-p4min / 2, -p4min),
(64.0, 64.0),
(63.0, 64.0),
(62.0, 64.0),
(61.0, 60.0),
(-64.0, -64.0),
(-63.0, -64.0),
(-62.0, -64.0),
(-61.0, -60.0),
(-58.0, -60.0),
),
),
),
)
def test_round_p3109b(mode: RoundMode, vals: list) -> None:
fi = format_info_p3109(4)
for sat in (True, False):
for val, expected in vals:
assert round_float(fi, val, mode, sat) == expected
p4max = 224.0
p4maxup = 240.0
p4maxhalfup = (p4max + p4maxup) / 2
@pytest.mark.parametrize(
"modesat, vals",
(
(
(RoundMode.TowardZero, True),
(
(p4max, p4max),
(p4maxhalfup, p4max),
(p4maxup, p4max),
(np.inf, p4max),
(-p4max, -p4max),
(-p4maxhalfup, -p4max),
(-p4maxup, -p4max),
(-np.inf, -p4max),
),
),
(
(RoundMode.TowardZero, False),
(
(p4max, p4max),
(p4maxhalfup, p4max),
(p4maxup, p4max),
(np.inf, np.inf),
(-p4max, -p4max),
(-p4maxhalfup, -p4max),
(-p4maxup, -p4max),
(-np.inf, -np.inf),
),
),
(
(RoundMode.TowardPositive, True),
(
(p4max, p4max),
(p4maxhalfup, p4max),
(p4maxup, p4max),
(np.inf, p4max),
(-p4max, -p4max),
(-p4maxhalfup, -p4max),
(-p4maxup, -p4max),
(-np.inf, -p4max),
),
),
(
(RoundMode.TowardPositive, False),
(
(p4max, p4max),
(p4maxhalfup, np.inf),
(p4maxup, np.inf),
(np.inf, np.inf),
(-p4max, -p4max),
(-p4maxhalfup, -p4max),
(-p4maxup, -p4max),
(-np.inf, -np.inf),
),
),
(
(RoundMode.TowardNegative, True),
(
(p4max, p4max),
(p4maxhalfup, p4max),
(p4maxup, p4max),
(np.inf, p4max),
(-p4max, -p4max),
(-p4maxhalfup, -p4max),
(-p4maxup, -p4max),
(-np.inf, -p4max),
),
),
(
(RoundMode.TowardNegative, False),
(
(p4max, p4max),
(p4maxhalfup, p4max),
(p4maxup, p4max),
(np.inf, np.inf),
(-p4max, -p4max),
(-p4maxhalfup, -np.inf),
(-p4maxup, -np.inf),
(-np.inf, -np.inf),
),
),
(
(RoundMode.TiesToEven, True),
(
(p4max, p4max),
(p4maxhalfup, p4max),
(p4maxup, p4max),
(np.inf, p4max),
(-p4max, -p4max),
(-p4maxhalfup, -p4max),
(-p4maxup, -p4max),
(-np.inf, -p4max),
),
),
(
(RoundMode.TiesToEven, False),
(
(p4max, p4max),
(p4maxhalfup, p4max),
(p4maxup, np.inf),
(np.inf, np.inf),
(-p4max, -p4max),
(-p4maxhalfup, -p4max),
(-p4maxup, -np.inf),
(-np.inf, -np.inf),
),
),
(
(RoundMode.TiesToAway, True),
(
(p4max, p4max),
(p4maxhalfup, p4max),
(p4maxup, p4max),
(np.inf, p4max),
(-p4max, -p4max),
(-p4maxhalfup, -p4max),
(-p4maxup, -p4max),
(-np.inf, -p4max),
),
),
(
(RoundMode.TiesToAway, False),
(
(p4max, p4max),
(p4maxhalfup, np.inf),
(p4maxup, np.inf),
(np.inf, np.inf),
(-p4max, -p4max),
(-p4maxhalfup, -np.inf),
(-p4maxup, -np.inf),
(-np.inf, -np.inf),
),
),
),
ids=lambda x: f"{str(x[0])}-{'Sat' if x[1] else 'Inf'}" if len(x) == 2 else None,
)
def test_round_p3109_sat(modesat: tuple[RoundMode, bool], vals: list) -> None:
fi = format_info_p3109(4)
for val, expected in vals:
assert round_float(fi, val, *modesat) == expected
def test_round_e5m2() -> None:
fi = format_info_ocp_e5m2
assert fi.max == 57344
assert round_float(fi, 1.5258789e-05) == 2**-16
# Default NONSAT rounding
assert round_float(fi, 57344.0) == 57344
assert round_float(fi, 57344.1) == 57344
assert round_float(fi, 61439.9) == 57344
assert round_float(fi, 61440.0) == np.inf
assert round_float(fi, np.inf, sat=False) == np.inf
assert round_float(fi, -np.inf, sat=False) == -np.inf
assert np.isnan(round_float(fi, np.nan, sat=False))
# SAT rounding
assert round_float(fi, 57344.0, sat=True) == 57344
assert round_float(fi, 57344.1, sat=True) == 57344
assert round_float(fi, 61439.9, sat=True) == 57344
assert round_float(fi, 61440.0, sat=True) == 57344
assert round_float(fi, np.inf, sat=True) == 57344
assert round_float(fi, -np.inf, sat=True) == -57344
assert np.isnan(round_float(fi, np.nan, sat=True))
def test_round_e4m3() -> None:
fi = format_info_ocp_e4m3
assert fi.max == 448
# Default NONSAT rounding
assert round_float(fi, 448.0) == 448
assert round_float(fi, 448.1) == 448
assert round_float(fi, 464.0) == 448
assert np.isnan(round_float(fi, 464.01))
assert np.isnan(round_float(fi, np.inf, sat=False))
assert np.isnan(round_float(fi, -np.inf, sat=False))
assert np.isnan(round_float(fi, np.nan, sat=False))
# SAT rounding
assert round_float(fi, 448.0, sat=True) == 448
assert round_float(fi, 448.1, sat=True) == 448
assert round_float(fi, 464.0, sat=True) == 448
assert round_float(fi, 464.01, sat=True) == 448
assert round_float(fi, np.inf, sat=True) == 448
assert round_float(fi, -np.inf, sat=True) == -448
assert np.isnan(round_float(fi, np.nan, sat=True))
some_positive_codepoints = (
0x00,
0x01,
0x02,
0x03,
0x07,
0x0F,
0x17,
0x21,
0x33,
0x40,
0x53,
0x65,
0x70,
)
@pytest.mark.parametrize(
"fi",
[
format_info_ocp_e5m2,
format_info_ocp_e4m3,
*p3109_formats,
],
)
def test_round(fi: FormatInfo) -> None:
"""
Test rounding from values between exact binary8 values
For integer code point i, let
v0 = the float value at i
v1 = the float value at i+1, i.e. nextUp(v0)
dv = v1 - v0
Then check that:
round(v0) == v0
round(v0 + 0.3*dv) == v0
round(v0 + 0.6*dv) == v1
"""
for i in some_positive_codepoints:
v0 = decode_float(fi, i + 0).fval
v1 = decode_float(fi, i + 1).fval
if np.isfinite([v0, v1]).all():
dv = v1 - v0
np.testing.assert_equal(round_float(fi, v0), v0)
np.testing.assert_equal(round_float(fi, v0 + 0.3 * dv), v0)
np.testing.assert_equal(round_float(fi, v0 + 0.49 * dv), v0)
np.testing.assert_equal(round_float(fi, v0 + 0.51 * dv), v1)
np.testing.assert_equal(round_float(fi, v0 + 0.99 * dv), v1)
nearest_even = v0 if (i & 1 == 0) else v1
np.testing.assert_equal(round_float(fi, v0 + 0.50 * dv), nearest_even)
test_formats = [
(format_info_ocp_e5m2, ml_dtypes.float8_e5m2),
(format_info_ocp_e4m3, ml_dtypes.float8_e4m3fn),
]
def _linterp(a: float, b: float, t: float) -> float:
return a * (1 - t) + b * t
def _mlround(v: float, dty: Type) -> float:
"""
Round `v` using ml_dtypes library
"""
return np.array([v]).astype(dty).astype(float).item()
@pytest.mark.parametrize("fi,mldtype", test_formats)
def test_ml_dtype_compatible(fi: FormatInfo, mldtype: Type) -> None:
"""
Test that rounding is compatible with ml_dtypes
"""
for i in range(255):
# For each float v, check values at various interpolations
# between v and nextUp(v)
v0 = decode_float(fi, i + 0).fval
v1 = decode_float(fi, i + 1).fval
for alpha in (0, 0.3, 0.5, 0.6, 0.9, 1.25):
v = _linterp(v0, v1, alpha)
if np.isfinite(v):
val = round_float(fi, v, RoundMode.TiesToEven)
mlval = _mlround(v, mldtype)
np.testing.assert_equal(val, mlval)
@pytest.mark.parametrize("fi,mldtype", test_formats)
def test_round_ints(fi: FormatInfo, mldtype: Type) -> None:
for v in np.arange(289).astype(float):
val = round_float(fi, v)
mlval = _mlround(v, mldtype)
np.testing.assert_equal(val, mlval)
@pytest.mark.parametrize("fi", all_formats)
def test_round_roundtrip(fi: FormatInfo) -> None:
if fi.bits <= 8:
step = 1
elif fi.bits <= 16:
step = 13
elif fi.bits <= 32:
step = 73013
elif fi.bits <= 64:
step = (73013 << 32) + 39
for i in range(0, 2**fi.bits, step):
fv = decode_float(fi, i)
fval2 = round_float(fi, fv.fval)
np.testing.assert_equal(fval2, fv.fval)
|
