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math.nextafter with steps as a pure Python prototype
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import math | |
import struct | |
from functools import reduce | |
from itertools import repeat | |
from hypothesis import assume, example, given, note | |
from hypothesis import strategies as st | |
def float_from_integer(integer): | |
return struct.unpack("!d", struct.pack("!Q", integer))[0] | |
def float_to_integer(float): | |
return struct.unpack("!Q", struct.pack("!d", float))[0] | |
def nextafter_reduce(start, goal, steps): | |
return reduce(math.nextafter, repeat(goal, steps), start) | |
def nextafter_loop(start, goal, steps): | |
for _ in range(steps): | |
start = math.nextafter(start, goal) | |
return start | |
# TODO: Think about supporting negative steps? | |
def my_nextafter_steps(start, goal, steps): | |
# We only check for zero steps, so that | |
# nextafter(start, nan, 0) returns start, | |
# instead of giving nan. | |
if steps == 0: | |
return start | |
if math.isnan(start) or math.isnan(goal): | |
return math.nan | |
if math.copysign(1, start) < 0: | |
return -my_nextafter_steps(-start, -goal, steps) | |
assert start >= 0 | |
if math.copysign(1, goal) < 0: | |
i = float_to_integer(start) | |
if steps > i: | |
return -my_nextafter_steps(0.0, -goal, steps - i) | |
else: | |
# Setting goal to 0 ain't necessary, but makes the invariants | |
# further down simpler to explain | |
goal = 0.0 | |
assert start >= 0 and goal >= 0 and steps > 0 | |
if start < goal: | |
steps = steps | |
cmp = min | |
elif start == goal: | |
return start | |
else: | |
steps = -steps | |
cmp = max | |
return float_from_integer( | |
cmp(float_to_integer(goal), steps + float_to_integer(start)) | |
) | |
@example(start=1.0, goal=math.nextafter(1.0, math.inf), steps=10) | |
@given( | |
start=st.floats(), | |
goal=st.floats(), | |
steps=st.integers(min_value=0, max_value=1_000_000), | |
) | |
def test(start, goal, steps): | |
soll = nextafter_reduce(start, goal, steps) | |
ist = my_nextafter_steps(start, goal, steps) | |
note(f"{soll} != {ist}") | |
assert math.isnan(soll) and math.isnan(ist) or soll == ist | |
@given( | |
start=st.floats(), | |
goal=st.floats(), | |
steps1=st.integers(min_value=0, max_value=1_000_000), | |
steps2=st.integers(min_value=0, max_value=1_000_000), | |
) | |
def test_goal2(start, goal, steps1, steps2): | |
goal1 = nextafter_reduce(start, goal, steps1) | |
soll = nextafter_reduce(start, goal1, steps2) | |
ist = my_nextafter_steps(start, goal1, steps2) | |
note(f"{soll} != {ist}") | |
assert math.isnan(soll) and math.isnan(ist) or soll == ist | |
if __name__ == "__main__": | |
test() | |
test_goal2() |
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Inspired by https://stackoverflow.com/questions/44991042/binary-search-bisection-for-floating-point-numbers