matthiasgoergens · April 25, 2023 11:36 · Apr 25, 2023 · Apr 25, 2023 · Aug 15, 2022 · Aug 15, 2022
diff --git a/nextafter.py b/nextafter.py
@@ -72,7 +72,7 @@ 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) == math.isnan(ist) or soll == ist
+    assert math.isnan(soll) and math.isnan(ist) or soll == ist
 
 
 @given(
@@ -86,7 +86,7 @@ def test_goal2(start, goal, steps1, steps2):
     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
+    assert math.isnan(soll) and math.isnan(ist) or soll == ist
 
 
 if __name__ == "__main__":

diff --git a/nextafter.py b/nextafter.py
@@ -1,5 +1,7 @@
 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
@@ -13,6 +15,10 @@ 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)
@@ -63,7 +69,7 @@ def my_nextafter_steps(start, goal, steps):
     steps=st.integers(min_value=0, max_value=1_000_000),
 )
 def test(start, goal, steps):
-    soll = nextafter_loop(start, goal, steps)
+    soll = nextafter_reduce(start, goal, steps)
     ist = my_nextafter_steps(start, goal, steps)
     note(f"{soll} != {ist}")
     assert math.isnan(soll) == math.isnan(ist) or soll == ist
@@ -76,11 +82,11 @@ def test(start, goal, steps):
     steps2=st.integers(min_value=0, max_value=1_000_000),
 )
 def test_goal2(start, goal, steps1, steps2):
-    goal1 = nextafter_loop(start, goal, steps1)
-    soll = nextafter_loop(start, goal1, 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) == math.isnan(ist) or soll == ist
+    assert (math.isnan(soll) and math.isnan(ist)) or soll == ist
 
 
 if __name__ == "__main__":

diff --git a/nextafter.py b/nextafter.py
@@ -19,7 +19,7 @@ def nextafter_loop(start, goal, steps):
     return start
 
 
-# TODO: Think about support negative steps.
+# 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,

diff --git a/nextafter.py b/nextafter.py
@@ -0,0 +1,88 @@
+import math
+import struct
+
+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_loop(start, goal, steps):
+    for _ in range(steps):
+        start = math.nextafter(start, goal)
+    return start
+
+
+# TODO: Think about support 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_loop(start, goal, steps)
+    ist = my_nextafter_steps(start, goal, steps)
+    note(f"{soll} != {ist}")
+    assert math.isnan(soll) == 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_loop(start, goal, steps1)
+    soll = nextafter_loop(start, goal1, steps2)
+    ist = my_nextafter_steps(start, goal1, steps2)
+    note(f"{soll} != {ist}")
+    assert math.isnan(soll) == math.isnan(ist) or soll == ist
+
+
+if __name__ == "__main__":
+    test()
+    test_goal2()
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