BUG: Fix inf and NaN-warnings in half float `nextafter` (#15988)

This commit fixes the at `nextafter(np.inf, ...)` should not return NaN unless the second value is NaN. Also `nextafter(NaN, ...)` and `nextafter(..., NaN) should not give the invalid value warning (no invalid value is created, the invalid value is propagated).

This aligns half-float `nextafter` with double/float `nextafter`.

Closes #15977

2 files changed, 28 insertions, 8 deletions

diff --git a/numpy/core/src/npymath/halffloat.c b/numpy/core/src/npymath/halffloat.c
index 84af86009..cbaa11e43 100644
--- a/numpy/core/src/npymath/halffloat.c
+++ b/numpy/core/src/npymath/halffloat.c
@@ -115,10 +115,7 @@ npy_half npy_half_nextafter(npy_half x, npy_half y)
 {
     npy_half ret;
 
-    if (!npy_half_isfinite(x) || npy_half_isnan(y)) {
-#if NPY_HALF_GENERATE_INVALID
-        npy_set_floatstatus_invalid();
-#endif
+    if (npy_half_isnan(x) || npy_half_isnan(y)) {
         ret = NPY_HALF_NAN;
     } else if (npy_half_eq_nonan(x, y)) {
         ret = x;
@@ -138,7 +135,7 @@ npy_half npy_half_nextafter(npy_half x, npy_half y)
         }
     }
 #if NPY_HALF_GENERATE_OVERFLOW
-    if (npy_half_isinf(ret)) {
+    if (npy_half_isinf(ret) && npy_half_isfinite(x)) {
         npy_set_floatstatus_overflow();
     }
 #endif
diff --git a/numpy/core/tests/test_half.py b/numpy/core/tests/test_half.py
index c6d046be1..ae9827bc7 100644
--- a/numpy/core/tests/test_half.py
+++ b/numpy/core/tests/test_half.py
@@ -329,6 +329,7 @@ class TestHalf:
         # 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])
@@ -337,6 +338,21 @@ class TestHalf:
         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
 
@@ -347,6 +363,12 @@ class TestHalf:
         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"""
 
@@ -487,9 +509,6 @@ class TestHalf:
             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))
-            assert_raises_fpe('invalid', np.nextafter, float16(np.inf), float16(0))
-            assert_raises_fpe('invalid', np.nextafter, float16(-np.inf), float16(0))
-            assert_raises_fpe('invalid', np.nextafter, float16(0), float16(np.nan))
 
             # These should not raise
             float16(65472)+float16(32)
@@ -498,6 +517,10 @@ class TestHalf:
             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)