fix directed rounding for sqrt

mpmath/lib.py

@@ -616,7 +616,7 @@ def fsqrt(s, prec=STANDARD_PREC, rounding=ROUND_HALF_EVEN):
     else:
         man = _sqrt_fixed2(man, prec2)
 
-    return normalize(man, (exp+shift-prec2)//2, prec, ROUND_HALF_EVEN)
+    return normalize(man, (exp+shift-prec2)//2, prec, rounding)
 
 
 def fhypot(x, y, prec=STANDARD_PREC, rounding=ROUND_HALF_EVEN):

tests/test_mpmath.py

@@ -229,6 +229,18 @@ def test_exact_sqrts():
             assert sqrt(mpf((a*a, 2*i))) == mpf((a, i))
             assert sqrt(mpf((a*a, -2*i))) == mpf((a, -i))
 
+def test_sqrt_rounding():
+    for i in [2, 3, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15]:
+        for dps in [7, 15, 83, 106, 2000]:
+            mpf.dps = dps
+            mpf.round_down()
+            assert (mpf(i)**0.5)**2 < i
+            mpf.round_up()
+            assert (mpf(i)**0.5)**2 > i
+    mpf.dps = 15
+    mpf.round_default()
+        
+
 
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