diff --git a/testfuncs.py b/testfuncs.py
index c4bdc34..2bd8c09 100644
--- a/testfuncs.py
+++ b/testfuncs.py
@@ -831,8 +831,10 @@ def do_tests():
     test('llCos(1000000.)', F('0x1.DF9DFAp-1'))
     test('llCos(1000000000.)', F('0x1.ACFF8Cp-1'))
     test('llCos(-1000000000.)', F('0x1.ACFF8Cp-1'))
-    #test('llCos(F("0x.FFFFFFp+63"))', F('-0x1.F4E122p-1')) # alas, doesn't match
-    test('abs(llCos(F("0x.FFFFFFp+63")) - F("-0x1.F4E122p-1")) < 0.003', True) # workaround
+    test('llCos(F("0x1.FFFFFEp+62"))', F('-0x1.F4E122p-1'))
+    test('llCos(F("-0x1.FFFFFEp+62"))', F('-0x1.F4E122p-1'))
+    test('llCos(F("0x1p63"))', F('0x1p63'))
+    test('llCos(F("-0x1p63"))', F('-0x1p63'))
     test('llSin(NaN)', NaN)
     test('llSin(Infinity)', Indet)
     test('llSin(-Infinity)', Indet)
@@ -842,13 +844,19 @@ def do_tests():
     test('llSin(1000000000.)', F('0x1.1778CAp-1'))
     test('llSin(-1000000000.)', F('-0x1.1778CAp-1'))
     test('llSin(F32(1e38))', F32(1e38))
-    #test('llSin(F("0x.FFFFFFp+63"))', F('0x1.A8862Cp-3')) # alas, doesn't match
-    test('abs(llSin(F("0x.FFFFFFp+63")) - F("0x1.A8862Cp-3")) < 0.012', True) # workaround
+    test('llSin(F("0x1.FFFFFEp+62"))', F('0x1.A8862Cp-3'))
+    test('llSin(F("-0x1.FFFFFEp+62"))', F('-0x1.A8862Cp-3'))
+    test('llSin(F("0x1p63"))', F('0x1p63'))
+    test('llSin(F("-0x1p63"))', F('-0x1p63'))
     test('llTan(F32(1e38))', F32(1e38))
     test('llTan(F32(4e38))', Indet)
     test('llTan(F32(math.pi))', F('0x1.777A5Cp-24'))
     test('llTan(F32(math.pi*.5))', -22877332.)
     test('llTan(F("0x1.921FB4p0"))', 13245402.)
+    test('llTan(F("0x1.FFFFFEp62"))', F('-0x1.B1F30Ep-3'))
+    test('llTan(F("-0x1.FFFFFEp62"))', F('0x1.B1F30Ep-3'))
+    test('llTan(F("0x1p63"))', F('0x1p63'))
+    test('llTan(F("-0x1p63"))', F('-0x1p63'))
     test('llAsin(2.0)', NaN)
     test('llAcos(2.0)', NaN)
     test('llAtan2(0.0, 0.0)', 0.0)