Test cases from Cowlishaw, v2.57. All are pased cleanly.
diff --git a/Lib/test/decimaltestdata/remainderNear.decTest b/Lib/test/decimaltestdata/remainderNear.decTest
index cfca91b..fdc1bd8 100644
--- a/Lib/test/decimaltestdata/remainderNear.decTest
+++ b/Lib/test/decimaltestdata/remainderNear.decTest
@@ -17,7 +17,7 @@
 --   IBM UK, PO Box 31, Birmingham Road, Warwick CV34 5JL, UK         --
 --   mfc@uk.ibm.com                                                   --
 ------------------------------------------------------------------------
-version: 2.55
+version: 2.57
 
 extended:    1
 precision:   9
@@ -413,6 +413,18 @@
 rmnx606 remaindernear  31.5 3  -> 1.5    -- i=10
 rmnx607 remaindernear  34.5 3  -> -1.5   -- i=11
 
+-- zero signs
+rmnx650 remaindernear  1  1 ->  0
+rmnx651 remaindernear -1  1 -> -0
+rmnx652 remaindernear  1 -1 ->  0
+rmnx653 remaindernear -1 -1 -> -0
+rmnx654 remaindernear  0  1 ->  0
+rmnx655 remaindernear -0  1 -> -0
+rmnx656 remaindernear  0 -1 ->  0
+rmnx657 remaindernear -0 -1 -> -0
+rmnx658 remaindernear  0.00  1  ->  0.00
+rmnx659 remaindernear -0.00  1  -> -0.00
+
 -- Specials
 rmnx680 remaindernear  Inf  -Inf   ->  NaN Invalid_operation
 rmnx681 remaindernear  Inf  -1000  ->  NaN Invalid_operation