Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
fully updated to the latests Decimal Specification (v1.66) and the
latests test cases (v2.56).
Thanks to Mark Dickinson for all his help during this process.
diff --git a/Lib/test/decimaltestdata/multiply.decTest b/Lib/test/decimaltestdata/multiply.decTest
index f650150..71f591a 100644
--- a/Lib/test/decimaltestdata/multiply.decTest
+++ b/Lib/test/decimaltestdata/multiply.decTest
@@ -1,6 +1,6 @@
------------------------------------------------------------------------
-- multiply.decTest -- decimal multiplication --
--- Copyright (c) IBM Corporation, 1981, 2004. All rights reserved. --
+-- Copyright (c) IBM Corporation, 1981, 2007. All rights reserved. --
------------------------------------------------------------------------
-- Please see the document "General Decimal Arithmetic Testcases" --
-- at http://www2.hursley.ibm.com/decimal for the description of --
@@ -17,7 +17,7 @@
-- IBM UK, PO Box 31, Birmingham Road, Warwick CV34 5JL, UK --
-- mfc@uk.ibm.com --
------------------------------------------------------------------------
-version: 2.39
+version: 2.56
extended: 1
precision: 9
@@ -44,21 +44,28 @@
mulx015 multiply 2.50 4 -> 10.00
precision: 6
mulx016 multiply 2.50 4 -> 10.00
-mulx017 multiply 9.999999999 9.999999999 -> 100.000 Inexact Rounded
+mulx017 multiply 9.999999999 9.999999999 -> 100.000 Inexact Rounded
+mulx018 multiply 9.999999999 -9.999999999 -> -100.000 Inexact Rounded
+mulx019 multiply -9.999999999 9.999999999 -> -100.000 Inexact Rounded
+mulx020 multiply -9.999999999 -9.999999999 -> 100.000 Inexact Rounded
-- 1999.12.21: next one is a edge case if intermediate longs are used
precision: 15
-mulx019 multiply 999999999999 9765625 -> 9.76562499999023E+18 Inexact Rounded
+mulx059 multiply 999999999999 9765625 -> 9.76562499999023E+18 Inexact Rounded
precision: 30
mulx160 multiply 999999999999 9765625 -> 9765624999990234375
precision: 9
-----
-- zeros, etc.
-mulx020 multiply 0 0 -> 0
-mulx021 multiply 0 -0 -> -0
-mulx022 multiply -0 0 -> -0
-mulx023 multiply -0 -0 -> 0
+mulx021 multiply 0 0 -> 0
+mulx022 multiply 0 -0 -> -0
+mulx023 multiply -0 0 -> -0
+mulx024 multiply -0 -0 -> 0
+mulx025 multiply -0.0 -0.0 -> 0.00
+mulx026 multiply -0.0 -0.0 -> 0.00
+mulx027 multiply -0.0 -0.0 -> 0.00
+mulx028 multiply -0.0 -0.0 -> 0.00
mulx030 multiply 5.00 1E-3 -> 0.00500
mulx031 multiply 00.00 0.000 -> 0.00000
mulx032 multiply 00.00 0E-3 -> 0.00000 -- rhs is 0
@@ -94,17 +101,17 @@
-- test some intermediate lengths
precision: 9
-mulx080 multiply 0.1 123456789 -> 12345678.9
-mulx081 multiply 0.1 1234567891 -> 123456789 Inexact Rounded
-mulx082 multiply 0.1 12345678912 -> 1.23456789E+9 Inexact Rounded
-mulx083 multiply 0.1 12345678912345 -> 1.23456789E+12 Inexact Rounded
-mulx084 multiply 0.1 123456789 -> 12345678.9
+mulx080 multiply 0.1 123456789 -> 12345678.9
+mulx081 multiply 0.1 1234567891 -> 123456789 Inexact Rounded
+mulx082 multiply 0.1 12345678912 -> 1.23456789E+9 Inexact Rounded
+mulx083 multiply 0.1 12345678912345 -> 1.23456789E+12 Inexact Rounded
+mulx084 multiply 0.1 123456789 -> 12345678.9
precision: 8
-mulx085 multiply 0.1 12345678912 -> 1.2345679E+9 Inexact Rounded
-mulx086 multiply 0.1 12345678912345 -> 1.2345679E+12 Inexact Rounded
+mulx085 multiply 0.1 12345678912 -> 1.2345679E+9 Inexact Rounded
+mulx086 multiply 0.1 12345678912345 -> 1.2345679E+12 Inexact Rounded
precision: 7
-mulx087 multiply 0.1 12345678912 -> 1.234568E+9 Inexact Rounded
-mulx088 multiply 0.1 12345678912345 -> 1.234568E+12 Inexact Rounded
+mulx087 multiply 0.1 12345678912 -> 1.234568E+9 Inexact Rounded
+mulx088 multiply 0.1 12345678912345 -> 1.234568E+12 Inexact Rounded
precision: 9
mulx090 multiply 123456789 0.1 -> 12345678.9
@@ -280,6 +287,41 @@
precision: 1
mulx278 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 1E+5 Inexact Rounded
+-- test some edge cases with exact rounding
+maxexponent: 9999
+minexponent: -9999
+precision: 9
+mulx301 multiply 9 9 -> 81
+mulx302 multiply 9 90 -> 810
+mulx303 multiply 9 900 -> 8100
+mulx304 multiply 9 9000 -> 81000
+mulx305 multiply 9 90000 -> 810000
+mulx306 multiply 9 900000 -> 8100000
+mulx307 multiply 9 9000000 -> 81000000
+mulx308 multiply 9 90000000 -> 810000000
+mulx309 multiply 9 900000000 -> 8.10000000E+9 Rounded
+mulx310 multiply 9 9000000000 -> 8.10000000E+10 Rounded
+mulx311 multiply 9 90000000000 -> 8.10000000E+11 Rounded
+mulx312 multiply 9 900000000000 -> 8.10000000E+12 Rounded
+mulx313 multiply 9 9000000000000 -> 8.10000000E+13 Rounded
+mulx314 multiply 9 90000000000000 -> 8.10000000E+14 Rounded
+mulx315 multiply 9 900000000000000 -> 8.10000000E+15 Rounded
+mulx316 multiply 9 9000000000000000 -> 8.10000000E+16 Rounded
+mulx317 multiply 9 90000000000000000 -> 8.10000000E+17 Rounded
+mulx318 multiply 9 900000000000000000 -> 8.10000000E+18 Rounded
+mulx319 multiply 9 9000000000000000000 -> 8.10000000E+19 Rounded
+mulx320 multiply 9 90000000000000000000 -> 8.10000000E+20 Rounded
+mulx321 multiply 9 900000000000000000000 -> 8.10000000E+21 Rounded
+mulx322 multiply 9 9000000000000000000000 -> 8.10000000E+22 Rounded
+mulx323 multiply 9 90000000000000000000000 -> 8.10000000E+23 Rounded
+
+-- fastpath breakers
+precision: 29
+mulx330 multiply 1.491824697641270317824852952837224 1.105170918075647624811707826490246514675628614562883537345747603 -> 1.6487212707001281468486507878 Inexact Rounded
+precision: 55
+mulx331 multiply 0.8958341352965282506768545828765117803873717284891040428 0.8958341352965282506768545828765117803873717284891040428 -> 0.8025187979624784829842553829934069955890983696752228299 Inexact Rounded
+
+
-- tryzeros cases
precision: 7
rounding: half_up
@@ -486,10 +528,10 @@
mulx752 multiply 1e+777777777 -1e+411111111 -> -Infinity Overflow Inexact Rounded
mulx753 multiply -1e+777777777 1e+411111111 -> -Infinity Overflow Inexact Rounded
mulx754 multiply -1e+777777777 -1e+411111111 -> Infinity Overflow Inexact Rounded
-mulx755 multiply 1e-777777777 1e-411111111 -> 0E-1000000007 Underflow Subnormal Inexact Rounded
-mulx756 multiply 1e-777777777 -1e-411111111 -> -0E-1000000007 Underflow Subnormal Inexact Rounded
-mulx757 multiply -1e-777777777 1e-411111111 -> -0E-1000000007 Underflow Subnormal Inexact Rounded
-mulx758 multiply -1e-777777777 -1e-411111111 -> 0E-1000000007 Underflow Subnormal Inexact Rounded
+mulx755 multiply 1e-777777777 1e-411111111 -> 0E-1000000007 Underflow Subnormal Inexact Rounded Clamped
+mulx756 multiply 1e-777777777 -1e-411111111 -> -0E-1000000007 Underflow Subnormal Inexact Rounded Clamped
+mulx757 multiply -1e-777777777 1e-411111111 -> -0E-1000000007 Underflow Subnormal Inexact Rounded Clamped
+mulx758 multiply -1e-777777777 -1e-411111111 -> 0E-1000000007 Underflow Subnormal Inexact Rounded Clamped
-- 'subnormal' boundary (all hard underflow or overflow in base arithemtic)
precision: 9
@@ -500,9 +542,9 @@
mulx764 multiply 1e-600000000 1e-400000005 -> 1E-1000000005 Subnormal
mulx765 multiply 1e-600000000 1e-400000006 -> 1E-1000000006 Subnormal
mulx766 multiply 1e-600000000 1e-400000007 -> 1E-1000000007 Subnormal
-mulx767 multiply 1e-600000000 1e-400000008 -> 0E-1000000007 Underflow Subnormal Inexact Rounded
-mulx768 multiply 1e-600000000 1e-400000009 -> 0E-1000000007 Underflow Subnormal Inexact Rounded
-mulx769 multiply 1e-600000000 1e-400000010 -> 0E-1000000007 Underflow Subnormal Inexact Rounded
+mulx767 multiply 1e-600000000 1e-400000008 -> 0E-1000000007 Underflow Subnormal Inexact Rounded Clamped
+mulx768 multiply 1e-600000000 1e-400000009 -> 0E-1000000007 Underflow Subnormal Inexact Rounded Clamped
+mulx769 multiply 1e-600000000 1e-400000010 -> 0E-1000000007 Underflow Subnormal Inexact Rounded Clamped
-- [no equivalent of 'subnormal' for overflow]
mulx770 multiply 1e+600000000 1e+400000001 -> Infinity Overflow Inexact Rounded
mulx771 multiply 1e+600000000 1e+400000002 -> Infinity Overflow Inexact Rounded
@@ -520,31 +562,31 @@
mulx780 multiply 1e-600000000 1e-400000007 -> 1E-1000000007 Subnormal
mulx781 multiply 1e-600000000 1e-400000008 -> 1E-1000000008 Subnormal
mulx782 multiply 1e-600000000 1e-400000097 -> 1E-1000000097 Subnormal
-mulx783 multiply 1e-600000000 1e-400000098 -> 0E-1000000097 Underflow Subnormal Inexact Rounded
+mulx783 multiply 1e-600000000 1e-400000098 -> 0E-1000000097 Underflow Subnormal Inexact Rounded Clamped
precision: 999
mulx784 multiply 1e-600000000 1e-400000997 -> 1E-1000000997 Subnormal
-mulx785 multiply 1e-600000000 1e-400000998 -> 0E-1000000997 Underflow Subnormal Inexact Rounded
+mulx785 multiply 1e-600000000 1e-400000998 -> 0E-1000000997 Underflow Subnormal Inexact Rounded Clamped
-- following testcases [through mulx800] not yet run against code
precision: 9999
mulx786 multiply 1e-600000000 1e-400009997 -> 1E-1000009997 Subnormal
-mulx787 multiply 1e-600000000 1e-400009998 -> 0E-1000009997 Underflow Subnormal Inexact Rounded
+mulx787 multiply 1e-600000000 1e-400009998 -> 0E-1000009997 Underflow Subnormal Inexact Rounded Clamped
precision: 99999
mulx788 multiply 1e-600000000 1e-400099997 -> 1E-1000099997 Subnormal
-mulx789 multiply 1e-600000000 1e-400099998 -> 0E-1000099997 Underflow Subnormal Inexact Rounded
+mulx789 multiply 1e-600000000 1e-400099998 -> 0E-1000099997 Underflow Subnormal Inexact Rounded Clamped
precision: 999999
mulx790 multiply 1e-600000000 1e-400999997 -> 1E-1000999997 Subnormal
-mulx791 multiply 1e-600000000 1e-400999998 -> 0E-1000999997 Underflow Subnormal Inexact Rounded
+mulx791 multiply 1e-600000000 1e-400999998 -> 0E-1000999997 Underflow Subnormal Inexact Rounded Clamped
precision: 9999999
mulx792 multiply 1e-600000000 1e-409999997 -> 1E-1009999997 Subnormal
-mulx793 multiply 1e-600000000 1e-409999998 -> 0E-1009999997 Underflow Subnormal Inexact Rounded
+mulx793 multiply 1e-600000000 1e-409999998 -> 0E-1009999997 Underflow Subnormal Inexact Rounded Clamped
precision: 99999999
mulx794 multiply 1e-600000000 1e-499999997 -> 1E-1099999997 Subnormal
-mulx795 multiply 1e-600000000 1e-499999998 -> 0E-1099999997 Underflow Subnormal Inexact Rounded
+mulx795 multiply 1e-600000000 1e-499999998 -> 0E-1099999997 Underflow Subnormal Inexact Rounded Clamped
precision: 999999999
mulx796 multiply 1e-999999999 1e-999999997 -> 1E-1999999996 Subnormal
mulx797 multiply 1e-999999999 1e-999999998 -> 1E-1999999997 Subnormal
-mulx798 multiply 1e-999999999 1e-999999999 -> 0E-1999999997 Underflow Subnormal Inexact Rounded
+mulx798 multiply 1e-999999999 1e-999999999 -> 0E-1999999997 Underflow Subnormal Inexact Rounded Clamped
mulx799 multiply 1e-600000000 1e-400000007 -> 1E-1000000007 Subnormal
mulx800 multiply 1e-600000000 1e-400000008 -> 1E-1000000008 Subnormal
@@ -573,19 +615,19 @@
mulx817 multiply 2.51E-999 1e-4 -> 3E-1003 Underflow Subnormal Inexact Rounded
mulx818 multiply 1E-999 1e-4 -> 1E-1003 Subnormal
-mulx819 multiply 3E-999 1e-5 -> 0E-1003 Underflow Subnormal Inexact Rounded
-mulx820 multiply 5E-999 1e-5 -> 0E-1003 Underflow Subnormal Inexact Rounded
+mulx819 multiply 3E-999 1e-5 -> 0E-1003 Underflow Subnormal Inexact Rounded Clamped
+mulx820 multiply 5E-999 1e-5 -> 0E-1003 Underflow Subnormal Inexact Rounded Clamped
mulx821 multiply 7E-999 1e-5 -> 1E-1003 Underflow Subnormal Inexact Rounded
mulx822 multiply 9E-999 1e-5 -> 1E-1003 Underflow Subnormal Inexact Rounded
mulx823 multiply 9.9E-999 1e-5 -> 1E-1003 Underflow Subnormal Inexact Rounded
mulx824 multiply 1E-999 -1e-4 -> -1E-1003 Subnormal
-mulx825 multiply 3E-999 -1e-5 -> -0E-1003 Underflow Subnormal Inexact Rounded
-mulx826 multiply -5E-999 1e-5 -> -0E-1003 Underflow Subnormal Inexact Rounded
+mulx825 multiply 3E-999 -1e-5 -> -0E-1003 Underflow Subnormal Inexact Rounded Clamped
+mulx826 multiply -5E-999 1e-5 -> -0E-1003 Underflow Subnormal Inexact Rounded Clamped
mulx827 multiply 7E-999 -1e-5 -> -1E-1003 Underflow Subnormal Inexact Rounded
mulx828 multiply -9E-999 1e-5 -> -1E-1003 Underflow Subnormal Inexact Rounded
mulx829 multiply 9.9E-999 -1e-5 -> -1E-1003 Underflow Subnormal Inexact Rounded
-mulx830 multiply 3.0E-999 -1e-5 -> -0E-1003 Underflow Subnormal Inexact Rounded
+mulx830 multiply 3.0E-999 -1e-5 -> -0E-1003 Underflow Subnormal Inexact Rounded Clamped
mulx831 multiply 1.0E-501 1e-501 -> 1.0E-1002 Subnormal
mulx832 multiply 2.0E-501 2e-501 -> 4.0E-1002 Subnormal
@@ -595,7 +637,7 @@
mulx836 multiply 40.0E-501 40e-501 -> 1.6000E-999
-- squares
-mulx840 multiply 1E-502 1e-502 -> 0E-1003 Underflow Subnormal Inexact Rounded
+mulx840 multiply 1E-502 1e-502 -> 0E-1003 Underflow Subnormal Inexact Rounded Clamped
mulx841 multiply 1E-501 1e-501 -> 1E-1002 Subnormal
mulx842 multiply 2E-501 2e-501 -> 4E-1002 Subnormal
mulx843 multiply 4E-501 4e-501 -> 1.6E-1001 Subnormal
@@ -604,7 +646,7 @@
mulx846 multiply 40E-501 40e-501 -> 1.600E-999
-- cubes
-mulx850 multiply 1E-670 1e-335 -> 0E-1003 Underflow Subnormal Inexact Rounded
+mulx850 multiply 1E-670 1e-335 -> 0E-1003 Underflow Subnormal Inexact Rounded Clamped
mulx851 multiply 1E-668 1e-334 -> 1E-1002 Subnormal
mulx852 multiply 4E-668 2e-334 -> 8E-1002 Subnormal
mulx853 multiply 9E-668 3e-334 -> 2.7E-1001 Subnormal
@@ -612,7 +654,7 @@
mulx855 multiply 25E-668 5e-334 -> 1.25E-1000 Subnormal
mulx856 multiply 10E-668 100e-334 -> 1.000E-999
--- test from 0.099 ** 999 at 15 digits
+-- test derived from result of 0.099 ** 999 at 15 digits with unlimited exponent
precision: 19
mulx860 multiply 6636851557994578716E-520 6636851557994578716E-520 -> 4.40477986028551E-1003 Underflow Subnormal Inexact Rounded
@@ -629,14 +671,16 @@
precision: 5
maxexponent: 79
minexponent: -79
-mulx881 multiply 1.2347E-40 1.2347E-40 -> 1.524E-80 Inexact Rounded Subnormal Underflow
-mulx882 multiply 1.234E-40 1.234E-40 -> 1.523E-80 Inexact Rounded Subnormal Underflow
-mulx883 multiply 1.23E-40 1.23E-40 -> 1.513E-80 Inexact Rounded Subnormal Underflow
-mulx884 multiply 1.2E-40 1.2E-40 -> 1.44E-80 Subnormal
-mulx885 multiply 1.2E-40 1.2E-41 -> 1.44E-81 Subnormal
-mulx886 multiply 1.2E-40 1.2E-42 -> 1.4E-82 Subnormal Inexact Rounded Underflow
-mulx887 multiply 1.2E-40 1.3E-42 -> 1.6E-82 Subnormal Inexact Rounded Underflow
-mulx888 multiply 1.3E-40 1.3E-42 -> 1.7E-82 Subnormal Inexact Rounded Underflow
+mulx881 multiply 1.2347E-40 1.2347E-40 -> 1.524E-80 Inexact Rounded Subnormal Underflow
+mulx882 multiply 1.234E-40 1.234E-40 -> 1.523E-80 Inexact Rounded Subnormal Underflow
+mulx883 multiply 1.23E-40 1.23E-40 -> 1.513E-80 Inexact Rounded Subnormal Underflow
+mulx884 multiply 1.2E-40 1.2E-40 -> 1.44E-80 Subnormal
+mulx885 multiply 1.2E-40 1.2E-41 -> 1.44E-81 Subnormal
+mulx886 multiply 1.2E-40 1.2E-42 -> 1.4E-82 Subnormal Inexact Rounded Underflow
+mulx887 multiply 1.2E-40 1.3E-42 -> 1.6E-82 Subnormal Inexact Rounded Underflow
+mulx888 multiply 1.3E-40 1.3E-42 -> 1.7E-82 Subnormal Inexact Rounded Underflow
+mulx889 multiply 1.3E-40 1.3E-43 -> 2E-83 Subnormal Inexact Rounded Underflow
+mulx890 multiply 1.3E-41 1.3E-43 -> 0E-83 Clamped Subnormal Inexact Rounded Underflow
mulx891 multiply 1.2345E-39 1.234E-40 -> 1.5234E-79 Inexact Rounded
mulx892 multiply 1.23456E-39 1.234E-40 -> 1.5234E-79 Inexact Rounded
@@ -645,7 +689,43 @@
mulx895 multiply 1.2345E-41 1.234E-40 -> 1.52E-81 Inexact Rounded Subnormal Underflow
mulx896 multiply 1.23456E-41 1.234E-40 -> 1.52E-81 Inexact Rounded Subnormal Underflow
+-- Now explore the case where we get a normal result with Underflow
+precision: 16
+rounding: half_up
+maxExponent: 384
+minExponent: -383
+
+mulx900 multiply 0.3000000000E-191 0.3000000000E-191 -> 9.00000000000000E-384 Subnormal Rounded
+mulx901 multiply 0.3000000001E-191 0.3000000001E-191 -> 9.00000000600000E-384 Underflow Inexact Subnormal Rounded
+mulx902 multiply 9.999999999999999E-383 0.0999999999999 -> 9.99999999999000E-384 Underflow Inexact Subnormal Rounded
+mulx903 multiply 9.999999999999999E-383 0.09999999999999 -> 9.99999999999900E-384 Underflow Inexact Subnormal Rounded
+mulx904 multiply 9.999999999999999E-383 0.099999999999999 -> 9.99999999999990E-384 Underflow Inexact Subnormal Rounded
+mulx905 multiply 9.999999999999999E-383 0.0999999999999999 -> 9.99999999999999E-384 Underflow Inexact Subnormal Rounded
+-- prove operands are exact
+mulx906 multiply 9.999999999999999E-383 1 -> 9.999999999999999E-383
+mulx907 multiply 1 0.09999999999999999 -> 0.09999999999999999
+-- the next rounds to Nmin
+mulx908 multiply 9.999999999999999E-383 0.09999999999999999 -> 1.000000000000000E-383 Underflow Inexact Subnormal Rounded
+mulx909 multiply 9.999999999999999E-383 0.099999999999999999 -> 1.000000000000000E-383 Underflow Inexact Subnormal Rounded
+mulx910 multiply 9.999999999999999E-383 0.0999999999999999999 -> 1.000000000000000E-383 Underflow Inexact Subnormal Rounded
+mulx911 multiply 9.999999999999999E-383 0.09999999999999999999 -> 1.000000000000000E-383 Underflow Inexact Subnormal Rounded
+
+
+-- Examples from SQL proposal (Krishna Kulkarni)
+precision: 34
+rounding: half_up
+maxExponent: 6144
+minExponent: -6143
+mulx1001 multiply 130E-2 120E-2 -> 1.5600
+mulx1002 multiply 130E-2 12E-1 -> 1.560
+mulx1003 multiply 130E-2 1E0 -> 1.30
+mulx1004 multiply 1E2 1E4 -> 1E+6
+
+-- payload decapitate
+precision: 5
+mulx1010 multiply 11 -sNaN1234567890 -> -NaN67890 Invalid_operation
+
-- Null tests
-mulx900 multiply 10 # -> NaN Invalid_operation
-mulx901 multiply # 10 -> NaN Invalid_operation
+mulx990 multiply 10 # -> NaN Invalid_operation
+mulx991 multiply # 10 -> NaN Invalid_operation