multiply.dectest

eda is an estimation of distributions algorithm

------------------------------------------------------------------------
-- multiply.decTest -- decimal multiplication                         --
-- Copyright (c) IBM Corporation, 1981, 2003.  All rights reserved.   --
------------------------------------------------------------------------
-- Please see the document "General Decimal Arithmetic Testcases"     --
-- at http://www2.hursley.ibm.com/decimal for the description of      --
-- these testcases.                                                   --
--                                                                    --
-- These testcases are experimental ('beta' versions), and they       --
-- may contain errors.  They are offered on an as-is basis.  In       --
-- particular, achieving the same results as the tests here is not    --
-- a guarantee that an implementation complies with any Standard      --
-- or specification.  The tests are not exhaustive.                   --
--                                                                    --
-- Please send comments, suggestions, and corrections to the author:  --
--   Mike Cowlishaw, IBM Fellow                                       --
--   IBM UK, PO Box 31, Birmingham Road, Warwick CV34 5JL, UK         --
--   [e-mail]                                                   --
------------------------------------------------------------------------
version: 2.15

extended:    1
precision:   9
rounding:    half_up
maxExponent: 999

-- sanity checks (as base, above)
mulx000 multiply 2      2 -> 4
mulx001 multiply 2      3 -> 6
mulx002 multiply 5      1 -> 5
mulx003 multiply 5      2 -> 10
mulx004 multiply 1.20   2 -> 2.40
mulx005 multiply 1.20   0 -> 0.00
mulx006 multiply 1.20  -2 -> -2.40
mulx007 multiply -1.20  2 -> -2.40
mulx008 multiply -1.20  0 -> -0.00
mulx009 multiply -1.20 -2 -> 2.40
mulx010 multiply 5.09 7.1 -> 36.139
mulx011 multiply 2.5    4 -> 10.0
mulx012 multiply 2.50   4 -> 10.00
mulx013 multiply 1.23456789 1.00000000 -> 1.23456789 Rounded
mulx014 multiply 9.999999999 9.999999999 -> 100.000000 Inexact Rounded
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

-- 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
precision: 30
mul160 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
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
mulx033 multiply  0E-3   00.00 ->  0.00000     -- lhs is 0
mulx034 multiply -5.00   1E-3  -> -0.00500
mulx035 multiply -00.00  0.000 -> -0.00000
mulx036 multiply -00.00  0E-3  -> -0.00000     -- rhs is 0
mulx037 multiply -0E-3   00.00 -> -0.00000     -- lhs is 0
mulx038 multiply  5.00  -1E-3  -> -0.00500
mulx039 multiply  00.00 -0.000 -> -0.00000
mulx040 multiply  00.00 -0E-3  -> -0.00000     -- rhs is 0
mulx041 multiply  0E-3  -00.00 -> -0.00000     -- lhs is 0
mulx042 multiply -5.00  -1E-3  ->  0.00500
mulx043 multiply -00.00 -0.000 ->  0.00000
mulx044 multiply -00.00 -0E-3  ->  0.00000     -- rhs is 0
mulx045 multiply -0E-3  -00.00 ->  0.00000     -- lhs is 0

-- examples from decarith
mulx050 multiply 1.20 3        -> 3.60
mulx051 multiply 7    3        -> 21
mulx052 multiply 0.9  0.8      -> 0.72
mulx053 multiply 0.9  -0       -> -0.0
mulx054 multiply 654321 654321 -> 4.28135971E+11  Inexact Rounded

mulx060 multiply 123.45 1e7  ->  1.2345E+9
mulx061 multiply 123.45 1e8  ->  1.2345E+10
mulx062 multiply 123.45 1e+9 ->  1.2345E+11
mulx063 multiply 123.45 1e10 ->  1.2345E+12
mulx064 multiply 123.45 1e11 ->  1.2345E+13
mulx065 multiply 123.45 1e12 ->  1.2345E+14
mulx066 multiply 123.45 1e13 ->  1.2345E+15


-- 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
precision: 8
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

precision: 9
mulx090 multiply 123456789          0.1 -> 12345678.9
mulx091 multiply 1234567891         0.1 -> 123456789 Inexact Rounded
mulx092 multiply 12345678912        0.1 -> 1.23456789E+9 Inexact Rounded
mulx093 multiply 12345678912345     0.1 -> 1.23456789E+12 Inexact Rounded
mulx094 multiply 123456789          0.1 -> 12345678.9
precision: 8
mulx095 multiply 12345678912        0.1 -> 1.2345679E+9 Inexact Rounded
mulx096 multiply 12345678912345     0.1 -> 1.2345679E+12 Inexact Rounded
precision: 7
mulx097 multiply 12345678912        0.1 -> 1.234568E+9 Inexact Rounded
mulx098 multiply 12345678912345     0.1 -> 1.234568E+12 Inexact Rounded

-- test some more edge cases and carries
maxexponent: 9999
precision: 33
mulx101 multiply 9 9   -> 81
mulx102 multiply 9 90   -> 810
mulx103 multiply 9 900   -> 8100
mulx104 multiply 9 9000   -> 81000
mulx105 multiply 9 90000   -> 810000
mulx106 multiply 9 900000   -> 8100000
mulx107 multiply 9 9000000   -> 81000000
mulx108 multiply 9 90000000   -> 810000000
mulx109 multiply 9 900000000   -> 8100000000
mulx110 multiply 9 9000000000   -> 81000000000
mulx111 multiply 9 90000000000   -> 810000000000
mulx112 multiply 9 900000000000   -> 8100000000000
mulx113 multiply 9 9000000000000   -> 81000000000000
mulx114 multiply 9 90000000000000   -> 810000000000000
mulx115 multiply 9 900000000000000   -> 8100000000000000
mulx116 multiply 9 9000000000000000   -> 81000000000000000
mulx117 multiply 9 90000000000000000   -> 810000000000000000
mulx118 multiply 9 900000000000000000   -> 8100000000000000000
mulx119 multiply 9 9000000000000000000   -> 81000000000000000000
mulx120 multiply 9 90000000000000000000   -> 810000000000000000000
mulx121 multiply 9 900000000000000000000   -> 8100000000000000000000
mulx122 multiply 9 9000000000000000000000   -> 81000000000000000000000
mulx123 multiply 9 90000000000000000000000   -> 810000000000000000000000
-- test some more edge cases without carries
mulx131 multiply 3 3   -> 9
mulx132 multiply 3 30   -> 90
mulx133 multiply 3 300   -> 900
mulx134 multiply 3 3000   -> 9000
mulx135 multiply 3 30000   -> 90000
mulx136 multiply 3 300000   -> 900000
mulx137 multiply 3 3000000   -> 9000000
mulx138 multiply 3 30000000   -> 90000000
mulx139 multiply 3 300000000   -> 900000000
mulx140 multiply 3 3000000000   -> 9000000000
mulx141 multiply 3 30000000000   -> 90000000000
mulx142 multiply 3 300000000000   -> 900000000000
mulx143 multiply 3 3000000000000   -> 9000000000000
mulx144 multiply 3 30000000000000   -> 90000000000000
mulx145 multiply 3 300000000000000   -> 900000000000000
mulx146 multiply 3 3000000000000000   -> 9000000000000000
mulx147 multiply 3 30000000000000000   -> 90000000000000000
mulx148 multiply 3 300000000000000000   -> 900000000000000000
mulx149 multiply 3 3000000000000000000   -> 9000000000000000000
mulx150 multiply 3 30000000000000000000   -> 90000000000000000000
mulx151 multiply 3 300000000000000000000   -> 900000000000000000000
mulx152 multiply 3 3000000000000000000000   -> 9000000000000000000000
mulx153 multiply 3 30000000000000000000000   -> 90000000000000000000000

maxexponent: 999999999
precision: 9
-- test some cases that are close to exponent overflow/underflow
mulx170 multiply 1 9e999999999    -> 9E+999999999
mulx171 multiply 1 9.9e999999999  -> 9.9E+999999999
mulx172 multiply 1 9.99e999999999 -> 9.99E+999999999
mulx173 multiply 9e999999999    1 -> 9E+999999999
mulx174 multiply 9.9e999999999  1 -> 9.9E+999999999
mulx176 multiply 9.99e999999999 1 -> 9.99E+999999999
mulx177 multiply 1 9.99999999e999999999 -> 9.99999999E+999999999
mulx178 multiply 9.99999999e999999999 1 -> 9.99999999E+999999999

mulx180 multiply 0.1 9e-999999998   -> 9E-999999999
mulx181 multiply 0.1 99e-999999998  -> 9.9E-999999998
mulx182 multiply 0.1 999e-999999998 -> 9.99E-999999997

mulx183 multiply 0.1 9e-999999998     -> 9E-999999999
mulx184 multiply 0.1 99e-999999998    -> 9.9E-999999998
mulx185 multiply 0.1 999e-999999998   -> 9.99E-999999997
mulx186 multiply 0.1 999e-999999997   -> 9.99E-999999996
mulx187 multiply 0.1 9999e-999999997  -> 9.999E-999999995
mulx188 multiply 0.1 99999e-999999997 -> 9.9999E-999999994

mulx190 multiply 1 9e-999999998   -> 9E-999999998
mulx191 multiply 1 99e-999999998  -> 9.9E-999999997
mulx192 multiply 1 999e-999999998 -> 9.99E-999999996
mulx193 multiply 9e-999999998   1 -> 9E-999999998
mulx194 multiply 99e-999999998  1 -> 9.9E-999999997
mulx195 multiply 999e-999999998 1 -> 9.99E-999999996

mulx196 multiply 1e-599999999 1e-400000000 -> 1E-999999999
mulx197 multiply 1e-600000000 1e-399999999 -> 1E-999999999
mulx198 multiply 1.2e-599999999 1.2e-400000000 -> 1.44E-999999999
mulx199 multiply 1.2e-600000000 1.2e-399999999 -> 1.44E-999999999

mulx201 multiply 1e599999999 1e400000000 -> 1E+999999999
mulx202 multiply 1e600000000 1e399999999 -> 1E+999999999
mulx203 multiply 1.2e599999999 1.2e400000000 -> 1.44E+999999999
mulx204 multiply 1.2e600000000 1.2e399999999 -> 1.44E+999999999

-- long operand triangle
precision: 33
mulx246 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.290801193369671916511992830 Inexact Rounded
precision: 32
mulx247 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.29080119336967191651199283  Inexact Rounded
precision: 31
mulx248 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.2908011933696719165119928   Inexact Rounded
precision: 30
mulx249 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.290801193369671916511993    Inexact Rounded
precision: 29
mulx250 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.29080119336967191651199     Inexact Rounded
precision: 28
mulx251 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.2908011933696719165120      Inexact Rounded
precision: 27
mulx252 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.290801193369671916512       Inexact Rounded
precision: 26
mulx253 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.29080119336967191651        Inexact Rounded
precision: 25
mulx254 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.2908011933696719165         Inexact Rounded
precision: 24
mulx255 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.290801193369671917          Inexact Rounded
precision: 23
mulx256 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.29080119336967192           Inexact Rounded
precision: 22
mulx257 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.2908011933696719            Inexact Rounded
precision: 21
mulx258 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.290801193369672             Inexact Rounded
precision: 20
mulx259 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.29080119336967              Inexact Rounded
precision: 19
mulx260 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.2908011933697               Inexact Rounded
precision: 18
mulx261 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.290801193370                Inexact Rounded
precision: 17
mulx262 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.29080119337                 Inexact Rounded
precision: 16
mulx263 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.2908011934                  Inexact Rounded
precision: 15
mulx264 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.290801193                   Inexact Rounded
precision: 14
mulx265 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.29080119                    Inexact Rounded
precision: 13
mulx266 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.2908012                     Inexact Rounded
precision: 12
mulx267 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.290801                      Inexact Rounded
precision: 11
mulx268 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.29080                       Inexact Rounded
precision: 10
mulx269 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.2908                        Inexact Rounded
precision:  9
mulx270 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.291                         Inexact Rounded
precision:  8
mulx271 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.29                          Inexact Rounded
precision:  7
mulx272 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.3                           Inexact Rounded
precision:  6
mulx273 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433                            Inexact Rounded
precision:  5
mulx274 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 1.4543E+5                         Inexact Rounded
precision:  4
mulx275 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 1.454E+5                         Inexact Rounded
precision:  3
mulx276 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 1.45E+5                         Inexact Rounded
precision:  2
mulx277 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 1.5E+5                         Inexact Rounded
precision:  1
mulx278 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 1E+5                          Inexact Rounded


-- mixed with zeros