multiply.dectest

eda is an estimation of distributions algorithm

precision: 9
mulx541 multiply  0    -1     -> -0
mulx542 multiply -0    -1     ->  0
mulx543 multiply  0     1     ->  0
mulx544 multiply -0     1     -> -0
mulx545 multiply -1     0     -> -0
mulx546 multiply -1    -0     ->  0
mulx547 multiply  1     0     ->  0
mulx548 multiply  1    -0     -> -0

mulx551 multiply  0.0  -1     -> -0.0
mulx552 multiply -0.0  -1     ->  0.0
mulx553 multiply  0.0   1     ->  0.0
mulx554 multiply -0.0   1     -> -0.0
mulx555 multiply -1.0   0     -> -0.0
mulx556 multiply -1.0  -0     ->  0.0
mulx557 multiply  1.0   0     ->  0.0
mulx558 multiply  1.0  -0     -> -0.0

mulx561 multiply  0    -1.0   -> -0.0
mulx562 multiply -0    -1.0   ->  0.0
mulx563 multiply  0     1.0   ->  0.0
mulx564 multiply -0     1.0   -> -0.0
mulx565 multiply -1     0.0   -> -0.0
mulx566 multiply -1    -0.0   ->  0.0
mulx567 multiply  1     0.0   ->  0.0
mulx568 multiply  1    -0.0   -> -0.0

mulx571 multiply  0.0  -1.0   -> -0.00
mulx572 multiply -0.0  -1.0   ->  0.00
mulx573 multiply  0.0   1.0   ->  0.00
mulx574 multiply -0.0   1.0   -> -0.00
mulx575 multiply -1.0   0.0   -> -0.00
mulx576 multiply -1.0  -0.0   ->  0.00
mulx577 multiply  1.0   0.0   ->  0.00
mulx578 multiply  1.0  -0.0   -> -0.00


-- Specials
mulx580 multiply  Inf  -Inf   -> -Infinity
mulx581 multiply  Inf  -1000  -> -Infinity
mulx582 multiply  Inf  -1     -> -Infinity
mulx583 multiply  Inf  -0     ->  NaN  Invalid_operation
mulx584 multiply  Inf   0     ->  NaN  Invalid_operation
mulx585 multiply  Inf   1     ->  Infinity
mulx586 multiply  Inf   1000  ->  Infinity
mulx587 multiply  Inf   Inf   ->  Infinity
mulx588 multiply -1000  Inf   -> -Infinity
mulx589 multiply -Inf   Inf   -> -Infinity
mulx590 multiply -1     Inf   -> -Infinity
mulx591 multiply -0     Inf   ->  NaN  Invalid_operation
mulx592 multiply  0     Inf   ->  NaN  Invalid_operation
mulx593 multiply  1     Inf   ->  Infinity
mulx594 multiply  1000  Inf   ->  Infinity
mulx595 multiply  Inf   Inf   ->  Infinity

mulx600 multiply -Inf  -Inf   ->  Infinity
mulx601 multiply -Inf  -1000  ->  Infinity
mulx602 multiply -Inf  -1     ->  Infinity
mulx603 multiply -Inf  -0     ->  NaN  Invalid_operation
mulx604 multiply -Inf   0     ->  NaN  Invalid_operation
mulx605 multiply -Inf   1     -> -Infinity
mulx606 multiply -Inf   1000  -> -Infinity
mulx607 multiply -Inf   Inf   -> -Infinity
mulx608 multiply -1000  Inf   -> -Infinity
mulx609 multiply -Inf  -Inf   ->  Infinity
mulx610 multiply -1    -Inf   ->  Infinity
mulx611 multiply -0    -Inf   ->  NaN  Invalid_operation
mulx612 multiply  0    -Inf   ->  NaN  Invalid_operation
mulx613 multiply  1    -Inf   -> -Infinity
mulx614 multiply  1000 -Inf   -> -Infinity
mulx615 multiply  Inf  -Inf   -> -Infinity

mulx621 multiply  NaN -Inf    ->  NaN
mulx622 multiply  NaN -1000   ->  NaN
mulx623 multiply  NaN -1      ->  NaN
mulx624 multiply  NaN -0      ->  NaN
mulx625 multiply  NaN  0      ->  NaN
mulx626 multiply  NaN  1      ->  NaN
mulx627 multiply  NaN  1000   ->  NaN
mulx628 multiply  NaN  Inf    ->  NaN
mulx629 multiply  NaN  NaN    ->  NaN
mulx630 multiply -Inf  NaN    ->  NaN
mulx631 multiply -1000 NaN    ->  NaN
mulx632 multiply -1    NaN    ->  NaN
mulx633 multiply -0    NaN    ->  NaN
mulx634 multiply  0    NaN    ->  NaN
mulx635 multiply  1    NaN    ->  NaN
mulx636 multiply  1000 NaN    ->  NaN
mulx637 multiply  Inf  NaN    ->  NaN

mulx641 multiply  sNaN -Inf   ->  NaN  Invalid_operation
mulx642 multiply  sNaN -1000  ->  NaN  Invalid_operation
mulx643 multiply  sNaN -1     ->  NaN  Invalid_operation
mulx644 multiply  sNaN -0     ->  NaN  Invalid_operation
mulx645 multiply  sNaN  0     ->  NaN  Invalid_operation
mulx646 multiply  sNaN  1     ->  NaN  Invalid_operation
mulx647 multiply  sNaN  1000  ->  NaN  Invalid_operation
mulx648 multiply  sNaN  NaN   ->  NaN  Invalid_operation
mulx649 multiply  sNaN sNaN   ->  NaN  Invalid_operation
mulx650 multiply  NaN  sNaN   ->  NaN  Invalid_operation
mulx651 multiply -Inf  sNaN   ->  NaN  Invalid_operation
mulx652 multiply -1000 sNaN   ->  NaN  Invalid_operation
mulx653 multiply -1    sNaN   ->  NaN  Invalid_operation
mulx654 multiply -0    sNaN   ->  NaN  Invalid_operation
mulx655 multiply  0    sNaN   ->  NaN  Invalid_operation
mulx656 multiply  1    sNaN   ->  NaN  Invalid_operation
mulx657 multiply  1000 sNaN   ->  NaN  Invalid_operation
mulx658 multiply  Inf  sNaN   ->  NaN  Invalid_operation
mulx659 multiply  NaN  sNaN   ->  NaN  Invalid_operation

-- overflow and underflow tests .. note subnormal results
maxexponent: 999999999
mulx730 multiply +1.23456789012345E-0 9E+999999999 -> Infinity Inexact Overflow Rounded
mulx731 multiply 9E+999999999 +1.23456789012345E-0 -> Infinity Inexact Overflow Rounded
mulx732 multiply +0.100 9E-999999999 -> 9.00E-1000000000 Subnormal
mulx733 multiply 9E-999999999 +0.100 -> 9.00E-1000000000 Subnormal
mulx735 multiply -1.23456789012345E-0 9E+999999999 -> -Infinity Inexact Overflow Rounded
mulx736 multiply 9E+999999999 -1.23456789012345E-0 -> -Infinity Inexact Overflow Rounded
mulx737 multiply -0.100 9E-999999999 -> -9.00E-1000000000 Subnormal
mulx738 multiply 9E-999999999 -0.100 -> -9.00E-1000000000 Subnormal

mulx739 multiply 1e-599999999 1e-400000001 -> 1E-1000000000 Subnormal
mulx740 multiply 1e-599999999 1e-400000000 -> 1E-999999999
mulx741 multiply 1e-600000000 1e-400000000 -> 1E-1000000000 Subnormal
mulx742 multiply 9e-999999998 0.01 -> 9E-1000000000 Subnormal
mulx743 multiply 9e-999999998 0.1  -> 9E-999999999
mulx744 multiply 0.01 9e-999999998 -> 9E-1000000000 Subnormal
mulx745 multiply 1e599999999 1e400000001 -> Infinity Overflow Inexact Rounded
mulx746 multiply 1e599999999 1e400000000 -> 1E+999999999
mulx747 multiply 1e600000000 1e400000000 -> Infinity Overflow Inexact Rounded
mulx748 multiply 9e999999998 100  -> Infinity Overflow Inexact Rounded
mulx749 multiply 9e999999998 10   -> 9.0E+999999999
mulx750 multiply 100  9e999999998 -> Infinity Overflow Inexact Rounded
-- signs
mulx751 multiply  1e+777777777  1e+411111111 ->  Infinity Overflow Inexact Rounded
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

-- 'subnormal' boundary (all hard underflow or overflow in base arithemtic)
precision: 9
mulx760 multiply 1e-600000000 1e-400000001 -> 1E-1000000001 Subnormal
mulx761 multiply 1e-600000000 1e-400000002 -> 1E-1000000002 Subnormal
mulx762 multiply 1e-600000000 1e-400000003 -> 1E-1000000003 Subnormal
mulx763 multiply 1e-600000000 1e-400000004 -> 1E-1000000004 Subnormal
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
-- [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
mulx772 multiply 1e+600000000 1e+400000003 -> Infinity Overflow Inexact Rounded
mulx773 multiply 1e+600000000 1e+400000004 -> Infinity Overflow Inexact Rounded
mulx774 multiply 1e+600000000 1e+400000005 -> Infinity Overflow Inexact Rounded
mulx775 multiply 1e+600000000 1e+400000006 -> Infinity Overflow Inexact Rounded
mulx776 multiply 1e+600000000 1e+400000007 -> Infinity Overflow Inexact Rounded
mulx777 multiply 1e+600000000 1e+400000008 -> Infinity Overflow Inexact Rounded
mulx778 multiply 1e+600000000 1e+400000009 -> Infinity Overflow Inexact Rounded
mulx779 multiply 1e+600000000 1e+400000010 -> Infinity Overflow Inexact Rounded

-- 'subnormal' test edge condition at higher precisions
precision: 99
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
precision: 999
mulx784 multiply 1e-600000000 1e-400000997 -> 1E-1000000997 Subnormal
mulx785 multiply 1e-600000000 1e-400000998 -> 0E-1000000997 Underflow Subnormal Inexact Rounded

-- 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
precision: 99999
mulx788 multiply 1e-600000000 1e-400099997 -> 1E-1000099997 Subnormal
mulx789 multiply 1e-600000000 1e-400099998 -> 0E-1000099997 Underflow Subnormal Inexact Rounded
precision: 999999
mulx790 multiply 1e-600000000 1e-400999997 -> 1E-1000999997 Subnormal
mulx791 multiply 1e-600000000 1e-400999998 -> 0E-1000999997 Underflow Subnormal Inexact Rounded
precision: 9999999
mulx792 multiply 1e-600000000 1e-409999997 -> 1E-1009999997 Subnormal
mulx793 multiply 1e-600000000 1e-409999998 -> 0E-1009999997 Underflow Subnormal Inexact Rounded
precision: 99999999
mulx794 multiply 1e-600000000 1e-499999997 -> 1E-1099999997 Subnormal
mulx795 multiply 1e-600000000 1e-499999998 -> 0E-1099999997 Underflow Subnormal Inexact Rounded
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
mulx799 multiply 1e-600000000 1e-400000007 -> 1E-1000000007 Subnormal
mulx800 multiply 1e-600000000 1e-400000008 -> 1E-1000000008 Subnormal

-- test subnormals rounding
precision:   5
maxExponent: 999
rounding:    half_even

mulx801 multiply  1.0000E-999  1     -> 1.0000E-999
mulx802 multiply  1.000E-999   1e-1  -> 1.000E-1000 Subnormal
mulx803 multiply  1.00E-999    1e-2  -> 1.00E-1001  Subnormal
mulx804 multiply  1.0E-999     1e-3  -> 1.0E-1002   Subnormal
mulx805 multiply  1.0E-999     1e-4  -> 1E-1003     Subnormal Rounded
mulx806 multiply  1.3E-999     1e-4  -> 1E-1003     Underflow Subnormal Inexact Rounded
mulx807 multiply  1.5E-999     1e-4  -> 2E-1003     Underflow Subnormal Inexact Rounded
mulx808 multiply  1.7E-999     1e-4  -> 2E-1003     Underflow Subnormal Inexact Rounded
mulx809 multiply  2.3E-999     1e-4  -> 2E-1003     Underflow Subnormal Inexact Rounded
mulx810 multiply  2.5E-999     1e-4  -> 2E-1003     Underflow Subnormal Inexact Rounded
mulx811 multiply  2.7E-999     1e-4  -> 3E-1003     Underflow Subnormal Inexact Rounded
mulx812 multiply  1.49E-999    1e-4  -> 1E-1003     Underflow Subnormal Inexact Rounded
mulx813 multiply  1.50E-999    1e-4  -> 2E-1003     Underflow Subnormal Inexact Rounded
mulx814 multiply  1.51E-999    1e-4  -> 2E-1003     Underflow Subnormal Inexact Rounded
mulx815 multiply  2.49E-999    1e-4  -> 2E-1003     Underflow Subnormal Inexact Rounded
mulx816 multiply  2.50E-999    1e-4  -> 2E-1003     Underflow Subnormal Inexact Rounded
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
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
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

mulx831 multiply  1.0E-501     1e-501 -> 1.0E-1002   Subnormal
mulx832 multiply  2.0E-501     2e-501 -> 4.0E-1002   Subnormal
mulx833 multiply  4.0E-501     4e-501 -> 1.60E-1001  Subnormal
mulx834 multiply 10.0E-501    10e-501 -> 1.000E-1000 Subnormal
mulx835 multiply 30.0E-501    30e-501 -> 9.000E-1000 Subnormal
mulx836 multiply 40.0E-501    40e-501 -> 1.6000E-999

-- squares
mulx840 multiply  1E-502       1e-502 -> 0E-1003     Underflow Subnormal Inexact Rounded
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
mulx844 multiply 10E-501      10e-501 -> 1.00E-1000  Subnormal
mulx845 multiply 30E-501      30e-501 -> 9.00E-1000  Subnormal
mulx846 multiply 40E-501      40e-501 -> 1.600E-999

-- cubes
mulx850 multiply  1E-670     1e-335 -> 0E-1003    Underflow Subnormal Inexact Rounded
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
mulx854 multiply 16E-668     4e-334 -> 6.4E-1001  Subnormal
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
precision: 19
mulx860 multiply  6636851557994578716E-520 6636851557994578716E-520 -> 4.40477986028551E-1003 Underflow Subnormal Inexact Rounded

-- Long operand overflow may be a different path
precision: 3
maxExponent: 999999999
mulx890 multiply 1  9.999E+999999999   ->  Infinity Inexact Overflow Rounded
mulx891 multiply 1 -9.999E+999999999   -> -Infinity Inexact Overflow Rounded
mulx892 multiply    9.999E+999999999 1 ->  Infinity Inexact Overflow Rounded
mulx893 multiply   -9.999E+999999999 1 -> -Infinity Inexact Overflow Rounded

-- Null tests
mulx900 multiply 10  # -> NaN Invalid_operation
mulx901 multiply  # 10 -> NaN Invalid_operation