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✏️ dqMultiply.decTest
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------------------------------------------------------------------------ -- dqMultiply.decTest -- decQuad multiplication -- -- Copyright (c) IBM Corporation, 1981, 2008. 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 -- -- mfc@uk.ibm.com -- ------------------------------------------------------------------------ version: 2.59 -- This set of tests are for decQuads only; all arguments are -- representable in a decQuad extended: 1 clamp: 1 precision: 34 maxExponent: 6144 minExponent: -6143 rounding: half_even -- sanity checks dqmul000 multiply 2 2 -> 4 dqmul001 multiply 2 3 -> 6 dqmul002 multiply 5 1 -> 5 dqmul003 multiply 5 2 -> 10 dqmul004 multiply 1.20 2 -> 2.40 dqmul005 multiply 1.20 0 -> 0.00 dqmul006 multiply 1.20 -2 -> -2.40 dqmul007 multiply -1.20 2 -> -2.40 dqmul008 multiply -1.20 0 -> -0.00 dqmul009 multiply -1.20 -2 -> 2.40 dqmul010 multiply 5.09 7.1 -> 36.139 dqmul011 multiply 2.5 4 -> 10.0 dqmul012 multiply 2.50 4 -> 10.00 dqmul013 multiply 1.23456789 1.0000000000000000000000000000 -> 1.234567890000000000000000000000000 Rounded dqmul015 multiply 2.50 4 -> 10.00 dqmul016 multiply 9.99999999999999999 9.99999999999999999 -> 99.99999999999999980000000000000000 Inexact Rounded dqmul017 multiply 9.99999999999999999 -9.99999999999999999 -> -99.99999999999999980000000000000000 Inexact Rounded dqmul018 multiply -9.99999999999999999 9.99999999999999999 -> -99.99999999999999980000000000000000 Inexact Rounded dqmul019 multiply -9.99999999999999999 -9.99999999999999999 -> 99.99999999999999980000000000000000 Inexact Rounded -- zeros, etc. dqmul021 multiply 0 0 -> 0 dqmul022 multiply 0 -0 -> -0 dqmul023 multiply -0 0 -> -0 dqmul024 multiply -0 -0 -> 0 dqmul025 multiply -0.0 -0.0 -> 0.00 dqmul026 multiply -0.0 -0.0 -> 0.00 dqmul027 multiply -0.0 -0.0 -> 0.00 dqmul028 multiply -0.0 -0.0 -> 0.00 dqmul030 multiply 5.00 1E-3 -> 0.00500 dqmul031 multiply 00.00 0.000 -> 0.00000 dqmul032 multiply 00.00 0E-3 -> 0.00000 -- rhs is 0 dqmul033 multiply 0E-3 00.00 -> 0.00000 -- lhs is 0 dqmul034 multiply -5.00 1E-3 -> -0.00500 dqmul035 multiply -00.00 0.000 -> -0.00000 dqmul036 multiply -00.00 0E-3 -> -0.00000 -- rhs is 0 dqmul037 multiply -0E-3 00.00 -> -0.00000 -- lhs is 0 dqmul038 multiply 5.00 -1E-3 -> -0.00500 dqmul039 multiply 00.00 -0.000 -> -0.00000 dqmul040 multiply 00.00 -0E-3 -> -0.00000 -- rhs is 0 dqmul041 multiply 0E-3 -00.00 -> -0.00000 -- lhs is 0 dqmul042 multiply -5.00 -1E-3 -> 0.00500 dqmul043 multiply -00.00 -0.000 -> 0.00000 dqmul044 multiply -00.00 -0E-3 -> 0.00000 -- rhs is 0 dqmul045 multiply -0E-3 -00.00 -> 0.00000 -- lhs is 0 -- examples from decarith dqmul050 multiply 1.20 3 -> 3.60 dqmul051 multiply 7 3 -> 21 dqmul052 multiply 0.9 0.8 -> 0.72 dqmul053 multiply 0.9 -0 -> -0.0 dqmul054 multiply 654321 654321 -> 428135971041 dqmul060 multiply 123.45 1e7 -> 1.2345E+9 dqmul061 multiply 123.45 1e8 -> 1.2345E+10 dqmul062 multiply 123.45 1e+9 -> 1.2345E+11 dqmul063 multiply 123.45 1e10 -> 1.2345E+12 dqmul064 multiply 123.45 1e11 -> 1.2345E+13 dqmul065 multiply 123.45 1e12 -> 1.2345E+14 dqmul066 multiply 123.45 1e13 -> 1.2345E+15 -- test some intermediate lengths -- 1234567890123456 dqmul080 multiply 0.1 1230123456456789 -> 123012345645678.9 dqmul084 multiply 0.1 1230123456456789 -> 123012345645678.9 dqmul090 multiply 1230123456456789 0.1 -> 123012345645678.9 dqmul094 multiply 1230123456456789 0.1 -> 123012345645678.9 -- test some more edge cases and carries dqmul101 multiply 9 9 -> 81 dqmul102 multiply 9 90 -> 810 dqmul103 multiply 9 900 -> 8100 dqmul104 multiply 9 9000 -> 81000 dqmul105 multiply 9 90000 -> 810000 dqmul106 multiply 9 900000 -> 8100000 dqmul107 multiply 9 9000000 -> 81000000 dqmul108 multiply 9 90000000 -> 810000000 dqmul109 multiply 9 900000000 -> 8100000000 dqmul110 multiply 9 9000000000 -> 81000000000 dqmul111 multiply 9 90000000000 -> 810000000000 dqmul112 multiply 9 900000000000 -> 8100000000000 dqmul113 multiply 9 9000000000000 -> 81000000000000 dqmul114 multiply 9 90000000000000 -> 810000000000000 dqmul115 multiply 9 900000000000000 -> 8100000000000000 --dqmul116 multiply 9 9000000000000000 -> 81000000000000000 --dqmul117 multiply 9 90000000000000000 -> 810000000000000000 --dqmul118 multiply 9 900000000000000000 -> 8100000000000000000 --dqmul119 multiply 9 9000000000000000000 -> 81000000000000000000 --dqmul120 multiply 9 90000000000000000000 -> 810000000000000000000 --dqmul121 multiply 9 900000000000000000000 -> 8100000000000000000000 --dqmul122 multiply 9 9000000000000000000000 -> 81000000000000000000000 --dqmul123 multiply 9 90000000000000000000000 -> 810000000000000000000000 -- test some more edge cases without carries dqmul131 multiply 3 3 -> 9 dqmul132 multiply 3 30 -> 90 dqmul133 multiply 3 300 -> 900 dqmul134 multiply 3 3000 -> 9000 dqmul135 multiply 3 30000 -> 90000 dqmul136 multiply 3 300000 -> 900000 dqmul137 multiply 3 3000000 -> 9000000 dqmul138 multiply 3 30000000 -> 90000000 dqmul139 multiply 3 300000000 -> 900000000 dqmul140 multiply 3 3000000000 -> 9000000000 dqmul141 multiply 3 30000000000 -> 90000000000 dqmul142 multiply 3 300000000000 -> 900000000000 dqmul143 multiply 3 3000000000000 -> 9000000000000 dqmul144 multiply 3 30000000000000 -> 90000000000000 dqmul145 multiply 3 300000000000000 -> 900000000000000 dqmul146 multiply 3 3000000000000000 -> 9000000000000000 dqmul147 multiply 3 30000000000000000 -> 90000000000000000 dqmul148 multiply 3 300000000000000000 -> 900000000000000000 dqmul149 multiply 3 3000000000000000000 -> 9000000000000000000 dqmul150 multiply 3 30000000000000000000 -> 90000000000000000000 dqmul151 multiply 3 300000000000000000000 -> 900000000000000000000 dqmul152 multiply 3 3000000000000000000000 -> 9000000000000000000000 dqmul153 multiply 3 30000000000000000000000 -> 90000000000000000000000 dqmul263 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.2908011933696719165119928296 Inexact Rounded -- test some edge cases with exact rounding dqmul301 multiply 900000000000000000 9 -> 8100000000000000000 dqmul302 multiply 900000000000000000 90 -> 81000000000000000000 dqmul303 multiply 900000000000000000 900 -> 810000000000000000000 dqmul304 multiply 900000000000000000 9000 -> 8100000000000000000000 dqmul305 multiply 900000000000000000 90000 -> 81000000000000000000000 dqmul306 multiply 900000000000000000 900000 -> 810000000000000000000000 dqmul307 multiply 900000000000000000 9000000 -> 8100000000000000000000000 dqmul308 multiply 900000000000000000 90000000 -> 81000000000000000000000000 dqmul309 multiply 900000000000000000 900000000 -> 810000000000000000000000000 dqmul310 multiply 900000000000000000 9000000000 -> 8100000000000000000000000000 dqmul311 multiply 900000000000000000 90000000000 -> 81000000000000000000000000000 dqmul312 multiply 900000000000000000 900000000000 -> 810000000000000000000000000000 dqmul313 multiply 900000000000000000 9000000000000 -> 8100000000000000000000000000000 dqmul314 multiply 900000000000000000 90000000000000 -> 81000000000000000000000000000000 dqmul315 multiply 900000000000000000 900000000000000 -> 810000000000000000000000000000000 dqmul316 multiply 900000000000000000 9000000000000000 -> 8100000000000000000000000000000000 dqmul317 multiply 9000000000000000000 9000000000000000 -> 8.100000000000000000000000000000000E+34 Rounded dqmul318 multiply 90000000000000000000 9000000000000000 -> 8.100000000000000000000000000000000E+35 Rounded dqmul319 multiply 900000000000000000000 9000000000000000 -> 8.100000000000000000000000000000000E+36 Rounded dqmul320 multiply 9000000000000000000000 9000000000000000 -> 8.100000000000000000000000000000000E+37 Rounded dqmul321 multiply 90000000000000000000000 9000000000000000 -> 8.100000000000000000000000000000000E+38 Rounded dqmul322 multiply 900000000000000000000000 9000000000000000 -> 8.100000000000000000000000000000000E+39 Rounded dqmul323 multiply 9000000000000000000000000 9000000000000000 -> 8.100000000000000000000000000000000E+40 Rounded -- tryzeros cases dqmul504 multiply 0E-4260 1000E-4260 -> 0E-6176 Clamped dqmul505 multiply 100E+4260 0E+4260 -> 0E+6111 Clamped -- mixed with zeros dqmul541 multiply 0 -1 -> -0 dqmul542 multiply -0 -1 -> 0 dqmul543 multiply 0 1 -> 0 dqmul544 multiply -0 1 -> -0 dqmul545 multiply -1 0 -> -0 dqmul546 multiply -1 -0 -> 0 dqmul547 multiply 1 0 -> 0 dqmul548 multiply 1 -0 -> -0 dqmul551 multiply 0.0 -1 -> -0.0 dqmul552 multiply -0.0 -1 -> 0.0 dqmul553 multiply 0.0 1 -> 0.0 dqmul554 multiply -0.0 1 -> -0.0 dqmul555 multiply -1.0 0 -> -0.0 dqmul556 multiply -1.0 -0 -> 0.0 dqmul557 multiply 1.0 0 -> 0.0 dqmul558 multiply 1.0 -0 -> -0.0 dqmul561 multiply 0 -1.0 -> -0.0 dqmul562 multiply -0 -1.0 -> 0.0 dqmul563 multiply 0 1.0 -> 0.0 dqmul564 multiply -0 1.0 -> -0.0 dqmul565 multiply -1 0.0 -> -0.0 dqmul566 multiply -1 -0.0 -> 0.0 dqmul567 multiply 1 0.0 -> 0.0 dqmul568 multiply 1 -0.0 -> -0.0 dqmul571 multiply 0.0 -1.0 -> -0.00 dqmul572 multiply -0.0 -1.0 -> 0.00 dqmul573 multiply 0.0 1.0 -> 0.00 dqmul574 multiply -0.0 1.0 -> -0.00 dqmul575 multiply -1.0 0.0 -> -0.00 dqmul576 multiply -1.0 -0.0 -> 0.00 dqmul577 multiply 1.0 0.0 -> 0.00 dqmul578 multiply 1.0 -0.0 -> -0.00 -- Specials dqmul580 multiply Inf -Inf -> -Infinity dqmul581 multiply Inf -1000 -> -Infinity dqmul582 multiply Inf -1 -> -Infinity dqmul583 multiply Inf -0 -> NaN Invalid_operation dqmul584 multiply Inf 0 -> NaN Invalid_operation dqmul585 multiply Inf 1 -> Infinity dqmul586 multiply Inf 1000 -> Infinity dqmul587 multiply Inf Inf -> Infinity dqmul588 multiply -1000 Inf -> -Infinity dqmul589 multiply -Inf Inf -> -Infinity dqmul590 multiply -1 Inf -> -Infinity dqmul591 multiply -0 Inf -> NaN Invalid_operation dqmul592 multiply 0 Inf -> NaN Invalid_operation dqmul593 multiply 1 Inf -> Infinity dqmul594 multiply 1000 Inf -> Infinity dqmul595 multiply Inf Inf -> Infinity dqmul600 multiply -Inf -Inf -> Infinity dqmul601 multiply -Inf -1000 -> Infinity dqmul602 multiply -Inf -1 -> Infinity dqmul603 multiply -Inf -0 -> NaN Invalid_operation dqmul604 multiply -Inf 0 -> NaN Invalid_operation dqmul605 multiply -Inf 1 -> -Infinity dqmul606 multiply -Inf 1000 -> -Infinity dqmul607 multiply -Inf Inf -> -Infinity dqmul608 multiply -1000 Inf -> -Infinity dqmul609 multiply -Inf -Inf -> Infinity dqmul610 multiply -1 -Inf -> Infinity dqmul611 multiply -0 -Inf -> NaN Invalid_operation dqmul612 multiply 0 -Inf -> NaN Invalid_operation dqmul613 multiply 1 -Inf -> -Infinity dqmul614 multiply 1000 -Inf -> -Infinity dqmul615 multiply Inf -Inf -> -Infinity dqmul621 multiply NaN -Inf -> NaN dqmul622 multiply NaN -1000 -> NaN dqmul623 multiply NaN -1 -> NaN dqmul624 multiply NaN -0 -> NaN dqmul625 multiply NaN 0 -> NaN dqmul626 multiply NaN 1 -> NaN dqmul627 multiply NaN 1000 -> NaN dqmul628 multiply NaN Inf -> NaN dqmul629 multiply NaN NaN -> NaN dqmul630 multiply -Inf NaN -> NaN dqmul631 multiply -1000 NaN -> NaN dqmul632 multiply -1 NaN -> NaN dqmul633 multiply -0 NaN -> NaN dqmul634 multiply 0 NaN -> NaN dqmul635 multiply 1 NaN -> NaN dqmul636 multiply 1000 NaN -> NaN dqmul637 multiply Inf NaN -> NaN dqmul641 multiply sNaN -Inf -> NaN Invalid_operation dqmul642 multiply sNaN -1000 -> NaN Invalid_operation dqmul643 multiply sNaN -1 -> NaN Invalid_operation dqmul644 multiply sNaN -0 -> NaN Invalid_operation dqmul645 multiply sNaN 0 -> NaN Invalid_operation dqmul646 multiply sNaN 1 -> NaN Invalid_operation dqmul647 multiply sNaN 1000 -> NaN Invalid_operation dqmul648 multiply sNaN NaN -> NaN Invalid_operation dqmul649 multiply sNaN sNaN -> NaN Invalid_operation dqmul650 multiply NaN sNaN -> NaN Invalid_operation dqmul651 multiply -Inf sNaN -> NaN Invalid_operation dqmul652 multiply -1000 sNaN -> NaN Invalid_operation dqmul653 multiply -1 sNaN -> NaN Invalid_operation dqmul654 multiply -0 sNaN -> NaN Invalid_operation dqmul655 multiply 0 sNaN -> NaN Invalid_operation dqmul656 multiply 1 sNaN -> NaN Invalid_operation dqmul657 multiply 1000 sNaN -> NaN Invalid_operation dqmul658 multiply Inf sNaN -> NaN Invalid_operation dqmul659 multiply NaN sNaN -> NaN Invalid_operation -- propagating NaNs dqmul661 multiply NaN9 -Inf -> NaN9 dqmul662 multiply NaN8 999 -> NaN8 dqmul663 multiply NaN71 Inf -> NaN71 dqmul664 multiply NaN6 NaN5 -> NaN6 dqmul665 multiply -Inf NaN4 -> NaN4 dqmul666 multiply -999 NaN33 -> NaN33 dqmul667 multiply Inf NaN2 -> NaN2 dqmul671 multiply sNaN99 -Inf -> NaN99 Invalid_operation dqmul672 multiply sNaN98 -11 -> NaN98 Invalid_operation dqmul673 multiply sNaN97 NaN -> NaN97 Invalid_operation dqmul674 multiply sNaN16 sNaN94 -> NaN16 Invalid_operation dqmul675 multiply NaN95 sNaN93 -> NaN93 Invalid_operation dqmul676 multiply -Inf sNaN92 -> NaN92 Invalid_operation dqmul677 multiply 088 sNaN91 -> NaN91 Invalid_operation dqmul678 multiply Inf sNaN90 -> NaN90 Invalid_operation dqmul679 multiply NaN sNaN89 -> NaN89 Invalid_operation dqmul681 multiply -NaN9 -Inf -> -NaN9 dqmul682 multiply -NaN8 999 -> -NaN8 dqmul683 multiply -NaN71 Inf -> -NaN71 dqmul684 multiply -NaN6 -NaN5 -> -NaN6 dqmul685 multiply -Inf -NaN4 -> -NaN4 dqmul686 multiply -999 -NaN33 -> -NaN33 dqmul687 multiply Inf -NaN2 -> -NaN2 dqmul691 multiply -sNaN99 -Inf -> -NaN99 Invalid_operation dqmul692 multiply -sNaN98 -11 -> -NaN98 Invalid_operation dqmul693 multiply -sNaN97 NaN -> -NaN97 Invalid_operation dqmul694 multiply -sNaN16 -sNaN94 -> -NaN16 Invalid_operation dqmul695 multiply -NaN95 -sNaN93 -> -NaN93 Invalid_operation dqmul696 multiply -Inf -sNaN92 -> -NaN92 Invalid_operation dqmul697 multiply 088 -sNaN91 -> -NaN91 Invalid_operation dqmul698 multiply Inf -sNaN90 -> -NaN90 Invalid_operation dqmul699 multiply -NaN -sNaN89 -> -NaN89 Invalid_operation dqmul701 multiply -NaN -Inf -> -NaN dqmul702 multiply -NaN 999 -> -NaN dqmul703 multiply -NaN Inf -> -NaN dqmul704 multiply -NaN -NaN -> -NaN dqmul705 multiply -Inf -NaN0 -> -NaN dqmul706 multiply -999 -NaN -> -NaN dqmul707 multiply Inf -NaN -> -NaN dqmul711 multiply -sNaN -Inf -> -NaN Invalid_operation dqmul712 multiply -sNaN -11 -> -NaN Invalid_operation dqmul713 multiply -sNaN00 NaN -> -NaN Invalid_operation dqmul714 multiply -sNaN -sNaN -> -NaN Invalid_operation dqmul715 multiply -NaN -sNaN -> -NaN Invalid_operation dqmul716 multiply -Inf -sNaN -> -NaN Invalid_operation dqmul717 multiply 088 -sNaN -> -NaN Invalid_operation dqmul718 multiply Inf -sNaN -> -NaN Invalid_operation dqmul719 multiply -NaN -sNaN -> -NaN Invalid_operation -- overflow and underflow tests .. note subnormal results -- signs dqmul751 multiply 1e+4277 1e+3311 -> Infinity Overflow Inexact Rounded dqmul752 multiply 1e+4277 -1e+3311 -> -Infinity Overflow Inexact Rounded dqmul753 multiply -1e+4277 1e+3311 -> -Infinity Overflow Inexact Rounded dqmul754 multiply -1e+4277 -1e+3311 -> Infinity Overflow Inexact Rounded dqmul755 multiply 1e-4277 1e-3311 -> 0E-6176 Underflow Subnormal Inexact Rounded Clamped dqmul756 multiply 1e-4277 -1e-3311 -> -0E-6176 Underflow Subnormal Inexact Rounded Clamped dqmul757 multiply -1e-4277 1e-3311 -> -0E-6176 Underflow Subnormal Inexact Rounded Clamped dqmul758 multiply -1e-4277 -1e-3311 -> 0E-6176 Underflow Subnormal Inexact Rounded Clamped -- 'subnormal' boundary (all hard underflow or overflow in base arithemtic) dqmul760 multiply 1e-6069 1e-101 -> 1E-6170 Subnormal dqmul761 multiply 1e-6069 1e-102 -> 1E-6171 Subnormal dqmul762 multiply 1e-6069 1e-103 -> 1E-6172 Subnormal dqmul763 multiply 1e-6069 1e-104 -> 1E-6173 Subnormal dqmul764 multiply 1e-6069 1e-105 -> 1E-6174 Subnormal dqmul765 multiply 1e-6069 1e-106 -> 1E-6175 Subnormal dqmul766 multiply 1e-6069 1e-107 -> 1E-6176 Subnormal dqmul767 multiply 1e-6069 1e-108 -> 0E-6176 Underflow Subnormal Inexact Rounded Clamped dqmul768 multiply 1e-6069 1e-109 -> 0E-6176 Underflow Subnormal Inexact Rounded Clamped dqmul769 multiply 1e-6069 1e-110 -> 0E-6176 Underflow Subnormal Inexact Rounded Clamped -- [no equivalent of 'subnormal' for overflow] dqmul770 multiply 1e+40 1e+6101 -> 1.000000000000000000000000000000E+6141 Clamped dqmul771 multiply 1e+40 1e+6102 -> 1.0000000000000000000000000000000E+6142 Clamped dqmul772 multiply 1e+40 1e+6103 -> 1.00000000000000000000000000000000E+6143 Clamped dqmul773 multiply 1e+40 1e+6104 -> 1.000000000000000000000000000000000E+6144 Clamped dqmul774 multiply 1e+40 1e+6105 -> Infinity Overflow Inexact Rounded dqmul775 multiply 1e+40 1e+6106 -> Infinity Overflow Inexact Rounded dqmul776 multiply 1e+40 1e+6107 -> Infinity Overflow Inexact Rounded dqmul777 multiply 1e+40 1e+6108 -> Infinity Overflow Inexact Rounded dqmul778 multiply 1e+40 1e+6109 -> Infinity Overflow Inexact Rounded dqmul779 multiply 1e+40 1e+6110 -> Infinity Overflow Inexact Rounded dqmul801 multiply 1.0000E-6172 1 -> 1.0000E-6172 Subnormal dqmul802 multiply 1.000E-6172 1e-1 -> 1.000E-6173 Subnormal dqmul803 multiply 1.00E-6172 1e-2 -> 1.00E-6174 Subnormal dqmul804 multiply 1.0E-6172 1e-3 -> 1.0E-6175 Subnormal dqmul805 multiply 1.0E-6172 1e-4 -> 1E-6176 Subnormal Rounded dqmul806 multiply 1.3E-6172 1e-4 -> 1E-6176 Underflow Subnormal Inexact Rounded dqmul807 multiply 1.5E-6172 1e-4 -> 2E-6176 Underflow Subnormal Inexact Rounded dqmul808 multiply 1.7E-6172 1e-4 -> 2E-6176 Underflow Subnormal Inexact Rounded dqmul809 multiply 2.3E-6172 1e-4 -> 2E-6176 Underflow Subnormal Inexact Rounded dqmul810 multiply 2.5E-6172 1e-4 -> 2E-6176 Underflow Subnormal Inexact Rounded dqmul811 multiply 2.7E-6172 1e-4 -> 3E-6176 Underflow Subnormal Inexact Rounded dqmul812 multiply 1.49E-6172 1e-4 -> 1E-6176 Underflow Subnormal Inexact Rounded dqmul813 multiply 1.50E-6172 1e-4 -> 2E-6176 Underflow Subnormal Inexact Rounded dqmul814 multiply 1.51E-6172 1e-4 -> 2E-6176 Underflow Subnormal Inexact Rounded dqmul815 multiply 2.49E-6172 1e-4 -> 2E-6176 Underflow Subnormal Inexact Rounded dqmul816 multiply 2.50E-6172 1e-4 -> 2E-6176 Underflow Subnormal Inexact Rounded dqmul817 multiply 2.51E-6172 1e-4 -> 3E-6176 Underflow Subnormal Inexact Rounded dqmul818 multiply 1E-6172 1e-4 -> 1E-6176 Subnormal dqmul819 multiply 3E-6172 1e-5 -> 0E-6176 Underflow Subnormal Inexact Rounded Clamped dqmul820 multiply 5E-6172 1e-5 -> 0E-6176 Underflow Subnormal Inexact Rounded Clamped dqmul821 multiply 7E-6172 1e-5 -> 1E-6176 Underflow Subnormal Inexact Rounded dqmul822 multiply 9E-6172 1e-5 -> 1E-6176 Underflow Subnormal Inexact Rounded dqmul823 multiply 9.9E-6172 1e-5 -> 1E-6176 Underflow Subnormal Inexact Rounded dqmul824 multiply 1E-6172 -1e-4 -> -1E-6176 Subnormal dqmul825 multiply 3E-6172 -1e-5 -> -0E-6176 Underflow Subnormal Inexact Rounded Clamped dqmul826 multiply -5E-6172 1e-5 -> -0E-6176 Underflow Subnormal Inexact Rounded Clamped dqmul827 multiply 7E-6172 -1e-5 -> -1E-6176 Underflow Subnormal Inexact Rounded dqmul828 multiply -9E-6172 1e-5 -> -1E-6176 Underflow Subnormal Inexact Rounded dqmul829 multiply 9.9E-6172 -1e-5 -> -1E-6176 Underflow Subnormal Inexact Rounded dqmul830 multiply 3.0E-6172 -1e-5 -> -0E-6176 Underflow Subnormal Inexact Rounded Clamped dqmul831 multiply 1.0E-5977 1e-200 -> 0E-6176 Underflow Subnormal Inexact Rounded Clamped dqmul832 multiply 1.0E-5977 1e-199 -> 1E-6176 Subnormal Rounded dqmul833 multiply 1.0E-5977 1e-198 -> 1.0E-6175 Subnormal dqmul834 multiply 2.0E-5977 2e-198 -> 4.0E-6175 Subnormal dqmul835 multiply 4.0E-5977 4e-198 -> 1.60E-6174 Subnormal dqmul836 multiply 10.0E-5977 10e-198 -> 1.000E-6173 Subnormal dqmul837 multiply 30.0E-5977 30e-198 -> 9.000E-6173 Subnormal dqmul838 multiply 40.0E-5982 40e-166 -> 1.6000E-6145 Subnormal dqmul839 multiply 40.0E-5982 40e-165 -> 1.6000E-6144 Subnormal dqmul840 multiply 40.0E-5982 40e-164 -> 1.6000E-6143 -- Long operand overflow may be a different path dqmul870 multiply 100 9.999E+6143 -> Infinity Inexact Overflow Rounded dqmul871 multiply 100 -9.999E+6143 -> -Infinity Inexact Overflow Rounded dqmul872 multiply 9.999E+6143 100 -> Infinity Inexact Overflow Rounded dqmul873 multiply -9.999E+6143 100 -> -Infinity Inexact Overflow Rounded -- check for double-rounded subnormals dqmul881 multiply 1.2347E-6133 1.2347E-40 -> 1.524E-6173 Inexact Rounded Subnormal Underflow dqmul882 multiply 1.234E-6133 1.234E-40 -> 1.523E-6173 Inexact Rounded Subnormal Underflow dqmul883 multiply 1.23E-6133 1.23E-40 -> 1.513E-6173 Inexact Rounded Subnormal Underflow dqmul884 multiply 1.2E-6133 1.2E-40 -> 1.44E-6173 Subnormal dqmul885 multiply 1.2E-6133 1.2E-41 -> 1.44E-6174 Subnormal dqmul886 multiply 1.2E-6133 1.2E-42 -> 1.4E-6175 Subnormal Inexact Rounded Underflow dqmul887 multiply 1.2E-6133 1.3E-42 -> 1.6E-6175 Subnormal Inexact Rounded Underflow dqmul888 multiply 1.3E-6133 1.3E-42 -> 1.7E-6175 Subnormal Inexact Rounded Underflow dqmul889 multiply 1.3E-6133 1.3E-43 -> 2E-6176 Subnormal Inexact Rounded Underflow dqmul890 multiply 1.3E-6134 1.3E-43 -> 0E-6176 Clamped Subnormal Inexact Rounded Underflow dqmul891 multiply 1.2345E-39 1.234E-6133 -> 1.5234E-6172 Inexact Rounded Subnormal Underflow dqmul892 multiply 1.23456E-39 1.234E-6133 -> 1.5234E-6172 Inexact Rounded Subnormal Underflow dqmul893 multiply 1.2345E-40 1.234E-6133 -> 1.523E-6173 Inexact Rounded Subnormal Underflow dqmul894 multiply 1.23456E-40 1.234E-6133 -> 1.523E-6173 Inexact Rounded Subnormal Underflow dqmul895 multiply 1.2345E-41 1.234E-6133 -> 1.52E-6174 Inexact Rounded Subnormal Underflow dqmul896 multiply 1.23456E-41 1.234E-6133 -> 1.52E-6174 Inexact Rounded Subnormal Underflow -- Now explore the case where we get a normal result with Underflow -- prove operands are exact dqmul906 multiply 9.999999999999999999999999999999999E-6143 1 -> 9.999999999999999999999999999999999E-6143 dqmul907 multiply 1 0.09999999999999999999999999999999999 -> 0.09999999999999999999999999999999999 -- the next rounds to Nmin dqmul908 multiply 9.999999999999999999999999999999999E-6143 0.09999999999999999999999999999999999 -> 1.000000000000000000000000000000000E-6143 Underflow Inexact Subnormal Rounded -- hugest dqmul909 multiply 9999999999999999999999999999999999 9999999999999999999999999999999999 -> 9.999999999999999999999999999999998E+67 Inexact Rounded -- VG case dqmul910 multiply 8.81125000000001349436E-1548 8.000000000000000000E-1550 -> 7.049000000000010795488000000000000E-3097 Rounded -- Examples from SQL proposal (Krishna Kulkarni) precision: 34 rounding: half_up maxExponent: 6144 minExponent: -6143 dqmul911 multiply 130E-2 120E-2 -> 1.5600 dqmul912 multiply 130E-2 12E-1 -> 1.560 dqmul913 multiply 130E-2 1E0 -> 1.30 dqmul914 multiply 1E2 1E4 -> 1E+6 -- power-of-ten edge cases dqmul1001 multiply 1 10 -> 10 dqmul1002 multiply 1 100 -> 100 dqmul1003 multiply 1 1000 -> 1000 dqmul1004 multiply 1 10000 -> 10000 dqmul1005 multiply 1 100000 -> 100000 dqmul1006 multiply 1 1000000 -> 1000000 dqmul1007 multiply 1 10000000 -> 10000000 dqmul1008 multiply 1 100000000 -> 100000000 dqmul1009 multiply 1 1000000000 -> 1000000000 dqmul1010 multiply 1 10000000000 -> 10000000000 dqmul1011 multiply 1 100000000000 -> 100000000000 dqmul1012 multiply 1 1000000000000 -> 1000000000000 dqmul1013 multiply 1 10000000000000 -> 10000000000000 dqmul1014 multiply 1 100000000000000 -> 100000000000000 dqmul1015 multiply 1 1000000000000000 -> 1000000000000000 dqmul1016 multiply 1 1000000000000000000 -> 1000000000000000000 dqmul1017 multiply 1 100000000000000000000000000 -> 100000000000000000000000000 dqmul1018 multiply 1 1000000000000000000000000000 -> 1000000000000000000000000000 dqmul1019 multiply 1 10000000000000000000000000000 -> 10000000000000000000000000000 dqmul1020 multiply 1 1000000000000000000000000000000000 -> 1000000000000000000000000000000000 dqmul1021 multiply 10 1 -> 10 dqmul1022 multiply 10 10 -> 100 dqmul1023 multiply 10 100 -> 1000 dqmul1024 multiply 10 1000 -> 10000 dqmul1025 multiply 10 10000 -> 100000 dqmul1026 multiply 10 100000 -> 1000000 dqmul1027 multiply 10 1000000 -> 10000000 dqmul1028 multiply 10 10000000 -> 100000000 dqmul1029 multiply 10 100000000 -> 1000000000 dqmul1030 multiply 10 1000000000 -> 10000000000 dqmul1031 multiply 10 10000000000 -> 100000000000 dqmul1032 multiply 10 100000000000 -> 1000000000000 dqmul1033 multiply 10 1000000000000 -> 10000000000000 dqmul1034 multiply 10 10000000000000 -> 100000000000000 dqmul1035 multiply 10 100000000000000 -> 1000000000000000 dqmul1036 multiply 10 100000000000000000 -> 1000000000000000000 dqmul1037 multiply 10 10000000000000000000000000 -> 100000000000000000000000000 dqmul1038 multiply 10 100000000000000000000000000 -> 1000000000000000000000000000 dqmul1039 multiply 10 1000000000000000000000000000 -> 10000000000000000000000000000 dqmul1040 multiply 10 100000000000000000000000000000000 -> 1000000000000000000000000000000000 dqmul1041 multiply 100 0.1 -> 10.0 dqmul1042 multiply 100 1 -> 100 dqmul1043 multiply 100 10 -> 1000 dqmul1044 multiply 100 100 -> 10000 dqmul1045 multiply 100 1000 -> 100000 dqmul1046 multiply 100 10000 -> 1000000 dqmul1047 multiply 100 100000 -> 10000000 dqmul1048 multiply 100 1000000 -> 100000000 dqmul1049 multiply 100 10000000 -> 1000000000 dqmul1050 multiply 100 100000000 -> 10000000000 dqmul1051 multiply 100 1000000000 -> 100000000000 dqmul1052 multiply 100 10000000000 -> 1000000000000 dqmul1053 multiply 100 100000000000 -> 10000000000000 dqmul1054 multiply 100 1000000000000 -> 100000000000000 dqmul1055 multiply 100 10000000000000 -> 1000000000000000 dqmul1056 multiply 100 10000000000000000 -> 1000000000000000000 dqmul1057 multiply 100 1000000000000000000000000 -> 100000000000000000000000000 dqmul1058 multiply 100 10000000000000000000000000 -> 1000000000000000000000000000 dqmul1059 multiply 100 100000000000000000000000000 -> 10000000000000000000000000000 dqmul1060 multiply 100 10000000000000000000000000000000 -> 1000000000000000000000000000000000 dqmul1061 multiply 1000 0.01 -> 10.00 dqmul1062 multiply 1000 0.1 -> 100.0 dqmul1063 multiply 1000 1 -> 1000 dqmul1064 multiply 1000 10 -> 10000 dqmul1065 multiply 1000 100 -> 100000 dqmul1066 multiply 1000 1000 -> 1000000 dqmul1067 multiply 1000 10000 -> 10000000 dqmul1068 multiply 1000 100000 -> 100000000 dqmul1069 multiply 1000 1000000 -> 1000000000 dqmul1070 multiply 1000 10000000 -> 10000000000 dqmul1071 multiply 1000 100000000 -> 100000000000 dqmul1072 multiply 1000 1000000000 -> 1000000000000 dqmul1073 multiply 1000 10000000000 -> 10000000000000 dqmul1074 multiply 1000 100000000000 -> 100000000000000 dqmul1075 multiply 1000 1000000000000 -> 1000000000000000 dqmul1076 multiply 1000 1000000000000000 -> 1000000000000000000 dqmul1077 multiply 1000 100000000000000000000000 -> 100000000000000000000000000 dqmul1078 multiply 1000 1000000000000000000000000 -> 1000000000000000000000000000 dqmul1079 multiply 1000 10000000000000000000000000 -> 10000000000000000000000000000 dqmul1080 multiply 1000 1000000000000000000000000000000 -> 1000000000000000000000000000000000 dqmul1081 multiply 10000 0.001 -> 10.000 dqmul1082 multiply 10000 0.01 -> 100.00 dqmul1083 multiply 10000 0.1 -> 1000.0 dqmul1084 multiply 10000 1 -> 10000 dqmul1085 multiply 10000 10 -> 100000 dqmul1086 multiply 10000 100 -> 1000000 dqmul1087 multiply 10000 1000 -> 10000000 dqmul1088 multiply 10000 10000 -> 100000000 dqmul1089 multiply 10000 100000 -> 1000000000 dqmul1090 multiply 10000 1000000 -> 10000000000 dqmul1091 multiply 10000 10000000 -> 100000000000 dqmul1092 multiply 10000 100000000 -> 1000000000000 dqmul1093 multiply 10000 1000000000 -> 10000000000000 dqmul1094 multiply 10000 10000000000 -> 100000000000000 dqmul1095 multiply 10000 100000000000 -> 1000000000000000 dqmul1096 multiply 10000 100000000000000 -> 1000000000000000000 dqmul1097 multiply 10000 10000000000000000000000 -> 100000000000000000000000000 dqmul1098 multiply 10000 100000000000000000000000 -> 1000000000000000000000000000 dqmul1099 multiply 10000 1000000000000000000000000 -> 10000000000000000000000000000 dqmul1100 multiply 10000 100000000000000000000000000000 -> 1000000000000000000000000000000000 dqmul1107 multiply 10000 99999999999 -> 999999999990000 dqmul1108 multiply 10000 99999999999 -> 999999999990000 -- Null tests dqmul9990 multiply 10 # -> NaN Invalid_operation dqmul9991 multiply # 10 -> NaN Invalid_operation
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