| ------------------------------------------------------------------------ |
| -- 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 |
| |
