1 | ------------------------------------------------------------------------
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2 | -- dqMultiply.decTest -- decQuad multiplication --
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3 | -- Copyright (c) IBM Corporation, 1981, 2008. All rights reserved. --
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4 | ------------------------------------------------------------------------
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5 | -- Please see the document "General Decimal Arithmetic Testcases" --
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6 | -- at http://www2.hursley.ibm.com/decimal for the description of --
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7 | -- these testcases. --
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8 | -- --
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9 | -- These testcases are experimental ('beta' versions), and they --
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10 | -- may contain errors. They are offered on an as-is basis. In --
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11 | -- particular, achieving the same results as the tests here is not --
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12 | -- a guarantee that an implementation complies with any Standard --
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13 | -- or specification. The tests are not exhaustive. --
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14 | -- --
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15 | -- Please send comments, suggestions, and corrections to the author: --
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16 | -- Mike Cowlishaw, IBM Fellow --
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17 | -- IBM UK, PO Box 31, Birmingham Road, Warwick CV34 5JL, UK --
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18 | -- mfc@uk.ibm.com --
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19 | ------------------------------------------------------------------------
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20 | version: 2.59
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21 |
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22 | -- This set of tests are for decQuads only; all arguments are
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23 | -- representable in a decQuad
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24 | extended: 1
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25 | clamp: 1
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26 | precision: 34
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27 | maxExponent: 6144
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28 | minExponent: -6143
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29 | rounding: half_even
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30 |
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31 | -- sanity checks
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32 | dqmul000 multiply 2 2 -> 4
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33 | dqmul001 multiply 2 3 -> 6
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34 | dqmul002 multiply 5 1 -> 5
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35 | dqmul003 multiply 5 2 -> 10
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36 | dqmul004 multiply 1.20 2 -> 2.40
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37 | dqmul005 multiply 1.20 0 -> 0.00
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38 | dqmul006 multiply 1.20 -2 -> -2.40
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39 | dqmul007 multiply -1.20 2 -> -2.40
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40 | dqmul008 multiply -1.20 0 -> -0.00
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41 | dqmul009 multiply -1.20 -2 -> 2.40
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42 | dqmul010 multiply 5.09 7.1 -> 36.139
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43 | dqmul011 multiply 2.5 4 -> 10.0
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44 | dqmul012 multiply 2.50 4 -> 10.00
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45 | dqmul013 multiply 1.23456789 1.0000000000000000000000000000 -> 1.234567890000000000000000000000000 Rounded
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46 | dqmul015 multiply 2.50 4 -> 10.00
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47 | dqmul016 multiply 9.99999999999999999 9.99999999999999999 -> 99.99999999999999980000000000000000 Inexact Rounded
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48 | dqmul017 multiply 9.99999999999999999 -9.99999999999999999 -> -99.99999999999999980000000000000000 Inexact Rounded
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49 | dqmul018 multiply -9.99999999999999999 9.99999999999999999 -> -99.99999999999999980000000000000000 Inexact Rounded
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50 | dqmul019 multiply -9.99999999999999999 -9.99999999999999999 -> 99.99999999999999980000000000000000 Inexact Rounded
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51 |
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52 | -- zeros, etc.
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53 | dqmul021 multiply 0 0 -> 0
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54 | dqmul022 multiply 0 -0 -> -0
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55 | dqmul023 multiply -0 0 -> -0
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56 | dqmul024 multiply -0 -0 -> 0
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57 | dqmul025 multiply -0.0 -0.0 -> 0.00
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58 | dqmul026 multiply -0.0 -0.0 -> 0.00
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59 | dqmul027 multiply -0.0 -0.0 -> 0.00
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60 | dqmul028 multiply -0.0 -0.0 -> 0.00
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61 | dqmul030 multiply 5.00 1E-3 -> 0.00500
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62 | dqmul031 multiply 00.00 0.000 -> 0.00000
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63 | dqmul032 multiply 00.00 0E-3 -> 0.00000 -- rhs is 0
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64 | dqmul033 multiply 0E-3 00.00 -> 0.00000 -- lhs is 0
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65 | dqmul034 multiply -5.00 1E-3 -> -0.00500
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66 | dqmul035 multiply -00.00 0.000 -> -0.00000
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67 | dqmul036 multiply -00.00 0E-3 -> -0.00000 -- rhs is 0
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68 | dqmul037 multiply -0E-3 00.00 -> -0.00000 -- lhs is 0
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69 | dqmul038 multiply 5.00 -1E-3 -> -0.00500
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70 | dqmul039 multiply 00.00 -0.000 -> -0.00000
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71 | dqmul040 multiply 00.00 -0E-3 -> -0.00000 -- rhs is 0
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72 | dqmul041 multiply 0E-3 -00.00 -> -0.00000 -- lhs is 0
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73 | dqmul042 multiply -5.00 -1E-3 -> 0.00500
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74 | dqmul043 multiply -00.00 -0.000 -> 0.00000
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75 | dqmul044 multiply -00.00 -0E-3 -> 0.00000 -- rhs is 0
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76 | dqmul045 multiply -0E-3 -00.00 -> 0.00000 -- lhs is 0
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77 |
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78 | -- examples from decarith
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79 | dqmul050 multiply 1.20 3 -> 3.60
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80 | dqmul051 multiply 7 3 -> 21
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81 | dqmul052 multiply 0.9 0.8 -> 0.72
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82 | dqmul053 multiply 0.9 -0 -> -0.0
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83 | dqmul054 multiply 654321 654321 -> 428135971041
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84 |
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85 | dqmul060 multiply 123.45 1e7 -> 1.2345E+9
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86 | dqmul061 multiply 123.45 1e8 -> 1.2345E+10
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87 | dqmul062 multiply 123.45 1e+9 -> 1.2345E+11
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88 | dqmul063 multiply 123.45 1e10 -> 1.2345E+12
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89 | dqmul064 multiply 123.45 1e11 -> 1.2345E+13
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90 | dqmul065 multiply 123.45 1e12 -> 1.2345E+14
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91 | dqmul066 multiply 123.45 1e13 -> 1.2345E+15
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92 |
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93 |
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94 | -- test some intermediate lengths
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95 | -- 1234567890123456
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96 | dqmul080 multiply 0.1 1230123456456789 -> 123012345645678.9
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97 | dqmul084 multiply 0.1 1230123456456789 -> 123012345645678.9
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98 | dqmul090 multiply 1230123456456789 0.1 -> 123012345645678.9
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99 | dqmul094 multiply 1230123456456789 0.1 -> 123012345645678.9
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100 |
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101 | -- test some more edge cases and carries
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102 | dqmul101 multiply 9 9 -> 81
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103 | dqmul102 multiply 9 90 -> 810
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104 | dqmul103 multiply 9 900 -> 8100
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105 | dqmul104 multiply 9 9000 -> 81000
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106 | dqmul105 multiply 9 90000 -> 810000
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107 | dqmul106 multiply 9 900000 -> 8100000
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108 | dqmul107 multiply 9 9000000 -> 81000000
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109 | dqmul108 multiply 9 90000000 -> 810000000
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110 | dqmul109 multiply 9 900000000 -> 8100000000
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111 | dqmul110 multiply 9 9000000000 -> 81000000000
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112 | dqmul111 multiply 9 90000000000 -> 810000000000
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113 | dqmul112 multiply 9 900000000000 -> 8100000000000
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114 | dqmul113 multiply 9 9000000000000 -> 81000000000000
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115 | dqmul114 multiply 9 90000000000000 -> 810000000000000
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116 | dqmul115 multiply 9 900000000000000 -> 8100000000000000
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117 | --dqmul116 multiply 9 9000000000000000 -> 81000000000000000
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118 | --dqmul117 multiply 9 90000000000000000 -> 810000000000000000
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119 | --dqmul118 multiply 9 900000000000000000 -> 8100000000000000000
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120 | --dqmul119 multiply 9 9000000000000000000 -> 81000000000000000000
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121 | --dqmul120 multiply 9 90000000000000000000 -> 810000000000000000000
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122 | --dqmul121 multiply 9 900000000000000000000 -> 8100000000000000000000
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123 | --dqmul122 multiply 9 9000000000000000000000 -> 81000000000000000000000
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124 | --dqmul123 multiply 9 90000000000000000000000 -> 810000000000000000000000
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125 | -- test some more edge cases without carries
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126 | dqmul131 multiply 3 3 -> 9
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127 | dqmul132 multiply 3 30 -> 90
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128 | dqmul133 multiply 3 300 -> 900
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129 | dqmul134 multiply 3 3000 -> 9000
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130 | dqmul135 multiply 3 30000 -> 90000
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131 | dqmul136 multiply 3 300000 -> 900000
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132 | dqmul137 multiply 3 3000000 -> 9000000
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133 | dqmul138 multiply 3 30000000 -> 90000000
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134 | dqmul139 multiply 3 300000000 -> 900000000
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135 | dqmul140 multiply 3 3000000000 -> 9000000000
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136 | dqmul141 multiply 3 30000000000 -> 90000000000
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137 | dqmul142 multiply 3 300000000000 -> 900000000000
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138 | dqmul143 multiply 3 3000000000000 -> 9000000000000
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139 | dqmul144 multiply 3 30000000000000 -> 90000000000000
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140 | dqmul145 multiply 3 300000000000000 -> 900000000000000
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141 | dqmul146 multiply 3 3000000000000000 -> 9000000000000000
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142 | dqmul147 multiply 3 30000000000000000 -> 90000000000000000
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143 | dqmul148 multiply 3 300000000000000000 -> 900000000000000000
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144 | dqmul149 multiply 3 3000000000000000000 -> 9000000000000000000
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145 | dqmul150 multiply 3 30000000000000000000 -> 90000000000000000000
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146 | dqmul151 multiply 3 300000000000000000000 -> 900000000000000000000
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147 | dqmul152 multiply 3 3000000000000000000000 -> 9000000000000000000000
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148 | dqmul153 multiply 3 30000000000000000000000 -> 90000000000000000000000
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149 |
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150 | dqmul263 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.2908011933696719165119928296 Inexact Rounded
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151 |
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152 | -- test some edge cases with exact rounding
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153 | dqmul301 multiply 900000000000000000 9 -> 8100000000000000000
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154 | dqmul302 multiply 900000000000000000 90 -> 81000000000000000000
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155 | dqmul303 multiply 900000000000000000 900 -> 810000000000000000000
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156 | dqmul304 multiply 900000000000000000 9000 -> 8100000000000000000000
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157 | dqmul305 multiply 900000000000000000 90000 -> 81000000000000000000000
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158 | dqmul306 multiply 900000000000000000 900000 -> 810000000000000000000000
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159 | dqmul307 multiply 900000000000000000 9000000 -> 8100000000000000000000000
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160 | dqmul308 multiply 900000000000000000 90000000 -> 81000000000000000000000000
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161 | dqmul309 multiply 900000000000000000 900000000 -> 810000000000000000000000000
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162 | dqmul310 multiply 900000000000000000 9000000000 -> 8100000000000000000000000000
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163 | dqmul311 multiply 900000000000000000 90000000000 -> 81000000000000000000000000000
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164 | dqmul312 multiply 900000000000000000 900000000000 -> 810000000000000000000000000000
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165 | dqmul313 multiply 900000000000000000 9000000000000 -> 8100000000000000000000000000000
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166 | dqmul314 multiply 900000000000000000 90000000000000 -> 81000000000000000000000000000000
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167 | dqmul315 multiply 900000000000000000 900000000000000 -> 810000000000000000000000000000000
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168 | dqmul316 multiply 900000000000000000 9000000000000000 -> 8100000000000000000000000000000000
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169 | dqmul317 multiply 9000000000000000000 9000000000000000 -> 8.100000000000000000000000000000000E+34 Rounded
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170 | dqmul318 multiply 90000000000000000000 9000000000000000 -> 8.100000000000000000000000000000000E+35 Rounded
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171 | dqmul319 multiply 900000000000000000000 9000000000000000 -> 8.100000000000000000000000000000000E+36 Rounded
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172 | dqmul320 multiply 9000000000000000000000 9000000000000000 -> 8.100000000000000000000000000000000E+37 Rounded
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173 | dqmul321 multiply 90000000000000000000000 9000000000000000 -> 8.100000000000000000000000000000000E+38 Rounded
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174 | dqmul322 multiply 900000000000000000000000 9000000000000000 -> 8.100000000000000000000000000000000E+39 Rounded
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175 | dqmul323 multiply 9000000000000000000000000 9000000000000000 -> 8.100000000000000000000000000000000E+40 Rounded
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176 |
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177 | -- tryzeros cases
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178 | dqmul504 multiply 0E-4260 1000E-4260 -> 0E-6176 Clamped
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179 | dqmul505 multiply 100E+4260 0E+4260 -> 0E+6111 Clamped
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180 |
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181 | -- mixed with zeros
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182 | dqmul541 multiply 0 -1 -> -0
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183 | dqmul542 multiply -0 -1 -> 0
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184 | dqmul543 multiply 0 1 -> 0
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185 | dqmul544 multiply -0 1 -> -0
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186 | dqmul545 multiply -1 0 -> -0
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187 | dqmul546 multiply -1 -0 -> 0
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188 | dqmul547 multiply 1 0 -> 0
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189 | dqmul548 multiply 1 -0 -> -0
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190 |
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191 | dqmul551 multiply 0.0 -1 -> -0.0
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192 | dqmul552 multiply -0.0 -1 -> 0.0
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193 | dqmul553 multiply 0.0 1 -> 0.0
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194 | dqmul554 multiply -0.0 1 -> -0.0
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195 | dqmul555 multiply -1.0 0 -> -0.0
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196 | dqmul556 multiply -1.0 -0 -> 0.0
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197 | dqmul557 multiply 1.0 0 -> 0.0
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198 | dqmul558 multiply 1.0 -0 -> -0.0
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199 |
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200 | dqmul561 multiply 0 -1.0 -> -0.0
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201 | dqmul562 multiply -0 -1.0 -> 0.0
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202 | dqmul563 multiply 0 1.0 -> 0.0
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203 | dqmul564 multiply -0 1.0 -> -0.0
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204 | dqmul565 multiply -1 0.0 -> -0.0
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205 | dqmul566 multiply -1 -0.0 -> 0.0
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206 | dqmul567 multiply 1 0.0 -> 0.0
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207 | dqmul568 multiply 1 -0.0 -> -0.0
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208 |
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209 | dqmul571 multiply 0.0 -1.0 -> -0.00
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210 | dqmul572 multiply -0.0 -1.0 -> 0.00
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211 | dqmul573 multiply 0.0 1.0 -> 0.00
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212 | dqmul574 multiply -0.0 1.0 -> -0.00
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213 | dqmul575 multiply -1.0 0.0 -> -0.00
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214 | dqmul576 multiply -1.0 -0.0 -> 0.00
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215 | dqmul577 multiply 1.0 0.0 -> 0.00
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216 | dqmul578 multiply 1.0 -0.0 -> -0.00
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217 |
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218 |
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219 | -- Specials
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220 | dqmul580 multiply Inf -Inf -> -Infinity
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221 | dqmul581 multiply Inf -1000 -> -Infinity
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222 | dqmul582 multiply Inf -1 -> -Infinity
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223 | dqmul583 multiply Inf -0 -> NaN Invalid_operation
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224 | dqmul584 multiply Inf 0 -> NaN Invalid_operation
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225 | dqmul585 multiply Inf 1 -> Infinity
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226 | dqmul586 multiply Inf 1000 -> Infinity
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227 | dqmul587 multiply Inf Inf -> Infinity
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228 | dqmul588 multiply -1000 Inf -> -Infinity
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229 | dqmul589 multiply -Inf Inf -> -Infinity
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230 | dqmul590 multiply -1 Inf -> -Infinity
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231 | dqmul591 multiply -0 Inf -> NaN Invalid_operation
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232 | dqmul592 multiply 0 Inf -> NaN Invalid_operation
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233 | dqmul593 multiply 1 Inf -> Infinity
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234 | dqmul594 multiply 1000 Inf -> Infinity
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235 | dqmul595 multiply Inf Inf -> Infinity
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236 |
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237 | dqmul600 multiply -Inf -Inf -> Infinity
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238 | dqmul601 multiply -Inf -1000 -> Infinity
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239 | dqmul602 multiply -Inf -1 -> Infinity
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240 | dqmul603 multiply -Inf -0 -> NaN Invalid_operation
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241 | dqmul604 multiply -Inf 0 -> NaN Invalid_operation
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242 | dqmul605 multiply -Inf 1 -> -Infinity
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243 | dqmul606 multiply -Inf 1000 -> -Infinity
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244 | dqmul607 multiply -Inf Inf -> -Infinity
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245 | dqmul608 multiply -1000 Inf -> -Infinity
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246 | dqmul609 multiply -Inf -Inf -> Infinity
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247 | dqmul610 multiply -1 -Inf -> Infinity
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248 | dqmul611 multiply -0 -Inf -> NaN Invalid_operation
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249 | dqmul612 multiply 0 -Inf -> NaN Invalid_operation
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250 | dqmul613 multiply 1 -Inf -> -Infinity
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251 | dqmul614 multiply 1000 -Inf -> -Infinity
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252 | dqmul615 multiply Inf -Inf -> -Infinity
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253 |
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254 | dqmul621 multiply NaN -Inf -> NaN
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255 | dqmul622 multiply NaN -1000 -> NaN
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256 | dqmul623 multiply NaN -1 -> NaN
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257 | dqmul624 multiply NaN -0 -> NaN
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258 | dqmul625 multiply NaN 0 -> NaN
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259 | dqmul626 multiply NaN 1 -> NaN
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260 | dqmul627 multiply NaN 1000 -> NaN
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261 | dqmul628 multiply NaN Inf -> NaN
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262 | dqmul629 multiply NaN NaN -> NaN
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263 | dqmul630 multiply -Inf NaN -> NaN
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264 | dqmul631 multiply -1000 NaN -> NaN
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265 | dqmul632 multiply -1 NaN -> NaN
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266 | dqmul633 multiply -0 NaN -> NaN
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267 | dqmul634 multiply 0 NaN -> NaN
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268 | dqmul635 multiply 1 NaN -> NaN
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269 | dqmul636 multiply 1000 NaN -> NaN
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270 | dqmul637 multiply Inf NaN -> NaN
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271 |
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272 | dqmul641 multiply sNaN -Inf -> NaN Invalid_operation
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273 | dqmul642 multiply sNaN -1000 -> NaN Invalid_operation
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274 | dqmul643 multiply sNaN -1 -> NaN Invalid_operation
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275 | dqmul644 multiply sNaN -0 -> NaN Invalid_operation
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276 | dqmul645 multiply sNaN 0 -> NaN Invalid_operation
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277 | dqmul646 multiply sNaN 1 -> NaN Invalid_operation
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278 | dqmul647 multiply sNaN 1000 -> NaN Invalid_operation
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279 | dqmul648 multiply sNaN NaN -> NaN Invalid_operation
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280 | dqmul649 multiply sNaN sNaN -> NaN Invalid_operation
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281 | dqmul650 multiply NaN sNaN -> NaN Invalid_operation
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282 | dqmul651 multiply -Inf sNaN -> NaN Invalid_operation
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283 | dqmul652 multiply -1000 sNaN -> NaN Invalid_operation
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284 | dqmul653 multiply -1 sNaN -> NaN Invalid_operation
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285 | dqmul654 multiply -0 sNaN -> NaN Invalid_operation
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286 | dqmul655 multiply 0 sNaN -> NaN Invalid_operation
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287 | dqmul656 multiply 1 sNaN -> NaN Invalid_operation
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288 | dqmul657 multiply 1000 sNaN -> NaN Invalid_operation
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289 | dqmul658 multiply Inf sNaN -> NaN Invalid_operation
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290 | dqmul659 multiply NaN sNaN -> NaN Invalid_operation
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291 |
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292 | -- propagating NaNs
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293 | dqmul661 multiply NaN9 -Inf -> NaN9
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294 | dqmul662 multiply NaN8 999 -> NaN8
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295 | dqmul663 multiply NaN71 Inf -> NaN71
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296 | dqmul664 multiply NaN6 NaN5 -> NaN6
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297 | dqmul665 multiply -Inf NaN4 -> NaN4
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298 | dqmul666 multiply -999 NaN33 -> NaN33
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299 | dqmul667 multiply Inf NaN2 -> NaN2
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300 |
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301 | dqmul671 multiply sNaN99 -Inf -> NaN99 Invalid_operation
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302 | dqmul672 multiply sNaN98 -11 -> NaN98 Invalid_operation
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303 | dqmul673 multiply sNaN97 NaN -> NaN97 Invalid_operation
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304 | dqmul674 multiply sNaN16 sNaN94 -> NaN16 Invalid_operation
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305 | dqmul675 multiply NaN95 sNaN93 -> NaN93 Invalid_operation
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306 | dqmul676 multiply -Inf sNaN92 -> NaN92 Invalid_operation
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307 | dqmul677 multiply 088 sNaN91 -> NaN91 Invalid_operation
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308 | dqmul678 multiply Inf sNaN90 -> NaN90 Invalid_operation
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309 | dqmul679 multiply NaN sNaN89 -> NaN89 Invalid_operation
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310 |
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311 | dqmul681 multiply -NaN9 -Inf -> -NaN9
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312 | dqmul682 multiply -NaN8 999 -> -NaN8
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313 | dqmul683 multiply -NaN71 Inf -> -NaN71
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314 | dqmul684 multiply -NaN6 -NaN5 -> -NaN6
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315 | dqmul685 multiply -Inf -NaN4 -> -NaN4
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316 | dqmul686 multiply -999 -NaN33 -> -NaN33
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317 | dqmul687 multiply Inf -NaN2 -> -NaN2
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318 |
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319 | dqmul691 multiply -sNaN99 -Inf -> -NaN99 Invalid_operation
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320 | dqmul692 multiply -sNaN98 -11 -> -NaN98 Invalid_operation
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321 | dqmul693 multiply -sNaN97 NaN -> -NaN97 Invalid_operation
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322 | dqmul694 multiply -sNaN16 -sNaN94 -> -NaN16 Invalid_operation
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323 | dqmul695 multiply -NaN95 -sNaN93 -> -NaN93 Invalid_operation
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324 | dqmul696 multiply -Inf -sNaN92 -> -NaN92 Invalid_operation
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325 | dqmul697 multiply 088 -sNaN91 -> -NaN91 Invalid_operation
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326 | dqmul698 multiply Inf -sNaN90 -> -NaN90 Invalid_operation
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327 | dqmul699 multiply -NaN -sNaN89 -> -NaN89 Invalid_operation
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328 |
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329 | dqmul701 multiply -NaN -Inf -> -NaN
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330 | dqmul702 multiply -NaN 999 -> -NaN
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331 | dqmul703 multiply -NaN Inf -> -NaN
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332 | dqmul704 multiply -NaN -NaN -> -NaN
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333 | dqmul705 multiply -Inf -NaN0 -> -NaN
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334 | dqmul706 multiply -999 -NaN -> -NaN
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335 | dqmul707 multiply Inf -NaN -> -NaN
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336 |
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337 | dqmul711 multiply -sNaN -Inf -> -NaN Invalid_operation
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338 | dqmul712 multiply -sNaN -11 -> -NaN Invalid_operation
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339 | dqmul713 multiply -sNaN00 NaN -> -NaN Invalid_operation
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340 | dqmul714 multiply -sNaN -sNaN -> -NaN Invalid_operation
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341 | dqmul715 multiply -NaN -sNaN -> -NaN Invalid_operation
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342 | dqmul716 multiply -Inf -sNaN -> -NaN Invalid_operation
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343 | dqmul717 multiply 088 -sNaN -> -NaN Invalid_operation
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344 | dqmul718 multiply Inf -sNaN -> -NaN Invalid_operation
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345 | dqmul719 multiply -NaN -sNaN -> -NaN Invalid_operation
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346 |
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347 | -- overflow and underflow tests .. note subnormal results
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348 | -- signs
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349 | dqmul751 multiply 1e+4277 1e+3311 -> Infinity Overflow Inexact Rounded
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350 | dqmul752 multiply 1e+4277 -1e+3311 -> -Infinity Overflow Inexact Rounded
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351 | dqmul753 multiply -1e+4277 1e+3311 -> -Infinity Overflow Inexact Rounded
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352 | dqmul754 multiply -1e+4277 -1e+3311 -> Infinity Overflow Inexact Rounded
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353 | dqmul755 multiply 1e-4277 1e-3311 -> 0E-6176 Underflow Subnormal Inexact Rounded Clamped
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354 | dqmul756 multiply 1e-4277 -1e-3311 -> -0E-6176 Underflow Subnormal Inexact Rounded Clamped
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355 | dqmul757 multiply -1e-4277 1e-3311 -> -0E-6176 Underflow Subnormal Inexact Rounded Clamped
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356 | dqmul758 multiply -1e-4277 -1e-3311 -> 0E-6176 Underflow Subnormal Inexact Rounded Clamped
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357 |
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358 | -- 'subnormal' boundary (all hard underflow or overflow in base arithemtic)
|
---|
359 | dqmul760 multiply 1e-6069 1e-101 -> 1E-6170 Subnormal
|
---|
360 | dqmul761 multiply 1e-6069 1e-102 -> 1E-6171 Subnormal
|
---|
361 | dqmul762 multiply 1e-6069 1e-103 -> 1E-6172 Subnormal
|
---|
362 | dqmul763 multiply 1e-6069 1e-104 -> 1E-6173 Subnormal
|
---|
363 | dqmul764 multiply 1e-6069 1e-105 -> 1E-6174 Subnormal
|
---|
364 | dqmul765 multiply 1e-6069 1e-106 -> 1E-6175 Subnormal
|
---|
365 | dqmul766 multiply 1e-6069 1e-107 -> 1E-6176 Subnormal
|
---|
366 | dqmul767 multiply 1e-6069 1e-108 -> 0E-6176 Underflow Subnormal Inexact Rounded Clamped
|
---|
367 | dqmul768 multiply 1e-6069 1e-109 -> 0E-6176 Underflow Subnormal Inexact Rounded Clamped
|
---|
368 | dqmul769 multiply 1e-6069 1e-110 -> 0E-6176 Underflow Subnormal Inexact Rounded Clamped
|
---|
369 | -- [no equivalent of 'subnormal' for overflow]
|
---|
370 | dqmul770 multiply 1e+40 1e+6101 -> 1.000000000000000000000000000000E+6141 Clamped
|
---|
371 | dqmul771 multiply 1e+40 1e+6102 -> 1.0000000000000000000000000000000E+6142 Clamped
|
---|
372 | dqmul772 multiply 1e+40 1e+6103 -> 1.00000000000000000000000000000000E+6143 Clamped
|
---|
373 | dqmul773 multiply 1e+40 1e+6104 -> 1.000000000000000000000000000000000E+6144 Clamped
|
---|
374 | dqmul774 multiply 1e+40 1e+6105 -> Infinity Overflow Inexact Rounded
|
---|
375 | dqmul775 multiply 1e+40 1e+6106 -> Infinity Overflow Inexact Rounded
|
---|
376 | dqmul776 multiply 1e+40 1e+6107 -> Infinity Overflow Inexact Rounded
|
---|
377 | dqmul777 multiply 1e+40 1e+6108 -> Infinity Overflow Inexact Rounded
|
---|
378 | dqmul778 multiply 1e+40 1e+6109 -> Infinity Overflow Inexact Rounded
|
---|
379 | dqmul779 multiply 1e+40 1e+6110 -> Infinity Overflow Inexact Rounded
|
---|
380 |
|
---|
381 | dqmul801 multiply 1.0000E-6172 1 -> 1.0000E-6172 Subnormal
|
---|
382 | dqmul802 multiply 1.000E-6172 1e-1 -> 1.000E-6173 Subnormal
|
---|
383 | dqmul803 multiply 1.00E-6172 1e-2 -> 1.00E-6174 Subnormal
|
---|
384 | dqmul804 multiply 1.0E-6172 1e-3 -> 1.0E-6175 Subnormal
|
---|
385 | dqmul805 multiply 1.0E-6172 1e-4 -> 1E-6176 Subnormal Rounded
|
---|
386 | dqmul806 multiply 1.3E-6172 1e-4 -> 1E-6176 Underflow Subnormal Inexact Rounded
|
---|
387 | dqmul807 multiply 1.5E-6172 1e-4 -> 2E-6176 Underflow Subnormal Inexact Rounded
|
---|
388 | dqmul808 multiply 1.7E-6172 1e-4 -> 2E-6176 Underflow Subnormal Inexact Rounded
|
---|
389 | dqmul809 multiply 2.3E-6172 1e-4 -> 2E-6176 Underflow Subnormal Inexact Rounded
|
---|
390 | dqmul810 multiply 2.5E-6172 1e-4 -> 2E-6176 Underflow Subnormal Inexact Rounded
|
---|
391 | dqmul811 multiply 2.7E-6172 1e-4 -> 3E-6176 Underflow Subnormal Inexact Rounded
|
---|
392 | dqmul812 multiply 1.49E-6172 1e-4 -> 1E-6176 Underflow Subnormal Inexact Rounded
|
---|
393 | dqmul813 multiply 1.50E-6172 1e-4 -> 2E-6176 Underflow Subnormal Inexact Rounded
|
---|
394 | dqmul814 multiply 1.51E-6172 1e-4 -> 2E-6176 Underflow Subnormal Inexact Rounded
|
---|
395 | dqmul815 multiply 2.49E-6172 1e-4 -> 2E-6176 Underflow Subnormal Inexact Rounded
|
---|
396 | dqmul816 multiply 2.50E-6172 1e-4 -> 2E-6176 Underflow Subnormal Inexact Rounded
|
---|
397 | dqmul817 multiply 2.51E-6172 1e-4 -> 3E-6176 Underflow Subnormal Inexact Rounded
|
---|
398 |
|
---|
399 | dqmul818 multiply 1E-6172 1e-4 -> 1E-6176 Subnormal
|
---|
400 | dqmul819 multiply 3E-6172 1e-5 -> 0E-6176 Underflow Subnormal Inexact Rounded Clamped
|
---|
401 | dqmul820 multiply 5E-6172 1e-5 -> 0E-6176 Underflow Subnormal Inexact Rounded Clamped
|
---|
402 | dqmul821 multiply 7E-6172 1e-5 -> 1E-6176 Underflow Subnormal Inexact Rounded
|
---|
403 | dqmul822 multiply 9E-6172 1e-5 -> 1E-6176 Underflow Subnormal Inexact Rounded
|
---|
404 | dqmul823 multiply 9.9E-6172 1e-5 -> 1E-6176 Underflow Subnormal Inexact Rounded
|
---|
405 |
|
---|
406 | dqmul824 multiply 1E-6172 -1e-4 -> -1E-6176 Subnormal
|
---|
407 | dqmul825 multiply 3E-6172 -1e-5 -> -0E-6176 Underflow Subnormal Inexact Rounded Clamped
|
---|
408 | dqmul826 multiply -5E-6172 1e-5 -> -0E-6176 Underflow Subnormal Inexact Rounded Clamped
|
---|
409 | dqmul827 multiply 7E-6172 -1e-5 -> -1E-6176 Underflow Subnormal Inexact Rounded
|
---|
410 | dqmul828 multiply -9E-6172 1e-5 -> -1E-6176 Underflow Subnormal Inexact Rounded
|
---|
411 | dqmul829 multiply 9.9E-6172 -1e-5 -> -1E-6176 Underflow Subnormal Inexact Rounded
|
---|
412 | dqmul830 multiply 3.0E-6172 -1e-5 -> -0E-6176 Underflow Subnormal Inexact Rounded Clamped
|
---|
413 |
|
---|
414 | dqmul831 multiply 1.0E-5977 1e-200 -> 0E-6176 Underflow Subnormal Inexact Rounded Clamped
|
---|
415 | dqmul832 multiply 1.0E-5977 1e-199 -> 1E-6176 Subnormal Rounded
|
---|
416 | dqmul833 multiply 1.0E-5977 1e-198 -> 1.0E-6175 Subnormal
|
---|
417 | dqmul834 multiply 2.0E-5977 2e-198 -> 4.0E-6175 Subnormal
|
---|
418 | dqmul835 multiply 4.0E-5977 4e-198 -> 1.60E-6174 Subnormal
|
---|
419 | dqmul836 multiply 10.0E-5977 10e-198 -> 1.000E-6173 Subnormal
|
---|
420 | dqmul837 multiply 30.0E-5977 30e-198 -> 9.000E-6173 Subnormal
|
---|
421 | dqmul838 multiply 40.0E-5982 40e-166 -> 1.6000E-6145 Subnormal
|
---|
422 | dqmul839 multiply 40.0E-5982 40e-165 -> 1.6000E-6144 Subnormal
|
---|
423 | dqmul840 multiply 40.0E-5982 40e-164 -> 1.6000E-6143
|
---|
424 |
|
---|
425 | -- Long operand overflow may be a different path
|
---|
426 | dqmul870 multiply 100 9.999E+6143 -> Infinity Inexact Overflow Rounded
|
---|
427 | dqmul871 multiply 100 -9.999E+6143 -> -Infinity Inexact Overflow Rounded
|
---|
428 | dqmul872 multiply 9.999E+6143 100 -> Infinity Inexact Overflow Rounded
|
---|
429 | dqmul873 multiply -9.999E+6143 100 -> -Infinity Inexact Overflow Rounded
|
---|
430 |
|
---|
431 | -- check for double-rounded subnormals
|
---|
432 | dqmul881 multiply 1.2347E-6133 1.2347E-40 -> 1.524E-6173 Inexact Rounded Subnormal Underflow
|
---|
433 | dqmul882 multiply 1.234E-6133 1.234E-40 -> 1.523E-6173 Inexact Rounded Subnormal Underflow
|
---|
434 | dqmul883 multiply 1.23E-6133 1.23E-40 -> 1.513E-6173 Inexact Rounded Subnormal Underflow
|
---|
435 | dqmul884 multiply 1.2E-6133 1.2E-40 -> 1.44E-6173 Subnormal
|
---|
436 | dqmul885 multiply 1.2E-6133 1.2E-41 -> 1.44E-6174 Subnormal
|
---|
437 | dqmul886 multiply 1.2E-6133 1.2E-42 -> 1.4E-6175 Subnormal Inexact Rounded Underflow
|
---|
438 | dqmul887 multiply 1.2E-6133 1.3E-42 -> 1.6E-6175 Subnormal Inexact Rounded Underflow
|
---|
439 | dqmul888 multiply 1.3E-6133 1.3E-42 -> 1.7E-6175 Subnormal Inexact Rounded Underflow
|
---|
440 | dqmul889 multiply 1.3E-6133 1.3E-43 -> 2E-6176 Subnormal Inexact Rounded Underflow
|
---|
441 | dqmul890 multiply 1.3E-6134 1.3E-43 -> 0E-6176 Clamped Subnormal Inexact Rounded Underflow
|
---|
442 |
|
---|
443 | dqmul891 multiply 1.2345E-39 1.234E-6133 -> 1.5234E-6172 Inexact Rounded Subnormal Underflow
|
---|
444 | dqmul892 multiply 1.23456E-39 1.234E-6133 -> 1.5234E-6172 Inexact Rounded Subnormal Underflow
|
---|
445 | dqmul893 multiply 1.2345E-40 1.234E-6133 -> 1.523E-6173 Inexact Rounded Subnormal Underflow
|
---|
446 | dqmul894 multiply 1.23456E-40 1.234E-6133 -> 1.523E-6173 Inexact Rounded Subnormal Underflow
|
---|
447 | dqmul895 multiply 1.2345E-41 1.234E-6133 -> 1.52E-6174 Inexact Rounded Subnormal Underflow
|
---|
448 | dqmul896 multiply 1.23456E-41 1.234E-6133 -> 1.52E-6174 Inexact Rounded Subnormal Underflow
|
---|
449 |
|
---|
450 | -- Now explore the case where we get a normal result with Underflow
|
---|
451 | -- prove operands are exact
|
---|
452 | dqmul906 multiply 9.999999999999999999999999999999999E-6143 1 -> 9.999999999999999999999999999999999E-6143
|
---|
453 | dqmul907 multiply 1 0.09999999999999999999999999999999999 -> 0.09999999999999999999999999999999999
|
---|
454 | -- the next rounds to Nmin
|
---|
455 | dqmul908 multiply 9.999999999999999999999999999999999E-6143 0.09999999999999999999999999999999999 -> 1.000000000000000000000000000000000E-6143 Underflow Inexact Subnormal Rounded
|
---|
456 |
|
---|
457 | -- hugest
|
---|
458 | dqmul909 multiply 9999999999999999999999999999999999 9999999999999999999999999999999999 -> 9.999999999999999999999999999999998E+67 Inexact Rounded
|
---|
459 | -- VG case
|
---|
460 | dqmul910 multiply 8.81125000000001349436E-1548 8.000000000000000000E-1550 -> 7.049000000000010795488000000000000E-3097 Rounded
|
---|
461 |
|
---|
462 | -- Examples from SQL proposal (Krishna Kulkarni)
|
---|
463 | precision: 34
|
---|
464 | rounding: half_up
|
---|
465 | maxExponent: 6144
|
---|
466 | minExponent: -6143
|
---|
467 | dqmul911 multiply 130E-2 120E-2 -> 1.5600
|
---|
468 | dqmul912 multiply 130E-2 12E-1 -> 1.560
|
---|
469 | dqmul913 multiply 130E-2 1E0 -> 1.30
|
---|
470 | dqmul914 multiply 1E2 1E4 -> 1E+6
|
---|
471 |
|
---|
472 | -- power-of-ten edge cases
|
---|
473 | dqmul1001 multiply 1 10 -> 10
|
---|
474 | dqmul1002 multiply 1 100 -> 100
|
---|
475 | dqmul1003 multiply 1 1000 -> 1000
|
---|
476 | dqmul1004 multiply 1 10000 -> 10000
|
---|
477 | dqmul1005 multiply 1 100000 -> 100000
|
---|
478 | dqmul1006 multiply 1 1000000 -> 1000000
|
---|
479 | dqmul1007 multiply 1 10000000 -> 10000000
|
---|
480 | dqmul1008 multiply 1 100000000 -> 100000000
|
---|
481 | dqmul1009 multiply 1 1000000000 -> 1000000000
|
---|
482 | dqmul1010 multiply 1 10000000000 -> 10000000000
|
---|
483 | dqmul1011 multiply 1 100000000000 -> 100000000000
|
---|
484 | dqmul1012 multiply 1 1000000000000 -> 1000000000000
|
---|
485 | dqmul1013 multiply 1 10000000000000 -> 10000000000000
|
---|
486 | dqmul1014 multiply 1 100000000000000 -> 100000000000000
|
---|
487 | dqmul1015 multiply 1 1000000000000000 -> 1000000000000000
|
---|
488 |
|
---|
489 | dqmul1016 multiply 1 1000000000000000000 -> 1000000000000000000
|
---|
490 | dqmul1017 multiply 1 100000000000000000000000000 -> 100000000000000000000000000
|
---|
491 | dqmul1018 multiply 1 1000000000000000000000000000 -> 1000000000000000000000000000
|
---|
492 | dqmul1019 multiply 1 10000000000000000000000000000 -> 10000000000000000000000000000
|
---|
493 | dqmul1020 multiply 1 1000000000000000000000000000000000 -> 1000000000000000000000000000000000
|
---|
494 |
|
---|
495 | dqmul1021 multiply 10 1 -> 10
|
---|
496 | dqmul1022 multiply 10 10 -> 100
|
---|
497 | dqmul1023 multiply 10 100 -> 1000
|
---|
498 | dqmul1024 multiply 10 1000 -> 10000
|
---|
499 | dqmul1025 multiply 10 10000 -> 100000
|
---|
500 | dqmul1026 multiply 10 100000 -> 1000000
|
---|
501 | dqmul1027 multiply 10 1000000 -> 10000000
|
---|
502 | dqmul1028 multiply 10 10000000 -> 100000000
|
---|
503 | dqmul1029 multiply 10 100000000 -> 1000000000
|
---|
504 | dqmul1030 multiply 10 1000000000 -> 10000000000
|
---|
505 | dqmul1031 multiply 10 10000000000 -> 100000000000
|
---|
506 | dqmul1032 multiply 10 100000000000 -> 1000000000000
|
---|
507 | dqmul1033 multiply 10 1000000000000 -> 10000000000000
|
---|
508 | dqmul1034 multiply 10 10000000000000 -> 100000000000000
|
---|
509 | dqmul1035 multiply 10 100000000000000 -> 1000000000000000
|
---|
510 |
|
---|
511 | dqmul1036 multiply 10 100000000000000000 -> 1000000000000000000
|
---|
512 | dqmul1037 multiply 10 10000000000000000000000000 -> 100000000000000000000000000
|
---|
513 | dqmul1038 multiply 10 100000000000000000000000000 -> 1000000000000000000000000000
|
---|
514 | dqmul1039 multiply 10 1000000000000000000000000000 -> 10000000000000000000000000000
|
---|
515 | dqmul1040 multiply 10 100000000000000000000000000000000 -> 1000000000000000000000000000000000
|
---|
516 |
|
---|
517 | dqmul1041 multiply 100 0.1 -> 10.0
|
---|
518 | dqmul1042 multiply 100 1 -> 100
|
---|
519 | dqmul1043 multiply 100 10 -> 1000
|
---|
520 | dqmul1044 multiply 100 100 -> 10000
|
---|
521 | dqmul1045 multiply 100 1000 -> 100000
|
---|
522 | dqmul1046 multiply 100 10000 -> 1000000
|
---|
523 | dqmul1047 multiply 100 100000 -> 10000000
|
---|
524 | dqmul1048 multiply 100 1000000 -> 100000000
|
---|
525 | dqmul1049 multiply 100 10000000 -> 1000000000
|
---|
526 | dqmul1050 multiply 100 100000000 -> 10000000000
|
---|
527 | dqmul1051 multiply 100 1000000000 -> 100000000000
|
---|
528 | dqmul1052 multiply 100 10000000000 -> 1000000000000
|
---|
529 | dqmul1053 multiply 100 100000000000 -> 10000000000000
|
---|
530 | dqmul1054 multiply 100 1000000000000 -> 100000000000000
|
---|
531 | dqmul1055 multiply 100 10000000000000 -> 1000000000000000
|
---|
532 |
|
---|
533 | dqmul1056 multiply 100 10000000000000000 -> 1000000000000000000
|
---|
534 | dqmul1057 multiply 100 1000000000000000000000000 -> 100000000000000000000000000
|
---|
535 | dqmul1058 multiply 100 10000000000000000000000000 -> 1000000000000000000000000000
|
---|
536 | dqmul1059 multiply 100 100000000000000000000000000 -> 10000000000000000000000000000
|
---|
537 | dqmul1060 multiply 100 10000000000000000000000000000000 -> 1000000000000000000000000000000000
|
---|
538 |
|
---|
539 | dqmul1061 multiply 1000 0.01 -> 10.00
|
---|
540 | dqmul1062 multiply 1000 0.1 -> 100.0
|
---|
541 | dqmul1063 multiply 1000 1 -> 1000
|
---|
542 | dqmul1064 multiply 1000 10 -> 10000
|
---|
543 | dqmul1065 multiply 1000 100 -> 100000
|
---|
544 | dqmul1066 multiply 1000 1000 -> 1000000
|
---|
545 | dqmul1067 multiply 1000 10000 -> 10000000
|
---|
546 | dqmul1068 multiply 1000 100000 -> 100000000
|
---|
547 | dqmul1069 multiply 1000 1000000 -> 1000000000
|
---|
548 | dqmul1070 multiply 1000 10000000 -> 10000000000
|
---|
549 | dqmul1071 multiply 1000 100000000 -> 100000000000
|
---|
550 | dqmul1072 multiply 1000 1000000000 -> 1000000000000
|
---|
551 | dqmul1073 multiply 1000 10000000000 -> 10000000000000
|
---|
552 | dqmul1074 multiply 1000 100000000000 -> 100000000000000
|
---|
553 | dqmul1075 multiply 1000 1000000000000 -> 1000000000000000
|
---|
554 |
|
---|
555 | dqmul1076 multiply 1000 1000000000000000 -> 1000000000000000000
|
---|
556 | dqmul1077 multiply 1000 100000000000000000000000 -> 100000000000000000000000000
|
---|
557 | dqmul1078 multiply 1000 1000000000000000000000000 -> 1000000000000000000000000000
|
---|
558 | dqmul1079 multiply 1000 10000000000000000000000000 -> 10000000000000000000000000000
|
---|
559 | dqmul1080 multiply 1000 1000000000000000000000000000000 -> 1000000000000000000000000000000000
|
---|
560 |
|
---|
561 | dqmul1081 multiply 10000 0.001 -> 10.000
|
---|
562 | dqmul1082 multiply 10000 0.01 -> 100.00
|
---|
563 | dqmul1083 multiply 10000 0.1 -> 1000.0
|
---|
564 | dqmul1084 multiply 10000 1 -> 10000
|
---|
565 | dqmul1085 multiply 10000 10 -> 100000
|
---|
566 | dqmul1086 multiply 10000 100 -> 1000000
|
---|
567 | dqmul1087 multiply 10000 1000 -> 10000000
|
---|
568 | dqmul1088 multiply 10000 10000 -> 100000000
|
---|
569 | dqmul1089 multiply 10000 100000 -> 1000000000
|
---|
570 | dqmul1090 multiply 10000 1000000 -> 10000000000
|
---|
571 | dqmul1091 multiply 10000 10000000 -> 100000000000
|
---|
572 | dqmul1092 multiply 10000 100000000 -> 1000000000000
|
---|
573 | dqmul1093 multiply 10000 1000000000 -> 10000000000000
|
---|
574 | dqmul1094 multiply 10000 10000000000 -> 100000000000000
|
---|
575 | dqmul1095 multiply 10000 100000000000 -> 1000000000000000
|
---|
576 |
|
---|
577 | dqmul1096 multiply 10000 100000000000000 -> 1000000000000000000
|
---|
578 | dqmul1097 multiply 10000 10000000000000000000000 -> 100000000000000000000000000
|
---|
579 | dqmul1098 multiply 10000 100000000000000000000000 -> 1000000000000000000000000000
|
---|
580 | dqmul1099 multiply 10000 1000000000000000000000000 -> 10000000000000000000000000000
|
---|
581 | dqmul1100 multiply 10000 100000000000000000000000000000 -> 1000000000000000000000000000000000
|
---|
582 |
|
---|
583 | dqmul1107 multiply 10000 99999999999 -> 999999999990000
|
---|
584 | dqmul1108 multiply 10000 99999999999 -> 999999999990000
|
---|
585 |
|
---|
586 | -- Null tests
|
---|
587 | dqmul9990 multiply 10 # -> NaN Invalid_operation
|
---|
588 | dqmul9991 multiply # 10 -> NaN Invalid_operation
|
---|
589 |
|
---|