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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: 2.58 |
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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) |
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359 dqmul760 multiply 1e-6069 1e-101 -> 1E-6170 Subnormal |
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360 dqmul761 multiply 1e-6069 1e-102 -> 1E-6171 Subnormal |
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361 dqmul762 multiply 1e-6069 1e-103 -> 1E-6172 Subnormal |
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362 dqmul763 multiply 1e-6069 1e-104 -> 1E-6173 Subnormal |
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363 dqmul764 multiply 1e-6069 1e-105 -> 1E-6174 Subnormal |
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364 dqmul765 multiply 1e-6069 1e-106 -> 1E-6175 Subnormal |
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365 dqmul766 multiply 1e-6069 1e-107 -> 1E-6176 Subnormal |
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366 dqmul767 multiply 1e-6069 1e-108 -> 0E-6176 Underflow Subnormal Inexact Rounded Clamped |
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367 dqmul768 multiply 1e-6069 1e-109 -> 0E-6176 Underflow Subnormal Inexact Rounded Clamped |
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368 dqmul769 multiply 1e-6069 1e-110 -> 0E-6176 Underflow Subnormal Inexact Rounded Clamped |
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369 -- [no equivalent of 'subnormal' for overflow] |
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370 dqmul770 multiply 1e+40 1e+6101 -> 1.000000000000000000000000000000E+6141 Clamped |
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371 dqmul771 multiply 1e+40 1e+6102 -> 1.0000000000000000000000000000000E+6142 Clamped |
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372 dqmul772 multiply 1e+40 1e+6103 -> 1.00000000000000000000000000000000E+6143 Clamped |
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373 dqmul773 multiply 1e+40 1e+6104 -> 1.000000000000000000000000000000000E+6144 Clamped |
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374 dqmul774 multiply 1e+40 1e+6105 -> Infinity Overflow Inexact Rounded |
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375 dqmul775 multiply 1e+40 1e+6106 -> Infinity Overflow Inexact Rounded |
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376 dqmul776 multiply 1e+40 1e+6107 -> Infinity Overflow Inexact Rounded |
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377 dqmul777 multiply 1e+40 1e+6108 -> Infinity Overflow Inexact Rounded |
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378 dqmul778 multiply 1e+40 1e+6109 -> Infinity Overflow Inexact Rounded |
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379 dqmul779 multiply 1e+40 1e+6110 -> Infinity Overflow Inexact Rounded |
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380 |
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381 dqmul801 multiply 1.0000E-6172 1 -> 1.0000E-6172 Subnormal |
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382 dqmul802 multiply 1.000E-6172 1e-1 -> 1.000E-6173 Subnormal |
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383 dqmul803 multiply 1.00E-6172 1e-2 -> 1.00E-6174 Subnormal |
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384 dqmul804 multiply 1.0E-6172 1e-3 -> 1.0E-6175 Subnormal |
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385 dqmul805 multiply 1.0E-6172 1e-4 -> 1E-6176 Subnormal Rounded |
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386 dqmul806 multiply 1.3E-6172 1e-4 -> 1E-6176 Underflow Subnormal Inexact Rounded |
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387 dqmul807 multiply 1.5E-6172 1e-4 -> 2E-6176 Underflow Subnormal Inexact Rounded |
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388 dqmul808 multiply 1.7E-6172 1e-4 -> 2E-6176 Underflow Subnormal Inexact Rounded |
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389 dqmul809 multiply 2.3E-6172 1e-4 -> 2E-6176 Underflow Subnormal Inexact Rounded |
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390 dqmul810 multiply 2.5E-6172 1e-4 -> 2E-6176 Underflow Subnormal Inexact Rounded |
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391 dqmul811 multiply 2.7E-6172 1e-4 -> 3E-6176 Underflow Subnormal Inexact Rounded |
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392 dqmul812 multiply 1.49E-6172 1e-4 -> 1E-6176 Underflow Subnormal Inexact Rounded |
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393 dqmul813 multiply 1.50E-6172 1e-4 -> 2E-6176 Underflow Subnormal Inexact Rounded |
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394 dqmul814 multiply 1.51E-6172 1e-4 -> 2E-6176 Underflow Subnormal Inexact Rounded |
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395 dqmul815 multiply 2.49E-6172 1e-4 -> 2E-6176 Underflow Subnormal Inexact Rounded |
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396 dqmul816 multiply 2.50E-6172 1e-4 -> 2E-6176 Underflow Subnormal Inexact Rounded |
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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 |
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400 dqmul819 multiply 3E-6172 1e-5 -> 0E-6176 Underflow Subnormal Inexact Rounded Clamped |
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401 dqmul820 multiply 5E-6172 1e-5 -> 0E-6176 Underflow Subnormal Inexact Rounded Clamped |
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402 dqmul821 multiply 7E-6172 1e-5 -> 1E-6176 Underflow Subnormal Inexact Rounded |
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403 dqmul822 multiply 9E-6172 1e-5 -> 1E-6176 Underflow Subnormal Inexact Rounded |
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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 |
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407 dqmul825 multiply 3E-6172 -1e-5 -> -0E-6176 Underflow Subnormal Inexact Rounded Clamped |
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408 dqmul826 multiply -5E-6172 1e-5 -> -0E-6176 Underflow Subnormal Inexact Rounded Clamped |
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409 dqmul827 multiply 7E-6172 -1e-5 -> -1E-6176 Underflow Subnormal Inexact Rounded |
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410 dqmul828 multiply -9E-6172 1e-5 -> -1E-6176 Underflow Subnormal Inexact Rounded |
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411 dqmul829 multiply 9.9E-6172 -1e-5 -> -1E-6176 Underflow Subnormal Inexact Rounded |
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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 |
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415 dqmul832 multiply 1.0E-5977 1e-199 -> 1E-6176 Subnormal Rounded |
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416 dqmul833 multiply 1.0E-5977 1e-198 -> 1.0E-6175 Subnormal |
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417 dqmul834 multiply 2.0E-5977 2e-198 -> 4.0E-6175 Subnormal |
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418 dqmul835 multiply 4.0E-5977 4e-198 -> 1.60E-6174 Subnormal |
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419 dqmul836 multiply 10.0E-5977 10e-198 -> 1.000E-6173 Subnormal |
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420 dqmul837 multiply 30.0E-5977 30e-198 -> 9.000E-6173 Subnormal |
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421 dqmul838 multiply 40.0E-5982 40e-166 -> 1.6000E-6145 Subnormal |
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422 dqmul839 multiply 40.0E-5982 40e-165 -> 1.6000E-6144 Subnormal |
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423 dqmul840 multiply 40.0E-5982 40e-164 -> 1.6000E-6143 |
|
424 |
|
425 -- Long operand overflow may be a different path |
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426 dqmul870 multiply 100 9.999E+6143 -> Infinity Inexact Overflow Rounded |
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427 dqmul871 multiply 100 -9.999E+6143 -> -Infinity Inexact Overflow Rounded |
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428 dqmul872 multiply 9.999E+6143 100 -> Infinity Inexact Overflow Rounded |
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429 dqmul873 multiply -9.999E+6143 100 -> -Infinity Inexact Overflow Rounded |
|
430 |
|
431 -- check for double-rounded subnormals |
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432 dqmul881 multiply 1.2347E-6133 1.2347E-40 -> 1.524E-6173 Inexact Rounded Subnormal Underflow |
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433 dqmul882 multiply 1.234E-6133 1.234E-40 -> 1.523E-6173 Inexact Rounded Subnormal Underflow |
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434 dqmul883 multiply 1.23E-6133 1.23E-40 -> 1.513E-6173 Inexact Rounded Subnormal Underflow |
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435 dqmul884 multiply 1.2E-6133 1.2E-40 -> 1.44E-6173 Subnormal |
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436 dqmul885 multiply 1.2E-6133 1.2E-41 -> 1.44E-6174 Subnormal |
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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 |