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"{ Package: 'stx:goodies/regression' }"
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"{ NameSpace: RegressionTests }"
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TestCase subclass:#QDoubleTests
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2436
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instanceVariableNames:''
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classVariableNames:''
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poolDictionaries:''
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category:'tests-Regression-Numbers'
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1606
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!
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!QDoubleTests class methodsFor:'documentation'!
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documentation
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"
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documentation to be added.
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[author:]
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2442
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cg
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1606
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[instance variables:]
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[class variables:]
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[see also:]
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"
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! !
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!QDoubleTests methodsFor:'tests'!
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test_01_instance_creation
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1617
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|q|
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q := QDouble fromFloat:1.0.
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self assert:(q d0 = 1.0).
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self assert:(q d1 = 0.0).
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self assert:(q d2 = 0.0).
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self assert:(q d3 = 0.0).
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2417
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q := QDouble fromInteger:1.
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self assert:(q d0 = 1.0).
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self assert:(q d1 = 0.0).
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self assert:(q d2 = 0.0).
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self assert:(q d3 = 0.0).
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q := 1 asQDouble.
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self assert:(q d0 = 1.0).
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self assert:(q d1 = 0.0).
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self assert:(q d2 = 0.0).
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self assert:(q d3 = 0.0).
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q := 1.0 asQDouble.
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self assert:(q d0 = 1.0).
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self assert:(q d1 = 0.0).
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self assert:(q d2 = 0.0).
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self assert:(q d3 = 0.0).
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1606
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1617
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q := 1e40 asQDouble + 1.0 asQDouble.
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self assert:(q d0 = 1e40).
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self assert:(q d1 = 1.0).
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self assert:(q d2 = 0.0).
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self assert:(q d3 = 0.0).
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q := 1e40 asQDouble + 1.0.
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self assert:(q d0 = 1e40).
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self assert:(q d1 = 1.0).
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self assert:(q d2 = 0.0).
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self assert:(q d3 = 0.0).
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q := 1e120 asQDouble + 1e40 + 1.0.
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self assert:(q d0 = 1e120).
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self assert:(q d1 = 1e40).
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self assert:(q d2 = 1.0).
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self assert:(q d3 = 0.0).
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q := 1e200 asQDouble + 1e120 + 1e40 + 1.0.
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self assert:(q d0 = 1e200).
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self assert:(q d1 = 1e120).
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self assert:(q d2 = 1e40).
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self assert:(q d3 = 1.0).
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"
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self run:#test_01_instance_creation
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self new test_01_instance_creation
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"
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"Created: / 12-06-2017 / 17:03:46 / cg"
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1617
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"Modified: / 20-06-2017 / 07:48:51 / cg"
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2269
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"Modified: / 05-06-2019 / 20:15:30 / Claus Gittinger"
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!
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test_02_addition
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|d1 d2 l1 l2 sum_l q1 q2 sum_d sum_q|
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d1 := 1.0.
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d2 := 1.0e-16.
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sum_d := d1 + d2.
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"/ precision is lost with doubles!!
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self assert:( sum_d - 1.0 = 0.0 ).
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2442
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l1 := 1.0 asLongFloat.
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l2 := 1.0e-16 asLongFloat.
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sum_l := l1 + l2.
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"/ no precision is lost with long doubles!!
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self assert:( (sum_l - (1.0 asLongFloat)) > 0.0 ).
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1607
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l1 := 1.0 asLongFloat.
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l2 := 1.0e-30 asLongFloat.
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sum_l := l1 + l2.
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"/ precision is lost!!
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self assert:( (sum_l - (1.0 asLongFloat)) = 0.0 ).
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q1 := QDouble fromFloat:1.0.
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q2 := QDouble fromFloat:1.0e-16.
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sum_q := q1 + q2.
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2442
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2419
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"/ no precision is lost with qDoubles
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1607
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self assert:( (sum_q - (QDouble fromFloat:1.0)) > 0.0 ).
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2419
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self assert:( (sum_q - (QDouble fromFloat:1.0)) = 1.0e-16 ).
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q1 := QDouble fromFloat:1.0.
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q2 := QDouble fromFloat:1.0e-30.
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sum_q := q1 + q2.
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"/ no precision is lost with qDoubles
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self assert:( (sum_q - (QDouble fromFloat:1.0)) > 0.0 ).
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self assert:( (sum_q - (QDouble fromFloat:1.0)) = 1.0e-30 ).
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1614
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q1 := QDouble fromFloat:1.0.
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q2 := QDouble fromFloat:2.0.
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sum_q := q1 + q2.
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self assert:( sum_q = 3.0 ).
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2442
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1614
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q1 := QDouble fromFloat:1.0.
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q2 := QDouble fromFloat:2.0.
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sum_q := q1 + 2.0.
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self assert:( sum_q = 3.0 ).
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q1 := QDouble fromFloat:1.0.
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q2 := QDouble fromFloat:2.0.
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sum_q := 1.0 + q2.
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self assert:( sum_q = 3.0 ).
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1617
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q1 := 1e200 asQDouble + 1e120 + 1e40 + 1.0.
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q2 := 1e120.
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sum_q := q1 + q2.
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self assert:(sum_q d0 = 1e200).
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self assert:(sum_q d1 = 2e120).
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self assert:(sum_q d2 = 1e40).
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self assert:(sum_q d3 = 1.0).
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2417
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'%.60f' printf:{QDouble pi}
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154 |
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1606
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"
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self run:#test_02_addition
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self new test_02_addition
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"
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"Created: / 12-06-2017 / 17:05:07 / cg"
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1617
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"Modified: / 20-06-2017 / 07:49:32 / cg"
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2269
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"Modified: / 05-06-2019 / 20:15:38 / Claus Gittinger"
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1606
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!
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2445
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test_02b_addition
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|q1 q2 sum_q|
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q1 := 1.0e20 asQDouble.
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q2 := 1.0e-16 asQDouble.
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sum_q := q1 + q2.
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self assert:( sum_q - q1 = q2 ).
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self assert:( sum_q - q2 = q1 ).
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sum_q := sum_q + 1e-30.
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self assert:( sum_q - q1 -q2 = 1e-30 ).
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sum_q := sum_q + 1e10.
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self assert:( sum_q - q1 - q2 - 1e10 = 1e-30 ).
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self assert:( sum_q - q1 - q2 - 1e-30 = 1e10 ).
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"
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self run:#test_02b_addition
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self new test_02b_addition
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"
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!
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1606
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test_03_subtract
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|d1 d2 l1 l2 diff_l q1 q2 diff_d diff_q|
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d1 := 1.0.
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d2 := 0.99999.
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diff_d := d1 - d2.
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"/ precision is lost with doubles!!
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2442
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1606
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l1 := 1.0 asLongFloat.
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l2 := 0.99999 asLongFloat.
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diff_l := l1 - l2.
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"/ no precision is lost with long doubles!!
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q1 := QDouble fromFloat:1.0.
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q2 := QDouble fromFloat:0.99999.
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diff_q := q1 - q2.
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2442
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1606
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"
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self run:#test_03_subtract
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self new test_03_subtract
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"
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"Created: / 12-06-2017 / 23:12:00 / cg"
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2269
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"Modified: / 05-06-2019 / 20:16:12 / Claus Gittinger"
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1608
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!
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test_04_relops
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2195
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1608
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self assert:(1.0 = 1.0 asQDouble).
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self assert:(1.0 asQDouble = 1.0).
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self assert:(1.0 asQDouble = 1.0 asQDouble).
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self assert:(1 = 1 asQDouble).
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self assert:(1 asQDouble = 1).
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self assert:(1 asQDouble = 1 asQDouble).
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self assert:(1 = 1.0 asQDouble).
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self assert:(1.0 asQDouble = 1).
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self assert:(1.0 asQDouble = 1 asQDouble).
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2442
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1608
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self assert:(1.0 = 1 asQDouble).
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self assert:(1 asQDouble = 1.0).
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self assert:(1 asQDouble = 1.0 asQDouble).
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2442
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1608
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self deny:(1.0 = 1.1 asQDouble).
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self deny:(1.0 asQDouble = 1.1).
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self deny:(1.0 asQDouble = 1.1 asQDouble).
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self deny:(1 = 2 asQDouble).
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self deny:(1 asQDouble = 2).
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self deny:(1 asQDouble = 2 asQDouble).
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self deny:(1 = 2.0 asQDouble).
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self deny:(1.0 asQDouble = 2).
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self deny:(1.0 asQDouble = 2 asQDouble).
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self deny:(2.0 = 1 asQDouble).
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self deny:(2 asQDouble = 1.0).
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self deny:(2 asQDouble = 1.0 asQDouble).
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2442
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1608
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self assert:(1.0 < 1.1 asQDouble).
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self assert:(1.0 asQDouble < 1.1).
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self assert:(1.0 asQDouble < 1.1 asQDouble).
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self assert:(1 < 2 asQDouble).
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self assert:(1 asQDouble < 2).
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self assert:(1 asQDouble < 2 asQDouble).
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self assert:(1 < 2.0 asQDouble).
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self assert:(1.0 asQDouble < 2).
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self assert:(1.0 asQDouble < 2 asQDouble).
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262 |
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self assert:(1.0 < 2 asQDouble).
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self assert:(1 asQDouble < 2.0).
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self assert:(1 asQDouble < 2.0 asQDouble).
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2442
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1608
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self deny:(1.0 < 1.0 asQDouble).
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self deny:(1.0 asQDouble < 1.0).
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self deny:(1.0 asQDouble < 1.0 asQDouble).
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271 |
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self deny:(1 < 1 asQDouble).
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self deny:(1 asQDouble < 1).
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self deny:(1 asQDouble < 1 asQDouble).
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self deny:(1 < 1.0 asQDouble).
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self deny:(1.0 asQDouble < 1).
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self deny:(1.0 asQDouble < 1 asQDouble).
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279 |
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self deny:(1.0 < 1 asQDouble).
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self deny:(1 asQDouble < 1.0).
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self deny:(1 asQDouble < 1.0 asQDouble).
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283 |
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284 |
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285 |
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self assert:(2.0 > 1.1 asQDouble).
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self assert:(2.0 asQDouble > 1.1).
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288 |
self assert:(2.0 asQDouble > 1.1 asQDouble).
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289 |
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290 |
self assert:(3 > 2 asQDouble).
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self assert:(3 asQDouble > 2).
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self assert:(3 asQDouble > 2 asQDouble).
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293 |
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self assert:(3 > 2.0 asQDouble).
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self assert:(3.0 asQDouble > 2).
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self assert:(3.0 asQDouble > 2 asQDouble).
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297 |
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self assert:(3.0 > 2 asQDouble).
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self assert:(3 asQDouble > 2.0).
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self assert:(3 asQDouble > 2.0 asQDouble).
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301 |
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302 |
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303 |
self deny:(1.0 > 3.0 asQDouble).
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304 |
self deny:(1.0 asQDouble > 3.0).
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305 |
self deny:(1.0 asQDouble > 3.0 asQDouble).
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306 |
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self deny:(1 > 3 asQDouble).
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self deny:(1 asQDouble > 3).
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self deny:(1 asQDouble > 3 asQDouble).
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310 |
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self deny:(1 > 3.0 asQDouble).
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self deny:(1.0 asQDouble > 3).
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self deny:(1.0 asQDouble > 3 asQDouble).
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314 |
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self deny:(1.0 > 3 asQDouble).
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self deny:(1 asQDouble > 3.0).
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self deny:(1 asQDouble > 3.0 asQDouble).
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318 |
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319 |
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self assert:(1.0 <= 3.0 asQDouble).
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self assert:(1.0 asQDouble <= 3.0).
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self assert:(1.0 asQDouble <= 3.0 asQDouble).
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323 |
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self assert:(1.0 <= 1.0 asQDouble).
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self assert:(1.0 asQDouble <= 1.0).
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self assert:(1.0 asQDouble <= 1.0 asQDouble).
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2442
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327 |
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1608
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self assert:(2.0 >= 1.0 asQDouble).
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329 |
self assert:(2.0 asQDouble >= 1.0).
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330 |
self assert:(2.0 asQDouble >= 1.0 asQDouble).
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331 |
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332 |
self assert:(1.0 >= 1.0 asQDouble).
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333 |
self assert:(1.0 asQDouble >= 1.0).
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334 |
self assert:(1.0 asQDouble >= 1.0 asQDouble).
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335 |
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1617
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336 |
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2442
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337 |
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1617
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self assert: ((1.0 asQDouble + 1e-40) > 1.0 asQDouble).
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339 |
self assert: (1.0 asQDouble < (1.0 asQDouble + 1e-40)).
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340 |
self assert: (1.0 asQDouble < (1.0 asQDouble + 1e-80)).
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341 |
self assert: (1.0 asQDouble < (1.0 asQDouble + 1e-120)).
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342 |
self assert: (1.0 asQDouble < (1.0 asQDouble + 1e-300)).
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343 |
self assert: (1.0 asQDouble < (1.0 asQDouble + 1e-300)).
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|
2442
|
344 |
|
|
1617
|
345 |
self assert: ((1.0 asQDouble + 1e-40) > 1.0).
|
|
|
346 |
self assert: (1.0 < (1.0 asQDouble + 1e-40)).
|
|
|
347 |
self assert: (1.0 < (1.0 asQDouble + 1e-80)).
|
|
|
348 |
self assert: (1.0 < (1.0 asQDouble + 1e-120)).
|
|
|
349 |
self assert: (1.0 < (1.0 asQDouble + 1e-300)).
|
|
2445
|
350 |
self assert: (1.0 < (1.0 asQDouble + 1e-308)).
|
|
|
351 |
|
|
|
352 |
self assert: (1.0 asQDouble < (1.0 asQDouble + 1e-40) ).
|
|
|
353 |
self assert: ((1.0 asQDouble + 1e-40) > 1.0 asQDouble ).
|
|
|
354 |
self assert: ((1.0 asQDouble + 1e-80) > 1.0 asQDouble ).
|
|
|
355 |
self assert: ((1.0 asQDouble + 1e-120) > 1.0 asQDouble ).
|
|
|
356 |
self assert: ((1.0 asQDouble + 1e-300) > 1.0 asQDouble ).
|
|
|
357 |
self assert: ((1.0 asQDouble + 1e-308) > 1.0 asQDouble ).
|
|
|
358 |
|
|
|
359 |
self assert: ((1.0 asQDouble + 1e-40) > 1.0).
|
|
|
360 |
self assert: (1.0 < (1.0 asQDouble + 1e-40)).
|
|
|
361 |
self assert: (1.0 < (1.0 asQDouble + 1e-80)).
|
|
|
362 |
self assert: (1.0 < (1.0 asQDouble + 1e-120)).
|
|
1617
|
363 |
self assert: (1.0 < (1.0 asQDouble + 1e-300)).
|
|
2445
|
364 |
self assert: (1.0 < (1.0 asQDouble + 1e-300)).
|
|
|
365 |
|
|
|
366 |
self assert: (1.0 < (1.0 asQDouble + 1e-40) ).
|
|
|
367 |
self assert: ((1.0 asQDouble + 1e-40) > 1.0 ).
|
|
|
368 |
self assert: ((1.0 asQDouble + 1e-80) > 1.0 ).
|
|
|
369 |
self assert: ((1.0 asQDouble + 1e-120) > 1.0 ).
|
|
|
370 |
self assert: ((1.0 asQDouble + 1e-300) > 1.0 ).
|
|
|
371 |
self assert: ((1.0 asQDouble + 1e-308) > 1.0 ).
|
|
1617
|
372 |
|
|
1619
|
373 |
self assert: (1e10 asQDouble + 1.0) = 10000000001.0.
|
|
|
374 |
"/ that's the problem with Floats...
|
|
2442
|
375 |
"/ (1e20 asQDouble + 1.0) ~= 100000000000000000001.0.
|
|
|
376 |
"/ (1e20 + 1.0) - 1e20 ~= 1.0.
|
|
|
377 |
self assert: (1e20 asQDouble + 1.0) - 1e20 = 1.0.
|
|
1617
|
378 |
|
|
|
379 |
"/ here the precision of QDOubles is no longer enough:
|
|
|
380 |
"/ self assert: 1.0 asQDouble < (1.0 asQDouble + 1e-310).
|
|
|
381 |
|
|
1608
|
382 |
"
|
|
|
383 |
self run:#test_03_subtract
|
|
|
384 |
self new test_03_subtract
|
|
|
385 |
"
|
|
|
386 |
|
|
|
387 |
"Created: / 13-06-2017 / 17:11:37 / cg"
|
|
1619
|
388 |
"Modified (comment): / 20-06-2017 / 09:18:50 / cg"
|
|
2269
|
389 |
"Modified: / 05-06-2019 / 20:16:21 / Claus Gittinger"
|
|
1614
|
390 |
!
|
|
|
391 |
|
|
|
392 |
test_05_multiply
|
|
|
393 |
|q1 q2 p|
|
|
|
394 |
|
|
|
395 |
q1 := QDouble fromFloat:3.0. "/ DoubleArray(2.0 0.0 0.0 0.0)
|
|
|
396 |
p := 2.0 * q1.
|
|
|
397 |
|
|
|
398 |
self assert:(p d0 = 6.0).
|
|
|
399 |
self assert:(p d1 = 0.0).
|
|
|
400 |
self assert:(p d2 = 0.0).
|
|
|
401 |
self assert:(p d3 = 0.0).
|
|
|
402 |
self assert:(p = 6.0).
|
|
|
403 |
self assert:(6.0 = p).
|
|
|
404 |
|
|
|
405 |
q1 := QDouble fromFloat:2.0. "/ DoubleArray(2.0 0.0 0.0 0.0)
|
|
|
406 |
p := q1 * 3.0.
|
|
|
407 |
|
|
|
408 |
self assert:(p d0 = 6.0).
|
|
|
409 |
self assert:(p d1 = 0.0).
|
|
|
410 |
self assert:(p d2 = 0.0).
|
|
|
411 |
self assert:(p d3 = 0.0).
|
|
|
412 |
self assert:(p = 6.0).
|
|
|
413 |
self assert:(6.0 = p).
|
|
|
414 |
|
|
|
415 |
q1 := QDouble fromFloat:2.0. "/ DoubleArray(2.0 0.0 0.0 0.0)
|
|
|
416 |
q2 := QDouble fromFloat:3.0. "/ DoubleArray(3.0 0.0 0.0 0.0)
|
|
|
417 |
p := q1 * q2.
|
|
2442
|
418 |
|
|
1614
|
419 |
self assert:(p d0 = 6.0).
|
|
|
420 |
self assert:(p d1 = 0.0).
|
|
|
421 |
self assert:(p d2 = 0.0).
|
|
|
422 |
self assert:(p d3 = 0.0).
|
|
|
423 |
self assert:(p = 6.0).
|
|
|
424 |
self assert:(6.0 = p).
|
|
1617
|
425 |
|
|
|
426 |
"/ the 1 is not forgotten!!
|
|
|
427 |
q1 := 1 asQDouble + 1e40.
|
|
|
428 |
q2 := 2.0.
|
|
|
429 |
p := q1 * q2.
|
|
|
430 |
|
|
|
431 |
self assert:(p d0 = 2e40).
|
|
|
432 |
self assert:(p d1 = 2.0).
|
|
|
433 |
self assert:(p d2 = 0.0).
|
|
|
434 |
self assert:(p d3 = 0.0).
|
|
|
435 |
self assert:(p > 2e40).
|
|
1751
|
436 |
self assert:(p - 2e40) = 2.0.
|
|
1617
|
437 |
|
|
|
438 |
"/ nothing is forgotten!!
|
|
|
439 |
q1 := 1 asQDouble + 1e40 + 1e120.
|
|
|
440 |
q2 := 2.0.
|
|
|
441 |
p := q1 * q2.
|
|
|
442 |
|
|
|
443 |
self assert:(p d0 = 2e120).
|
|
|
444 |
self assert:(p d1 = 2e40).
|
|
|
445 |
self assert:(p d2 = 2.0).
|
|
|
446 |
self assert:(p d3 = 0.0).
|
|
|
447 |
self assert:(p > 2e120).
|
|
|
448 |
self assert:(p > (2e120 asQDouble + 2)).
|
|
|
449 |
self assert:(p > (2e120 asQDouble + 1e40)).
|
|
1751
|
450 |
self assert:(p - 2e120) = (2 asQDouble + 2e40).
|
|
|
451 |
self assert:(p - 2e120 - 2e40) = 2.0.
|
|
1617
|
452 |
|
|
1614
|
453 |
"
|
|
|
454 |
self run:#test_05_multiply
|
|
|
455 |
self new test_05_multiply
|
|
|
456 |
"
|
|
|
457 |
|
|
|
458 |
"Created: / 19-06-2017 / 16:58:29 / cg"
|
|
1617
|
459 |
"Modified (comment): / 20-06-2017 / 07:42:52 / cg"
|
|
2269
|
460 |
"Modified: / 05-06-2019 / 20:16:30 / Claus Gittinger"
|
|
1616
|
461 |
!
|
|
|
462 |
|
|
|
463 |
test_06_exp
|
|
|
464 |
|f1 q1|
|
|
|
465 |
|
|
1623
|
466 |
f1 := 2.0 exp.
|
|
|
467 |
q1 := 2.0 asQDouble exp.
|
|
2435
|
468 |
self assert:(q1 d0 - f1) abs < 0.00000001.
|
|
1616
|
469 |
|
|
2434
|
470 |
"/ the first 113 digits are (wolfram):
|
|
|
471 |
"/ 7.3890560989306502272304274605750078131803155705518473240871278225225737960790577633843124850791217947737531612654...
|
|
2442
|
472 |
"/ 2.0 exp
|
|
2434
|
473 |
"/ 7.38905609893065
|
|
2442
|
474 |
"/ 2.0QD exp
|
|
|
475 |
"/ 7.389056098930650227230427460575
|
|
|
476 |
"/ 2.0QD exp printfPrintString:'%.60f'
|
|
2434
|
477 |
"/ 7.389056098930650227230427460575007813180315570551847324087128
|
|
|
478 |
|
|
2442
|
479 |
f1 := 3.0 exp.
|
|
2434
|
480 |
q1 := 3.0 asQDouble exp.
|
|
2435
|
481 |
self assert:(q1 d0 - f1) abs < 0.00000001.
|
|
2434
|
482 |
|
|
|
483 |
"/ the first 113 digits are (wolfram):
|
|
|
484 |
"/ 20.0855369231876677409285296545817178969879078385541501443789342296988458780919737312044971602530177021536076158519...
|
|
2442
|
485 |
"/ 3.0 exp
|
|
2434
|
486 |
"/ 20.0855369231877
|
|
2442
|
487 |
"/ 3.0QD exp
|
|
2434
|
488 |
"/ 20.08553692318766774092852965458
|
|
2442
|
489 |
"/ 3.0QD exp printfPrintString:'%.60f'
|
|
2434
|
490 |
"/ 20.085536923187667740928529654581717896987907838554150144378934
|
|
|
491 |
|
|
|
492 |
|
|
2442
|
493 |
f1 := 0.5 exp.
|
|
2434
|
494 |
q1 := 0.5 asQDouble exp.
|
|
2435
|
495 |
self assert:(q1 d0 - f1) abs < 0.00000001.
|
|
2434
|
496 |
|
|
|
497 |
"/ the first digits are (wolfram):
|
|
|
498 |
"/ 1.648721270700128146848650787814163571653776100710148011575...
|
|
2442
|
499 |
"/ 0.5 exp
|
|
2434
|
500 |
"/ 1.64872127070013
|
|
2442
|
501 |
"/ 0.5QD exp
|
|
2434
|
502 |
"/ 1.648721270700128146848650787814
|
|
2442
|
503 |
"/ 0.5QD exp printfPrintString:'%.60f'
|
|
2434
|
504 |
"/ 1.648721270700128146848650787814163571653776100710148011575079
|
|
|
505 |
|
|
2442
|
506 |
f1 := -1.0 exp.
|
|
|
507 |
q1 := -1.0 asQDouble exp.
|
|
2435
|
508 |
self assert:(q1 d0 - f1) abs < 0.00000001.
|
|
|
509 |
|
|
2442
|
510 |
f1 := -3.0 exp.
|
|
|
511 |
q1 := -3.0 asQDouble exp.
|
|
2436
|
512 |
self assert:(q1 d0 - f1) abs < 0.00000001.
|
|
|
513 |
|
|
2434
|
514 |
|
|
2442
|
515 |
"/ 1.0 exp -> 2.71828182845905
|
|
2435
|
516 |
"/ 1.0 asQDouble exp 2.718281828459045235360287471353
|
|
|
517 |
"/ 1.0 exp asQDouble 2.718281828459045090795598298428
|
|
|
518 |
"/
|
|
|
519 |
"/ 3.0 ln -> 1.09861228866811
|
|
|
520 |
"/ 3.0 asQDouble ln 8.148220079427205481478375773976
|
|
|
521 |
"/ 3.0 ln asQDouble 1.098612288668109782108217586938
|
|
|
522 |
"/
|
|
2442
|
523 |
"/ 1.0 exp ln -> 1.0
|
|
2435
|
524 |
"/ 1.0 exp ln asQDouble -> 1.0
|
|
|
525 |
"/ 1.0 asQDouble exp ln 6.316187310732210430808896199868
|
|
|
526 |
"/ 1.0 exp asQDouble ln 6.316187310732210132396290848094
|
|
|
527 |
"/
|
|
2442
|
528 |
"/ f1 := 100 exp asQDouble 2.68811714181614E+.
|
|
2434
|
529 |
|
|
2442
|
530 |
f1 := 100 exp.
|
|
2434
|
531 |
q1 := 100 asQDouble exp.
|
|
2436
|
532 |
"/ self assert:(q1 d0 - f1) abs < 0.00000001.
|
|
2434
|
533 |
|
|
|
534 |
"/ the first digits are (wolfram):
|
|
2445
|
535 |
"/ 2.688117141816135448412625551580013587361111877374192241519160861528028703490956491415887109721984571081167087... × 10^43
|
|
2442
|
536 |
"/ 100 exp
|
|
2434
|
537 |
"/ 2.688117141816135448E+43
|
|
2442
|
538 |
"/ 100QD exp
|
|
2434
|
539 |
"/ 2.6881171418161354 109477678826e43
|
|
2442
|
540 |
"/ 100QD exp printfPrintString:'%2.60g'
|
|
2434
|
541 |
"/ 2.688117141816135410947767882599577473393902466198400202846738e43'
|
|
|
542 |
|
|
1616
|
543 |
"
|
|
|
544 |
self run:#test_06_exp
|
|
|
545 |
self new test_06_exp
|
|
|
546 |
"
|
|
|
547 |
|
|
|
548 |
"Created: / 19-06-2017 / 17:58:08 / cg"
|
|
1623
|
549 |
"Modified (comment): / 21-06-2017 / 13:45:56 / cg"
|
|
2269
|
550 |
"Modified: / 05-06-2019 / 20:16:35 / Claus Gittinger"
|
|
1617
|
551 |
!
|
|
|
552 |
|
|
1627
|
553 |
test_06b_log10
|
|
|
554 |
|q1 q2 d3a q3a d3b q3b q4 i|
|
|
|
555 |
|
|
2441
|
556 |
"/ 5.5...e-18
|
|
2442
|
557 |
q1 := QDouble d0: 5.55111512312578E-18
|
|
|
558 |
d1: -3.08148791101958E-34
|
|
|
559 |
d2: 1.71056941445901E-50
|
|
|
560 |
d3: 0.0.
|
|
1627
|
561 |
|
|
|
562 |
q2 := 10 / q1.
|
|
|
563 |
self assert:(q2 > 1e18).
|
|
|
564 |
|
|
|
565 |
d3a := q2 asFloat ln.
|
|
|
566 |
self assert:(d3a isNaN not).
|
|
2442
|
567 |
|
|
1627
|
568 |
q3a := q2 ln.
|
|
|
569 |
self assert:(q3a isNaN not).
|
|
2442
|
570 |
|
|
1627
|
571 |
d3b := q2 asFloat log10.
|
|
|
572 |
self assert:(d3b isNaN not).
|
|
|
573 |
|
|
|
574 |
q3b := q2 log10.
|
|
|
575 |
self assert:(q3b isNaN not).
|
|
|
576 |
|
|
|
577 |
q4 := q3b floor.
|
|
|
578 |
i := q4 asInteger.
|
|
|
579 |
|
|
2441
|
580 |
self assert:(1.0 asQDouble ln = 0.0).
|
|
2442
|
581 |
self assert:(QDouble e ln - 1.0) < (2*QDouble epsilon).
|
|
|
582 |
self assert:(QDouble e squared ln - 2.0) < (2*QDouble epsilon).
|
|
2441
|
583 |
|
|
|
584 |
self assert:(1.0 asQDouble log10 = 0.0).
|
|
2442
|
585 |
self assert:(10.0 asQDouble log10 - 1.0) < (2*QDouble epsilon).
|
|
|
586 |
self assert:(10000.0 asQDouble log10 - 5.0) < (2*QDouble epsilon).
|
|
2441
|
587 |
self assert:(1e20 asQDouble log10 - 20.0) < (2*QDouble epsilon).
|
|
|
588 |
self assert:(1e-20 asQDouble log10 + 20.0) < (2*QDouble epsilon).
|
|
|
589 |
|
|
|
590 |
"/ nope: too inaccurate
|
|
2442
|
591 |
"/ self assert:(1e-100 asQDouble log10 + 100.0) < (2*QDouble epsilon).
|
|
2441
|
592 |
|
|
|
593 |
"/ QDouble fmax abs log10 floor asInteger.
|
|
1627
|
594 |
|
|
|
595 |
"
|
|
|
596 |
self run:#test_06b_log10
|
|
|
597 |
self new test_06b_log10
|
|
|
598 |
"
|
|
|
599 |
|
|
|
600 |
"Created: / 03-07-2017 / 10:31:53 / cg"
|
|
2270
|
601 |
"Modified: / 05-06-2019 / 20:18:26 / Claus Gittinger"
|
|
1627
|
602 |
!
|
|
|
603 |
|
|
2432
|
604 |
test_06c_exp
|
|
|
605 |
|f1 q1 f2 q2 f3 q3|
|
|
|
606 |
|
|
|
607 |
f1 := 3.0 ln.
|
|
|
608 |
q1 := 3.0 ln asQDouble.
|
|
|
609 |
self assert:(q1 - f1) abs < 0.0001.
|
|
|
610 |
|
|
|
611 |
f2 := f1 negated.
|
|
|
612 |
q2 := q1 negated.
|
|
|
613 |
self assert:(q2 - f2) abs < 0.0001.
|
|
|
614 |
|
|
|
615 |
f3 := f2 exp.
|
|
|
616 |
q3 := q2 exp.
|
|
|
617 |
self assert:(q3 - f3) abs < 0.0001.
|
|
|
618 |
|
|
|
619 |
"
|
|
|
620 |
self run:#test_06c_exp
|
|
|
621 |
self new test_06c_exp
|
|
|
622 |
"
|
|
|
623 |
!
|
|
|
624 |
|
|
1617
|
625 |
test_07_reading
|
|
|
626 |
|q1 s|
|
|
|
627 |
|
|
|
628 |
q1 := QDouble readFrom: '3.1415926535897'.
|
|
|
629 |
s := '%55.54f' printf:{ q1 }.
|
|
|
630 |
self assert:(s = ' 3.1415926535897').
|
|
|
631 |
|
|
|
632 |
q1 := QDouble readFrom: '3.141592653589793238462643383'.
|
|
|
633 |
s := '%55.54f' printf:{ q1 }.
|
|
|
634 |
self assert:(s = ' 3.141592653589793238462643383').
|
|
|
635 |
|
|
|
636 |
q1 := QDouble readFrom: '3.141592653589793238462643383279502884197169399375105820'.
|
|
|
637 |
s := '%55.54f' printf:{ q1 }.
|
|
|
638 |
self assert:(s = '3.14159265358979323846264338327950288419716939937510582').
|
|
|
639 |
|
|
|
640 |
"
|
|
|
641 |
self run:#test_07_reading
|
|
|
642 |
self new test_07_reading
|
|
|
643 |
"
|
|
|
644 |
|
|
|
645 |
"Created: / 19-06-2017 / 23:29:34 / cg"
|
|
2270
|
646 |
"Modified: / 05-06-2019 / 20:18:51 / Claus Gittinger"
|
|
1617
|
647 |
!
|
|
|
648 |
|
|
|
649 |
test_08_conversion
|
|
|
650 |
|q i|
|
|
2195
|
651 |
|
|
1617
|
652 |
q := 1e10 asQDouble + 1.0.
|
|
|
653 |
i := q asInteger.
|
|
|
654 |
|
|
|
655 |
self assert:(i = 10000000001).
|
|
|
656 |
|
|
|
657 |
"
|
|
|
658 |
self run:#test_08_conversion
|
|
|
659 |
self new test_08_conversion
|
|
|
660 |
"
|
|
|
661 |
|
|
|
662 |
"Created: / 20-06-2017 / 07:51:50 / cg"
|
|
2270
|
663 |
"Modified: / 05-06-2019 / 20:18:48 / Claus Gittinger"
|
|
2417
|
664 |
!
|
|
|
665 |
|
|
2418
|
666 |
test_09_truncatingAndRounding
|
|
|
667 |
self assert:(1.0 truncatedAsFloat = 1.0).
|
|
|
668 |
self assert:(1.0 asQDouble truncatedAsFloat = 1.0 asQDouble).
|
|
|
669 |
self assert:(1.0 asQDouble truncatedAsFloat = 1.0).
|
|
|
670 |
|
|
|
671 |
self assert:(1.1 truncatedAsFloat = 1.0).
|
|
|
672 |
self assert:(1.1 asQDouble truncatedAsFloat = 1.0 asQDouble).
|
|
|
673 |
self assert:(1.1 asQDouble truncatedAsFloat = 1.0).
|
|
|
674 |
|
|
|
675 |
self assert:(1.999 truncatedAsFloat = 1.0).
|
|
|
676 |
self assert:(1.999 asQDouble truncatedAsFloat = 1.0 asQDouble).
|
|
|
677 |
self assert:(1.999 asQDouble truncatedAsFloat = 1.0).
|
|
|
678 |
|
|
|
679 |
self assert:(-1.999 truncatedAsFloat = -1.0).
|
|
|
680 |
self assert:(-1.999 asQDouble truncatedAsFloat = -1.0 asQDouble).
|
|
|
681 |
self assert:(-1.999 asQDouble truncatedAsFloat = -1.0).
|
|
|
682 |
|
|
|
683 |
self assert:(1.0 truncated == 1).
|
|
|
684 |
self assert:(1.0 asQDouble truncated == 1).
|
|
|
685 |
self assert:(1.0 asQDouble truncated == 1).
|
|
|
686 |
|
|
|
687 |
self assert:(1.1 truncated == 1).
|
|
|
688 |
self assert:(1.1 asQDouble truncated == 1).
|
|
|
689 |
self assert:(1.1 asQDouble truncated == 1).
|
|
|
690 |
|
|
|
691 |
self assert:(1.999 truncated == 1).
|
|
|
692 |
self assert:(1.999 asQDouble truncated == 1).
|
|
|
693 |
self assert:(1.999 asQDouble truncated == 1).
|
|
|
694 |
|
|
|
695 |
self assert:(-1.999 truncated == -1).
|
|
|
696 |
self assert:(-1.999 asQDouble truncated == -1).
|
|
|
697 |
self assert:(-1.999 asQDouble truncated == -1).
|
|
|
698 |
|
|
|
699 |
"/ ---------
|
|
|
700 |
self assert:(1.0 floorAsFloat = 1.0).
|
|
|
701 |
self assert:(1.0 asQDouble floorAsFloat = 1.0 asQDouble).
|
|
|
702 |
self assert:(1.0 asQDouble floorAsFloat = 1.0).
|
|
|
703 |
|
|
|
704 |
self assert:(1.1 floorAsFloat = 1.0).
|
|
|
705 |
self assert:(1.1 asQDouble floorAsFloat = 1.0 asQDouble).
|
|
|
706 |
self assert:(1.1 asQDouble floorAsFloat = 1.0).
|
|
|
707 |
|
|
|
708 |
self assert:(1.999 floorAsFloat = 1.0).
|
|
|
709 |
self assert:(1.999 asQDouble floorAsFloat = 1.0 asQDouble).
|
|
|
710 |
self assert:(1.999 asQDouble floorAsFloat = 1.0).
|
|
|
711 |
|
|
|
712 |
self assert:(-1.999 floorAsFloat = -2.0).
|
|
|
713 |
self assert:(-1.999 asQDouble floorAsFloat = -2.0 asQDouble).
|
|
|
714 |
self assert:(-1.999 asQDouble floorAsFloat = -2.0).
|
|
|
715 |
|
|
|
716 |
self assert:(1.0 floor == 1).
|
|
|
717 |
self assert:(1.0 asQDouble floor == 1).
|
|
|
718 |
self assert:(1.0 asQDouble floor == 1).
|
|
|
719 |
|
|
|
720 |
self assert:(1.1 floor == 1).
|
|
|
721 |
self assert:(1.1 asQDouble floor == 1).
|
|
|
722 |
self assert:(1.1 asQDouble floor == 1).
|
|
|
723 |
|
|
|
724 |
self assert:(1.999 floor == 1).
|
|
|
725 |
self assert:(1.999 asQDouble floor == 1).
|
|
|
726 |
self assert:(1.999 asQDouble floor == 1).
|
|
|
727 |
|
|
|
728 |
self assert:(-1.999 floor == -2).
|
|
|
729 |
self assert:(-1.999 asQDouble floor == -2).
|
|
|
730 |
self assert:(-1.999 asQDouble floor == -2).
|
|
|
731 |
|
|
|
732 |
"/ -------
|
|
|
733 |
self assert:(1.0 ceilingAsFloat = 1.0).
|
|
|
734 |
self assert:(1.0 asQDouble ceilingAsFloat = 1.0 asQDouble).
|
|
|
735 |
self assert:(1.0 asQDouble ceilingAsFloat = 1.0).
|
|
|
736 |
|
|
|
737 |
self assert:(1.1 ceilingAsFloat = 2.0).
|
|
|
738 |
self assert:(1.1 asQDouble ceilingAsFloat = 2.0 asQDouble).
|
|
|
739 |
self assert:(1.1 asQDouble ceilingAsFloat = 2.0).
|
|
2417
|
740 |
|
|
2418
|
741 |
self assert:(1.999 ceilingAsFloat = 2.0).
|
|
|
742 |
self assert:(1.999 asQDouble ceilingAsFloat = 2.0 asQDouble).
|
|
|
743 |
self assert:(1.999 asQDouble ceilingAsFloat = 2.0).
|
|
|
744 |
|
|
|
745 |
self assert:(-1.999 ceilingAsFloat = -1.0).
|
|
|
746 |
self assert:(-1.999 asQDouble ceilingAsFloat = -1.0 asQDouble).
|
|
|
747 |
self assert:(-1.999 asQDouble ceilingAsFloat = -1.0).
|
|
|
748 |
|
|
|
749 |
self assert:(1.0 ceiling == 1).
|
|
|
750 |
self assert:(1.0 asQDouble ceiling == 1).
|
|
|
751 |
self assert:(1.0 asQDouble ceiling == 1).
|
|
|
752 |
|
|
|
753 |
self assert:(1.1 ceiling == 2).
|
|
|
754 |
self assert:(1.1 asQDouble ceiling == 2).
|
|
|
755 |
self assert:(1.1 asQDouble ceiling == 2).
|
|
|
756 |
|
|
|
757 |
self assert:(1.999 ceiling == 2).
|
|
|
758 |
self assert:(1.999 asQDouble ceiling == 2).
|
|
|
759 |
self assert:(1.999 asQDouble ceiling == 2).
|
|
|
760 |
|
|
|
761 |
self assert:(-1.999 ceiling == -1).
|
|
|
762 |
self assert:(-1.999 asQDouble ceiling == -1).
|
|
|
763 |
self assert:(-1.999 asQDouble ceiling == -1).
|
|
|
764 |
|
|
|
765 |
"/ ---------
|
|
|
766 |
self assert:(1.0 roundedAsFloat = 1.0).
|
|
|
767 |
self assert:(1.0 asQDouble roundedAsFloat = 1.0 asQDouble).
|
|
|
768 |
self assert:(1.0 asQDouble roundedAsFloat = 1.0).
|
|
|
769 |
|
|
|
770 |
self assert:(1.1 roundedAsFloat = 1.0).
|
|
|
771 |
self assert:(1.1 asQDouble roundedAsFloat = 1.0 asQDouble).
|
|
|
772 |
self assert:(1.1 asQDouble roundedAsFloat = 1.0).
|
|
|
773 |
|
|
|
774 |
self assert:(1.999 roundedAsFloat = 2.0).
|
|
|
775 |
self assert:(1.999 asQDouble roundedAsFloat = 2.0 asQDouble).
|
|
|
776 |
self assert:(1.999 asQDouble roundedAsFloat = 2.0).
|
|
|
777 |
|
|
|
778 |
self assert:(1.499 roundedAsFloat = 1.0).
|
|
|
779 |
self assert:(1.499 asQDouble roundedAsFloat = 1.0 asQDouble).
|
|
|
780 |
self assert:(1.499 asQDouble roundedAsFloat = 1.0).
|
|
2417
|
781 |
|
|
2418
|
782 |
self assert:(1.5 roundedAsFloat = 2.0).
|
|
|
783 |
self assert:(1.5 asQDouble roundedAsFloat = 2.0 asQDouble).
|
|
|
784 |
self assert:(1.5 asQDouble roundedAsFloat = 2.0).
|
|
|
785 |
|
|
|
786 |
self assert:(-1.999 roundedAsFloat = -2.0).
|
|
|
787 |
self assert:(-1.999 asQDouble roundedAsFloat = -2.0 asQDouble).
|
|
|
788 |
self assert:(-1.999 asQDouble roundedAsFloat = -2.0).
|
|
|
789 |
|
|
|
790 |
self assert:(-1.499 roundedAsFloat = -1.0).
|
|
|
791 |
self assert:(-1.499 asQDouble roundedAsFloat = -1.0 asQDouble).
|
|
|
792 |
self assert:(-1.499 asQDouble roundedAsFloat = -1.0).
|
|
|
793 |
|
|
|
794 |
self assert:(-1.5 roundedAsFloat = -2.0).
|
|
|
795 |
self assert:(-1.5 asQDouble roundedAsFloat = -2.0 asQDouble).
|
|
|
796 |
self assert:(-1.5 asQDouble roundedAsFloat = -2.0).
|
|
|
797 |
|
|
|
798 |
self assert:(1.0 rounded == 1).
|
|
|
799 |
self assert:(1.0 asQDouble rounded == 1).
|
|
2417
|
800 |
|
|
2418
|
801 |
self assert:(1.1 rounded == 1).
|
|
|
802 |
self assert:(1.1 asQDouble rounded == 1).
|
|
|
803 |
|
|
|
804 |
self assert:(1.999 rounded == 2).
|
|
|
805 |
self assert:(1.999 asQDouble rounded == 2).
|
|
|
806 |
|
|
|
807 |
self assert:(1.499 rounded == 1).
|
|
|
808 |
self assert:(1.499 asQDouble rounded == 1).
|
|
|
809 |
|
|
|
810 |
self assert:(1.5 rounded == 2).
|
|
|
811 |
self assert:(1.5 asQDouble rounded == 2).
|
|
|
812 |
|
|
|
813 |
self assert:(-1.999 rounded == -2).
|
|
|
814 |
self assert:(-1.999 asQDouble rounded == -2).
|
|
2454
|
815 |
|
|
|
816 |
self assert:((-1.6 roundTo:0.5) = -1.5).
|
|
|
817 |
self assert:((-1.6 asQDouble roundTo:0.5) = -1.5).
|
|
|
818 |
self assert:((-1.6 asQDouble roundTo:0.5) = -1.5 asQDouble).
|
|
2418
|
819 |
|
|
2417
|
820 |
|
|
|
821 |
"
|
|
2418
|
822 |
self run:#test_09_truncatingAndRounding
|
|
|
823 |
self new test_09_truncatingAndRounding
|
|
|
824 |
"
|
|
|
825 |
!
|
|
|
826 |
|
|
|
827 |
test_10_printing
|
|
|
828 |
"/ 1.0001 asQDouble printString.
|
|
|
829 |
|
|
|
830 |
self assert:(1.0 asQDouble printString = 1.0 printString).
|
|
|
831 |
self assert:(1.0 asQDouble printString = '1.0').
|
|
|
832 |
self assert:(-1.0 asQDouble printString = -1.0 printString).
|
|
|
833 |
self assert:(-1.0 asQDouble printString = '-1.0').
|
|
|
834 |
|
|
2436
|
835 |
|
|
2442
|
836 |
"/ self assert:(1.125QD printString = 1.125 printString).
|
|
2436
|
837 |
self assert:(1.125 asQDouble printString = '1.125').
|
|
|
838 |
self assert:(-1.125 asQDouble printString = -1.125 printString).
|
|
|
839 |
self assert:(-1.125 asQDouble printString = '-1.125').
|
|
|
840 |
|
|
2418
|
841 |
"/ loose bits in double prec.: (1e10 + 1) - 1e10 -> 1.0
|
|
|
842 |
"/ loose bits in double prec.: (1e20 + 1) - 1e20 -> 0.0
|
|
|
843 |
self assert:((1e20 asQDouble + 1) - 1e20) = 1.0.
|
|
|
844 |
self assert:(((1e20 asQDouble + 1) - 1e20) printString = '1.0').
|
|
|
845 |
self assert:((1e40 asQDouble + 1) - 1e40) = 1.0.
|
|
|
846 |
self assert:(((1e40 asQDouble + 1) - 1e40) printString = '1.0').
|
|
|
847 |
|
|
|
848 |
self assert:((1e40 asQDouble + 1 + 1e-40) - 1e40 - 1) = 1e-40.
|
|
|
849 |
self assert:((1e40 asQDouble + 1 + 1e-40) + 1e-40 - 1e40 - 1) = 2e-40.
|
|
|
850 |
|
|
|
851 |
"
|
|
|
852 |
self run:#test_10_printing
|
|
|
853 |
self new test_10_printing
|
|
2417
|
854 |
"
|
|
2439
|
855 |
!
|
|
|
856 |
|
|
|
857 |
test_11a_pi
|
|
|
858 |
"/ Machin's Formula for Pi pi / 4 = 4 arctan(1/5) - arctan(1/239)
|
|
|
859 |
|
|
|
860 |
| at1_5 at1_239 pi_4 pi err|
|
|
|
861 |
|
|
|
862 |
at1_5 := (1 asQDouble / 5) arcTan.
|
|
|
863 |
at1_239 := (1 asQDouble / 239) arcTan.
|
|
|
864 |
pi_4 := (at1_5 * 4) - at1_239.
|
|
2442
|
865 |
pi := pi_4 * 4.
|
|
2439
|
866 |
err := QDouble pi - pi.
|
|
|
867 |
self assert:(err < (8 * QDouble epsilon)).
|
|
|
868 |
!
|
|
|
869 |
|
|
|
870 |
test_11b_pi
|
|
|
871 |
"/ Salamin-Brent Quadratic Formula for Pi
|
|
|
872 |
|
|
|
873 |
| max_iter a b s m a_new b_new p_old pi err|
|
|
|
874 |
|
|
|
875 |
max_iter := 6.
|
|
|
876 |
|
|
|
877 |
a := 1.0 asQDouble.
|
|
|
878 |
b := 0.5 asQDouble sqrt.
|
|
|
879 |
s := 0.5 asQDouble.
|
|
|
880 |
m := 1.0 asQDouble.
|
|
|
881 |
|
|
|
882 |
pi := 2.0 asQDouble * a squared / s.
|
|
|
883 |
1 to:max_iter do:[:i |
|
|
2442
|
884 |
m := m * 2.
|
|
|
885 |
a_new := 0.5 * (a+b).
|
|
|
886 |
b_new := a * b.
|
|
|
887 |
s := s - (m * (a_new squared - b_new)).
|
|
|
888 |
a := a_new.
|
|
|
889 |
b := b_new sqrt.
|
|
|
890 |
p_old := pi.
|
|
|
891 |
pi := 2 * a squared / s.
|
|
2439
|
892 |
].
|
|
|
893 |
|
|
|
894 |
err := QDouble pi - pi.
|
|
|
895 |
self assert:(err < (8 * QDouble epsilon)).
|
|
|
896 |
!
|
|
|
897 |
|
|
|
898 |
test_12_e
|
|
|
899 |
"/ Taylor for e
|
|
|
900 |
|
|
|
901 |
| e t n i err|
|
|
|
902 |
|
|
|
903 |
e := 2.0 asQDouble.
|
|
|
904 |
t := 1.0 asQDouble.
|
|
|
905 |
n := 1.0.
|
|
|
906 |
i := 0.
|
|
|
907 |
|
|
|
908 |
[t > QDouble epsilon] whileTrue:[
|
|
2442
|
909 |
i := i + 1.
|
|
|
910 |
n := n + 1.0.
|
|
|
911 |
t := t / n.
|
|
|
912 |
e := e + t.
|
|
2439
|
913 |
].
|
|
|
914 |
|
|
|
915 |
err := QDouble e - e.
|
|
|
916 |
self assert:(err < (8 * QDouble epsilon)).
|
|
1606
|
917 |
! !
|
|
|
918 |
|
|
|
919 |
!QDoubleTests class methodsFor:'documentation'!
|
|
|
920 |
|
|
|
921 |
version
|
|
|
922 |
^ '$Header$'
|
|
|
923 |
!
|
|
|
924 |
|
|
|
925 |
version_CVS
|
|
|
926 |
^ '$Header$'
|
|
|
927 |
! !
|
|
2445
|
928 |
|