|
80 | 80 | @test_throws MethodError logfactorial(1.0)
|
81 | 81 | end
|
82 | 82 |
|
83 |
| - # loggamma & logabsgamma test cases (from Wolfram Alpha) |
84 |
| - @test loggamma(-300im) ≅ -473.17185074259241355733179182866544204963885920016823743 - 1410.3490664555822107569308046418321236643870840962522425im |
85 |
| - @test loggamma(3.099) ≅ loggamma(3.099+0im) ≅ 0.786413746900558058720665860178923603134125854451168869796 |
86 |
| - @test loggamma(1.15) ≅ loggamma(1.15+0im) ≅ -0.06930620867104688224241731415650307100375642207340564554 |
87 |
| - @test logabsgamma(0.89)[1] ≅ loggamma(0.89+0im) ≅ 0.074022173958081423702265889979810658434235008344573396963 |
88 |
| - @test loggamma(0.91) ≅ loggamma(0.91+0im) ≅ 0.058922567623832379298241751183907077883592982094770449167 |
89 |
| - @test loggamma(0.01) ≅ loggamma(0.01+0im) ≅ 4.599479878042021722513945411008748087261001413385289652419 |
90 |
| - @test loggamma(-3.4-0.1im) ≅ -1.1733353322064779481049088558918957440847715003659143454 + 12.331465501247826842875586104415980094316268974671819281im |
91 |
| - @test loggamma(-13.4-0.1im) ≅ -22.457344044212827625152500315875095825738672314550695161 + 43.620560075982291551250251193743725687019009911713182478im |
92 |
| - @test loggamma(-13.4+0.0im) ≅ conj(loggamma(-13.4-0.0im)) ≅ -22.404285036964892794140985332811433245813398559439824988 - 43.982297150257105338477007365913040378760371591251481493im |
93 |
| - @test loggamma(-13.4+8im) ≅ -44.705388949497032519400131077242200763386790107166126534 - 22.208139404160647265446701539526205774669649081807864194im |
94 |
| - @test logabsgamma(1+exp2(-20))[1] ≅ loggamma(1+exp2(-20)+0im) ≅ -5.504750066148866790922434423491111098144565651836914e-7 |
95 |
| - @test loggamma(1+exp2(-20)+exp2(-19)*im) ≅ -5.5047799872835333673947171235997541985495018556426e-7 - 1.1009485171695646421931605642091915847546979851020e-6im |
96 |
| - @test loggamma(-300+2im) ≅ -1419.3444991797240659656205813341478289311980525970715668 - 932.63768120761873747896802932133229201676713644684614785im |
97 |
| - @test loggamma(300+2im) ≅ 1409.19538972991765122115558155209493891138852121159064304 + 11.4042446282102624499071633666567192538600478241492492652im |
98 |
| - @test loggamma(1-6im) ≅ -7.6099596929506794519956058191621517065972094186427056304 - 5.5220531255147242228831899544009162055434670861483084103im |
99 |
| - @test loggamma(1-8im) ≅ -10.607711310314582247944321662794330955531402815576140186 - 9.4105083803116077524365029286332222345505790217656796587im |
100 |
| - @test loggamma(1+6.5im) ≅ conj(loggamma(1-6.5im)) ≅ -8.3553365025113595689887497963634069303427790125048113307 + 6.4392816159759833948112929018407660263228036491479825744im |
101 |
| - @test loggamma(1+1im) ≅ conj(loggamma(1-1im)) ≅ -0.6509231993018563388852168315039476650655087571397225919 - 0.3016403204675331978875316577968965406598997739437652369im |
102 |
| - @test loggamma(-pi*1e7 + 6im) ≅ -5.10911758892505772903279926621085326635236850347591e8 - 9.86959420047365966439199219724905597399295814979993e7im |
103 |
| - @test loggamma(-pi*1e7 + 8im) ≅ -5.10911765175690634449032797392631749405282045412624e8 - 9.86959074790854911974415722927761900209557190058925e7im |
104 |
| - @test loggamma(-pi*1e14 + 6im) ≅ -1.0172766411995621854526383224252727000270225301426e16 - 9.8696044010873714715264929863618267642124589569347e14im |
105 |
| - @test loggamma(-pi*1e14 + 8im) ≅ -1.0172766411995628137711690403794640541491261237341e16 - 9.8696044010867038531027376655349878694397362250037e14im |
106 |
| - @test loggamma(2.05 + 0.03im) ≅ conj(loggamma(2.05 - 0.03im)) ≅ 0.02165570938532611215664861849215838847758074239924127515 + 0.01363779084533034509857648574107935425251657080676603919im |
107 |
| - @test loggamma(2+exp2(-20)+exp2(-19)*im) ≅ 4.03197681916768997727833554471414212058404726357753e-7 + 8.06398296652953575754782349984315518297283664869951e-7im |
| 83 | + # values taken from Wolfram Alpha |
| 84 | + @testset "loggamma & logabsgamma test cases" begin |
| 85 | + @test loggamma(-300im) ≅ -473.17185074259241355733179182866544204963885920016823743 - 1410.3490664555822107569308046418321236643870840962522425im |
| 86 | + @test loggamma(3.099) ≅ loggamma(3.099+0im) ≅ 0.786413746900558058720665860178923603134125854451168869796 |
| 87 | + @test loggamma(1.15) ≅ loggamma(1.15+0im) ≅ -0.06930620867104688224241731415650307100375642207340564554 |
| 88 | + @test logabsgamma(0.89)[1] ≅ loggamma(0.89+0im) ≅ 0.074022173958081423702265889979810658434235008344573396963 |
| 89 | + @test loggamma(0.91) ≅ loggamma(0.91+0im) ≅ 0.058922567623832379298241751183907077883592982094770449167 |
| 90 | + @test loggamma(0.01) ≅ loggamma(0.01+0im) ≅ 4.599479878042021722513945411008748087261001413385289652419 |
| 91 | + @test loggamma(-3.4-0.1im) ≅ -1.1733353322064779481049088558918957440847715003659143454 + 12.331465501247826842875586104415980094316268974671819281im |
| 92 | + @test loggamma(-13.4-0.1im) ≅ -22.457344044212827625152500315875095825738672314550695161 + 43.620560075982291551250251193743725687019009911713182478im |
| 93 | + @test loggamma(-13.4+0.0im) ≅ conj(loggamma(-13.4-0.0im)) ≅ -22.404285036964892794140985332811433245813398559439824988 - 43.982297150257105338477007365913040378760371591251481493im |
| 94 | + @test loggamma(-13.4+8im) ≅ -44.705388949497032519400131077242200763386790107166126534 - 22.208139404160647265446701539526205774669649081807864194im |
| 95 | + @test logabsgamma(1+exp2(-20))[1] ≅ loggamma(1+exp2(-20)+0im) ≅ -5.504750066148866790922434423491111098144565651836914e-7 |
| 96 | + @test loggamma(1+exp2(-20)+exp2(-19)*im) ≅ -5.5047799872835333673947171235997541985495018556426e-7 - 1.1009485171695646421931605642091915847546979851020e-6im |
| 97 | + @test loggamma(-300+2im) ≅ -1419.3444991797240659656205813341478289311980525970715668 - 932.63768120761873747896802932133229201676713644684614785im |
| 98 | + @test loggamma(300+2im) ≅ 1409.19538972991765122115558155209493891138852121159064304 + 11.4042446282102624499071633666567192538600478241492492652im |
| 99 | + @test loggamma(1-6im) ≅ -7.6099596929506794519956058191621517065972094186427056304 - 5.5220531255147242228831899544009162055434670861483084103im |
| 100 | + @test loggamma(1-8im) ≅ -10.607711310314582247944321662794330955531402815576140186 - 9.4105083803116077524365029286332222345505790217656796587im |
| 101 | + @test loggamma(1+6.5im) ≅ conj(loggamma(1-6.5im)) ≅ -8.3553365025113595689887497963634069303427790125048113307 + 6.4392816159759833948112929018407660263228036491479825744im |
| 102 | + @test loggamma(1+1im) ≅ conj(loggamma(1-1im)) ≅ -0.6509231993018563388852168315039476650655087571397225919 - 0.3016403204675331978875316577968965406598997739437652369im |
| 103 | + @test loggamma(-pi*1e7 + 6im) ≅ -5.10911758892505772903279926621085326635236850347591e8 - 9.86959420047365966439199219724905597399295814979993e7im |
| 104 | + @test loggamma(-pi*1e7 + 8im) ≅ -5.10911765175690634449032797392631749405282045412624e8 - 9.86959074790854911974415722927761900209557190058925e7im |
| 105 | + @test loggamma(-pi*1e14 + 6im) ≅ -1.0172766411995621854526383224252727000270225301426e16 - 9.8696044010873714715264929863618267642124589569347e14im |
| 106 | + @test loggamma(-pi*1e14 + 8im) ≅ -1.0172766411995628137711690403794640541491261237341e16 - 9.8696044010867038531027376655349878694397362250037e14im |
| 107 | + @test loggamma(2.05 + 0.03im) ≅ conj(loggamma(2.05 - 0.03im)) ≅ 0.02165570938532611215664861849215838847758074239924127515 + 0.01363779084533034509857648574107935425251657080676603919im |
| 108 | + @test loggamma(2+exp2(-20)+exp2(-19)*im) ≅ 4.03197681916768997727833554471414212058404726357753e-7 + 8.06398296652953575754782349984315518297283664869951e-7im |
| 109 | + end |
108 | 110 |
|
109 | 111 | @testset "loggamma for non-finite arguments" begin
|
110 | 112 | @test loggamma(Inf + 0im) === Inf + 0im
|
|
118 | 120 | @test loggamma(Inf + Inf*im) === loggamma(NaN + 0im) === loggamma(NaN*im) === NaN + NaN*im
|
119 | 121 | end
|
120 | 122 |
|
| 123 | + @testset "BigFloat" begin |
| 124 | + # test cases (taken from WolframAlpha, computed to 78 digits ≈ 256 bits) |
| 125 | + @test loggamma(big"3.099") ≈ big"0.78641374690055805872066586017892360313412585445116886979672329071050823224651" rtol=1e-75 |
| 126 | + @test loggamma(big"1.15") ≈ big"-0.06930620867104688224241731415650307100375642207340564554412494594148673455871" rtol=1e-75 |
| 127 | + @test logabsgamma(big"0.89")[1] ≈ big"0.0740221739580814237022658899798106584342350083445733969634566129726762260738245" rtol=1e-75 |
| 128 | + @test loggamma(big"0.91") ≈ big"0.0589225676238323792982417511839070778835929820947704491677379048793029707373113" rtol=1e-75 |
| 129 | + @test loggamma(big"0.01") ≈ big"4.59947987804202172251394541100874808726100141338528965241917138771477998920321" rtol=1e-75 |
| 130 | + @test loggamma(1 + exp2(big"-20.0")) ≈ big"-5.50475006614886679092243442349111109814456565183691425527816079744208067935466e-7" rtol=1e-75 |
| 131 | + |
| 132 | + # consistency |
| 133 | + @test loggamma(big(3124.0)) == log(gamma(big(3124.0))) |
| 134 | + @test loggamma(big(3124.0)) ≈ loggamma(3124.0) |
| 135 | + @test logabsgamma(big(3124.0)) == (loggamma(big(3124.0)), 1) |
| 136 | + @test logabsgamma(big(3124.0))[1] ≈ logabsgamma(3124.0)[1] |
| 137 | + |
| 138 | + # promotions |
| 139 | + @test loggamma(big(3124)) == loggamma(big(3124.0)) |
| 140 | + @test loggamma(big(3//2)) == loggamma(big(1.5)) |
| 141 | + @test logabsgamma(big(3124)) == logabsgamma(big(3124.0)) |
| 142 | + @test logabsgamma(big(3//2)) == logabsgamma(big(1.5)) |
| 143 | + |
| 144 | + # negative values |
| 145 | + @test loggamma(big(-3.0)) == big(Inf) |
| 146 | + @test_throws DomainError loggamma(big(-2.76)) |
| 147 | + |
| 148 | + # non-finite values |
| 149 | + @test isnan(loggamma(big(NaN))) |
| 150 | + @test isnan(logabsgamma(big(NaN))[1]) |
| 151 | + @test loggamma(big(Inf)) == big(Inf) |
| 152 | + @test logabsgamma(big(Inf))[1] == big(Inf) |
| 153 | + end |
| 154 | + |
121 | 155 | @testset "Other float types" begin
|
122 | 156 | struct NotAFloat <: AbstractFloat
|
123 | 157 | end
|
|
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