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more accurate and faster lgamma, and use a more standard branch cut #18330

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merged 10 commits into from
Sep 7, 2016
Merged

more accurate and faster lgamma, and use a more standard branch cut #18330

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69542e8
more accurate and faster lgamma, and use a more standard branch cut f…
stevengj Sep 2, 2016
f2db1ca
more tests
stevengj Sep 2, 2016
e1d72fc
use trick from Hare (1997) to compute log(prod of shifts) rather than…
stevengj Sep 2, 2016
be2084c
even more tests
stevengj Sep 2, 2016
d2aa66d
whoops, use 1e14 and not 10^14 to avoid integer overflow on 32-bit Wi…
stevengj Sep 2, 2016
afbcdbf
fix accuracy near zero at z=2
stevengj Sep 2, 2016
cb8caba
update manual for lgamma
stevengj Sep 2, 2016
7f5cede
news for lgamma changes
stevengj Sep 2, 2016
0debff5
can use a lower-degree Taylor series around z=2 because the coefficie…
stevengj Sep 2, 2016
6f6ff37
linewrap poly coefs
stevengj Sep 3, 2016
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more tests
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stevengj committed Sep 2, 2016
commit f2db1caef8381a2b7ade6ab25f201e95eab73cf6
17 changes: 17 additions & 0 deletions test/math.jl
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@test lgamma(-13.4-0.1im) ≅ -22.457344044212827625152500315875095825738672314550695161 + 43.620560075982291551250251193743725687019009911713182478im
@test lgamma(-13.4+0im) ≅ -22.404285036964892794140985332811433245813398559439824988 - 43.982297150257105338477007365913040378760371591251481493im
@test lgamma(-13.4+8im) ≅ -44.705388949497032519400131077242200763386790107166126534 - 22.208139404160647265446701539526205774669649081807864194im
@test lgamma(1+exp2(-20)) ≅ lgamma(1+exp2(-20)+0im) ≅ -5.504750066148866790922434423491111098144565651836914e-7
@test lgamma(1+exp2(-20)+exp2(-19)*im) ≅ -5.5047799872835333673947171235997541985495018556426e-7 - 1.1009485171695646421931605642091915847546979851020e-6im
@test lgamma(-300+2im) ≅ -1419.3444991797240659656205813341478289311980525970715668 - 932.63768120761873747896802932133229201676713644684614785im
@test lgamma(300+2im) ≅ 1409.19538972991765122115558155209493891138852121159064304 + 11.4042446282102624499071633666567192538600478241492492652im
@test lgamma(1-6im) ≅ -7.6099596929506794519956058191621517065972094186427056304 - 5.5220531255147242228831899544009162055434670861483084103im
@test lgamma(1-8im) ≅ -10.607711310314582247944321662794330955531402815576140186 - 9.4105083803116077524365029286332222345505790217656796587im

# lgamma for non-finite arguments:
@test lgamma(Inf + 0im) === Inf + 0im
@test lgamma(Inf - 0.0im) === Inf - 0.0im
@test lgamma(Inf + 1im) === Inf + Inf*im
@test lgamma(Inf - 1im) === Inf - Inf*im
@test lgamma(-Inf + 0.0im) === -Inf - Inf*im
@test lgamma(-Inf - 0.0im) === -Inf + Inf*im
@test lgamma(Inf*im) === -Inf + Inf*im
@test lgamma(-Inf*im) === -Inf - Inf*im
@test lgamma(Inf + Inf*im) === lgamma(NaN + 0im) === lgamma(NaN*im) === NaN + NaN*im

# digamma, trigamma, polygamma & zeta test cases (compared to Wolfram Alpha)
@test digamma(7+0im) ≅ 1.872784335098467139393487909917597568957840664060076401194232
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