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Cin function #397

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6a7899c
Update SpecialFunctions.jl
seadra Apr 21, 2022
ac80545
Update sincosint.jl
seadra Apr 21, 2022
308a363
Update chainrules.jl
seadra Apr 21, 2022
60d9d37
Update sincosint.jl
seadra Jul 6, 2022
017be91
Update sincosint.jl
seadra Jul 7, 2022
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1 change: 1 addition & 0 deletions src/SpecialFunctions.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -78,6 +78,7 @@ export
expintx,
sinint,
cosint,
cosint2,
lbinomial

include("bessel.jl")
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1 change: 1 addition & 0 deletions src/chainrules.jl
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Expand Up @@ -193,6 +193,7 @@ ChainRulesCore.@scalar_rule(
ChainRulesCore.@scalar_rule(expinti(x), exp(x) / x)
ChainRulesCore.@scalar_rule(sinint(x), sinc(invπ * x))
ChainRulesCore.@scalar_rule(cosint(x), cos(x) / x)
ChainRulesCore.@scalar_rule(cosint2(x), iszero(x) ? zero(x) : (one(x)-cos(x))/x )

# elliptic integrals
ChainRulesCore.@scalar_rule(
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13 changes: 12 additions & 1 deletion src/sincosint.jl
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Expand Up @@ -216,7 +216,18 @@ function cosint(x::Float64)
end
end

for f in (:sinint, :cosint)
function cosint2(x::Float64)
y = abs(x)
if y < 0.5
z = y*y
return z * @horner(z, 1/4, -1/96, 1/4320, -1/322560, 1/36288000, 1/5748019200)
else
return MathConstants.eulergamma + log(y) - cosint(y)
end
end


for f in (:sinint, :cosint, :cosint2)
@eval begin
($f)(x::Float32) = Float32(($f)(Float64(x)))
($f)(x::Float16) = Float16(($f)(Float64(x)))
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8 changes: 8 additions & 0 deletions test/sincosint.jl
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Expand Up @@ -23,16 +23,22 @@

@test sinint(Float16(1)) == Float16(sinint(1))
@test cosint(Float16(1)) == Float16(cosint(1))
@test cosint2(Float16(1)) == Float16(cosint2(1))
@test sinint(Float32(1)) == Float32(sinint(1))
@test cosint(Float32(1)) == Float32(cosint(1))
@test cosint2(Float32(1)) == Float32(cosint2(1))

@test sinint(1//2) == sinint(0.5)
@test cosint(1//2) == cosint(0.5)
@test cosint2(1//2) == cosint2(0.5)

@test sinint(1e300) ≅ π/2
@test cosint(1e300) ≅ -8.17881912115908554103E-301
@test sinint(1e-300) ≅ 1.0E-300
@test cosint(1e-300) ≅ -690.1983122333121

@test cosint2(0.0) == 0.0
@test cosint2(0.05) ≅ 0.0006249348994501105 # Computed with Mathematica: SetPrecision[EulerGamma + Log[1/20] - CosIntegral[1/20], 20]

@test sinint(Inf) == π/2
@test cosint(Inf) == 0.0
Expand All @@ -41,10 +47,12 @@

@test_throws ErrorException sinint(big(1.0))
@test_throws ErrorException cosint(big(1.0))
@test_throws ErrorException cosint2(big(1.0))
@test_throws DomainError cosint(-1.0)
@test_throws DomainError cosint(Float32(-1.0))
@test_throws DomainError cosint(Float16(-1.0))
@test_throws DomainError cosint(-1//2)
@test_throws MethodError sinint(Complex(1))
@test_throws MethodError cosint(Complex(1))
@test_throws MethodError cosint2(Complex(1))
end