remove gamma calls

Author: heltonmc

src/airy.jl

@@ -387,7 +387,7 @@ function airy_large_arg_a(x::ComplexOrReal{T}) where T
     xsqr = sqrt(x)
 
     out = zero(S)
-    t = gamma(one(T) / 6) * gamma(T(5) / 6) / 4
+    t = GAMMA_ONE_SIXTH(T) * GAMMA_FIVE_SIXTHS(T) / 4
     a = 4*xsqr*x
     for i in 0:MaxIter
         out += t
@@ -403,7 +403,7 @@ function airy_large_arg_b(x::ComplexOrReal{T}) where T
     xsqr = sqrt(x)
 
     out = zero(S)
-    t = gamma(one(T) / 6) * gamma(T(5) / 6) / 4
+    t = GAMMA_ONE_SIXTH(T) * GAMMA_FIVE_SIXTHS(T) / 4
     a = 4*xsqr*x
     for i in 0:MaxIter
         out += t
@@ -419,7 +419,9 @@ function airy_large_arg_c(x::ComplexOrReal{T}) where T
     xsqr = sqrt(x)
 
     out = zero(S)
-    t = gamma(-one(T) / 6) * gamma(T(7) / 6) / 4
+    # use identities of gamma to relate to defined constants
+    # t = gamma(-one(T) / 6) * gamma(T(7) / 6) / 4
+    t = -GAMMA_FIVE_SIXTHS(T) * GAMMA_ONE_SIXTH(T) / 4
     a = 4*xsqr*x
     for i in 0:MaxIter
         out += t
@@ -435,7 +437,9 @@ function airy_large_arg_d(x::ComplexOrReal{T}) where T
     xsqr = sqrt(x)
 
     out = zero(S)
-    t = gamma(-one(T) / 6) * gamma(T(7) / 6) / 4
+    # use identities of gamma to relate to defined constants
+    # t = gamma(-one(T) / 6) * gamma(T(7) / 6) / 4
+    t = -GAMMA_FIVE_SIXTHS(T) * GAMMA_ONE_SIXTH(T) / 4
     a = 4*xsqr*x
     for i in 0:MaxIter
         out += t

src/gamma.jl

@@ -66,4 +66,3 @@ function small_gamma(x)
     q = evalpoly(x, Q)
     return z * p / q
 end
-

src/math_constants.jl

@@ -25,5 +25,10 @@ const SQPIO2(::Type{Float32}) = 1.25331413731550025f0
 
 const GAMMA_TWO_THIRDS(::Type{Float64}) = 1.3541179394264005
 const GAMMA_ONE_THIRD(::Type{Float64}) = 2.6789385347077475
+const GAMMA_ONE_SIXTH(::Type{Float64}) = 5.566316001780235
+const GAMMA_FIVE_SIXTHS(::Type{Float64}) = 1.128787029908126
+
 const GAMMA_TWO_THIRDS(::Type{Float32}) = 1.3541179394264005f0
 const GAMMA_ONE_THIRD(::Type{Float32}) = 2.6789385347077475f0
+const GAMMA_ONE_SIXTH(::Type{Float32}) = 5.566316001780235f0
+const GAMMA_FIVE_SIXTHS(::Type{Float32}) = 1.128787029908126f0