fix coverage remove 0 branch

Author: heltonmc

src/besselj.jl

@@ -8,7 +8,8 @@
 #    where r1 and r2 are zeros of J0
 #    and P3 and Q8 are a 3 and 8 degree polynomial respectively
 #    Polynomial coefficients are from [1] which is based on [2]
-#    See [1] for more details and [2] for coefficients of polynomials
+#    See [1] for more details and [2] for coefficients of polynomials.
+#    For tiny arugments the power series expansion is used.
 #
 #    Branch 2: 5.0 < x < 80.0
 #              besselj0 = sqrt(2/(pi*x))*(cos(x - pi/4)*R7(x) - sin(x - pi/4)*R8(x))
@@ -75,7 +76,6 @@ end
 function besselj0(x::Float32)
     T = Float32
     x = abs(x)
-    iszero(x) && return one(x)
     isinf(x) && return zero(x)
 
     if x <= 2.0f0
@@ -100,15 +100,14 @@ end
 function besselj1(x::Float64)
     T = Float64
     x = abs(x)
-    iszero(x) && return zero(x)
     isinf(x) && return zero(x)
 
     if x <= 5.0
         z = x * x
         w = evalpoly(z, RP_j1(T)) / evalpoly(z, RQ_j1(T))
         w = w * x * (z - 1.46819706421238932572e1) * (z - 4.92184563216946036703e1)
         return w
-    elseif x < 100.0
+    elseif x < 75.0
         w = 5.0 / x
         z = w * w
         p = evalpoly(z, PP_j1(T)) / evalpoly(z, PQ_j1(T))
@@ -140,7 +139,6 @@ end
 
 function besselj1(x::Float32)
     x = abs(x)
-    iszero(x) && return zero(x)
     isinf(x) && return zero(x)
 
     if x <= 2.0f0
@@ -158,66 +156,3 @@ function besselj1(x::Float32)
         return p
     end
 end
-
-function besselj(n::Int, x::Float64)
-    if n < 0
-        n = -n
-        if (n & 1) == 0
-            sign = 1
-        else
-            sign = -1
-        end
-    else
-        sign = 1
-    end
-
-    if x < zero(x)
-        if (n & 1)
-            sign = -sign
-            x = -x
-        end
-    end
-
-    if n == 0
-        return sign * besselj0(x)
-    elseif n == 1
-        return sign * besselj1(x)
-    elseif n == 2
-        return sign * (2.0 * besselj1(x) / x  -  besselj0(x))
-    end
-
-    #if x < MACHEP
-     #   return 0.0
-    #end
-
-    k = 40 # or 53
-    pk = 2 * (n + k)
-    ans = pk
-    xk = x * x
-
-    for _ in 1:k
-        pk -= 2.0
-        ans = pk - (xk / ans)
-    end
-
-    ans = x / ans
-
-    pk = 1.0
-    pkm1 = inv(ans)
-    k = n - 1
-    r = 2 * k
-
-    for _ in 1:k
-        pkm2 = (pkm1 * r  -  pk * x) / x
-	    pk = pkm1
-	    pkm1 = pkm2
-	    r -= 2.0
-    end
-    if abs(pk) > abs(pkm1)
-        ans = besselj1(x) / pk
-    else
-        ans = besselj0(x) / pkm1
-    end
-
-    return sign * ans
-end

src/bessely.jl

@@ -138,55 +138,3 @@ function _bessely1_compute(x::Float32)
         return p
     end
 end
-
-#	Bessel function of second kind, order zero
-#
-#	Bessel function of second kind, order one
-#=
-Ported to Julia from:
-Cephes Math Library Release 2.2:  June, 1992
-Copyright 1984, 1987, 1992 by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-https://github.com/jeremybarnes/cephes/blob/master/single/j0f.c
-https://github.com/jeremybarnes/cephes/blob/master/single/j1f.c
-=#
-
-#=
-function bessely(n::Int, x)
-    if n < 0
-        n = -n
-        if n & 1 == 0
-            sign = 1
-        else sign = -1
-        end
-    else
-        sign = 1
-    end
-
-    if n == 0
-        return sign * bessely0(x)
-    elseif n == 1
-        return sign * bessely1(x)
-    end
-
-    if x <= 0.0
-        return NaN
-    end
-
-    anm2 = bessely0(x)
-    anm1 = bessely1(x)
-    an = zero(x)
-
-    k = 1
-    r = 2 * k
-
-    for _ in 1:n
-        an = r * anm1 / x - anm2
-        anm2 = anm1
-        anm1 = an
-        r += 2.0
-    end
-
-    return sign * an
-end
-=#

src/math_constants.jl

@@ -2,8 +2,8 @@ const ONEOSQPI(::Type{BigFloat}) = big"5.641895835477562869480794515607725858440
 const TWOOPI(::Type{BigFloat}) = big"6.3661977236758134307553505349005744813784E-1"
 #const SQPIO2(::Type{BigFloat}) = big"1.253314137315500251207882642405522626503493370304969158314961788171146827303924"
 #const SQ1O2PI(::Type{BigFloat}) = big"0.3989422804014326779399460599343818684758586311649346576659258296706579258993008"
-const SQ2OPI(::Type{BigFloat}) = big"0.7978845608028653558798921198687637369517172623298693153318516593413158517986017"
-const PIO4(::Type{BigFloat}) = big"0.7853981633974483096156608458198757210492923498437764552437361480769541015715495"
+#const SQ2OPI(::Type{BigFloat}) = big"0.7978845608028653558798921198687637369517172623298693153318516593413158517986017"
+#const PIO4(::Type{BigFloat}) = big"0.7853981633974483096156608458198757210492923498437764552437361480769541015715495"
 
 const PIO4(::Type{Float64}) = .78539816339744830962
 const THPIO4(::Type{Float64}) = 2.35619449019234492885