RoundNearest argument for rem

Author: simonbyrne

base/exports.jl

@@ -407,6 +407,7 @@ export
     reinterpret,
     rem,
     rem1,
+    rem2pi,
     round,
     sec,
     secd,

base/linalg/diagonal.jl

@@ -90,7 +90,7 @@ det(D::Diagonal) = prod(D.diag)
 logdet{T<:Real}(D::Diagonal{T}) = sum(log(D.diag))
 function logdet{T<:Complex}(D::Diagonal{T}) #Make sure branch cut is correct
     x = sum(log(D.diag))
-    -pi<imag(x)<pi ? x : real(x)+(mod2pi(imag(x)+pi)-pi)*im
+    complex(real(x),rem2pi(imag(x),RoundNearest))
 end
 # identity matrices via eye(Diagonal{type},n)
 eye{T}(::Type{Diagonal{T}}, n::Int) = Diagonal(ones(T,n))

base/linalg/lu.jl

@@ -175,9 +175,7 @@ function logdet{T<:Complex,S}(A::LU{T,S})
     if isodd(sum(A.ipiv .!= 1:n))
         s = Complex(real(s), imag(s)+π)
     end
-    r, a = reim(s)
-    a = π-mod2pi(π-a) #Take principal branch with argument (-pi,pi]
-    complex(r,a)
+    complex(real(s),rem2pi(imag(s),RoundNearest))
 end
 
 inv!{T<:BlasFloat,S<:StridedMatrix}(A::LU{T,S}) = @assertnonsingular LAPACK.getri!(A.factors, A.ipiv) A.info

base/math.jl

@@ -11,7 +11,7 @@ export sin, cos, tan, sinh, cosh, tanh, asin, acos, atan,
        cbrt, sqrt, erf, erfc, erfcx, erfi, dawson,
        significand,
        lgamma, hypot, gamma, lfact, max, min, minmax, ldexp, frexp,
-       clamp, modf, ^, mod2pi,
+       clamp, modf, ^, mod2pi, rem2pi,
        airy, airyai, airyprime, airyaiprime, airybi, airybiprime, airyx,
        besselj0, besselj1, besselj, besseljx,
        bessely0, bessely1, bessely, besselyx,
@@ -22,7 +22,7 @@ export sin, cos, tan, sinh, cosh, tanh, asin, acos, atan,
 
 import Base: log, exp, sin, cos, tan, sinh, cosh, tanh, asin,
              acos, atan, asinh, acosh, atanh, sqrt, log2, log10,
-             max, min, minmax, ^, exp2,
+             max, min, minmax, ^, exp2, rem,
              exp10, expm1, log1p,
              sign_mask, exponent_mask, exponent_one, exponent_half,
              significand_mask, significand_bits, exponent_bits, exponent_bias
@@ -247,6 +247,12 @@ function frexp{T<:FloatingPoint}(A::Array{T})
     return (f, e)
 end
 
+
+rem(x::Float64, y::Float64, ::RoundingMode{:Nearest}) =
+    ccall((:remainder, libm),Float64,(Float64,Float64),x,y)
+rem(x::Float32, y::Float32, ::RoundingMode{:Nearest}) =
+    ccall((:remainderf, libm),Float32,(Float32,Float32),x,y)
+
 modf(x) = rem(x,one(x)), trunc(x)
 
 const _modff_temp = Float32[0]
@@ -324,6 +330,35 @@ const pi3o2_l  = 1.8369701987210297e-16 # convert(Float64, pi * BigFloat(3/2) -
 const pi4o2_h  = 6.283185307179586      # convert(Float64, pi * BigFloat(2))
 const pi4o2_l  = 2.4492935982947064e-16 # convert(Float64, pi * BigFloat(2) - pi4o2_h)
 
+function rem2pi(x::Float64, ::RoundingMode{:Nearest})
+    abs(x) < pi && return x
+
+    (n,y) = ieee754_rem_pio2(x)
+
+    if iseven(n)
+        if n&2 == 2 # add pi
+            return add22condh(y[1],y[2],pi2o2_h,pi2o2_l)
+        else # add 0
+            return y[1]
+        end
+    else
+        if n&2 == 2 # subtract pi/2
+            return add22condh(y[1],y[2],-pi1o2_h,-pi1o2_l)
+        else # add pi/2
+            return add22condh(y[1],y[2],pi1o2_h,pi1o2_l)
+        end
+    end
+end
+
+rem2pi(x::Float32, ::RoundingMode{:Nearest}) = Float32(rem2pi(Float64(x),RoundNearest))
+rem2pi(x::Int32, ::RoundingMode{:Nearest}) = rem2pi(Float64(x),RoundNearest)
+function rem2pi(x::Int64, ::RoundingMode{:Nearest})
+  fx = Float64(x)
+  fx == x || throw(ArgumentError("Int64 argument to rem2pi is too large: $x"))
+  rem2pi(fx,RoundNearest)
+end
+
+
 function mod2pi(x::Float64) # or modtau(x)
 # with r = mod2pi(x)
 # a) 0 <= r < 2π  (note: boundary open or closed - a bit fuzzy, due to rem_pio2 implementation)

base/mpfr.jl

@@ -541,6 +541,13 @@ function rem(x::BigFloat, y::BigFloat)
     return z
 end
 
+function rem(x::BigFloat, y::BigFloat, ::RoundingMode{:Nearest})
+    z = BigFloat()
+    ccall((:mpfr_remainder, :libmpfr), Int32, (Ptr{BigFloat}, Ptr{BigFloat}, Ptr{BigFloat}, Int32), &z, &x, &y, ROUNDING_MODE[end])
+    return z
+end
+
+
 function sum(arr::AbstractArray{BigFloat})
     z = BigFloat(0)
     for i in arr