From c15a97997ea6fce892c0bdd12b436b9eecfbea9f Mon Sep 17 00:00:00 2001
From: Simon Byrne <simonbyrne@gmail.com>
Date: Thu, 19 Jul 2018 14:28:36 -0700
Subject: [PATCH] handle round(x; base=...)

Fixes #28160.
---
 base/floatfuncs.jl | 35 ++++++++++++++++++++++++-----------
 test/rounding.jl   |  1 +
 2 files changed, 25 insertions(+), 11 deletions(-)

diff --git a/base/floatfuncs.jl b/base/floatfuncs.jl
index 82e2ef7119c8b..68dad13bcdfa8 100644
--- a/base/floatfuncs.jl
+++ b/base/floatfuncs.jl
@@ -123,19 +123,35 @@ round(::Type{T}, x::AbstractFloat, r::RoundingMode) where {T<:Integer} = trunc(T
 
 # NOTE: this relies on the current keyword dispatch behaviour (#9498).
 function round(x::Real, r::RoundingMode=RoundNearest;
-    digits::Union{Nothing,Integer}=nothing, sigdigits::Union{Nothing,Integer}=nothing, base=10)
+               digits::Union{Nothing,Integer}=nothing, sigdigits::Union{Nothing,Integer}=nothing, base::Union{Nothing,Integer}=nothing)
     isfinite(x) || return x
-    _round(x,r,digits,sigdigits,base)
+    if digits === nothing
+        if sigdigits === nothing
+            if base === nothing
+                # avoid recursive calls
+                throw(MethodError(round, (x,r)))
+            else
+                round(x,r)
+                # or throw(ArgumentError("`round` cannot use `base` argument without `digits` or `sigdigits` arguments."))
+            end
+        else
+            _round_sigdigits(x, r, sigdigits, base === nothing ? 10 : base)
+        end
+    else
+        if sigdigits === nothing
+            _round_digits(x, r, digits, base === nothing ? 10 : base)
+        else
+            throw(ArgumentError("`round` cannot use both `digits` and `sigdigits` arguments."))
+        end
+    end
 end
+
 trunc(x::Real; kwargs...) = round(x, RoundToZero; kwargs...)
 floor(x::Real; kwargs...) = round(x, RoundDown; kwargs...)
 ceil(x::Real; kwargs...)  = round(x, RoundUp; kwargs...)
 
 round(x::Integer, r::RoundingMode) = x
 
-# if we hit this method, it means that no `round(x, r)` method is defined
-_round(x::Real, r::RoundingMode, digits::Nothing, sigdigits::Nothing, base) = throw(MethodError(round, (x,r)))
-
 # round x to multiples of 1/invstep
 function _round_invstep(x, invstep, r::RoundingMode)
     y = round(x * invstep, r) / invstep
@@ -161,7 +177,7 @@ function _round_step(x, step, r::RoundingMode)
     return y
 end
 
-function _round(x, r::RoundingMode, digits::Integer, sigdigits::Nothing, base)
+function _round_digits(x, r::RoundingMode, digits::Integer, base)
     fx = float(x)
     if digits >= 0
         invstep = oftype(fx, base)^digits
@@ -185,14 +201,11 @@ function hidigit(x::AbstractFloat, base)
 end
 hidigit(x::Real, base) = hidigit(float(x), base)
 
-function _round(x, r::RoundingMode, digits::Nothing, sigdigits::Integer, base)
+function _round_sigdigits(x, r::RoundingMode, sigdigits::Integer, base)
     h = hidigit(x, base)
-    _round(x, r, sigdigits-h, nothing, base)
+    _round_digits(x, r, sigdigits-h, base)
 end
 
-_round(x, r::RoundingMode, digits::Integer, sigdigits::Integer, base) =
-    throw(ArgumentError("`round` cannot use both `digits` and `sigdigits` arguments."))
-
 # C-style round
 function round(x::AbstractFloat, ::RoundingMode{:NearestTiesAway})
     y = trunc(x)
diff --git a/test/rounding.jl b/test/rounding.jl
index a5cebccea5941..f9537180f0616 100644
--- a/test/rounding.jl
+++ b/test/rounding.jl
@@ -211,6 +211,7 @@ end
 # custom rounding and significant-digit ops
 @testset "rounding to digits relative to the decimal point" begin
     @test round(pi) ≈ 3.
+    @test round(pi, base=10) ≈ 3.
     @test round(pi, digits=0) ≈ 3.
     @test round(pi, digits=1) ≈ 3.1
     @test round(pi, digits=3, base=2) ≈ 3.125