[WIP] Optimize colormap

This uses `Tuple` instead of `Vector` for the colormap parameters.
This also unifies the type of preset values to `Float64`.

docs/src/colormapsandcolorscales.md

@@ -104,7 +104,9 @@ This package provides some pre-defined colormaps (described below). There are al
 
 The `colormap()` function returns a predefined sequential or diverging colormap computed using the algorithm by Wijffelaars, M., et al. (2008).
 
-`colormap(cname::String [, N::Int=100; mid=0.5, logscale=false, kvs...])`
+```julia
+colormap(cname::String [, N::Int=100; mid=0.5, logscale=false, <keyword arguments>])
+```
 
 The optional arguments are:
 
@@ -167,7 +169,10 @@ colormap
 
 You can create your own color palettes by using `sequential_palette()`:
 
-`sequential_palette(h, [N::Int=100; c=0.88, s=0.6, b=0.75, w=0.15, d=0.0, wcolor=RGB(1,1,0), dcolor=RGB(0,0,1), logscale=false])`
+```julia
+sequential_palette(h, [N::Int=100; c=0.88, s=0.6, b=0.75, w=0.15, d=0.0,
+                   wcolor=RGB(1,1,0), dcolor=RGB(0,0,1), logscale=false])
+```
 
 which creates a sequential map for a hue `h` (defined in LCHuv space).
 
@@ -185,7 +190,10 @@ Other possible parameters that you can fine tune are:
 
 Two sequential maps can also be combined into a diverging colormap by using:
 
-`diverging_palette(h1, h2 [, N::Int=100; mid=0.5,c=0.88, s=0.6, b=0.75, w=0.15, d1=0.0, d2=0.0, wcolor=RGB(1,1,0), dcolor1=RGB(1,0,0), dcolor2=RGB(0,0,1), logscale=false])`
+```julia
+diverging_palette(h1, h2 [, N::Int=100; mid=0.5,c=0.88, s=0.6, b=0.75, w=0.15, d1=0.0, d2=0.0,
+                  wcolor=RGB(1,1,0), dcolor1=RGB(1,0,0), dcolor2=RGB(0,0,1), logscale=false])
+```
 
 where the arguments are:
 

src/algorithms.jl

@@ -234,36 +234,35 @@ function MSC(h, l; linear::Bool=false)
         pend_l = l > pmid.l ? 100.0 : 0.0
         return (pend_l - l) / (pend_l - pmid.l) * pmid.c
     end
-    return find_maximum_chroma(LCHuv{Float64}(l, 0, h))
+    return find_maximum_chroma(LCHuv{Float64}(l, 0.0, h))
 end
 
 # This function finds the maximum chroma for the lightness `c.l` and hue `c.h`
 # by means of the binary search. Even though this requires more than 20
 # iterations, somehow, this is fast.
 function find_maximum_chroma(c::C,
-                             low::Real=0,
-                             high::Real=180) where {T, C<:Union{LCHab{T}, LCHuv{T}}}
+                             low::Real=0.0,
+                             high::Real=180.0) where {T, C<:Union{LCHab{T}, LCHuv{T}}}
     err = convert(T, 1e-6)
     l, h = convert(T, low), convert(T, high)
-    h - l < err && return l
-
-    mid = convert(T, (l + h) / 2)
-    min(mid - l, h - mid) == zero(T) && return l
-    lchm = C(c.l, mid, c.h)
-    rgbm = xyz_to_linear_rgb(convert(XYZ{T}, lchm))
-    clamped = max(red(rgbm), green(rgbm), blue(rgbm)) > 1-err ||
-              min(red(rgbm), green(rgbm), blue(rgbm)) <= 0
-    if clamped
-        return find_maximum_chroma(c, l, mid)::T
-    else
-        return find_maximum_chroma(c, mid, h)::T
+    while true
+        h - l < err && return l
+
+        mid = convert(T, (l + h) * oftype(l, 0.5))
+        min(mid - l, h - mid) == zero(T) && return l
+        lchm = C(c.l, mid, c.h)
+        rgbm = xyz_to_linear_rgb(convert(XYZ{T}, lchm))
+        clamped = max(red(rgbm), green(rgbm), blue(rgbm)) > 1-err ||
+                  min(red(rgbm), green(rgbm), blue(rgbm)) <= 0
+        l = clamped ? l : mid
+        h = clamped ? mid : h
     end
 end
 
 const LAB_HUE_Y = hue(convert(Lab, RGB(1.0, 1.0, 0.0)))
 
 function find_maximum_chroma(c::LCHab{T}) where T
-    maxc = find_maximum_chroma(c, 0, 135)
+    maxc = find_maximum_chroma(c, 0.0, 135.0)
 
     # The sRGB gamut in LCHab space has a *hollow* around the yellow corner.
     # Since the following boundary is based on the D65 white point, the values