This is a 6,154-byte text/plain file, placed in the public domain, which has been consulted 107 times since the year 2026.
// This function written in F# is not affiliated with the CIE (International Commission on Illumination),
// and is released into the public domain. It is provided "as is" without any warranty, express or implied.
open System
// The classic CIE ΔE2000 implementation, which operates on two L*a*b* colors, and returns their difference.
// "l" ranges from 0 to 100, while "a" and "b" are unbounded and commonly clamped to the range of -128 to 127.
let ciede_2000 (l_1: float) (a_1: float) (b_1: float) (l_2: float) (a_2: float) (b_2: float) : float =
// Working in F# with the CIEDE2000 color-difference formula.
// k_l, k_c, k_h are parametric factors to be adjusted according to
// different viewing parameters such as textures, backgrounds...
let k_l = 1.0
let k_c = 1.0
let k_h = 1.0
let mutable n = (Math.Sqrt(a_1 * a_1 + b_1 * b_1) + Math.Sqrt(a_2 * a_2 + b_2 * b_2)) * 0.5
n <- n * n * n * n * n * n * n
// A factor involving chroma raised to the power of 7 designed to make
// the influence of chroma on the total color difference more accurate.
n <- 1.0 + 0.5 * (1.0 - Math.Sqrt(n / (n + 6103515625.0)))
// Application of the chroma correction factor.
let c_1 = Math.Sqrt(a_1 * a_1 * n * n + b_1 * b_1)
let c_2 = Math.Sqrt(a_2 * a_2 * n * n + b_2 * b_2)
// atan2 is preferred over atan because it accurately computes the angle of
// a point (x, y) in all quadrants, handling the signs of both coordinates.
let mutable h_1 = Math.Atan2(b_1, a_1 * n)
let mutable h_2 = Math.Atan2(b_2, a_2 * n)
if h_1 < 0.0 then h_1 <- h_1 + 2.0 * Math.PI
if h_2 < 0.0 then h_2 <- h_2 + 2.0 * Math.PI
n <- Math.Abs(h_2 - h_1)
// Cross-implementation consistent rounding.
if Math.PI - 1E-14 < n && n < Math.PI + 1E-14 then n <- Math.PI
// When the hue angles lie in different quadrants, the straightforward
// average can produce a mean that incorrectly suggests a hue angle in
// the wrong quadrant, the next lines handle this issue.
let mutable h_m = (h_1 + h_2) * 0.5
let mutable h_d = (h_2 - h_1) * 0.5
if Math.PI < n then
h_d <- h_d + Math.PI
// 📜 Sharma’s formulation doesn’t use the next line, but the one after it,
// and these two variants differ by ±0.0003 on the final color differences.
h_m <- h_m + Math.PI
// h_m <- h_m + (if h_m < Math.PI then Math.PI else -Math.PI)
let p = 36.0 * h_m - 55.0 * Math.PI
n <- (c_1 + c_2) * 0.5
n <- n * n * n * n * n * n * n
// The hue rotation correction term is designed to account for the
// non-linear behavior of hue differences in the blue region.
let r_t = -2.0 * Math.Sqrt(n / (n + 6103515625.0))
* Math.Sin(Math.PI / 3.0 * Math.Exp(p * p / (-25.0 * Math.PI * Math.PI)))
n <- (l_1 + l_2) * 0.5
n <- (n - 50.0) * (n - 50.0)
// Lightness.
let l = (l_2 - l_1) / (k_l * (1.0 + 0.015 * n / Math.Sqrt(20.0 + n)))
// These coefficients adjust the impact of different harmonic
// components on the hue difference calculation.
let t = 1.0 + 0.24 * Math.Sin(2.0 * h_m + Math.PI / 2.0)
+ 0.32 * Math.Sin(3.0 * h_m + 8.0 * Math.PI / 15.0)
- 0.17 * Math.Sin(h_m + Math.PI / 3.0)
- 0.20 * Math.Sin(4.0 * h_m + 3.0 * Math.PI / 20.0)
n <- c_1 + c_2
// Hue.
let h = 2.0 * Math.Sqrt(c_1 * c_2) * Math.Sin(h_d) / (k_h * (1.0 + 0.0075 * n * t))
// Chroma.
let c = (c_2 - c_1) / (k_c * (1.0 + 0.0225 * n))
// Returning the square root ensures that dE00 accurately reflects the
// geometric distance in color space, which can range from 0 to around 185.
Math.Sqrt(l * l + h * h + c * c + c * h * r_t)
// GitHub Project : https://github.com/michel-leonard/ciede2000-color-matching
// Online Tests : https://michel-leonard.github.io/ciede2000-color-matching
// L1 = 97.0 a1 = 20.1 b1 = -4.1
// L2 = 98.7 a2 = 14.2 b2 = 3.3
// CIE ΔE00 = 6.4461817566 (Bruce Lindbloom, Netflix’s VMAF, ...)
// CIE ΔE00 = 6.4461652749 (Gaurav Sharma, OpenJDK, ...)
// Deviation between implementations ≈ 1.6e-5
// See the source code comments for easy switching between these two widely used ΔE*00 implementation variants.
///////////////////////////////////////////////
///////////////////////////////////////////////
/////// ///////
/////// CIEDE 2000 ///////
/////// Testing Random Colors ///////
/////// ///////
///////////////////////////////////////////////
///////////////////////////////////////////////
// This F# program outputs a CSV file to standard output, with its length determined by the first CLI argument.
// Each line contains seven columns :
// - Three columns for the random standard L*a*b* color
// - Three columns for the random sample L*a*b* color
// - And the seventh column for the precise Delta E 2000 color difference between the standard and sample
// The output will be correct, this can be verified :
// - With the C driver, which provides a dedicated verification feature
// - By using the JavaScript validator at https://michel-leonard.github.io/ciede2000-color-matching
let rnd = Random()
let round0or2 (value: float) : float =
if rnd.Next(2) = 0.0 then
Math.Round(value, 0)
else
Math.Round(value, 2)
let randInRange (minv: float) (maxv: float) : float =
let v = minv + rnd.NextDouble() * (maxv - minv)
round0or2 v
let args = Environment.GetCommandLineArgs()
let iterations =
if args.Length > 1 then
match Int32.TryParse(args.[1]) with
| (true, n) when n > 0 -> n
| _ -> 10000
else
10000
for _ in 1 .. iterations do
let l_1 = randInRange 0.0 100.0
let a_1 = randInRange -128.0 128.0
let b_1 = randInRange -128.0 128.0
let l_2 = randInRange 0.0 100.0
let a_2 = randInRange -128.0 128.0
let b_2 = randInRange -128.0 128.0
let delta_e = ciede_2000 l_1 a_1 b_1 l_2 a_2 b_2
printfn "%.02f,%.02f,%.02f,%.02f,%.02f,%.02f,%.015f" l_1 a_1 b_1 l_2 a_2 b_2 delta_e