From a93401cdb53d350e87f12ceb3b18cef4232c61af Mon Sep 17 00:00:00 2001
From: Jarl Holta <jarlholta@gmail.com>
Date: Thu, 9 Jan 2025 22:29:23 +0100
Subject: [PATCH] cbrt -> fcbrt & move to colormath_conversion

function is similar to fcbrt in colorlib, while not limited to x86 assembler, and rather than int magic we do sqrt and one more pass of newtons method.
---
 Source/simba.colormath_conversion.pas        | 23 ++++++++++++++--
 Source/simba.colormath_distance_unrolled.pas | 29 ++++++--------------
 2 files changed, 29 insertions(+), 23 deletions(-)

diff --git a/Source/simba.colormath_conversion.pas b/Source/simba.colormath_conversion.pas
index 765afb0e7..854ddbba9 100644
--- a/Source/simba.colormath_conversion.pas
+++ b/Source/simba.colormath_conversion.pas
@@ -60,8 +60,25 @@   TSimbaColorConversion = class
     class function XYZToRGB(const XYZ: TColorXYZ): TColorRGB; static;
   end;
 
+  function fcbrt(x: Single): Single; inline;
+
 implementation
 
+(*
+ * 2-4x speedup over Power(x, 1/3) in LAB colorspace finding
+ * Not a generalizable solution, but good for small numbers
+ * For number beyond this, consider the less accurate (for small numbers)
+ * https://pastebin.com/uRAwkm7s - Sun Microsystems (C) 1993
+ *)
+function fcbrt(x: Single): Single; inline;
+begin
+  Result := Sqrt(x);
+  Result := (2.0 * Result + x / Sqr(Result)) / 3.0;
+  Result := (2.0 * Result + x / Sqr(Result)) / 3.0;
+  Result := (2.0 * Result + x / Sqr(Result)) / 3.0;
+//Result := (2.0 * Result + x / Sqr(Result)) / 3.0; // Can't see that we need one more
+end;
+
 class function TSimbaColorConversion.ColorToBGRA(const Color: TColor; const Alpha: Byte): TColorBGRA;
 begin
   Result.R := (Color and R_MASK) shr R_BIT;
@@ -140,11 +157,11 @@ class function TSimbaColorConversion.RGBToLAB(const RGB: TColorRGB): TColorLAB;
   Z := (vR * 0.0193 + vG * 0.1192 + vB * 0.9505) * D65_Zn_Inv;
 
   // XYZ To LAB
-  if X > 0.008856 then X := Power(X, ONE_DIV_THREE)
+  if X > 0.008856 then X := fcbrt(x)
   else                 X := (7.787 * X) + 0.137931;
-  if Y > 0.008856 then Y := Power(Y, ONE_DIV_THREE)
+  if Y > 0.008856 then Y := fcbrt(y)
   else                 Y := (7.787 * Y) + 0.137931;
-  if Z > 0.008856 then Z := Power(Z, ONE_DIV_THREE)
+  if Z > 0.008856 then Z := fcbrt(z)
   else                 Z := (7.787 * Z) + 0.137931;
 
   Result.L := (116.0 * Y) - 16.0;
diff --git a/Source/simba.colormath_distance_unrolled.pas b/Source/simba.colormath_distance_unrolled.pas
index 74b13d66c..af82b3d2e 100644
--- a/Source/simba.colormath_distance_unrolled.pas
+++ b/Source/simba.colormath_distance_unrolled.pas
@@ -29,17 +29,6 @@ function DistanceDeltaE_UnRolled(const C1: PColorLAB; const C2: TColorBGRA; cons
 
 implementation
 
-// 2-4x speedup over Power(x, 1/3) in LAB colorspace finding
-function Cbrt(x: Single): Single; inline;
-begin
-  Result := Sqrt(x);
-  Result := (2.0 * Result + x / Sqr(Result)) / 3.0;
-  Result := (2.0 * Result + x / Sqr(Result)) / 3.0;
-  Result := (2.0 * Result + x / Sqr(Result)) / 3.0;
-//Result := (2.0 * Result + x / Sqr(Result)) / 3.0; // Can't see that we need one more
-end;
-
-
 function DistanceRGB_UnRolled(const C1: PColorRGB; const C2: TColorBGRA; const mul: TChannelMultipliers): Single;
 begin
   Result := Sqrt(Sqr((C1^.R-C2.R) * mul[0]) + Sqr((C1^.G-C2.G) * mul[1]) + Sqr((C1^.B-C2.B) * mul[2]));
@@ -196,11 +185,11 @@ function DistanceLAB_UnRolled(const C1: PColorLAB; const C2: TColorBGRA; const m
   Y := (vR * 0.2126 + vG * 0.7152 + vB * 0.0722) * D65_Yn_Inv;
   Z := (vR * 0.0193 + vG * 0.1192 + vB * 0.9505) * D65_Zn_Inv;
 
-  if X > 0.008856 then X := Cbrt(X)
+  if X > 0.008856 then X := fcbrt(X)
   else                 X := (7.787 * X) + 0.137931;
-  if Y > 0.008856 then Y := Cbrt(Y)
+  if Y > 0.008856 then Y := fcbrt(Y)
   else                 Y := (7.787 * Y) + 0.137931;
-  if Z > 0.008856 then Z := Cbrt(Z)
+  if Z > 0.008856 then Z := fcbrt(Z)
   else                 Z := (7.787 * Z) + 0.137931;
 
   Color2.L := (116.0 * Y) - 16.0;
@@ -234,11 +223,11 @@ function DistanceLCH_UnRolled(const C1: PColorLCH; const C2: TColorBGRA; const m
   Y := (vR * 0.2126 + vG * 0.7152 + vB * 0.0722) * D65_Yn_Inv;
   Z := (vR * 0.0193 + vG * 0.1192 + vB * 0.9505) * D65_Zn_Inv;
 
-  if X > 0.008856 then X := Cbrt(X)
+  if X > 0.008856 then X := fcbrt(X)
   else                 X := (7.787 * X) + 0.137931;
-  if Y > 0.008856 then Y := Cbrt(Y)
+  if Y > 0.008856 then Y := fcbrt(Y)
   else                 Y := (7.787 * Y) + 0.137931;
-  if Z > 0.008856 then Z := Cbrt(Z)
+  if Z > 0.008856 then Z := fcbrt(Z)
   else                 Z := (7.787 * Z) + 0.137931;
 
   L := (116.0 * Y) - 16.0;
@@ -298,11 +287,11 @@ function DistanceDeltaE_UnRolled(const C1: PColorLAB; const C2: TColorBGRA; cons
   Y := (vR * 0.2126 + vG * 0.7152 + vB * 0.0722) * D65_Yn_Inv;
   Z := (vR * 0.0193 + vG * 0.1192 + vB * 0.9505) * D65_Zn_Inv;
 
-  if X > 0.008856 then X := Cbrt(X)
+  if X > 0.008856 then X := fcbrt(X)
   else                 X := (7.787 * X) + 0.137931;
-  if Y > 0.008856 then Y := Cbrt(Y)
+  if Y > 0.008856 then Y := fcbrt(Y)
   else                 Y := (7.787 * Y) + 0.137931;
-  if Z > 0.008856 then Z := Cbrt(Z)
+  if Z > 0.008856 then Z := fcbrt(Z)
   else                 Z := (7.787 * Z) + 0.137931;
 
   Color2.L := (116.0 * Y) - 16.0;