From 2b1298cd69fe014dc61b73db47daefacf0328cce Mon Sep 17 00:00:00 2001
From: Alden <aldenbradford@gmail.com>
Date: Mon, 13 Feb 2023 03:50:30 -0500
Subject: [PATCH] use a method less prone to cancellation near x=1

---
 decimal.js  | 7 +++----
 decimal.mjs | 5 ++---
 2 files changed, 5 insertions(+), 7 deletions(-)

diff --git a/decimal.js b/decimal.js
index aa6526a..8eabf43 100644
--- a/decimal.js
+++ b/decimal.js
@@ -744,14 +744,13 @@
 
     Ctor.precision = pr + 6;
     Ctor.rounding = 1;
-
-    x = x.asin();
-    halfPi = getPi(Ctor, pr + 4, rm).times(0.5);
+    
+    x = (new Ctor(1)).minus(x).div(x.plus(1)).sqrt().atan();
 
     Ctor.precision = pr;
     Ctor.rounding = rm;
 
-    return halfPi.minus(x);
+    return x.times(2);
   };
 
 
diff --git a/decimal.mjs b/decimal.mjs
index 909300c..293ee8e 100644
--- a/decimal.mjs
+++ b/decimal.mjs
@@ -741,13 +741,12 @@ P.inverseCosine = P.acos = function () {
   Ctor.precision = pr + 6;
   Ctor.rounding = 1;
 
-  x = x.asin();
-  halfPi = getPi(Ctor, pr + 4, rm).times(0.5);
+  x = (new Ctor(1)).minus(x).div(x.plus(1)).sqrt().atan();
 
   Ctor.precision = pr;
   Ctor.rounding = rm;
 
-  return halfPi.minus(x);
+  return x.times(2);
 };