From cfbdf90ab02f618d6c23980b74ed3bea1ee70284 Mon Sep 17 00:00:00 2001
From: florian <florian@freepascal.org>
Date: Mon, 2 Jan 2023 18:55:23 +0100
Subject: [PATCH]   * patch by Rika to optimize ArcCos, resolves #40078

---
 rtl/objpas/math.pp               | 24 +++---------------------
 tests/test/units/math/tsincos.pp | 20 ++++++++++++++++++++
 2 files changed, 23 insertions(+), 21 deletions(-)

diff --git a/rtl/objpas/math.pp b/rtl/objpas/math.pp
index 288a29c1d1..a0e7b8c394 100644
--- a/rtl/objpas/math.pp
+++ b/rtl/objpas/math.pp
@@ -1179,37 +1179,19 @@ end;
 {$ifdef FPC_HAS_TYPE_SINGLE}
 function Arccos(x : Single) : Single;
 begin
-  if abs(x)=1.0 then
-    if x<0.0 then
-      arccos:=Pi
-    else
-      arccos:=0
-  else
-    arccos:=arctan2(sqrt((1.0-x)*(1.0+x)),x);
+  arccos:=arctan2(sqrt((1.0-x)*(1.0+x)),x);
 end;
 {$ENDIF}
 {$ifdef FPC_HAS_TYPE_DOUBLE}
 function Arccos(x : Double) : Double;
 begin
-  if abs(x)=1.0 then
-    if x<0.0 then
-      arccos:=Pi
-    else
-      arccos:=0
-  else
-    arccos:=arctan2(sqrt((1.0-x)*(1.0+x)),x);
+  arccos:=arctan2(sqrt((1.0-x)*(1.0+x)),x);
 end;
 {$ENDIF}
 {$ifdef FPC_HAS_TYPE_EXTENDED}
 function Arccos(x : Extended) : Extended;
 begin
-  if abs(x)=1.0 then
-    if x<0.0 then
-      arccos:=Pi
-    else
-      arccos:=0
-  else
-    arccos:=arctan2(sqrt((1.0-x)*(1.0+x)),x);
+  arccos:=arctan2(sqrt((1.0-x)*(1.0+x)),x);
 end;
 {$ENDIF}
 
diff --git a/tests/test/units/math/tsincos.pp b/tests/test/units/math/tsincos.pp
index 660ea31a00..04efbadfd7 100644
--- a/tests/test/units/math/tsincos.pp
+++ b/tests/test/units/math/tsincos.pp
@@ -37,6 +37,26 @@ begin
     halt(11);
   if not(SameValue(e2,-1)) then
     halt(12);
+
+  { ArcCos relies on ArcTan2 edge cases. }
+  s1:=arccos(single(1));
+  if s1<>0 then
+    halt(13);
+  s1:=arccos(single(-1));
+  if not SameValue(s1,single(pi)) then
+    halt(14);
+  d1:=arccos(double(1));
+  if d1<>0 then
+    halt(15);
+  d1:=arccos(double(-1));
+  if not SameValue(d1,double(pi)) then
+    halt(16);
+  e1:=arccos(extended(1));
+  if e1<>0 then
+    halt(17);
+  e1:=arccos(extended(-1));
+  if not SameValue(e1,extended(pi),1e-12) then
+    halt(18);
   writeln('ok');
 end.