From c62804ed7d17d0c254308a8a9a0ab0f0bc83818e Mon Sep 17 00:00:00 2001
From: Fabian Bieler <fabianbieler@fastmail.fm>
Date: Mon, 22 Apr 2013 19:50:51 +0200
Subject: [PATCH] glsl: Improve the accuracy of the asin() builtin function.
To: mesa-dev@lists.freedesktop.org

Extended the 3rd degree Series by two elements to 5th degree.

The function is now approximated by:
asin(x) = sign(x) * (pi/2 - pi/2 * sqrt(1 - |x|) * (1 + |x| * ((1/2 - 2/pi) + |x| * (A + |x| * (B + |x| * (C + |x| * D))))))
with constants A, B, C, D found by numerical fitting.
---
 src/glsl/builtins/ir/asin.ir |   80 +++++++++++++++++++++++++++++-------------
 1 file changed, 56 insertions(+), 24 deletions(-)

diff --git a/src/glsl/builtins/ir/asin.ir b/src/glsl/builtins/ir/asin.ir
index 45d9e67..4259447 100644
--- a/src/glsl/builtins/ir/asin.ir
+++ b/src/glsl/builtins/ir/asin.ir
@@ -19,12 +19,20 @@
 		    (constant float (-0.21460183))
 		    (expression float *
 		     (expression float abs (var_ref x))
-                     (expression float +
-                      (constant float (0.086566724))
-                      (expression float *
-                       (expression float abs (var_ref x))
-                       (constant float (-0.03102955))
-		     ))))))))))))
+		     (expression float +
+		      (constant float (0.08873435))
+		      (expression float *
+		       (expression float abs (var_ref x))
+		       (expression float +
+			(constant float (-0.047800794))
+			(expression float *
+			 (expression float abs (var_ref x))
+			 (expression float +
+			  (constant float (0.023164911))
+			  (expression float *
+			   (expression float abs (var_ref x))
+			   (constant float (-0.006116644))
+   ))))))))))))))))
 
    (signature vec2
      (parameters
@@ -46,12 +54,20 @@
 		    (constant float (-0.21460183))
 		    (expression vec2 *
 		     (expression vec2 abs (var_ref x))
-                     (expression vec2 +
-                      (constant float (0.086566724))
-                      (expression vec2 *
-                       (expression vec2 abs (var_ref x))
-                       (constant float (-0.03102955))
-		     ))))))))))))
+		     (expression vec2 +
+		      (constant float (0.08873435))
+		      (expression vec2 *
+		       (expression vec2 abs (var_ref x))
+		       (expression vec2 +
+			(constant float (-0.047800794))
+			(expression vec2 *
+			 (expression vec2 abs (var_ref x))
+			 (expression vec2 +
+			  (constant float (0.023164911))
+			  (expression vec2 *
+			   (expression vec2 abs (var_ref x))
+			   (constant float (-0.006116644))
+   ))))))))))))))))
 
    (signature vec3
      (parameters
@@ -73,12 +89,20 @@
 		    (constant float (-0.21460183))
 		    (expression vec3 *
 		     (expression vec3 abs (var_ref x))
-                     (expression vec3 +
-                      (constant float (0.086566724))
-                      (expression vec3 *
-                       (expression vec3 abs (var_ref x))
-                       (constant float (-0.03102955))
-		     ))))))))))))
+		     (expression vec3 +
+		      (constant float (0.08873435))
+		      (expression vec3 *
+		       (expression vec3 abs (var_ref x))
+		       (expression vec3 +
+			(constant float (-0.047800794))
+			(expression vec3 *
+			 (expression vec3 abs (var_ref x))
+			 (expression vec3 +
+			  (constant float (0.023164911))
+			  (expression vec3 *
+			   (expression vec3 abs (var_ref x))
+			   (constant float (-0.006116644))
+   ))))))))))))))))
 
    (signature vec4
      (parameters
@@ -100,10 +124,18 @@
 		    (constant float (-0.21460183))
 		    (expression vec4 *
 		     (expression vec4 abs (var_ref x))
-                     (expression vec4 +
-                      (constant float (0.086566724))
-                      (expression vec4 *
-                       (expression vec4 abs (var_ref x))
-                       (constant float (-0.03102955))
-		     ))))))))))))
+		     (expression vec4 +
+		      (constant float (0.08873435))
+		      (expression vec4 *
+		       (expression vec4 abs (var_ref x))
+		       (expression vec4 +
+			(constant float (-0.047800794))
+			(expression vec4 *
+			 (expression vec4 abs (var_ref x))
+			 (expression vec4 +
+			  (constant float (0.023164911))
+			  (expression vec4 *
+			   (expression vec4 abs (var_ref x))
+			   (constant float (-0.006116644))
+   ))))))))))))))))
 ))
-- 
1.7.10.4