From b43eccd4cffed5bd1017c5821524fb6e49202f78 Mon Sep 17 00:00:00 2001
From: Sandeep Gupta
Date: Sun, 18 Jun 2017 23:55:40 +0530
Subject: First commit

---
 2.3-1/src/c/elementaryFunctions/lnp1m1/dlnp1m1s.c | 77 +++++++++++++++++++++++
 1 file changed, 77 insertions(+)
 create mode 100644 2.3-1/src/c/elementaryFunctions/lnp1m1/dlnp1m1s.c

(limited to '2.3-1/src/c/elementaryFunctions/lnp1m1/dlnp1m1s.c')

diff --git a/2.3-1/src/c/elementaryFunctions/lnp1m1/dlnp1m1s.c b/2.3-1/src/c/elementaryFunctions/lnp1m1/dlnp1m1s.c
new file mode 100644
index 00000000..7e1759be
--- /dev/null
+++ b/2.3-1/src/c/elementaryFunctions/lnp1m1/dlnp1m1s.c
@@ -0,0 +1,77 @@
+/*
+ *  Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
+ *  Copyright (C) 2008-2008 - INRIA - Bruno JOFRET
+ *  Copyright (C) Bruno Pincon
+ *
+ *  This file must be used under the terms of the CeCILL.
+ *  This source file is licensed as described in the file COPYING, which
+ *  you should have received as part of this distribution.  The terms
+ *  are also available at
+ *  http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
+ *
+ */
+
+#include "lnp1m1.h"
+#include "abs.h"
+
+/*
+	PURPOSE :  Compute   v = log ( (1 + s)/(1 - s) )
+	for small s, this is for |s| < SLIM = 0.20
+
+	ALGORITHM :
+	1/ if |s| is "very small" we use a truncated
+	taylor dvp (by keeping 3 terms) from :
+	2        4          6
+	t = 2 * s * ( 1 + 1/3 s  + 1/5 s  + [ 1/7 s  + ....] )
+	2        4
+	t = 2 * s * ( 1 + 1/3 s  + 1/5 s  + er)
+
+	The limit E until we use this formula may be simply
+	gotten so that the negliged part er is such that :
+	2        4
+	(#) er <= epsm * ( 1 + 1/3 s  + 1/5 s )   for all |s|<= E
+
+	As  er  = 1/7 s^6 + 1/9 s^8 + ...
+	er <= 1/7 * s^6 ( 1 + s^2 + s^4 + ...) = 1/7  s^6/(1-s^2)
+
+	the inequality (#) is forced if :
+
+	1/7  s^6 / (1-s^2)  <= epsm * ( 1 + 1/3 s^2  + 1/5 s^4 )
+
+	s^6 <= 7 epsm * (1 - 2/3 s^2 - 3/15 s^4 - 1/5 s^6)
+
+	So that E is very near (7 epsm)^(1/6) (approximately 3.032d-3):
+
+	2/ For larger |s| we used a minimax polynome :
+
+	yi = s * (2  + d3 s^3 + d5 s^5 .... + d13 s^13 + d15 s^15)
+
+	This polynome was computed (by some remes algorithm) following
+	(*) the sin(x) example (p 39) of the book :
+
+	"ELEMENTARY FUNCTIONS"
+	"Algorithms and implementation"
+	J.M. Muller (Birkhauser)
+
+	(*) without the additionnal raffinement to get the first coefs
+	very near floating point numbers)
+*/
+double dlnp1m1s(double Var)
+{
+	static double D3	= 0.66666666666672679472;
+	static double D5	= 0.39999999996176889299;
+	static double D7	= 0.28571429392829380980;
+	static double D9	= 0.22222138684562683797;
+	static double D11	= 0.18186349187499222459;
+	static double D13	= 0.15250315884469364710;
+	static double D15	= 0.15367270224757008114;
+	static double E		= 3.032E-3;
+	static double C3	= 2.0/3.0;
+	static double C5	= 2.0/5.0;
+
+	double S2 = Var * Var;
+	if( dabss(Var) <= E)
+		return Var * (2 + S2 * (C3 + C5 * S2));
+	else
+		return Var * (2 + S2 * (D3 + S2 * (D5 + S2 * (D7 + S2 * (D9 + S2 * (D11 + S2 * (D13 + S2 * D15)))))));
+}
-- 
cgit