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| author | yash1112 | 2017-07-07 21:20:49 +0530 |
|---|---|---|
| committer | yash1112 | 2017-07-07 21:20:49 +0530 |
| commit | 9e5793a7b05b23e6044a6d7a9ddd5db39ba375f0 (patch) | |
| tree | f50d6e06d8fe6bc1a9053ef10d4b4d857800ab51 /2.3-1/src/c/elementaryFunctions/lnp1m1/dlnp1m1s.c | |
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sci2c arduino updated
Diffstat (limited to '2.3-1/src/c/elementaryFunctions/lnp1m1/dlnp1m1s.c')
| -rw-r--r-- | 2.3-1/src/c/elementaryFunctions/lnp1m1/dlnp1m1s.c | 77 |
1 files changed, 77 insertions, 0 deletions
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)))))));
+}
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