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| author | Siddhesh Wani | 2015-05-25 14:46:31 +0530 |
|---|---|---|
| committer | Siddhesh Wani | 2015-05-25 14:46:31 +0530 |
| commit | db464f35f5a10b58d9ed1085e0b462689adee583 (patch) | |
| tree | de5cdbc71a54765d9fec33414630ae2c8904c9b8 /src/c/elementaryFunctions/asin/zasins.c | |
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Original Version
Diffstat (limited to 'src/c/elementaryFunctions/asin/zasins.c')
| -rw-r--r-- | src/c/elementaryFunctions/asin/zasins.c | 146 |
1 files changed, 146 insertions, 0 deletions
diff --git a/src/c/elementaryFunctions/asin/zasins.c b/src/c/elementaryFunctions/asin/zasins.c new file mode 100644 index 0000000..5bd586a --- /dev/null +++ b/src/c/elementaryFunctions/asin/zasins.c @@ -0,0 +1,146 @@ +/*
+ * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
+ * Copyright (C) 2007-2008 - 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
+ *
+ */
+
+/*
+ * REFERENCE
+ * This is a Fortran-77 translation of an algorithm by
+ * T.E. Hull, T. F. Fairgrieve and P.T.P. Tang which
+ * appears in their article :
+ * "Implementing the Complex Arcsine and Arccosine
+ * Functions Using Exception Handling", ACM, TOMS,
+ * Vol 23, No. 3, Sept 1997, p. 299-335
+ * Thanks to Tom Fairgrieve
+ */
+
+#include "lapack.h"
+#include "asin.h"
+#include "atan.h"
+#include "sqrt.h"
+#include "abs.h"
+#include "log.h"
+#include "log1p.h"
+#include "min.h"
+#include "max.h"
+
+doubleComplex zasins(doubleComplex z) {
+ static double sdblPi_2 = 1.5707963267948966192313216;
+ static double sdblLn2 = 0.6931471805599453094172321;
+ static double sdblAcross = 1.5;
+ static double sdblBcross = 0.6417;
+
+ double dblLsup = dsqrts(getOverflowThreshold())/8.0;
+ double dblLinf = 4 * dsqrts(getUnderflowThreshold());
+ double dblEpsm = dsqrts(getRelativeMachinePrecision());
+
+ double _dblReal = zreals(z);
+ double _dblImg = zimags(z);
+
+ double dblAbsReal = dabss(_dblReal);
+ double dblAbsImg = dabss(_dblImg);
+ int iSignReal = _dblReal < 0 ? -1 : 1;
+ int iSignImg = _dblImg < 0 ? -1 : 1;
+
+ double dblR = 0, dblS = 0, dblA = 0, dblB = 0;
+
+ double dblTemp = 0;
+
+ double _pdblReal = 0;
+ double _pdblImg = 0;
+
+ if( min(dblAbsReal, dblAbsImg) > dblLinf && max(dblAbsReal, dblAbsImg) <= dblLsup)
+ {
+ /* we are in the safe region */
+ dblR = dsqrts( (dblAbsReal + 1) * (dblAbsReal + 1) + dblAbsImg * dblAbsImg);
+ dblS = dsqrts( (dblAbsReal - 1) * (dblAbsReal - 1) + dblAbsImg * dblAbsImg);
+ dblA = 0.5 * ( dblR + dblS );
+ dblB = dblAbsReal / dblA;
+
+
+ /* compute the real part */
+ if(dblB <= sdblBcross)
+ _pdblReal = dasins(dblB);
+ else if( dblAbsReal <= 1)
+ _pdblReal = datans(dblAbsReal / dsqrts( 0.5 * (dblA + dblAbsReal) * ( (dblAbsImg * dblAbsImg) / (dblR + (dblAbsReal + 1)) + (dblS + (1 - dblAbsReal)))));
+ else
+ _pdblReal = datans(dblAbsReal / (dblAbsImg * dsqrts(0.5 * ((dblA + dblAbsReal) / (dblR + (dblAbsReal + 1)) + (dblA + dblAbsReal) / (dblS + (dblAbsReal-1))))));
+
+ /* compute the imaginary part */
+ if(dblA <= sdblAcross)
+ {
+ double dblImg1 = 0;
+
+ if(dblAbsReal < 1)
+ /* Am1 = 0.5d0*((y**2)/(R+(x+1.d0))+(y**2)/(S+(1.d0-x))) */
+ dblImg1 = 0.5 * (dblAbsImg * dblAbsImg / (dblR + (dblAbsReal + 1)) + dblAbsImg * dblAbsImg / (dblS + (1 - dblAbsReal)));
+ else
+ /* Am1 = 0.5d0*((y**2)/(R+(x+1.d0))+(S+(x-1.d0))) */
+ dblImg1 = 0.5 * (dblAbsImg * dblAbsImg / (dblR + (dblAbsReal + 1)) + (dblS + (dblAbsReal - 1)));
+ /* ai = logp1(Am1 + sqrt(Am1*(A+1.d0))) */
+ dblTemp = dblImg1 + dsqrts(dblImg1 * (dblA + 1));
+ _pdblImg = dlog1ps(dblTemp);
+ }
+ else
+ /* ai = log(A + sqrt(A**2 - 1.d0)) */
+ _pdblImg = dlogs(dblA + dsqrts(dblA * dblA - 1));
+ }
+ else
+ {
+ /* evaluation in the special regions ... */
+ if(dblAbsImg <= dblEpsm * dabss(dblAbsReal - 1))
+ {
+ if(dblAbsReal < 1)
+ {
+ _pdblReal = dasins(dblAbsReal);
+ _pdblImg = dblAbsImg / dsqrts((1 + dblAbsReal) * (1 - dblAbsReal));
+ }
+ else
+ {
+ _pdblReal = sdblPi_2;
+ if(dblAbsReal <= dblLsup)
+ {
+ dblTemp = (dblAbsReal - 1) + dsqrts((dblAbsReal - 1) * (dblAbsReal + 1));
+ _pdblImg = dlog1ps(dblTemp);
+ }
+ else
+ _pdblImg = sdblLn2 + dlogs(dblAbsReal);
+ }
+ }
+ else if(dblAbsImg < dblLinf)
+ {
+ _pdblReal = sdblPi_2 - dsqrts(dblAbsImg);
+ _pdblImg = dsqrts(dblAbsImg);
+ }
+ else if((dblEpsm * dblAbsImg - 1 >= dblAbsReal))
+ {
+ _pdblReal = dblAbsReal * dblAbsImg;
+ _pdblImg = sdblLn2 + dlogs(dblAbsReal);
+ }
+ else if(dblAbsReal > 1)
+ {
+ _pdblReal = datans(dblAbsReal / dblAbsImg);
+ dblTemp = (dblAbsReal / dblAbsImg) * (dblAbsReal / dblAbsImg);
+ _pdblImg = sdblLn2 + dlogs(dblAbsReal) + 0.5 * dlog1ps(dblTemp);
+ }
+ else
+ {
+ double dblTemp2 = dsqrts(1 + dblAbsImg * dblAbsImg);
+ _pdblReal = dblAbsReal / dblTemp2;
+ dblTemp = 2 * dblAbsImg * (dblAbsImg + dblTemp2);
+ _pdblImg = 0.5 * dlog1ps(dblTemp);
+ }
+ }
+ _pdblReal *= iSignReal;
+ _pdblImg *= iSignImg;
+
+ return (DoubleComplex(_pdblReal, _pdblImg));
+}
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