summaryrefslogtreecommitdiff
path: root/src/c/elementaryFunctions/asin/zasins.c
diff options
context:
space:
mode:
Diffstat (limited to 'src/c/elementaryFunctions/asin/zasins.c')
-rw-r--r--src/c/elementaryFunctions/asin/zasins.c290
1 files changed, 146 insertions, 144 deletions
diff --git a/src/c/elementaryFunctions/asin/zasins.c b/src/c/elementaryFunctions/asin/zasins.c
index 5d2110ff..5bd586a8 100644
--- a/src/c/elementaryFunctions/asin/zasins.c
+++ b/src/c/elementaryFunctions/asin/zasins.c
@@ -1,144 +1,146 @@
-/*
- * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
- * Copyright (C) 2007-2008 - INRIA - Bruno JOFRET
- *
- * 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
- */
-
-#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));
-}
+/*
+ * 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));
+}
generated by cgit (git 2.34.1) at 2025-03-13 14:56:44 +0000