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authorSunil Shetye2019-05-16 12:18:48 +0530
committerSunil Shetye2019-05-29 11:08:01 +0530
commit26b77d7593b5ee0792b6b556f5569ea4227c2b02 (patch)
tree8f92052234b01bf39b9c3a6e3cb12b3962d96b1b /src/c/elementaryFunctions/asin/casins.c
parent5a73e6bec4a12db7afae9de300e39256f754d8d3 (diff)
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Diffstat (limited to 'src/c/elementaryFunctions/asin/casins.c')
-rw-r--r--src/c/elementaryFunctions/asin/casins.c292
1 files changed, 146 insertions, 146 deletions
diff --git a/src/c/elementaryFunctions/asin/casins.c b/src/c/elementaryFunctions/asin/casins.c
index 35a4a8d8..caed038e 100644
--- a/src/c/elementaryFunctions/asin/casins.c
+++ b/src/c/elementaryFunctions/asin/casins.c
@@ -1,146 +1,146 @@
-/*
- * 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
- *
- */
-
-/*
- * 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"
-
-floatComplex casins(floatComplex z) {
- static float sdblPi_2 = 1.5707963267948966192313216f;
- static float sdblLn2 = 0.6931471805599453094172321f;
- static float sdblAcross = 1.5f;
- static float sdblBcross = 0.6417f;
-
- float dblLsup = ssqrts((float) getOverflowThreshold())/ 8.0f;
- float dblLinf = 4.0f * ssqrts((float) getUnderflowThreshold());
- float dblEpsm = ssqrts((float) getRelativeMachinePrecision());
-
- float _dblReal = creals(z);
- float _dblImg = cimags(z);
-
- float dblAbsReal = sabss(_dblReal);
- float dblAbsImg = sabss(_dblImg);
- float iSignReal = _dblReal < 0 ? -1.0f : 1.0f;
- float iSignImg = _dblImg < 0 ? -1.0f : 1.0f;
-
- float dblR = 0, dblS = 0, dblA = 0, dblB = 0;
-
- float dblTemp = 0;
-
- float _pdblReal = 0;
- float _pdblImg = 0;
-
- if( min(dblAbsReal, dblAbsImg) > dblLinf && max(dblAbsReal, dblAbsImg) <= dblLsup)
- {
- /* we are in the safe region */
- dblR = ssqrts( (dblAbsReal + 1) * (dblAbsReal + 1) + dblAbsImg * dblAbsImg);
- dblS = ssqrts( (dblAbsReal - 1) * (dblAbsReal - 1) + dblAbsImg * dblAbsImg);
- dblA = (float) 0.5 * ( dblR + dblS );
- dblB = dblAbsReal / dblA;
-
-
- /* compute the real part */
- if(dblB <= sdblBcross)
- _pdblReal = sasins(dblB);
- else if( dblAbsReal <= 1)
- _pdblReal = satans(dblAbsReal / ssqrts( 0.5f * (dblA + dblAbsReal) * ( (dblAbsImg * dblAbsImg) / (dblR + (dblAbsReal + 1)) + (dblS + (1 - dblAbsReal)))));
- else
- _pdblReal = satans(dblAbsReal / (dblAbsImg * ssqrts( 0.5f * ((dblA + dblAbsReal) / (dblR + (dblAbsReal + 1)) + (dblA + dblAbsReal) / (dblS + (dblAbsReal-1))))));
-
- /* compute the imaginary part */
- if(dblA <= sdblAcross)
- {
- float dblImg1 = 0;
-
- if(dblAbsReal < 1)
- /* Am1 = 0.5d0*((y**2)/(R+(x+1.d0))+(y**2)/(S+(1.d0-x))) */
- dblImg1 = 0.5f * (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 = 0.5f * (dblAbsImg * dblAbsImg / (dblR + (dblAbsReal + 1)) + (dblS + (dblAbsReal - 1)));
- /* ai = logp1(Am1 + sqrt(Am1*(A+1.d0))) */
- dblTemp = dblImg1 + ssqrts(dblImg1 * (dblA + 1));
- _pdblImg = slog1ps(dblTemp);
- }
- else
- /* ai = log(A + sqrt(A**2 - 1.d0)) */
- _pdblImg = slogs(dblA + ssqrts(dblA * dblA - (float) 1.0));
- }
- else
- {
- /* evaluation in the special regions ... */
- if(dblAbsImg <= dblEpsm * dabss(dblAbsReal - 1))
- {
- if(dblAbsReal < 1)
- {
- _pdblReal = sasins(dblAbsReal);
- _pdblImg = dblAbsImg / ssqrts((1 + dblAbsReal) * (1 - dblAbsReal));
- }
- else
- {
- _pdblReal = sdblPi_2;
- if(dblAbsReal <= dblLsup)
- {
- dblTemp = (dblAbsReal - 1) + ssqrts((dblAbsReal - 1) * (dblAbsReal + 1));
- _pdblImg = slog1ps(dblTemp);
- }
- else
- _pdblImg = sdblLn2 + slogs(dblAbsReal);
- }
- }
- else if(dblAbsImg < dblLinf)
- {
- _pdblReal = sdblPi_2 - ssqrts(dblAbsImg);
- _pdblImg = ssqrts(dblAbsImg);
- }
- else if((dblEpsm * dblAbsImg - 1 >= dblAbsReal))
- {
- _pdblReal = dblAbsReal * dblAbsImg;
- _pdblImg = sdblLn2 + slogs(dblAbsReal);
- }
- else if(dblAbsReal > 1)
- {
- _pdblReal = satans(dblAbsReal / dblAbsImg);
- dblTemp = (dblAbsReal / dblAbsImg) * (dblAbsReal / dblAbsImg);
- _pdblImg = sdblLn2 + slogs(dblAbsReal) + 0.5f * slog1ps(dblTemp);
- }
- else
- {
- float dblTemp2 = ssqrts(1 + dblAbsImg * dblAbsImg);
- _pdblReal = dblAbsReal / dblTemp2;
- dblTemp = 2.0f * dblAbsImg * (dblAbsImg + dblTemp2);
- _pdblImg = 0.5f * slog1ps(dblTemp);
- }
- }
- _pdblReal *= iSignReal;
- _pdblImg *= iSignImg;
-
- return (FloatComplex(_pdblReal, _pdblImg));
-}
+/*
+ * 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
+ *
+ */
+
+/*
+ * 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"
+
+floatComplex casins(floatComplex z) {
+ static float sdblPi_2 = 1.5707963267948966192313216f;
+ static float sdblLn2 = 0.6931471805599453094172321f;
+ static float sdblAcross = 1.5f;
+ static float sdblBcross = 0.6417f;
+
+ float dblLsup = ssqrts((float) getOverflowThreshold())/ 8.0f;
+ float dblLinf = 4.0f * ssqrts((float) getUnderflowThreshold());
+ float dblEpsm = ssqrts((float) getRelativeMachinePrecision());
+
+ float _dblReal = creals(z);
+ float _dblImg = cimags(z);
+
+ float dblAbsReal = sabss(_dblReal);
+ float dblAbsImg = sabss(_dblImg);
+ float iSignReal = _dblReal < 0 ? -1.0f : 1.0f;
+ float iSignImg = _dblImg < 0 ? -1.0f : 1.0f;
+
+ float dblR = 0, dblS = 0, dblA = 0, dblB = 0;
+
+ float dblTemp = 0;
+
+ float _pdblReal = 0;
+ float _pdblImg = 0;
+
+ if( min(dblAbsReal, dblAbsImg) > dblLinf && max(dblAbsReal, dblAbsImg) <= dblLsup)
+ {
+ /* we are in the safe region */
+ dblR = ssqrts( (dblAbsReal + 1) * (dblAbsReal + 1) + dblAbsImg * dblAbsImg);
+ dblS = ssqrts( (dblAbsReal - 1) * (dblAbsReal - 1) + dblAbsImg * dblAbsImg);
+ dblA = (float) 0.5 * ( dblR + dblS );
+ dblB = dblAbsReal / dblA;
+
+
+ /* compute the real part */
+ if(dblB <= sdblBcross)
+ _pdblReal = sasins(dblB);
+ else if( dblAbsReal <= 1)
+ _pdblReal = satans(dblAbsReal / ssqrts( 0.5f * (dblA + dblAbsReal) * ( (dblAbsImg * dblAbsImg) / (dblR + (dblAbsReal + 1)) + (dblS + (1 - dblAbsReal)))));
+ else
+ _pdblReal = satans(dblAbsReal / (dblAbsImg * ssqrts( 0.5f * ((dblA + dblAbsReal) / (dblR + (dblAbsReal + 1)) + (dblA + dblAbsReal) / (dblS + (dblAbsReal-1))))));
+
+ /* compute the imaginary part */
+ if(dblA <= sdblAcross)
+ {
+ float dblImg1 = 0;
+
+ if(dblAbsReal < 1)
+ /* Am1 = 0.5d0*((y**2)/(R+(x+1.d0))+(y**2)/(S+(1.d0-x))) */
+ dblImg1 = 0.5f * (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 = 0.5f * (dblAbsImg * dblAbsImg / (dblR + (dblAbsReal + 1)) + (dblS + (dblAbsReal - 1)));
+ /* ai = logp1(Am1 + sqrt(Am1*(A+1.d0))) */
+ dblTemp = dblImg1 + ssqrts(dblImg1 * (dblA + 1));
+ _pdblImg = slog1ps(dblTemp);
+ }
+ else
+ /* ai = log(A + sqrt(A**2 - 1.d0)) */
+ _pdblImg = slogs(dblA + ssqrts(dblA * dblA - (float) 1.0));
+ }
+ else
+ {
+ /* evaluation in the special regions ... */
+ if(dblAbsImg <= dblEpsm * dabss(dblAbsReal - 1))
+ {
+ if(dblAbsReal < 1)
+ {
+ _pdblReal = sasins(dblAbsReal);
+ _pdblImg = dblAbsImg / ssqrts((1 + dblAbsReal) * (1 - dblAbsReal));
+ }
+ else
+ {
+ _pdblReal = sdblPi_2;
+ if(dblAbsReal <= dblLsup)
+ {
+ dblTemp = (dblAbsReal - 1) + ssqrts((dblAbsReal - 1) * (dblAbsReal + 1));
+ _pdblImg = slog1ps(dblTemp);
+ }
+ else
+ _pdblImg = sdblLn2 + slogs(dblAbsReal);
+ }
+ }
+ else if(dblAbsImg < dblLinf)
+ {
+ _pdblReal = sdblPi_2 - ssqrts(dblAbsImg);
+ _pdblImg = ssqrts(dblAbsImg);
+ }
+ else if((dblEpsm * dblAbsImg - 1 >= dblAbsReal))
+ {
+ _pdblReal = dblAbsReal * dblAbsImg;
+ _pdblImg = sdblLn2 + slogs(dblAbsReal);
+ }
+ else if(dblAbsReal > 1)
+ {
+ _pdblReal = satans(dblAbsReal / dblAbsImg);
+ dblTemp = (dblAbsReal / dblAbsImg) * (dblAbsReal / dblAbsImg);
+ _pdblImg = sdblLn2 + slogs(dblAbsReal) + 0.5f * slog1ps(dblTemp);
+ }
+ else
+ {
+ float dblTemp2 = ssqrts(1 + dblAbsImg * dblAbsImg);
+ _pdblReal = dblAbsReal / dblTemp2;
+ dblTemp = 2.0f * dblAbsImg * (dblAbsImg + dblTemp2);
+ _pdblImg = 0.5f * slog1ps(dblTemp);
+ }
+ }
+ _pdblReal *= iSignReal;
+ _pdblImg *= iSignImg;
+
+ return (FloatComplex(_pdblReal, _pdblImg));
+}