diff options
Diffstat (limited to 'src/c/elementaryFunctions/acos/zacoss.c')
| -rw-r--r-- | src/c/elementaryFunctions/acos/zacoss.c | 146 |
1 files changed, 146 insertions, 0 deletions
diff --git a/src/c/elementaryFunctions/acos/zacoss.c b/src/c/elementaryFunctions/acos/zacoss.c new file mode 100644 index 00000000..7758a932 --- /dev/null +++ b/src/c/elementaryFunctions/acos/zacoss.c @@ -0,0 +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 + * + */ + +/* + * This fonction is a translation of fortran wacos write by Bruno Pincon <Bruno.Pincon@iecn.u-nancy.fr> + * 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 "acos.h" +#include "atan.h" +#include "log.h" +#include "log1p.h" +#include "sqrt.h" +#include "abs.h" +#include "lapack.h" +#include "min.h" +#include "max.h" + +#define localSign(x) (x>0 ? 1 : -1) + +doubleComplex zacoss(doubleComplex z) { + static double sdblPi = 3.1415926535897932384626433; + 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 = 4.0 * dsqrts(getUnderflowThreshold()); + double dblEpsm = dsqrts(getRelativeMachinePrecision()); + + double dblAbsReal = dabss(zreals(z)); + double dblAbsImg = dabss(zimags(z)); + double dblSignReal = localSign(zreals(z)); + double dblSignImg = localSign(zimags(z)); + + 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 = dacoss(dblB); + else if( dblAbsReal <= 1) + _pdblReal = datans(dsqrts(0.5 * (dblA + dblAbsReal) * (dblAbsImg*dblAbsImg / (dblR + (dblAbsReal + 1)) + (dblS + (1 - dblAbsReal)))) / dblAbsReal); + else + _pdblReal = datans((dblAbsImg * dsqrts(0.5 * ((dblA + dblAbsReal) / (dblR + (dblAbsReal + 1)) + (dblA + dblAbsReal) / (dblS + (dblAbsReal - 1))))) / dblAbsReal); + + /* 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 = dacoss(dblAbsReal); + _pdblImg = dblAbsImg / dsqrts((1 + dblAbsReal) * (1 - dblAbsReal)); + } + else + { + _pdblReal = 0; + if(dblAbsReal <= dblLsup) + { + dblTemp = (dblAbsReal - 1) + dsqrts((dblAbsReal - 1) * (dblAbsReal + 1)); + _pdblImg = dlog1ps(dblTemp); + } + else + _pdblImg = sdblLn2 + dlogs(dblAbsReal); + } + } + else if(dblAbsImg < dblLinf) + { + _pdblReal = dsqrts(dblAbsImg); + _pdblImg = _pdblReal; + } + else if((dblEpsm * dblAbsImg - 1 >= dblAbsReal)) + { + _pdblReal = sdblPi_2; + _pdblImg = sdblLn2 + dlogs(dblAbsImg); + } + else if(dblAbsReal > 1) + { + _pdblReal = datans(dblAbsImg / dblAbsReal); + dblTemp = (dblAbsReal / dblAbsImg)*(dblAbsReal / dblAbsImg); + _pdblImg = sdblLn2 + dlogs(dblAbsImg) + 0.5 * dlog1ps(dblTemp); + } + else + { + double dblTemp2 = dsqrts(1 + dblAbsImg*dblAbsImg); + _pdblReal = sdblPi_2; + dblTemp = 2 * dblAbsImg * (dblAbsImg + dblTemp2); + _pdblImg = 0.5 * dlog1ps(dblTemp); + } + } + if(dblSignReal < 0) + _pdblReal = sdblPi - _pdblReal; + + if(dblAbsImg != 0 || dblSignReal < 0) + _pdblImg = - dblSignImg * _pdblImg; + + return DoubleComplex(_pdblReal, _pdblImg); +} |