193 lines
3.6 KiB
C
193 lines
3.6 KiB
C
/* i0.c
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*
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* Modified Bessel function of order zero
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*
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*
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*
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* SYNOPSIS:
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*
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* double x, y, i0();
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*
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* y = i0( x );
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*
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*
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*
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* DESCRIPTION:
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*
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* Returns modified Bessel function of order zero of the
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* argument.
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*
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* The function is defined as i0(x) = j0( ix ).
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*
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* The range is partitioned into the two intervals [0,8] and
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* (8, infinity). Chebyshev polynomial expansions are employed
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* in each interval.
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*
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*
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*
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* ACCURACY:
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*
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* Relative error:
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* arithmetic domain # trials peak rms
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* DEC 0,30 6000 8.2e-17 1.9e-17
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* IEEE 0,30 30000 5.8e-16 1.4e-16
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*
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*/
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/* i0e.c
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*
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* Modified Bessel function of order zero,
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* exponentially scaled
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*
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*
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*
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* SYNOPSIS:
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*
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* double x, y, i0e();
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*
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* y = i0e( x );
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*
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*
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*
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* DESCRIPTION:
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*
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* Returns exponentially scaled modified Bessel function
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* of order zero of the argument.
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*
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* The function is defined as i0e(x) = exp(-|x|) j0( ix ).
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*
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*
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*
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* ACCURACY:
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*
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* Relative error:
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* arithmetic domain # trials peak rms
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* IEEE 0,30 30000 5.4e-16 1.2e-16
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* See i0().
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*
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*/
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/* i0.c */
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/*
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Cephes Math Library Release 2.8: June, 2000
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Copyright 1984, 1987, 2000 by Stephen L. Moshier
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*/
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#include <math.h>
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/* Chebyshev coefficients for exp(-x) I0(x)
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* in the interval [0,8].
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*
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* lim(x->0){ exp(-x) I0(x) } = 1.
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*/
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static double A[] =
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{
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-4.41534164647933937950E-18,
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3.33079451882223809783E-17,
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-2.43127984654795469359E-16,
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1.71539128555513303061E-15,
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-1.16853328779934516808E-14,
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7.67618549860493561688E-14,
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-4.85644678311192946090E-13,
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2.95505266312963983461E-12,
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-1.72682629144155570723E-11,
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9.67580903537323691224E-11,
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-5.18979560163526290666E-10,
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2.65982372468238665035E-9,
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-1.30002500998624804212E-8,
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6.04699502254191894932E-8,
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-2.67079385394061173391E-7,
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1.11738753912010371815E-6,
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-4.41673835845875056359E-6,
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1.64484480707288970893E-5,
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-5.75419501008210370398E-5,
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1.88502885095841655729E-4,
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-5.76375574538582365885E-4,
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1.63947561694133579842E-3,
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-4.32430999505057594430E-3,
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1.05464603945949983183E-2,
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-2.37374148058994688156E-2,
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4.93052842396707084878E-2,
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-9.49010970480476444210E-2,
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1.71620901522208775349E-1,
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-3.04682672343198398683E-1,
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6.76795274409476084995E-1
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};
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/* Chebyshev coefficients for exp(-x) sqrt(x) I0(x)
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* in the inverted interval [8,infinity].
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*
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* lim(x->inf){ exp(-x) sqrt(x) I0(x) } = 1/sqrt(2pi).
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*/
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static double B[] =
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{
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-7.23318048787475395456E-18,
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-4.83050448594418207126E-18,
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4.46562142029675999901E-17,
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3.46122286769746109310E-17,
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-2.82762398051658348494E-16,
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-3.42548561967721913462E-16,
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1.77256013305652638360E-15,
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3.81168066935262242075E-15,
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-9.55484669882830764870E-15,
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-4.15056934728722208663E-14,
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1.54008621752140982691E-14,
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3.85277838274214270114E-13,
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7.18012445138366623367E-13,
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-1.79417853150680611778E-12,
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-1.32158118404477131188E-11,
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-3.14991652796324136454E-11,
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1.18891471078464383424E-11,
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4.94060238822496958910E-10,
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3.39623202570838634515E-9,
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2.26666899049817806459E-8,
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2.04891858946906374183E-7,
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2.89137052083475648297E-6,
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6.88975834691682398426E-5,
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3.36911647825569408990E-3,
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8.04490411014108831608E-1
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};
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extern double chbevl ( double, void *, int );
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double i0(x)
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double x;
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{
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double y;
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if( x < 0 )
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x = -x;
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if( x <= 8.0 )
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{
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y = (x/2.0) - 2.0;
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return( exp(x) * chbevl( y, A, 30 ) );
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}
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return( exp(x) * chbevl( 32.0/x - 2.0, B, 25 ) / sqrt(x) );
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}
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double i0e( x )
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double x;
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{
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double y;
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if( x < 0 )
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x = -x;
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if( x <= 8.0 )
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{
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y = (x/2.0) - 2.0;
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return( chbevl( y, A, 30 ) );
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}
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return( chbevl( 32.0/x - 2.0, B, 25 ) / sqrt(x) );
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}
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