/* dawsnf.c * * Dawson's Integral * * * * SYNOPSIS: * * float x, y, dawsnf(); * * y = dawsnf( x ); * * * * DESCRIPTION: * * Approximates the integral * * x * - * 2 | | 2 * dawsn(x) = exp( -x ) | exp( t ) dt * | | * - * 0 * * Three different rational approximations are employed, for * the intervals 0 to 3.25; 3.25 to 6.25; and 6.25 up. * * * ACCURACY: * * Relative error: * arithmetic domain # trials peak rms * IEEE 0,10 50000 4.4e-7 6.3e-8 * * */ /* dawsn.c */ /* Cephes Math Library Release 2.1: January, 1989 Copyright 1984, 1987, 1989 by Stephen L. Moshier Direct inquiries to 30 Frost Street, Cambridge, MA 02140 */ #include /* Dawson's integral, interval 0 to 3.25 */ static float AN[10] = { 1.13681498971755972054E-11, 8.49262267667473811108E-10, 1.94434204175553054283E-8, 9.53151741254484363489E-7, 3.07828309874913200438E-6, 3.52513368520288738649E-4, -8.50149846724410912031E-4, 4.22618223005546594270E-2, -9.17480371773452345351E-2, 9.99999999999999994612E-1, }; static float AD[11] = { 2.40372073066762605484E-11, 1.48864681368493396752E-9, 5.21265281010541664570E-8, 1.27258478273186970203E-6, 2.32490249820789513991E-5, 3.25524741826057911661E-4, 3.48805814657162590916E-3, 2.79448531198828973716E-2, 1.58874241960120565368E-1, 5.74918629489320327824E-1, 1.00000000000000000539E0, }; /* interval 3.25 to 6.25 */ static float BN[11] = { 5.08955156417900903354E-1, -2.44754418142697847934E-1, 9.41512335303534411857E-2, -2.18711255142039025206E-2, 3.66207612329569181322E-3, -4.23209114460388756528E-4, 3.59641304793896631888E-5, -2.14640351719968974225E-6, 9.10010780076391431042E-8, -2.40274520828250956942E-9, 3.59233385440928410398E-11, }; static float BD[10] = { /* 1.00000000000000000000E0,*/ -6.31839869873368190192E-1, 2.36706788228248691528E-1, -5.31806367003223277662E-2, 8.48041718586295374409E-3, -9.47996768486665330168E-4, 7.81025592944552338085E-5, -4.55875153252442634831E-6, 1.89100358111421846170E-7, -4.91324691331920606875E-9, 7.18466403235734541950E-11, }; /* 6.25 to infinity */ static float CN[5] = { -5.90592860534773254987E-1, 6.29235242724368800674E-1, -1.72858975380388136411E-1, 1.64837047825189632310E-2, -4.86827613020462700845E-4, }; static float CD[5] = { /* 1.00000000000000000000E0,*/ -2.69820057197544900361E0, 1.73270799045947845857E0, -3.93708582281939493482E-1, 3.44278924041233391079E-2, -9.73655226040941223894E-4, }; extern float PIF, MACHEPF; #define fabsf(x) ( (x) < 0 ? -(x) : (x) ) #ifdef ANSIC float polevlf(float, float *, int); float p1evlf(float, float *, int); #else float polevlf(), p1evlf(); #endif float dawsnf( float xxx ) { float xx, x, y; int sign; xx = xxx; sign = 1; if( xx < 0.0 ) { sign = -1; xx = -xx; } if( xx < 3.25 ) { x = xx*xx; y = xx * polevlf( x, AN, 9 )/polevlf( x, AD, 10 ); return( sign * y ); } x = 1.0/(xx*xx); if( xx < 6.25 ) { y = 1.0/xx + x * polevlf( x, BN, 10) / (p1evlf( x, BD, 10) * xx); return( sign * 0.5 * y ); } if( xx > 1.0e9 ) return( (sign * 0.5)/xx ); /* 6.25 to infinity */ y = 1.0/xx + x * polevlf( x, CN, 4) / (p1evlf( x, CD, 5) * xx); return( sign * 0.5 * y ); }