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-rw-r--r--libm/float/sicif.c279
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diff --git a/libm/float/sicif.c b/libm/float/sicif.c
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-/* sicif.c
- *
- * Sine and cosine integrals
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, Ci, Si;
- *
- * sicif( x, &Si, &Ci );
- *
- *
- * DESCRIPTION:
- *
- * Evaluates the integrals
- *
- * x
- * -
- * | cos t - 1
- * Ci(x) = eul + ln x + | --------- dt,
- * | t
- * -
- * 0
- * x
- * -
- * | sin t
- * Si(x) = | ----- dt
- * | t
- * -
- * 0
- *
- * where eul = 0.57721566490153286061 is Euler's constant.
- * The integrals are approximated by rational functions.
- * For x > 8 auxiliary functions f(x) and g(x) are employed
- * such that
- *
- * Ci(x) = f(x) sin(x) - g(x) cos(x)
- * Si(x) = pi/2 - f(x) cos(x) - g(x) sin(x)
- *
- *
- * ACCURACY:
- * Test interval = [0,50].
- * Absolute error, except relative when > 1:
- * arithmetic function # trials peak rms
- * IEEE Si 30000 2.1e-7 4.3e-8
- * IEEE Ci 30000 3.9e-7 2.2e-8
- */
-
-/*
-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 <math.h>
-
-static float SN[] = {
--8.39167827910303881427E-11,
- 4.62591714427012837309E-8,
--9.75759303843632795789E-6,
- 9.76945438170435310816E-4,
--4.13470316229406538752E-2,
- 1.00000000000000000302E0,
-};
-static float SD[] = {
- 2.03269266195951942049E-12,
- 1.27997891179943299903E-9,
- 4.41827842801218905784E-7,
- 9.96412122043875552487E-5,
- 1.42085239326149893930E-2,
- 9.99999999999999996984E-1,
-};
-
-static float CN[] = {
- 2.02524002389102268789E-11,
--1.35249504915790756375E-8,
- 3.59325051419993077021E-6,
--4.74007206873407909465E-4,
- 2.89159652607555242092E-2,
--1.00000000000000000080E0,
-};
-static float CD[] = {
- 4.07746040061880559506E-12,
- 3.06780997581887812692E-9,
- 1.23210355685883423679E-6,
- 3.17442024775032769882E-4,
- 5.10028056236446052392E-2,
- 4.00000000000000000080E0,
-};
-
-
-static float FN4[] = {
- 4.23612862892216586994E0,
- 5.45937717161812843388E0,
- 1.62083287701538329132E0,
- 1.67006611831323023771E-1,
- 6.81020132472518137426E-3,
- 1.08936580650328664411E-4,
- 5.48900223421373614008E-7,
-};
-static float FD4[] = {
-/* 1.00000000000000000000E0,*/
- 8.16496634205391016773E0,
- 7.30828822505564552187E0,
- 1.86792257950184183883E0,
- 1.78792052963149907262E-1,
- 7.01710668322789753610E-3,
- 1.10034357153915731354E-4,
- 5.48900252756255700982E-7,
-};
-
-
-static float FN8[] = {
- 4.55880873470465315206E-1,
- 7.13715274100146711374E-1,
- 1.60300158222319456320E-1,
- 1.16064229408124407915E-2,
- 3.49556442447859055605E-4,
- 4.86215430826454749482E-6,
- 3.20092790091004902806E-8,
- 9.41779576128512936592E-11,
- 9.70507110881952024631E-14,
-};
-static float FD8[] = {
-/* 1.00000000000000000000E0,*/
- 9.17463611873684053703E-1,
- 1.78685545332074536321E-1,
- 1.22253594771971293032E-2,
- 3.58696481881851580297E-4,
- 4.92435064317881464393E-6,
- 3.21956939101046018377E-8,
- 9.43720590350276732376E-11,
- 9.70507110881952025725E-14,
-};
-
-static float GN4[] = {
- 8.71001698973114191777E-2,
- 6.11379109952219284151E-1,
- 3.97180296392337498885E-1,
- 7.48527737628469092119E-2,
- 5.38868681462177273157E-3,
- 1.61999794598934024525E-4,
- 1.97963874140963632189E-6,
- 7.82579040744090311069E-9,
-};
-static float GD4[] = {
-/* 1.00000000000000000000E0,*/
- 1.64402202413355338886E0,
- 6.66296701268987968381E-1,
- 9.88771761277688796203E-2,
- 6.22396345441768420760E-3,
- 1.73221081474177119497E-4,
- 2.02659182086343991969E-6,
- 7.82579218933534490868E-9,
-};
-
-static float GN8[] = {
- 6.97359953443276214934E-1,
- 3.30410979305632063225E-1,
- 3.84878767649974295920E-2,
- 1.71718239052347903558E-3,
- 3.48941165502279436777E-5,
- 3.47131167084116673800E-7,
- 1.70404452782044526189E-9,
- 3.85945925430276600453E-12,
- 3.14040098946363334640E-15,
-};
-static float GD8[] = {
-/* 1.00000000000000000000E0,*/
- 1.68548898811011640017E0,
- 4.87852258695304967486E-1,
- 4.67913194259625806320E-2,
- 1.90284426674399523638E-3,
- 3.68475504442561108162E-5,
- 3.57043223443740838771E-7,
- 1.72693748966316146736E-9,
- 3.87830166023954706752E-12,
- 3.14040098946363335242E-15,
-};
-
-#define EUL 0.57721566490153286061
-extern float MAXNUMF, PIO2F, MACHEPF;
-
-
-
-#ifdef ANSIC
-float logf(float), sinf(float), cosf(float);
-float polevlf(float, float *, int);
-float p1evlf(float, float *, int);
-#else
-float logf(), sinf(), cosf(), polevlf(), p1evlf();
-#endif
-
-
-int sicif( float xx, float *si, float *ci )
-{
-float x, z, c, s, f, g;
-int sign;
-
-x = xx;
-if( x < 0.0 )
- {
- sign = -1;
- x = -x;
- }
-else
- sign = 0;
-
-
-if( x == 0.0 )
- {
- *si = 0.0;
- *ci = -MAXNUMF;
- return( 0 );
- }
-
-
-if( x > 1.0e9 )
- {
- *si = PIO2F - cosf(x)/x;
- *ci = sinf(x)/x;
- return( 0 );
- }
-
-
-
-if( x > 4.0 )
- goto asympt;
-
-z = x * x;
-s = x * polevlf( z, SN, 5 ) / polevlf( z, SD, 5 );
-c = z * polevlf( z, CN, 5 ) / polevlf( z, CD, 5 );
-
-if( sign )
- s = -s;
-*si = s;
-*ci = EUL + logf(x) + c; /* real part if x < 0 */
-return(0);
-
-
-
-/* The auxiliary functions are:
- *
- *
- * *si = *si - PIO2;
- * c = cos(x);
- * s = sin(x);
- *
- * t = *ci * s - *si * c;
- * a = *ci * c + *si * s;
- *
- * *si = t;
- * *ci = -a;
- */
-
-
-asympt:
-
-s = sinf(x);
-c = cosf(x);
-z = 1.0/(x*x);
-if( x < 8.0 )
- {
- f = polevlf( z, FN4, 6 ) / (x * p1evlf( z, FD4, 7 ));
- g = z * polevlf( z, GN4, 7 ) / p1evlf( z, GD4, 7 );
- }
-else
- {
- f = polevlf( z, FN8, 8 ) / (x * p1evlf( z, FD8, 8 ));
- g = z * polevlf( z, GN8, 8 ) / p1evlf( z, GD8, 9 );
- }
-*si = PIO2F - f * c - g * s;
-if( sign )
- *si = -( *si );
-*ci = f * s - g * c;
-
-return(0);
-}