uClibc now has a math library. muahahahaha!

 -Erik

1 files changed, 473 insertions, 0 deletions

diff --git a/libm/ldouble/ndtrl.c b/libm/ldouble/ndtrl.c
new file mode 100644
index 000000000..2c53314a5
--- /dev/null
+++ b/libm/ldouble/ndtrl.c
@@ -0,0 +1,473 @@
+/*							ndtrl.c
+ *
+ *	Normal distribution function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double x, y, ndtrl();
+ *
+ * y = ndtrl( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the area under the Gaussian probability density
+ * function, integrated from minus infinity to x:
+ *
+ *                            x
+ *                             -
+ *                   1        | |          2
+ *    ndtr(x)  = ---------    |    exp( - t /2 ) dt
+ *               sqrt(2pi)  | |
+ *                           -
+ *                          -inf.
+ *
+ *             =  ( 1 + erf(z) ) / 2
+ *             =  erfc(z) / 2
+ *
+ * where z = x/sqrt(2). Computation is via the functions
+ * erf and erfc.
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    IEEE     -13,0        30000       1.6e-17     2.9e-18
+ *    IEEE     -150.7,0      2000       1.6e-15     3.8e-16
+ * Accuracy is limited by error amplification in computing exp(-x^2).
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ *   message         condition           value returned
+ * erfcl underflow    x^2 / 2 > MAXLOGL        0.0
+ *
+ */
+/*							erfl.c
+ *
+ *	Error function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double x, y, erfl();
+ *
+ * y = erfl( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * The integral is
+ *
+ *                           x 
+ *                            -
+ *                 2         | |          2
+ *   erf(x)  =  --------     |    exp( - t  ) dt.
+ *              sqrt(pi)   | |
+ *                          -
+ *                           0
+ *
+ * The magnitude of x is limited to about 106.56 for IEEE
+ * arithmetic; 1 or -1 is returned outside this range.
+ *
+ * For 0 <= |x| < 1, erf(x) = x * P6(x^2)/Q6(x^2); otherwise
+ * erf(x) = 1 - erfc(x).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    IEEE      0,1         50000       2.0e-19     5.7e-20
+ *
+ */
+/*							erfcl.c
+ *
+ *	Complementary error function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double x, y, erfcl();
+ *
+ * y = erfcl( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ *
+ *  1 - erf(x) =
+ *
+ *                           inf. 
+ *                             -
+ *                  2         | |          2
+ *   erfc(x)  =  --------     |    exp( - t  ) dt
+ *               sqrt(pi)   | |
+ *                           -
+ *                            x
+ *
+ *
+ * For small x, erfc(x) = 1 - erf(x); otherwise rational
+ * approximations are computed.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    IEEE      0,13        20000      7.0e-18      1.8e-18
+ *    IEEE      0,106.56    10000      4.4e-16      1.2e-16
+ * Accuracy is limited by error amplification in computing exp(-x^2).
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ *   message          condition              value returned
+ * erfcl underflow    x^2 > MAXLOGL              0.0
+ *
+ *
+ */
+
+
+/*
+Cephes Math Library Release 2.3:  January, 1995
+Copyright 1984, 1995 by Stephen L. Moshier
+*/
+
+
+#include <math.h>
+
+extern long double MAXLOGL;
+static long double SQRTHL = 7.071067811865475244008e-1L;
+
+/* erfc(x) = exp(-x^2) P(1/x)/Q(1/x)
+   1/8 <= 1/x <= 1
+   Peak relative error 5.8e-21  */
+#if UNK
+static long double P[10] = {
+ 1.130609921802431462353E9L,
+ 2.290171954844785638925E9L,
+ 2.295563412811856278515E9L,
+ 1.448651275892911637208E9L,
+ 6.234814405521647580919E8L,
+ 1.870095071120436715930E8L,
+ 3.833161455208142870198E7L,
+ 4.964439504376477951135E6L,
+ 3.198859502299390825278E5L,
+-9.085943037416544232472E-6L,
+};
+static long double Q[10] = {
+/* 1.000000000000000000000E0L, */
+ 1.130609910594093747762E9L,
+ 3.565928696567031388910E9L,
+ 5.188672873106859049556E9L,
+ 4.588018188918609726890E9L,
+ 2.729005809811924550999E9L,
+ 1.138778654945478547049E9L,
+ 3.358653716579278063988E8L,
+ 6.822450775590265689648E7L,
+ 8.799239977351261077610E6L,
+ 5.669830829076399819566E5L,
+};
+#endif
+#if IBMPC
+static short P[] = {
+0x4bf0,0x9ad8,0x7a03,0x86c7,0x401d, XPD
+0xdf23,0xd843,0x4032,0x8881,0x401e, XPD
+0xd025,0xcfd5,0x8494,0x88d3,0x401e, XPD
+0xb6d0,0xc92b,0x5417,0xacb1,0x401d, XPD
+0xada8,0x356a,0x4982,0x94a6,0x401c, XPD
+0x4e13,0xcaee,0x9e31,0xb258,0x401a, XPD
+0x5840,0x554d,0x37a3,0x9239,0x4018, XPD
+0x3b58,0x3da2,0xaf02,0x9780,0x4015, XPD
+0x0144,0x489e,0xbe68,0x9c31,0x4011, XPD
+0x333b,0xd9e6,0xd404,0x986f,0xbfee, XPD
+};
+static short Q[] = {
+/* 0x0000,0x0000,0x0000,0x8000,0x3fff, XPD */
+0x0e43,0x302d,0x79ed,0x86c7,0x401d, XPD
+0xf817,0x9128,0xc0f8,0xd48b,0x401e, XPD
+0x8eae,0x8dad,0x6eb4,0x9aa2,0x401f, XPD
+0x00e7,0x7595,0xcd06,0x88bb,0x401f, XPD
+0x4991,0xcfda,0x52f1,0xa2a9,0x401e, XPD
+0xc39d,0xe415,0xc43d,0x87c0,0x401d, XPD
+0xa75d,0x436f,0x30dd,0xa027,0x401b, XPD
+0xc4cb,0x305a,0xbf78,0x8220,0x4019, XPD
+0x3708,0x33b1,0x07fa,0x8644,0x4016, XPD
+0x24fa,0x96f6,0x7153,0x8a6c,0x4012, XPD
+};
+#endif
+#if MIEEE
+static long P[30] = {
+0x401d0000,0x86c77a03,0x9ad84bf0,
+0x401e0000,0x88814032,0xd843df23,
+0x401e0000,0x88d38494,0xcfd5d025,
+0x401d0000,0xacb15417,0xc92bb6d0,
+0x401c0000,0x94a64982,0x356aada8,
+0x401a0000,0xb2589e31,0xcaee4e13,
+0x40180000,0x923937a3,0x554d5840,
+0x40150000,0x9780af02,0x3da23b58,
+0x40110000,0x9c31be68,0x489e0144,
+0xbfee0000,0x986fd404,0xd9e6333b,
+};
+static long Q[30] = {
+/* 0x3fff0000,0x80000000,0x00000000, */
+0x401d0000,0x86c779ed,0x302d0e43,
+0x401e0000,0xd48bc0f8,0x9128f817,
+0x401f0000,0x9aa26eb4,0x8dad8eae,
+0x401f0000,0x88bbcd06,0x759500e7,
+0x401e0000,0xa2a952f1,0xcfda4991,
+0x401d0000,0x87c0c43d,0xe415c39d,
+0x401b0000,0xa02730dd,0x436fa75d,
+0x40190000,0x8220bf78,0x305ac4cb,
+0x40160000,0x864407fa,0x33b13708,
+0x40120000,0x8a6c7153,0x96f624fa,
+};
+#endif
+
+/* erfc(x) = exp(-x^2) 1/x R(1/x^2) / S(1/x^2)
+   1/128 <= 1/x < 1/8
+   Peak relative error 1.9e-21  */
+#if UNK
+static long double R[5] = {
+ 3.621349282255624026891E0L,
+ 7.173690522797138522298E0L,
+ 3.445028155383625172464E0L,
+ 5.537445669807799246891E-1L,
+ 2.697535671015506686136E-2L,
+};
+static long double S[5] = {
+/* 1.000000000000000000000E0L, */
+ 1.072884067182663823072E1L,
+ 1.533713447609627196926E1L,
+ 6.572990478128949439509E0L,
+ 1.005392977603322982436E0L,
+ 4.781257488046430019872E-2L,
+};
+#endif
+#if IBMPC
+static short R[] = {
+0x260a,0xab95,0x2fc7,0xe7c4,0x4000, XPD
+0x4761,0x613e,0xdf6d,0xe58e,0x4001, XPD
+0x0615,0x4b00,0x575f,0xdc7b,0x4000, XPD
+0x521d,0x8527,0x3435,0x8dc2,0x3ffe, XPD
+0x22cf,0xc711,0x6c5b,0xdcfb,0x3ff9, XPD
+};
+static short S[] = {
+/* 0x0000,0x0000,0x0000,0x8000,0x3fff, XPD */
+0x5de6,0x17d7,0x54d6,0xaba9,0x4002, XPD
+0x55d5,0xd300,0xe71e,0xf564,0x4002, XPD
+0xb611,0x8f76,0xf020,0xd255,0x4001, XPD
+0x3684,0x3798,0xb793,0x80b0,0x3fff, XPD
+0xf5af,0x2fb2,0x1e57,0xc3d7,0x3ffa, XPD
+};
+#endif
+#if MIEEE
+static long R[15] = {
+0x40000000,0xe7c42fc7,0xab95260a,
+0x40010000,0xe58edf6d,0x613e4761,
+0x40000000,0xdc7b575f,0x4b000615,
+0x3ffe0000,0x8dc23435,0x8527521d,
+0x3ff90000,0xdcfb6c5b,0xc71122cf,
+};
+static long S[15] = {
+/* 0x3fff0000,0x80000000,0x00000000, */
+0x40020000,0xaba954d6,0x17d75de6,
+0x40020000,0xf564e71e,0xd30055d5,
+0x40010000,0xd255f020,0x8f76b611,
+0x3fff0000,0x80b0b793,0x37983684,
+0x3ffa0000,0xc3d71e57,0x2fb2f5af,
+};
+#endif
+
+/* erf(x)  = x P(x^2)/Q(x^2)
+   0 <= x <= 1
+   Peak relative error 7.6e-23  */
+#if UNK
+static long double T[7] = {
+ 1.097496774521124996496E-1L,
+ 5.402980370004774841217E0L,
+ 2.871822526820825849235E2L,
+ 2.677472796799053019985E3L,
+ 4.825977363071025440855E4L,
+ 1.549905740900882313773E5L,
+ 1.104385395713178565288E6L,
+};
+static long double U[6] = {
+/* 1.000000000000000000000E0L, */
+ 4.525777638142203713736E1L,
+ 9.715333124857259246107E2L,
+ 1.245905812306219011252E4L,
+ 9.942956272177178491525E4L,
+ 4.636021778692893773576E5L,
+ 9.787360737578177599571E5L,
+};
+#endif
+#if IBMPC
+static short T[] = {
+0xfd7a,0x3a1a,0x705b,0xe0c4,0x3ffb, XPD
+0x3128,0xc337,0x3716,0xace5,0x4001, XPD
+0x9517,0x4e93,0x540e,0x8f97,0x4007, XPD
+0x6118,0x6059,0x9093,0xa757,0x400a, XPD
+0xb954,0xa987,0xc60c,0xbc83,0x400e, XPD
+0x7a56,0xe45a,0xa4bd,0x975b,0x4010, XPD
+0xc446,0x6bab,0x0b2a,0x86d0,0x4013, XPD
+};
+static short U[] = {
+/* 0x0000,0x0000,0x0000,0x8000,0x3fff, XPD */
+0x3453,0x1f8e,0xf688,0xb507,0x4004, XPD
+0x71ac,0xb12f,0x21ca,0xf2e2,0x4008, XPD
+0xffe8,0x9cac,0x3b84,0xc2ac,0x400c, XPD
+0x481d,0x445b,0xc807,0xc232,0x400f, XPD
+0x9ad5,0x1aef,0x45b1,0xe25e,0x4011, XPD
+0x71a7,0x1cad,0x012e,0xeef3,0x4012, XPD
+};
+#endif
+#if MIEEE
+static long T[21] = {
+0x3ffb0000,0xe0c4705b,0x3a1afd7a,
+0x40010000,0xace53716,0xc3373128,
+0x40070000,0x8f97540e,0x4e939517,
+0x400a0000,0xa7579093,0x60596118,
+0x400e0000,0xbc83c60c,0xa987b954,
+0x40100000,0x975ba4bd,0xe45a7a56,
+0x40130000,0x86d00b2a,0x6babc446,
+};
+static long U[18] = {
+/* 0x3fff0000,0x80000000,0x00000000, */
+0x40040000,0xb507f688,0x1f8e3453,
+0x40080000,0xf2e221ca,0xb12f71ac,
+0x400c0000,0xc2ac3b84,0x9cacffe8,
+0x400f0000,0xc232c807,0x445b481d,
+0x40110000,0xe25e45b1,0x1aef9ad5,
+0x40120000,0xeef3012e,0x1cad71a7,
+};
+#endif
+#ifdef ANSIPROT
+extern long double polevll ( long double, void *, int );
+extern long double p1evll ( long double, void *, int );
+extern long double expl ( long double );
+extern long double logl ( long double );
+extern long double erfl ( long double );
+extern long double erfcl ( long double );
+extern long double fabsl ( long double );
+#else
+long double polevll(), p1evll(), expl(), logl(), erfl(), erfcl(), fabsl();
+#endif
+#ifdef INFINITIES
+extern long double INFINITYL;
+#endif
+
+long double ndtrl(a)
+long double a;
+{
+long double x, y, z;
+
+x = a * SQRTHL;
+z = fabsl(x);
+
+if( z < SQRTHL )
+	y = 0.5L + 0.5L * erfl(x);
+
+else
+	{
+	y = 0.5L * erfcl(z);
+
+	if( x > 0.0L )
+		y = 1.0L - y;
+	}
+
+return(y);
+}
+
+
+long double erfcl(a)
+long double a;
+{
+long double p,q,x,y,z;
+
+#ifdef INFINITIES
+if( a == INFINITYL )
+	return(0.0L);
+if( a == -INFINITYL )
+	return(2.0L);
+#endif
+if( a < 0.0L )
+	x = -a;
+else
+	x = a;
+
+if( x < 1.0L )
+	return( 1.0L - erfl(a) );
+
+z = -a * a;
+
+if( z < -MAXLOGL )
+	{
+under:
+	mtherr( "erfcl", UNDERFLOW );
+	if( a < 0 )
+		return( 2.0L );
+	else
+		return( 0.0L );
+	}
+
+z = expl(z);
+y = 1.0L/x;
+
+if( x < 8.0L )
+	{
+	p = polevll( y, P, 9 );
+	q = p1evll( y, Q, 10 );
+	}
+else
+	{
+	q = y * y;
+	p = y * polevll( q, R, 4 );
+	q = p1evll( q, S, 5 );
+	}
+y = (z * p)/q;
+
+if( a < 0.0L )
+	y = 2.0L - y;
+
+if( y == 0.0L )
+	goto under;
+
+return(y);
+}
+
+
+
+long double erfl(x)
+long double x;
+{
+long double y, z;
+
+#if MINUSZERO
+if( x == 0.0L )
+	return(x);
+#endif
+#ifdef INFINITIES
+if( x == -INFINITYL )
+	return(-1.0L);
+if( x == INFINITYL )
+	return(1.0L);
+#endif
+if( fabsl(x) > 1.0L )
+	return( 1.0L - erfcl(x) );
+
+z = x * x;
+y = x * polevll( z, T, 6 ) / p1evll( z, U, 6 );
+return( y );
+}