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components/external/espruino/libs/math/atanh.c

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+/*							atanh.c
+ *
+ *	Inverse hyperbolic tangent
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, atanh();
+ *
+ * y = atanh( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns inverse hyperbolic tangent of argument in the range
+ * MINLOG to MAXLOG.
+ *
+ * If |x| < 0.5, the rational form x + x**3 P(x)/Q(x) is
+ * employed.  Otherwise,
+ *        atanh(x) = 0.5 * log( (1+x)/(1-x) ).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC       -1,1        50000       2.4e-17     6.4e-18
+ *    IEEE      -1,1        30000       1.9e-16     5.2e-17
+ *
+ */
+
+/*						atanh.c	*/
+
+
+/*
+Cephes Math Library Release 2.8:  June, 2000
+Copyright (C) 1987, 1995, 2000 by Stephen L. Moshier
+*/
+
+#include "mconf.h"
+
+#ifdef UNK
+const static double P[] = {
+-8.54074331929669305196E-1,
+ 1.20426861384072379242E1,
+-4.61252884198732692637E1,
+ 6.54566728676544377376E1,
+-3.09092539379866942570E1
+};
+const static double Q[] = {
+/* 1.00000000000000000000E0,*/
+-1.95638849376911654834E1,
+ 1.08938092147140262656E2,
+-2.49839401325893582852E2,
+ 2.52006675691344555838E2,
+-9.27277618139601130017E1
+};
+#endif
+#ifdef DEC
+static unsigned short P[] = {
+0140132,0122235,0105775,0130300,
+0041100,0127327,0124407,0034722,
+0141470,0100113,0115607,0130535,
+0041602,0164721,0003257,0013673,
+0141367,0043046,0166673,0045750
+};
+static unsigned short Q[] = {
+/*0040200,0000000,0000000,0000000,*/
+0141234,0101326,0015460,0134564,
+0041731,0160115,0116451,0032045,
+0142171,0153343,0000532,0167226,
+0042174,0000665,0077604,0000310,
+0141671,0072235,0031114,0074377
+};
+#endif
+
+#ifdef IBMPC
+static unsigned short P[] = {
+0xb618,0xb17f,0x5493,0xbfeb,
+0xe73a,0xf520,0x15da,0x4028,
+0xf62c,0x7370,0x1009,0xc047,
+0xe2f7,0x20d5,0x5d3a,0x4050,
+0x697d,0xddb7,0xe8c4,0xc03e
+};
+static unsigned short Q[] = {
+/*0x0000,0x0000,0x0000,0x3ff0,*/
+0x172f,0xc366,0x905a,0xc033,
+0x2685,0xb3a5,0x3c09,0x405b,
+0x5dd3,0x602b,0x3adc,0xc06f,
+0x8019,0xaff0,0x8036,0x406f,
+0x8f20,0xa649,0x2e93,0xc057
+};
+#endif
+
+#ifdef MIEEE
+static unsigned short P[] = {
+0xbfeb,0x5493,0xb17f,0xb618,
+0x4028,0x15da,0xf520,0xe73a,
+0xc047,0x1009,0x7370,0xf62c,
+0x4050,0x5d3a,0x20d5,0xe2f7,
+0xc03e,0xe8c4,0xddb7,0x697d
+};
+static unsigned short Q[] = {
+0xc033,0x905a,0xc366,0x172f,
+0x405b,0x3c09,0xb3a5,0x2685,
+0xc06f,0x3adc,0x602b,0x5dd3,
+0x406f,0x8036,0xaff0,0x8019,
+0xc057,0x2e93,0xa649,0x8f20
+};
+#endif
+
+#ifdef ANSIPROT
+extern double fabs ( double );
+extern double log ( double x );
+extern double polevl ( double x, void *P, int N );
+extern double p1evl ( double x, void *P, int N );
+#else
+double fabs(), log(), polevl(), p1evl();
+#endif
+extern double INFINITY, NAN;
+
+double atanh(x)
+double x;
+{
+double s, z;
+
+#ifdef MINUSZERO
+if( x == 0.0 )
+	return(x);
+#endif
+z = fabs(x);
+if( z >= 1.0 )
+	{
+	if( x == 1.0 )
+		return( INFINITY );
+	if( x == -1.0 )
+		return( -INFINITY );
+	mtherr( "atanh", DOMAIN );
+	return( NAN );
+	}
+
+if( z < 1.0e-7 )
+	return(x);
+
+if( z < 0.5 )
+	{
+	z = x * x;
+	s = x   +  x * z * (polevl(z, P, 4) / p1evl(z, Q, 5));
+	return(s);
+	}
+
+return( 0.5 * log((1.0+x)/(1.0-x)) );
+}