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+/* tanh.c
+ *
+ * Hyperbolic tangent
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, tanh();
+ *
+ * y = tanh( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns hyperbolic tangent of argument in the range MINLOG to
+ * MAXLOG.
+ *
+ * A rational function is used for |x| < 0.625. The form
+ * x + x**3 P(x)/Q(x) of Cody _& Waite is employed.
+ * Otherwise,
+ * tanh(x) = sinh(x)/cosh(x) = 1 - 2/(exp(2x) + 1).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC -2,2 50000 3.3e-17 6.4e-18
+ * IEEE -2,2 30000 2.5e-16 5.8e-17
+ *
+ */
+
+/*
+Cephes Math Library Release 2.8: June, 2000
+Copyright 1984, 1995, 2000 by Stephen L. Moshier
+*/
+
+#include <math.h>
+
+#ifdef UNK
+static double P[] = {
+-9.64399179425052238628E-1,
+-9.92877231001918586564E1,
+-1.61468768441708447952E3
+};
+static double Q[] = {
+/* 1.00000000000000000000E0,*/
+ 1.12811678491632931402E2,
+ 2.23548839060100448583E3,
+ 4.84406305325125486048E3
+};
+#endif
+#ifdef DEC
+static unsigned short P[] = {
+0140166,0161335,0053753,0075126,
+0141706,0111520,0070463,0040552,
+0142711,0153001,0101300,0025430
+};
+static unsigned short Q[] = {
+/*0040200,0000000,0000000,0000000,*/
+0041741,0117624,0051300,0156060,
+0043013,0133720,0071251,0127717,
+0043227,0060201,0021020,0020136
+};
+#endif
+
+#ifdef IBMPC
+static unsigned short P[] = {
+0x6f4b,0xaafd,0xdc5b,0xbfee,
+0x682d,0x0e26,0xd26a,0xc058,
+0x0563,0x3058,0x3ac0,0xc099
+};
+static unsigned short Q[] = {
+/*0x0000,0x0000,0x0000,0x3ff0,*/
+0x1b86,0x8a58,0x33f2,0x405c,
+0x35fa,0x0e55,0x76fa,0x40a1,
+0x040c,0x2442,0xec10,0x40b2
+};
+#endif
+
+#ifdef MIEEE
+static unsigned short P[] = {
+0xbfee,0xdc5b,0xaafd,0x6f4b,
+0xc058,0xd26a,0x0e26,0x682d,
+0xc099,0x3ac0,0x3058,0x0563
+};
+static unsigned short Q[] = {
+0x405c,0x33f2,0x8a58,0x1b86,
+0x40a1,0x76fa,0x0e55,0x35fa,
+0x40b2,0xec10,0x2442,0x040c
+};
+#endif
+
+#ifdef ANSIPROT
+extern double fabs ( double );
+extern double exp ( double );
+extern double polevl ( double, void *, int );
+extern double p1evl ( double, void *, int );
+#else
+double fabs(), exp(), polevl(), p1evl();
+#endif
+extern double MAXLOG;
+
+double tanh(x)
+double x;
+{
+double s, z;
+
+#ifdef MINUSZERO
+if( x == 0.0 )
+ return(x);
+#endif
+z = fabs(x);
+if( z > 0.5 * MAXLOG )
+ {
+ if( x > 0 )
+ return( 1.0 );
+ else
+ return( -1.0 );
+ }
+if( z >= 0.625 )
+ {
+ s = exp(2.0*z);
+ z = 1.0 - 2.0/(s + 1.0);
+ if( x < 0 )
+ z = -z;
+ }
+else
+ {
+ if( x == 0.0 )
+ return(x);
+ s = x * x;
+ z = polevl( s, P, 2 )/p1evl(s, Q, 3);
+ z = x * s * z;
+ z = x + z;
+ }
+return( z );
+}