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components/external/espruino/libs/math/exp2.c

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+/*							exp2.c
+ *
+ *	Base 2 exponential function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, exp2();
+ *
+ * y = exp2( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns 2 raised to the x power.
+ *
+ * Range reduction is accomplished by separating the argument
+ * into an integer k and fraction f such that
+ *     x    k  f
+ *    2  = 2  2.
+ *
+ * A Pade' form
+ *
+ *   1 + 2x P(x**2) / (Q(x**2) - x P(x**2) )
+ *
+ * approximates 2**x in the basic range [-0.5, 0.5].
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    IEEE    -1022,+1024   30000       1.8e-16     5.4e-17
+ *
+ *
+ * See exp.c for comments on error amplification.
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ *   message         condition      value returned
+ * exp underflow    x < -MAXL2        0.0
+ * exp overflow     x > MAXL2         MAXNUM
+ *
+ * For DEC arithmetic, MAXL2 = 127.
+ * For IEEE arithmetic, MAXL2 = 1024.
+ */
+
+
+/*
+Cephes Math Library Release 2.8:  June, 2000
+Copyright 1984, 1995, 2000 by Stephen L. Moshier
+*/
+
+
+
+#include "mconf.h"
+
+#ifdef UNK
+const static double P[] = {
+ 2.30933477057345225087E-2,
+ 2.02020656693165307700E1,
+ 1.51390680115615096133E3,
+};
+const static double Q[] = {
+/* 1.00000000000000000000E0,*/
+ 2.33184211722314911771E2,
+ 4.36821166879210612817E3,
+};
+#define MAXL2 1024.0
+#define MINL2 -1024.0
+#endif
+
+#ifdef DEC
+static unsigned short P[] = {
+0036675,0027102,0122327,0053227,
+0041241,0116724,0115412,0157355,
+0042675,0036404,0101733,0132226,
+};
+static unsigned short Q[] = {
+/*0040200,0000000,0000000,0000000,*/
+0042151,0027450,0077732,0160744,
+0043210,0100661,0077550,0056560,
+};
+#define MAXL2 127.0
+#define MINL2 -127.0
+#endif
+
+#ifdef IBMPC
+static unsigned short P[] = {
+0xead3,0x549a,0xa5c8,0x3f97,
+0x5bde,0x9361,0x33ba,0x4034,
+0x7693,0x907b,0xa7a0,0x4097,
+};
+static unsigned short Q[] = {
+/*0x0000,0x0000,0x0000,0x3ff0,*/
+0x5c3c,0x0ffb,0x25e5,0x406d,
+0x0bae,0x2fed,0x1036,0x40b1,
+};
+#define MAXL2 1024.0
+#define MINL2 -1022.0
+#endif
+
+#ifdef MIEEE
+static unsigned short P[] = {
+0x3f97,0xa5c8,0x549a,0xead3,
+0x4034,0x33ba,0x9361,0x5bde,
+0x4097,0xa7a0,0x907b,0x7693,
+};
+static unsigned short Q[] = {
+/*0x3ff0,0x0000,0x0000,0x0000,*/
+0x406d,0x25e5,0x0ffb,0x5c3c,
+0x40b1,0x1036,0x2fed,0x0bae,
+};
+#define MAXL2 1024.0
+#define MINL2 -1022.0
+#endif
+
+#ifdef ANSIPROT
+extern double polevl ( double, void *, int );
+extern double p1evl ( double, void *, int );
+extern double floor ( double );
+extern double ldexp ( double, int );
+extern int isnan ( double );
+extern int isfinite ( double );
+#else
+double polevl(), p1evl(), floor(), ldexp();
+int isnan(), isfinite();
+#endif
+#ifdef INFINITIES
+extern double INFINITY;
+#endif
+extern double MAXNUM;
+
+double exp2(x)
+double x;
+{
+double px, xx;
+short n;
+
+#ifdef NANS
+if( isnan(x) )
+	return(x);
+#endif
+if( x > MAXL2)
+	{
+#ifdef INFINITIES
+	return( INFINITY );
+#else
+	mtherr( "exp2", OVERFLOW );
+	return( MAXNUM );
+#endif
+	}
+
+if( x < MINL2 )
+	{
+#ifndef INFINITIES
+	mtherr( "exp2", UNDERFLOW );
+#endif
+	return(0.0);
+	}
+
+xx = x;	/* save x */
+/* separate into integer and fractional parts */
+px = floor(x+0.5);
+n = px;
+x = x - px;
+
+/* rational approximation
+ * exp2(x) = 1 +  2xP(xx)/(Q(xx) - P(xx))
+ * where xx = x**2
+ */
+xx = x * x;
+px = x * polevl( xx, P, 2 );
+x =  px / ( p1evl( xx, Q, 2 ) - px );
+x = 1.0 + ldexp( x, 1 );
+
+/* scale by power of 2 */
+x = ldexp( x, n );
+return(x);
+}