Initial import

libc/math/expl.c

@@ -0,0 +1,128 @@
+/* origin: OpenBSD /usr/src/lib/libm/src/ld80/e_expl.c */
+/*
+ * Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net>
+ *
+ * Permission to use, copy, modify, and distribute this software for any
+ * purpose with or without fee is hereby granted, provided that the above
+ * copyright notice and this permission notice appear in all copies.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
+ * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
+ * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
+ * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
+ * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
+ * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
+ * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
+ */
+/*
+ *      Exponential function, long double precision
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double x, y, expl();
+ *
+ * y = expl( x );
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns e (2.71828...) 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
+ *    e  = 2  e.
+ *
+ * A Pade' form of degree 5/6 is used to approximate exp(f) - 1
+ * in the basic range [-0.5 ln 2, 0.5 ln 2].
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    IEEE      +-10000     50000       1.12e-19    2.81e-20
+ *
+ *
+ * Error amplification in the exponential function can be
+ * a serious matter.  The error propagation involves
+ * exp( X(1+delta) ) = exp(X) ( 1 + X*delta + ... ),
+ * which shows that a 1 lsb error in representing X produces
+ * a relative error of X times 1 lsb in the function.
+ * While the routine gives an accurate result for arguments
+ * that are exactly represented by a long double precision
+ * computer number, the result contains amplified roundoff
+ * error for large arguments not exactly represented.
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ *   message         condition      value returned
+ * exp underflow    x < MINLOG         0.0
+ * exp overflow     x > MAXLOG         MAXNUM
+ *
+ */
+
+#include "libc/math/libm.h"
+
+#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
+long double expl(long double x)
+{
+	return exp(x);
+}
+#elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384
+
+static const long double P[3] = {
+ 1.2617719307481059087798E-4L,
+ 3.0299440770744196129956E-2L,
+ 9.9999999999999999991025E-1L,
+};
+static const long double Q[4] = {
+ 3.0019850513866445504159E-6L,
+ 2.5244834034968410419224E-3L,
+ 2.2726554820815502876593E-1L,
+ 2.0000000000000000000897E0L,
+};
+static const long double
+LN2HI = 6.9314575195312500000000E-1L,
+LN2LO = 1.4286068203094172321215E-6L,
+LOG2E = 1.4426950408889634073599E0L;
+
+long double expl(long double x)
+{
+	long double px, xx;
+	int k;
+
+	if (isnan(x))
+		return x;
+	if (x > 11356.5234062941439488L) /* x > ln(2^16384 - 0.5) */
+		return x * 0x1p16383L;
+	if (x < -11399.4985314888605581L) /* x < ln(2^-16446) */
+		return -0x1p-16445L/x;
+
+	/* Express e**x = e**f 2**k
+	 *   = e**(f + k ln(2))
+	 */
+	px = floorl(LOG2E * x + 0.5);
+	k = px;
+	x -= px * LN2HI;
+	x -= px * LN2LO;
+
+	/* rational approximation of the fractional part:
+	 * e**x =  1 + 2x P(x**2)/(Q(x**2) - x P(x**2))
+	 */
+	xx = x * x;
+	px = x * __polevll(xx, P, 2);
+	x = px/(__polevll(xx, Q, 3) - px);
+	x = 1.0 + 2.0 * x;
+	return scalbnl(x, k);
+}
+#elif LDBL_MANT_DIG == 113 && LDBL_MAX_EXP == 16384
+// TODO: broken implementation to make things compile
+long double expl(long double x)
+{
+	return exp(x);
+}
+#endif