Initial import

libc/math/expm1l.c

@@ -0,0 +1,123 @@
+/* origin: OpenBSD /usr/src/lib/libm/src/ld80/e_expm1l.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, minus 1
+ *      Long double precision
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double x, y, expm1l();
+ *
+ * y = expm1l( x );
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns e (2.71828...) raised to the x power, minus 1.
+ *
+ * Range reduction is accomplished by separating the argument
+ * into an integer k and fraction f such that
+ *
+ *     x    k  f
+ *    e  = 2  e.
+ *
+ * An expansion x + .5 x^2 + x^3 R(x) approximates exp(f) - 1
+ * in the basic range [-0.5 ln 2, 0.5 ln 2].
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    IEEE    -45,+maxarg   200,000     1.2e-19     2.5e-20
+ */
+
+#include "libc/math/libm.h"
+
+#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
+long double expm1l(long double x)
+{
+	return expm1(x);
+}
+#elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384
+
+/* exp(x) - 1 = x + 0.5 x^2 + x^3 P(x)/Q(x)
+   -.5 ln 2  <  x  <  .5 ln 2
+   Theoretical peak relative error = 3.4e-22  */
+static const long double
+P0 = -1.586135578666346600772998894928250240826E4L,
+P1 =  2.642771505685952966904660652518429479531E3L,
+P2 = -3.423199068835684263987132888286791620673E2L,
+P3 =  1.800826371455042224581246202420972737840E1L,
+P4 = -5.238523121205561042771939008061958820811E-1L,
+Q0 = -9.516813471998079611319047060563358064497E4L,
+Q1 =  3.964866271411091674556850458227710004570E4L,
+Q2 = -7.207678383830091850230366618190187434796E3L,
+Q3 =  7.206038318724600171970199625081491823079E2L,
+Q4 = -4.002027679107076077238836622982900945173E1L,
+/* Q5 = 1.000000000000000000000000000000000000000E0 */
+/* C1 + C2 = ln 2 */
+C1 = 6.93145751953125E-1L,
+C2 = 1.428606820309417232121458176568075500134E-6L,
+/* ln 2^-65 */
+minarg = -4.5054566736396445112120088E1L,
+/* ln 2^16384 */
+maxarg = 1.1356523406294143949492E4L;
+
+long double expm1l(long double x)
+{
+	long double px, qx, xx;
+	int k;
+
+	if (isnan(x))
+		return x;
+	if (x > maxarg)
+		return x*0x1p16383L; /* overflow, unless x==inf */
+	if (x == 0.0)
+		return x;
+	if (x < minarg)
+		return -1.0;
+
+	xx = C1 + C2;
+	/* Express x = ln 2 (k + remainder), remainder not exceeding 1/2. */
+	px = floorl(0.5 + x / xx);
+	k = px;
+	/* remainder times ln 2 */
+	x -= px * C1;
+	x -= px * C2;
+
+	/* Approximate exp(remainder ln 2).*/
+	px = (((( P4 * x + P3) * x + P2) * x + P1) * x + P0) * x;
+	qx = (((( x + Q4) * x + Q3) * x + Q2) * x + Q1) * x + Q0;
+	xx = x * x;
+	qx = x + (0.5 * xx + xx * px / qx);
+
+	/* exp(x) = exp(k ln 2) exp(remainder ln 2) = 2^k exp(remainder ln 2).
+	 We have qx = exp(remainder ln 2) - 1, so
+	 exp(x) - 1  =  2^k (qx + 1) - 1  =  2^k qx + 2^k - 1.  */
+	px = scalbnl(1.0, k);
+	x = px * qx + (px - 1.0);
+	return x;
+}
+#elif LDBL_MANT_DIG == 113 && LDBL_MAX_EXP == 16384
+// TODO: broken implementation to make things compile
+long double expm1l(long double x)
+{
+	return expm1(x);
+}
+#endif