first commit of the new libm!

[musl] / src / math / log1pl.c

diff --git a/src/math/log1pl.c b/src/math/log1pl.c
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+/* origin: OpenBSD /usr/src/lib/libm/src/ld80/s_log1pl.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.
+ */
+/*
+ *      Relative error logarithm
+ *      Natural logarithm of 1+x, long double precision
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double x, y, log1pl();
+ *
+ * y = log1pl( x );
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the base e (2.718...) logarithm of 1+x.
+ *
+ * The argument 1+x is separated into its exponent and fractional
+ * parts.  If the exponent is between -1 and +1, the logarithm
+ * of the fraction is approximated by
+ *
+ *     log(1+x) = x - 0.5 x^2 + x^3 P(x)/Q(x).
+ *
+ * Otherwise, setting  z = 2(x-1)/x+1),
+ *
+ *     log(x) = z + z^3 P(z)/Q(z).
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    IEEE     -1.0, 9.0    100000      8.2e-20    2.5e-20
+ *
+ * ERROR MESSAGES:
+ *
+ * log singularity:  x-1 = 0; returns -INFINITY
+ * log domain:       x-1 < 0; returns NAN
+ */
+
+#include "libm.h"
+
+#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
+long double log1pl(long double x)
+{
+       return log1p(x);
+}
+#elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384
+/* Coefficients for log(1+x) = x - x^2 / 2 + x^3 P(x)/Q(x)
+ * 1/sqrt(2) <= x < sqrt(2)
+ * Theoretical peak relative error = 2.32e-20
+ */
+static long double P[] = {
+ 4.5270000862445199635215E-5L,
+ 4.9854102823193375972212E-1L,
+ 6.5787325942061044846969E0L,
+ 2.9911919328553073277375E1L,
+ 6.0949667980987787057556E1L,
+ 5.7112963590585538103336E1L,
+ 2.0039553499201281259648E1L,
+};
+static long double Q[] = {
+/* 1.0000000000000000000000E0,*/
+ 1.5062909083469192043167E1L,
+ 8.3047565967967209469434E1L,
+ 2.2176239823732856465394E2L,
+ 3.0909872225312059774938E2L,
+ 2.1642788614495947685003E2L,
+ 6.0118660497603843919306E1L,
+};
+
+/* Coefficients for log(x) = z + z^3 P(z^2)/Q(z^2),
+ * where z = 2(x-1)/(x+1)
+ * 1/sqrt(2) <= x < sqrt(2)
+ * Theoretical peak relative error = 6.16e-22
+ */
+static long double R[4] = {
+ 1.9757429581415468984296E-3L,
+-7.1990767473014147232598E-1L,
+ 1.0777257190312272158094E1L,
+-3.5717684488096787370998E1L,
+};
+static long double S[4] = {
+/* 1.00000000000000000000E0L,*/
+-2.6201045551331104417768E1L,
+ 1.9361891836232102174846E2L,
+-4.2861221385716144629696E2L,
+};
+static const long double C1 = 6.9314575195312500000000E-1L;
+static const long double C2 = 1.4286068203094172321215E-6L;
+
+#define SQRTH 0.70710678118654752440L
+
+long double log1pl(long double xm1)
+{
+       long double x, y, z;
+       int e;
+
+       if (isnan(xm1))
+               return xm1;
+       if (xm1 == INFINITY)
+               return xm1;
+       if (xm1 == 0.0)
+               return xm1;
+
+       x = xm1 + 1.0L;
+
+       /* Test for domain errors.  */
+       if (x <= 0.0L) {
+               if (x == 0.0L)
+                       return -INFINITY;
+               return NAN;
+       }
+
+       /* Separate mantissa from exponent.
+          Use frexp so that denormal numbers will be handled properly.  */
+       x = frexpl(x, &e);
+
+       /* logarithm using log(x) = z + z^3 P(z)/Q(z),
+          where z = 2(x-1)/x+1)  */
+       if (e > 2 || e < -2) {
+               if (x < SQRTH) { /* 2(2x-1)/(2x+1) */
+                       e -= 1;
+                       z = x - 0.5L;
+                       y = 0.5L * z + 0.5L;
+               } else { /*  2 (x-1)/(x+1)   */
+                       z = x - 0.5L;
+                       z -= 0.5L;
+                       y = 0.5L * x  + 0.5L;
+               }
+               x = z / y;
+               z = x*x;
+               z = x * (z * __polevll(z, R, 3) / __p1evll(z, S, 3));
+               z = z + e * C2;
+               z = z + x;
+               z = z + e * C1;
+               return z;
+       }
+
+       /* logarithm using log(1+x) = x - .5x**2 + x**3 P(x)/Q(x) */
+       if (x < SQRTH) {
+               e -= 1;
+               if (e != 0)
+                       x = 2.0 * x - 1.0L;
+               else
+                       x = xm1;
+       } else {
+               if (e != 0)
+                       x = x - 1.0L;
+               else
+                       x = xm1;
+       }
+       z = x*x;
+       y = x * (z * __polevll(x, P, 6) / __p1evll(x, Q, 6));
+       y = y + e * C2;
+       z = y - 0.5 * z;
+       z = z + x;
+       z = z + e * C1;
+       return z;
+}
+#endif