Add a "fork" of musl as //fusl.

fusl/src/math/logl.c

+/* origin: OpenBSD /usr/src/lib/libm/src/ld80/e_logl.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.
+ */
+/*
+ *      Natural logarithm, long double precision
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double x, y, logl();
+ *
+ * y = logl( x );
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the base e (2.718...) logarithm of x.
+ *
+ * The argument 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) = log(1+z/2) - log(1-z/2) = z + z**3 P(z)/Q(z).
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    IEEE      0.5, 2.0    150000      8.71e-20    2.75e-20
+ *    IEEE     exp(+-10000) 100000      5.39e-20    2.34e-20
+ *
+ * In the tests over the interval exp(+-10000), the logarithms
+ * of the random arguments were uniformly distributed over
+ * [-10000, +10000].
+ */
+
+#include "libm.h"
+
+#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
+long double logl(long double x)
+{
+        return log(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 const long double P[] = {
+ 4.5270000862445199635215E-5L,
+ 4.9854102823193375972212E-1L,
+ 6.5787325942061044846969E0L,
+ 2.9911919328553073277375E1L,
+ 6.0949667980987787057556E1L,
+ 5.7112963590585538103336E1L,
+ 2.0039553499201281259648E1L,
+};
+static const 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 const long double R[4] = {
+ 1.9757429581415468984296E-3L,
+-7.1990767473014147232598E-1L,
+ 1.0777257190312272158094E1L,
+-3.5717684488096787370998E1L,
+};
+static const 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 logl(long double x)
+{
+        long double y, z;
+        int e;
+
+        if (isnan(x))
+                return x;
+        if (x == INFINITY)
+                return x;
+        if (x <= 0.0) {
+                if (x == 0.0)
+                        return -1/(x*x); /* -inf with divbyzero */
+                return 0/0.0f; /* nan with invalid */
+        }
+
+        /* separate mantissa from exponent */
+        /* Note, frexp is used 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 - 0.5;
+                        y = 0.5 * z + 0.5;
+                } else {  /*  2 (x-1)/(x+1)   */
+                        z = x - 0.5;
+                        z -= 0.5;
+                        y = 0.5 * x  + 0.5;
+                }
+                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;
+                x = 2.0*x - 1.0;
+        } else {
+                x = x - 1.0;
+        }
+        z = x*x;
+        y = x * (z * __polevll(x, P, 6) / __p1evll(x, Q, 6));
+        y = y + e * C2;
+        z = y - 0.5*z;
+        /* Note, the sum of above terms does not exceed x/4,
+         * so it contributes at most about 1/4 lsb to the error.
+         */
+        z = z + x;
+        z = z + e * C1; /* This sum has an error of 1/2 lsb. */
+        return z;
+}
+#elif LDBL_MANT_DIG == 113 && LDBL_MAX_EXP == 16384
+// TODO: broken implementation to make things compile
+long double logl(long double x)
+{
+        return log(x);
+}
+#endif