Index: fusl/src/math/logl.c |
diff --git a/fusl/src/math/logl.c b/fusl/src/math/logl.c |
new file mode 100644 |
index 0000000000000000000000000000000000000000..5d5365929e62a351c4544bd9e6aace6e02834292 |
--- /dev/null |
+++ b/fusl/src/math/logl.c |
@@ -0,0 +1,175 @@ |
+/* 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 |