diff options
author | Gregory Nutt <gnutt@nuttx.org> | 2015-04-09 10:35:07 -0600 |
---|---|---|
committer | Gregory Nutt <gnutt@nuttx.org> | 2015-04-09 10:35:07 -0600 |
commit | 139cf5a68a77007992d23eb36442206bdea796f7 (patch) | |
tree | d29babbd351883e04d86d54cfec85a92a30de7b7 | |
parent | 0741880a14fd021477a20922f81bd4b79bb495e4 (diff) | |
download | px4-nuttx-139cf5a68a77007992d23eb36442206bdea796f7.tar.gz px4-nuttx-139cf5a68a77007992d23eb36442206bdea796f7.tar.bz2 px4-nuttx-139cf5a68a77007992d23eb36442206bdea796f7.zip |
Fixes to asinh(), atanh(), and sinh(): The 'basic' expansions all exhibited bad cancellation errors near zero (<= 1E-10). This can be easily seen e.g. with x = 1E-30, the results are all zero though they should be extremely close to x. The cutoff values (1E-5, 1E-9) are chosen so that the next term in the Taylor series is negligible (for double). Functions could maybe be optimized to use only first term (x) and a smaller cutoff, just bigger than where the cancellation occurs.
-rw-r--r-- | nuttx/libc/math/lib_asinh.c | 16 | ||||
-rw-r--r-- | nuttx/libc/math/lib_atanh.c | 17 | ||||
-rw-r--r-- | nuttx/libc/math/lib_sinh.c | 21 |
3 files changed, 49 insertions, 5 deletions
diff --git a/nuttx/libc/math/lib_asinh.c b/nuttx/libc/math/lib_asinh.c index 7b573fcdd..5a30ac1aa 100644 --- a/nuttx/libc/math/lib_asinh.c +++ b/nuttx/libc/math/lib_asinh.c @@ -49,6 +49,20 @@ #ifdef CONFIG_HAVE_DOUBLE double asinh(double x) { - return log(x + sqrt(x * x + 1)); + double y; + double z = x * x; + + if (z < 1E-9) + { + /* x - 1/6 * x^3 + 3/40 * x^5 - 5/112 * x^7 + ... */ + + y = x * (1 - z / 6.0); + } + else + { + y = log(x + sqrt(z + 1)); + } + + return y; } #endif diff --git a/nuttx/libc/math/lib_atanh.c b/nuttx/libc/math/lib_atanh.c index 9932a5e9b..396e80852 100644 --- a/nuttx/libc/math/lib_atanh.c +++ b/nuttx/libc/math/lib_atanh.c @@ -49,6 +49,21 @@ #ifdef CONFIG_HAVE_DOUBLE double atanh(double x) { - return 0.5 * log((1 + x) / (1 - x)); + double y; + + if (fabs(x) < 1E-5) + { + double z = x * x; + + /* x + 1/3 * x^3 + 1/5 * x^5 + 1/7 * x^7 + ... */ + + y = x * (1 + z / 3.0); + } + else + { + y = log((1 + x) / (1 - x)) / 2.0; + } + + return y; } #endif diff --git a/nuttx/libc/math/lib_sinh.c b/nuttx/libc/math/lib_sinh.c index da79e7cfd..714a52816 100644 --- a/nuttx/libc/math/lib_sinh.c +++ b/nuttx/libc/math/lib_sinh.c @@ -3,7 +3,7 @@ * * This file is a part of NuttX: * - * Copyright (C) 2012 Gregory Nutt. All rights reserved. + * Copyright (C) 2012, 2015 Gregory Nutt. All rights reserved. * Ported by: Darcy Gong * * It derives from the Rhombs OS math library by Nick Johnson which has @@ -41,7 +41,22 @@ #ifdef CONFIG_HAVE_DOUBLE double sinh(double x) { - x = exp(x); - return ((x - (1.0 / x)) / 2.0); + double y; + double z; + + if (fabs(x) < 1E-5) + { + /* x + 1/3! * x^3 + 1/5! * x^5 + 1/7! * x^7 + ... */ + + z = x * x; + y = x * (1.0 + z / 6.0); + } + else + { + z = exp(x); + y = (z - 1.0 / z) / 2.0; + } + + return y; } #endif |