/* Exponential function minus one.
- Copyright (C) 2012 Free Software Foundation, Inc.
+ Copyright (C) 2012-2013 Free Software Foundation, Inc.
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
+ 21844/6081075 * z^13
- 929569/638512875 * z^15
+ ...
- Since |z| <= log(2)/1024 < 0.0007, the relative error of the z^7 term
- is < 0.0007^6 < 2^-60 <= 2^-DBL_MANT_DIG, therefore we can truncate
- the series after the z^5 term.
+ Since |z| <= log(2)/1024 < 0.0007, the relative contribution of the
+ z^7 term is < 0.0007^6 < 2^-60 <= 2^-DBL_MANT_DIG, therefore we can
+ truncate the series after the z^5 term.
Given the usual bounds DBL_MAX_EXP <= 16384, DBL_MANT_DIG <= 120, we
can estimate x: -84 <= x <= 11357.