Opened 12 years ago
Closed 12 years ago
#5113 closed Bugs (fixed)
math/special_functions/acosh.hpp wrong approximation for x near 1
| Reported by: | Owned by: | John Maddock | |
|---|---|---|---|
| Milestone: | Boost 1.47.0 | Component: | math |
| Version: | Boost 1.45.0 | Severity: | Problem |
| Keywords: | Cc: |
Description
The documentation and the code have different bugs for the approximation of acosh(x) for x near 1.
First of all they use different definitions of y. The documentation has y=1-x and the code has y=x-1. They both use the formula
(1+(1/12)*y+(3/160)*y^2)*sqrt(2*y), but neither of them is correct.
correct formulas [1]
y=1-x -> (1+(1/12)*y+(3/160)*y^2)*sqrt(-2*y)
y=x-1 -> (1-(1/12)*y+(3/160)*y^2)*sqrt(2*y)
[1] http://functions.wolfram.com/ElementaryFunctions/ArcCosh/06/01/04/01/0001/
Change History (2)
comment:1 by , 12 years ago
| Milestone: | To Be Determined → Boost 1.47.0 |
|---|---|
| Status: | new → assigned |
comment:2 by , 12 years ago
| Resolution: | → fixed |
|---|---|
| Status: | assigned → closed |
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