*Do 6 Newton method iterations in cuberoot#550
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## dev/gfdl #550 +/- ##
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- Coverage 37.20% 37.19% -0.01%
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Files 271 271
Lines 80355 80341 -14
Branches 14985 14982 -3
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- Hits 29894 29882 -12
+ Misses 44903 44902 -1
+ Partials 5558 5557 -1 ☔ View full report in Codecov by Sentry. |
Modified the cuberoot function to do 6 iterations with Newton's method, starting from the optimal first guess of (3/8)**(1/3). Following guidance from performance testing of the previous version, all convergence testing has been removed and the same number of iterations are applied regardless of the input value. The form of Newton's method used here does one division per iteration, but it is good at polishing the root to give an accurate final solution and by simply repeatedly using the same instructions it appears to optimize well. This commit changes answers at roundoff for code that uses the cuberoot function, so ideally this PR would be dealt with before the cuberoot becomes widely used.
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Handled in #544 |
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Modified the
cuberoot()function to do 6 iterations with Newton's method, starting from the optimal first guess of (3/8)**(1/3). Following guidance from performance testing of the previous version (documented in the conversation surrounding #544), all convergence testing has been removed and the same number of iterations are applied regardless of the input value. The form of Newton's method used here does one division per iteration, but it is good at polishing the root to give an accurate final solution and by simply repeatedly using the same instructions it appears to optimize well. This commit changes answers at roundoff for code that uses thecuberoot()function, so ideally this PR would be dealt with before thecuberoot()becomes widely used.