| 7344 | |
| 7345 | namespace { |
| 7346 | double erf_inv(double x) { |
| 7347 | // Code accompanying the article "Approximating the erfinv function" in GPU Computing Gems, Volume 2 |
| 7348 | double w, p; |
| 7349 | |
| 7350 | w = -log((1.0 - x) * (1.0 + x)); |
| 7351 | |
| 7352 | if (w < 6.250000) { |
| 7353 | w = w - 3.125000; |
| 7354 | p = -3.6444120640178196996e-21; |
| 7355 | p = -1.685059138182016589e-19 + p * w; |
| 7356 | p = 1.2858480715256400167e-18 + p * w; |
| 7357 | p = 1.115787767802518096e-17 + p * w; |
| 7358 | p = -1.333171662854620906e-16 + p * w; |
| 7359 | p = 2.0972767875968561637e-17 + p * w; |
| 7360 | p = 6.6376381343583238325e-15 + p * w; |
| 7361 | p = -4.0545662729752068639e-14 + p * w; |
| 7362 | p = -8.1519341976054721522e-14 + p * w; |
| 7363 | p = 2.6335093153082322977e-12 + p * w; |
| 7364 | p = -1.2975133253453532498e-11 + p * w; |
| 7365 | p = -5.4154120542946279317e-11 + p * w; |
| 7366 | p = 1.051212273321532285e-09 + p * w; |
| 7367 | p = -4.1126339803469836976e-09 + p * w; |
| 7368 | p = -2.9070369957882005086e-08 + p * w; |
| 7369 | p = 4.2347877827932403518e-07 + p * w; |
| 7370 | p = -1.3654692000834678645e-06 + p * w; |
| 7371 | p = -1.3882523362786468719e-05 + p * w; |
| 7372 | p = 0.0001867342080340571352 + p * w; |
| 7373 | p = -0.00074070253416626697512 + p * w; |
| 7374 | p = -0.0060336708714301490533 + p * w; |
| 7375 | p = 0.24015818242558961693 + p * w; |
| 7376 | p = 1.6536545626831027356 + p * w; |
| 7377 | } else if (w < 16.000000) { |
| 7378 | w = sqrt(w) - 3.250000; |
| 7379 | p = 2.2137376921775787049e-09; |
| 7380 | p = 9.0756561938885390979e-08 + p * w; |
| 7381 | p = -2.7517406297064545428e-07 + p * w; |
| 7382 | p = 1.8239629214389227755e-08 + p * w; |
| 7383 | p = 1.5027403968909827627e-06 + p * w; |
| 7384 | p = -4.013867526981545969e-06 + p * w; |
| 7385 | p = 2.9234449089955446044e-06 + p * w; |
| 7386 | p = 1.2475304481671778723e-05 + p * w; |
| 7387 | p = -4.7318229009055733981e-05 + p * w; |
| 7388 | p = 6.8284851459573175448e-05 + p * w; |
| 7389 | p = 2.4031110387097893999e-05 + p * w; |
| 7390 | p = -0.0003550375203628474796 + p * w; |
| 7391 | p = 0.00095328937973738049703 + p * w; |
| 7392 | p = -0.0016882755560235047313 + p * w; |
| 7393 | p = 0.0024914420961078508066 + p * w; |
| 7394 | p = -0.0037512085075692412107 + p * w; |
| 7395 | p = 0.005370914553590063617 + p * w; |
| 7396 | p = 1.0052589676941592334 + p * w; |
| 7397 | p = 3.0838856104922207635 + p * w; |
| 7398 | } else { |
| 7399 | w = sqrt(w) - 5.000000; |
| 7400 | p = -2.7109920616438573243e-11; |
| 7401 | p = -2.5556418169965252055e-10 + p * w; |
| 7402 | p = 1.5076572693500548083e-09 + p * w; |
| 7403 | p = -3.7894654401267369937e-09 + p * w; |