On Thu, Mar 10, 2016 at 11:16:08PM -0500, Ganesh Ajjanagadde wrote: > Code taken from the Julia project, licensed under MIT: > https://github.com/JuliaLang/julia/blob/master/base/random.jl, in turn > derived from: "The Ziggurat Method for generating random variables" - > Marsaglia and Tsang. > > Paper and reference code: http://www.jstatsoft.org/v05/i08/. This is > well known to be the fastest method empirically for generating normal random > variables. Note that there are a large number of implementations with > various tunings, this was one of the simpler ones and also has a friendly > license. > > This results in ~ 3x speedup of random number generation: > old: > 15090 decicycles in av_bmg_get, 1 runs, 0 skips > 13140 decicycles in av_bmg_get, 2 runs, 0 skips > 10117 decicycles in av_bmg_get, 4 runs, 0 skips > [...] > 2133 decicycles in av_bmg_get, 524268 runs, 20 skips=60.4x > 2134 decicycles in av_bmg_get, 1048531 runs, 45 skips=61.3x > 2135 decicycles in av_bmg_get, 2097061 runs, 91 skips=61.9x > > new: > 7950 decicycles in av_bmg_get, 1 runs, 0 skips > 6000 decicycles in av_bmg_get, 2 runs, 0 skips > 4432 decicycles in av_bmg_get, 4 runs, 0 skips > [...] > 755 decicycles in av_bmg_get, 524281 runs, 7 skips= 62x > 754 decicycles in av_bmg_get, 1048563 runs, 13 skips=63.4x > 754 decicycles in av_bmg_get, 2097125 runs, 27 skips=63.8x > > and accordingly a ~2% speedup in aac encoding (-march=native, Haswell, clang): > > old: > ffmpeg -f lavfi -i anoisesrc -t 300 -y sin_new.aac 5.29s user 0.01s system > 99% cpu 5.303 total > new: > ffmpeg -f lavfi -i anoisesrc -t 300 -y sin_new.aac 5.14s user 0.02s system > 99% cpu 5.166 total > > Documentation is also changed accordingly. > > Signed-off-by: Ganesh Ajjanagadde <gajja...@gmail.com> > --- > libavutil/lfg.c | 309 > ++++++++++++++++++++++++++++++++++++++++++++++++++++++-- > libavutil/lfg.h | 2 +- > 2 files changed, 299 insertions(+), 12 deletions(-) > > diff --git a/libavutil/lfg.c b/libavutil/lfg.c > index ffa2f1f..9507754 100644 > --- a/libavutil/lfg.c > +++ b/libavutil/lfg.c > @@ -44,19 +44,306 @@ av_cold void av_lfg_init(AVLFG *c, unsigned int seed) > c->index = 0; > } > > +/* Code adapted from the Julia project: > + https://github.com/JuliaLang/julia/blob/master/base/random.jl. > + This is licensed under MIT > (https://github.com/JuliaLang/julia/blob/master/LICENSE.md) > + Copyright (c) 2009-2016: Jeff Bezanson, Stefan Karpinski, Viral B. Shah, > and other contributors: > + > + https://github.com/JuliaLang/julia/contributors > + > + Permission is hereby granted, free of charge, to any person obtaining a > copy of this software and associated documentation files (the "Software"), to > deal in the Software without restriction, including without limitation the > rights to use, copy, modify, merge, publish, distribute, sublicense, and/or > sell copies of the Software, and to permit persons to whom the Software is > furnished to do so, subject to the following conditions: > + > + The above copyright notice and this permission notice shall be included > in all copies or substantial portions of the Software. > + > + THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS > OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, > FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE > AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER > LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, > OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE > SOFTWARE. > +*/ > + > + /* The Ziggurat Method for generating random variables - Marsaglia and > Tsang > + Paper and reference code: http://www.jstatsoft.org/v05/i08/. */ > + /* Tables for normal distribution */ > +static const uint64_t ki[] = { > + > UINT64_C(0x0007799ec012f7b2),UINT64_C(0x0000000000000000),UINT64_C(0x0006045f4c7de363),UINT64_C(0x0006d1aa7d5ec0a5), > + > UINT64_C(0x000728fb3f60f777),UINT64_C(0x0007592af4e9fbc0),UINT64_C(0x000777a5c0bf655d),UINT64_C(0x00078ca3857d2256), > + > UINT64_C(0x00079bf6b0ffe58b),UINT64_C(0x0007a7a34ab092ad),UINT64_C(0x0007b0d2f20dd1cb),UINT64_C(0x0007b83d3aa9cb52), > + > UINT64_C(0x0007be597614224d),UINT64_C(0x0007c3788631abe9),UINT64_C(0x0007c7d32bc192ee),UINT64_C(0x0007cb9263a6e86d), > + > UINT64_C(0x0007ced483edfa84),UINT64_C(0x0007d1b07ac0fd39),UINT64_C(0x0007d437ef2da5fc),UINT64_C(0x0007d678b069aa6e), > + > UINT64_C(0x0007d87db38c5c87),UINT64_C(0x0007da4fc6a9ba62),UINT64_C(0x0007dbf611b37f3b),UINT64_C(0x0007dd7674d0f286), > + > UINT64_C(0x0007ded5ce8205f6),UINT64_C(0x0007e018307fb62b),UINT64_C(0x0007e141081bd124),UINT64_C(0x0007e2533d712de8), > + > UINT64_C(0x0007e3514bbd7718),UINT64_C(0x0007e43d54944b52),UINT64_C(0x0007e5192f25ef42),UINT64_C(0x0007e5e67481118d), > + > UINT64_C(0x0007e6a6897c1ce2),UINT64_C(0x0007e75aa6c7f64c),UINT64_C(0x0007e803df8ee498),UINT64_C(0x0007e8a326eb6272), > + > UINT64_C(0x0007e93954717a28),UINT64_C(0x0007e9c727f8648f),UINT64_C(0x0007ea4d4cc85a3c),UINT64_C(0x0007eacc5c4907a9), > + > UINT64_C(0x0007eb44e0474cf6),UINT64_C(0x0007ebb754e47419),UINT64_C(0x0007ec242a3d8474),UINT64_C(0x0007ec8bc5d69645), > + > UINT64_C(0x0007ecee83d3d6e9),UINT64_C(0x0007ed4cb8082f45),UINT64_C(0x0007eda6aee0170f),UINT64_C(0x0007edfcae2dfe68), > + > UINT64_C(0x0007ee4ef5dccd3e),UINT64_C(0x0007ee9dc08c394e),UINT64_C(0x0007eee9441a17c7),UINT64_C(0x0007ef31b21b4fb1), > + > UINT64_C(0x0007ef773846a8a7),UINT64_C(0x0007efba00d35a17),UINT64_C(0x0007effa32ccf69f),UINT64_C(0x0007f037f25e1278), > + > UINT64_C(0x0007f0736112d12c),UINT64_C(0x0007f0ac9e145c25),UINT64_C(0x0007f0e3c65e1fcc),UINT64_C(0x0007f118f4ed8e54), > + > UINT64_C(0x0007f14c42ed0dc8),UINT64_C(0x0007f17dc7daa0c3),UINT64_C(0x0007f1ad99aac6a5),UINT64_C(0x0007f1dbcce80015), > + > UINT64_C(0x0007f20874cf56bf),UINT64_C(0x0007f233a36a3b9a),UINT64_C(0x0007f25d69a604ad),UINT64_C(0x0007f285d7694a92), > + > UINT64_C(0x0007f2acfba75e3b),UINT64_C(0x0007f2d2e4720909),UINT64_C(0x0007f2f79f09c344),UINT64_C(0x0007f31b37ec883b), > + > UINT64_C(0x0007f33dbae36abc),UINT64_C(0x0007f35f330f08d5),UINT64_C(0x0007f37faaf2fa79),UINT64_C(0x0007f39f2c805380), > + > UINT64_C(0x0007f3bdc11f4f1c),UINT64_C(0x0007f3db71b83850),UINT64_C(0x0007f3f846bba121),UINT64_C(0x0007f4144829f846), > + > UINT64_C(0x0007f42f7d9a8b9d),UINT64_C(0x0007f449ee420432),UINT64_C(0x0007f463a0f8675e),UINT64_C(0x0007f47c9c3ea77b), > + > UINT64_C(0x0007f494e643cd8e),UINT64_C(0x0007f4ac84e9c475),UINT64_C(0x0007f4c37dc9cd50),UINT64_C(0x0007f4d9d638a432), > + > UINT64_C(0x0007f4ef934a5b6a),UINT64_C(0x0007f504b9d5f33d),UINT64_C(0x0007f5194e78b352),UINT64_C(0x0007f52d55994a96), > + > UINT64_C(0x0007f540d36aba0c),UINT64_C(0x0007f553cbef0e77),UINT64_C(0x0007f56642f9ec8f),UINT64_C(0x0007f5783c32f31e), > + > UINT64_C(0x0007f589bb17f609),UINT64_C(0x0007f59ac2ff1525),UINT64_C(0x0007f5ab5718b15a),UINT64_C(0x0007f5bb7a71427c), > + > UINT64_C(0x0007f5cb2ff31009),UINT64_C(0x0007f5da7a67cebe),UINT64_C(0x0007f5e95c7a24e7),UINT64_C(0x0007f5f7d8b7171e), > + > UINT64_C(0x0007f605f18f5ef4),UINT64_C(0x0007f613a958ad0a),UINT64_C(0x0007f621024ed7e9),UINT64_C(0x0007f62dfe94f8cb), > + > UINT64_C(0x0007f63aa036777a),UINT64_C(0x0007f646e928065a),UINT64_C(0x0007f652db488f88),UINT64_C(0x0007f65e786213ff), > + > UINT64_C(0x0007f669c22a7d8a),UINT64_C(0x0007f674ba446459),UINT64_C(0x0007f67f623fc8db),UINT64_C(0x0007f689bb9ac294), > + > UINT64_C(0x0007f693c7c22481),UINT64_C(0x0007f69d881217a6),UINT64_C(0x0007f6a6fdd6ac36),UINT64_C(0x0007f6b02a4c61ee), > + > UINT64_C(0x0007f6b90ea0a7f4),UINT64_C(0x0007f6c1abf254c0),UINT64_C(0x0007f6ca03521664),UINT64_C(0x0007f6d215c2db82), > + > UINT64_C(0x0007f6d9e43a3559),UINT64_C(0x0007f6e16fa0b329),UINT64_C(0x0007f6e8b8d23729),UINT64_C(0x0007f6efc09e4569), > + > UINT64_C(0x0007f6f687c84cbf),UINT64_C(0x0007f6fd0f07ea09),UINT64_C(0x0007f703570925e2),UINT64_C(0x0007f709606cad03), > + > UINT64_C(0x0007f70f2bc8036f),UINT64_C(0x0007f714b9a5b292),UINT64_C(0x0007f71a0a85725d),UINT64_C(0x0007f71f1edc4d9e), > + > UINT64_C(0x0007f723f714c179),UINT64_C(0x0007f728938ed843),UINT64_C(0x0007f72cf4a03fa0),UINT64_C(0x0007f7311a945a16), > + > UINT64_C(0x0007f73505ac4bf8),UINT64_C(0x0007f738b61f03bd),UINT64_C(0x0007f73c2c193dc0),UINT64_C(0x0007f73f67bd835c), > + > UINT64_C(0x0007f74269242559),UINT64_C(0x0007f745305b31a1),UINT64_C(0x0007f747bd666428),UINT64_C(0x0007f74a103f12ed), > + > UINT64_C(0x0007f74c28d414f5),UINT64_C(0x0007f74e0709a42d),UINT64_C(0x0007f74faab939f9),UINT64_C(0x0007f75113b16657), > + > UINT64_C(0x0007f75241b5a155),UINT64_C(0x0007f753347e16b8),UINT64_C(0x0007f753ebb76b7c),UINT64_C(0x0007f75467027d05), > + > UINT64_C(0x0007f754a5f4199d),UINT64_C(0x0007f754a814b207),UINT64_C(0x0007f7546ce003ae),UINT64_C(0x0007f753f3c4bb29), > + > UINT64_C(0x0007f7533c240e92),UINT64_C(0x0007f75245514f41),UINT64_C(0x0007f7510e91726c),UINT64_C(0x0007f74f971a9012), > + > UINT64_C(0x0007f74dde135797),UINT64_C(0x0007f74be2927971),UINT64_C(0x0007f749a39e051c),UINT64_C(0x0007f747202aba8a), > + > UINT64_C(0x0007f744571b4e3c),UINT64_C(0x0007f741473f9efe),UINT64_C(0x0007f73def53dc43),UINT64_C(0x0007f73a4dff9bff), > + > UINT64_C(0x0007f73661d4deaf),UINT64_C(0x0007f732294f003f),UINT64_C(0x0007f72da2d19444),UINT64_C(0x0007f728cca72bda), > + > UINT64_C(0x0007f723a5000367),UINT64_C(0x0007f71e29f09627),UINT64_C(0x0007f7185970156b),UINT64_C(0x0007f7123156c102), > + > UINT64_C(0x0007f70baf5c1e2c),UINT64_C(0x0007f704d1150a23),UINT64_C(0x0007f6fd93f1a4e5),UINT64_C(0x0007f6f5f53b10b6), > + > UINT64_C(0x0007f6edf211023e),UINT64_C(0x0007f6e587671ce9),UINT64_C(0x0007f6dcb2021679),UINT64_C(0x0007f6d36e749c64), > + > UINT64_C(0x0007f6c9b91bf4c6),UINT64_C(0x0007f6bf8e1c541b),UINT64_C(0x0007f6b4e95ce015),UINT64_C(0x0007f6a9c68356ff), > + > UINT64_C(0x0007f69e20ef5211),UINT64_C(0x0007f691f3b517eb),UINT64_C(0x0007f6853997f321),UINT64_C(0x0007f677ed03ff19), > + > UINT64_C(0x0007f66a08075bdc),UINT64_C(0x0007f65b844ab75a),UINT64_C(0x0007f64c5b091860),UINT64_C(0x0007f63c8506d4bc), > + > UINT64_C(0x0007f62bfa8798fe),UINT64_C(0x0007f61ab34364b0),UINT64_C(0x0007f608a65a599a),UINT64_C(0x0007f5f5ca4737e8), > + > UINT64_C(0x0007f5e214d05b48),UINT64_C(0x0007f5cd7af7066e),UINT64_C(0x0007f5b7f0e4c2a1),UINT64_C(0x0007f5a169d68fcf), > + > UINT64_C(0x0007f589d80596a5),UINT64_C(0x0007f5712c8d0174),UINT64_C(0x0007f557574c912b),UINT64_C(0x0007f53c46c77193), > + > UINT64_C(0x0007f51fe7feb9f2),UINT64_C(0x0007f5022646ecfb),UINT64_C(0x0007f4e2eb17ab1d),UINT64_C(0x0007f4c21dd4a3d1), > + > UINT64_C(0x0007f49fa38ea394),UINT64_C(0x0007f47b5ebb62eb),UINT64_C(0x0007f4552ee27473),UINT64_C(0x0007f42cf03d58f5), > + > UINT64_C(0x0007f4027b48549f),UINT64_C(0x0007f3d5a44119df),UINT64_C(0x0007f3a63a8fb552),UINT64_C(0x0007f37408155100), > + > UINT64_C(0x0007f33ed05b55ec),UINT64_C(0x0007f3064f9c183e),UINT64_C(0x0007f2ca399c7ba1),UINT64_C(0x0007f28a384bb940), > + > UINT64_C(0x0007f245ea1b7a2b),UINT64_C(0x0007f1fcdffe8f1b),UINT64_C(0x0007f1ae9af758cd),UINT64_C(0x0007f15a8917f27e), > + > UINT64_C(0x0007f10001ccaaab),UINT64_C(0x0007f09e413c418a),UINT64_C(0x0007f034627733d7),UINT64_C(0x0007efc15815b8d5), > + > UINT64_C(0x0007ef43e2bf7f55),UINT64_C(0x0007eeba84e31dfe),UINT64_C(0x0007ee237294df89),UINT64_C(0x0007ed7c7c170141), > + > UINT64_C(0x0007ecc2f0d95d3a),UINT64_C(0x0007ebf377a46782),UINT64_C(0x0007eb09d6deb285),UINT64_C(0x0007ea00a4f17808), > + > UINT64_C(0x0007e8d0d3da63d6),UINT64_C(0x0007e771023b0fcf),UINT64_C(0x0007e5d46c2f08d8),UINT64_C(0x0007e3e937669691), > + > UINT64_C(0x0007e195978f1176),UINT64_C(0x0007deb2c0e05c1c),UINT64_C(0x0007db0362002a19),UINT64_C(0x0007d6202c151439), > + > UINT64_C(0x0007cf4b8f00a2cb),UINT64_C(0x0007c4fd24520efd),UINT64_C(0x0007b362fbf81816),UINT64_C(0x00078d2d25998e24), > +}; > + > +static const double wi[] = { > + 1.7367254121602630e-15,9.5586603514556339e-17,1.2708704834810623e-16, > + 1.4909740962495474e-16,1.6658733631586268e-16,1.8136120810119029e-16, > + 1.9429720153135588e-16,2.0589500628482093e-16,2.1646860576895422e-16, > + 2.2622940392218116e-16,2.3532718914045892e-16,2.4387234557428771e-16, > + 2.5194879829274225e-16,2.5962199772528103e-16,2.6694407473648285e-16, > + 2.7395729685142446e-16,2.8069646002484804e-16,2.8719058904113930e-16, > + 2.9346417484728883e-16,2.9953809336782113e-16,3.0543030007192440e-16, > + 3.1115636338921572e-16,3.1672988018581815e-16,3.2216280350549905e-16, > + 3.2746570407939751e-16,3.3264798116841710e-16,3.3771803417353232e-16, > + 3.4268340353119356e-16,3.4755088731729758e-16,3.5232663846002031e-16, > + 3.5701624633953494e-16,3.6162480571598339e-16,3.6615697529653540e-16, > + 3.7061702777236077e-16,3.7500889278747798e-16,3.7933619401549554e-16, > + 3.8360228129677279e-16,3.8781025861250247e-16,3.9196300853257678e-16, > + 3.9606321366256378e-16,4.0011337552546690e-16,4.0411583124143332e-16, > + 4.0807276830960448e-16,4.1198623774807442e-16,4.1585816580828064e-16, > + 4.1969036444740733e-16,4.2348454071520708e-16,4.2724230518899761e-16, > + 4.3096517957162941e-16,4.3465460355128760e-16,4.3831194100854571e-16, > + 4.4193848564470665e-16,4.4553546609579137e-16,4.4910405058828750e-16, > + 4.5264535118571397e-16,4.5616042766900381e-16,4.5965029108849407e-16, > + 4.6311590702081647e-16,4.6655819856008752e-16,4.6997804906941950e-16, > + 4.7337630471583237e-16,4.7675377680908526e-16,4.8011124396270155e-16, > + 4.8344945409350080e-16,4.8676912627422087e-16,4.9007095245229938e-16, > + 4.9335559904654139e-16,4.9662370843221783e-16,4.9987590032409088e-16, > + 5.0311277306593187e-16,5.0633490483427195e-16,5.0954285476338923e-16, > + 5.1273716399787966e-16,5.1591835667857364e-16,5.1908694086703434e-16, > + 5.2224340941340417e-16,5.2538824077194543e-16,5.2852189976823820e-16, > + 5.3164483832166176e-16,5.3475749612647295e-16,5.3786030129452348e-16, > + 5.4095367096239933e-16,5.4403801186554671e-16,5.4711372088173611e-16, > + 5.5018118554603362e-16,5.5324078453927836e-16,5.5629288815190902e-16, > + 5.5933785872484621e-16,5.6237605106900435e-16,5.6540781286489604e-16, > + 5.6843348504368141e-16,5.7145340215092040e-16,5.7446789269419609e-16, > + 5.7747727947569648e-16,5.8048187991076857e-16,5.8348200633338921e-16, > + 5.8647796628943653e-16,5.8947006281858718e-16,5.9245859472561339e-16, > + 5.9544385684180598e-16,5.9842614027720281e-16,6.0140573266426640e-16, > + 6.0438291839361250e-16,6.0735797884236057e-16,6.1033119259564394e-16, > + 6.1330283566179110e-16,6.1627318168165963e-16,6.1924250213258470e-16, > + 6.2221106652737879e-16,6.2517914260879998e-16,6.2814699653988953e-16, > + 6.3111489309056042e-16,6.3408309582080600e-16,6.3705186726088149e-16, > + 6.4002146908880247e-16,6.4299216230548961e-16,6.4596420740788321e-16, > + 6.4893786456033965e-16,6.5191339376461587e-16,6.5489105502874154e-16, > + 6.5787110853507413e-16,6.6085381480782587e-16,6.6383943488035057e-16, > + 6.6682823046247459e-16,6.6982046410815579e-16,6.7281639938375311e-16, > + 6.7581630103719006e-16,6.7882043516829803e-16,6.8182906940062540e-16, > + 6.8484247305500383e-16,6.8786091732516637e-16,6.9088467545571690e-16, > + 6.9391402292275690e-16,6.9694923761748294e-16,6.9999060003307640e-16, > + 7.0303839345521508e-16,7.0609290415654822e-16,7.0915442159548734e-16, > + 7.1222323861967788e-16,7.1529965167453030e-16,7.1838396101720629e-16, > + 7.2147647093647067e-16,7.2457748997883870e-16,7.2768733118146927e-16, > + 7.3080631231227429e-16,7.3393475611774048e-16,7.3707299057898310e-16, > + 7.4022134917657997e-16,7.4338017116476479e-16,7.4654980185558890e-16, > + 7.4973059291369793e-16,7.5292290266240584e-16,7.5612709640179217e-16, > + 7.5934354673958895e-16,7.6257263393567558e-16,7.6581474626104873e-16, > + 7.6907028037219191e-16,7.7233964170182985e-16,7.7562324486711744e-16, > + 7.7892151409638524e-16,7.8223488367564108e-16,7.8556379841610841e-16, > + 7.8890871414417552e-16,7.9227009821522709e-16,7.9564843005293662e-16, > + 7.9904420171571300e-16,8.0245791849212591e-16,8.0589009952726568e-16, > + 8.0934127848215009e-16,8.1281200422845008e-16,8.1630284158098775e-16, > + 8.1981437207065329e-16,8.2334719476060504e-16,8.2690192710884700e-16, > + 8.3047920588053737e-16,8.3407968811366288e-16,8.3770405214202216e-16, > + 8.4135299867980282e-16,8.4502725197240968e-16,8.4872756101861549e-16, > + 8.5245470086955962e-16,8.5620947401062333e-16,8.5999271183276646e-16, > + 8.6380527620052589e-16,8.6764806112455816e-16,8.7152199454736980e-16, > + 8.7542804025171749e-16,8.7936719990210427e-16,8.8334051523084080e-16, > + 8.8734907038131345e-16,8.9139399442240861e-16,8.9547646404950677e-16, > + 8.9959770648910994e-16,9.0375900262601175e-16,9.0796169037400680e-16, > + 9.1220716831348461e-16,9.1649689962191353e-16,9.2083241632623076e-16, > + 9.2521532390956933e-16,9.2964730630864167e-16,9.3413013134252651e-16, > + 9.3866565661866598e-16,9.4325583596767065e-16,9.4790272646517382e-16, > + 9.5260849610662787e-16,9.5737543220974496e-16,9.6220595062948384e-16, > + 9.6710260588230542e-16,9.7206810229016259e-16,9.7710530627072088e-16, > + 9.8221725991905411e-16,9.8740719604806711e-16,9.9267855488079765e-16, > + 9.9803500261836449e-16,1.0034804521436181e-15,1.0090190861637457e-15, > + 1.0146553831467086e-15,1.0203941464683124e-15,1.0262405372613567e-15, > + 1.0322001115486456e-15,1.0382788623515399e-15,1.0444832676000471e-15, > + 1.0508203448355195e-15,1.0572977139009890e-15,1.0639236690676801e-15, > + 1.0707072623632994e-15,1.0776584002668106e-15,1.0847879564403425e-15, > + 1.0921079038149563e-15,1.0996314701785628e-15,1.1073733224935752e-15, > + 1.1153497865853155e-15,1.1235791107110833e-15,1.1320817840164846e-15, > + 1.1408809242582780e-15,1.1500027537839792e-15,1.1594771891449189e-15, > + 1.1693385786910960e-15,1.1796266352955801e-15,1.1903876299282890e-15, > + 1.2016759392543819e-15,1.2135560818666897e-15,1.2261054417450561e-15, > + 1.2394179789163251e-15,1.2536093926602567e-15,1.2688244814255010e-15, > + 1.2852479319096109e-15,1.3031206634689985e-15,1.3227655770195326e-15, > + 1.3446300925011171e-15,1.3693606835128518e-15,1.3979436672775240e-15, > + 1.4319989869661328e-15,1.4744848603597596e-15,1.5317872741611144e-15, > + 1.6227698675312968e-15 > +}; > + > +static const double fi[] = { > + 1.0000000000000000e+00,9.7710170126767082e-01,9.5987909180010600e-01, > + 9.4519895344229909e-01,9.3206007595922991e-01,9.1999150503934646e-01, > + 9.0872644005213032e-01,8.9809592189834297e-01,8.8798466075583282e-01, > + 8.7830965580891684e-01,8.6900868803685649e-01,8.6003362119633109e-01, > + 8.5134625845867751e-01,8.4291565311220373e-01,8.3471629298688299e-01, > + 8.2672683394622093e-01,8.1892919160370192e-01,8.1130787431265572e-01, > + 8.0384948317096383e-01,7.9654233042295841e-01,7.8937614356602404e-01, > + 7.8234183265480195e-01,7.7543130498118662e-01,7.6863731579848571e-01, > + 7.6195334683679483e-01,7.5537350650709567e-01,7.4889244721915638e-01, > + 7.4250529634015061e-01,7.3620759812686210e-01,7.2999526456147568e-01, > + 7.2386453346862967e-01,7.1781193263072152e-01,7.1183424887824798e-01, > + 7.0592850133275376e-01,7.0009191813651117e-01,6.9432191612611627e-01, > + 6.8861608300467136e-01,6.8297216164499430e-01,6.7738803621877308e-01, > + 6.7186171989708166e-01,6.6639134390874977e-01,6.6097514777666277e-01, > + 6.5561147057969693e-01,6.5029874311081637e-01,6.4503548082082196e-01, > + 6.3982027745305614e-01,6.3465179928762327e-01,6.2952877992483625e-01, > + 6.2445001554702606e-01,6.1941436060583399e-01,6.1442072388891344e-01, > + 6.0946806492577310e-01,6.0455539069746733e-01,5.9968175261912482e-01, > + 5.9484624376798689e-01,5.9004799633282545e-01,5.8528617926337090e-01, > + 5.8055999610079034e-01,5.7586868297235316e-01,5.7121150673525267e-01, > + 5.6658776325616389e-01,5.6199677581452390e-01,5.5743789361876550e-01, > + 5.5291049042583185e-01,5.4841396325526537e-01,5.4394773119002582e-01, > + 5.3951123425695158e-01,5.3510393238045717e-01,5.3072530440366150e-01, > + 5.2637484717168403e-01,5.2205207467232140e-01,5.1775651722975591e-01, > + 5.1348772074732651e-01,5.0924524599574761e-01,5.0502866794346790e-01, > + 5.0083757512614835e-01,4.9667156905248933e-01,4.9253026364386815e-01, > + 4.8841328470545758e-01,4.8432026942668288e-01,4.8025086590904642e-01, > + 4.7620473271950547e-01,4.7218153846772976e-01,4.6818096140569321e-01, > + 4.6420268904817391e-01,4.6024641781284248e-01,4.5631185267871610e-01, > + 4.5239870686184824e-01,4.4850670150720273e-01,4.4463556539573912e-01, > + 4.4078503466580377e-01,4.3695485254798533e-01,4.3314476911265209e-01, > + 4.2935454102944126e-01,4.2558393133802180e-01,4.2183270922949573e-01, > + 4.1810064983784795e-01,4.1438753404089090e-01,4.1069314827018799e-01, > + 4.0701728432947315e-01,4.0335973922111429e-01,3.9972031498019700e-01, > + 3.9609881851583223e-01,3.9249506145931540e-01,3.8890886001878855e-01, > + 3.8534003484007706e-01,3.8178841087339344e-01,3.7825381724561896e-01, > + 3.7473608713789086e-01,3.7123505766823922e-01,3.6775056977903225e-01, > + 3.6428246812900372e-01,3.6083060098964775e-01,3.5739482014578022e-01, > + 3.5397498080007656e-01,3.5057094148140588e-01,3.4718256395679348e-01, > + 3.4380971314685055e-01,3.4045225704452164e-01,3.3711006663700588e-01, > + 3.3378301583071823e-01,3.3047098137916342e-01,3.2717384281360129e-01, > + 3.2389148237639104e-01,3.2062378495690530e-01,3.1737063802991350e-01, > + 3.1413193159633707e-01,3.1090755812628634e-01,3.0769741250429189e-01, > + 3.0450139197664983e-01,3.0131939610080288e-01,2.9815132669668531e-01, > + 2.9499708779996164e-01,2.9185658561709499e-01,2.8872972848218270e-01, > + 2.8561642681550159e-01,2.8251659308370741e-01,2.7943014176163772e-01, > + 2.7635698929566810e-01,2.7329705406857691e-01,2.7025025636587519e-01, > + 2.6721651834356114e-01,2.6419576399726080e-01,2.6118791913272082e-01, > + 2.5819291133761890e-01,2.5521066995466168e-01,2.5224112605594190e-01, > + 2.4928421241852824e-01,2.4633986350126363e-01,2.4340801542275012e-01, > + 2.4048860594050039e-01,2.3758157443123795e-01,2.3468686187232990e-01, > + 2.3180441082433859e-01,2.2893416541468023e-01,2.2607607132238020e-01, > + 2.2323007576391746e-01,2.2039612748015194e-01,2.1757417672433113e-01, > + 2.1476417525117358e-01,2.1196607630703015e-01,2.0917983462112499e-01, > + 2.0640540639788071e-01,2.0364274931033485e-01,2.0089182249465656e-01, > + 1.9815258654577511e-01,1.9542500351413428e-01,1.9270903690358912e-01, > + 1.9000465167046496e-01,1.8731181422380025e-01,1.8463049242679927e-01, > + 1.8196065559952254e-01,1.7930227452284767e-01,1.7665532144373500e-01, > + 1.7401977008183875e-01,1.7139559563750595e-01,1.6878277480121151e-01, > + 1.6618128576448205e-01,1.6359110823236570e-01,1.6101222343751107e-01, > + 1.5844461415592431e-01,1.5588826472447920e-01,1.5334316106026283e-01, > + 1.5080929068184568e-01,1.4828664273257453e-01,1.4577520800599403e-01, > + 1.4327497897351341e-01,1.4078594981444470e-01,1.3830811644855071e-01, > + 1.3584147657125373e-01,1.3338602969166913e-01,1.3094177717364430e-01, > + 1.2850872227999952e-01,1.2608687022018586e-01,1.2367622820159654e-01, > + 1.2127680548479021e-01,1.1888861344290998e-01,1.1651166562561080e-01, > + 1.1414597782783835e-01,1.1179156816383801e-01,1.0944845714681163e-01, > + 1.0711666777468364e-01,1.0479622562248690e-01,1.0248715894193508e-01, > + 1.0018949876880981e-01,9.7903279038862284e-02,9.5628536713008819e-02, > + 9.3365311912690860e-02,9.1113648066373634e-02,8.8873592068275789e-02, > + 8.6645194450557961e-02,8.4428509570353374e-02,8.2223595813202863e-02, > + 8.0030515814663056e-02,7.7849336702096039e-02,7.5680130358927067e-02, > + 7.3522973713981268e-02,7.1377949058890375e-02,6.9245144397006769e-02, > + 6.7124653827788497e-02,6.5016577971242842e-02,6.2921024437758113e-02, > + 6.0838108349539864e-02,5.8767952920933758e-02,5.6710690106202902e-02, > + 5.4666461324888914e-02,5.2635418276792176e-02,5.0617723860947761e-02, > + 4.8613553215868521e-02,4.6623094901930368e-02,4.4646552251294443e-02, > + 4.2684144916474431e-02,4.0736110655940933e-02,3.8802707404526113e-02, > + 3.6884215688567284e-02,3.4980941461716084e-02,3.3093219458578522e-02, > + 3.1221417191920245e-02,2.9365939758133314e-02,2.7527235669603082e-02, > + 2.5705804008548896e-02,2.3902203305795882e-02,2.2117062707308864e-02, > + 2.0351096230044517e-02,1.8605121275724643e-02,1.6880083152543166e-02, > + 1.5177088307935325e-02,1.3497450601739880e-02,1.1842757857907888e-02, > + 1.0214971439701471e-02,8.6165827693987316e-03,7.0508754713732268e-03, > + 5.5224032992509968e-03,4.0379725933630305e-03,2.6090727461021627e-03, > + 1.2602859304985975e-03 > +}; > + > +static const double ziggurat_nor_r = 3.6541528853610088; > +static const double ziggurat_nor_inv_r = 0.2736612373297583; > + > +static inline double uniform(AVLFG *lfg) > +{ > + return (double)av_lfg_get(lfg) / UINT_MAX; > +} > + > +static inline double ziggurat(AVLFG *lfg) > +{ > + while (1) {
> + uint64_t r = (av_lfg_get(lfg) << 31) + av_lfg_get(lfg); this looks like undefined behavior also the numbers that come out of this look different libavutil/lfg-test before: ... 940.937691 925.827770 870.001279 1093.348026 990.938631 1067.552107 936.441162 956.066787 1001.705214 1007.198453 956.883661 1033.645356 1036.395999 954.941658 1015.720547 1023.147999 after: ... 999.999972 1000.000023 999.999983 999.999980 1000.000012 1000.000069 999.999923 1000.000096 999.999968 999.999915 999.999980 999.999955 1000.000017 1000.000016 -- Michael GnuPG fingerprint: 9FF2128B147EF6730BADF133611EC787040B0FAB Democracy is the form of government in which you can choose your dictator
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