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[libcxx][algorithm] Optimize std::stable_sort via radix sort algorithm (#104683)
The radix sort (LSD) algorithm allows to speed up std::stable_sort dramatically in case we sort integers. The speed up varies from a relatively small to x10 times, depending on type of sorted elements and the initial state of the sorted array. ``` Running ./libcxx/test/benchmarks/stable_sort.bench.out Run on (12 X 2600 MHz CPU s) CPU Caches: L1 Data 32 KiB L1 Instruction 32 KiB L2 Unified 256 KiB (x6) L3 Unified 12288 KiB Load Average: 3.48, 3.38, 3.08 --------------------------------------------------------------------------- Benchmark After Before --------------------------------------------------------------------------- BM_StableSort_int8_Random_1 3.39 ns 3.58 ns BM_StableSort_int8_Random_4 21.1 ns 21.9 ns BM_StableSort_int8_Random_16 142 ns 147 ns BM_StableSort_int8_Random_64 893 ns 903 ns BM_StableSort_int8_Random_256 409 ns 5810 ns BM_StableSort_int8_Random_1024 1235 ns 29973 ns BM_StableSort_int8_Random_4096 4410 ns 141880 ns BM_StableSort_int8_Random_16384 18044 ns 620540 ns BM_StableSort_int8_Random_65536 144030 ns 2592013 ns BM_StableSort_int8_Random_262144 858350 ns 10935814 ns BM_StableSort_int8_Random_524288 2929988 ns 27060729 ns BM_StableSort_int8_Random_1048576 6058292 ns 49622720 ns BM_StableSort_int8_Ascending_1 3.42 ns 3.92 ns BM_StableSort_int8_Ascending_4 5.86 ns 8.08 ns BM_StableSort_int8_Ascending_16 10.6 ns 12.0 ns BM_StableSort_int8_Ascending_64 28.9 ns 30.6 ns BM_StableSort_int8_Ascending_256 415 ns 391 ns BM_StableSort_int8_Ascending_1024 1666 ns 2309 ns BM_StableSort_int8_Ascending_4096 7748 ns 12269 ns BM_StableSort_int8_Ascending_16384 40588 ns 60181 ns BM_StableSort_int8_Ascending_65536 178843 ns 298221 ns BM_StableSort_int8_Ascending_262144 919959 ns 1402692 ns BM_StableSort_int8_Ascending_524288 2397397 ns 3036984 ns BM_StableSort_int8_Ascending_1048576 5080043 ns 7218581 ns BM_StableSort_int8_Descending_1 3.44 ns 3.53 ns BM_StableSort_int8_Descending_4 7.94 ns 8.29 ns BM_StableSort_int8_Descending_16 59.6 ns 57.7 ns BM_StableSort_int8_Descending_64 1051 ns 1027 ns BM_StableSort_int8_Descending_256 422 ns 4718 ns BM_StableSort_int8_Descending_1024 1676 ns 21044 ns BM_StableSort_int8_Descending_4096 7766 ns 64827 ns BM_StableSort_int8_Descending_16384 40230 ns 93981 ns BM_StableSort_int8_Descending_65536 190978 ns 421151 ns BM_StableSort_int8_Descending_262144 1055141 ns 1918927 ns BM_StableSort_int8_Descending_524288 2875115 ns 3809153 ns BM_StableSort_int8_Descending_1048576 5854135 ns 8713690 ns BM_StableSort_int8_SingleElement_1 3.52 ns 3.46 ns BM_StableSort_int8_SingleElement_4 6.25 ns 5.79 ns BM_StableSort_int8_SingleElement_16 10.7 ns 11.4 ns BM_StableSort_int8_SingleElement_64 29.3 ns 30.3 ns BM_StableSort_int8_SingleElement_256 858 ns 380 ns BM_StableSort_int8_SingleElement_1024 3036 ns 2231 ns BM_StableSort_int8_SingleElement_4096 11580 ns 11866 ns BM_StableSort_int8_SingleElement_16384 44956 ns 59621 ns BM_StableSort_int8_SingleElement_65536 182006 ns 297853 ns BM_StableSort_int8_SingleElement_262144 962181 ns 1432857 ns BM_StableSort_int8_SingleElement_524288 2256687 ns 2975707 ns BM_StableSort_int8_SingleElement_1048576 4522556 ns 6949948 ns BM_StableSort_int8_PipeOrgan_1 3.26 ns 3.64 ns BM_StableSort_int8_PipeOrgan_4 6.21 ns 6.58 ns BM_StableSort_int8_PipeOrgan_16 23.7 ns 25.4 ns BM_StableSort_int8_PipeOrgan_64 250 ns 248 ns BM_StableSort_int8_PipeOrgan_256 414 ns 2498 ns BM_StableSort_int8_PipeOrgan_1024 1697 ns 10946 ns BM_StableSort_int8_PipeOrgan_4096 7840 ns 37238 ns BM_StableSort_int8_PipeOrgan_16384 41402 ns 74805 ns BM_StableSort_int8_PipeOrgan_65536 180107 ns 357891 ns BM_StableSort_int8_PipeOrgan_262144 988273 ns 1647296 ns BM_StableSort_int8_PipeOrgan_524288 2547374 ns 3245991 ns BM_StableSort_int8_PipeOrgan_1048576 5128783 ns 7342444 ns BM_StableSort_int8_QuickSortAdversary_1 3.14 ns 4.01 ns BM_StableSort_int8_QuickSortAdversary_4 6.05 ns 7.02 ns BM_StableSort_int8_QuickSortAdversary_16 10.5 ns 11.9 ns BM_StableSort_int8_QuickSortAdversary_64 520 ns 516 ns BM_StableSort_int8_QuickSortAdversary_256 920 ns 386 ns BM_StableSort_int8_QuickSortAdversary_1024 3083 ns 2299 ns BM_StableSort_int8_QuickSortAdversary_4096 11659 ns 12295 ns BM_StableSort_int8_QuickSortAdversary_16384 45721 ns 60931 ns BM_StableSort_int8_QuickSortAdversary_65536 186334 ns 295423 ns BM_StableSort_int8_QuickSortAdversary_262144 946262 ns 1399973 ns BM_StableSort_int8_QuickSortAdversary_524288 2282004 ns 2832266 ns BM_StableSort_int8_QuickSortAdversary_1048576 4691123 ns 6963253 ns BM_StableSort_uint8_Random_1 3.11 ns 3.44 ns BM_StableSort_uint8_Random_4 21.9 ns 23.1 ns BM_StableSort_uint8_Random_16 154 ns 171 ns BM_StableSort_uint8_Random_64 1000 ns 1051 ns BM_StableSort_uint8_Random_256 402 ns 6498 ns BM_StableSort_uint8_Random_1024 1176 ns 35310 ns BM_StableSort_uint8_Random_4096 4415 ns 164087 ns BM_StableSort_uint8_Random_16384 17849 ns 686769 ns BM_StableSort_uint8_Random_65536 146109 ns 2932051 ns BM_StableSort_uint8_Random_262144 876710 ns 12163988 ns BM_StableSort_uint8_Random_524288 2858089 ns 26458830 ns BM_StableSort_uint8_Random_1048576 5766942 ns 54836214 ns BM_StableSort_uint8_Ascending_1 3.11 ns 3.43 ns BM_StableSort_uint8_Ascending_4 6.18 ns 7.24 ns BM_StableSort_uint8_Ascending_16 14.5 ns 17.0 ns BM_StableSort_uint8_Ascending_64 50.7 ns 59.2 ns BM_StableSort_uint8_Ascending_256 395 ns 536 ns BM_StableSort_uint8_Ascending_1024 1752 ns 2956 ns BM_StableSort_uint8_Ascending_4096 7785 ns 15146 ns BM_StableSort_uint8_Ascending_16384 41442 ns 74136 ns BM_StableSort_uint8_Ascending_65536 180879 ns 354261 ns BM_StableSort_uint8_Ascending_262144 945880 ns 1674256 ns BM_StableSort_uint8_Ascending_524288 2287832 ns 3138581 ns BM_StableSort_uint8_Ascending_1048576 4630290 ns 7296278 ns BM_StableSort_uint8_Descending_1 3.19 ns 3.63 ns BM_StableSort_uint8_Descending_4 9.60 ns 11.5 ns BM_StableSort_uint8_Descending_16 78.3 ns 86.0 ns BM_StableSort_uint8_Descending_64 1265 ns 1308 ns BM_StableSort_uint8_Descending_256 395 ns 6556 ns BM_StableSort_uint8_Descending_1024 1712 ns 24669 ns BM_StableSort_uint8_Descending_4096 7748 ns 83407 ns BM_StableSort_uint8_Descending_16384 40779 ns 104043 ns BM_StableSort_uint8_Descending_65536 181560 ns 467680 ns BM_StableSort_uint8_Descending_262144 1146627 ns 2102769 ns BM_StableSort_uint8_Descending_524288 2874096 ns 4572229 ns BM_StableSort_uint8_Descending_1048576 5873195 ns 10170663 ns BM_StableSort_uint8_SingleElement_1 3.28 ns 3.58 ns BM_StableSort_uint8_SingleElement_4 6.44 ns 7.40 ns BM_StableSort_uint8_SingleElement_16 14.9 ns 16.4 ns BM_StableSort_uint8_SingleElement_64 51.2 ns 52.9 ns BM_StableSort_uint8_SingleElement_256 876 ns 490 ns BM_StableSort_uint8_SingleElement_1024 3041 ns 2750 ns BM_StableSort_uint8_SingleElement_4096 11947 ns 14326 ns BM_StableSort_uint8_SingleElement_16384 46669 ns 69984 ns BM_StableSort_uint8_SingleElement_65536 197903 ns 328961 ns BM_StableSort_uint8_SingleElement_262144 1031466 ns 1551436 ns BM_StableSort_uint8_SingleElement_524288 2447672 ns 3049553 ns BM_StableSort_uint8_SingleElement_1048576 4793087 ns 7615245 ns BM_StableSort_uint8_PipeOrgan_1 3.38 ns 3.56 ns BM_StableSort_uint8_PipeOrgan_4 7.16 ns 8.70 ns BM_StableSort_uint8_PipeOrgan_16 31.7 ns 35.3 ns BM_StableSort_uint8_PipeOrgan_64 326 ns 366 ns BM_StableSort_uint8_PipeOrgan_256 409 ns 2942 ns BM_StableSort_uint8_PipeOrgan_1024 1994 ns 12571 ns BM_StableSort_uint8_PipeOrgan_4096 8086 ns 46278 ns BM_StableSort_uint8_PipeOrgan_16384 41749 ns 79813 ns BM_StableSort_uint8_PipeOrgan_65536 180697 ns 375120 ns BM_StableSort_uint8_PipeOrgan_262144 1004899 ns 1676143 ns BM_StableSort_uint8_PipeOrgan_524288 2456081 ns 3333949 ns BM_StableSort_uint8_PipeOrgan_1048576 5030857 ns 7591303 ns BM_StableSort_uint8_QuickSortAdversary_1 3.12 ns 3.46 ns BM_StableSort_uint8_QuickSortAdversary_4 7.25 ns 6.83 ns BM_StableSort_uint8_QuickSortAdversary_16 14.6 ns 16.2 ns BM_StableSort_uint8_QuickSortAdversary_64 650 ns 665 ns BM_StableSort_uint8_QuickSortAdversary_256 395 ns 2982 ns BM_StableSort_uint8_QuickSortAdversary_1024 3125 ns 2583 ns BM_StableSort_uint8_QuickSortAdversary_4096 11797 ns 13929 ns BM_StableSort_uint8_QuickSortAdversary_16384 45803 ns 66513 ns BM_StableSort_uint8_QuickSortAdversary_65536 190745 ns 313467 ns BM_StableSort_uint8_QuickSortAdversary_262144 974646 ns 1469014 ns BM_StableSort_uint8_QuickSortAdversary_524288 2317553 ns 3022065 ns BM_StableSort_uint8_QuickSortAdversary_1048576 4898703 ns 6854079 ns BM_StableSort_int16_Random_1 3.94 ns 3.49 ns BM_StableSort_int16_Random_4 20.8 ns 23.2 ns BM_StableSort_int16_Random_16 133 ns 163 ns BM_StableSort_int16_Random_64 903 ns 953 ns BM_StableSort_int16_Random_256 5638 ns 6258 ns BM_StableSort_int16_Random_1024 3056 ns 34587 ns BM_StableSort_int16_Random_4096 10596 ns 168397 ns BM_StableSort_int16_Random_16384 49908 ns 753031 ns BM_StableSort_int16_Random_65536 444605 ns 3838368 ns BM_StableSort_int16_Random_262144 2419345 ns 15657285 ns BM_StableSort_int16_Random_524288 7984040 ns 32726933 ns BM_StableSort_int16_Random_1048576 16092424 ns 67999766 ns BM_StableSort_int16_Ascending_1 3.40 ns 3.43 ns BM_StableSort_int16_Ascending_4 5.45 ns 5.79 ns BM_StableSort_int16_Ascending_16 12.0 ns 15.3 ns BM_StableSort_int16_Ascending_64 39.6 ns 52.6 ns BM_StableSort_int16_Ascending_256 470 ns 550 ns BM_StableSort_int16_Ascending_1024 1686 ns 2707 ns BM_StableSort_int16_Ascending_4096 5676 ns 14165 ns BM_StableSort_int16_Ascending_16384 21413 ns 69483 ns BM_StableSort_int16_Ascending_65536 88010 ns 334466 ns BM_StableSort_int16_Ascending_262144 567239 ns 1570620 ns BM_StableSort_int16_Ascending_524288 1553063 ns 3424666 ns BM_StableSort_int16_Ascending_1048576 3145577 ns 8499649 ns BM_StableSort_int16_Descending_1 3.22 ns 3.54 ns BM_StableSort_int16_Descending_4 6.85 ns 10.2 ns BM_StableSort_int16_Descending_16 62.7 ns 62.2 ns BM_StableSort_int16_Descending_64 1138 ns 1036 ns BM_StableSort_int16_Descending_256 5541 ns 4696 ns BM_StableSort_int16_Descending_1024 3046 ns 19577 ns BM_StableSort_int16_Descending_4096 10962 ns 79149 ns BM_StableSort_int16_Descending_16384 58182 ns 327709 ns BM_StableSort_int16_Descending_65536 447025 ns 1424896 ns BM_StableSort_int16_Descending_262144 1104973 ns 5921903 ns BM_StableSort_int16_Descending_524288 2547840 ns 17956789 ns BM_StableSort_int16_Descending_1048576 5093555 ns 17044318 ns BM_StableSort_int16_SingleElement_1 3.56 ns 3.96 ns BM_StableSort_int16_SingleElement_4 5.75 ns 6.72 ns BM_StableSort_int16_SingleElement_16 12.4 ns 16.1 ns BM_StableSort_int16_SingleElement_64 36.9 ns 54.4 ns BM_StableSort_int16_SingleElement_256 473 ns 557 ns BM_StableSort_int16_SingleElement_1024 1828 ns 2826 ns BM_StableSort_int16_SingleElement_4096 6239 ns 14252 ns BM_StableSort_int16_SingleElement_16384 23695 ns 70369 ns BM_StableSort_int16_SingleElement_65536 93281 ns 361641 ns BM_StableSort_int16_SingleElement_262144 599078 ns 1640216 ns BM_StableSort_int16_SingleElement_524288 1659678 ns 3343087 ns BM_StableSort_int16_SingleElement_1048576 3184033 ns 7770271 ns BM_StableSort_int16_PipeOrgan_1 3.75 ns 3.76 ns BM_StableSort_int16_PipeOrgan_4 5.94 ns 7.74 ns BM_StableSort_int16_PipeOrgan_16 26.7 ns 25.9 ns BM_StableSort_int16_PipeOrgan_64 300 ns 263 ns BM_StableSort_int16_PipeOrgan_256 2769 ns 2760 ns BM_StableSort_int16_PipeOrgan_1024 2996 ns 10544 ns BM_StableSort_int16_PipeOrgan_4096 11641 ns 44750 ns BM_StableSort_int16_PipeOrgan_16384 57224 ns 200464 ns BM_StableSort_int16_PipeOrgan_65536 416873 ns 887631 ns BM_StableSort_int16_PipeOrgan_262144 843264 ns 3588669 ns BM_StableSort_int16_PipeOrgan_524288 2027741 ns 11056924 ns BM_StableSort_int16_PipeOrgan_1048576 4223773 ns 13261276 ns BM_StableSort_int16_QuickSortAdversary_1 3.83 ns 3.68 ns BM_StableSort_int16_QuickSortAdversary_4 5.55 ns 6.93 ns BM_StableSort_int16_QuickSortAdversary_16 12.3 ns 15.2 ns BM_StableSort_int16_QuickSortAdversary_64 646 ns 632 ns BM_StableSort_int16_QuickSortAdversary_256 2751 ns 2542 ns BM_StableSort_int16_QuickSortAdversary_1024 3028 ns 16901 ns BM_StableSort_int16_QuickSortAdversary_4096 10862 ns 80222 ns BM_StableSort_int16_QuickSortAdversary_16384 57753 ns 317281 ns BM_StableSort_int16_QuickSortAdversary_65536 94064 ns 328502 ns BM_StableSort_int16_QuickSortAdversary_262144 557796 ns 1613208 ns BM_StableSort_int16_QuickSortAdversary_524288 1518451 ns 3479740 ns BM_StableSort_int16_QuickSortAdversary_1048576 3165129 ns 7655880 ns BM_StableSort_uint16_Random_1 3.26 ns 3.44 ns BM_StableSort_uint16_Random_4 21.1 ns 22.2 ns BM_StableSort_uint16_Random_16 157 ns 156 ns BM_StableSort_uint16_Random_64 955 ns 947 ns BM_StableSort_uint16_Random_256 5886 ns 6097 ns BM_StableSort_uint16_Random_1024 2787 ns 30776 ns BM_StableSort_uint16_Random_4096 9973 ns 155652 ns BM_StableSort_uint16_Random_16384 48628 ns 741072 ns BM_StableSort_uint16_Random_65536 439609 ns 3478966 ns BM_StableSort_uint16_Random_262144 2336983 ns 15197642 ns BM_StableSort_uint16_Random_524288 7888701 ns 34234254 ns BM_StableSort_uint16_Random_1048576 14865180 ns 68516386 ns BM_StableSort_uint16_Ascending_1 3.33 ns 4.00 ns BM_StableSort_uint16_Ascending_4 5.79 ns 6.64 ns BM_StableSort_uint16_Ascending_16 14.9 ns 15.5 ns BM_StableSort_uint16_Ascending_64 50.2 ns 52.5 ns BM_StableSort_uint16_Ascending_256 538 ns 546 ns BM_StableSort_uint16_Ascending_1024 1645 ns 2652 ns BM_StableSort_uint16_Ascending_4096 5559 ns 14517 ns BM_StableSort_uint16_Ascending_16384 22803 ns 70275 ns BM_StableSort_uint16_Ascending_65536 83109 ns 333446 ns BM_StableSort_uint16_Ascending_262144 562667 ns 1568670 ns BM_StableSort_uint16_Ascending_524288 1564646 ns 3059839 ns BM_StableSort_uint16_Ascending_1048576 3178826 ns 7048327 ns BM_StableSort_uint16_Descending_1 3.34 ns 3.93 ns BM_StableSort_uint16_Descending_4 8.75 ns 9.73 ns BM_StableSort_uint16_Descending_16 55.9 ns 55.5 ns BM_StableSort_uint16_Descending_64 1021 ns 1035 ns BM_StableSort_uint16_Descending_256 4752 ns 4931 ns BM_StableSort_uint16_Descending_1024 2982 ns 19727 ns BM_StableSort_uint16_Descending_4096 10432 ns 83165 ns BM_StableSort_uint16_Descending_16384 56593 ns 326131 ns BM_StableSort_uint16_Descending_65536 439134 ns 1371346 ns BM_StableSort_uint16_Descending_262144 1220925 ns 5735665 ns BM_StableSort_uint16_Descending_524288 2767234 ns 16758330 ns BM_StableSort_uint16_Descending_1048576 5673769 ns 17541715 ns BM_StableSort_uint16_SingleElement_1 3.53 ns 3.73 ns BM_StableSort_uint16_SingleElement_4 6.27 ns 5.81 ns BM_StableSort_uint16_SingleElement_16 14.8 ns 15.1 ns BM_StableSort_uint16_SingleElement_64 51.5 ns 50.9 ns BM_StableSort_uint16_SingleElement_256 536 ns 540 ns BM_StableSort_uint16_SingleElement_1024 1669 ns 2690 ns BM_StableSort_uint16_SingleElement_4096 5840 ns 14230 ns BM_StableSort_uint16_SingleElement_16384 22468 ns 68524 ns BM_StableSort_uint16_SingleElement_65536 89845 ns 332187 ns BM_StableSort_uint16_SingleElement_262144 590736 ns 1550868 ns BM_StableSort_uint16_SingleElement_524288 1573677 ns 3095703 ns BM_StableSort_uint16_SingleElement_1048576 3183421 ns 8251180 ns BM_StableSort_uint16_PipeOrgan_1 3.70 ns 3.64 ns BM_StableSort_uint16_PipeOrgan_4 7.01 ns 6.81 ns BM_StableSort_uint16_PipeOrgan_16 25.7 ns 26.4 ns BM_StableSort_uint16_PipeOrgan_64 283 ns 277 ns BM_StableSort_uint16_PipeOrgan_256 2562 ns 2852 ns BM_StableSort_uint16_PipeOrgan_1024 2863 ns 10892 ns BM_StableSort_uint16_PipeOrgan_4096 10585 ns 45668 ns BM_StableSort_uint16_PipeOrgan_16384 59151 ns 194358 ns BM_StableSort_uint16_PipeOrgan_65536 508579 ns 854692 ns BM_StableSort_uint16_PipeOrgan_262144 901294 ns 3606346 ns BM_StableSort_uint16_PipeOrgan_524288 2192498 ns 10449279 ns BM_StableSort_uint16_PipeOrgan_1048576 4204368 ns 11956606 ns BM_StableSort_uint16_QuickSortAdversary_1 3.20 ns 3.63 ns BM_StableSort_uint16_QuickSortAdversary_4 5.30 ns 6.38 ns BM_StableSort_uint16_QuickSortAdversary_16 14.5 ns 15.3 ns BM_StableSort_uint16_QuickSortAdversary_64 575 ns 611 ns BM_StableSort_uint16_QuickSortAdversary_256 2423 ns 2577 ns BM_StableSort_uint16_QuickSortAdversary_1024 2794 ns 16854 ns BM_StableSort_uint16_QuickSortAdversary_4096 10511 ns 75952 ns BM_StableSort_uint16_QuickSortAdversary_16384 56214 ns 333824 ns BM_StableSort_uint16_QuickSortAdversary_65536 422512 ns 1354867 ns BM_StableSort_uint16_QuickSortAdversary_262144 583301 ns 1564443 ns BM_StableSort_uint16_QuickSortAdversary_524288 1584319 ns 3265575 ns BM_StableSort_uint16_QuickSortAdversary_1048576 3197732 ns 7945245 ns BM_StableSort_int32_Random_1 3.81 ns 3.70 ns BM_StableSort_int32_Random_4 20.8 ns 23.4 ns BM_StableSort_int32_Random_16 134 ns 161 ns BM_StableSort_int32_Random_64 895 ns 984 ns BM_StableSort_int32_Random_256 5640 ns 5897 ns BM_StableSort_int32_Random_1024 6994 ns 32118 ns BM_StableSort_int32_Random_4096 27367 ns 168960 ns BM_StableSort_int32_Random_16384 183261 ns 843240 ns BM_StableSort_int32_Random_65536 950914 ns 3953588 ns BM_StableSort_int32_Random_262144 3673311 ns 16790171 ns BM_StableSort_int32_Random_524288 11515700 ns 36023098 ns BM_StableSort_int32_Random_1048576 24492515 ns 78116028 ns BM_StableSort_int32_Ascending_1 3.31 ns 4.48 ns BM_StableSort_int32_Ascending_4 5.96 ns 6.99 ns BM_StableSort_int32_Ascending_16 13.0 ns 16.0 ns BM_StableSort_int32_Ascending_64 36.7 ns 53.0 ns BM_StableSort_int32_Ascending_256 391 ns 471 ns BM_StableSort_int32_Ascending_1024 2705 ns 2682 ns BM_StableSort_int32_Ascending_4096 8773 ns 14231 ns BM_StableSort_int32_Ascending_16384 34709 ns 70625 ns BM_StableSort_int32_Ascending_65536 142907 ns 344482 ns BM_StableSort_int32_Ascending_262144 745483 ns 1591418 ns BM_StableSort_int32_Ascending_524288 1873701 ns 3190305 ns BM_StableSort_int32_Ascending_1048576 3851590 ns 7570095 ns BM_StableSort_int32_Descending_1 3.22 ns 4.23 ns BM_StableSort_int32_Descending_4 7.58 ns 11.2 ns BM_StableSort_int32_Descending_16 63.9 ns 58.6 ns BM_StableSort_int32_Descending_64 1133 ns 1017 ns BM_StableSort_int32_Descending_256 4850 ns 4464 ns BM_StableSort_int32_Descending_1024 7023 ns 18954 ns BM_StableSort_int32_Descending_4096 28550 ns 75163 ns BM_StableSort_int32_Descending_16384 200880 ns 341104 ns BM_StableSort_int32_Descending_65536 1095910 ns 1398021 ns BM_StableSort_int32_Descending_262144 3818864 ns 5695486 ns BM_StableSort_int32_Descending_524288 5606779 ns 17593982 ns BM_StableSort_int32_Descending_1048576 16416366 ns 26649503 ns BM_StableSort_int32_SingleElement_1 3.81 ns 3.71 ns BM_StableSort_int32_SingleElement_4 6.57 ns 6.61 ns BM_StableSort_int32_SingleElement_16 14.0 ns 15.8 ns BM_StableSort_int32_SingleElement_64 38.7 ns 53.5 ns BM_StableSort_int32_SingleElement_256 386 ns 554 ns BM_StableSort_int32_SingleElement_1024 2761 ns 3046 ns BM_StableSort_int32_SingleElement_4096 9179 ns 15188 ns BM_StableSort_int32_SingleElement_16384 34794 ns 70119 ns BM_StableSort_int32_SingleElement_65536 135190 ns 354755 ns BM_StableSort_int32_SingleElement_262144 760995 ns 1644072 ns BM_StableSort_int32_SingleElement_524288 1969575 ns 3343419 ns BM_StableSort_int32_SingleElement_1048576 4423816 ns 8346971 ns BM_StableSort_int32_PipeOrgan_1 3.79 ns 3.63 ns BM_StableSort_int32_PipeOrgan_4 6.21 ns 6.73 ns BM_StableSort_int32_PipeOrgan_16 27.5 ns 26.0 ns BM_StableSort_int32_PipeOrgan_64 291 ns 265 ns BM_StableSort_int32_PipeOrgan_256 2557 ns 2518 ns BM_StableSort_int32_PipeOrgan_1024 6765 ns 10976 ns BM_StableSort_int32_PipeOrgan_4096 26373 ns 44537 ns BM_StableSort_int32_PipeOrgan_16384 201466 ns 188582 ns BM_StableSort_int32_PipeOrgan_65536 1148533 ns 802368 ns BM_StableSort_int32_PipeOrgan_262144 2255177 ns 3477829 ns BM_StableSort_int32_PipeOrgan_524288 3947015 ns 10356637 ns BM_StableSort_int32_PipeOrgan_1048576 10274312 ns 16405366 ns BM_StableSort_int32_QuickSortAdversary_1 3.32 ns 4.36 ns BM_StableSort_int32_QuickSortAdversary_4 5.98 ns 7.44 ns BM_StableSort_int32_QuickSortAdversary_16 13.0 ns 16.3 ns BM_StableSort_int32_QuickSortAdversary_64 657 ns 616 ns BM_StableSort_int32_QuickSortAdversary_256 2569 ns 2483 ns BM_StableSort_int32_QuickSortAdversary_1024 6898 ns 19635 ns BM_StableSort_int32_QuickSortAdversary_4096 27092 ns 75108 ns BM_StableSort_int32_QuickSortAdversary_16384 190379 ns 316463 ns BM_StableSort_int32_QuickSortAdversary_65536 1109040 ns 1319018 ns BM_StableSort_int32_QuickSortAdversary_262144 4361925 ns 5472779 ns BM_StableSort_int32_QuickSortAdversary_524288 6528215 ns 17538983 ns BM_StableSort_int32_QuickSortAdversary_1048576 18345325 ns 27223926 ns BM_StableSort_uint32_Random_1 3.67 ns 3.82 ns BM_StableSort_uint32_Random_4 22.3 ns 21.8 ns BM_StableSort_uint32_Random_16 155 ns 153 ns BM_StableSort_uint32_Random_64 946 ns 976 ns BM_StableSort_uint32_Random_256 5824 ns 6019 ns BM_StableSort_uint32_Random_1024 4525 ns 32764 ns BM_StableSort_uint32_Random_4096 17223 ns 158608 ns BM_StableSort_uint32_Random_16384 134821 ns 748525 ns BM_StableSort_uint32_Random_65536 716644 ns 3453325 ns BM_StableSort_uint32_Random_262144 3628062 ns 16065414 ns BM_StableSort_uint32_Random_524288 10971334 ns 36567712 ns BM_StableSort_uint32_Random_1048576 22688377 ns 77533497 ns BM_StableSort_uint32_Ascending_1 3.57 ns 3.44 ns BM_StableSort_uint32_Ascending_4 5.73 ns 5.33 ns BM_StableSort_uint32_Ascending_16 14.5 ns 14.0 ns BM_StableSort_uint32_Ascending_64 50.3 ns 51.3 ns BM_StableSort_uint32_Ascending_256 465 ns 467 ns BM_StableSort_uint32_Ascending_1024 3042 ns 2530 ns BM_StableSort_uint32_Ascending_4096 9842 ns 12207 ns BM_StableSort_uint32_Ascending_16384 37994 ns 61726 ns BM_StableSort_uint32_Ascending_65536 148890 ns 294385 ns BM_StableSort_uint32_Ascending_262144 855080 ns 1422167 ns BM_StableSort_uint32_Ascending_524288 2154903 ns 3203018 ns BM_StableSort_uint32_Ascending_1048576 5002518 ns 7563817 ns BM_StableSort_uint32_Descending_1 3.51 ns 3.40 ns BM_StableSort_uint32_Descending_4 9.09 ns 7.95 ns BM_StableSort_uint32_Descending_16 54.8 ns 74.4 ns BM_StableSort_uint32_Descending_64 1003 ns 1305 ns BM_StableSort_uint32_Descending_256 4545 ns 5300 ns BM_StableSort_uint32_Descending_1024 4361 ns 21884 ns BM_StableSort_uint32_Descending_4096 16018 ns 90534 ns BM_StableSort_uint32_Descending_16384 146274 ns 381943 ns BM_StableSort_uint32_Descending_65536 938248 ns 1536806 ns BM_StableSort_uint32_Descending_262144 3899300 ns 6387843 ns BM_StableSort_uint32_Descending_524288 5808157 ns 21959858 ns BM_StableSort_uint32_Descending_1048576 17520047 ns 26351912 ns BM_StableSort_uint32_SingleElement_1 4.03 ns 3.97 ns BM_StableSort_uint32_SingleElement_4 6.55 ns 6.41 ns BM_StableSort_uint32_SingleElement_16 15.6 ns 15.8 ns BM_StableSort_uint32_SingleElement_64 52.3 ns 58.7 ns BM_StableSort_uint32_SingleElement_256 473 ns 485 ns BM_StableSort_uint32_SingleElement_1024 3020 ns 2407 ns BM_StableSort_uint32_SingleElement_4096 9998 ns 12527 ns BM_StableSort_uint32_SingleElement_16384 38072 ns 62228 ns BM_StableSort_uint32_SingleElement_65536 153706 ns 295662 ns BM_StableSort_uint32_SingleElement_262144 836532 ns 1477099 ns BM_StableSort_uint32_SingleElement_524288 2144900 ns 3157204 ns BM_StableSort_uint32_SingleElement_1048576 4995525 ns 7617233 ns BM_StableSort_uint32_PipeOrgan_1 4.02 ns 3.99 ns BM_StableSort_uint32_PipeOrgan_4 6.97 ns 6.84 ns BM_StableSort_uint32_PipeOrgan_16 26.1 ns 29.7 ns BM_StableSort_uint32_PipeOrgan_64 266 ns 333 ns BM_StableSort_uint32_PipeOrgan_256 2462 ns 2892 ns BM_StableSort_uint32_PipeOrgan_1024 4291 ns 12431 ns BM_StableSort_uint32_PipeOrgan_4096 15638 ns 51449 ns BM_StableSort_uint32_PipeOrgan_16384 154563 ns 217460 ns BM_StableSort_uint32_PipeOrgan_65536 907724 ns 925873 ns BM_StableSort_uint32_PipeOrgan_262144 2394580 ns 4103575 ns BM_StableSort_uint32_PipeOrgan_524288 4177145 ns 13947158 ns BM_StableSort_uint32_PipeOrgan_1048576 11848224 ns 18807297 ns BM_StableSort_uint32_QuickSortAdversary_1 3.50 ns 3.43 ns BM_StableSort_uint32_QuickSortAdversary_4 5.88 ns 4.96 ns BM_StableSort_uint32_QuickSortAdversary_16 14.6 ns 14.0 ns BM_StableSort_uint32_QuickSortAdversary_64 576 ns 715 ns BM_StableSort_uint32_QuickSortAdversary_256 2353 ns 2797 ns BM_StableSort_uint32_QuickSortAdversary_1024 4176 ns 21775 ns BM_StableSort_uint32_QuickSortAdversary_4096 15565 ns 96188 ns BM_StableSort_uint32_QuickSortAdversary_16384 149092 ns 398332 ns BM_StableSort_uint32_QuickSortAdversary_65536 902488 ns 1552393 ns BM_StableSort_uint32_QuickSortAdversary_262144 3946517 ns 6560414 ns BM_StableSort_uint32_QuickSortAdversary_524288 6247114 ns 22420977 ns BM_StableSort_uint32_QuickSortAdversary_1048576 19892446 ns 26529576 ns BM_StableSort_int64_Random_1 3.83 ns 3.98 ns BM_StableSort_int64_Random_4 21.1 ns 24.0 ns BM_StableSort_int64_Random_16 129 ns 136 ns BM_StableSort_int64_Random_64 890 ns 906 ns BM_StableSort_int64_Random_256 5542 ns 5901 ns BM_StableSort_int64_Random_1024 16085 ns 33112 ns BM_StableSort_int64_Random_4096 63895 ns 162181 ns BM_StableSort_int64_Random_16384 348827 ns 790045 ns BM_StableSort_int64_Random_65536 1488237 ns 3557506 ns BM_StableSort_int64_Random_262144 8195713 ns 16315808 ns BM_StableSort_int64_Random_524288 16586833 ns 38274075 ns BM_StableSort_int64_Random_1048576 40346644 ns 79182089 ns BM_StableSort_int64_Ascending_1 3.76 ns 3.55 ns BM_StableSort_int64_Ascending_4 5.82 ns 6.19 ns BM_StableSort_int64_Ascending_16 11.7 ns 11.8 ns BM_StableSort_int64_Ascending_64 32.9 ns 36.8 ns BM_StableSort_int64_Ascending_256 415 ns 550 ns BM_StableSort_int64_Ascending_1024 5352 ns 3347 ns BM_StableSort_int64_Ascending_4096 17516 ns 19134 ns BM_StableSort_int64_Ascending_16384 64147 ns 91099 ns BM_StableSort_int64_Ascending_65536 322126 ns 434009 ns BM_StableSort_int64_Ascending_262144 1554669 ns 2057056 ns BM_StableSort_int64_Ascending_524288 3656527 ns 5016650 ns BM_StableSort_int64_Ascending_1048576 10469979 ns 12908613 ns BM_StableSort_int64_Descending_1 4.09 ns 3.35 ns BM_StableSort_int64_Descending_4 9.13 ns 8.01 ns BM_StableSort_int64_Descending_16 76.8 ns 92.9 ns BM_StableSort_int64_Descending_64 1336 ns 1417 ns BM_StableSort_int64_Descending_256 5525 ns 5674 ns BM_StableSort_int64_Descending_1024 17461 ns 22558 ns BM_StableSort_int64_Descending_4096 64285 ns 102360 ns BM_StableSort_int64_Descending_16384 336946 ns 388940 ns BM_StableSort_int64_Descending_65536 837912 ns 1662169 ns BM_StableSort_int64_Descending_262144 3680806 ns 7494323 ns BM_StableSort_int64_Descending_524288 11023784 ns 24935033 ns BM_StableSort_int64_Descending_1048576 20023568 ns 33220712 ns BM_StableSort_int64_SingleElement_1 3.37 ns 3.98 ns BM_StableSort_int64_SingleElement_4 5.32 ns 6.92 ns BM_StableSort_int64_SingleElement_16 10.9 ns 13.3 ns BM_StableSort_int64_SingleElement_64 32.1 ns 43.8 ns BM_StableSort_int64_SingleElement_256 420 ns 541 ns BM_StableSort_int64_SingleElement_1024 5689 ns 3381 ns BM_StableSort_int64_SingleElement_4096 19199 ns 17989 ns BM_StableSort_int64_SingleElement_16384 75754 ns 91963 ns BM_StableSort_int64_SingleElement_65536 357106 ns 500326 ns BM_StableSort_int64_SingleElement_262144 1672975 ns 2417734 ns BM_StableSort_int64_SingleElement_524288 3642891 ns 5200878 ns BM_StableSort_int64_SingleElement_1048576 11172007 ns 13729511 ns BM_StableSort_int64_PipeOrgan_1 3.38 ns 3.94 ns BM_StableSort_int64_PipeOrgan_4 5.73 ns 6.44 ns BM_StableSort_int64_PipeOrgan_16 27.5 ns 29.0 ns BM_StableSort_int64_PipeOrgan_64 310 ns 321 ns BM_StableSort_int64_PipeOrgan_256 2761 ns 2918 ns BM_StableSort_int64_PipeOrgan_1024 16105 ns 12525 ns BM_StableSort_int64_PipeOrgan_4096 65289 ns 59990 ns BM_StableSort_int64_PipeOrgan_16384 341757 ns 270636 ns BM_StableSort_int64_PipeOrgan_65536 587452 ns 1126132 ns BM_StableSort_int64_PipeOrgan_262144 2837955 ns 5034180 ns BM_StableSort_int64_PipeOrgan_524288 6617313 ns 15267354 ns BM_StableSort_int64_PipeOrgan_1048576 15208796 ns 23162989 ns BM_StableSort_int64_QuickSortAdversary_1 3.77 ns 3.45 ns BM_StableSort_int64_QuickSortAdversary_4 5.55 ns 5.20 ns BM_StableSort_int64_QuickSortAdversary_16 12.5 ns 11.5 ns BM_StableSort_int64_QuickSortAdversary_64 646 ns 750 ns BM_StableSort_int64_QuickSortAdversary_256 2655 ns 3539 ns BM_StableSort_int64_QuickSortAdversary_1024 16373 ns 22349 ns BM_StableSort_int64_QuickSortAdversary_4096 62306 ns 97248 ns BM_StableSort_int64_QuickSortAdversary_16384 321755 ns 388084 ns BM_StableSort_int64_QuickSortAdversary_65536 1374694 ns 1596091 ns BM_StableSort_int64_QuickSortAdversary_262144 4374661 ns 6894139 ns BM_StableSort_int64_QuickSortAdversary_524288 12736074 ns 23932229 ns BM_StableSort_int64_QuickSortAdversary_1048576 22615219 ns 33355629 ns BM_StableSort_uint64_Random_1 3.82 ns 3.49 ns BM_StableSort_uint64_Random_4 22.4 ns 23.4 ns BM_StableSort_uint64_Random_16 154 ns 146 ns BM_StableSort_uint64_Random_64 924 ns 926 ns BM_StableSort_uint64_Random_256 5864 ns 5913 ns BM_StableSort_uint64_Random_1024 7168 ns 31746 ns BM_StableSort_uint64_Random_4096 27668 ns 154224 ns BM_StableSort_uint64_Random_16384 219526 ns 755205 ns BM_StableSort_uint64_Random_65536 965251 ns 3490165 ns BM_StableSort_uint64_Random_262144 6262162 ns 15889589 ns BM_StableSort_uint64_Random_524288 12530078 ns 36458581 ns BM_StableSort_uint64_Random_1048576 38462191 ns 75168445 ns BM_StableSort_uint64_Ascending_1 3.30 ns 3.35 ns BM_StableSort_uint64_Ascending_4 5.65 ns 5.84 ns BM_StableSort_uint64_Ascending_16 14.7 ns 12.6 ns BM_StableSort_uint64_Ascending_64 55.3 ns 34.6 ns BM_StableSort_uint64_Ascending_256 513 ns 533 ns BM_StableSort_uint64_Ascending_1024 5541 ns 3189 ns BM_StableSort_uint64_Ascending_4096 17706 ns 20326 ns BM_StableSort_uint64_Ascending_16384 66420 ns 93757 ns BM_StableSort_uint64_Ascending_65536 341425 ns 435016 ns BM_StableSort_uint64_Ascending_262144 1595691 ns 2088317 ns BM_StableSort_uint64_Ascending_524288 3808703 ns 5092832 ns BM_StableSort_uint64_Ascending_1048576 11060417 ns 13023250 ns BM_StableSort_uint64_Descending_1 3.29 ns 3.35 ns BM_StableSort_uint64_Descending_4 8.65 ns 7.92 ns BM_StableSort_uint64_Descending_16 54.7 ns 80.2 ns BM_StableSort_uint64_Descending_64 1028 ns 1307 ns BM_StableSort_uint64_Descending_256 4521 ns 5635 ns BM_StableSort_uint64_Descending_1024 7122 ns 23323 ns BM_StableSort_uint64_Descending_4096 30538 ns 95892 ns BM_StableSort_uint64_Descending_16384 195565 ns 392721 ns BM_StableSort_uint64_Descending_65536 852002 ns 1720358 ns BM_StableSort_uint64_Descending_262144 3737884 ns 7484130 ns BM_StableSort_uint64_Descending_524288 11159345 ns 25690770 ns BM_StableSort_uint64_Descending_1048576 20648864 ns 33057383 ns BM_StableSort_uint64_SingleElement_1 3.62 ns 4.10 ns BM_StableSort_uint64_SingleElement_4 6.73 ns 6.64 ns BM_StableSort_uint64_SingleElement_16 14.9 ns 11.3 ns BM_StableSort_uint64_SingleElement_64 52.0 ns 33.0 ns BM_StableSort_uint64_SingleElement_256 511 ns 582 ns BM_StableSort_uint64_SingleElement_1024 6499 ns 3287 ns BM_StableSort_uint64_SingleElement_4096 22190 ns 17616 ns BM_StableSort_uint64_SingleElement_16384 84378 ns 86885 ns BM_StableSort_uint64_SingleElement_65536 466257 ns 457144 ns BM_StableSort_uint64_SingleElement_262144 1993687 ns 2361999 ns BM_StableSort_uint64_SingleElement_524288 4759565 ns 5096771 ns BM_StableSort_uint64_SingleElement_1048576 12426111 ns 13468453 ns BM_StableSort_uint64_PipeOrgan_1 3.73 ns 3.94 ns BM_StableSort_uint64_PipeOrgan_4 7.18 ns 7.54 ns BM_StableSort_uint64_PipeOrgan_16 25.2 ns 29.1 ns BM_StableSort_uint64_PipeOrgan_64 260 ns 321 ns BM_StableSort_uint64_PipeOrgan_256 2468 ns 2970 ns BM_StableSort_uint64_PipeOrgan_1024 7025 ns 12912 ns BM_StableSort_uint64_PipeOrgan_4096 28968 ns 53379 ns BM_StableSort_uint64_PipeOrgan_16384 194156 ns 239790 ns BM_StableSort_uint64_PipeOrgan_65536 599491 ns 993800 ns BM_StableSort_uint64_PipeOrgan_262144 2648585 ns 4689680 ns BM_StableSort_uint64_PipeOrgan_524288 7621109 ns 15401808 ns BM_StableSort_uint64_PipeOrgan_1048576 15608814 ns 23484821 ns BM_StableSort_uint64_QuickSortAdversary_1 3.38 ns 3.54 ns BM_StableSort_uint64_QuickSortAdversary_4 5.50 ns 6.03 ns BM_StableSort_uint64_QuickSortAdversary_16 14.2 ns 11.0 ns BM_StableSort_uint64_QuickSortAdversary_64 597 ns 688 ns BM_StableSort_uint64_QuickSortAdversary_256 2446 ns 2818 ns BM_StableSort_uint64_QuickSortAdversary_1024 7266 ns 20319 ns BM_StableSort_uint64_QuickSortAdversary_4096 31155 ns 89112 ns BM_StableSort_uint64_QuickSortAdversary_16384 201033 ns 390574 ns BM_StableSort_uint64_QuickSortAdversary_65536 871014 ns 1685639 ns BM_StableSort_uint64_QuickSortAdversary_262144 3978535 ns 7265830 ns BM_StableSort_uint64_QuickSortAdversary_524288 10279721 ns 25350004 ns BM_StableSort_uint64_QuickSortAdversary_1048576 20256585 ns 33054393 ns ```
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‎libcxx/docs/ReleaseNotes/19.rst

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@@ -126,6 +126,8 @@ Improvements and New Features
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- In C++23 and C++26 the number of transitive includes in several headers has been reduced, improving the compilation speed.
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- ``std::stable_sort`` uses radix sort for integral types now, which can improve the performance up to 10 times, depending
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on type of sorted elements and the initial state of the sorted array.
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Deprecations and Removals
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-------------------------

‎libcxx/include/CMakeLists.txt

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@@ -73,6 +73,7 @@ set(files
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__algorithm/prev_permutation.h
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__algorithm/pstl.h
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__algorithm/push_heap.h
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__algorithm/radix_sort.h
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__algorithm/ranges_adjacent_find.h
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__algorithm/ranges_all_of.h
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__algorithm/ranges_any_of.h

‎libcxx/include/__algorithm/radix_sort.h

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// -*- C++ -*-
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//===----------------------------------------------------------------------===//
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//
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// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
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// See https://llvm.org/LICENSE.txt for license information.
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// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
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//
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//===----------------------------------------------------------------------===//
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#ifndef _LIBCPP___ALGORITHM_RADIX_SORT_H
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#define _LIBCPP___ALGORITHM_RADIX_SORT_H
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// This is an implementation of classic LSD radix sort algorithm, running in linear time and using `O(max(N, M))`
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// additional memory, where `N` is size of an input range, `M` - maximum value of
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// a radix of the sorted integer type. Type of the radix and its maximum value are determined at compile time
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// based on type returned by function `__radix`. The default radix is uint8.
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// The algorithm is equivalent to several consecutive calls of counting sort for each
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// radix of the sorted numbers from low to high byte.
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// The algorithm uses a temporary buffer of size equal to size of the input range. Each `i`-th pass
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// of the algorithm sorts values by `i`-th radix and moves values to the temporary buffer (for each even `i`, counted
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// from zero), or moves them back to the initial range (for each odd `i`). If there is only one radix in sorted integers
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// (e.g. int8), the sorted values are placed to the buffer, and then moved back to the initial range.
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// The implementation also has several optimizations:
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// - the counters for the counting sort are calculated in one pass for all radices;
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// - if all values of a radix are the same, we do not sort that radix, and just move items to the buffer;
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// - if two consecutive radices satisfies condition above, we do nothing for these two radices.
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#include <__algorithm/for_each.h>
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#include <__algorithm/move.h>
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#include <__bit/bit_log2.h>
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#include <__bit/countl.h>
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#include <__config>
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#include <__functional/identity.h>
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#include <__iterator/distance.h>
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#include <__iterator/iterator_traits.h>
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#include <__iterator/move_iterator.h>
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#include <__iterator/next.h>
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#include <__iterator/reverse_iterator.h>
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#include <__numeric/partial_sum.h>
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#include <__type_traits/decay.h>
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#include <__type_traits/enable_if.h>
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#include <__type_traits/invoke.h>
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#include <__type_traits/is_assignable.h>
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#include <__type_traits/is_integral.h>
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#include <__type_traits/is_unsigned.h>
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#include <__type_traits/make_unsigned.h>
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#include <__utility/forward.h>
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#include <__utility/integer_sequence.h>
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#include <__utility/move.h>
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#include <__utility/pair.h>
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#include <climits>
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#include <cstdint>
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#include <initializer_list>
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#include <limits>
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#if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
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# pragma GCC system_header
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#endif
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_LIBCPP_PUSH_MACROS
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#include <__undef_macros>
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_LIBCPP_BEGIN_NAMESPACE_STD
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#if _LIBCPP_STD_VER >= 14
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template <class _InputIterator, class _OutputIterator>
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_LIBCPP_HIDE_FROM_ABI pair<_OutputIterator, __iter_value_type<_InputIterator>>
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__partial_sum_max(_InputIterator __first, _InputIterator __last, _OutputIterator __result) {
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if (__first == __last)
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return {__result, 0};
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auto __max = *__first;
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__iter_value_type<_InputIterator> __sum = *__first;
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*__result = __sum;
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while (++__first != __last) {
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if (__max < *__first) {
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__max = *__first;
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}
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__sum = std::move(__sum) + *__first;
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*++__result = __sum;
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}
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return {++__result, __max};
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}
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template <class _Value, class _Map, class _Radix>
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struct __radix_sort_traits {
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using __image_type = decay_t<typename __invoke_of<_Map, _Value>::type>;
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static_assert(is_unsigned<__image_type>::value);
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using __radix_type = decay_t<typename __invoke_of<_Radix, __image_type>::type>;
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static_assert(is_integral<__radix_type>::value);
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static constexpr auto __radix_value_range = numeric_limits<__radix_type>::max() + 1;
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static constexpr auto __radix_size = std::__bit_log2<uint64_t>(__radix_value_range);
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static constexpr auto __radix_count = sizeof(__image_type) * CHAR_BIT / __radix_size;
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};
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template <class _Value, class _Map>
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struct __counting_sort_traits {
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using __image_type = decay_t<typename __invoke_of<_Map, _Value>::type>;
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static_assert(is_unsigned<__image_type>::value);
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static constexpr const auto __value_range = numeric_limits<__image_type>::max() + 1;
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static constexpr auto __radix_size = std::__bit_log2<uint64_t>(__value_range);
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};
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template <class _Radix, class _Integer>
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_LIBCPP_HIDE_FROM_ABI auto __nth_radix(size_t __radix_number, _Radix __radix, _Integer __n) {
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static_assert(is_unsigned<_Integer>::value);
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using __traits = __counting_sort_traits<_Integer, _Radix>;
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return __radix(static_cast<_Integer>(__n >> __traits::__radix_size * __radix_number));
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}
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template <class _ForwardIterator, class _Map, class _RandomAccessIterator>
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_LIBCPP_HIDE_FROM_ABI void
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__collect(_ForwardIterator __first, _ForwardIterator __last, _Map __map, _RandomAccessIterator __counters) {
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using __value_type = __iter_value_type<_ForwardIterator>;
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using __traits = __counting_sort_traits<__value_type, _Map>;
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std::for_each(__first, __last, [&__counters, &__map](const auto& __preimage) { ++__counters[__map(__preimage)]; });
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const auto __counters_end = __counters + __traits::__value_range;
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std::partial_sum(__counters, __counters_end, __counters);
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}
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template <class _ForwardIterator, class _RandomAccessIterator1, class _Map, class _RandomAccessIterator2>
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_LIBCPP_HIDE_FROM_ABI void
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__dispose(_ForwardIterator __first,
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_ForwardIterator __last,
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_RandomAccessIterator1 __result,
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_Map __map,
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_RandomAccessIterator2 __counters) {
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std::for_each(__first, __last, [&__result, &__counters, &__map](auto&& __preimage) {
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auto __index = __counters[__map(__preimage)]++;
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__result[__index] = std::move(__preimage);
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});
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}
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template <class _ForwardIterator,
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class _Map,
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class _Radix,
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class _RandomAccessIterator1,
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class _RandomAccessIterator2,
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size_t... _Radices>
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_LIBCPP_HIDE_FROM_ABI bool __collect_impl(
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_ForwardIterator __first,
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_ForwardIterator __last,
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_Map __map,
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_Radix __radix,
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_RandomAccessIterator1 __counters,
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_RandomAccessIterator2 __maximums,
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index_sequence<_Radices...>) {
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using __value_type = __iter_value_type<_ForwardIterator>;
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constexpr auto __radix_value_range = __radix_sort_traits<__value_type, _Map, _Radix>::__radix_value_range;
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auto __previous = numeric_limits<typename __invoke_of<_Map, __value_type>::type>::min();
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auto __is_sorted = true;
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std::for_each(__first, __last, [&__counters, &__map, &__radix, &__previous, &__is_sorted](const auto& __value) {
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auto __current = __map(__value);
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__is_sorted &= (__current >= __previous);
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__previous = __current;
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(++__counters[_Radices][std::__nth_radix(_Radices, __radix, __current)], ...);
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});
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((__maximums[_Radices] =
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std::__partial_sum_max(__counters[_Radices], __counters[_Radices] + __radix_value_range, __counters[_Radices])
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.second),
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...);
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return __is_sorted;
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}
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template <class _ForwardIterator, class _Map, class _Radix, class _RandomAccessIterator1, class _RandomAccessIterator2>
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_LIBCPP_HIDE_FROM_ABI bool
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__collect(_ForwardIterator __first,
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_ForwardIterator __last,
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_Map __map,
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_Radix __radix,
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_RandomAccessIterator1 __counters,
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_RandomAccessIterator2 __maximums) {
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using __value_type = __iter_value_type<_ForwardIterator>;
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constexpr auto __radix_count = __radix_sort_traits<__value_type, _Map, _Radix>::__radix_count;
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return std::__collect_impl(
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__first, __last, __map, __radix, __counters, __maximums, make_index_sequence<__radix_count>());
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}
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template <class _BidirectionalIterator, class _RandomAccessIterator1, class _Map, class _RandomAccessIterator2>
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_LIBCPP_HIDE_FROM_ABI void __dispose_backward(
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_BidirectionalIterator __first,
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_BidirectionalIterator __last,
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_RandomAccessIterator1 __result,
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_Map __map,
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_RandomAccessIterator2 __counters) {
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std::for_each(std::make_reverse_iterator(__last),
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std::make_reverse_iterator(__first),
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[&__result, &__counters, &__map](auto&& __preimage) {
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auto __index = --__counters[__map(__preimage)];
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__result[__index] = std::move(__preimage);
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});
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}
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template <class _ForwardIterator, class _RandomAccessIterator, class _Map>
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_LIBCPP_HIDE_FROM_ABI _RandomAccessIterator
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__counting_sort_impl(_ForwardIterator __first, _ForwardIterator __last, _RandomAccessIterator __result, _Map __map) {
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using __value_type = __iter_value_type<_ForwardIterator>;
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using __traits = __counting_sort_traits<__value_type, _Map>;
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__iter_diff_t<_RandomAccessIterator> __counters[__traits::__value_range + 1] = {0};
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std::__collect(__first, __last, __map, std::next(std::begin(__counters)));
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std::__dispose(__first, __last, __result, __map, std::begin(__counters));
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return __result + __counters[__traits::__value_range];
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}
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template <class _RandomAccessIterator1,
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class _RandomAccessIterator2,
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class _Map,
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class _Radix,
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enable_if_t< __radix_sort_traits<__iter_value_type<_RandomAccessIterator1>, _Map, _Radix>::__radix_count == 1,
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int> = 0>
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_LIBCPP_HIDE_FROM_ABI void __radix_sort_impl(
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_RandomAccessIterator1 __first,
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_RandomAccessIterator1 __last,
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_RandomAccessIterator2 __buffer,
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_Map __map,
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_Radix __radix) {
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auto __buffer_end = std::__counting_sort_impl(__first, __last, __buffer, [&__map, &__radix](const auto& __value) {
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return __radix(__map(__value));
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});
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std::move(__buffer, __buffer_end, __first);
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}
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template <
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class _RandomAccessIterator1,
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class _RandomAccessIterator2,
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class _Map,
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class _Radix,
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enable_if_t< __radix_sort_traits<__iter_value_type<_RandomAccessIterator1>, _Map, _Radix>::__radix_count % 2 == 0,
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int> = 0 >
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_LIBCPP_HIDE_FROM_ABI void __radix_sort_impl(
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_RandomAccessIterator1 __first,
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_RandomAccessIterator1 __last,
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_RandomAccessIterator2 __buffer_begin,
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_Map __map,
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_Radix __radix) {
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using __value_type = __iter_value_type<_RandomAccessIterator1>;
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using __traits = __radix_sort_traits<__value_type, _Map, _Radix>;
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__iter_diff_t<_RandomAccessIterator1> __counters[__traits::__radix_count][__traits::__radix_value_range] = {{0}};
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__iter_diff_t<_RandomAccessIterator1> __maximums[__traits::__radix_count] = {0};
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const auto __is_sorted = std::__collect(__first, __last, __map, __radix, __counters, __maximums);
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if (!__is_sorted) {
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const auto __range_size = std::distance(__first, __last);
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auto __buffer_end = __buffer_begin + __range_size;
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for (size_t __radix_number = 0; __radix_number < __traits::__radix_count; __radix_number += 2) {
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const auto __n0th_is_single = __maximums[__radix_number] == __range_size;
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const auto __n1th_is_single = __maximums[__radix_number + 1] == __range_size;
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if (__n0th_is_single && __n1th_is_single) {
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continue;
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}
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if (__n0th_is_single) {
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std::move(__first, __last, __buffer_begin);
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} else {
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auto __n0th = [__radix_number, &__map, &__radix](const auto& __v) {
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return std::__nth_radix(__radix_number, __radix, __map(__v));
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};
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std::__dispose_backward(__first, __last, __buffer_begin, __n0th, __counters[__radix_number]);
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}
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if (__n1th_is_single) {
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std::move(__buffer_begin, __buffer_end, __first);
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} else {
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auto __n1th = [__radix_number, &__map, &__radix](const auto& __v) {
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return std::__nth_radix(__radix_number + 1, __radix, __map(__v));
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};
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std::__dispose_backward(__buffer_begin, __buffer_end, __first, __n1th, __counters[__radix_number + 1]);
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}
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}
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}
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}
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_LIBCPP_HIDE_FROM_ABI constexpr auto __shift_to_unsigned(bool __b) { return __b; }
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template <class _Ip>
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_LIBCPP_HIDE_FROM_ABI constexpr auto __shift_to_unsigned(_Ip __n) {
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constexpr const auto __min_value = numeric_limits<_Ip>::min();
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return static_cast<make_unsigned_t<_Ip> >(__n ^ __min_value);
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}
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struct __low_byte_fn {
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template <class _Ip>
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_LIBCPP_HIDE_FROM_ABI constexpr uint8_t operator()(_Ip __integer) const {
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static_assert(is_unsigned<_Ip>::value);
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return static_cast<uint8_t>(__integer & 0xff);
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}
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};
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template <class _RandomAccessIterator1, class _RandomAccessIterator2, class _Map, class _Radix>
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_LIBCPP_HIDE_FROM_ABI void
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__radix_sort(_RandomAccessIterator1 __first,
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_RandomAccessIterator1 __last,
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_RandomAccessIterator2 __buffer,
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_Map __map,
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_Radix __radix) {
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auto __map_to_unsigned = [__map = std::move(__map)](const auto& __x) { return std::__shift_to_unsigned(__map(__x)); };
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std::__radix_sort_impl(__first, __last, __buffer, __map_to_unsigned, __radix);
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}
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template <class _RandomAccessIterator1, class _RandomAccessIterator2>
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_LIBCPP_HIDE_FROM_ABI void
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__radix_sort(_RandomAccessIterator1 __first, _RandomAccessIterator1 __last, _RandomAccessIterator2 __buffer) {
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std::__radix_sort(__first, __last, __buffer, __identity{}, __low_byte_fn{});
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}
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#endif // _LIBCPP_STD_VER >= 14
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_LIBCPP_END_NAMESPACE_STD
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_LIBCPP_POP_MACROS
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#endif // _LIBCPP___ALGORITHM_RADIX_SORT_H

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