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Update EIP-2537: MSM gas repricing #9116

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Update EIP-2537: MSM gas repricing #9116

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a3a032d
add new discount tables
Marchhill Dec 9, 2024
cd30655
double g1 msm cost one pair
Marchhill Dec 9, 2024
788087e
use pawel discount table
Marchhill Dec 13, 2024
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22 changes: 18 additions & 4 deletions EIPS/eip-2537.md
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Expand Up @@ -269,21 +269,35 @@ Assuming a constant `30 MGas/second`, the following prices are suggested.

#### G2 multiplication

`45000` gas
`22500` gas

#### G1/G2 MSM

MSMs are expected to be performed by Pippenger's algorithm (we can also say that it **must** be performed by Pippenger's algorithm to have a speedup that results in a discount over naive implementation by multiplying each pair separately and adding the results). For this case there was a table prepared for discount in case of `k <= 128` points in the MSM with a discount cap `max_discount` for `k > 128`.

To avoid non-integer arithmetic, the call cost is calculated as `(k * multiplication_cost * discount) / multiplier` where `multiplier = 1000`, `k` is a number of (scalar, point) pairs for the call, `multiplication_cost` is a corresponding single multiplication call cost for G1/G2.

Discounts table as a vector of pairs `[k, discount]`:
G1 and G2 are priced separately, each having their own discount table and `max_discount`.

##### G1 discounts

Discounts table for G1 MSM as a vector of pairs `[k, discount]`:

```
[[1, 1800], [2, 888], [3, 955], [4, 802], [5, 743], [6, 821], [7, 750], [8, 680], [9, 657], [10, 635], [11, 612], [12, 591], [13, 664], [14, 637], [15, 611], [16, 585], [17, 578], [18, 571], [19, 564], [20, 557], [21, 628], [22, 620], [23, 612], [24, 604], [25, 596], [26, 588], [27, 578], [28, 570], [29, 562], [30, 693], [31, 683], [32, 673], [33, 670], [34, 665], [35, 663], [36, 658], [37, 655], [38, 650], [39, 648], [40, 643], [41, 640], [42, 635], [43, 633], [44, 628], [45, 625], [46, 620], [47, 618], [48, 613], [49, 610], [50, 605], [51, 603], [52, 598], [53, 595], [54, 590], [55, 588], [56, 583], [57, 580], [58, 578], [59, 573], [60, 570], [61, 565], [62, 563], [63, 558], [64, 555], [65, 553], [66, 550], [67, 548], [68, 548], [69, 545], [70, 543], [71, 540], [72, 540], [73, 538], [74, 535], [75, 533], [76, 533], [77, 530], [78, 528], [79, 528], [80, 525], [81, 523], [82, 520], [83, 520], [84, 518], [85, 515], [86, 513], [87, 513], [88, 510], [89, 508], [90, 505], [91, 505], [92, 503], [93, 500], [94, 498], [95, 498], [96, 495], [97, 493], [98, 490], [99, 490], [100, 488], [101, 485], [102, 483], [103, 483], [104, 480], [105, 478], [106, 478], [107, 475], [108, 473], [109, 470], [110, 470], [111, 468], [112, 465], [113, 463], [114, 463], [115, 460], [116, 458], [117, 455], [118, 455], [119, 453], [120, 450], [121, 448], [122, 448], [123, 445], [124, 443], [125, 440], [126, 440], [127, 438], [128, 435]]
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For k=1 we should put 1000 (the same cost as multiplication). Otherwise, we incentivize contracts to put a condition to redirect inputs from MSM to MUL in case they have single point.
In other words, if you have single point to multiply, you should not use any MSM algorithm. Just use regular multiplication in your MSM precompile implementation.

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These values are not monotonic, so you have to fix this.

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For me the terminal value k=128 is 520.

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These values are not monotonic, so you have to fix this.

missed that. they should definitely be monotonic, regardless of the performance profile for any particular k,

```

`max_discount = 435`

##### G2 discounts

Discounts table for G2 MSM as a vector of pairs `[k, discount]`:

```
[[1, 1200], [2, 888], [3, 764], [4, 641], [5, 594], [6, 547], [7, 500], [8, 453], [9, 438], [10, 423], [11, 408], [12, 394], [13, 379], [14, 364], [15, 349], [16, 334], [17, 330], [18, 326], [19, 322], [20, 318], [21, 314], [22, 310], [23, 306], [24, 302], [25, 298], [26, 294], [27, 289], [28, 285], [29, 281], [30, 277], [31, 273], [32, 269], [33, 268], [34, 266], [35, 265], [36, 263], [37, 262], [38, 260], [39, 259], [40, 257], [41, 256], [42, 254], [43, 253], [44, 251], [45, 250], [46, 248], [47, 247], [48, 245], [49, 244], [50, 242], [51, 241], [52, 239], [53, 238], [54, 236], [55, 235], [56, 233], [57, 232], [58, 231], [59, 229], [60, 228], [61, 226], [62, 225], [63, 223], [64, 222], [65, 221], [66, 220], [67, 219], [68, 219], [69, 218], [70, 217], [71, 216], [72, 216], [73, 215], [74, 214], [75, 213], [76, 213], [77, 212], [78, 211], [79, 211], [80, 210], [81, 209], [82, 208], [83, 208], [84, 207], [85, 206], [86, 205], [87, 205], [88, 204], [89, 203], [90, 202], [91, 202], [92, 201], [93, 200], [94, 199], [95, 199], [96, 198], [97, 197], [98, 196], [99, 196], [100, 195], [101, 194], [102, 193], [103, 193], [104, 192], [105, 191], [106, 191], [107, 190], [108, 189], [109, 188], [110, 188], [111, 187], [112, 186], [113, 185], [114, 185], [115, 184], [116, 183], [117, 182], [118, 182], [119, 181], [120, 180], [121, 179], [122, 179], [123, 178], [124, 177], [125, 176], [126, 176], [127, 175], [128, 174]]
[[1, 1800], [2, 1776], [3, 1528], [4, 1282], [5, 1188], [6, 1368], [7, 1250], [8, 1133], [9, 1095], [10, 1269], [11, 1224], [12, 1182], [13, 1137], [14, 1274], [15, 1222], [16, 1169], [17, 1155], [18, 1141], [19, 1127], [20, 1113], [21, 1256], [22, 1240], [23, 1224], [24, 1208], [25, 1192], [26, 1176], [27, 1156], [28, 1140], [29, 1124], [30, 1108], [31, 1092], [32, 1076], [33, 1072], [34, 1064], [35, 1060], [36, 1052], [37, 1048], [38, 1040], [39, 1036], [40, 1028], [41, 1024], [42, 1016], [43, 1012], [44, 1004], [45, 1000], [46, 992], [47, 988], [48, 980], [49, 976], [50, 968], [51, 964], [52, 956], [53, 952], [54, 944], [55, 940], [56, 932], [57, 928], [58, 924], [59, 916], [60, 912], [61, 904], [62, 900], [63, 892], [64, 888], [65, 884], [66, 880], [67, 876], [68, 876], [69, 872], [70, 868], [71, 864], [72, 864], [73, 860], [74, 856], [75, 852], [76, 852], [77, 848], [78, 844], [79, 844], [80, 840], [81, 836], [82, 832], [83, 832], [84, 828], [85, 824], [86, 820], [87, 820], [88, 816], [89, 812], [90, 808], [91, 808], [92, 804], [93, 800], [94, 796], [95, 796], [96, 792], [97, 788], [98, 784], [99, 784], [100, 780], [101, 776], [102, 772], [103, 772], [104, 768], [105, 764], [106, 764], [107, 760], [108, 756], [109, 752], [110, 752], [111, 748], [112, 744], [113, 740], [114, 740], [115, 736], [116, 732], [117, 728], [118, 728], [119, 724], [120, 720], [121, 716], [122, 716], [123, 712], [124, 708], [125, 704], [126, 704], [127, 700], [128, 696]]
```

`max_discount = 174`
`max_discount = 696`

#### Pairing check operation

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