pchain_runtime/
formulas.rs

1/*
2    Copyright © 2023, ParallelChain Lab
3    Licensed under the Apache License, Version 2.0: http://www.apache.org/licenses/LICENSE-2.0
4*/
5
6//! Defines constants and formulas which are used in `pchain_runtime`.
7//!
8//! For example, they are
9//! - the portion of gas fee burning into Tresury account ([TREASURY_CUT_OF_BASE_FEE])
10//! - the calculation of issuance to reward the network ([issuance_reward])
11//! - issuance rate ([ISSUANCE_RATE_FACTORS])
12//! - calculation of pool reward and stake reward
13
14/// Send 20% of gas to Treasury
15pub const TREASURY_CUT_OF_BASE_FEE: u64 = 20;
16/// denominator of Treasury cut of Base fee
17pub const TOTAL_BASE_FEE: u64 = 100;
18
19/// Calculate issuance reward at particular epoch.
20///
21/// Equations:
22/// - Issuance_n = (0.0835 * 0.85^(n/365)) / 365 if epoch number < [ISSUANCE_STABLE_EPOCH].
23/// - Issuance_n = 0.0150 / 365 otherwise.
24///
25/// Returns the value as tuple of (numerator, denominator). i.e. value = numerator / denominator 
26/// where denominator is a non-zero value.
27/// 
28/// The return value is represented by two u128 numbers, instead of floating point number, for 
29/// preserving the information of frational part which could be lost in floating point representation. 
30/// It is up to the method caller to perform division or other numeric calculations.
31pub const fn issuance_reward(epoch_number: u64, amount: u64) -> (u128, u128) {
32    if epoch_number as usize >= ISSUANCE_STABLE_EPOCH {
33        // 15 = 0.015 mutliplied by 1_000
34        return (amount as u128 * 15, 365 * 1_000);
35    }
36    // 835 = 0.0835 mutliplied by 10_000 x value in ISSURANCE_RATE_FACTORS multiplied by 10_000
37    let rate = 835 * ISSUANCE_RATE_FACTORS[epoch_number as usize];
38    (amount as u128 * rate as u128, 365 * 100_000_000)
39}
40
41/// Number of epoch to reach for applying a constant issurance rate in reward calculation
42pub const ISSUANCE_STABLE_EPOCH: usize = 3650;
43/// 0.85 ^ (n / 365) (and then multply by 10000 to make it integer)
44pub const ISSUANCE_RATE_FACTORS: [u64; ISSUANCE_STABLE_EPOCH] =
45[
46    10000,9996,9991,9987,9982,9978,9973,9969,9964,9960,9956,9951,9947,9942,9938,9933,9929,9925,9920,9916,9911,9907,9903,9898,9894,
47    9889,9885,9881,9876,9872,9867,9863,9859,9854,9850,9845,9841,9837,9832,9828,9823,9819,9815,9810,9806,9802,9797,9793,9789,9784,
48    9780,9775,9771,9767,9762,9758,9754,9749,9745,9741,9736,9732,9728,9723,9719,9715,9710,9706,9702,9697,9693,9689,9684,9680,9676,
49    9672,9667,9663,9659,9654,9650,9646,9641,9637,9633,9629,9624,9620,9616,9611,9607,9603,9599,9594,9590,9586,9582,9577,9573,9569,
50    9565,9560,9556,9552,9547,9543,9539,9535,9531,9526,9522,9518,9514,9509,9505,9501,9497,9492,9488,9484,9480,9475,9471,9467,9463,
51    9459,9454,9450,9446,9442,9438,9433,9429,9425,9421,9417,9412,9408,9404,9400,9396,9391,9387,9383,9379,9375,9371,9366,9362,9358,
52    9354,9350,9346,9341,9337,9333,9329,9325,9321,9317,9312,9308,9304,9300,9296,9292,9288,9283,9279,9275,9271,9267,9263,9259,9255,
53    9250,9246,9242,9238,9234,9230,9226,9222,9217,9213,9209,9205,9201,9197,9193,9189,9185,9181,9177,9172,9168,9164,9160,9156,9152,
54    9148,9144,9140,9136,9132,9128,9124,9120,9115,9111,9107,9103,9099,9095,9091,9087,9083,9079,9075,9071,9067,9063,9059,9055,9051,
55    9047,9043,9039,9035,9031,9027,9023,9019,9015,9011,9007,9003,8999,8995,8991,8986,8982,8978,8975,8971,8967,8963,8959,8955,8951,
56    8947,8943,8939,8935,8931,8927,8923,8919,8915,8911,8907,8903,8899,8895,8891,8887,8883,8879,8875,8871,8867,8863,8859,8855,8851,
57    8848,8844,8840,8836,8832,8828,8824,8820,8816,8812,8808,8804,8800,8796,8793,8789,8785,8781,8777,8773,8769,8765,8761,8757,8753,
58    8750,8746,8742,8738,8734,8730,8726,8722,8718,8715,8711,8707,8703,8699,8695,8691,8687,8684,8680,8676,8672,8668,8664,8660,8657,
59    8653,8649,8645,8641,8637,8634,8630,8626,8622,8618,8614,8610,8607,8603,8599,8595,8591,8587,8584,8580,8576,8572,8568,8565,8561,
60    8557,8553,8549,8546,8542,8538,8534,8530,8527,8523,8519,8515,8511,8508,8504,8500,8496,8492,8489,8485,8481,8477,8474,8470,8466,
61    8462,8458,8455,8451,8447,8443,8440,8436,8432,8428,8425,8421,8417,8413,8410,8406,8402,8398,8395,8391,8387,8383,8380,8376,8372,
62    8369,8365,8361,8357,8354,8350,8346,8343,8339,8335,8331,8328,8324,8320,8317,8313,8309,8305,8302,8298,8294,8291,8287,8283,8280,
63    8276,8272,8269,8265,8261,8258,8254,8250,8246,8243,8239,8235,8232,8228,8224,8221,8217,8214,8210,8206,8203,8199,8195,8192,8188,
64    8184,8181,8177,8173,8170,8166,8162,8159,8155,8152,8148,8144,8141,8137,8133,8130,8126,8123,8119,8115,8112,8108,8105,8101,8097,
65    8094,8090,8087,8083,8079,8076,8072,8069,8065,8061,8058,8054,8051,8047,8043,8040,8036,8033,8029,8026,8022,8018,8015,8011,8008,
66    8004,8001,7997,7993,7990,7986,7983,7979,7976,7972,7969,7965,7961,7958,7954,7951,7947,7944,7940,7937,7933,7930,7926,7923,7919,
67    7916,7912,7908,7905,7901,7898,7894,7891,7887,7884,7880,7877,7873,7870,7866,7863,7859,7856,7852,7849,7845,7842,7838,7835,7831,
68    7828,7824,7821,7817,7814,7810,7807,7804,7800,7797,7793,7790,7786,7783,7779,7776,7772,7769,7765,7762,7758,7755,7752,7748,7745,
69    7741,7738,7734,7731,7727,7724,7721,7717,7714,7710,7707,7703,7700,7697,7693,7690,7686,7683,7679,7676,7673,7669,7666,7662,7659,
70    7656,7652,7649,7645,7642,7639,7635,7632,7628,7625,7622,7618,7615,7611,7608,7605,7601,7598,7594,7591,7588,7584,7581,7578,7574,
71    7571,7567,7564,7561,7557,7554,7551,7547,7544,7541,7537,7534,7530,7527,7524,7520,7517,7514,7510,7507,7504,7500,7497,7494,7490,
72    7487,7484,7480,7477,7474,7470,7467,7464,7460,7457,7454,7450,7447,7444,7440,7437,7434,7431,7427,7424,7421,7417,7414,7411,7407,
73    7404,7401,7398,7394,7391,7388,7384,7381,7378,7375,7371,7368,7365,7361,7358,7355,7352,7348,7345,7342,7338,7335,7332,7329,7325,
74    7322,7319,7316,7312,7309,7306,7303,7299,7296,7293,7290,7286,7283,7280,7277,7273,7270,7267,7264,7260,7257,7254,7251,7248,7244,
75    7241,7238,7235,7231,7228,7225,7222,7219,7215,7212,7209,7206,7203,7199,7196,7193,7190,7186,7183,7180,7177,7174,7171,7167,7164,
76    7161,7158,7155,7151,7148,7145,7142,7139,7135,7132,7129,7126,7123,7120,7116,7113,7110,7107,7104,7101,7097,7094,7091,7088,7085,
77    7082,7079,7075,7072,7069,7066,7063,7060,7056,7053,7050,7047,7044,7041,7038,7035,7031,7028,7025,7022,7019,7016,7013,7010,7006,
78    7003,7000,6997,6994,6991,6988,6985,6981,6978,6975,6972,6969,6966,6963,6960,6957,6954,6950,6947,6944,6941,6938,6935,6932,6929,
79    6926,6923,6920,6917,6913,6910,6907,6904,6901,6898,6895,6892,6889,6886,6883,6880,6877,6874,6870,6867,6864,6861,6858,6855,6852,
80    6849,6846,6843,6840,6837,6834,6831,6828,6825,6822,6819,6816,6813,6810,6807,6804,6800,6797,6794,6791,6788,6785,6782,6779,6776,
81    6773,6770,6767,6764,6761,6758,6755,6752,6749,6746,6743,6740,6737,6734,6731,6728,6725,6722,6719,6716,6713,6710,6707,6704,6701,
82    6698,6695,6692,6689,6686,6683,6680,6677,6674,6672,6669,6666,6663,6660,6657,6654,6651,6648,6645,6642,6639,6636,6633,6630,6627,
83    6624,6621,6618,6615,6612,6609,6606,6604,6601,6598,6595,6592,6589,6586,6583,6580,6577,6574,6571,6568,6565,6563,6560,6557,6554,
84    6551,6548,6545,6542,6539,6536,6533,6530,6528,6525,6522,6519,6516,6513,6510,6507,6504,6501,6499,6496,6493,6490,6487,6484,6481,
85    6478,6475,6473,6470,6467,6464,6461,6458,6455,6452,6450,6447,6444,6441,6438,6435,6432,6429,6427,6424,6421,6418,6415,6412,6409,
86    6407,6404,6401,6398,6395,6392,6390,6387,6384,6381,6378,6375,6372,6370,6367,6364,6361,6358,6355,6353,6350,6347,6344,6341,6338,
87    6336,6333,6330,6327,6324,6322,6319,6316,6313,6310,6308,6305,6302,6299,6296,6294,6291,6288,6285,6282,6280,6277,6274,6271,6268,
88    6266,6263,6260,6257,6254,6252,6249,6246,6243,6240,6238,6235,6232,6229,6227,6224,6221,6218,6216,6213,6210,6207,6204,6202,6199,
89    6196,6193,6191,6188,6185,6182,6180,6177,6174,6171,6169,6166,6163,6160,6158,6155,6152,6149,6147,6144,6141,6139,6136,6133,6130,
90    6128,6125,6122,6119,6117,6114,6111,6109,6106,6103,6100,6098,6095,6092,6090,6087,6084,6081,6079,6076,6073,6071,6068,6065,6062,
91    6060,6057,6054,6052,6049,6046,6044,6041,6038,6036,6033,6030,6027,6025,6022,6019,6017,6014,6011,6009,6006,6003,6001,5998,5995,
92    5993,5990,5987,5985,5982,5979,5977,5974,5971,5969,5966,5963,5961,5958,5955,5953,5950,5947,5945,5942,5940,5937,5934,5932,5929,
93    5926,5924,5921,5918,5916,5913,5911,5908,5905,5903,5900,5897,5895,5892,5890,5887,5884,5882,5879,5876,5874,5871,5869,5866,5863,
94    5861,5858,5856,5853,5850,5848,5845,5843,5840,5837,5835,5832,5830,5827,5824,5822,5819,5817,5814,5811,5809,5806,5804,5801,5798,
95    5796,5793,5791,5788,5786,5783,5780,5778,5775,5773,5770,5768,5765,5762,5760,5757,5755,5752,5750,5747,5744,5742,5739,5737,5734,
96    5732,5729,5727,5724,5722,5719,5716,5714,5711,5709,5706,5704,5701,5699,5696,5694,5691,5688,5686,5683,5681,5678,5676,5673,5671,
97    5668,5666,5663,5661,5658,5656,5653,5651,5648,5646,5643,5641,5638,5636,5633,5631,5628,5626,5623,5621,5618,5616,5613,5611,5608,
98    5606,5603,5601,5598,5596,5593,5591,5588,5586,5583,5581,5578,5576,5573,5571,5568,5566,5563,5561,5558,5556,5553,5551,5548,5546,
99    5543,5541,5539,5536,5534,5531,5529,5526,5524,5521,5519,5516,5514,5511,5509,5507,5504,5502,5499,5497,5494,5492,5489,5487,5485,
100    5482,5480,5477,5475,5472,5470,5467,5465,5463,5460,5458,5455,5453,5450,5448,5446,5443,5441,5438,5436,5433,5431,5429,5426,5424,
101    5421,5419,5417,5414,5412,5409,5407,5405,5402,5400,5397,5395,5393,5390,5388,5385,5383,5381,5378,5376,5373,5371,5369,5366,5364,
102    5361,5359,5357,5354,5352,5349,5347,5345,5342,5340,5338,5335,5333,5330,5328,5326,5323,5321,5319,5316,5314,5312,5309,5307,5304,
103    5302,5300,5297,5295,5293,5290,5288,5286,5283,5281,5278,5276,5274,5271,5269,5267,5264,5262,5260,5257,5255,5253,5250,5248,5246,
104    5243,5241,5239,5236,5234,5232,5229,5227,5225,5222,5220,5218,5215,5213,5211,5208,5206,5204,5202,5199,5197,5195,5192,5190,5188,
105    5185,5183,5181,5178,5176,5174,5171,5169,5167,5165,5162,5160,5158,5155,5153,5151,5149,5146,5144,5142,5139,5137,5135,5132,5130,
106    5128,5126,5123,5121,5119,5117,5114,5112,5110,5107,5105,5103,5101,5098,5096,5094,5092,5089,5087,5085,5082,5080,5078,5076,5073,
107    5071,5069,5067,5064,5062,5060,5058,5055,5053,5051,5049,5046,5044,5042,5040,5037,5035,5033,5031,5028,5026,5024,5022,5019,5017,
108    5015,5013,5011,5008,5006,5004,5002,4999,4997,4995,4993,4991,4988,4986,4984,4982,4979,4977,4975,4973,4971,4968,4966,4964,4962,
109    4959,4957,4955,4953,4951,4948,4946,4944,4942,4940,4937,4935,4933,4931,4929,4926,4924,4922,4920,4918,4916,4913,4911,4909,4907,
110    4905,4902,4900,4898,4896,4894,4892,4889,4887,4885,4883,4881,4878,4876,4874,4872,4870,4868,4865,4863,4861,4859,4857,4855,4852,
111    4850,4848,4846,4844,4842,4840,4837,4835,4833,4831,4829,4827,4824,4822,4820,4818,4816,4814,4812,4809,4807,4805,4803,4801,4799,
112    4797,4794,4792,4790,4788,4786,4784,4782,4780,4777,4775,4773,4771,4769,4767,4765,4763,4760,4758,4756,4754,4752,4750,4748,4746,
113    4744,4741,4739,4737,4735,4733,4731,4729,4727,4725,4722,4720,4718,4716,4714,4712,4710,4708,4706,4704,4701,4699,4697,4695,4693,
114    4691,4689,4687,4685,4683,4681,4678,4676,4674,4672,4670,4668,4666,4664,4662,4660,4658,4656,4654,4651,4649,4647,4645,4643,4641,
115    4639,4637,4635,4633,4631,4629,4627,4625,4623,4621,4618,4616,4614,4612,4610,4608,4606,4604,4602,4600,4598,4596,4594,4592,4590,
116    4588,4586,4584,4582,4580,4578,4575,4573,4571,4569,4567,4565,4563,4561,4559,4557,4555,4553,4551,4549,4547,4545,4543,4541,4539,
117    4537,4535,4533,4531,4529,4527,4525,4523,4521,4519,4517,4515,4513,4511,4509,4507,4505,4503,4501,4499,4497,4495,4493,4491,4489,
118    4487,4485,4483,4481,4479,4477,4475,4473,4471,4469,4467,4465,4463,4461,4459,4457,4455,4453,4451,4449,4447,4445,4443,4441,4439,
119    4437,4435,4433,4431,4429,4427,4425,4423,4421,4419,4417,4415,4413,4411,4409,4408,4406,4404,4402,4400,4398,4396,4394,4392,4390,
120    4388,4386,4384,4382,4380,4378,4376,4374,4372,4370,4368,4366,4365,4363,4361,4359,4357,4355,4353,4351,4349,4347,4345,4343,4341,
121    4339,4337,4336,4334,4332,4330,4328,4326,4324,4322,4320,4318,4316,4314,4312,4310,4309,4307,4305,4303,4301,4299,4297,4295,4293,
122    4291,4289,4288,4286,4284,4282,4280,4278,4276,4274,4272,4270,4268,4267,4265,4263,4261,4259,4257,4255,4253,4251,4249,4248,4246,
123    4244,4242,4240,4238,4236,4234,4233,4231,4229,4227,4225,4223,4221,4219,4217,4216,4214,4212,4210,4208,4206,4204,4202,4201,4199,
124    4197,4195,4193,4191,4189,4188,4186,4184,4182,4180,4178,4176,4174,4173,4171,4169,4167,4165,4163,4161,4160,4158,4156,4154,4152,
125    4150,4149,4147,4145,4143,4141,4139,4137,4136,4134,4132,4130,4128,4126,4125,4123,4121,4119,4117,4115,4114,4112,4110,4108,4106,
126    4104,4103,4101,4099,4097,4095,4093,4092,4090,4088,4086,4084,4083,4081,4079,4077,4075,4073,4072,4070,4068,4066,4064,4063,4061,
127    4059,4057,4055,4054,4052,4050,4048,4046,4045,4043,4041,4039,4037,4036,4034,4032,4030,4028,4027,4025,4023,4021,4019,4018,4016,
128    4014,4012,4011,4009,4007,4005,4003,4002,4000,3998,3996,3994,3993,3991,3989,3987,3986,3984,3982,3980,3978,3977,3975,3973,3971,
129    3970,3968,3966,3964,3963,3961,3959,3957,3956,3954,3952,3950,3948,3947,3945,3943,3941,3940,3938,3936,3934,3933,3931,3929,3927,
130    3926,3924,3922,3920,3919,3917,3915,3913,3912,3910,3908,3907,3905,3903,3901,3900,3898,3896,3894,3893,3891,3889,3887,3886,3884,
131    3882,3881,3879,3877,3875,3874,3872,3870,3868,3867,3865,3863,3862,3860,3858,3856,3855,3853,3851,3850,3848,3846,3844,3843,3841,
132    3839,3838,3836,3834,3832,3831,3829,3827,3826,3824,3822,3821,3819,3817,3815,3814,3812,3810,3809,3807,3805,3804,3802,3800,3798,
133    3797,3795,3793,3792,3790,3788,3787,3785,3783,3782,3780,3778,3777,3775,3773,3771,3770,3768,3766,3765,3763,3761,3760,3758,3756,
134    3755,3753,3751,3750,3748,3746,3745,3743,3741,3740,3738,3736,3735,3733,3731,3730,3728,3726,3725,3723,3721,3720,3718,3716,3715,
135    3713,3712,3710,3708,3707,3705,3703,3702,3700,3698,3697,3695,3693,3692,3690,3688,3687,3685,3684,3682,3680,3679,3677,3675,3674,
136    3672,3670,3669,3667,3666,3664,3662,3661,3659,3657,3656,3654,3653,3651,3649,3648,3646,3644,3643,3641,3640,3638,3636,3635,3633,
137    3631,3630,3628,3627,3625,3623,3622,3620,3619,3617,3615,3614,3612,3610,3609,3607,3606,3604,3602,3601,3599,3598,3596,3594,3593,
138    3591,3590,3588,3586,3585,3583,3582,3580,3578,3577,3575,3574,3572,3570,3569,3567,3566,3564,3563,3561,3559,3558,3556,3555,3553,
139    3551,3550,3548,3547,3545,3544,3542,3540,3539,3537,3536,3534,3533,3531,3529,3528,3526,3525,3523,3522,3520,3518,3517,3515,3514,
140    3512,3511,3509,3507,3506,3504,3503,3501,3500,3498,3497,3495,3493,3492,3490,3489,3487,3486,3484,3483,3481,3479,3478,3476,3475,
141    3473,3472,3470,3469,3467,3466,3464,3462,3461,3459,3458,3456,3455,3453,3452,3450,3449,3447,3446,3444,3442,3441,3439,3438,3436,
142    3435,3433,3432,3430,3429,3427,3426,3424,3423,3421,3420,3418,3417,3415,3413,3412,3410,3409,3407,3406,3404,3403,3401,3400,3398,
143    3397,3395,3394,3392,3391,3389,3388,3386,3385,3383,3382,3380,3379,3377,3376,3374,3373,3371,3370,3368,3367,3365,3364,3362,3361,
144    3359,3358,3356,3355,3353,3352,3350,3349,3347,3346,3344,3343,3341,3340,3338,3337,3335,3334,3332,3331,3329,3328,3326,3325,3323,
145    3322,3321,3319,3318,3316,3315,3313,3312,3310,3309,3307,3306,3304,3303,3301,3300,3298,3297,3296,3294,3293,3291,3290,3288,3287,
146    3285,3284,3282,3281,3279,3278,3276,3275,3274,3272,3271,3269,3268,3266,3265,3263,3262,3260,3259,3258,3256,3255,3253,3252,3250,
147    3249,3247,3246,3245,3243,3242,3240,3239,3237,3236,3234,3233,3232,3230,3229,3227,3226,3224,3223,3222,3220,3219,3217,3216,3214,
148    3213,3211,3210,3209,3207,3206,3204,3203,3201,3200,3199,3197,3196,3194,3193,3192,3190,3189,3187,3186,3184,3183,3182,3180,3179,
149    3177,3176,3175,3173,3172,3170,3169,3167,3166,3165,3163,3162,3160,3159,3158,3156,3155,3153,3152,3151,3149,3148,3146,3145,3144,
150    3142,3141,3139,3138,3137,3135,3134,3132,3131,3130,3128,3127,3125,3124,3123,3121,3120,3118,3117,3116,3114,3113,3112,3110,3109,
151    3107,3106,3105,3103,3102,3100,3099,3098,3096,3095,3094,3092,3091,3089,3088,3087,3085,3084,3083,3081,3080,3078,3077,3076,3074,
152    3073,3072,3070,3069,3068,3066,3065,3063,3062,3061,3059,3058,3057,3055,3054,3053,3051,3050,3048,3047,3046,3044,3043,3042,3040,
153    3039,3038,3036,3035,3034,3032,3031,3030,3028,3027,3025,3024,3023,3021,3020,3019,3017,3016,3015,3013,3012,3011,3009,3008,3007,
154    3005,3004,3003,3001,3000,2999,2997,2996,2995,2993,2992,2991,2989,2988,2987,2985,2984,2983,2981,2980,2979,2977,2976,2975,2973,
155    2972,2971,2969,2968,2967,2965,2964,2963,2962,2960,2959,2958,2956,2955,2954,2952,2951,2950,2948,2947,2946,2944,2943,2942,2940,
156    2939,2938,2937,2935,2934,2933,2931,2930,2929,2927,2926,2925,2924,2922,2921,2920,2918,2917,2916,2914,2913,2912,2911,2909,2908,
157    2907,2905,2904,2903,2901,2900,2899,2898,2896,2895,2894,2892,2891,2890,2889,2887,2886,2885,2883,2882,2881,2880,2878,2877,2876,
158    2874,2873,2872,2871,2869,2868,2867,2866,2864,2863,2862,2860,2859,2858,2857,2855,2854,2853,2852,2850,2849,2848,2846,2845,2844,
159    2843,2841,2840,2839,2838,2836,2835,2834,2833,2831,2830,2829,2827,2826,2825,2824,2822,2821,2820,2819,2817,2816,2815,2814,2812,
160    2811,2810,2809,2807,2806,2805,2804,2802,2801,2800,2799,2797,2796,2795,2794,2792,2791,2790,2789,2787,2786,2785,2784,2783,2781,
161    2780,2779,2778,2776,2775,2774,2773,2771,2770,2769,2768,2766,2765,2764,2763,2762,2760,2759,2758,2757,2755,2754,2753,2752,2751,
162    2749,2748,2747,2746,2744,2743,2742,2741,2740,2738,2737,2736,2735,2733,2732,2731,2730,2729,2727,2726,2725,2724,2722,2721,2720,
163    2719,2718,2716,2715,2714,2713,2712,2710,2709,2708,2707,2706,2704,2703,2702,2701,2700,2698,2697,2696,2695,2694,2692,2691,2690,
164    2689,2688,2686,2685,2684,2683,2682,2680,2679,2678,2677,2676,2674,2673,2672,2671,2670,2668,2667,2666,2665,2664,2663,2661,2660,
165    2659,2658,2657,2655,2654,2653,2652,2651,2650,2648,2647,2646,2645,2644,2642,2641,2640,2639,2638,2637,2635,2634,2633,2632,2631,
166    2630,2628,2627,2626,2625,2624,2623,2621,2620,2619,2618,2617,2616,2614,2613,2612,2611,2610,2609,2607,2606,2605,2604,2603,2602,
167    2600,2599,2598,2597,2596,2595,2594,2592,2591,2590,2589,2588,2587,2585,2584,2583,2582,2581,2580,2579,2577,2576,2575,2574,2573,
168    2572,2571,2569,2568,2567,2566,2565,2564,2563,2561,2560,2559,2558,2557,2556,2555,2553,2552,2551,2550,2549,2548,2547,2545,2544,
169    2543,2542,2541,2540,2539,2538,2536,2535,2534,2533,2532,2531,2530,2529,2527,2526,2525,2524,2523,2522,2521,2520,2518,2517,2516,
170    2515,2514,2513,2512,2511,2509,2508,2507,2506,2505,2504,2503,2502,2501,2499,2498,2497,2496,2495,2494,2493,2492,2491,2489,2488,
171    2487,2486,2485,2484,2483,2482,2481,2479,2478,2477,2476,2475,2474,2473,2472,2471,2470,2468,2467,2466,2465,2464,2463,2462,2461,
172    2460,2459,2457,2456,2455,2454,2453,2452,2451,2450,2449,2448,2447,2445,2444,2443,2442,2441,2440,2439,2438,2437,2436,2435,2434,
173    2432,2431,2430,2429,2428,2427,2426,2425,2424,2423,2422,2421,2419,2418,2417,2416,2415,2414,2413,2412,2411,2410,2409,2408,2407,
174    2406,2404,2403,2402,2401,2400,2399,2398,2397,2396,2395,2394,2393,2392,2391,2389,2388,2387,2386,2385,2384,2383,2382,2381,2380,
175    2379,2378,2377,2376,2375,2374,2373,2371,2370,2369,2368,2367,2366,2365,2364,2363,2362,2361,2360,2359,2358,2357,2356,2355,2354,
176    2353,2352,2350,2349,2348,2347,2346,2345,2344,2343,2342,2341,2340,2339,2338,2337,2336,2335,2334,2333,2332,2331,2330,2329,2328,
177    2327,2325,2324,2323,2322,2321,2320,2319,2318,2317,2316,2315,2314,2313,2312,2311,2310,2309,2308,2307,2306,2305,2304,2303,2302,
178    2301,2300,2299,2298,2297,2296,2295,2294,2293,2292,2291,2290,2288,2287,2286,2285,2284,2283,2282,2281,2280,2279,2278,2277,2276,
179    2275,2274,2273,2272,2271,2270,2269,2268,2267,2266,2265,2264,2263,2262,2261,2260,2259,2258,2257,2256,2255,2254,2253,2252,2251,
180    2250,2249,2248,2247,2246,2245,2244,2243,2242,2241,2240,2239,2238,2237,2236,2235,2234,2233,2232,2231,2230,2229,2228,2227,2226,
181    2225,2224,2223,2222,2221,2220,2219,2218,2217,2216,2215,2214,2213,2212,2211,2210,2209,2208,2207,2206,2205,2204,2203,2203,2202,
182    2201,2200,2199,2198,2197,2196,2195,2194,2193,2192,2191,2190,2189,2188,2187,2186,2185,2184,2183,2182,2181,2180,2179,2178,2177,
183    2176,2175,2174,2173,2172,2171,2170,2169,2168,2167,2167,2166,2165,2164,2163,2162,2161,2160,2159,2158,2157,2156,2155,2154,2153,
184    2152,2151,2150,2149,2148,2147,2146,2145,2144,2143,2143,2142,2141,2140,2139,2138,2137,2136,2135,2134,2133,2132,2131,2130,2129,
185    2128,2127,2126,2125,2124,2124,2123,2122,2121,2120,2119,2118,2117,2116,2115,2114,2113,2112,2111,2110,2109,2108,2108,2107,2106,
186    2105,2104,2103,2102,2101,2100,2099,2098,2097,2096,2095,2094,2094,2093,2092,2091,2090,2089,2088,2087,2086,2085,2084,2083,2082,
187    2081,2080,2080,2079,2078,2077,2076,2075,2074,2073,2072,2071,2070,2069,2068,2068,2067,2066,2065,2064,2063,2062,2061,2060,2059,
188    2058,2057,2057,2056,2055,2054,2053,2052,2051,2050,2049,2048,2047,2047,2046,2045,2044,2043,2042,2041,2040,2039,2038,2037,2037,
189    2036,2035,2034,2033,2032,2031,2030,2029,2028,2027,2027,2026,2025,2024,2023,2022,2021,2020,2019,2018,2018,2017,2016,2015,2014,
190    2013,2012,2011,2010,2009,2009,2008,2007,2006,2005,2004,2003,2002,2001,2001,2000,1999,1998,1997,1996,1995,1994,1993,1993,1992,
191    1991,1990,1989,1988,1987,1986,1985,1985,1984,1983,1982,1981,1980,1979,1978,1978,1977,1976,1975,1974,1973,1972,1971,1970,1970
192];
193
194
195/// Calculate reward of a pool. It is fraction of the pool power to network power, and
196/// block performance. Baseline is calculated by: number of blocks per term / number of validators.
197///
198/// ```text
199/// Issuance * PoolStake * min(NumBlocksProposed/Baseline , 1)
200/// ```
201/// 
202/// ## Safety
203/// `num_of_proposed_blocks` should be reasonable amount to avoid overflow. It should be at maximum 8640 blocks per term in the protocol.
204pub const fn pool_reward(
205    current_epoch: u64,
206    pool_power: u64,
207    num_of_proposed_blocks: u32,
208    baseline: u32,
209) -> u64 {
210    // no reward if it is not expected to propose block
211    if baseline == 0 {
212        return 0;
213    }
214    // should not over reward
215    if num_of_proposed_blocks > baseline {
216        // Issuance * PoolStake * 1
217        let (numerator, denominator) = issuance_reward(current_epoch, pool_power);
218        return (numerator / denominator) as u64;
219    }
220    // Issuance * PoolStake * NumBlocksProposed / Baseline
221    let (numerator, denominator) = issuance_reward(current_epoch, pool_power);
222    ((numerator * num_of_proposed_blocks as u128) / (denominator * baseline as u128)) as u64
223}
224
225/// Return reward to the stakes and commission_fee. 
226/// 
227/// ## Safety
228/// - `commission_rate` is in percentage (i.e. <= 100).
229/// - `stake_power` should be less than `total_stakes`
230pub const fn stake_reward(
231    pool_reward: u64,
232    commission_rate: u8,
233    stake_power: u64,
234    total_stakes: u64,
235) -> (u64, u64) {
236    // no reward if there is no stakes at all
237    if total_stakes == 0 {
238        return (0, 0);
239    }
240    let reward = (pool_reward as u128 * stake_power as u128) / (total_stakes as u128);
241    let commission_fee = (commission_rate as u128 * pool_reward as u128 * stake_power as u128)
242        / (100 * total_stakes as u128);
243    (
244        (reward.saturating_sub(commission_fee)) as u64,
245        commission_fee as u64,
246    )
247}
248
249/// This test is mainly for checking whether the methods `pool_reward` and `stake_reward` panics on boundary inputs.
250/// It is expected to pass without panic.
251#[test]
252fn test_boundary_inputs() {
253    // Return zero if num_of_proposed_blocks is zero.
254    assert_eq!(0, pool_reward(0, 0, 0, 0));
255
256    // Situation 1: expected to produce 1 block but finally produce all blocks in a term (8640 blocks).
257    let max_pool_reward_no_muldiv = pool_reward(0, u64::MAX, 8640, 1); 
258
259    // Situation 2: produce all expected blocks in a term (8640 blocks).
260    let max_pool_reward = pool_reward(0, u64::MAX, 8640, 8640); 
261    
262    // Both should return same value.
263    assert_eq!(max_pool_reward_no_muldiv, max_pool_reward);
264    assert_eq!(4220008575766431, max_pool_reward);
265
266    // Return zero if total_stakes is zero.
267    assert_eq!((0, 0), stake_reward(max_pool_reward, 100, 0, 0));
268
269    // Getting commission fee (100%) from all of the the max_pool_reward because stake_power = total_stakes.
270    let (reward_to_stake, commission_fee) = stake_reward(max_pool_reward, 100, u64::MAX, u64::MAX);
271    assert_eq!(0, reward_to_stake);
272    assert_eq!(max_pool_reward, commission_fee);
273}
pchain_runtime/formulas.rs

pchain_runtime/
formulas.rs
