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feat: fast const pow (#336)
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<!--- Please provide a general summary of your changes in the title
above -->

# Implement efficient pow2 and pow10 using const arrays

## Pull Request type

<!-- Please try to limit your pull request to one type; submit multiple
pull requests if needed. -->

Please check the type of change your PR introduces:

- [ ] Bugfix
- [x] Feature
- [ ] Code style update (formatting, renaming)
- [ ] Refactoring (no functional changes, no API changes)
- [ ] Build-related changes
- [ ] Documentation content changes
- [ ] Other (please describe):

## What is the current behavior?

<!-- Please describe the current behavior that you are modifying, or
link to a relevant issue. -->

Currently, the implementation of pow2 and pow10 functions uses if/else
branches, which is less efficient than using lookup tables.

Issue Number: N/A

## What is the new behavior?

<!-- Please describe the behavior or changes that are being added by
this PR. -->

- Implement pow2 and pow10 using const arrays for efficient lookup
- Update keccak code to use the new pow2 implementation
- Significant gas usage reduction (e.g., keccak test gas usage reduced
from 2,399,388 to 1,289,988)

## Does this introduce a breaking change?

- [ ] Yes
- [x] No

<!-- If this does introduce a breaking change, please describe the
impact and migration path for existing applications below. -->

## Other information

<!-- Any other information that is important to this PR, such as
screenshots of how the component looks before and after the change. -->

This PR takes advantage of Cairo 2.7.0's reintroduction of "`dw` like
hardcoded function results" via const arrays to implement efficient
lookup tables for pow2 and pow10. These functions are commonly used in
various projects, including Alexandria for bitshifting and in DeFi
applications for handling ERC20 decimals. I introduced a u128 version
(should be the one used in most usecases), and a u256 version for both
pow2 and pow10. The u256 version of pow2 uses the u128 one.

The new implementation significantly reduces gas usage. For example, I
updated keccak implementation to use this new function and the
`test_bytes_keccak` test saw a reduction in estimated gas usage from
2,399,388 to 1,289,988.

closes #323
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@Th0rgal
Th0rgal authored Oct 15, 2024
1 parent 33d56f2 commit 0adfaab
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3 changes: 3 additions & 0 deletions Scarb.lock
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Original file line number Diff line number Diff line change
Expand Up @@ -50,6 +50,9 @@ version = "0.2.1"
[[package]]
name = "alexandria_merkle_tree"
version = "0.1.0"
dependencies = [
"alexandria_math",
]

[[package]]
name = "alexandria_numeric"
Expand Down
270 changes: 4 additions & 266 deletions packages/bytes/src/utils.cairo
View file
Original file line number Diff line number Diff line change
@@ -1,4 +1,5 @@
use alexandria_bytes::{Bytes, BytesTrait};
use alexandria_math::const_pow::pow2;
use alexandria_data_structures::array_ext::ArrayTraitExt;
use core::fmt::{Debug, Display, Formatter, Error};
use core::integer::u128_byte_reverse;
Expand Down Expand Up @@ -94,7 +95,7 @@ fn keccak_add_uint128_be(ref keccak_input: Array::<u64>, value: u128, value_size
keccak_input.append(reversed_value.try_into().unwrap());
} else {
let (high, low) = DivRem::div_rem(
reversed_value, u128_fast_pow2(64).try_into().expect('Division by 0')
reversed_value, pow2(64).try_into().expect('Division by 0')
);
keccak_input.append(low.try_into().unwrap());
keccak_input.append(high.try_into().unwrap());
Expand Down Expand Up @@ -209,7 +210,7 @@ pub fn u128_split(value: u128, value_size: usize, left_size: usize) -> (u128, u1
if left_size == 0 {
(0, value)
} else {
let power = u128_fast_pow2((value_size - left_size) * 8);
let power = pow2((value_size - left_size) * 8);
DivRem::div_rem(value, power.try_into().expect('Division by 0'))
}
}
Expand Down Expand Up @@ -253,7 +254,7 @@ pub fn read_sub_u128(value: u128, value_size: usize, offset: usize, size: usize)
pub fn u128_join(left: u128, right: u128, right_size: usize) -> u128 {
let left_size = u128_bytes_len(left);
assert(left_size + right_size <= 16, 'left shift overflow');
let shift = u128_fast_pow2(right_size * 8);
let shift = pow2(right_size * 8);
left * shift + right
}

Expand Down Expand Up @@ -295,266 +296,3 @@ fn u128_bytes_len(value: u128) -> usize {
16_usize
}
}

/// return 2^exp where exp in [0, 127]
fn u128_fast_pow2(exp: usize) -> u128 {
assert(exp <= 127, 'invalid exp');

if exp == 0_usize {
1_u128
} else if exp == 1_usize {
2_u128
} else if exp == 2_usize {
4_u128
} else if exp == 3_usize {
8_u128
} else if exp == 4_usize {
16_u128
} else if exp == 5_usize {
32_u128
} else if exp == 6_usize {
64_u128
} else if exp == 7_usize {
128_u128
} else if exp == 8_usize {
256_u128
} else if exp == 9_usize {
512_u128
} else if exp == 10_usize {
1024_u128
} else if exp == 11_usize {
2048_u128
} else if exp == 12_usize {
4096_u128
} else if exp == 13_usize {
8192_u128
} else if exp == 14_usize {
16384_u128
} else if exp == 15_usize {
32768_u128
} else if exp == 16_usize {
65536_u128
} else if exp == 17_usize {
131072_u128
} else if exp == 18_usize {
262144_u128
} else if exp == 19_usize {
524288_u128
} else if exp == 20_usize {
1048576_u128
} else if exp == 21_usize {
2097152_u128
} else if exp == 22_usize {
4194304_u128
} else if exp == 23_usize {
8388608_u128
} else if exp == 24_usize {
16777216_u128
} else if exp == 25_usize {
33554432_u128
} else if exp == 26_usize {
67108864_u128
} else if exp == 27_usize {
134217728_u128
} else if exp == 28_usize {
268435456_u128
} else if exp == 29_usize {
536870912_u128
} else if exp == 30_usize {
1073741824_u128
} else if exp == 31_usize {
2147483648_u128
} else if exp == 32_usize {
4294967296_u128
} else if exp == 33_usize {
8589934592_u128
} else if exp == 34_usize {
17179869184_u128
} else if exp == 35_usize {
34359738368_u128
} else if exp == 36_usize {
68719476736_u128
} else if exp == 37_usize {
137438953472_u128
} else if exp == 38_usize {
274877906944_u128
} else if exp == 39_usize {
549755813888_u128
} else if exp == 40_usize {
1099511627776_u128
} else if exp == 41_usize {
2199023255552_u128
} else if exp == 42_usize {
4398046511104_u128
} else if exp == 43_usize {
8796093022208_u128
} else if exp == 44_usize {
17592186044416_u128
} else if exp == 45_usize {
35184372088832_u128
} else if exp == 46_usize {
70368744177664_u128
} else if exp == 47_usize {
140737488355328_u128
} else if exp == 48_usize {
281474976710656_u128
} else if exp == 49_usize {
562949953421312_u128
} else if exp == 50_usize {
1125899906842624_u128
} else if exp == 51_usize {
2251799813685248_u128
} else if exp == 52_usize {
4503599627370496_u128
} else if exp == 53_usize {
9007199254740992_u128
} else if exp == 54_usize {
18014398509481984_u128
} else if exp == 55_usize {
36028797018963968_u128
} else if exp == 56_usize {
72057594037927936_u128
} else if exp == 57_usize {
144115188075855872_u128
} else if exp == 58_usize {
288230376151711744_u128
} else if exp == 59_usize {
576460752303423488_u128
} else if exp == 60_usize {
1152921504606846976_u128
} else if exp == 61_usize {
2305843009213693952_u128
} else if exp == 62_usize {
4611686018427387904_u128
} else if exp == 63_usize {
9223372036854775808_u128
} else if exp == 64_usize {
18446744073709551616_u128
} else if exp == 65_usize {
36893488147419103232_u128
} else if exp == 66_usize {
73786976294838206464_u128
} else if exp == 67_usize {
147573952589676412928_u128
} else if exp == 68_usize {
295147905179352825856_u128
} else if exp == 69_usize {
590295810358705651712_u128
} else if exp == 70_usize {
1180591620717411303424_u128
} else if exp == 71_usize {
2361183241434822606848_u128
} else if exp == 72_usize {
4722366482869645213696_u128
} else if exp == 73_usize {
9444732965739290427392_u128
} else if exp == 74_usize {
18889465931478580854784_u128
} else if exp == 75_usize {
37778931862957161709568_u128
} else if exp == 76_usize {
75557863725914323419136_u128
} else if exp == 77_usize {
151115727451828646838272_u128
} else if exp == 78_usize {
302231454903657293676544_u128
} else if exp == 79_usize {
604462909807314587353088_u128
} else if exp == 80_usize {
1208925819614629174706176_u128
} else if exp == 81_usize {
2417851639229258349412352_u128
} else if exp == 82_usize {
4835703278458516698824704_u128
} else if exp == 83_usize {
9671406556917033397649408_u128
} else if exp == 84_usize {
19342813113834066795298816_u128
} else if exp == 85_usize {
38685626227668133590597632_u128
} else if exp == 86_usize {
77371252455336267181195264_u128
} else if exp == 87_usize {
154742504910672534362390528_u128
} else if exp == 88_usize {
309485009821345068724781056_u128
} else if exp == 89_usize {
618970019642690137449562112_u128
} else if exp == 90_usize {
1237940039285380274899124224_u128
} else if exp == 91_usize {
2475880078570760549798248448_u128
} else if exp == 92_usize {
4951760157141521099596496896_u128
} else if exp == 93_usize {
9903520314283042199192993792_u128
} else if exp == 94_usize {
19807040628566084398385987584_u128
} else if exp == 95_usize {
39614081257132168796771975168_u128
} else if exp == 96_usize {
79228162514264337593543950336_u128
} else if exp == 97_usize {
158456325028528675187087900672_u128
} else if exp == 98_usize {
316912650057057350374175801344_u128
} else if exp == 99_usize {
633825300114114700748351602688_u128
} else if exp == 100_usize {
1267650600228229401496703205376_u128
} else if exp == 101_usize {
2535301200456458802993406410752_u128
} else if exp == 102_usize {
5070602400912917605986812821504_u128
} else if exp == 103_usize {
10141204801825835211973625643008_u128
} else if exp == 104_usize {
20282409603651670423947251286016_u128
} else if exp == 105_usize {
40564819207303340847894502572032_u128
} else if exp == 106_usize {
81129638414606681695789005144064_u128
} else if exp == 107_usize {
162259276829213363391578010288128_u128
} else if exp == 108_usize {
324518553658426726783156020576256_u128
} else if exp == 109_usize {
649037107316853453566312041152512_u128
} else if exp == 110_usize {
1298074214633706907132624082305024_u128
} else if exp == 111_usize {
2596148429267413814265248164610048_u128
} else if exp == 112_usize {
5192296858534827628530496329220096_u128
} else if exp == 113_usize {
10384593717069655257060992658440192_u128
} else if exp == 114_usize {
20769187434139310514121985316880384_u128
} else if exp == 115_usize {
41538374868278621028243970633760768_u128
} else if exp == 116_usize {
83076749736557242056487941267521536_u128
} else if exp == 117_usize {
166153499473114484112975882535043072_u128
} else if exp == 118_usize {
332306998946228968225951765070086144_u128
} else if exp == 119_usize {
664613997892457936451903530140172288_u128
} else if exp == 120_usize {
1329227995784915872903807060280344576_u128
} else if exp == 121_usize {
2658455991569831745807614120560689152_u128
} else if exp == 122_usize {
5316911983139663491615228241121378304_u128
} else if exp == 123_usize {
10633823966279326983230456482242756608_u128
} else if exp == 124_usize {
21267647932558653966460912964485513216_u128
} else if exp == 125_usize {
42535295865117307932921825928971026432_u128
} else if exp == 126_usize {
85070591730234615865843651857942052864_u128
} else {
170141183460469231731687303715884105728_u128
}
}
2 changes: 1 addition & 1 deletion packages/math/src/armstrong_number.cairo
View file
Original file line number Diff line number Diff line change
Expand Up @@ -15,7 +15,7 @@ pub fn is_armstrong_number(mut num: u128) -> bool {
}

let lastDigit = num % 10;
let sum = pow(lastDigit, digits);
let sum = pow(lastDigit, digits.into());
num = num / 10;
if sum > original_num {
break false;
Expand Down
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