Skip to content
New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Jump to bottom

Add sinus and cosinus for SD59x18 #230

Open
wants to merge 5 commits into
base: main
Choose a base branch
from
+238 −0
Open

Add sinus and cosinus for SD59x18 #230

Show file tree
Hide file tree
Changes from all commits
Commits
Show all changes
5 commits
Select commit Hold shift + click to select a range
2bd4cca
add sinus and cosinus for SD59x18
Amxx May 9, 2024
c286fe5
Update SD59x18.sol
Amxx May 9, 2024
eb9b811
lint
Amxx May 9, 2024
34a8357
add tests for sin & cos
Amxx May 10, 2024
961666b
linting
Amxx May 20, 2024
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
1 change: 1 addition & 0 deletions src/SD59x18.sol
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -26,3 +26,4 @@ import "./sd59x18/Errors.sol";
import "./sd59x18/Helpers.sol";
import "./sd59x18/Math.sol";
import "./sd59x18/ValueType.sol";
import { cos, sin } from "./sd59x18/Trigonometry.sol";
139 changes: 139 additions & 0 deletions src/sd59x18/Trigonometry.sol
View file
Open in desktop
Original file line number Diff line number Diff line change
@@ -0,0 +1,139 @@
// SPDX-License-Identifier: MIT
pragma solidity >=0.8.19;

import { SD59x18 } from "./ValueType.sol";
import { uUNIT } from "./Constants.sol";

// Pi / 2;
int256 constant uPI2 = 1_570796326794896619;

// Cordic renormalisation factor
int256 constant K = 607252935008881256;

// ATANXX is atan(2**-x) ie the angle (in rad) which tan is 2**-x
int256 constant ATAN00 = 785398163397448320;
int256 constant ATAN01 = 463647609000806080;
int256 constant ATAN02 = 244978663126864128;
int256 constant ATAN03 = 124354994546761440;
int256 constant ATAN04 = 62418809995957352;
int256 constant ATAN05 = 31239833430268276;
int256 constant ATAN06 = 15623728620476832;
int256 constant ATAN07 = 7812341060101111;
int256 constant ATAN08 = 3906230131966972;
int256 constant ATAN09 = 1953122516478819;
int256 constant ATAN10 = 976562189559320;
int256 constant ATAN11 = 488281211194898;
int256 constant ATAN12 = 244140620149362;
int256 constant ATAN13 = 122070311893670;
int256 constant ATAN14 = 61035156174209;
int256 constant ATAN15 = 30517578115526;
int256 constant ATAN16 = 15258789061316;
int256 constant ATAN17 = 7629394531102;
int256 constant ATAN18 = 3814697265606;
int256 constant ATAN19 = 1907348632810;
int256 constant ATAN20 = 953674316406;
int256 constant ATAN21 = 476837158203;
int256 constant ATAN22 = 238418579102;
int256 constant ATAN23 = 119209289551;
int256 constant ATAN24 = 59604644775;
int256 constant ATAN25 = 29802322388;
int256 constant ATAN26 = 14901161194;
int256 constant ATAN27 = 7450580597;
int256 constant ATAN28 = 3725290298;
int256 constant ATAN29 = 1862645149;
int256 constant ATAN30 = 931322575;
int256 constant ATAN31 = 465661287;
// int256 constant ATAN32 = 232830644;
// int256 constant ATAN33 = 116415322;
// int256 constant ATAN34 = 58207661;
// int256 constant ATAN35 = 29103830;
// int256 constant ATAN36 = 14551915;
// int256 constant ATAN37 = 7275958;
// int256 constant ATAN38 = 3637979;
// int256 constant ATAN39 = 1818989;
// int256 constant ATAN40 = 909495;
// int256 constant ATAN41 = 454747;
// int256 constant ATAN42 = 227374;
// int256 constant ATAN43 = 113687;
// int256 constant ATAN44 = 56843;
// int256 constant ATAN45 = 28422;
// int256 constant ATAN46 = 14211;
// int256 constant ATAN47 = 7105;
// int256 constant ATAN48 = 3553;
// int256 constant ATAN49 = 1776;
// int256 constant ATAN50 = 888;
// int256 constant ATAN51 = 444;
// int256 constant ATAN52 = 222;
// int256 constant ATAN53 = 111;
// int256 constant ATAN54 = 56;
// int256 constant ATAN55 = 28;
// int256 constant ATAN56 = 14;
// int256 constant ATAN57 = 7;
// int256 constant ATAN58 = 3;
// int256 constant ATAN59 = 2;
// int256 constant ATAN60 = 1;

function cordic_step(int256 x, int256 y, int256 z, int256 f, int256 t) pure returns (int256 x2, int256 y2, int256 z2, int256 f2) {
assembly {
let delta := sub(mul(sgt(z, 0), 2), 1) // z > 0 ? 1 : -1
x2 := sub(x, sdiv(mul(mul(delta, y), f), uUNIT)) // x - delta * y * f / uUNIT
y2 := add(y, sdiv(mul(mul(delta, x), f), uUNIT)) // y + delta * x * f / uUNIT
z2 := sub(z, mul(delta, t)) // z + delta * t
f2 := shr(1, f) // f / 2
}
}

function cordic(int256 t) pure returns (int256, int256) {
unchecked {
int256 q = ((t / uPI2) % 4 + 4) % 4;
int256 x = uUNIT;
int256 y = 0;
int256 z = t % uPI2;
int256 f = uUNIT;
(x, y, z, f) = cordic_step(x, y, z, f, ATAN00);
(x, y, z, f) = cordic_step(x, y, z, f, ATAN01);
(x, y, z, f) = cordic_step(x, y, z, f, ATAN02);
(x, y, z, f) = cordic_step(x, y, z, f, ATAN03);
(x, y, z, f) = cordic_step(x, y, z, f, ATAN04);
(x, y, z, f) = cordic_step(x, y, z, f, ATAN05);
(x, y, z, f) = cordic_step(x, y, z, f, ATAN06);
(x, y, z, f) = cordic_step(x, y, z, f, ATAN07);
(x, y, z, f) = cordic_step(x, y, z, f, ATAN08);
(x, y, z, f) = cordic_step(x, y, z, f, ATAN09);
(x, y, z, f) = cordic_step(x, y, z, f, ATAN10);
(x, y, z, f) = cordic_step(x, y, z, f, ATAN11);
(x, y, z, f) = cordic_step(x, y, z, f, ATAN12);
(x, y, z, f) = cordic_step(x, y, z, f, ATAN13);
(x, y, z, f) = cordic_step(x, y, z, f, ATAN14);
(x, y, z, f) = cordic_step(x, y, z, f, ATAN15);
(x, y, z, f) = cordic_step(x, y, z, f, ATAN16);
(x, y, z, f) = cordic_step(x, y, z, f, ATAN17);
(x, y, z, f) = cordic_step(x, y, z, f, ATAN18);
(x, y, z, f) = cordic_step(x, y, z, f, ATAN19);
(x, y, z, f) = cordic_step(x, y, z, f, ATAN20);
(x, y, z, f) = cordic_step(x, y, z, f, ATAN21);
(x, y, z, f) = cordic_step(x, y, z, f, ATAN22);
(x, y, z, f) = cordic_step(x, y, z, f, ATAN23);
(x, y, z, f) = cordic_step(x, y, z, f, ATAN24);
(x, y, z, f) = cordic_step(x, y, z, f, ATAN25);
(x, y, z, f) = cordic_step(x, y, z, f, ATAN26);
(x, y, z, f) = cordic_step(x, y, z, f, ATAN27);
(x, y, z, f) = cordic_step(x, y, z, f, ATAN28);
(x, y, z, f) = cordic_step(x, y, z, f, ATAN29);
(x, y, z, f) = cordic_step(x, y, z, f, ATAN30);
(x, y, z, f) = cordic_step(x, y, z, f, ATAN31);
x = x * K / uUNIT;
y = y * K / uUNIT;
return (q == 0) ? (x, y) : (q == 1) ? (-y, x) : (q == 2) ? (-x, -y) : (y, -x);
}
}

function cos(SD59x18 t) pure returns (SD59x18) {
(int256 x,) = cordic(SD59x18.unwrap(t));
return SD59x18.wrap(x);
}

function sin(SD59x18 t) pure returns (SD59x18) {
(, int256 y) = cordic(SD59x18.unwrap(t));
return SD59x18.wrap(y);
}
49 changes: 49 additions & 0 deletions test/unit/sd59x18/math/cos/cos.t.sol
View file
Open in desktop
Original file line number Diff line number Diff line change
@@ -0,0 +1,49 @@
// SPDX-License-Identifier: UNLICENSED
pragma solidity >=0.8.19 <0.9.0;

import { sd } from "src/sd59x18/Casting.sol";
import { PI, ZERO, uUNIT } from "src/sd59x18/Constants.sol";
import { sqrt } from "src/sd59x18/Math.sol";
import { cos } from "src/sd59x18/Trigonometry.sol";
import { SD59x18 } from "src/sd59x18/ValueType.sol";

import { SD59x18_Unit_Test } from "../../SD59x18.t.sol";

contract Cos_Unit_Test is SD59x18_Unit_Test {
function cos_Sets() internal returns (Set[] memory) {
delete sets;
SD59x18 SD1 = sd(1 * uUNIT);
SD59x18 SD2 = sd(2 * uUNIT);
SD59x18 SD3 = sd(3 * uUNIT);
SD59x18 SD4 = sd(4 * uUNIT);
SD59x18 SD5 = sd(5 * uUNIT);
SD59x18 SD6 = sd(6 * uUNIT);
sets.push(set({ x: -PI, expected: -SD1 })); // cos(-pi) = -1
sets.push(set({ x: -PI * SD5 / SD6, expected: -sqrt(SD3) / SD2 })); // cos(-5*pi/6) = -sqrt(3)/2
sets.push(set({ x: -PI * SD3 / SD4, expected: -sqrt(SD2) / SD2 })); // cos(-3*pi/4) = -sqrt(2)/2
sets.push(set({ x: -PI * SD2 / SD3, expected: -SD1 / SD2 })); // cos(-2*pi/3) = -1/2
sets.push(set({ x: -PI / SD2, expected: ZERO })); // cos(-pi/2) = 0
sets.push(set({ x: -PI / SD3, expected: SD1 / SD2 })); // cos(-pi/3) = 1/2
sets.push(set({ x: -PI / SD4, expected: sqrt(SD2) / SD2 })); // cos(-pi/4) = sqrt(2)/2
sets.push(set({ x: -PI / SD6, expected: sqrt(SD3) / SD2 })); // cos(-pi/6) = sqrt(3)/2
sets.push(set({ x: ZERO, expected: SD1 })); // cos(0) = 1
sets.push(set({ x: PI / SD6, expected: sqrt(SD3) / SD2 })); // cos(pi/6) = sqrt(3)/2
sets.push(set({ x: PI / SD4, expected: sqrt(SD2) / SD2 })); // cos(pi/4) = sqrt(2)/2
sets.push(set({ x: PI / SD3, expected: SD1 / SD2 })); // cos(pi/3) = 1/2
sets.push(set({ x: PI / SD2, expected: ZERO })); // cos(pi/2) = 0
sets.push(set({ x: PI * SD2 / SD3, expected: -SD1 / SD2 })); // cos(2*pi/3) = -1/2
sets.push(set({ x: PI * SD3 / SD4, expected: -sqrt(SD2) / SD2 })); // cos(3*pi/4) = -sqrt(2)/2
sets.push(set({ x: PI * SD5 / SD6, expected: -sqrt(SD3) / SD2 })); // cos(5*pi/6) = -sqrt(3)/2
sets.push(set({ x: PI, expected: -SD1 })); // cos(pi) = -1
return sets;
}

function test_Cos() external parameterizedTest(cos_Sets()) {
assertApproxEqAbs(
cos(s.x).intoInt256(),
s.expected.intoInt256(),
0.000_000_001 ether, // 8 correct decimals
"SD59x18 cos"
);
}
}
49 changes: 49 additions & 0 deletions test/unit/sd59x18/math/sin/sin.t.sol
View file
Open in desktop
Original file line number Diff line number Diff line change
@@ -0,0 +1,49 @@
// SPDX-License-Identifier: UNLICENSED
pragma solidity >=0.8.19 <0.9.0;

import { sd } from "src/sd59x18/Casting.sol";
import { PI, ZERO, uUNIT } from "src/sd59x18/Constants.sol";
import { sqrt } from "src/sd59x18/Math.sol";
import { sin } from "src/sd59x18/Trigonometry.sol";
import { SD59x18 } from "src/sd59x18/ValueType.sol";

import { SD59x18_Unit_Test } from "../../SD59x18.t.sol";

contract Sin_Unit_Test is SD59x18_Unit_Test {
function sin_Sets() internal returns (Set[] memory) {
delete sets;
SD59x18 SD1 = sd(1 * uUNIT);
SD59x18 SD2 = sd(2 * uUNIT);
SD59x18 SD3 = sd(3 * uUNIT);
SD59x18 SD4 = sd(4 * uUNIT);
SD59x18 SD5 = sd(5 * uUNIT);
SD59x18 SD6 = sd(6 * uUNIT);
sets.push(set({ x: -PI, expected: ZERO })); // sin(-pi) = 0
sets.push(set({ x: -PI * SD5 / SD6, expected: -SD1 / SD2 })); // sin(-5*pi/6) = -1/2
sets.push(set({ x: -PI * SD3 / SD4, expected: -sqrt(SD2) / SD2 })); // sin(-3*pi/4) = -sqrt(2)/2
sets.push(set({ x: -PI * SD2 / SD3, expected: -sqrt(SD3) / SD2 })); // sin(-2*pi/3) = -sqrt(3)/2
sets.push(set({ x: -PI / SD2, expected: -SD1 })); // sin(-pi/2) = -1
sets.push(set({ x: -PI / SD3, expected: -sqrt(SD3) / SD2 })); // sin(-pi/3) = -sqrt(3)/2
sets.push(set({ x: -PI / SD4, expected: -sqrt(SD2) / SD2 })); // sin(-pi/4) = -sqrt(2)/2
sets.push(set({ x: -PI / SD6, expected: -SD1 / SD2 })); // sin(-pi/6) = -1/2
sets.push(set({ x: ZERO, expected: ZERO })); // sin(0) = 0
sets.push(set({ x: PI / SD6, expected: SD1 / SD2 })); // sin(pi/6) = 1/2
sets.push(set({ x: PI / SD4, expected: sqrt(SD2) / SD2 })); // sin(pi/4) = sqrt(2)/2
sets.push(set({ x: PI / SD3, expected: sqrt(SD3) / SD2 })); // sin(pi/3) = sqrt(3)/2
sets.push(set({ x: PI / SD2, expected: SD1 })); // sin(pi/2) = 1
sets.push(set({ x: PI * SD2 / SD3, expected: sqrt(SD3) / SD2 })); // sin(2*pi/3) = sqrt(3)/2
sets.push(set({ x: PI * SD3 / SD4, expected: sqrt(SD2) / SD2 })); // sin(3*pi/4) = sqrt(2)/2
sets.push(set({ x: PI * SD5 / SD6, expected: SD1 / SD2 })); // sin(5*pi/6) = 1/2
sets.push(set({ x: PI, expected: ZERO })); // sin(pi) = 0
return sets;
}

function test_Sin() external parameterizedTest(sin_Sets()) {
assertApproxEqAbs(
sin(s.x).intoInt256(),
s.expected.intoInt256(),
0.000_000_001 ether, // 8 correct decimals
"SD59x18 sin"
);
}
}