Contract Source Code:

/**
 *Submitted for verification at Etherscan.io on 2021-08-18
*/

// SPDX-License-Identifier: AGPL-3.0-or-later

// Copyright (C) 2020 Maker Ecosystem Growth Holdings, INC.
//
// This program is free software: you can redistribute it and/or modify
// it under the terms of the GNU Affero General Public License as published
// by the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.
//
// This program is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
// GNU Affero General Public License for more details.
//
// You should have received a copy of the GNU Affero General Public License
// along with this program.  If not, see <https://www.gnu.org/licenses/>.

pragma solidity >=0.6.12;

interface Abacus {
    // 1st arg: initial price               [ray]
    // 2nd arg: seconds since auction start [seconds]
    // returns: current auction price       [ray]
    function price(uint256, uint256) external view returns (uint256);
}

contract LinearDecrease is Abacus {

    // --- Auth ---
    mapping (address => uint256) public wards;
    function rely(address usr) external auth { wards[usr] = 1; emit Rely(usr); }
    function deny(address usr) external auth { wards[usr] = 0; emit Deny(usr); }
    modifier auth {
        require(wards[msg.sender] == 1, "LinearDecrease/not-authorized");
        _;
    }

    // --- Data ---
    uint256 public tau;  // Seconds after auction start when the price reaches zero [seconds]

    // --- Events ---
    event Rely(address indexed usr);
    event Deny(address indexed usr);

    event File(bytes32 indexed what, uint256 data);

    // --- Init ---
    constructor() public {
        wards[msg.sender] = 1;
        emit Rely(msg.sender);
    }

    // --- Administration ---
    function file(bytes32 what, uint256 data) external auth {
        if (what ==  "tau") tau = data;
        else revert("LinearDecrease/file-unrecognized-param");
        emit File(what, data);
    }

    // --- Math ---
    uint256 constant RAY = 10 ** 27;
    function add(uint256 x, uint256 y) internal pure returns (uint256 z) {
        require((z = x + y) >= x);
    }
    function mul(uint256 x, uint256 y) internal pure returns (uint256 z) {
        require(y == 0 || (z = x * y) / y == x);
    }
    function rmul(uint256 x, uint256 y) internal pure returns (uint256 z) {
        z = x * y;
        require(y == 0 || z / y == x);
        z = z / RAY;
    }

    // Price calculation when price is decreased linearly in proportion to time:
    // tau: The number of seconds after the start of the auction where the price will hit 0
    // top: Initial price
    // dur: current seconds since the start of the auction
    //
    // Returns y = top * ((tau - dur) / tau)
    //
    // Note the internal call to mul multiples by RAY, thereby ensuring that the rmul calculation
    // which utilizes top and tau (RAY values) is also a RAY value.
    function price(uint256 top, uint256 dur) override external view returns (uint256) {
        if (dur >= tau) return 0;
        return rmul(top, mul(tau - dur, RAY) / tau);
    }
}

contract StairstepExponentialDecrease is Abacus {

    // --- Auth ---
    mapping (address => uint256) public wards;
    function rely(address usr) external auth { wards[usr] = 1; emit Rely(usr); }
    function deny(address usr) external auth { wards[usr] = 0; emit Deny(usr); }
    modifier auth {
        require(wards[msg.sender] == 1, "StairstepExponentialDecrease/not-authorized");
        _;
    }

    // --- Data ---
    uint256 public step; // Length of time between price drops [seconds]
    uint256 public cut;  // Per-step multiplicative factor     [ray]

    // --- Events ---
    event Rely(address indexed usr);
    event Deny(address indexed usr);

    event File(bytes32 indexed what, uint256 data);

    // --- Init ---
    // @notice: `cut` and `step` values must be correctly set for
    //     this contract to return a valid price
    constructor() public {
        wards[msg.sender] = 1;
        emit Rely(msg.sender);
    }

    // --- Administration ---
    function file(bytes32 what, uint256 data) external auth {
        if      (what ==  "cut") require((cut = data) <= RAY, "StairstepExponentialDecrease/cut-gt-RAY");
        else if (what == "step") step = data;
        else revert("StairstepExponentialDecrease/file-unrecognized-param");
        emit File(what, data);
    }

    // --- Math ---
    uint256 constant RAY = 10 ** 27;
    function rmul(uint256 x, uint256 y) internal pure returns (uint256 z) {
        z = x * y;
        require(y == 0 || z / y == x);
        z = z / RAY;
    }
    // optimized version from dss PR #78
    function rpow(uint256 x, uint256 n, uint256 b) internal pure returns (uint256 z) {
        assembly {
            switch n case 0 { z := b }
            default {
                switch x case 0 { z := 0 }
                default {
                    switch mod(n, 2) case 0 { z := b } default { z := x }
                    let half := div(b, 2)  // for rounding.
                    for { n := div(n, 2) } n { n := div(n,2) } {
                        let xx := mul(x, x)
                        if shr(128, x) { revert(0,0) }
                        let xxRound := add(xx, half)
                        if lt(xxRound, xx) { revert(0,0) }
                        x := div(xxRound, b)
                        if mod(n,2) {
                            let zx := mul(z, x)
                            if and(iszero(iszero(x)), iszero(eq(div(zx, x), z))) { revert(0,0) }
                            let zxRound := add(zx, half)
                            if lt(zxRound, zx) { revert(0,0) }
                            z := div(zxRound, b)
                        }
                    }
                }
            }
        }
    }

    // top: initial price
    // dur: seconds since the auction has started
    // step: seconds between a price drop
    // cut: cut encodes the percentage to decrease per step.
    //   For efficiency, the values is set as (1 - (% value / 100)) * RAY
    //   So, for a 1% decrease per step, cut would be (1 - 0.01) * RAY
    //
    // returns: top * (cut ^ dur)
    //
    //
    function price(uint256 top, uint256 dur) override external view returns (uint256) {
        return rmul(top, rpow(cut, dur / step, RAY));
    }
}

// While an equivalent function can be obtained by setting step = 1 in StairstepExponentialDecrease,
// this continous (i.e. per-second) exponential decrease has be implemented as it is more gas-efficient
// than using the stairstep version with step = 1 (primarily due to 1 fewer SLOAD per price calculation).
contract ExponentialDecrease is Abacus {

    // --- Auth ---
    mapping (address => uint256) public wards;
    function rely(address usr) external auth { wards[usr] = 1; emit Rely(usr); }
    function deny(address usr) external auth { wards[usr] = 0; emit Deny(usr); }
    modifier auth {
        require(wards[msg.sender] == 1, "ExponentialDecrease/not-authorized");
        _;
    }

    // --- Data ---
    uint256 public cut;  // Per-second multiplicative factor [ray]

    // --- Events ---
    event Rely(address indexed usr);
    event Deny(address indexed usr);

    event File(bytes32 indexed what, uint256 data);

    // --- Init ---
    // @notice: `cut` value must be correctly set for
    //     this contract to return a valid price
    constructor() public {
        wards[msg.sender] = 1;
        emit Rely(msg.sender);
    }

    // --- Administration ---
    function file(bytes32 what, uint256 data) external auth {
        if      (what ==  "cut") require((cut = data) <= RAY, "ExponentialDecrease/cut-gt-RAY");
        else revert("ExponentialDecrease/file-unrecognized-param");
        emit File(what, data);
    }

    // --- Math ---
    uint256 constant RAY = 10 ** 27;
    function rmul(uint256 x, uint256 y) internal pure returns (uint256 z) {
        z = x * y;
        require(y == 0 || z / y == x);
        z = z / RAY;
    }
    // optimized version from dss PR #78
    function rpow(uint256 x, uint256 n, uint256 b) internal pure returns (uint256 z) {
        assembly {
            switch n case 0 { z := b }
            default {
                switch x case 0 { z := 0 }
                default {
                    switch mod(n, 2) case 0 { z := b } default { z := x }
                    let half := div(b, 2)  // for rounding.
                    for { n := div(n, 2) } n { n := div(n,2) } {
                        let xx := mul(x, x)
                        if shr(128, x) { revert(0,0) }
                        let xxRound := add(xx, half)
                        if lt(xxRound, xx) { revert(0,0) }
                        x := div(xxRound, b)
                        if mod(n,2) {
                            let zx := mul(z, x)
                            if and(iszero(iszero(x)), iszero(eq(div(zx, x), z))) { revert(0,0) }
                            let zxRound := add(zx, half)
                            if lt(zxRound, zx) { revert(0,0) }
                            z := div(zxRound, b)
                        }
                    }
                }
            }
        }
    }

    // top: initial price
    // dur: seconds since the auction has started
    // cut: cut encodes the percentage to decrease per second.
    //   For efficiency, the values is set as (1 - (% value / 100)) * RAY
    //   So, for a 1% decrease per second, cut would be (1 - 0.01) * RAY
    //
    // returns: top * (cut ^ dur)
    //
    function price(uint256 top, uint256 dur) override external view returns (uint256) {
        return rmul(top, rpow(cut, dur, RAY));
    }
}

/// DssDeploy.sol

// Copyright (C) 2018-2020 Maker Ecosystem Growth Holdings, INC.

// This program is free software: you can redistribute it and/or modify
// it under the terms of the GNU Affero General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.
//
// This program is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
// GNU Affero General Public License for more details.
//
// You should have received a copy of the GNU Affero General Public License
// along with this program.  If not, see <https://www.gnu.org/licenses/>.

/* pragma solidity >=0.5.12; */

contract CalcFab {
    function newLinearDecrease(address owner) public returns (LinearDecrease calc) {
        calc = new LinearDecrease();
        calc.rely(owner);
        calc.deny(address(this));
    }

    function newStairstepExponentialDecrease(address owner) public returns (StairstepExponentialDecrease calc) {
        calc = new StairstepExponentialDecrease();
        calc.rely(owner);
        calc.deny(address(this));
    }

    function newExponentialDecrease(address owner) public returns (ExponentialDecrease calc) {
        calc = new ExponentialDecrease();
        calc.rely(owner);
        calc.deny(address(this));
    }
}