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• library Math
•    - function max(uint256 a, uint256 b)
•    - function min(uint256 a, uint256 b)
•    - function average(uint256 a, uint256 b ...
•    - function ceilDiv(uint256 a, uint256 b ...
•    - function mulDiv(
•    - function mulDiv(
•    - function sqrt(uint256 a)
•    - function sqrt(uint256 a, Rounding rou ...
•    - function log2(uint256 value)
•    - function log2(uint256 value, Rounding ...
•    - function log10(uint256 value)
•    - function log10(uint256 value, Roundin ...
•    - function log256(uint256 value)
•    - function log256(uint256 value, Roundi ...
• library Strings
•    - function toString(uint256 value)
•    - function toHexString(uint256 value)
•    - function toHexString(uint256 value, u ...
•    - function toHexString(address addr)
• interface ITerraforms
•    - function tokenSupplementalData(uint t ...
•    - function tokenHeightmapIndices(uint t ...
•    - function tokenTerrainValues(uint toke ...
•    - function tokenToPlacement(uint)
•    - function seed()
• interface ITerraformsData
•    - function resourceLevel(uint placement ...
•    - function characterSet(uint placement, ...
•    - function tokenTerrainValues(uint toke ...
•  contract TerraformsDataHelper *
•    - function chromaString(uint256 tokenId ...
•    - function resourceString(uint256 token ...
•    - function biomeString(uint256 tokenId)
•    - function zoneNameString(uint256 token ...
•    - function zoneColorsString(uint256 tok ...
•    - function heightmapIndicesString(uint2 ...
•    - function terrainValuesString(uint256 ...
•    - function toString(int256 value)

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/**
 *Submitted for verification at Etherscan.io on 2023-02-18
*/

// SPDX-License-Identifier: MIT
pragma solidity 0.8.12;

library Math {
    enum Rounding {
        Down, // Toward negative infinity
        Up, // Toward infinity
        Zero // Toward zero
    }

    /**
     * @dev Returns the largest of two numbers.
     */
    function max(uint256 a, uint256 b) internal pure returns (uint256) {
        return a > b ? a : b;
    }

    /**
     * @dev Returns the smallest of two numbers.
     */
    function min(uint256 a, uint256 b) internal pure returns (uint256) {
        return a < b ? a : b;
    }

    /**
     * @dev Returns the average of two numbers. The result is rounded towards
     * zero.
     */
    function average(uint256 a, uint256 b) internal pure returns (uint256) {
        // (a + b) / 2 can overflow.
        return (a & b) + (a ^ b) / 2;
    }

    /**
     * @dev Returns the ceiling of the division of two numbers.
     *
     * This differs from standard division with `/` in that it rounds up instead
     * of rounding down.
     */
    function ceilDiv(uint256 a, uint256 b) internal pure returns (uint256) {
        // (a + b - 1) / b can overflow on addition, so we distribute.
        return a == 0 ? 0 : (a - 1) / b + 1;
    }

    /**
     * @notice Calculates floor(x * y / denominator) with full precision. Throws if result overflows a uint256 or denominator == 0
     * @dev Original credit to Remco Bloemen under MIT license (https://xn--2-umb.com/21/muldiv)
     * with further edits by Uniswap Labs also under MIT license.
     */
    function mulDiv(
        uint256 x,
        uint256 y,
        uint256 denominator
    ) internal pure returns (uint256 result) {
        unchecked {
            // 512-bit multiply [prod1 prod0] = x * y. Compute the product mod 2^256 and mod 2^256 - 1, then use
            // use the Chinese Remainder Theorem to reconstruct the 512 bit result. The result is stored in two 256
            // variables such that product = prod1 * 2^256 + prod0.
            uint256 prod0; // Least significant 256 bits of the product
            uint256 prod1; // Most significant 256 bits of the product
            assembly {
                let mm := mulmod(x, y, not(0))
                prod0 := mul(x, y)
                prod1 := sub(sub(mm, prod0), lt(mm, prod0))
            }

            // Handle non-overflow cases, 256 by 256 division.
            if (prod1 == 0) {
                return prod0 / denominator;
            }

            // Make sure the result is less than 2^256. Also prevents denominator == 0.
            require(denominator > prod1);

            ///////////////////////////////////////////////
            // 512 by 256 division.
            ///////////////////////////////////////////////

            // Make division exact by subtracting the remainder from [prod1 prod0].
            uint256 remainder;
            assembly {
                // Compute remainder using mulmod.
                remainder := mulmod(x, y, denominator)

                // Subtract 256 bit number from 512 bit number.
                prod1 := sub(prod1, gt(remainder, prod0))
                prod0 := sub(prod0, remainder)
            }

            // Factor powers of two out of denominator and compute largest power of two divisor of denominator. Always >= 1.
            // See https://cs.stackexchange.com/q/138556/92363.

            // Does not overflow because the denominator cannot be zero at this stage in the function.
            uint256 twos = denominator & (~denominator + 1);
            assembly {
                // Divide denominator by twos.
                denominator := div(denominator, twos)

                // Divide [prod1 prod0] by twos.
                prod0 := div(prod0, twos)

                // Flip twos such that it is 2^256 / twos. If twos is zero, then it becomes one.
                twos := add(div(sub(0, twos), twos), 1)
            }

            // Shift in bits from prod1 into prod0.
            prod0 |= prod1 * twos;

            // Invert denominator mod 2^256. Now that denominator is an odd number, it has an inverse modulo 2^256 such
            // that denominator * inv = 1 mod 2^256. Compute the inverse by starting with a seed that is correct for
            // four bits. That is, denominator * inv = 1 mod 2^4.
            uint256 inverse = (3 * denominator) ^ 2;

            // Use the Newton-Raphson iteration to improve the precision. Thanks to Hensel's lifting lemma, this also works
            // in modular arithmetic, doubling the correct bits in each step.
            inverse *= 2 - denominator * inverse; // inverse mod 2^8
            inverse *= 2 - denominator * inverse; // inverse mod 2^16
            inverse *= 2 - denominator * inverse; // inverse mod 2^32
            inverse *= 2 - denominator * inverse; // inverse mod 2^64
            inverse *= 2 - denominator * inverse; // inverse mod 2^128
            inverse *= 2 - denominator * inverse; // inverse mod 2^256

            // Because the division is now exact we can divide by multiplying with the modular inverse of denominator.
            // This will give us the correct result modulo 2^256. Since the preconditions guarantee that the outcome is
            // less than 2^256, this is the final result. We don't need to compute the high bits of the result and prod1
            // is no longer required.
            result = prod0 * inverse;
            return result;
        }
    }

    /**
     * @notice Calculates x * y / denominator with full precision, following the selected rounding direction.
     */
    function mulDiv(
        uint256 x,
        uint256 y,
        uint256 denominator,
        Rounding rounding
    ) internal pure returns (uint256) {
        uint256 result = mulDiv(x, y, denominator);
        if (rounding == Rounding.Up && mulmod(x, y, denominator) > 0) {
            result += 1;
        }
        return result;
    }

    /**
     * @dev Returns the square root of a number. If the number is not a perfect square, the value is rounded down.
     *
     * Inspired by Henry S. Warren, Jr.'s "Hacker's Delight" (Chapter 11).
     */
    function sqrt(uint256 a) internal pure returns (uint256) {
        if (a == 0) {
            return 0;
        }

        // For our first guess, we get the biggest power of 2 which is smaller than the square root of the target.
        //
        // We know that the "msb" (most significant bit) of our target number `a` is a power of 2 such that we have
        // `msb(a) <= a < 2*msb(a)`. This value can be written `msb(a)=2**k` with `k=log2(a)`.
        //
        // This can be rewritten `2**log2(a) <= a < 2**(log2(a) + 1)`
        // → `sqrt(2**k) <= sqrt(a) < sqrt(2**(k+1))`
        // → `2**(k/2) <= sqrt(a) < 2**((k+1)/2) <= 2**(k/2 + 1)`
        //
        // Consequently, `2**(log2(a) / 2)` is a good first approximation of `sqrt(a)` with at least 1 correct bit.
        uint256 result = 1 << (log2(a) >> 1);

        // At this point `result` is an estimation with one bit of precision. We know the true value is a uint128,
        // since it is the square root of a uint256. Newton's method converges quadratically (precision doubles at
        // every iteration). We thus need at most 7 iteration to turn our partial result with one bit of precision
        // into the expected uint128 result.
        unchecked {
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            return min(result, a / result);
        }
    }

    /**
     * @notice Calculates sqrt(a), following the selected rounding direction.
     */
    function sqrt(uint256 a, Rounding rounding) internal pure returns (uint256) {
        unchecked {
            uint256 result = sqrt(a);
            return result + (rounding == Rounding.Up && result * result < a ? 1 : 0);
        }
    }

    /**
     * @dev Return the log in base 2, rounded down, of a positive value.
     * Returns 0 if given 0.
     */
    function log2(uint256 value) internal pure returns (uint256) {
        uint256 result = 0;
        unchecked {
            if (value >> 128 > 0) {
                value >>= 128;
                result += 128;
            }
            if (value >> 64 > 0) {
                value >>= 64;
                result += 64;
            }
            if (value >> 32 > 0) {
                value >>= 32;
                result += 32;
            }
            if (value >> 16 > 0) {
                value >>= 16;
                result += 16;
            }
            if (value >> 8 > 0) {
                value >>= 8;
                result += 8;
            }
            if (value >> 4 > 0) {
                value >>= 4;
                result += 4;
            }
            if (value >> 2 > 0) {
                value >>= 2;
                result += 2;
            }
            if (value >> 1 > 0) {
                result += 1;
            }
        }
        return result;
    }

    /**
     * @dev Return the log in base 2, following the selected rounding direction, of a positive value.
     * Returns 0 if given 0.
     */
    function log2(uint256 value, Rounding rounding) internal pure returns (uint256) {
        unchecked {
            uint256 result = log2(value);
            return result + (rounding == Rounding.Up && 1 << result < value ? 1 : 0);
        }
    }

    /**
     * @dev Return the log in base 10, rounded down, of a positive value.
     * Returns 0 if given 0.
     */
    function log10(uint256 value) internal pure returns (uint256) {
        uint256 result = 0;
        unchecked {
            if (value >= 10**64) {
                value /= 10**64;
                result += 64;
            }
            if (value >= 10**32) {
                value /= 10**32;
                result += 32;
            }
            if (value >= 10**16) {
                value /= 10**16;
                result += 16;
            }
            if (value >= 10**8) {
                value /= 10**8;
                result += 8;
            }
            if (value >= 10**4) {
                value /= 10**4;
                result += 4;
            }
            if (value >= 10**2) {
                value /= 10**2;
                result += 2;
            }
            if (value >= 10**1) {
                result += 1;
            }
        }
        return result;
    }

    /**
     * @dev Return the log in base 10, following the selected rounding direction, of a positive value.
     * Returns 0 if given 0.
     */
    function log10(uint256 value, Rounding rounding) internal pure returns (uint256) {
        unchecked {
            uint256 result = log10(value);
            return result + (rounding == Rounding.Up && 10**result < value ? 1 : 0);
        }
    }

    /**
     * @dev Return the log in base 256, rounded down, of a positive value.
     * Returns 0 if given 0.
     *
     * Adding one to the result gives the number of pairs of hex symbols needed to represent `value` as a hex string.
     */
    function log256(uint256 value) internal pure returns (uint256) {
        uint256 result = 0;
        unchecked {
            if (value >> 128 > 0) {
                value >>= 128;
                result += 16;
            }
            if (value >> 64 > 0) {
                value >>= 64;
                result += 8;
            }
            if (value >> 32 > 0) {
                value >>= 32;
                result += 4;
            }
            if (value >> 16 > 0) {
                value >>= 16;
                result += 2;
            }
            if (value >> 8 > 0) {
                result += 1;
            }
        }
        return result;
    }

    /**
     * @dev Return the log in base 10, following the selected rounding direction, of a positive value.
     * Returns 0 if given 0.
     */
    function log256(uint256 value, Rounding rounding) internal pure returns (uint256) {
        unchecked {
            uint256 result = log256(value);
            return result + (rounding == Rounding.Up && 1 << (result * 8) < value ? 1 : 0);
        }
    }
}

/**
 * @dev String operations.
 */
library Strings {
    bytes16 private constant _SYMBOLS = "0123456789abcdef";
    uint8 private constant _ADDRESS_LENGTH = 20;

    /**
     * @dev Converts a `uint256` to its ASCII `string` decimal representation.
     */
    function toString(uint256 value) internal pure returns (string memory) {
        unchecked {
            uint256 length = Math.log10(value) + 1;
            string memory buffer = new string(length);
            uint256 ptr;
            /// @solidity memory-safe-assembly
            assembly {
                ptr := add(buffer, add(32, length))
            }
            while (true) {
                ptr--;
                /// @solidity memory-safe-assembly
                assembly {
                    mstore8(ptr, byte(mod(value, 10), _SYMBOLS))
                }
                value /= 10;
                if (value == 0) break;
            }
            return buffer;
        }
    }

    /**
     * @dev Converts a `uint256` to its ASCII `string` hexadecimal representation.
     */
    function toHexString(uint256 value) internal pure returns (string memory) {
        unchecked {
            return toHexString(value, Math.log256(value) + 1);
        }
    }

    /**
     * @dev Converts a `uint256` to its ASCII `string` hexadecimal representation with fixed length.
     */
    function toHexString(uint256 value, uint256 length) internal pure returns (string memory) {
        bytes memory buffer = new bytes(2 * length + 2);
        buffer[0] = "0";
        buffer[1] = "x";
        for (uint256 i = 2 * length + 1; i > 1; --i) {
            buffer[i] = _SYMBOLS[value & 0xf];
            value >>= 4;
        }
        require(value == 0, "Strings: hex length insufficient");
        return string(buffer);
    }

    /**
     * @dev Converts an `address` with fixed length of 20 bytes to its not checksummed ASCII `string` hexadecimal representation.
     */
    function toHexString(address addr) internal pure returns (string memory) {
        return toHexString(uint256(uint160(addr)), _ADDRESS_LENGTH);
    }
}

struct TokenData {
    uint tokenId;
    uint level;
    uint xCoordinate;
    uint yCoordinate;
    int elevation;
    int structureSpaceX;
    int structureSpaceY;
    int structureSpaceZ;
    string zoneName;
    string[10] zoneColors;
    string[9] characterSet;
}

interface ITerraforms {
  function tokenSupplementalData(uint tokenId) 
    external 
    view
    returns (TokenData memory); 

  function tokenHeightmapIndices(uint tokenId) 
    external 
    view 
    returns (uint[32][32] memory);

  function tokenTerrainValues(uint tokenId) 
    external 
    view 
    returns (int[32][32] memory);

  function tokenToPlacement(uint) 
    external 
    view 
    returns (uint);

  function seed() 
    external 
    view 
    returns (uint);
}

interface ITerraformsData {
  function resourceLevel(uint placement, uint seed) 
    external 
    view
    returns (uint); 

  function characterSet(uint placement, uint seed) 
    external 
    view 
    returns (
      string[9] memory charset,
      uint font, 
      uint fontsize,
      uint index
      );

  function tokenTerrainValues(uint tokenId) 
    external 
    view 
    returns (int[32][32] memory);
}

/// @title Terraforms by Mathcastles Data Helper Contract (not affiliated with Mathcastles) 
/// @author yeetljuice
/// @notice Helper contract to get Terraform data in string format for use in other on-chain generated scripts 
contract TerraformsDataHelper {

  ITerraforms terraforms = ITerraforms(0x4E1f41613c9084FdB9E34E11fAE9412427480e56);
  ITerraformsData terraformsData = ITerraformsData(0xA5aFC9fE76a28fB12C60954Ed6e2e5f8ceF64Ff2);

  function chromaString(uint256 tokenId) public view returns (string memory) {
    uint placement = terraforms.tokenToPlacement(tokenId);
    uint seed = terraforms.seed(); 

    if (uint(keccak256(abi.encodePacked(placement, seed, "activation"))) % 10_000 >= 9_990) {
      return "Plague";
    }

    uint sorter = uint(keccak256(abi.encodePacked(placement, seed)));

    if (sorter % 100 < 60){
      return "Flow";
    } else if (sorter % 100 < 90) {
      return "Pulse";
    } else {
      return "Hyper";
    }
  }

  function resourceString(uint256 tokenId) public view returns (string memory) {
    return Strings.toString(terraformsData.resourceLevel(terraforms.tokenToPlacement(tokenId), terraforms.seed()));
  }

  function biomeString(uint256 tokenId) public view returns (string memory) {
    (,,,uint biome) = terraformsData.characterSet(terraforms.tokenToPlacement(tokenId), terraforms.seed());
    return Strings.toString(biome);
  }

  function zoneNameString(uint256 tokenId) public view returns (string memory) {
    return terraforms.tokenSupplementalData(tokenId).zoneName;
  }

  function zoneColorsString(uint256 tokenId) public view returns (string memory) {
    string[10] memory zc = terraforms.tokenSupplementalData(tokenId).zoneColors;
    string memory s = '["';    
    for (uint i; i < 9; i++) {
        s = string.concat(s, zc[i], '","');
        }
    s = string.concat(s, zc[9], '"]');
    return s;
  }

  function heightmapIndicesString(uint256 tokenId) public view returns (string memory) {
    uint[32][32] memory _arr = terraforms.tokenHeightmapIndices(tokenId);
    uint row;
    uint col;
    string memory rs;
    string memory cs = "[";    
    for (row; row < 32; row++) {        
        rs = "[";
        for (col = 0; col < 31; col++) {
          rs = string.concat(rs, Strings.toString(uint(_arr[row][col])), ",");
        }
        rs = string.concat(rs, Strings.toString(uint(_arr[row][31])), "]");
        if (row < 31) {cs = string.concat(cs, rs, ",");} else {cs = string.concat(cs, rs);}
    }
    cs = string.concat(cs, "]");
    return cs;
  }

  function terrainValuesString(uint256 tokenId) public view returns (string memory) {
    int[32][32] memory _arr = terraforms.tokenTerrainValues(tokenId);
    uint row;
    uint col;
    string memory rs;
    string memory cs = "[";    
    for (row; row < 32; row++) {         
        rs = "[";
        for (col = 0; col < 31; col++) {
          rs = string.concat(rs, toString(_arr[row][col]), ",");
        }
        rs = string.concat(rs, toString(_arr[row][31]), "]");
        if (row < 31) {cs = string.concat(cs, rs, ",");} else {cs = string.concat(cs, rs);}
    }
    cs = string.concat(cs, "]");
    return cs;
  }

  function toString(int256 value) internal pure returns (string memory) {
    if (value < 0) {
      return string.concat("-", Strings.toString(uint256(value*-1)));
    }
    return Strings.toString(uint256(value));
  }
}

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[{"inputs":[{"internalType":"uint256","name":"tokenId","type":"uint256"}],"name":"biomeString","outputs":[{"internalType":"string","name":"","type":"string"}],"stateMutability":"view","type":"function"},{"inputs":[{"internalType":"uint256","name":"tokenId","type":"uint256"}],"name":"chromaString","outputs":[{"internalType":"string","name":"","type":"string"}],"stateMutability":"view","type":"function"},{"inputs":[{"internalType":"uint256","name":"tokenId","type":"uint256"}],"name":"heightmapIndicesString","outputs":[{"internalType":"string","name":"","type":"string"}],"stateMutability":"view","type":"function"},{"inputs":[{"internalType":"uint256","name":"tokenId","type":"uint256"}],"name":"resourceString","outputs":[{"internalType":"string","name":"","type":"string"}],"stateMutability":"view","type":"function"},{"inputs":[{"internalType":"uint256","name":"tokenId","type":"uint256"}],"name":"terrainValuesString","outputs":[{"internalType":"string","name":"","type":"string"}],"stateMutability":"view","type":"function"},{"inputs":[{"internalType":"uint256","name":"tokenId","type":"uint256"}],"name":"zoneColorsString","outputs":[{"internalType":"string","name":"","type":"string"}],"stateMutability":"view","type":"function"},{"inputs":[{"internalType":"uint256","name":"tokenId","type":"uint256"}],"name":"zoneNameString","outputs":[{"internalType":"string","name":"","type":"string"}],"stateMutability":"view","type":"function"}]

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