// SPDX-License-Identifier: MIT // // ES-DE // MathUtil.cpp // // Math utility functions. // The GLM library headers are also included from here. // #define MD5_MAX_FILE_CHUNK_SIZE 32768 #if defined(_MSC_VER) // MSVC compiler. #define _CRT_SECURE_NO_WARNINGS #endif #include "utils/MathUtil.h" #include "utils/FileSystemUtil.h" #include "utils/StringUtil.h" #include #include #include #include namespace Utils { namespace Math { float smoothStep(const float left, const float right, const float value) { const float x {glm::clamp((value - left) / (right - left), 0.0f, 1.0f)}; return x * x * (3.0f - (2.0f * x)); } float smootherStep(const float left, const float right, const float value) { const float x {glm::clamp((value - left) / (right - left), 0.0f, 1.0f)}; return x * x * x * (x * ((x * 6.0f) - 15.0f) + 10.0f); } float loop(const float delayTime, const float scrollTime, const float currentTime, const float scrollLength) { if (currentTime < delayTime) { // Wait. return 0.0f; } else if (currentTime < (delayTime + scrollTime)) { // Interpolate from 0 to scrollLength. const float fraction {(currentTime - delayTime) / scrollTime}; return glm::mix(0.0f, scrollLength, fraction); } // And back to waiting. return 0.0f; } float bounce(const float delayTime, const float scrollTime, const float currentTime, const float scrollLength) { if (currentTime < delayTime) { // Wait. return 0.0f; } else if (currentTime < (delayTime + scrollTime)) { // Interpolate from 0 to scrollLength. const float fraction {(currentTime - delayTime) / scrollTime}; return glm::mix(0.0f, scrollLength, smootherStep(0.0f, 1.0f, fraction)); } else if (currentTime < (delayTime + scrollTime + delayTime)) { // Wait some more. return scrollLength; } else if (currentTime < (delayTime + scrollTime + delayTime + scrollTime)) { // Interpolate back from scrollLength to 0. const float fraction {(currentTime - delayTime - scrollTime - delayTime) / scrollTime}; return glm::mix(scrollLength, 0.0f, smootherStep(0.0f, 1.0f, fraction)); } // And back to waiting. return 0.0f; } std::string md5Hash(const std::string& hashArg, bool isFilePath) { // This function deviates from the md5sum command in that it will return a blank // hash rather than d41d8cd98f00b204e9800998ecf8427e if the input is null. This is // done so it can be easily detected in the calling function if no data was hashed. if (hashArg == "") return ""; // Data that didn't fit in last 64 byte chunk. unsigned char buffer[64] {}; // 64 bit counter for the number of bits (low, high). unsigned int count[2] {}; // Digest so far. unsigned int state[4]; // RFC 1321, 3.3: Step 3. state[0] = 0x67452301; state[1] = 0xefcdab89; state[2] = 0x98badcfe; state[3] = 0x10325476; if (isFilePath) { if (Utils::FileSystem::isDirectory(hashArg)) return ""; #if defined(_WIN64) std::ifstream inputFile {Utils::String::stringToWideString(hashArg).c_str(), std::ios::binary}; #else std::ifstream inputFile {hashArg, std::ios::binary}; #endif if (inputFile.fail()) { inputFile.close(); return ""; } inputFile.seekg(0, std::ios::end); long fileLength {static_cast(inputFile.tellg())}; inputFile.seekg(0, std::ios::beg); std::vector chunk(MD5_MAX_FILE_CHUNK_SIZE); long bytesRead {0}; // Process in chunks so we don't need to load the whole file into memory at once. while (bytesRead < fileLength) { const int chunkSize {static_cast( fileLength - bytesRead > MD5_MAX_FILE_CHUNK_SIZE ? MD5_MAX_FILE_CHUNK_SIZE : fileLength - bytesRead)}; inputFile.read(&chunk[0], chunkSize); md5Update(reinterpret_cast(&chunk[0]), chunkSize, state, count, buffer); bytesRead += chunkSize; } inputFile.close(); if (bytesRead == 0) return ""; } else { md5Update(reinterpret_cast(hashArg.c_str()), static_cast(hashArg.length()), state, count, buffer); } static unsigned char padding[64] {0x80, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}; // Encodes unsigned int input into unsigned char output. Assumes len is a multiple of 4. auto encodeFunc = [](unsigned char output[], const unsigned int input[], unsigned int len) { for (unsigned int i {0}, j {0}; j < len; ++i, j += 4) { output[j] = input[i] & 0xff; output[j + 1] = (input[i] >> 8) & 0xff; output[j + 2] = (input[i] >> 16) & 0xff; output[j + 3] = (input[i] >> 24) & 0xff; } }; // Save number of bits. unsigned char bits[8]; encodeFunc(bits, count, 8); // Pad out to 56 mod 64. unsigned int index {count[0] / 8 % 64}; unsigned int padLen {(index < 56) ? (56 - index) : (120 - index)}; md5Update(padding, padLen, state, count, buffer); // Append length (before padding). md5Update(bits, 8, state, count, buffer); // The result. unsigned char digest[16]; // Store state in digest. encodeFunc(digest, state, 16); // Convert to hex string. char buf[33]; for (int i {0}; i < 16; ++i) snprintf(buf + i * 2, 16, "%02x", digest[i]); buf[32] = 0; return std::string(buf); } void md5Update(const unsigned char input[], unsigned int length, unsigned int (&state)[4], unsigned int (&count)[2], unsigned char (&buffer)[64]) { // Compute number of bytes (mod 64). unsigned int index {count[0] / 8 % 64}; // Update number of bits. if ((count[0] += (length << 3)) < (length << 3)) ++count[1]; count[1] += (length >> 29); // Number of bytes we need to fill in buffer. unsigned int firstpart {64 - index}; unsigned int i {0}; // Encodes unsigned int input into unsigned char output. Assumes len is a multiple of 4. // Transform as many times as possible. if (length >= firstpart) { // Fill buffer first, then transform. memcpy(&buffer[index], input, firstpart); md5Transform(buffer, state); // Transform chunks of 64 (64 bytes). for (i = firstpart; i + 64 <= length; i += 64) md5Transform(&input[i], state); index = 0; } else i = 0; // Buffer remaining input. memcpy(&buffer[index], &input[i], length - i); } void md5Transform(const unsigned char block[64], unsigned int (&state)[4]) { unsigned int a {state[0]}; unsigned int b {state[1]}; unsigned int c {state[2]}; unsigned int d {state[3]}; unsigned int x[16] {}; // Encodes unsigned int input into unsigned char output. Assumes len is a multiple of 4. for (unsigned int i {0}, j {0}; j < 64; ++i, j += 4) x[i] = (static_cast(block[j])) | ((static_cast(block[j + 1])) << 8) | ((static_cast(block[j + 2])) << 16) | ((static_cast(block[j + 3])) << 24); const unsigned int S11 {7}; const unsigned int S12 {12}; const unsigned int S13 {17}; const unsigned int S14 {22}; const unsigned int S21 {5}; const unsigned int S22 {9}; const unsigned int S23 {14}; const unsigned int S24 {20}; const unsigned int S31 {4}; const unsigned int S32 {11}; const unsigned int S33 {16}; const unsigned int S34 {23}; const unsigned int S41 {6}; const unsigned int S42 {10}; const unsigned int S43 {15}; const unsigned int S44 {21}; // fFunc, gFunc, hFunc and iFunc are basic MD5 functions. auto fFunc = [](unsigned int x, unsigned int y, unsigned int z) { return (x & y) | (~x & z); }; auto gFunc = [](unsigned int x, unsigned int y, unsigned int z) { return (x & z) | (y & ~z); }; auto hFunc = [](unsigned int x, unsigned int y, unsigned int z) { return x ^ y ^ z; }; auto iFunc = [](unsigned int x, unsigned int y, unsigned int z) { return y ^ (x | ~z); }; auto rotateLeftFunc = [](unsigned int x, int n) { return (x << n) | (x >> (32 - n)); }; // ffFunc, ggFunc, hhFunc, and iiFunc transformations for rounds 1, 2, 3, and 4. // Rotation is separate from addition to prevent recomputation. auto ffFunc = [fFunc, rotateLeftFunc](unsigned int& a, unsigned int b, unsigned int c, unsigned int d, unsigned int x, unsigned int s, unsigned int ac) { a = rotateLeftFunc(a + fFunc(b, c, d) + x + ac, s) + b; }; auto ggFunc = [gFunc, rotateLeftFunc](unsigned int& a, unsigned int b, unsigned int c, unsigned int d, unsigned int x, unsigned int s, unsigned int ac) { a = rotateLeftFunc(a + gFunc(b, c, d) + x + ac, s) + b; }; auto hhFunc = [hFunc, rotateLeftFunc](unsigned int& a, unsigned int b, unsigned int c, unsigned int d, unsigned int x, unsigned int s, unsigned int ac) { a = rotateLeftFunc(a + hFunc(b, c, d) + x + ac, s) + b; }; auto iiFunc = [iFunc, rotateLeftFunc](unsigned int& a, unsigned int b, unsigned int c, unsigned int d, unsigned int x, unsigned int s, unsigned int ac) { a = rotateLeftFunc(a + iFunc(b, c, d) + x + ac, s) + b; }; // Round 1. ffFunc(a, b, c, d, x[0], S11, 0xd76aa478); // 1 ffFunc(d, a, b, c, x[1], S12, 0xe8c7b756); // 2 ffFunc(c, d, a, b, x[2], S13, 0x242070db); // 3 ffFunc(b, c, d, a, x[3], S14, 0xc1bdceee); // 4 ffFunc(a, b, c, d, x[4], S11, 0xf57c0faf); // 5 ffFunc(d, a, b, c, x[5], S12, 0x4787c62a); // 6 ffFunc(c, d, a, b, x[6], S13, 0xa8304613); // 7 ffFunc(b, c, d, a, x[7], S14, 0xfd469501); // 8 ffFunc(a, b, c, d, x[8], S11, 0x698098d8); // 9 ffFunc(d, a, b, c, x[9], S12, 0x8b44f7af); // 10 ffFunc(c, d, a, b, x[10], S13, 0xffff5bb1); // 11 ffFunc(b, c, d, a, x[11], S14, 0x895cd7be); // 12 ffFunc(a, b, c, d, x[12], S11, 0x6b901122); // 13 ffFunc(d, a, b, c, x[13], S12, 0xfd987193); // 14 ffFunc(c, d, a, b, x[14], S13, 0xa679438e); // 15 ffFunc(b, c, d, a, x[15], S14, 0x49b40821); // 16 // Round 2. ggFunc(a, b, c, d, x[1], S21, 0xf61e2562); // 17 ggFunc(d, a, b, c, x[6], S22, 0xc040b340); // 18 ggFunc(c, d, a, b, x[11], S23, 0x265e5a51); // 19 ggFunc(b, c, d, a, x[0], S24, 0xe9b6c7aa); // 20 ggFunc(a, b, c, d, x[5], S21, 0xd62f105d); // 21 ggFunc(d, a, b, c, x[10], S22, 0x2441453); // 22 ggFunc(c, d, a, b, x[15], S23, 0xd8a1e681); // 23 ggFunc(b, c, d, a, x[4], S24, 0xe7d3fbc8); // 24 ggFunc(a, b, c, d, x[9], S21, 0x21e1cde6); // 25 ggFunc(d, a, b, c, x[14], S22, 0xc33707d6); // 26 ggFunc(c, d, a, b, x[3], S23, 0xf4d50d87); // 27 ggFunc(b, c, d, a, x[8], S24, 0x455a14ed); // 28 ggFunc(a, b, c, d, x[13], S21, 0xa9e3e905); // 29 ggFunc(d, a, b, c, x[2], S22, 0xfcefa3f8); // 30 ggFunc(c, d, a, b, x[7], S23, 0x676f02d9); // 31 ggFunc(b, c, d, a, x[12], S24, 0x8d2a4c8a); // 32 // Round 3. hhFunc(a, b, c, d, x[5], S31, 0xfffa3942); // 33 hhFunc(d, a, b, c, x[8], S32, 0x8771f681); // 34 hhFunc(c, d, a, b, x[11], S33, 0x6d9d6122); // 35 hhFunc(b, c, d, a, x[14], S34, 0xfde5380c); // 36 hhFunc(a, b, c, d, x[1], S31, 0xa4beea44); // 37 hhFunc(d, a, b, c, x[4], S32, 0x4bdecfa9); // 38 hhFunc(c, d, a, b, x[7], S33, 0xf6bb4b60); // 39 hhFunc(b, c, d, a, x[10], S34, 0xbebfbc70); // 40 hhFunc(a, b, c, d, x[13], S31, 0x289b7ec6); // 41 hhFunc(d, a, b, c, x[0], S32, 0xeaa127fa); // 42 hhFunc(c, d, a, b, x[3], S33, 0xd4ef3085); // 43 hhFunc(b, c, d, a, x[6], S34, 0x4881d05); // 44 hhFunc(a, b, c, d, x[9], S31, 0xd9d4d039); // 45 hhFunc(d, a, b, c, x[12], S32, 0xe6db99e5); // 46 hhFunc(c, d, a, b, x[15], S33, 0x1fa27cf8); // 47 hhFunc(b, c, d, a, x[2], S34, 0xc4ac5665); // 48 // Round 4. iiFunc(a, b, c, d, x[0], S41, 0xf4292244); // 49 iiFunc(d, a, b, c, x[7], S42, 0x432aff97); // 50 iiFunc(c, d, a, b, x[14], S43, 0xab9423a7); // 51 iiFunc(b, c, d, a, x[5], S44, 0xfc93a039); // 52 iiFunc(a, b, c, d, x[12], S41, 0x655b59c3); // 53 iiFunc(d, a, b, c, x[3], S42, 0x8f0ccc92); // 54 iiFunc(c, d, a, b, x[10], S43, 0xffeff47d); // 55 iiFunc(b, c, d, a, x[1], S44, 0x85845dd1); // 56 iiFunc(a, b, c, d, x[8], S41, 0x6fa87e4f); // 57 iiFunc(d, a, b, c, x[15], S42, 0xfe2ce6e0); // 58 iiFunc(c, d, a, b, x[6], S43, 0xa3014314); // 59 iiFunc(b, c, d, a, x[13], S44, 0x4e0811a1); // 60 iiFunc(a, b, c, d, x[4], S41, 0xf7537e82); // 61 iiFunc(d, a, b, c, x[11], S42, 0xbd3af235); // 62 iiFunc(c, d, a, b, x[2], S43, 0x2ad7d2bb); // 63 iiFunc(b, c, d, a, x[9], S44, 0xeb86d391); // 64 state[0] += a; state[1] += b; state[2] += c; state[3] += d; } } // namespace Math } // namespace Utils