perf: remove cmath library dependency

src/impl/algorithm.inc

@@ -58,15 +58,15 @@ struct md5_ctx {
 };
 
 /// MD5 data block index, input between 0 and 63.
-constexpr int K(int i) {
-    const int step[4] = {1, 5, 3, 7};
-    const int begin[4] = {0, 1, 5, 0};
+constexpr int K(const int i) {
+    constexpr int step[4] = {1, 5, 3, 7};
+    constexpr int begin[4] = {0, 1, 5, 0};
     return (begin[i >> 4] + step[i >> 4] * i) & 0b1111;
 }
 
 /// MD5 circular shift times, input between 0 and 63.
-constexpr int S(int i) {
-    const int shift[4][4] = {
+constexpr int S(const int i) {
+    constexpr int shift[4][4] = {
         {7, 12, 17, 22},
         {5, 9, 14, 20},
         {4, 11, 16, 23},
@@ -76,9 +76,9 @@ constexpr int S(int i) {
 }
 
 /// MD5 T-table constant, input between 0 and 63.
-constexpr uint32_t T(int i) {
-    auto val = ::md5::math::sin(i + 1);
-    return static_cast<uint32_t>(::std::abs(val) * 0x100000000);
+constexpr uint32_t T(const int i) {
+    const auto val = ::md5::math::sin(i + 1);
+    return static_cast<uint32_t>(::md5::math::abs(val) * 0x100000000);
 }
 
 } // namespace md5::impl

src/impl/sine.inc

@@ -1,12 +1,24 @@
-#pragma once
+/// This is the mathematical calculation implementation of MD5. It is not an
+/// efficient implementation and is only used for compile-time expansion
+/// calculations. In addition, in terms of accuracy, it is only used to ensure
+/// the MD5 T-table constants.
 
-#include <cmath>
+#pragma once
 
 namespace md5::math {
 
 constexpr double PI = 3.14159265358979323846264338327950;
 
-constexpr double pow(double x, int n) {
+constexpr double abs(const double x) {
+    return x < 0 ? -x : x;
+}
+
+constexpr double fmod(const double x, const double y) {
+    const auto tmp = static_cast<int64_t>(x / y);
+    return x - y * static_cast<double>(tmp);
+}
+
+constexpr double pow(const double x, const int n) {
     double res = 1;
     for (int i = 0; i < n; ++i) {
         res *= x;
@@ -14,7 +26,7 @@ constexpr double pow(double x, int n) {
     return res;
 }
 
-constexpr double factorial(int n) {
+constexpr double factorial(const int n) {
     double res = 1;
     for (int i = 2 ; i <= n ; ++i) {
         res *= i;
@@ -23,11 +35,11 @@ constexpr double factorial(int n) {
 }
 
 /// Calculate sin(x) value with Maclaurin series.
-constexpr double sin_core(double x) {
+constexpr double sin_core(const double x) {
     double res = x;
     for (int i = 1; i < 80; ++i) {
         const int n = i * 2 + 1;
-        const int sign = (i & 1) ? -1 : 1;
+        const int sign = i & 1 ? -1 : 1;
         res += sign * pow(x, n) / factorial(n);
     }
     return res;
@@ -35,14 +47,14 @@ constexpr double sin_core(double x) {
 
 /// Calculate the sin(x) value in radians.
 constexpr double sin(double x) {
-    x = ::std::fmod(x, 2 * PI); // -2PI < x < 2PI
+    x = fmod(x, 2 * PI); // -2PI < x < 2PI
 
-    if (::std::abs(x) > PI) {
-        x -= ((x > 0) ? 2 : -2) * PI; // -PI < x < PI
+    if (abs(x) > PI) {
+        x -= (x > 0 ? 2 : -2) * PI; // -PI < x < PI
     }
 
-    if (::std::abs(x) > PI / 2) {
-        x = ((x > 0) ? 1 : -1) * PI - x; // -PI / 2 < x < PI / 2
+    if (abs(x) > PI / 2) {
+        x = (x > 0 ? 1 : -1) * PI - x; // -PI / 2 < x < PI / 2
     }
     return sin_core(x); // closer to 0 for better accuracy
 }