Fastest implementation of log2(int) and log2(float) in C#

Fastest implementation of log2(int) and log2(float) in C#

In C#, you can use the BitOperations class to calculate the log base 2 of an integer. For floating point values, you can use the Math class.

Here's an example of how to calculate the log base 2 of an integer using the BitOperations class:

int log2 = BitOperations.Log2(value);

In this example, value is the integer value you want to calculate the log base 2 of, and log2 is the result.

For floating point values, you can use the Math class and the log function:

float log2 = (float)Math.Log(value, 2);

In this example, value is the floating point value you want to calculate the log base 2 of, and log2 is the result.

Note that the BitOperations.Log2 method was introduced in .NET 5.0, so if you're using an earlier version of .NET, you can use the following implementation:

int log2 = (int)Math.Log(value, 2);

This implementation uses the Math.Log function to calculate the natural logarithm of the value, and then divides the result by the natural logarithm of 2 to get the log base 2.

Examples

  1. "C# Integer Log2 with Bit Manipulation"

    • Code Implementation:
      int log2Int = 31 - (int)System.Numerics.BitOperations.LeadingZeroCount(value);
    • Description: Utilizes bit manipulation to find the integer logarithm base 2, exploiting the leading zero count.

  2. "C# Integer Log2 with Bitwise Shift"

    • Code Implementation:
      int log2Int = 31 - (int)Math.Floor(Math.Log2(value));
    • Description: Uses bitwise shift and mathematical operations to calculate the integer logarithm base 2.

  3. "C# Integer Log2 with Lookup Table"

    • Code Implementation:
      int[] log2Table = new int[32]; for (int i = 0; i < log2Table.Length; i++) log2Table[1 << i] = i; int log2Int = log2Table[value];
    • Description: Precomputes a lookup table for powers of 2 and retrieves the log2 using the table.

  4. "C# Integer Log2 with Binary Search"

    • Code Implementation:
      int log2Int = Array.BinarySearch(powersOfTwoArray, value);
    • Description: Utilizes binary search on a precomputed array of powers of 2 to find the integer logarithm base 2.

Floating-Point Log2:

  1. "C# Float Log2 with Math.Log"

    • Code Implementation:
      float log2Float = (float)Math.Log(value, 2);
    • Description: Uses Math.Log to calculate the logarithm base 2 for floating-point numbers.

  2. "C# Float Log2 with Bitwise Manipulation"

    • Code Implementation:
      int bits = BitConverter.SingleToInt32Bits(value); int exponent = ((bits >> 23) & 0xFF) - 127; float log2Float = exponent;
    • Description: Extracts the exponent from the IEEE 754 representation to calculate the logarithm base 2 for floating-point numbers.

  3. "C# Float Log2 with Lookup Table"

    • Code Implementation:
      float[] log2Table = new float[256]; for (int i = 0; i < log2Table.Length; i++) log2Table[i] = (float)Math.Log(i, 2); int bits = BitConverter.SingleToInt32Bits(value); int index = (bits >> 23) & 0xFF; float log2Float = log2Table[index];
    • Description: Precomputes a lookup table for values between 0 and 1 and retrieves the log2 using the table.

  4. "C# Float Log2 with Polynomial Approximation"

    • Code Implementation:
      float log2Float = PolynomialApproximation(value); // Polynomial approximation function static float PolynomialApproximation(float x) { float log2 = x * (1.19209290f - 0.70523040f * x); return log2; }
    • Description: Employs a polynomial approximation for faster computation of the logarithm base 2 for floating-point numbers.

  5. "C# Float Log2 with Integer Conversion"

    • Code Implementation:
      int bits = BitConverter.SingleToInt32Bits(value); int exponent = ((bits >> 23) & 0xFF) - 127; float log2Float = exponent;
    • Description: Converts the exponent part of the IEEE 754 representation to calculate the logarithm base 2 for floating-point numbers.

  6. "C# Float Log2 with Assembly Intrinsics"

    • Code Implementation:
      float log2Float = System.Runtime.Intrinsics.X86.Sse41.RoundToPositiveInfinity( System.Runtime.Intrinsics.X86.Sse2.Log(value)) * System.Runtime.Intrinsics.X86.Sse41.RoundToPositiveInfinity( System.Runtime.Intrinsics.X86.Sse2.Reciprocal(System.Runtime.Intrinsics.X86.Sse2.Log(System.Runtime.Intrinsics.X86.Sse2.SetAllVector128(2.0f))));
    • Description: Uses assembly intrinsics for SIMD operations to accelerate the calculation of the logarithm base 2 for floating-point numbers.

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