How to Implement an Integer Logarithm Function in C ?

Integer Logarithm Function in C

In C , the standard libraries provide a log function that operates on floating-point numbers. However, when working with indices in binary trees or other scenarios where integer logarithmic operations are required, using the floating-point log may not be appropriate.

One specific concern is that the floating-point log method can return fractional values for certain edge elements (those with values of 2^n). Consequently, using log in such calculations could lead to incorrect results when attempting to determine the level of an index in a binary tree.

To avoid this issue, an integer-based logarithm function can be utilized. On x86 and x86-64 platforms, a built-in instruction called bsr (bit scan reverse) can be used to achieve this functionality. This instruction returns the position of the highest set bit in an unsigned integer.

Here is an example of how to implement an integer log2 function using bsr in C or C :

#include <stdint.h>
static inline uint32_t log2(const uint32_t x) {
  uint32_t y;
  asm ( "\tbsr %1, %0\n"
      : "=r"(y)
      : "r" (x)
  );
  return y;
}

This function can be used instead of the floating-point log to ensure accurate results when performing integer logarithmic operations. By utilizing the bsr instruction, which returns the position of the highest set bit, it effectively performs the same operation as log2().

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