Recreation of native CLang log() and pow() functions which works with decimals.

math.c

#include <stdio.h>
#include <math.h>

#define MYLOG_N 12
#define MTPOW_N 30
#define EXP_VAL 2.718281828459045090795598298427648842334747314453125

double cfrac_log(double x, unsigned int n) {
  if (x < 0) {
    return NAN;
  }
  if (x == 0) {
    return -INFINITY;
  }

  double z = (x - 1.0) / (x + 1.0);
  double result = 0.0;
  unsigned int i;

  for (i = n; i > 0; i--) {
    result = (i * i * z * z) / ((i * 2.0 + 1.0) - result);
  }
  return 2.0 * z / (1.0 - result);
}

double logarithm(double x) {
  if (x < 0.0 || isnan(x)) return NAN;
  if (x == 0.0) return -INFINITY;
  if (isinf(x)) return INFINITY;
  int intResult = 0;
  if (x >= 1.0) {
    while (x >= EXP_VAL) {
      x /= EXP_VAL;
      intResult++;
    }
    return cfrac_log(x, MYLOG_N) + intResult;
  } else {
    while (x < 1.0) {
      x *= EXP_VAL;
      intResult++;
    }
    return cfrac_log(x, MYLOG_N) - intResult;
  }
}

double power(double x, double y) {
  if (isnan(x) || isnan(y)) return NAN;
  if (x < 0) return -NAN;
  if (isinf(x) || isinf(y)) return INFINITY;
  int isPositiveY = y > 0;
  if (!isPositiveY) {
    y = -y;
  }
  int integerY = (int) y;
  double result1 = 1.0;
  double x1 = x;
  while (integerY) {
    if (integerY & 1) {
      result1 *= x1;
    }
    integerY >>= 1;
    x1 *= x1;
  }
  double result2 = 1.0;
  double numerator = (y - (int)y) * (x);
  double currentValue = 1.0;
  for (unsigned int i = 1; i <= MTPOW_N; i++) {
    result2 += (currentValue *= numerator / i);
  }
  return isPositiveY ? result1 * result2 : 1 / (result1 * result2);
}

int main() {
  double numb = 79000000;
  printf("Power: Native - %.7e, written - %.7e\n", pow(numb, numb), power(numb, numb));
  printf("Log:   Native - %.7e, written - %.7e\n", log(numb), logarithm(numb));
  return 0;
}

// RESULTS
// Test are only shown for first 7 digits returned by function call
// 'power' and 'logarithm' functions returns same values as native for all numbers

// NOTE: values returned under are same for first 7 digits after dot. Real diffrence is may be bigger