How to make math logarithm functions in C99?

Question

I'm finally back at building my functions, which is what I'm doing before making the actual BPML language. In Part 3 - Math, I want to make some logarithm functions.

I never knew what logarithm functions were at the very beginning, but as I went deeper, I learned it and made this:

float log_num(int num) {
    int mult;
    float result = 0;
    for (int i = 0; ; i++) {
        mult = 10 ^ i;
        if (mult >= num) {
            result = i;
            break;
        }
    }
    return result;
}

log_num only supports int and float and double will have their separate ones.

Now I got 2 problems with this function:

When I tried to run it and use 100 as the number in the function, the result should've been 2.00, but it gave me 1.00.
Since the value to be returned is a float, I want the function to actually give me different values if it is not a power of 10. An example of it is 2 = 0.30102999566398119521373889472449.

Q: How do I fix problem 1 and how do I make the function work as how I explained in problem 2?

I want to make the function from scratch and not relying on other functions.

How do you expect to compute the logarithm of a number without ever *using* said number? — EOF, Oct 18 '20 at 12:44
Since the only statements in the code that affect the value of `result` are `float result = 0;` and `result = 1;`, how do you think the function could ever return 2? — Eric Postpischil, Oct 18 '20 at 12:44
`^` is not an exponential operator in C. It is an XOR operator. — Eric Postpischil, Oct 18 '20 at 12:47
Let us [continue this discussion in chat](https://chat.stackoverflow.com/rooms/223239/discussion-between-bpml-and-eric-postpischil). — BMPL, Oct 18 '20 at 12:49
[log10()](https://en.cppreference.com/w/c/numeric/math/log10) is not an option? I mean, if you implement your functions in C you could use the C math lib. (which is part of the C standard libraries). — Scheff's Cat, Oct 18 '20 at 14:46
see [Building a logarithm function in C without using float type](https://stackoverflow.com/a/42108287/2521214) for some ideas ... — Spektre, Oct 19 '20 at 08:05

chux - Reinstate Monica · Accepted Answer · 2020-10-18T15:22:42.033

Q: How do I fix problem 1 ... ?

10 ^ i is 10 exclusive-or'ed with i. It is not 10ⁱ.

To find the integer portion of log₁₀(num)

int i_portion = 0;
if (num <= 0) Handle_elsewhere();
else {
  int i_portion = 0;
  int n = num;
  while (n >= 10) {
    n /= 10;
    i_portion++;
  } 
  printf("%d\n", i_portion);
}

Q: ... and how do I make the function work as how I explained in problem 2?

Below is a quick solution since C99:

#include <math.h>
float log_num(int num) {
  return log10f(num);
}

To code without <math.h> is fairly broad. For efficient construction, we need design parameters.

First, be clear about base. The standard log() is base e, not base 10 as the question implies.

Corner/Error handling: How do you want to handle negative inputs? Log_{any positive base}(0) is usually returned as -∞. For finite positive values, no range issues. What should be returned for +∞, perhaps +∞? What should be returned for NaN, perhaps NaN?

Accuracy/precision: Do you want the best result or willing to given up accuracy for speed or small code foot-print? Why return float versus the more common double?

Performance: simply code that is of poor run-time performance OK? Just code per Logarithm Calculation. Since the goal includes my_log_i(int), my_log_f(float), my_log_d(double), for now, just code my_log_d(double) and have the the others call it.

Portability - how portable?

Sure we can code up a simply float my_log_10(int), but without the design details, the result would be lacking in many ways.

How to make math logarithm functions in C99?

1 Answers1

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