Question

I am trying to multiply two floats as follows:

float number1 = 321.12;
float number2 = 345.34;
float rexsult = number1 * number2;

The result I want to see is 110895.582, but when I run the code it just gives me 110896. Most of the time I’m having this issue. Any calculator gives me the exact result with all decimals. How can I achive that result?

edit : It’s C code. I’m using XCode iOS simulator.

Answer 1

There’s a lot of rounding going on.

float a = 321.12; // this number will be rounded
float b = 345.34; // this number will also be rounded
float r = a * b;  // and this number will be rounded too
printf("%.15f\n", r);

I get 110895.578125000000000 after the three separate roundings.

1. If you want more than 6 decimal digits’ worth of precision, you will have to use double and not float. (Note that I said “decimal digits’ worth”, because you don’t get decimal digits, you get binary.) As it stands, 1/2 ULP of error (a worst-case bound for a perfectly rounded result) is about 0.004.

2. If you want exactly rounded decimal numbers, you will have to use a specialized decimal library for such a task. A double has more than enough precision for scientists, but if you work with money everything has to be 100% exact. No floating point numbers for money.

Unlike integers, floating point numbers take some real work before you can get accustomed to their pitfalls. See “What Every Computer Scientist Should Know About Floating-Point Arithmetic“, which is the classic introduction to the topic.

Edit: Actually, I’m not sure that the code rounds three times. It might round five times, since the constants for a and b might be rounded first to double-precision and then to single-precision when they are stored. But I don’t know the rules of this part of C very well.