c++ 中的三角函数不会返回正确的值

Question

cout << sinf(M_PI) << ", " << cosf(M_PI/2);

returns -8.74228e-08, -4.37114e-08

what is the smartest way to approach this problem?

I already found out that as the fewer decimal places I round PI to, the closer the functions returns the correct result. See here:

    float pi = 3.14;
    cout << sinf(pi) << ", " << cosf(pi/2);

returns:

0.00159255, 0.000796274

But is there a way to maximize the accuracy without eliminating the decimal places?

Answer 1

The number 8.74228e-08 is less than a tenth of a millionth; this is a much smaller number than 0.00159255. Single precision floats only give you about 7 significant digits of precision so this is essentially zero as far as a 32-bit float is concerned.

Generally you should not expect floating point numbers to have exact values. It is not uncommon for floating point numbers to have a small amount of error when compared to the true value of a number to begin with (as some numbers, even with non-repeating decimal expansions, cannot be represented exactly with floating point numbers) and pi obviously can't be represented exactly in decimal form at all.

If you want to display floating point numbers and not get scientific notation in your output, use std::setprecision . When working with floating point numbers, never test them for equality against exact values. Test that the absolute value of their difference from exact values is less than a tolerance, usually referred to as epsilon.