arithmetic
Computers as overgrown calculators.
Simple arithmetic.
Addition and subtraction work intuitively, using + and -. Multiplication is performed using * and division using /. The one principle to remember is 'precedence'. When you combine arithmetic calculations in one statement, it can lead to unexpected results.
2 + 3 * 4 = 14
If you were expecting 20, you are reading the arithmetic as you would enter it into a calculator. The compiler uses precedence rules to resolve the ambiguity in the example calculation. Multiplication and division have the higher precedence, so the compiler actually performs 3*4 before the 2 + in the example. To make sure your calculation works as expected, use parentheses:
(2 + 3) * 4 = 20
2 + (3 * 4) = 14
Modulus
Many computerised systems use numerical codes to represent real-world products. To prevent simple typing errors causing the selection of the wrong product, these codes are not sequential. Instead, the first or final digit of the code is calculated from the rest of the digits to create a checksum. Validation of this checksum is possibly the most frequent arithmetic calculation because it is used every time a barcode is scanned. An important part of the calculation is usually the modulus operator which calculates the remainder of a division. Instead of calculating a floating point number to express the fraction, the modulus operator returns the remainder.
12 % 3 = 0; // (12 / 3 = 4.00000 or 4 with no remainder)
13 % 3 = 1; // (13 / 3 = 4.33333 or 4 with a remainder of 1)
Mathematical functions
The standard library provides functions for angles, logs, exponentials, powers and square roots.
Function Description
sin(x),asin(x),sinh(x) sine, arcsine, hyperbolic sine of value x
cos(x),acos(x),cosh(x) cosine, arccosine, hyperbolic cosine of x
tan(x),atan(x),tanh(x) tangent, arctangent, hyperbolic tangent
log(x), log10(x) natural base or base-10 logarithm of x
exp(x) e to the power of x
pow(x,y) x to the power y
sqrt(x) square root of x
Remember that most of these functions will return a float value and that sqrt(-1) is not valid in simple arithmetic!
Number and text conversions
printf can convert digits into strings and C also provides functions to convert char string[] = "100"; into int digit = 100;.
char string[] = "100";
int digit = atoi(string);
atoi() converts an alphanumeric string to an integer. Other examples include:
float fraction = atof(string);
long number = atol(string);
string = itoa(100);
string = ftoa(100.00);
string = ltoa(number);
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