Lesson 211 +5 XP

<cmath> Functions Reference

Math lives in the <cmath> header. These functions take numeric arguments and hand back a number you can use immediately.

Almost all of these are double -> double: they take any double (or an int that upcasts) and return a double.

Function	Signature (as you'll call it)	Returns
`abs`	`abs(x)`	the absolute value of `x` (no sign)
`ceil`	`ceil(x)`	rounds `x` up to the next whole number
`floor`	`floor(x)`	rounds `x` down to the previous whole number
`round`	`round(x)`	rounds `x` to the nearest whole number (C++11)
`sqrt`	`sqrt(x)`	the square root of `x`
`pow`	`pow(x, y)`	`x` raised to the power `y`

Examples: ceil(2.1) is 3, floor(2.9) is 2, round(2.5) is 3, sqrt(16) is 4.

Function	Signature	Returns
`exp`	`exp(x)`	e raised to the power of `x` (inverse of natural log)
`log`	`log(x)`	natural logarithm (base e) of `x`
`log10`	`log10(x)`	base-10 logarithm of `x`

log gives base e; log10 gives base 10. Need a different base? Use log(x) / log(base).

Function	Signature	Returns
`sin`	`sin(x)`	the sine of `x`
`cos`	`cos(x)`	the cosine of `x`
`tan`	`tan(x)`	the tangent of `x`
`asin`	`asin(x)`	arc-sine (inverse sine), result in radians
`acos`	`acos(x)`	arc-cosine, result in radians
`atan`	`atan(x)`	arc-tangent, result in radians
`atan2`	`atan2(y, x)`	angle of the vector (y, x), handles the quadrant correctly

All angles in radians, not degrees. To convert: radians = degrees * 3.14159 / 180.

Function	Signature	Returns
`std::max`	`max(a, b)`	larger of the two
`std::min`	`min(a, b)`	smaller of the two

Heads-up: max and min live in the <algorithm> header, not in <cmath>. Include both when you need math plus min/max.

Math can error out: sqrt(-1) has no real value. These functions often return a special NaN (not a number) or inf for inputs without answers.
Watch the domain: log(0) is negative infinity; sqrt on a negative is not defined.
Overflows for huge numbers (exp(1000)) produce inf.
abs in <cmath> handles doubles; the same-named one in <cstdlib> handles integers - the compiler picks the overload.