mod

(mod number divisor)

Returns the remainder of number divided by divisor using floored division, so a nonzero result always takes the sign of the divisor. This makes it the companion of floor. Use rem instead when you want the result to follow the sign of the dividend.

A zero float result is 0.0, and -0.0 only when the dividend is -0.0 and the divisor is positive. mod is the second value of floor -- number - divisor*quotient for a quotient that is an exact integer -- so the sign of a zero falls out of that subtraction rather than following the divisor.

The float result is the exact remainder at every magnitude: number - divisor*quotient is the value of that expression in exact arithmetic, not its floating-point evaluation, so a dividend past 2^53 still gets its true remainder. An infinite divisor leaves the quotient at zero, so the result is the dividend -- or the divisor's infinity when the two signs differ, which is what the floored quotient of -1 gives. Where floor has no quotient, mod has no remainder and signals as floor does: a zero divisor, exact or float, is a division-by-zero ((mod 7.5 0), (mod 7.5 0.0)), and a NaN or infinite dividend (or a NaN divisor) reports the non-finite rounding first.