rem

(rem number divisor)

Returns the remainder of number divided by divisor using truncated division, so a nonzero result always takes the sign of the dividend. It is the companion of truncate. Use mod instead when you want the result to follow the sign of the divisor.

A zero float result is 0.0, and -0.0 only when the dividend is -0.0 and the divisor is positive. rem is the second value of truncate -- number - divisor*quotient for a quotient that is an exact integer -- so the sign of a zero falls out of that subtraction instead of being copied from the dividend.

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. Where truncate has no quotient, rem has no remainder and signals as truncate does: a zero divisor, exact or float, is a division-by-zero ((rem 7.5 0), (rem 7.5 0.0)), and a NaN or infinite dividend (or a NaN divisor) reports the non-finite rounding first.