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.Dd March 30, 2008 .Dt REMAINDER 3 .Os .Sh NAME .Nm remainder , .Nm remainderf , .Nm remainderl , .Nm remquo , .Nm remquof , .Nm remquol .Nd minimal residue functions .Sh LIBRARY .Lb libm .Sh SYNOPSIS n math.h .Ft double .Fn remainder "double x" "double y" .Ft float .Fn remainderf "float x" "float y" .Ft long double .Fn remainderl "long double x" "long double y" .Ft double .Fn remquo "double x" "double y" "int *quo" .Ft float .Fn remquof "float x" "float y" "int *quo" .Ft long double .Fn remquol "long double x" "long double y" "int *quo" .Sh DESCRIPTION .Fn remainder , .Fn remainderf , .Fn remainderl , .Fn remquo , .Fn remquof , and .Fn remquol return the remainder .Fa r := .Fa x - .Fa n\(**y where .Fa n is the integer nearest the exact value of k -words .Fa x Ns / Ns Fa y ; .Ek moreover if
f \*(Ba Fa n - .Sm off .Fa x No / Fa y No \*(Ba .Sm on = 1/2 then .Fa n is even. Consequently the remainder is computed exactly and .Sm off
f \*(Ba Fa r No \*(Ba .Sm on \*(Le .Sm off
f \*(Ba Fa y No \*(Ba/2 . .Sm on But attempting to take the remainder when .Fa y is 0 or .Fa x is \*(Pm\*(If is an invalid operation that produces a \*(Na.
p The .Fn remquo , .Fn remquof , and .Fn remquol functions also store the last .Va k bits of .Fa n in the location pointed to by .Fa quo , provided that .Fa n exists. The number of bits .Va k is platform-specific, but is guaranteed to be at least 3. .Sh SEE ALSO .Xr fmod 3 , .Xr ieee 3 , .Xr math 3 .Sh STANDARDS The .Fn remainder , .Fn remainderf , .Fn remainderl , .Fn remquo , .Fn remquof , and .Fn remquol routines conform to .St -isoC-99 . The remainder is as defined in .St -ieee754 . .Sh HISTORY The .Fn remainder and .Fn remainderf functions appeared in x 4.3 and .Fx 2.0 , respectively. The .Fn remquo and .Fn remquof functions were added in .Fx 6.0 , and .Fn remainderl and .Fn remquol were added in .Fx 8.0 .