IEEE(3M) UNIX Programmer's Manual IEEE(3M) NAME copysign, drem, finite, logb, scalb - copysign, remainder, exponent manipulations SYNOPSIS #include double copysign(x,y) double x,y; double drem(x,y) double x,y; int finite(x) double x; double logb(x) double x; double scalb(x,n) double x; int n; DESCRIPTION These functions are required for, or recommended by the IEEE standard 754 for floating-point arithmetic. Copysign(x,y) returns x with its sign changed to y's. Drem(x,y) returns the remainder r := x - n*y where n is the integer nearest the exact value of x/y; moreover if |n-x/y|=1/2 then n is even. Consequently the remainder is computed exactly and |r| <_ |y|/2. But drem(x,0) is excep- tional; see below under DIAGNOSTICS. Finite(x) = 1 just when -infinity < x < +infinity, = 0 otherwise (when |x| = infinity or x is _N_a_N or x is the VAX's reserved operand.) Logb(x) returns x's exponent n, a signed integer converted to double-precision floating-point and so chosen that 1 <_ |x|/2**n < 2 unless x = 0 or (only on machines that con- form to IEEE 754) |x| = infinity or x lies between 0 and the Underflow Threshold; see below under "BUGS". Scalb(x,n) = x*(2**n) computed, for integer n, without first computing 2**n. DIAGNOSTICS IEEE 754 defines drem(x,0) and drem(infinity,y) to be invalid operations that produce a _N_a_N. On a VAX, drem(x,0) returns the reserved operand. No infinity exists on a VAX. Printed 11/26/99 May 12, 1986 1 IEEE(3M) UNIX Programmer's Manual IEEE(3M) IEEE 754 defines logb(+_infinity) = +infinity and logb(0) = -infinity, requires the latter to signal Division-by-Zero. But on a VAX, logb(0) = 1.0 - 2.0**31 = -2,147,483,647.0. And if the correct value of scalb(x,n) would overflow on a VAX, it returns the reserved operand and sets _e_r_r_n_o to ERANGE. SEE ALSO floor(3M), math(3M), infnan(3M) AUTHOR Kwok-Choi Ng BUGS Should drem(x,0) and logb(0) on a VAX signal invalidity by setting _e_r_r_n_o = EDOM? Should logb(0) return -1.7e38? IEEE 754 currently specifies that logb(denormalized no.) = logb(tiniest normalized no. > 0) but the consensus has changed to the specification in the new proposed IEEE stan- dard p854, namely that logb(x) satisfy 1 <_ scalb(|x|,-logb(x)) < Radix ... = 2 for IEEE 754 for every x except 0, infinity and _N_a_N. Almost every pro- gram that assumes 754's specification will work correctly if logb follows 854's specification instead. IEEE 754 requires copysign(x,_N_a_N) = +_x but says nothing else about the sign of a _N_a_N. A _N_a_N (_Not _a _Number) is simi- lar in spirit to the VAX's reserved operand, but very dif- ferent in important details. Since the sign bit of a reserved operand makes it look negative, copysign(x,reserved operand) = -x; should this return the reserved operand instead? Printed 11/26/99 May 12, 1986 2