IEEE(3) BSD Library Functions Manual IEEE(3)[top]NAMEcopysign, drem, finite, logb, scalb — IEEE 754 floating point supportSYNOPSIS#include <math.h> double copysign(double x, double y); double drem(double x, double y); int finite(double x); double logb(double x); double scalb(double x, int n);DESCRIPTIONThese functions are required for, or recommended by the IEEE standard 754 for floating-point arithmetic. The copysign() function returns x with its sign changed to y's. The drem() function 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 exceptional. (See below under DIAGNOSTICS.) The finite() function returns the value 1 just when -∞ < x < +∞; other‐ wise a zero is returned (when |x| = ∞ or x is NaN or is the VAX's reserved operand). The logb() function 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 conform to IEEE 754) |x| = ∞ or x lies between 0 and the Underflow Threshold. (See below under BUGS.) The scalb() function returns x∗(2**n) computed, for integer n, without first computing 2∗n.RETURN VALUESThe IEEE standard 754 defines drem(x, 0) and drem(∞, y) to be invalid operations that produce a NaN. On the VAX, drem(x, 0) generates a reserved operand fault. No ∞ exists on a VAX. IEEE 754 defines logb(±∞) = ∞ and logb(0) = -∞, and requires the latter to signal Division-by-Zero. But on a VAX, logb(0) = 1.0 - 2.0**31 =,147,483,647.0. And if the correct value of scalb() would overflow on a VAX, it generates a reserved operand fault and sets the global variable errno to ERANGE.-2SEE ALSOfloor(3), math(3), infnan(3)HISTORYTheieeefunctions appeared in 4.3BSD.BUGSShould drem(x, 0) and logb(0) on a VAX signal invalidity by setting errno = 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 standard p854, namely that logb(x) satisfy 1 ≤ scalb(|x|, -logb(x)) < Radix ... = 2 for IEEE 754 for every x except 0, ∞ and NaN. Almost every program that assumes 754's specification will work correctly if logb() follows 854's specification instead. IEEE 754 requires copysign(x, NaN)) = ±x but says nothing else about the sign of a NaN. A NaN (Not a Number) is similar in spirit to the VAX's reserved operand, but very different 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?4.3 Berkeley DistributionJune 4, 1993 4.3 Berkeley Distribution

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