NAME

copysign, drem, finite, logb, scalb − copysign, remainder, exponent manipulations

SYNOPSIS

#include <math.h>

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 exceptional; see below under DIAGNOSTICS.

Finite(x)= 1 just when −∞ < x < +∞,
= 0 otherwise(when |x| = ∞ or x is NaN 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 conform to IEEE 754) |x| = ∞ 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(∞,y) to be invalid operations that produce a NaN.  On a VAX, drem(x,0) returns the reserved operand.  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 = −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 errno to ERANGE. 

SEE ALSO

floor(3M), math(3M), infnan(3M)

AUTHOR

Kwok−Choi Ng

BUGS

Scalb is in libc not libm. 

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 Distribution  —  Revision 1.4 of 17/12/88