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floor(3M)

fp_class(3)

math(3M)

ieee(3m)  —  RISC

Name

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

Syntax

#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, 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(x,y) function returns the remainder r := x − n∗y where n is the integer nearest the exact value of x/y.  Additionally if |n−x/y|=1/2, then n is even.  Consequently the remainder is computed exactly and |r| ≤ |y|/2.  Note that drem(x,0) is the exception (see DIAGNOTICS).

Finite(x)= 1 just when −∞ < x < +∞,
= 0 otherwise(when |x| = ∞ or x is NaN)

The logb(x)returns a signed integer converted to double−precision floating−point and so chosen that 1 ≤ |x|/2**n < 2 unless x = 0 or |x| = ∞ or x lies between 0 and the Underflow Threshold.

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. 

IEEE 754 defines logb(±∞) = +∞ and logb(0) = −∞, and requires the latter to signal Division−by−Zero. 

Restrictions

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. 

See Also

floor(3M), fp_class(3), math(3M)
 

Typewritten Software • bear@typewritten.org • Edmonds, WA 98026