MATH-FP(2)MATH-FP(2)NAMEmath-fp - floating point
SYNOPSIS
include "math.m";
math := load Math Math->PATH;
Infinity, NaN, MachEps, Pi, Degree: real;
INVAL, ZDIV, OVFL, UNFL, INEX: int;
RND_NR, RND_NINF, RND_PINF, RND_Z, RND_MASK: int;
getFPcontrol, getFPstatus: fn(): int;
FPcontrol, FPstatus: fn(r, mask: int): int;
ilogb: fn(x: real): int;
scalbn: fn(x: real, n: int): real;
copysign: fn(x, s: real): real;
finite, isnan: fn(x: real): int;
nextafter: fn(x, y: real): real;
fdim, fmin, fmax: fn(x, y: real): real;
fabs: fn(x: real): real;
ceil, floor: fn(x: real): real;
remainder: fn(x, p: real): real;
fmod: fn(x, y: real): real;
modf: fn(x: real): (int,real);
rint: fn(x: real): real;
DESCRIPTION
These constants and functions provide control over rounding modes,
exceptions, and other properties of floating point arithmetic.
Infinity and NaN are constants containing the positive infinity and
quiet not-a-number values of the IEEE binary floating point standard,
double precision. MachEps is 2-52, the smallest e such that 1+e is not
equal to 1. Pi is the nearest machine number to the infinitely precise
value. Degree is Pi/180.
Each thread has a floating point control word (governing rounding mode
and whether a particular floating point exception causes a trap) and a
floating point status word (storing accumulated exception flags). The
functions FPcontrol and FPstatus copy bits to the control or status
word, in positions specified by a mask, returning the previous values
of the bits specified in the mask. The functions getFPcontrol and
getFPstatus return the words unchanged.
INVAL, ZDIV, OVFL, UNFL, and INEX are non-overlapping single-bit masks
used to compose arguments or return values. They stand for the five
IEEE exceptions: `invalid operation' (0/0,0+NaN,Infinity-Infin‐
ity,sqrt(-1)), `division by zero' (1/0), `overflow' (1.8e308), `under‐
flow' (1.1e-308), and `inexact' (.3*.3).
RND_NR, RND_NINF, RND_PINF, and RND_Z are distinct bit patterns for
`round to nearest even', `round toward negative infinity', `round
toward infinity', and `round toward 0', any of which can be set or
extracted from the floating point control word using RND_MASK. For
example, FPcontrol(0, UNFL) makes underflow silent; FPstatus(0, INEX)
checks and clears the inexact flag; and FPcontrol(RND_PINF, RND_MASK)
sets directed rounding.
By default, INEX is quiet, OVFL, UNFL, and ZDIV are fatal, and rounding
is to nearest even. Limbo modules are entitled to assume this, and if
they wish to use quiet underflow, overflow, or zero-divide, they must
either set and restore the control register or clearly document that
their caller must do so.
The ilogb function returns the nearest integral logarithm base 2 of the
absolute value of x: for positive finite x, 1 ≤ x*2-ilogb(x) < 2, and
ilogb(-x) = ilogb(x). Scalbn(x,n) is a scaled power of two: x*2n.
Copysign(x,s) has the magnitude of x and the sign bit of s.
Nextafter(x,y) is the machine number nearest x closer to y. Finally,
finite(x) is 0 if x is Nan or Infinity, 1 otherwise, and isnan(x) is 1
if x is Nan and 0 otherwise.
The function fdim(x,y) = x-y if x is greater than y, otherwise it is 0.
The functions fmin, fmax, fabs, ceil, and floor are the customary mini‐
mum, maximum, absolute value, and integer rounding routines.
There are two functions for computing the modulus: fmod(x,y) is the
function defined by the C standard which gives the value x-i*y for some
i such that the remainder has the sign of x and magnitude less than the
magnitude of y, while remainder(x,y) is the function defined by the
IEEE standard which gives a remainder of magnitude no more than half
the magnitude of y. The function modf(x) breaks x into integer and
fractional parts returned in a tuple, and rint rounds to an integer,
following the rounding mode specified in the floating point control
word.
SOURCE
/libinterp/math.c
SEE ALSOmath-intro(2)MATH-FP(2)
