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math-fp - floating point


include	"math.m";
math := load Math Math->PATH;

Infinity, NaN, MachEps, Pi, Degree: real;

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;


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 2ud, 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-Infinity,sqrt(-1)), `division by zero' (1/0), `overflow' (1.8e308), `underflow' (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*2u-SIZE=-2>ilogb(x)d < 2, and ilogb(-x) = ilogb(x). Scalbn(x,n) is a scaled power of two: x*2uSIZE=-2>nd. 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 minimum, 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.





MATH-FP(2 ) Rev:  Thu Feb 15 14:43:26 GMT 2007