ref: 728eff896074bfa69130c243941ffc6d5c19a735
dir: /man/2/math-fp/
.TH MATH-FP 2 .SH NAME math-fp \- floating point .SH SYNOPSIS .EX 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; .EE .SH DESCRIPTION These constants and functions provide control over rounding modes, exceptions, and other properties of floating point arithmetic. .PP .B Infinity and .B NaN are constants containing the positive infinity and quiet not-a-number values of the IEEE binary floating point standard, double precision. .B MachEps is 2\u\s-2-52\s0\d, the smallest .I e such that 1+\f2e\f1 is not equal to 1. .B Pi is the nearest machine number to the infinitely precise value. .B Degree is .BR Pi/ 180. .PP 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 .B FPcontrol and .B 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 .B getFPcontrol and .B getFPstatus return the words unchanged. .PP .BR INVAL , .BR ZDIV , .BR OVFL , .BR UNFL , and .B 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). .PP .BR RND_NR , .BR RND_NINF , .BR RND_PINF , and .BR 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 .BR RND_MASK . For example, .B FPcontrol(0, .B UNFL) makes underflow silent; .B FPstatus(0, .B INEX) checks and clears the inexact flag; and .B FPcontrol(RND_PINF, .B RND_MASK) sets directed rounding. .PP By default, .B INEX is quiet, .BR OVFL , .BR UNFL , and .B 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. .PP The .B ilogb function returns the nearest integral logarithm base 2 of the absolute value of .IR x: for positive finite .IR x , 1 \(<= .IB x *2\u-\s-2ilogb( x )\s0\d < 2, and .BI ilogb(- x ) .B = .BI ilogb( x )\f1. .BI Scalbn( x , n ) is a scaled power of two: .IB x *2\u\s-2n\s0\d\f1. .BI Copysign( x , s ) has the magnitude of .I x and the sign bit of .IR s . .BI Nextafter( x , y ) is the machine number nearest x closer to y. Finally, .BI finite( x ) is 0 if .I x is .B Nan or .B Infinity, 1 otherwise, and .BI isnan( x ) is 1 if .I x is .B Nan and 0 otherwise. .PP The function .BI fdim( x , y) = .IB x - y if .I x is greater than .IR y , otherwise it is 0. The functions .BR fmin , .BR fmax , .BR fabs , .BR ceil , and .B floor are the customary minimum, maximum, absolute value, and integer rounding routines. .PP There are two functions for computing the modulus: .BI fmod( x , y ) is the function defined by the C standard which gives the value .IB x - i*y for some .I i such that the remainder has the sign of .I x and magnitude less than the magnitude of .IR y , while .BI remainder( x , y ) is the function defined by the IEEE standard which gives a remainder of magnitude no more than half the magnitude of .IR y . The function .BI modf( x ) breaks .I x into integer and fractional parts returned in a tuple, and .B rint rounds to an integer, following the rounding mode specified in the floating point control word. .SH SOURCE .B /libinterp/math.c .SH SEE ALSO .IR math-intro (2)