mirror of
https://github.com/freebsd/freebsd-src
synced 2024-10-05 16:10:55 +00:00
Document exp2() and exp2f(), and make other minor tweaks and updates.
This commit is contained in:
David Schultz
parent
f8d6ede6b5
commit
90232fdf16
Notes:
svn2git
2020-12-20 02:59:44 +00:00
svn path=/head/; revision=144649
|
|
@ -32,12 +32,15 @@
|
|||
.\" from: @(#)exp.3 6.12 (Berkeley) 7/31/91
|
||||
.\" $FreeBSD$
|
||||
.\"
|
||||
.Dd January 14, 2005
|
||||
.Dd April 5, 2005
|
||||
.Dt EXP 3
|
||||
.Os
|
||||
.Sh NAME
|
||||
.Nm exp ,
|
||||
.Nm expf ,
|
||||
.\" The sorting error is intentional. exp and expf should be adjacent.
|
||||
.Nm exp2 ,
|
||||
.Nm exp2f ,
|
||||
.Nm expm1 ,
|
||||
.Nm expm1f ,
|
||||
.Nm log ,
|
||||
|
|
@ -58,6 +61,10 @@
|
|||
.Ft float
|
||||
.Fn expf "float x"
|
||||
.Ft double
|
||||
.Fn exp2 "double x"
|
||||
.Ft float
|
||||
.Fn exp2f "float x"
|
||||
.Ft double
|
||||
.Fn expm1 "double x"
|
||||
.Ft float
|
||||
.Fn expm1f "float x"
|
||||
|
|
@ -82,7 +89,16 @@ The
|
|||
.Fn exp
|
||||
and the
|
||||
.Fn expf
|
||||
functions compute the exponential value of the given argument
|
||||
functions compute the base
|
||||
.Ms e
|
||||
exponential value of the given argument
|
||||
.Fa x .
|
||||
.Pp
|
||||
The
|
||||
.Fn exp2
|
||||
and the
|
||||
.Fn exp2f
|
||||
functions compute the base 2 exponential of the given argument
|
||||
.Fa x .
|
||||
.Pp
|
||||
The
|
||||
|
|
@ -125,57 +141,16 @@ of
|
|||
to the exponent
|
||||
.Ar y .
|
||||
.Sh ERROR (due to Roundoff etc.)
|
||||
.Fn exp x ,
|
||||
.Fn log x ,
|
||||
.Fn expm1 x
|
||||
The values of
|
||||
.Fn exp 0 ,
|
||||
.Fn expm1 0 ,
|
||||
.Fn exp2 integer ,
|
||||
and
|
||||
.Fn log1p x
|
||||
are accurate to within
|
||||
an
|
||||
.Em ulp ,
|
||||
and
|
||||
.Fn log10 x
|
||||
to within about 2
|
||||
.Em ulps ;
|
||||
an
|
||||
.Em ulp
|
||||
is one
|
||||
.Em Unit
|
||||
in the
|
||||
.Em Last
|
||||
.Em Place .
|
||||
The error in
|
||||
.Fn pow x y
|
||||
is below about 2
|
||||
.Em ulps
|
||||
when its
|
||||
magnitude is moderate, but increases as
|
||||
.Fn pow x y
|
||||
approaches
|
||||
the over/underflow thresholds until almost as many bits could be
|
||||
lost as are occupied by the floating\-point format's exponent
|
||||
field; that is 8 bits for
|
||||
.Tn "VAX D"
|
||||
and 11 bits for IEEE 754 Double.
|
||||
No such drastic loss has been exposed by testing; the worst
|
||||
errors observed have been below 20
|
||||
.Em ulps
|
||||
for
|
||||
.Tn "VAX D" ,
|
||||
300
|
||||
.Em ulps
|
||||
for
|
||||
.Tn IEEE
|
||||
754 Double.
|
||||
Moderate values of
|
||||
.Fn pow
|
||||
are accurate enough that
|
||||
.Fn pow integer integer
|
||||
is exact until it is bigger than 2**56 on a
|
||||
.Tn VAX ,
|
||||
2**53 for
|
||||
.Tn IEEE
|
||||
754.
|
||||
are exact provided that they are representable.
|
||||
.\" XXX Is this really true for pow()?
|
||||
Otherwise the error in these functions is generally below one
|
||||
.Em ulp .
|
||||
.Sh RETURN VALUES
|
||||
These functions will return the appropriate computation unless an error
|
||||
occurs or an argument is out of range.
|
||||
|
|
@ -214,15 +189,7 @@ They also provide accurate inverse hyperbolic functions.
|
|||
.Pp
|
||||
The function
|
||||
.Fn pow x 0
|
||||
returns x**0 = 1 for all x including x = 0,
|
||||
\*(If
|
||||
(not found on a
|
||||
.Tn VAX ) ,
|
||||
and
|
||||
.Em NaN
|
||||
(the reserved
|
||||
operand on a
|
||||
.Tn VAX ) .
|
||||
returns x**0 = 1 for all x including x = 0, \*(If, and \*(Na .
|
||||
Previous implementations of pow may
|
||||
have defined x**0 to be undefined in some or all of these
|
||||
cases.
|
||||
|
|
@ -267,23 +234,3 @@ and infinite x, i.e., independently of x.
|
|||
.Sh SEE ALSO
|
||||
.Xr fenv 3 ,
|
||||
.Xr math 3
|
||||
.Sh HISTORY
|
||||
A
|
||||
.Fn exp ,
|
||||
.Fn log
|
||||
and
|
||||
.Fn pow
|
||||
functions
|
||||
appeared in
|
||||
.At v6 .
|
||||
A
|
||||
.Fn log10
|
||||
function
|
||||
appeared in
|
||||
.At v7 .
|
||||
The
|
||||
.Fn log1p
|
||||
and
|
||||
.Fn expm1
|
||||
functions appeared in
|
||||
.Bx 4.3 .
|
||||
|
|
|
|||
|
|
@ -32,7 +32,7 @@
|
|||
.\" from: @(#)math.3 6.10 (Berkeley) 5/6/91
|
||||
.\" $FreeBSD$
|
||||
.\"
|
||||
.Dd March 24, 2005
|
||||
.Dd April 5, 2005
|
||||
.Dt MATH 3
|
||||
.Os
|
||||
.if n \{\
|
||||
|
|
@ -174,7 +174,7 @@ cosh hyperbolic cosine
|
|||
erf error function
|
||||
erfc complementary error function
|
||||
exp exponential base e
|
||||
.\" exp2 exponential base 2
|
||||
exp2 exponential base 2
|
||||
expm1 exp(x)\-1
|
||||
j0 Bessel function of the first kind of the order 0
|
||||
j1 Bessel function of the first kind of the order 1
|
||||
|
|
@ -196,10 +196,10 @@ yn Bessel function of the second kind of the order n
|
|||
.El
|
||||
.Pp
|
||||
Unlike the algebraic functions listed earlier, the routines
|
||||
in this section may not produce a result that is correctly rounded.
|
||||
In general, an unbounded number of digits of a value taken by a
|
||||
transcendental function may be needed to determine the correctly rounded
|
||||
result.
|
||||
in this section may not produce a result that is correctly rounded,
|
||||
so reproducible results cannot be guaranteed across platforms.
|
||||
For most of these functions, however, incorrect rounding occurs
|
||||
rarely, and then only in very-close-to-halfway cases.
|
||||
.Sh SEE ALSO
|
||||
.Xr fenv 3 ,
|
||||
.Xr ieee 3
|
||||
|
|
@ -221,14 +221,16 @@ and
|
|||
values, were written for or imported into subsequent versions of FreeBSD.
|
||||
.Sh BUGS
|
||||
The
|
||||
.Fn exp2 ,
|
||||
.Fn log2 ,
|
||||
.Fn log2
|
||||
and
|
||||
.Fn nan
|
||||
functions are missing, and many functions are not available in their
|
||||
.Vt "long double"
|
||||
variants.
|
||||
.Pp
|
||||
Many of the routines to compute transcendental functions produce
|
||||
inaccurate results in other than the default rounding mode.
|
||||
.Pp
|
||||
On some architectures, trigonometric argument reduction is not
|
||||
performed accurately, resulting in errors greater than 1
|
||||
.Em ulp
|
||||
|
|
|
|||
Loading…
Reference in a new issue