*nix Documentation Project
·  Home
 +   man pages
·  Linux HOWTOs
·  FreeBSD Tips
·  *niX Forums

  man pages->OpenBSD man pages -> log1pf (3)              
Title
Content
Arch
Section
 

EXP(3)

Contents


NAME    [Toc]    [Back]

     exp, expf, expm1, expm1f, log, logf, log10,  log10f,  log1p,
log1pf, pow,
     powf - exponential, logarithm, power functions

SYNOPSIS    [Toc]    [Back]

     #include <math.h>

     double
     exp(double x);

     float
     expf(float x);

     double
     expm1(double x);

     float
     expm1f(float x);

     double
     log(double x);

     float
     logf(float x);

     double
     log10(double x);

     float
     log10f(float x);

     double
     log1p(double x);

     float
     log1pf(float x);

     double
     pow(double x, double y);

     float
     powf(float x, float y);

DESCRIPTION    [Toc]    [Back]

     The  exp()  function  computes  the exponential value of the
given argument
     x.  The expf() function is a  single  precision  version  of
exp().

     The  expm1() function computes the value exp(x)-1 accurately
even for tiny
     argument x.  The expm1f() function  is  a  single  precision
version of
     expm1().

     The  log()  function computes the value of the natural logarithm of argument
 x.  The logf() function is a single  precision  version
of log().

     The  log10() function computes the value of the logarithm of
argument x to
     base 10.  The log10f() function is a single  precision  version of log10().

     The  log1p()  function  computes the value of log(1+x) accurately even for
     tiny argument x.  The log1pf() function is a  single  precision version of
     log1p().

     The  pow()  function computes the value of x to the exponent
y.  The powf()
     function is a single precision version of pow().

RETURN VALUES    [Toc]    [Back]

     These functions will return the appropriate computation  unless an error
     occurs or an argument is out of range.  The functions exp(),
expm1() and
     pow() detect if the computed value will  overflow,  set  the
global variable
     errno  to ERANGE and cause a reserved operand fault on a VAX
or Tahoe.
     The function pow(x, y) checks to see if x < 0 and y  is  not
an integer, in
     the  event this is true, the global variable errno is set to
EDOM and on
     the VAX and Tahoe generate a reserved operand fault.   On  a
VAX and Tahoe,
     errno is set to EDOM and the reserved operand is returned by
log unless x
     > 0, by log1p() unless x > -1.

ERRORS (due to Roundoff etc.)    [Toc]    [Back]

     exp(x), log(x), expm1(x) and log1p(x) are accurate to within
an ulp, and
     log10(x)  to  within about 2 ulps; an ulp is one Unit in the
Last Place.
     The error in pow(x, y) is below about 2 ulps when its magnitude is moderate,
  but  increases as 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 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 ulps for VAX D,
300 ulps for
     IEEE 754 Double.  Moderate  values  of  pow()  are  accurate
enough that
     pow(integer, integer) is exact until it is bigger than 2**56
on a VAX,
     2**53 for IEEE 754.

NOTES    [Toc]    [Back]

     The functions exp(x)-1 and log(1+x)  are  called  expm1  and
logp1 in BASIC
     on  the Hewlett-Packard HP-71B and APPLE Macintosh, EXP1 and
LN1 in Pascal,
 exp1 and log1 in C on  APPLE  Macintoshes,  where  they
have been provided
 to make sure financial calculations of ((1+x)**n-1)/x,
namely
     expm1(n*log1p(x))/x, will be accurate when x is tiny.   They
also provide
     accurate inverse hyperbolic functions.

     The  function pow(x, 0) returns x**0 = 1 for all x including
x = 0, Infinity
 (not found on a VAX), and NaN (the reserved operand on a
VAX).  Previous
 implementations of pow may have defined x**0 to be undefined in
     some or all of these cases.  Here are reasons for  returning
x**0 = 1 always:


     1.      Any program that already tests whether x is zero (or
infinite or
             NaN) before computing x**0 cannot care whether  0**0
= 1 or not.
             Any  program that depends upon 0**0 to be invalid is
dubious anyway
 since that expression's meaning and, if invalid,
its consequences
 vary from one computer system to another.

     2.       Some Algebra texts (e.g., Sigler's) define x**0 = 1
for all x,
             including x = 0.  This is compatible with  the  convention that accepts
 a[0] as the value of polynomial

                   p(x) = a[0]*x**0 + a[1]*x**1 + a[2]*x**2 +...+
a[n]*x**n

             at x = 0 rather than reject a[0]*0**0 as invalid.

     3.      Analysts will accept 0**0 = 1 despite that x**y  can
approach anything
  or nothing as x and y approach 0 independently.  The reason
             for setting 0**0 = 1 anyway is this:

                   If x(z) and y(z) are  any  functions  analytic
(expandable in
                   power  series) in z around z = 0, and if there
x(0) = y(0) =
                   0, then x(z)**y(z) -> 1 as z -> 0.

     4.      If 0**0 = 1, then infinity**0 = 1/0**0 = 1 too;  and
then NaN**0 =
             1  too  because x**0 = 1 for all finite and infinite
x, i.e., independently
 of x.

SEE ALSO    [Toc]    [Back]

      
      
     infnan(3), math(3)

HISTORY    [Toc]    [Back]

     A exp(), log() and pow() functions  appeared  in  Version  6
AT&T UNIX.  A
     log10()  function  appeared  in  Version  7  AT&T UNIX.  The
log1p() and
     expm1() functions appeared in 4.3BSD.

OpenBSD     3.6                           July      31,      1991
[ Back ]
 Similar pages
Name OS Title
pow Tru64 Exponential, logarithm, and power functions
log1p Tru64 Exponential, logarithm, and power functions
log Tru64 Exponential, logarithm, and power functions
log10 Tru64 Exponential, logarithm, and power functions
exp Tru64 Exponential, logarithm, and power functions
log2 Tru64 Exponential, logarithm, and power functions
expm1 Tru64 Exponential, logarithm, and power functions
cplxexp IRIX exponential, logarithm, power, square root functions for the C++ complex library
exp IRIX exponential, logarithm, power
log IRIX exponential, logarithm, power
Copyright © 2004-2005 DeniX Solutions SRL
newsletter delivery service