EXP(3M) EXP(3M)
exp, expm1, log, log10, log1p, pow, fexp, expf, fexpm1, expm1f, flog,
logf, flog10, log10f, flog1p, log1pf, fpow, powf, expl, expm1l, logl,
log10l, log1pl, powl - exponential, logarithm, power
#include <math.h>
double exp(double x);
float fexp(float x);
float expf(float x);
long double expl(long double x);
long double expm1l(long double x);
double expm1(double x);
float fexpm1(float x);
float expm1f(float x);
double log(double x);
float flog(float x);
float logf(float x);
long double logl(long double x);
double log10(double x);
float flog10(float x);
float log10f(float x);
long double log10l(long double x);
double log1p(double x);
float flog1p(float x);
float log1pf(float x);
long double log1pl(long double x);
double pow(double x, double y);
float powf(float x, float y);
long double powl(long double x, \
long double y);
The long double and single-precision routines listed above are only
available in the standard math library, -lm, and in -lmx.
The exp family return the exponential function of x, e**x.
The expm1 family return exp(x)-1 accurately even for tiny x.
The log functions return the natural logarithm of x.
The log10 functions return the base 10 logarithm of x.
EXP(3M) EXP(3M)
The log1p family return log(1+x) accurately even for tiny x.
pow(x,y), its single-precision counterpart powf(x,y), and its long double
counterpart powl(x,y), return x**y.
ERROR (due to Roundoff etc.) [Toc] [Back] exp(x), log(x), expm1(x) and log1p(x) are accurate to within an ulp, and
log10(x) and pow(x,y) to within about 2 ulps; an ulp is one Unit in the
Last Place. Moderate values of pow are accurate enough that
pow(integer,integer) is exact until it is bigger than 2**53 for double.
In the diagnostics below, functions in the standard math library libm.a,
are referred to as -lm versions, those in math library libmx.a are
referred to as -lmx versions, and those in the the BSD math library
libm43.a are referred to as -lm43 versions.
When NaN is used as an argument, a NaN is returned. The -lm and -lmx
versions always return the default Quiet NaN and set errno to EDOM. The
-lm43 versions never set errno.
The value of HUGE_VAL is IEEE Infinity.
The exp functions return HUGE_VAL when the correct value would overflow,
and return zero if the correct value would underflow. The -lm and -lmx
versions set the value of errno to ERANGE for both underflow and
overflow.
The log functions return NaN when x is less than zero, indicating an
invalid operation. The -lm and -lmx versions also set errno to EDOM.
When x is zero, the log functions return -HUGE_VAL. The -lm and -lmx
versions set errno to ERANGE.
The pow functions return NaN indicating an invalid operation, if x is
negative and y is not an integer. The -lm and -lmx versions also set
errno to EDOM.
When x is zero and y is negative, the -lm and -lmx versions return
HUGE_VAL and set errno to EDOM. The -lm43 versions return HUGE_VAL.
When both arguments are zero, the pow functions return one.
When the correct value for pow would overflow or underflow the pow
functions return +/-HUGE_VAL or zero, respectively. The -lm and -lmx
versions set errno to ERANGE.
See matherr(3M) for a description of error handling for -lmx functions.
Long double operations on this system are only supported in round to
nearest rounding mode (the default). The system must be in round to
nearest rounding mode when calling any of the long double functions, or
incorrect answers will result.
Users concerned with portability to other computer systems should note
that the long double and float versions of these functions are optional
according to the ANSI C Programming Language Specification ISO/IEC 9899 :
Page 2
EXP(3M) EXP(3M)
1990 (E).
Long double functions have been renamed to be compliant with the ANSI-C
standard, however to be backward compatible, they may still be called
with the double precision function name prefixed with a q.
Pow(x,0) returns x**0 = 1 for all x including x = 0 and Infinity.
Previous implementations of pow defined NaN**0 to be 1 as well, but this
behavior has been changed to conform to the IEEE standard. Here are
reasons for returning x**0 = 1 in all other cases:
(1) Any program that already tests whether x is zero (or infinite) 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 because x**0 = 1
for all finite and infinite non-NaN x.
math(3M), matherr(3M)
Page 3
LOG10(3F) LOG10(3F)
log10, alog10, dlog10, qlog10 - FORTRAN common logarithm intrinsic
function
real r1, r2
double precision dp1, dp2
real*16 qp1, qp2
r2 = alog10(r1)
r2 = log10(r1)
dp2 = dlog10(dp1)
dp2 = log10(dp1)
qp2 = qlog10(qp1)
qp2 = log10(qp1)
alog10 returns the real common logarithm of its real argument. dlog10
returns the double-precision common logarithm of its double-precision
argument. qlog10 returns the real*16 common logarithm of its real*16
argument. The absolute value of the argument for alog10, dlog10, and
qlog10 must be greater than zero. The generic function log10 becomes a
call to alog10, dlog10, or qlog10 depending on the type of its argument.
exp(3M).
PPPPaaaaggggeeee 1111 [ Back ]
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