exp.3m

来自「<B>Digital的Unix操作系统VAX 4.2源码</B>」· 3M 代码 · 共 173 行

.TH exp 3m RISC
.ds nn \fINaN\fR
.ds up \fIulp\fR
.SH Name
exp, expm1, log, log10, log1p, pow \- exponential, logarithm, power
.SH Syntax
.nf
.B #include <math.h>
.PP
.B double exp(\fIx\fP)
.B double \fIx\fP;
.PP
.B float fexp(\fIx\fP)
.B float \fIx\fP;
.PP
.B double expm1(\fIx\fP)
.B double \fIx\fP;
.PP
.B float fexpm1(\fIx\fP)
.B float \fIx\fP;
.PP
.B double log(\fIx\fP)
.B double \fIx\fP;
.PP
.B float flog(\fIx\fP)
.B float \fIx\fP;
.PP
.B double log10(\fIx\fP)
.B double \fIx\fP;
.PP
.B float flog10(\fIx\fP)
.B float \fIx\fP;
.PP
.B double log1p(\fIx\fP)
.B double \fIx\fP;
.PP
.B float flog1p(\fIx\fP)
.B float \fIx\fP;
.PP
.B double pow(\fIx,y\fP)
.B double \fIx,y\fP;
.fi
.SH Description
.NXR "exp function"
.NXR "fexp function"
.NXR "expm1 function"
.NXR "fexpm1 function"
.NXR "log function"
.NXR "flog function"
.NXR "log10 function"
.NXR "flog10 function"
.NXR "log1p function"
.NXR "flog1p function"
.PP
The 
.PN exp
and 
.PN fexp
functions return the exponential function of \fIx\fP
for double and float data types, respectively.
.PP
The 
.PN expm1 
and 
.PN fexpm1
functions return exp(\fIx\fP\)-1 accurately, including tiny \fIx\fP for double
and float data types, respectively.
.PP
The
.PN log
and
.PN flog
functions return the natural logarithm of \fIx\fP
for double and float data types, respectively.
.PP
The 
.PN log10
and 
.PN flog10
functions return the logarithm of \fIx\fP to base 10
for double and float data types, respectively.
.PP
The 
.PN log1p
and
.PN flog1p
functions return log(1+\fIx\fP) accurately, including tiny \fIx\fP
for double and float data types, respectively.
.PP
The
.PN pow
function returns 
.I x**y.
.NXR "pow function"
.SS Error (due to roundoff) 
The 
.PN exp ,
.PN log ,
.PN expm1 ,
and 
.PN log1p
functions are accurate to within 
an \*(up, and 
.PN log10 
is accurate to within approximately 2 \*(ups;
an \*(up is one \fIU\fRnit in the \fIL\fRast \fIP\fRlace.
.PP
The 
.PN pow
function is accurate to within 2 \*(ups when its
magnitude is moderate, but becomes less accurate as the 
.PN pow 
result approaches the overflow or underflow thresholds. 
Theoretically, as these thresholds are approached, almost as many bits
could be lost from the result as are indicated in the exponent field of
the floating-point format for the resultant number.  In other words, up
to 11 bits for an IEEE 754 double-precision floating-point number.  
However, testing has never verified loss of precision as drastic as 11
bits.  The worst cases have shown accuracy of results to within 
300 \*(ups for IEEE 754 double-precision floating-point numbers.  In
general, a
.PN pow
(integer, integer) result is exact until it is larger than 2**53
(for IEEE 754 double-precision floating-point).
.SH Return Values
All of the double precision functions return \*(nn if
.I x
or
.I y
is \*(nn.
.PP
The 
.PN exp
function returns HUGE_VAL when the correct value would overflow,
and zero when the correct value would underflow.
.PP
The 
.PN log
and
.PN log10
functions 
return \*(nn when
.I x
is less than or equal to zero or when the correct value would overflow.
.PP
The
.PN pow
function returns \*(nn if
.I x
or
.I y
is \*(nn.  When both
.I x
and
.I y
are zero, 1.0 is returned.  When
.I x
is negative and
.I y
is not an integer, \*(nn is returned.  If
.I x
is zero and
.I y
is negative, -HUGE_VAL is returned.
.PP
The
.PN sqrt
function returns \*(nn when
.I x
is negative.
.SH See Also
math(3m)