blitz_3.html

c++经典教材 Blitz++ v0.8

<TD VALIGN="MIDDLE" ALIGN="LEFT">[Index]</TD>
<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="blitz_abt.html#SEC_About"> ? </A>]</TD>
</TR></TABLE>
<H2> 3.8 Single-argument math functions </H2>
<!--docid::SEC86::-->
<P>

All of the functions described in this section are <EM>element-wise</EM>.  For
example, this code--
</P><P>

<TABLE><tr><td>&nbsp;</td><td class=example><pre>Array&#60;float,2&#62; A, B;   //
A = sin(B);
</pre></td></tr></table></P><P>

results in <CODE>A(i,j) = sin(B(i,j))</CODE> for all (i,j).
</P><P>

<HR SIZE="6">
<A NAME="SEC87"></A>
<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0>
<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="blitz_3.html#SEC86"> &lt; </A>]</TD>
<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="blitz_3.html#SEC88"> &gt; </A>]</TD>
<TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT">[ &lt;&lt; ]</TD>
<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="blitz.html#SEC_Top"> Up </A>]</TD>
<TD VALIGN="MIDDLE" ALIGN="LEFT">[ &gt;&gt; ]</TD>
<TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="blitz.html#SEC_Top">Top</A>]</TD>
<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="blitz_toc.html#SEC_Contents">Contents</A>]</TD>
<TD VALIGN="MIDDLE" ALIGN="LEFT">[Index]</TD>
<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="blitz_abt.html#SEC_About"> ? </A>]</TD>
</TR></TABLE>
<H3> ANSI C++ math functions </H3>
<!--docid::SEC87::-->
<P>

These math functions are available on all platforms:
</P><P>

<A NAME="IDX191"></A>
<A NAME="IDX192"></A>
</P><P>

<DL COMPACT>
<DT><CODE>abs()</CODE>
<DD><A NAME="IDX193"></A>
Absolute value 
<P>

<DT><CODE>acos()</CODE>
<DD><A NAME="IDX194"></A>
Inverse cosine. For real arguments, the return value is in the range 
<EM>[0, \pi]</EM>.  
<P>

<DT><CODE>arg()</CODE>
<DD><A NAME="IDX195"></A>
Argument of a complex number (<CODE>atan2(Im,Re)</CODE>). 
<P>

<DT><CODE>asin()</CODE>
<DD><A NAME="IDX196"></A>
Inverse sine. For real arguments, the return value is in the range 
<EM>[-\pi/2, \pi/2]</EM>.  
<P>

<DT><CODE>atan()</CODE>
<DD><A NAME="IDX197"></A>
Inverse tangent.  For real arguments, the return value is in the range
<EM>[-\pi/2, \pi/2]</EM>.  See also <CODE>atan2()</CODE> in section
<A HREF="blitz_3.html#SEC89">3.9 Two-argument math functions</A>.  
<P>

<DT><CODE>ceil()</CODE>
<DD><A NAME="IDX198"></A>
Ceiling function: smallest floating-point integer value not less than the
argument. 
<P>

<DT><CODE>cexp()</CODE>
<DD><A NAME="IDX199"></A>
Complex exponential; same as <CODE>exp()</CODE>. 
<P>

<DT><CODE>conj()</CODE>
<DD><A NAME="IDX200"></A>
Conjugate of a complex number. 
<P>

<DT><CODE>cos()</CODE>
<DD><A NAME="IDX201"></A>
Cosine.  Works for <CODE>complex&#60;T&#62;</CODE>.  
<P>

<DT><CODE>cosh()</CODE>
<DD><A NAME="IDX202"></A>
Hyperbolic cosine.  Works for <CODE>complex&#60;T&#62;</CODE>. 
<P>

<DT><CODE>csqrt()</CODE>
<DD><A NAME="IDX203"></A>
Complex square root; same as <CODE>sqrt()</CODE>. 
<P>

<DT><CODE>exp()</CODE>
<DD><A NAME="IDX204"></A>
Exponential.  Works for <CODE>complex&#60;T&#62;</CODE>. 
<P>

<DT><CODE>fabs()</CODE>
<DD><A NAME="IDX205"></A>
Same as <CODE>abs()</CODE>.  
<P>

<DT><CODE>floor()</CODE>
<DD><A NAME="IDX206"></A>
Floor function: largest floating-point integer value not greater than the
argument. 
<P>

<DT><CODE>log()</CODE>
<DD><A NAME="IDX207"></A>
Natural logarithm.  Works for <CODE>complex&#60;T&#62;</CODE>. 
<P>

<DT><CODE>log10()</CODE>
<DD><A NAME="IDX208"></A>
Base 10 logarithm.  Works for <CODE>complex&#60;T&#62;</CODE>. 
<P>

<DT><CODE>pow2(), pow3(), pow4(), pow5(), pow6(), pow7(), pow8()</CODE>
<DD><A NAME="IDX209"></A>
<A NAME="IDX210"></A>
<A NAME="IDX211"></A>
These functions compute an integer power.  They expand to a series of
multiplications, so they can be used on any type for which multiplication is
well-defined.
<P>

<DT><CODE>sin()</CODE>
<DD><A NAME="IDX212"></A>
Sine.  Works for <CODE>complex&#60;T&#62;</CODE>. 
<P>

<DT><CODE>sinh()</CODE>
<DD><A NAME="IDX213"></A>
Hyperbolic sine.  Works for <CODE>complex&#60;T&#62;</CODE>. 
<P>

<DT><CODE>sqr()</CODE>
<DD><A NAME="IDX214"></A>
Same as <CODE>pow2()</CODE>.  Computes <CODE>x*x</CODE>. Works for <CODE>complex&#60;T&#62;</CODE>. 
<P>

<DT><CODE>sqrt()</CODE>
<DD><A NAME="IDX215"></A>
Square root.  Works for <CODE>complex&#60;T&#62;</CODE>. 
<P>

<DT><CODE>tan()</CODE>
<DD><A NAME="IDX216"></A>
Tangent.  Works for <CODE>complex&#60;T&#62;</CODE>. 
<P>

<DT><CODE>tanh()</CODE>
<DD><A NAME="IDX217"></A>
Hyperbolic tangent.  Works for <CODE>complex&#60;T&#62;</CODE>. 
</DL>
<P>

<HR SIZE="6">
<A NAME="SEC88"></A>
<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0>
<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="blitz_3.html#SEC87"> &lt; </A>]</TD>
<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="blitz_3.html#SEC89"> &gt; </A>]</TD>
<TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT">[ &lt;&lt; ]</TD>
<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="blitz.html#SEC_Top"> Up </A>]</TD>
<TD VALIGN="MIDDLE" ALIGN="LEFT">[ &gt;&gt; ]</TD>
<TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="blitz.html#SEC_Top">Top</A>]</TD>
<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="blitz_toc.html#SEC_Contents">Contents</A>]</TD>
<TD VALIGN="MIDDLE" ALIGN="LEFT">[Index]</TD>
<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="blitz_abt.html#SEC_About"> ? </A>]</TD>
</TR></TABLE>
<H3> IEEE/System V math functions </H3>
<!--docid::SEC88::-->
<P>

<A NAME="IDX218"></A>
<A NAME="IDX219"></A>
<A NAME="IDX220"></A>
<A NAME="IDX221"></A>
</P><P>

These functions are only available on platforms which provide the IEEE Math
library (libm.a) and/or System V Math Library (libmsaa.a).  Apparently not
all platforms provide all of these functions, so what you can use on your
platform may be a subset of these.  If you choose to use one of these
functions, be aware that you may be limiting the portability of your code.
</P><P>

<A NAME="IDX222"></A>
<A NAME="IDX223"></A>
</P><P>

On some platforms, the preprocessor symbols <CODE>_XOPEN_SOURCE</CODE> and/or
<CODE>_XOPEN_SOURCE_EXTENDED</CODE> need to be defined to use these functions.
These symbols can be enabled by compiling with
<CODE>-DBZ_ENABLE_XOPEN_SOURCE</CODE>.  (In previous version of Blitz++,
<CODE>_XOPEN_SOURCE</CODE> and <CODE>_XOPEN_SOURCE_EXTENDED</CODE> were declared by
default.  This was found to cause too many problems, so users must manually
enable them with <CODE>-DBZ_ENABLE_XOPEN_SOURCE</CODE>.).
</P><P>

In the current version, Blitz++ divides these functions into two groups:
IEEE and System V.  This distinction is probably artificial.  If one of the
functions in a group is missing, Blitz++ won't allow you to use any of them.
You can see the division of these functions in the files
<TT>`Blitz++/compiler/ieeemath.cpp'</TT> and
<TT>`Blitz++/compiler/sysvmath.cpp'</TT>.  This arrangement is unsatisfactory
and will probably change in a future version.
</P><P>

You may have to link with <CODE>-lm</CODE> and/or <CODE>-lmsaa</CODE> to use these
functions.
</P><P>

None of these functions are available for <CODE>complex&#60;T&#62;</CODE>.
</P><P>

<DL COMPACT>
<DT><CODE>acosh()</CODE>
<DD><A NAME="IDX224"></A>
Inverse hyperbolic cosine 
<P>

<DT><CODE>asinh()</CODE>
<DD><A NAME="IDX225"></A>
Inverse hyperbolic sine 
<P>

<DT><CODE>atanh()</CODE>
<DD><A NAME="IDX226"></A>
Inverse hyperbolic tangent 
<P>

<DT><CODE>_class()</CODE>
<DD><A NAME="IDX227"></A>
Classification of floating point values.  The return type is integer and
will be one of: 
<P>

<DL COMPACT>
<DT><CODE>FP_PLUS_NORM</CODE>
<DD><A NAME="IDX228"></A>
			Positive normalized, nonzero 
<P>

<DT><CODE>FP_MINUS_NORM</CODE>
<DD><A NAME="IDX229"></A>
			Negative normalized, nonzero 
<P>

<DT><CODE>FP_PLUS_DENORM</CODE>
<DD><A NAME="IDX230"></A>
			Positive denormalized, nonzero 
<P>

<DT><CODE>FP_MINUS_DENORM</CODE>
<DD><A NAME="IDX231"></A>
			Negative denormalized, nonzero 
<P>

<DT><CODE>FP_PLUS_ZERO</CODE>
<DD><A NAME="IDX232"></A>
			+0.0 
<P>

<DT><CODE>FP_MINUS_ZERO</CODE>
<DD><A NAME="IDX233"></A>
			-0.0 
<P>

<DT><CODE>FP_PLUS_INF</CODE>
<DD><A NAME="IDX234"></A>
			Positive infinity  
<P>

<DT><CODE>FP_MINUS_INF</CODE>
<DD><A NAME="IDX235"></A>
			Negative infinity 
<P>

<DT><CODE>FP_NANS</CODE>
<DD><A NAME="IDX236"></A>
			Signalling Not a Number (NaNS) 
<P>

<DT><CODE>FP_NANQ</CODE>
<DD><A NAME="IDX237"></A>
			Quiet Not a Number (NaNQ) 
</DL>
<P>

<DT><CODE>cbrt()</CODE>
<DD><A NAME="IDX238"></A>
Cubic root 
<P>

<DT><CODE>expm1()</CODE>
<DD><A NAME="IDX239"></A>
Computes exp(x)-1 
<P>

<DT><CODE>erf()</CODE>
<DD><A NAME="IDX240"></A>
Computes the error function:  
@erf(x) = 2/sqrt(Pi) * integral(exp(-t^2), t=0..x)
<P>

Note that for large values of the parameter, calculating can result in
extreme loss of accuracy.  Instead, use <CODE>erfc()</CODE>.
</P><P>

<DT><CODE>erfc()</CODE>
<DD><A NAME="IDX241"></A>
Computes the complementary error function <EM>erfc(x) = 1 - erf(x)</EM>.
<P>

<DT><CODE>finite()</CODE>
<DD><A NAME="IDX242"></A>
Returns a nonzero integer if the parameter is a finite number (i.e. not
+INF, -INF, NaNQ or NaNS).
<P>

<DT><CODE>ilogb()</CODE>
<DD><A NAME="IDX243"></A>
Returns an integer which is equal to the unbiased exponent of
the parameter.               
<P>

<DT><CODE>blitz_isnan()</CODE>
<DD><A NAME="IDX244"></A>
<A NAME="IDX245"></A>
Returns a nonzero integer if the parameter is NaNQ or
NaNS (quiet or signalling Not a Number). 
<P>

<DT><CODE>itrunc()</CODE>
<DD><A NAME="IDX246"></A>
Round a floating-point number to a signed integer.  Returns
the nearest signed integer to the parameter in the direction of 0.
<P>

<DT><CODE>j0()</CODE>
<DD><A NAME="IDX247"></A>
<A NAME="IDX248"></A>
Bessel function of the first kind, order 0. 
<P>

<DT><CODE>j1()</CODE>
<DD><A NAME="IDX249"></A>
Bessel function of the first kind, order 1. 
<P>

<DT><CODE>lgamma()</CODE>
<DD><A NAME="IDX250"></A>
<A NAME="IDX251"></A>
Natural logarithm of the gamma function.  The gamma function
is defined as:
Gamma(x) = integral(e^(-t) * t^(x-1), t=0..infinity))
              
<DT><CODE>logb()</CODE>
<DD><A NAME="IDX252"></A>
Returns a floating-point double that is equal to the unbiased
exponent of the parameter.