math.texi

一个C源代码分析器

@comment ANSI
@deftypefun double pow (double @var{base}, double @var{power})
This is a general exponentiation function, returning @var{base} raised
to @var{power}.

@need 250
The following @code{errno} error conditions are defined for this function:

@table @code
@item EDOM
The argument @var{base} is negative and @var{power} is not an integral
value.  Mathematically, the result would be a complex number in this case.

@item ERANGE
An underflow or overflow condition was detected in the result.
@end table
@end deftypefun

@cindex square root function
@comment math.h
@comment ANSI
@deftypefun double sqrt (double @var{x})
This function returns the nonnegative square root of @var{x}.

The @code{sqrt} function fails, and sets @code{errno} to @code{EDOM}, if
@var{x} is negative.  Mathematically, the square root would be a complex
number.
@end deftypefun

@cindex cube root function
@comment math.h
@comment BSD
@deftypefun double cbrt (double @var{x})
This function returns the cube root of @var{x}.  This function cannot
fail; every representable real value has a representable real cube root.
@end deftypefun

@comment math.h
@comment BSD
@deftypefun double hypot (double @var{x}, double @var{y})
The @code{hypot} function returns @code{sqrt (@var{x}*@var{x} +
@var{y}*@var{y})}.  (This is the length of the hypotenuse of a right
triangle with sides of length @var{x} and @var{y}, or the distance
of the point (@var{x}, @var{y}) from the origin.)  See also the function
@code{cabs} in @ref{Absolute Value}.
@end deftypefun

@comment math.h
@comment BSD
@deftypefun double expm1 (double @var{x})
This function returns a value equivalent to @code{exp (@var{x}) - 1}.
It is computed in a way that is accurate even if the value of @var{x} is
near zero---a case where @code{exp (@var{x}) - 1} would be inaccurate due
to subtraction of two numbers that are nearly equal.
@end deftypefun

@comment math.h
@comment BSD
@deftypefun double log1p (double @var{x})
This function returns a value equivalent to @w{@code{log (1 + @var{x})}}.
It is computed in a way that is accurate even if the value of @var{x} is
near zero.
@end deftypefun

@node Hyperbolic Functions
@section Hyperbolic Functions
@cindex hyperbolic functions

The functions in this section are related to the exponential functions;
see @ref{Exponents and Logarithms}.

@comment math.h
@comment ANSI
@deftypefun double sinh (double @var{x})
The @code{sinh} function returns the hyperbolic sine of @var{x}, defined
mathematically as @w{@code{exp (@var{x}) - exp (-@var{x}) / 2}}.  The
function fails, and sets @code{errno} to @code{ERANGE}, if the value of
@var{x} is too large; that is, if overflow occurs.
@end deftypefun

@comment math.h
@comment ANSI
@deftypefun double cosh (double @var{x})
The @code{cosh} function returns the hyperbolic cosine of @var{x},
defined mathematically as @w{@code{exp (@var{x}) + exp (-@var{x}) / 2}}.
The function fails, and sets @code{errno} to @code{ERANGE}, if the value
of @var{x} is too large; that is, if overflow occurs.
@end deftypefun

@comment math.h
@comment ANSI
@deftypefun double tanh (double @var{x})
This function returns the hyperbolic tangent of @var{x}, whose 
mathematical definition is @w{@code{sinh (@var{x}) / cosh (@var{x})}}.
@end deftypefun

@cindex inverse hyperbolic functions

@comment math.h
@comment BSD
@deftypefun double asinh (double @var{x})
This function returns the inverse hyperbolic sine of @var{x}---the
value whose hyperbolic sine is @var{x}.
@end deftypefun

@comment math.h
@comment BSD
@deftypefun double acosh (double @var{x})
This function returns the inverse hyperbolic cosine of @var{x}---the
value whose hyperbolic cosine is @var{x}.  If @var{x} is less than
@code{1}, @code{acosh} returns @code{HUGE_VAL}.
@end deftypefun

@comment math.h
@comment BSD
@deftypefun double atanh (double @var{x})
This function returns the inverse hyperbolic tangent of @var{x}---the
value whose hyperbolic tangent is @var{x}.  If the absolute value of
@var{x} is greater than or equal to @code{1}, @code{atanh} returns
@code{HUGE_VAL}.
@end deftypefun

@node Pseudo-Random Numbers
@section Pseudo-Random Numbers
@cindex random numbers
@cindex pseudo-random numbers
@cindex seed (for random numbers)

This section describes the GNU facilities for generating a series of
pseudo-random numbers.  The numbers generated are not truly random;
typically, they form a sequence that repeats periodically, with a
period so large that you can ignore it for ordinary purposes.  The
random number generator works by remembering at all times a @dfn{seed}
value which it uses to compute the next random number and also to
compute a new seed.

Although the generated numbers look unpredictable within one run of a
program, the sequence of numbers is @emph{exactly the same} from one run
to the next.  This is because the initial seed is always the same.  This
is convenient when you are debugging a program, but it is unhelpful if
you want the program to behave unpredictably.  If you want truly random
numbers, not just pseudo-random, specify a seed based on the current
time.

You can get repeatable sequences of numbers on a particular machine type
by specifying the same initial seed value for the random number
generator.  There is no standard meaning for a particular seed value;
the same seed, used in different C libraries or on different CPU types,
will give you different random numbers.

The GNU library supports the standard ANSI C random number functions
plus another set derived from BSD.  We recommend you use the standard
ones, @code{rand} and @code{srand}.

@menu
* ANSI Random::      @code{rand} and friends.
* BSD Random::       @code{random} and friends.
@end menu

@node ANSI Random
@subsection ANSI C Random Number Functions

This section describes the random number functions that are part of
the ANSI C standard.

To use these facilities, you should include the header file
@file{stdlib.h} in your program.
@pindex stdlib.h

@comment stdlib.h
@comment ANSI
@deftypevr Macro int RAND_MAX
The value of this macro is an integer constant expression that
represents the maximum possible value returned by the @code{rand}
function.  In the GNU library, it is @code{037777777}, which is the
largest signed integer representable in 32 bits.  In other libraries, it
may be as low as @code{32767}.
@end deftypevr

@comment stdlib.h
@comment ANSI
@deftypefun int rand ()
The @code{rand} function returns the next pseudo-random number in the
series.  The value is in the range from @code{0} to @code{RAND_MAX}.
@end deftypefun

@comment stdlib.h
@comment ANSI
@deftypefun void srand (unsigned int @var{seed})
This function establishes @var{seed} as the seed for a new series of
pseudo-random numbers.  If you call @code{rand} before a seed has been
established with @code{srand}, it uses the value @code{1} as a default
seed.

To produce truly random numbers (not just pseudo-random), do @code{srand
(time (0))}.
@end deftypefun

@node BSD Random
@subsection BSD Random Number Functions

This section describes a set of random number generation functions that
are derived from BSD.  There is no advantage to using these functions
with the GNU C library; we support them for BSD compatibility only.

The prototypes for these functions are in @file{stdlib.h}.
@pindex stdlib.h

@comment stdlib.h
@comment BSD
@deftypefun {long int} random ()
This function returns the next pseudo-random number in the sequence.
The range of values returned is from @code{0} to @code{RAND_MAX}.
@end deftypefun

@comment stdlib.h
@comment BSD
@deftypefun void srandom (unsigned int @var{seed})
The @code{srandom} function sets the seed for the current random number
state based on the integer @var{seed}.  If you supply a @var{seed} value
of @code{1}, this will cause @code{random} to reproduce the default set
of random numbers.

To produce truly random numbers (not just pseudo-random), do
@code{srandom (time (0))}.
@end deftypefun

@comment stdlib.h
@comment BSD
@deftypefun {void *} initstate (unsigned int @var{seed}, void *@var{state}, size_t @var{size})
The @code{initstate} function is used to initialize the random number
generator state.  The argument @var{state} is an array of @var{size}
bytes, used to hold the state information.  The size must be at least 8
bytes, and optimal sizes are 8, 16, 32, 64, 128, and 256.  The bigger
the @var{state} array, the better.

The return value is the previous value of the state information array.
You can use this value later as an argument to @code{setstate} to
restore that state.
@end deftypefun

@comment stdlib.h
@comment BSD
@deftypefun {void *} setstate (void *@var{state})
The @code{setstate} function restores the random number state
information @var{state}.  The argument must have been the result of
a previous call to @var{initstate} or @var{setstate}.  

The return value is the previous value of the state information array.
You can use thise value later as an argument to @code{setstate} to
restore that state.
@end deftypefun