-@node Mathematics
+@node Mathematics, Arithmetic, Low-Level Terminal Interface, Top
@chapter Mathematics
This chapter contains information about functions for performing
-mathematical computations, such as trigonometric functions. Most
-of these functions have prototypes declared in the header file
+mathematical computations, such as trigonometric functions. Most of
+these functions have prototypes declared in the header file
@file{math.h}.
@pindex math.h
All of the functions that operate on floating-point numbers accept
-arguments and return results of type @code{double}. In future revisions
-of the ANSI C standard, additional functions may be added that operate
-on @code{float} and @code{long double} values. For example, @code{cosf}
-and @code{cosl} would be versions of the @code{cos} function that
-operate on @code{float} and @code{long double} arguments, respectively.
-In the meantime, you should avoid using these names yourself.
-@xref{Reserved Names}.
-
-@strong{Incomplete:} This chapter doesn't have any examples.
+arguments and return results of type @code{double}. In the future,
+there may be additional functions that operate on @code{float} and
+@code{long double} values. For example, @code{cosf} and @code{cosl}
+would be versions of the @code{cos} function that operate on
+@code{float} and @code{long double} arguments, respectively. In the
+meantime, you should avoid using these names yourself. @xref{Reserved
+Names}.
@menu
-* Domain and Range Errors:: How overflow conditions and the like
- are reported.
-* Not a Number:: Making NANs and testing for NANs.
-* Trigonometric Functions:: Sine, cosine, and tangent.
-* Inverse Trigonometric Functions:: Arc sine, arc cosine, and arc tangent.
-* Exponentiation and Logarithms:: Also includes square root.
-* Hyperbolic Functions:: Hyperbolic sine and friends.
-* Pseudo-Random Numbers:: Functions for generating pseudo-random
- numbers.
-* Absolute Value:: Absolute value functions.
+* Domain and Range Errors:: Detecting overflow conditions and the like.
+* Trig Functions:: Sine, cosine, and tangent.
+* Inverse Trig Functions:: Arc sine, arc cosine, and arc tangent.
+* Exponents and Logarithms:: Also includes square root.
+* Hyperbolic Functions:: Hyperbolic sine and friends.
+* Pseudo-Random Numbers:: Functions for generating pseudo-random
+ numbers.
@end menu
@node Domain and Range Errors
over a domain that is only a subset of real numbers. For example, the
@code{acos} function is defined over the domain between @code{-1} and
@code{1}. If you pass an argument to one of these functions that is
-outside the domain over which it is defined, the function returns
-an unspecified value and sets @code{errno} to @code{EDOM} to indicate
-a @dfn{domain error}.
+outside the domain over which it is defined, the function sets
+@code{errno} to @code{EDOM} to indicate a @dfn{domain error}. On
+machines that support IEEE floating point, functions reporting error
+@code{EDOM} also return a NaN.
Some of these functions are defined mathematically to result in a
complex value over parts of their domains. The most familiar example of
-this is taking the square root of a negative number. Since the C
-language has no support for complex numbers, this is considered a
-domain error.
+this is taking the square root of a negative number. The functions in
+this chapter take only real arguments and return only real values;
+therefore, if the value ought to be nonreal, this is treated as a domain
+error.
@cindex range error
A related problem is that the mathematical result of a function may not
correct result is too large to be represented, the function sets
@code{errno} to @code{ERANGE} to indicate a @dfn{range error}, and
returns a particular very large value (named by the macro
-@code{HUGE_VAL}) or its negation.
+@code{HUGE_VAL}) or its negation (@w{@code{- HUGE_VAL}}).
If the magnitude of the result is too small, a value of zero is returned
instead. In this case, @code{errno} might or might not be
set to @code{ERANGE}.
-None of the mathematical functions ever generates signals as a result of
-domain or range errors. In particular, this means that you won't see
-@code{SIGFPE} signals generated within these functions. (@xref{Signal
-Handling}, for more information about signals.)
-
The only completely reliable way to check for domain and range errors is
to set @code{errno} to @code{0} before you call the mathematical function
and test @code{errno} afterward. As a consequence of this use of
@code{errno}, use of the mathematical functions is not reentrant if you
check for errors.
+@c !!! this isn't always true at the moment....
+None of the mathematical functions ever generates signals as a result of
+domain or range errors. In particular, this means that you won't see
+@code{SIGFPE} signals generated within these functions. (@xref{Signal
+Handling}, for more information about signals.)
+
@comment math.h
@comment ANSI
@deftypevr Macro double HUGE_VAL
@end deftypevr
For more information about floating-point representations and limits,
-@xref{Floating-Point Limits}. In particular, the macro @code{DBL_MAX}
-might be more appropriate than @code{HUGE_VAL} for many uses.
-
-@node Not a Number
-@section ``Not a Number'' Values
-@cindex NAN
-@cindex not a number
-@cindex IEEE floating point
-
-The IEEE floating point format used by most modern computers supports
-values that are ``not a number''. These values are called @dfn{NANs}.
-``Not a number'' values result from certain operations which have no
-meaningful numeric result, such as zero divided by zero or infinity
-divided by infinity.
-
-One noteworthy property of NANs is that they are not equal to
-themselves. Thus, @code{x == x} can be 0 if the value of @code{x} is a
-NAN. In fact, this is the way to test whether a value is a NAN or not:
-if it is not equal to itself, then it is a NAN.
-
-Almost any arithmetic operation in which one argument is a NAN returns
-a NAN.
-
-@comment math.h
-@comment GNU
-@deftypevr Macro double NAN
-An expression representing a value which is ``not a number''. This
-macro is a GNU extension, available only on machines that support ``not
-a number'' values---that is to say, on all machines that support IEEE
-floating point.
-@end deftypevr
+see @ref{Floating Point Parameters}. In particular, the macro
+@code{DBL_MAX} might be more appropriate than @code{HUGE_VAL} for many
+uses other than testing for an error in a mathematical function.
-@node Trigonometric Functions
+@node Trig Functions
@section Trigonometric Functions
-@cindex trignometric functions
+@cindex trigonometric functions
These are the familiar @code{sin}, @code{cos}, and @code{tan} functions.
The arguments to all of these functions are in units of radians; recall
The math library doesn't define a symbolic constant for pi, but you can
define your own if you need one:
-@example
+@smallexample
#define PI 3.14159265358979323846264338327
-@end example
+@end smallexample
@noindent
You can also compute the value of pi with the expression @code{acos
@table @code
@item ERANGE
-Mathematically, the tangent function has singularities at odd multiples of
-pi/2. If the argument @var{x} is too close to one of these singularities,
-@code{tan} sets this error condition and returns either positive or
-negative @code{HUGE_VAL}.
+Mathematically, the tangent function has singularities at odd multiples
+of pi/2. If the argument @var{x} is too close to one of these
+singularities, @code{tan} sets @code{errno} to @code{ERANGE} and returns
+either positive or negative @code{HUGE_VAL}.
@end table
@end deftypefun
-@node Inverse Trigonometric Functions
+@node Inverse Trig Functions
@section Inverse Trigonometric Functions
@cindex inverse trigonmetric functions
there are infinitely many such values; the one actually returned is the
one between @code{-pi/2} and @code{pi/2} (inclusive).
-The following @code{errno} error conditions are defined for this function:
-
-@table @code
-@item EDOM
-The argument @var{x} is out of range. The arc sine function is defined
-mathematically only over the domain @code{-1} to @code{1}.
-@end table
+@code{asin} fails, and sets @code{errno} to @code{EDOM}, if @var{x} is
+out of range. The arc sine function is defined mathematically only
+over the domain @code{-1} to @code{1}.
@end deftypefun
@comment math.h
Mathematically, there are infinitely many such values; the one actually
returned is the one between @code{0} and @code{pi} (inclusive).
-The following @code{errno} error conditions are defined for this function:
-
-@table @code
-@item EDOM
-The argument @var{x} is out of range. The arc cosine function is defined
-mathematically only over the domain @code{-1} to @code{1}.
-@end table
+@code{acos} fails, and sets @code{errno} to @code{EDOM}, if @var{x} is
+out of range. The arc cosine function is defined mathematically only
+over the domain @code{-1} to @code{1}.
@end deftypefun
@code{atan2} returns the signed angle between the line from the origin
to that point and the x-axis. Thus, @code{atan2} is useful for
converting Cartesian coordinates to polar coordinates. (To compute the
-radial coordinate, use @code{hypot}; see @ref{Exponentiation and
+radial coordinate, use @code{hypot}; see @ref{Exponents and
Logarithms}.)
-The following @code{errno} error conditions are defined for this function:
-
-@table @code
-@item EDOM
-Both the @var{x} and @var{y} arguments are zero; the value of the
-function is not defined in this case.
-@end table
+The function @code{atan2} sets @code{errno} to @code{EDOM} if both
+@var{x} and @var{y} are zero; the return value is not defined in this
+case.
@end deftypefun
-@node Exponentiation and Logarithms
+@node Exponents and Logarithms
@section Exponentiation and Logarithms
@cindex exponentiation functions
@cindex power functions
The @code{exp} function returns the value of e (the base of natural
logarithms) raised to power @var{x}.
-The following @code{errno} error conditions are defined for this function:
-
-@table @code
-@item ERANGE
-The magnitude of the result is too large to be representable.
-@end table
+The function fails, and sets @code{errno} to @code{ERANGE}, if the
+magnitude of the result is too large to be representable.
@end deftypefun
@comment math.h
@table @code
@item EDOM
-The log function is defined mathematically to return a non-complex
-result only on positive arguments. This error is used to report a
-negative argument @var{x}.
+The argument @var{x} is negative. The log function is defined
+mathematically to return a real result only on positive arguments.
@item ERANGE
-The result of the function on an argument of zero is not defined.
+The argument is zero. The log of zero is not defined.
@end table
@end deftypefun
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
@deftypefun double sqrt (double @var{x})
This function returns the nonnegative square root of @var{x}.
-The following @code{errno} error conditions are defined for this function:
-
-@table @code
-@item EDOM
-The argument @var{x} is negative. Mathematically, the square root would
-be a complex number.
-@end table
+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 GNU
+@comment BSD
@deftypefun double cbrt (double @var{x})
-This function returns the cube root of @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 GNU
+@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.)
+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 GNU
-@deftypefun double cabs (struct @{ double x, y; @} @var{z})
-The @code{cabs} function is similar to @code{hypot}, but the argument
-is specified as a @code{struct} representing a complex number.
-@end deftypefun
-
-
-@comment math.h
-@comment GNU
+@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
@end deftypefun
@comment math.h
-@comment GNU
+@comment BSD
@deftypefun double log1p (double @var{x})
-This function returns a value equivalent to @code{log (1 + @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
@cindex hyperbolic functions
The functions in this section are related to the exponential functions;
-see @ref{Exponentiation and Logarithms}.
+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 @code{(exp (@var{x}) - exp (-@var{x}) / 2}.
-The following @code{errno} error conditions are defined for this
-function:
-
-@table @code
-@item ERANGE
-The value of the argument @var{x} is too large; an overflow condition
-was detected.
-@end table
+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 @code{(exp (@var{x}) + exp (-@var{x}) /
-2}. The following @code{errno} error conditions are defined for this
-function:
-
-@table @code
-@item ERANGE
-The value of the argument @var{x} is too large; an overflow condition
-was detected.
-@end table
+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}, defined
-mathematically as @code{sinh (@var{x}) / cosh (@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 GNU
+@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 GNU
+@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
@end deftypefun
@comment math.h
-@comment GNU
+@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
@node Pseudo-Random Numbers
@section Pseudo-Random Numbers
-
-This section describes the GNU facilities for generating a series of
-pseudo-random numbers. The numbers generated are not necessarily truly
-random; typically, the sequences repeat periodically, with the period
-being a function of the number of bits in the @dfn{seed} or initial
-state.
@cindex random numbers
@cindex pseudo-random numbers
@cindex seed (for random numbers)
-There are actually two sets of random number functions provided.
-
-@itemize @bullet
-@item
-The @code{rand} and @code{srand} functions, described in @ref{ANSI C
-Random Number Functions}, are part of the ANSI C standard. You can use
-these functions portably in many C implementations.
-
-@item
-The @code{random} and @code{srandom} functions, described in @ref{BSD
-Random Number Functions}, are derived from BSD Unix. This uses a better
-random number generator (producing numbers that are more random), but
-is less portable.
-@end itemize
-
-For both sets of functions, you can get repeatable sequences of numbers
-within a single implementation on a single machine type by specifying
-the same initial seed value for the random number generator. Other C
-libraries may produce different sequences of values for the same seed.
-
+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 C Random Number Functions:: @code{rand} and friends.
-* BSD Random Number Functions:: @code{random} and friends.
+* ANSI Random:: @code{rand} and friends.
+* BSD Random:: @code{random} and friends.
@end menu
-@node ANSI C Random Number Functions
+@node ANSI Random
@subsection ANSI C Random Number Functions
This section describes the random number functions that are part of
-the ANSI C standard. These functions represent the state of the
-random number generator as an @code{int}.
+the ANSI C standard.
To use these facilities, you should include the header file
@file{stdlib.h} in your program.
@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}. In other
-libraries, it may be as low as @code{32767}.
+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 (void)
+@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
(time (0))}.
@end deftypefun
-@node BSD Random Number Functions
+@node BSD Random
@subsection BSD Random Number Functions
-This section describes a set of random number generation functions
-that are derived from BSD Unix. The @code{random} function can generate
-better random numbers than @code{rand}, because it maintains more bits
-of internal state.
+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 (void)
+@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
@code{srandom (time (0))}.
@end deftypefun
-Because this random number generator uses more state information than
-will fit in an @code{int}, @code{srandom} does not return a value that
-is useful for saving and restoring the random number state. Instead,
-you should use the @code{initstate} and @code{setstate} functions to do
-this.
-
@comment stdlib.h
@comment BSD
@deftypefun {void *} initstate (unsigned int @var{seed}, void *@var{state}, size_t @var{size})
You can use thise value later as an argument to @code{setstate} to
restore that state.
@end deftypefun
-
-@node Absolute Value
-@section Absolute Value
-@cindex absolute value functions
-
-These functions are provided for obtaining the @dfn{absolute value} (or
-@dfn{magnitude}) of a number. The absolute value of @var{x} is @var{x}
-is @var{x} is positive, @minus{}@var{x} if @var{x} is negative.
-
-Prototypes for @code{abs} and @code{abs} are declared in
-@file{stdlib.h}; @code{fabs} is declared in @file{math.h}.
-@pindex math.h
-@pindex stdlib.h
-
-@comment stdlib.h
-@comment ANSI
-@deftypefun int abs (int @var{number})
-This function returns the absolute value of @var{number}.
-
-Most computers use a two's complement integer representation, in which
-the absolute value of @code{INT_MIN} (the smallest possible @code{int})
-cannot be represented; thus, @code{abs (INT_MIN)} is not defined.
-@end deftypefun
-
-@comment stdlib.h
-@comment ANSI
-@deftypefun {long int} labs (long int @var{number})
-This is similar to @code{abs}, except that both the argument and result
-are of type @code{long int} rather than @code{int}.
-@end deftypefun
-
-@comment math.h
-@comment ANSI
-@deftypefun double fabs (double @var{number})
-This function returns the absolute value of the floating-point number
-@var{number}.
-@end deftypefun
-
-There is also the function @code{cabs} for computing the absolute value
-of a complex number; see @ref{Exponentiation and Logarithms}.
-
-@node Arithmetic
-@chapter Low-Level Arithmetic Functions
-
-This chapter contains information about functions for doing basic
-arithmetic operations, such as splitting a float into its integer and
-fractional parts. These functions are declared in the header file
-@file{math.h}.
-
-@menu
-* Normalization Functions:: Hacks for radix-2 representations.
-* Rounding and Remainder Functions:: Determinining the integer and
- fractional parts of a float.
-* Integer Division:: Functions for performing integer
- division.
-* Parsing of Numbers:: Functions for ``reading'' numbers
- from strings.
-* Predicates on Floats:: Some miscellaneous test functions.
-@end menu
-
-@node Normalization Functions
-@section Normalization Functions
-@cindex normalization functions (floating-point)
-
-The functions described in this section are primarily provided as a way
-to efficiently perform certain low-level manipulations on floating point
-numbers that are represented internally using a binary radix;
-see @ref{Floating-Point Representation}. These functions are required to
-have equivalent behavior even if the representation does not use a radix
-of 2, but of course they are unlikely to be particularly efficient in
-those cases.
-
-@comment math.h
-@comment GNU
-@deftypefun double copysign (double @var{value}, double @var{sign})
-The @code{copysign} function returns a value whose absolute value is the
-same as that of @var{value}, and whose sign matches that of @var{sign}.
-@end deftypefun
-
-@comment math.h
-@comment ANSI
-@deftypefun double frexp (double @var{value}, int *@var{exponent})
-The @code{frexp} function is used to normalize the number @var{value}.
-
-If the argument @var{value} is not zero, the return value is a
-floating-point number with magnitude in the range 1/2 (inclusive) to 1
-(exclusive). The corresponding exponent is stored in the location
-pointed at by @var{exponent}; the return value multiplied by 2 raised to
-this exponent would equal the original number @var{value}.
-
-If @var{value} is zero, then both parts of the result are zero.
-@end deftypefun
-
-@comment math.h
-@comment ANSI
-@deftypefun double ldexp (double @var{value}, int @var{exponent})
-This function returns the result of multiplying the floating-point
-number @var{value} by 2 raised to the power @var{exponent}. (It can
-be used to reassemble floating-point numbers that were taken apart
-by @code{frexp}.)
-@end deftypefun
-
-@c ??? Where does this come from?
-@comment math.h
-@comment GNU
-@deftypefun double scalb (double @var{value}, int @var{exponent})
-The @code{scalb} function does the same thing as @code{ldexp}.
-@end deftypefun
-
-@c ??? Where does this come from?
-@comment math.h
-@comment GNU
-@deftypefun double logb (double @var{x})
-This function returns the integer part of the base-2 logarithm of
-@var{x}, an integer value represented in type @code{double}. This is
-the highest integer power of @code{2} contained in @var{x}.
-
-When @code{2} raised to this power is divided into @var{x}, it gives a
-quotient between @code{1} (inclusive) and @code{2} (exclusive).
-
-@strong{Incomplete:} What happens if @var{x} is zero?
-@end deftypefun
-
-
-@node Rounding and Remainder Functions
-@section Rounding and Remainder Functions
-@cindex rounding functions
-@cindex remainder functions
-@cindex converting floats to integers
-
-The functions listed here perform operations such as rounding,
-truncation, and remainder in division of floating point numbers. Some
-of these functions convert floating point numbers to integer values.
-
-You can also convert floating-point numbers to integers simply by
-casting them to @code{int}. This discards the fractional part,
-effectively rounding towards zero. However, this only works if the
-result can actually be represented as an @code{int}---for very large
-numbers, this is impossible. The functions listed here return the
-result as a @code{double} instead to get around this problem.
-
-@comment math.h
-@comment ANSI
-@deftypefun double ceil (double @var{x})
-The @code{ceil} function rounds @var{x} upwards to the nearest integer,
-returning that value as a @code{double}.
-@end deftypefun
-
-@comment math.h
-@comment ANSI
-@deftypefun double floor (double @var{x})
-The @code{ceil} function rounds @var{x} downwards to the nearest
-integer, returning that value as a @code{double}.
-@end deftypefun
-
-@comment math.h
-@comment GNU
-@deftypefun double rint (double @var{x})
-This function returns the integer nearest @var{x} according to the
-current rounding mode. @xref{Floating-Point Parameters}, for information
-about the @code{FLT_ROUNDS} macro.
-@end deftypefun
-
-@comment math.h
-@comment ANSI
-@deftypefun double modf (double @var{value}, double *@var{integer_part})
-This function breaks the argument @var{value} into an integer part and a
-fractional part (between @code{-1} and @code{1}, exclusive). The
-integer part is stored at the location pointed at by @var{integer_part},
-and the fractional part is returned. Their sum equals @var{value}.
-Each of the parts has the same sign as @var{value}, so the rounding of
-the integer part is towards zero.
-@end deftypefun
-
-
-@comment math.h
-@comment ANSI
-@deftypefun double fmod (double @var{numerator}, double @var{denominator})
-This function computes the remainder of dividing @var{numerator} by
-@var{denominator}. Specifically, the return value is
-@code{@var{numerator} - @var{n} * @var{denominator}}, where @var{n} is
-the quotient of @var{numerator} by @var{denominator}, rounded down to
-the next lower integer.
-
-The result has the same sign as the @var{numerator} and has magnitude
-less than the magnitude of the @var{denominator}. (Recall that the
-built-in @samp{%} operator isn't defined on floating-point values.)
-
-The following @code{errno} error conditions are defined for this function:
-
-@table @code
-@item EDOM
-The @var{denominator} is zero.
-@end table
-@end deftypefun
-
-@comment math.h
-@comment GNU
-@deftypefun double drem (double @var{numerator}, double @var{denominator})
-This function returns the remainder from dividing @var{numerator} by
-@var{denominator}. Specifically, the return value is @code{@var{numerator}
-- @var{n} * @var{denominator}}, where @var{n} is the integer closest to
-the exact quotient of @var{numerator} and @var{denominator}. The absolute
-value of the result is less than or equal to one half the absolute value
-of the @var{denominator}.
-
-The following @code{errno} error conditions are defined for this function:
-
-@table @code
-@item EDOM
-The @var{denominator} is zero.
-@end table
-@end deftypefun
-
-
-@node Integer Division
-@section Integer Division
-@cindex integer division functions
-
-This section describes functions for performing integer division. These
-functions are redundant in the GNU C library, since in GNU C the @samp{/}
-operator always rounds towards zero. But in other C implementations,
-@samp{/} may round differently with negative arguments. @code{div} and
-@code{ldiv} are useful because they specify how to round the quotient.
-
-These functions are specified to return a result @var{r} such that
-@code{@var{r}.quot*@var{denominator} + @var{r}.rem} equals
-@var{numerator}.
-
-To use these facilities, you should include the header file
-@file{stdlib.h} in your program.
-@pindex stdlib.h
-
-@comment stdlib.h
-@comment ANSI
-@deftp {Data Type} div_t
-This is a structure type used to hold the result returned by the @code{div}
-function. It has the following members:
-
-@table @code
-@item int quot
-The quotient from the division.
-
-@item int rem
-The remainder from the division.
-@end table
-@end deftp
-
-@comment stdlib.h
-@comment ANSI
-@deftypefun div_t div (int @var{numerator}, int @var{denominator})
-This function @code{div} computes the quotient and remainder from
-the division of @var{numerator} by @var{denominator}, returning the
-result in a structure of type @code{div_t}.
-
-If the result cannot be represented (as in a division by zero), the
-behavior is undefined.
-@end deftypefun
-
-
-@comment stdlib.h
-@comment ANSI
-@deftp {Data Type} ldiv_t
-This is a structure type used to hold the result returned by the @code{ldiv}
-function. It has the following members:
-
-@table @code
-@item long int quot
-The quotient from the division.
-
-@item long int rem
-The remainder from the division.
-@end table
-
-(This is identical to the type @code{div_t} except that the components
-are of type @code{long int} rather than @code{int}.)
-@end deftp
-
-@comment stdlib.h
-@comment ANSI
-@deftypefun ldiv_t ldiv (long int @var{numerator}, long int @var{denominator})
-The @code{ldiv} function is similar to @code{div}, except that the
-arguments are of type @code{long int} and the result is returned as a
-structure of type @code{ldiv}.
-@end deftypefun
-
-
-@node Parsing of Numbers
-@section Parsing of Numbers
-@cindex parsing numbers (in formatted input)
-@cindex converting strings to numbers
-@cindex number syntax, parsing
-@cindex syntax, for reading numbers
-
-This section describes functions for ``reading'' integer and
-floating-point numbers from a string. In many cases, it is more
-appropriate to use @code{sscanf} or one of the related functions;
-see @ref{Formatted Input}. The syntax recognized by the formatted input
-functions for the numeric conversions is exactly the same as the syntax
-recognized by the functions described in this section.
-
-These functions are declared in @file{stdlib.h}.
-@pindex stdlib.h
-
-@menu
-* Parsing of Integers:: Functions for conversion of integer values.
-* Parsing of Floats:: Functions for conversion of floating-point
- values.
-@end menu
-
-@node Parsing of Integers
-@subsection Parsing of Integers
-
-@comment stdlib.h
-@comment ANSI
-@deftypefun {long int} strtol (const char *@var{string}, char **@var{tailptr}, int @var{base})
-The @code{strtol} (``string-to-long'') function converts the initial
-part of @var{string} to a signed integer, which is returned as a value
-of type @code{long int}.
-
-This function attempts to decompose @var{string} as follows:
-
-@itemize @bullet
-@item
-A (possibly empty) sequence of whitespace characters. Which characters
-are whitespace is determined by the @code{isspace} function
-(@pxref{Classification of Characters}). These are discarded.
-
-@item
-An optional plus or minus sign (@samp{+} or @samp{-}).
-
-@item
-A nonempty sequence of digits in the radix specified by @var{base}. If
-@var{base} is zero, decimal radix is assumed unless the series of digits
-begins with @samp{0} (specifying octal radix), or @samp{0x} or @samp{0X}
-(specifying hexadecimal radix); in other words, the same syntax that is
-used for integer constants in the C language is recognized. Otherwise
-@var{base} must have a value between @code{2} and @code{35}. If
-@var{base} is @code{16}, the digits may optionally be preceeded by
-@samp{0x} or @samp{0X}.
-
-@item
-Any remaining characters in the string. If @var{tailptr} is not a null
-pointer, a pointer to this tail of the string is stored in
-@code{*@var{tailptr}}.
-@end itemize
-
-If the string is empty, contains only whitespace, or does not contain an
-initial substring that has the expected syntax for an integer in the
-specified @var{base}, no conversion is performed. In this case,
-@code{strtol} returns a value of zero and the value returned in
-@code{*@var{tailptr}} is the value of @var{string}.
-
-In a locale other than the standard @code{"C"} locale, this function
-may recognize additional implementation-dependent syntax.
-
-If the string has valid syntax for an integer but the value is not
-representable because of overflow, @code{strtol} returns either
-@code{LONG_MAX} or @code{LONG_MIN} (@pxref{Integer Representation
-Limits}), as appropriate for the sign of the value.
-
-The following @code{errno} error conditions are defined for this
-function:
-
-@table @code
-@item ERANGE
-An overflow condition was detected.
-@end table
-@end deftypefun
-
-@comment stdlib.h
-@comment ANSI
-@deftypefun {unsigned long int} strtoul (const char *@var{string}, char **@var{tailptr}, int @var{base})
-The @code{strtoul} (``string-to-unsigned-long'') function is similar to
-@code{strtol} except that it returns its value as an object of type
-@code{unsigned long int}. The value returned in case of overflow is
-@code{ULONG_MAX} (@pxref{Integer Representation Limits}).
-@end deftypefun
-
-@comment stdlib.h
-@comment ANSI
-@deftypefun {long int} atol (const char *@var{string})
-This function is similar to the @code{strtol} function with a @var{base}
-argument of @code{10}, except that it need not detect overflow errors.
-The @code{atol} function is provided mostly for compatibility with
-existing code; using @code{strtol} is more robust.
-@end deftypefun
-
-@comment stdlib.h
-@comment ANSI
-@deftypefun int atoi (const char *@var{string})
-This function is similar to the @code{atol} function, except that
-returns its value as an @code{int} rather than @code{long int}. The
-@code{atoi} function is also considered obsolete; use @code{strtol}
-instead.
-@end deftypefun
-
-
-@node Parsing of Floats
-@subsection Parsing of Floats
-
-@comment stdlib.h
-@comment ANSI
-@deftypefun double strtod (const char *@var{string}, char **@var{tailptr})
-The @code{strtod} (``string-to-double'') function converts the initial
-part of @var{string} to a floating-point number, which is returned as a
-value of type @code{double}.
-
-This function attempts to decompose @var{string} as follows:
-
-@itemize @bullet
-@item
-A (possibly empty) sequence of whitespace characters. Which characters
-are whitespace is determined by the @code{isspace} function
-(@pxref{Classification of Characters}). These are discarded.
-
-@item
-An optional plus or minus sign (@samp{+} or @samp{-}).
-
-@item
-A nonempty sequence of digits optionally containing a decimal-point
-character (@samp{.}).
-
-@item
-An optional exponent part, consisting of a character @samp{e} or
-@samp{E}, an optional sign, and a sequence of digits.
-
-@item
-Any remaining characters in the string. If @var{tailptr} is not a null
-pointer, a pointer to this tail of the string is stored in
-@code{*@var{tailptr}}.
-@end itemize
-
-If the string is empty, contains only whitespace, or does not contain an
-initial substring that has the expected syntax for a floating-point
-number, no conversion is performed. In this case, @code{strtod} returns
-a value of zero and the value returned in @code{*@var{tailptr}} is the
-value of @var{string}.
-
-In a locale other than the standard @code{"C"} locale, this function may
-recognize additional locale-dependent syntax.
-
-If the string has valid syntax for a floating-point number but the value
-is not representable because of overflow, @code{strtod} returns either
-positive or negative @code{HUGE_VAL} (@pxref{Mathematics}), depending on
-the sign of the value. Similarly, if the value is not representable
-because of underflow, @code{strtod} returns zero.
-
-The following @code{errno} error conditions are defined for this
-function:
-
-@table @code
-@item ERANGE
-An overflow or underflow condition was detected.
-@end table
-@end deftypefun
-
-@comment stdlib.h
-@comment ANSI
-@deftypefun double atof (const char *@var{string})
-This function is similar to the @code{strtod} function, except that it
-need not detect overflow and underflow errors. The @code{atof} function
-is provided mostly for compatibility with existing code; using
-@code{strtod} is more robust.
-@end deftypefun
-
-@node Predicates on Floats
-@section Predicates on Floats
-@cindex predicates on floats
-
-This section describes some miscellaneous test functions on doubles.
-Prototypes for these functions appear in @file{math.h}.
-@pindex math.h
-
-@comment math.h
-@comment GNU
-@deftypefun int isinf (double @var{x})
-This function returns @code{-1} if @var{x} represents negative infinity,
-@code{1} if @var{x} represents positive infinity, and @code{0} otherwise.
-@end deftypefun
-
-@comment math.h
-@comment GNU
-@deftypefun int isnan (double @var{x})
-This function returns a nonzero value if @var{x} is a ``not a number''
-value, and zero otherwise.
-@end deftypefun
-
-@comment math.h
-@comment GNU
-@deftypefun int finite (double @var{x})
-This function returns a nonzero value if @var{x} is finite or a ``not a
-number'' value, and zero otherwise.
-@end deftypefun
-
-@comment math.h
-@comment GNU
-@deftypefun double infnan (int @var{error})
-@strong{Incomplete:} I don't understand what this function does.
-@end deftypefun
-
-@strong{Portability Note:} The functions listed in this section are GNU
-extensions.
-
-
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