@file{complex.h}.
@menu
+* Integers:: Basic integer types and concepts
+* Integer Division:: Integer division with guaranteed rounding.
* Floating Point Numbers:: Basic concepts. IEEE 754.
* Floating Point Classes:: The five kinds of floating-point number.
* Floating Point Errors:: When something goes wrong in a calculation.
* Arithmetic Functions:: Fundamental operations provided by the library.
* Complex Numbers:: The types. Writing complex constants.
* Operations on Complex:: Projection, conjugation, decomposition.
-* Integer Division:: Integer division with guaranteed rounding.
* Parsing of Numbers:: Converting strings to numbers.
+* Printing of Floats:: Converting floating-point numbers to strings.
* System V Number Conversion:: An archaic way to convert numbers to strings.
@end menu
+@node Integers
+@section Integers
+@cindex integer
+
+The C language defines several integer data types: integer, short integer,
+long integer, and character, all in both signed and unsigned varieties.
+The GNU C compiler extends the language to contain long long integers
+as well.
+@cindex signedness
+
+The C integer types were intended to allow code to be portable among
+machines with different inherent data sizes (word sizes), so each type
+may have different ranges on different machines. The problem with
+this is that a program often needs to be written for a particular range
+of integers, and sometimes must be written for a particular size of
+storage, regardless of what machine the program runs on.
+
+To address this problem, @theglibc{} contains C type definitions
+you can use to declare integers that meet your exact needs. Because the
+@glibcadj{} header files are customized to a specific machine, your
+program source code doesn't have to be.
+
+These @code{typedef}s are in @file{stdint.h}.
+@pindex stdint.h
+
+If you require that an integer be represented in exactly N bits, use one
+of the following types, with the obvious mapping to bit size and signedness:
+
+@itemize @bullet
+@item int8_t
+@item int16_t
+@item int32_t
+@item int64_t
+@item uint8_t
+@item uint16_t
+@item uint32_t
+@item uint64_t
+@end itemize
+
+If your C compiler and target machine do not allow integers of a certain
+size, the corresponding above type does not exist.
+
+If you don't need a specific storage size, but want the smallest data
+structure with @emph{at least} N bits, use one of these:
+
+@itemize @bullet
+@item int_least8_t
+@item int_least16_t
+@item int_least32_t
+@item int_least64_t
+@item uint_least8_t
+@item uint_least16_t
+@item uint_least32_t
+@item uint_least64_t
+@end itemize
+
+If you don't need a specific storage size, but want the data structure
+that allows the fastest access while having at least N bits (and
+among data structures with the same access speed, the smallest one), use
+one of these:
+
+@itemize @bullet
+@item int_fast8_t
+@item int_fast16_t
+@item int_fast32_t
+@item int_fast64_t
+@item uint_fast8_t
+@item uint_fast16_t
+@item uint_fast32_t
+@item uint_fast64_t
+@end itemize
+
+If you want an integer with the widest range possible on the platform on
+which it is being used, use one of the following. If you use these,
+you should write code that takes into account the variable size and range
+of the integer.
+
+@itemize @bullet
+@item intmax_t
+@item uintmax_t
+@end itemize
+
+@Theglibc{} also provides macros that tell you the maximum and
+minimum possible values for each integer data type. The macro names
+follow these examples: @code{INT32_MAX}, @code{UINT8_MAX},
+@code{INT_FAST32_MIN}, @code{INT_LEAST64_MIN}, @code{UINTMAX_MAX},
+@code{INTMAX_MAX}, @code{INTMAX_MIN}. Note that there are no macros for
+unsigned integer minima. These are always zero. Similiarly, there
+are macros such as @code{INTMAX_WIDTH} for the width of these types.
+Those macros for integer type widths come from TS 18661-1:2014.
+@cindex maximum possible integer
+@cindex minimum possible integer
+
+There are similar macros for use with C's built in integer types which
+should come with your C compiler. These are described in @ref{Data Type
+Measurements}.
+
+Don't forget you can use the C @code{sizeof} function with any of these
+data types to get the number of bytes of storage each uses.
+
+
+@node Integer Division
+@section Integer Division
+@cindex integer division functions
+
+This section describes functions for performing integer division. These
+functions are redundant when GNU CC is used, because 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: towards zero. The remainder has the same sign as the
+numerator.
+
+These functions are specified to return a result @var{r} such that the value
+@code{@var{r}.quot*@var{denominator} + @var{r}.rem} equals
+@var{numerator}.
+
+@pindex stdlib.h
+To use these facilities, you should include the header file
+@file{stdlib.h} in your program.
+
+@deftp {Data Type} div_t
+@standards{ISO, stdlib.h}
+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
+
+@deftypefun div_t div (int @var{numerator}, int @var{denominator})
+@standards{ISO, stdlib.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
+@c Functions in this section are pure, and thus safe.
+The 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.
+
+Here is an example, albeit not a very useful one.
+
+@smallexample
+div_t result;
+result = div (20, -6);
+@end smallexample
+
+@noindent
+Now @code{result.quot} is @code{-3} and @code{result.rem} is @code{2}.
+@end deftypefun
+
+@deftp {Data Type} ldiv_t
+@standards{ISO, stdlib.h}
+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 @code{div_t} except that the components are of
+type @code{long int} rather than @code{int}.)
+@end deftp
+
+@deftypefun ldiv_t ldiv (long int @var{numerator}, long int @var{denominator})
+@standards{ISO, stdlib.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
+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_t}.
+@end deftypefun
+
+@deftp {Data Type} lldiv_t
+@standards{ISO, stdlib.h}
+This is a structure type used to hold the result returned by the @code{lldiv}
+function. It has the following members:
+
+@table @code
+@item long long int quot
+The quotient from the division.
+
+@item long long int rem
+The remainder from the division.
+@end table
+
+(This is identical to @code{div_t} except that the components are of
+type @code{long long int} rather than @code{int}.)
+@end deftp
+
+@deftypefun lldiv_t lldiv (long long int @var{numerator}, long long int @var{denominator})
+@standards{ISO, stdlib.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
+The @code{lldiv} function is like the @code{div} function, but the
+arguments are of type @code{long long int} and the result is returned as
+a structure of type @code{lldiv_t}.
+
+The @code{lldiv} function was added in @w{ISO C99}.
+@end deftypefun
+
+@deftp {Data Type} imaxdiv_t
+@standards{ISO, inttypes.h}
+This is a structure type used to hold the result returned by the @code{imaxdiv}
+function. It has the following members:
+
+@table @code
+@item intmax_t quot
+The quotient from the division.
+
+@item intmax_t rem
+The remainder from the division.
+@end table
+
+(This is identical to @code{div_t} except that the components are of
+type @code{intmax_t} rather than @code{int}.)
+
+See @ref{Integers} for a description of the @code{intmax_t} type.
+
+@end deftp
+
+@deftypefun imaxdiv_t imaxdiv (intmax_t @var{numerator}, intmax_t @var{denominator})
+@standards{ISO, inttypes.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
+The @code{imaxdiv} function is like the @code{div} function, but the
+arguments are of type @code{intmax_t} and the result is returned as
+a structure of type @code{imaxdiv_t}.
+
+See @ref{Integers} for a description of the @code{intmax_t} type.
+
+The @code{imaxdiv} function was added in @w{ISO C99}.
+@end deftypefun
+
+
@node Floating Point Numbers
@section Floating Point Numbers
@cindex floating point
@cindex classes, floating-point
@pindex math.h
-@w{ISO C 9x} defines macros that let you determine what sort of
+@w{ISO C99} defines macros that let you determine what sort of
floating-point number a variable holds.
-@comment math.h
-@comment ISO
@deftypefn {Macro} int fpclassify (@emph{float-type} @var{x})
+@standards{ISO, math.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
This is a generic macro which works on all floating-point types and
which returns a value of type @code{int}. The possible values are:
@vtable @code
@item FP_NAN
+@standards{C99, math.h}
The floating-point number @var{x} is ``Not a Number'' (@pxref{Infinity
and NaN})
@item FP_INFINITE
+@standards{C99, math.h}
The value of @var{x} is either plus or minus infinity (@pxref{Infinity
and NaN})
@item FP_ZERO
+@standards{C99, math.h}
The value of @var{x} is zero. In floating-point formats like @w{IEEE
754}, where zero can be signed, this value is also returned if
@var{x} is negative zero.
@item FP_SUBNORMAL
+@standards{C99, math.h}
Numbers whose absolute value is too small to be represented in the
normal format are represented in an alternate, @dfn{denormalized} format
(@pxref{Floating Point Concepts}). This format is less precise but can
represent values closer to zero. @code{fpclassify} returns this value
for values of @var{x} in this alternate format.
@item FP_NORMAL
+@standards{C99, math.h}
This value is returned for all other values of @var{x}. It indicates
that there is nothing special about the number.
@end vtable
@code{fpclassify}, since there is special hardware support for them.
You should therefore use the specific macros whenever possible.
-@comment math.h
-@comment ISO
+@deftypefn {Macro} int iscanonical (@emph{float-type} @var{x})
+@standards{ISO, math.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
+In some floating-point formats, some values have canonical (preferred)
+and noncanonical encodings (for IEEE interchange binary formats, all
+encodings are canonical). This macro returns a nonzero value if
+@var{x} has a canonical encoding. It is from TS 18661-1:2014.
+
+Note that some formats have multiple encodings of a value which are
+all equally canonical; @code{iscanonical} returns a nonzero value for
+all such encodings. Also, formats may have encodings that do not
+correspond to any valid value of the type. In ISO C terms these are
+@dfn{trap representations}; in @theglibc{}, @code{iscanonical} returns
+zero for such encodings.
+@end deftypefn
+
@deftypefn {Macro} int isfinite (@emph{float-type} @var{x})
+@standards{ISO, math.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
This macro returns a nonzero value if @var{x} is finite: not plus or
minus infinity, and not NaN. It is equivalent to
floating-point type.
@end deftypefn
-@comment math.h
-@comment ISO
@deftypefn {Macro} int isnormal (@emph{float-type} @var{x})
+@standards{ISO, math.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
This macro returns a nonzero value if @var{x} is finite and normalized.
It is equivalent to
@end smallexample
@end deftypefn
-@comment math.h
-@comment ISO
@deftypefn {Macro} int isnan (@emph{float-type} @var{x})
+@standards{ISO, math.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
This macro returns a nonzero value if @var{x} is NaN. It is equivalent
to
@end smallexample
@end deftypefn
+@deftypefn {Macro} int issignaling (@emph{float-type} @var{x})
+@standards{ISO, math.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
+This macro returns a nonzero value if @var{x} is a signaling NaN
+(sNaN). It is from TS 18661-1:2014.
+@end deftypefn
+
+@deftypefn {Macro} int issubnormal (@emph{float-type} @var{x})
+@standards{ISO, math.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
+This macro returns a nonzero value if @var{x} is subnormal. It is
+from TS 18661-1:2014.
+@end deftypefn
+
+@deftypefn {Macro} int iszero (@emph{float-type} @var{x})
+@standards{ISO, math.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
+This macro returns a nonzero value if @var{x} is zero. It is from TS
+18661-1:2014.
+@end deftypefn
+
Another set of floating-point classification functions was provided by
-BSD. The GNU C library also supports these functions; however, we
-recommend that you use the C9x macros in new code. Those are standard
+BSD. @Theglibc{} also supports these functions; however, we
+recommend that you use the ISO C99 macros in new code. Those are standard
and will be available more widely. Also, since they are macros, you do
not have to worry about the type of their argument.
-@comment math.h
-@comment BSD
@deftypefun int isinf (double @var{x})
-@comment math.h
-@comment BSD
@deftypefunx int isinff (float @var{x})
-@comment math.h
-@comment BSD
@deftypefunx int isinfl (long double @var{x})
+@standards{BSD, math.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
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 BSD
@deftypefun int isnan (double @var{x})
-@comment math.h
-@comment BSD
@deftypefunx int isnanf (float @var{x})
-@comment math.h
-@comment BSD
@deftypefunx int isnanl (long double @var{x})
+@standards{BSD, math.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
This function returns a nonzero value if @var{x} is a ``not a number''
value, and zero otherwise.
-@strong{Note:} The @code{isnan} macro defined by @w{ISO C 9x} overrides
+@strong{NB:} The @code{isnan} macro defined by @w{ISO C99} overrides
the BSD function. This is normally not a problem, because the two
routines behave identically. However, if you really need to get the BSD
function for some reason, you can write
@end smallexample
@end deftypefun
-@comment math.h
-@comment BSD
@deftypefun int finite (double @var{x})
-@comment math.h
-@comment BSD
@deftypefunx int finitef (float @var{x})
-@comment math.h
-@comment BSD
@deftypefunx int finitel (long 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 BSD
-@deftypefun double infnan (int @var{error})
-This function is provided for compatibility with BSD. Its argument is
-an error code, @code{EDOM} or @code{ERANGE}; @code{infnan} returns the
-value that a math function would return if it set @code{errno} to that
-value. @xref{Math Error Reporting}. @code{-ERANGE} is also acceptable
-as an argument, and corresponds to @code{-HUGE_VAL} as a value.
-
-In the BSD library, on certain machines, @code{infnan} raises a fatal
-signal in all cases. The GNU library does not do likewise, because that
-does not fit the @w{ISO C} specification.
+@standards{BSD, math.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
+This function returns a nonzero value if @var{x} is neither infinite nor
+a ``not a number'' value, and zero otherwise.
@end deftypefun
@strong{Portability Note:} The functions listed in this section are BSD
program. @xref{Signal Handling}, for how you can change the effect of
the signal.
-@findex matherr
-In the System V math library, the user-defined function @code{matherr}
-is called when certain exceptions occur inside math library functions.
-However, the Unix98 standard deprecates this interface. We support it
-for historical compatibility, but recommend that you do not use it in
-new programs.
-
@noindent
The exceptions defined in @w{IEEE 754} are:
Remainder: @math{x} REM @math{y}, where @math{y} is zero or @math{x} is
infinite.
@item
-Square root if the operand is less then zero. More generally, any
+Square root if the operand is less than zero. More generally, any
mathematical function evaluated outside its domain produces this
exception.
@item
@file{math.h} defines macros that allow you to explicitly set a variable
to infinity or NaN.
-@comment math.h
-@comment ISO
@deftypevr Macro float INFINITY
+@standards{ISO, math.h}
An expression representing positive infinity. It is equal to the value
produced by mathematical operations like @code{1.0 / 0.0}.
@code{-INFINITY} represents negative infinity.
to this macro. However, this is not recommended; you should use the
@code{isfinite} macro instead. @xref{Floating Point Classes}.
-This macro was introduced in the @w{ISO C 9X} standard.
+This macro was introduced in the @w{ISO C99} standard.
@end deftypevr
-@comment math.h
-@comment GNU
@deftypevr Macro float NAN
+@standards{GNU, math.h}
An expression representing a value which is ``not a number''. This
macro is a GNU extension, available only on machines that support the
``not a number'' value---that is to say, on all machines that support
@file{math.h}.)
@end deftypevr
+@deftypevr Macro float SNANF
+@deftypevrx Macro double SNAN
+@deftypevrx Macro {long double} SNANL
+@deftypevrx Macro _FloatN SNANFN
+@deftypevrx Macro _FloatNx SNANFNx
+@standards{TS 18661-1:2014, math.h}
+@standardsx{SNANFN, TS 18661-3:2015, math.h}
+@standardsx{SNANFNx, TS 18661-3:2015, math.h}
+These macros, defined by TS 18661-1:2014 and TS 18661-3:2015, are
+constant expressions for signaling NaNs.
+@end deftypevr
+
+@deftypevr Macro int FE_SNANS_ALWAYS_SIGNAL
+@standards{ISO, fenv.h}
+This macro, defined by TS 18661-1:2014, is defined to @code{1} in
+@file{fenv.h} to indicate that functions and operations with signaling
+NaN inputs and floating-point results always raise the invalid
+exception and return a quiet NaN, even in cases (such as @code{fmax},
+@code{hypot} and @code{pow}) where a quiet NaN input can produce a
+non-NaN result. Because some compiler optimizations may not handle
+signaling NaNs correctly, this macro is only defined if compiler
+support for signaling NaNs is enabled. That support can be enabled
+with the GCC option @option{-fsignaling-nans}.
+@end deftypevr
+
@w{IEEE 754} also allows for another unusual value: negative zero. This
value is produced when you divide a positive number by negative
infinity, or when a negative result is smaller than the limits of
-representation. Negative zero behaves identically to zero in all
-calculations, unless you explicitly test the sign bit with
-@code{signbit} or @code{copysign}.
+representation.
@node Status bit operations
@subsection Examining the FPU status word
-@w{ISO C 9x} defines functions to query and manipulate the
+@w{ISO C99} defines functions to query and manipulate the
floating-point status word. You can use these functions to check for
untrapped exceptions when it's convenient, rather than worrying about
them in the middle of a calculation.
@file{fenv.h}.
@vtable @code
-@comment fenv.h
-@comment ISO
@item FE_INEXACT
+@standards{ISO, fenv.h}
The inexact exception.
-@comment fenv.h
-@comment ISO
@item FE_DIVBYZERO
+@standards{ISO, fenv.h}
The divide by zero exception.
-@comment fenv.h
-@comment ISO
@item FE_UNDERFLOW
+@standards{ISO, fenv.h}
The underflow exception.
-@comment fenv.h
-@comment ISO
@item FE_OVERFLOW
+@standards{ISO, fenv.h}
The overflow exception.
-@comment fenv.h
-@comment ISO
@item FE_INVALID
+@standards{ISO, fenv.h}
The invalid exception.
@end vtable
These functions allow you to clear exception flags, test for exceptions,
and save and restore the set of exceptions flagged.
-@comment fenv.h
-@comment ISO
-@deftypefun void feclearexcept (int @var{excepts})
+@deftypefun int feclearexcept (int @var{excepts})
+@standards{ISO, fenv.h}
+@safety{@prelim{}@mtsafe{}@assafe{@assposix{}}@acsafe{@acsposix{}}}
+@c The other functions in this section that modify FP status register
+@c mostly do so with non-atomic load-modify-store sequences, but since
+@c the register is thread-specific, this should be fine, and safe for
+@c cancellation. As long as the FP environment is restored before the
+@c signal handler returns control to the interrupted thread (like any
+@c kernel should do), the functions are also safe for use in signal
+@c handlers.
This function clears all of the supported exception flags indicated by
@var{excepts}.
+
+The function returns zero in case the operation was successful, a
+non-zero value otherwise.
+@end deftypefun
+
+@deftypefun int feraiseexcept (int @var{excepts})
+@standards{ISO, fenv.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
+This function raises the supported exceptions indicated by
+@var{excepts}. If more than one exception bit in @var{excepts} is set
+the order in which the exceptions are raised is undefined except that
+overflow (@code{FE_OVERFLOW}) or underflow (@code{FE_UNDERFLOW}) are
+raised before inexact (@code{FE_INEXACT}). Whether for overflow or
+underflow the inexact exception is also raised is also implementation
+dependent.
+
+The function returns zero in case the operation was successful, a
+non-zero value otherwise.
+@end deftypefun
+
+@deftypefun int fesetexcept (int @var{excepts})
+@standards{ISO, fenv.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
+This function sets the supported exception flags indicated by
+@var{excepts}, like @code{feraiseexcept}, but without causing enabled
+traps to be taken. @code{fesetexcept} is from TS 18661-1:2014.
+
+The function returns zero in case the operation was successful, a
+non-zero value otherwise.
@end deftypefun
-@comment fenv.h
-@comment ISO
@deftypefun int fetestexcept (int @var{excepts})
+@standards{ISO, fenv.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
Test whether the exception flags indicated by the parameter @var{except}
are currently set. If any of them are, a nonzero value is returned
which specifies which exceptions are set. Otherwise the result is zero.
feclearexcept (FE_ALL_EXCEPT);
f = compute ();
raised = fetestexcept (FE_OVERFLOW | FE_INVALID);
- if (raised & FE_OVERFLOW) @{ /* ... */ @}
- if (raised & FE_INVALID) @{ /* ... */ @}
- /* ... */
+ if (raised & FE_OVERFLOW) @{ /* @dots{} */ @}
+ if (raised & FE_INVALID) @{ /* @dots{} */ @}
+ /* @dots{} */
@}
@end smallexample
save the entire status word and restore it later. This is done with the
following functions:
-@comment fenv.h
-@comment ISO
-@deftypefun void fegetexceptflag (fexcept_t *@var{flagp}, int @var{excepts})
+@deftypefun int fegetexceptflag (fexcept_t *@var{flagp}, int @var{excepts})
+@standards{ISO, fenv.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
This function stores in the variable pointed to by @var{flagp} an
implementation-defined value representing the current setting of the
exception flags indicated by @var{excepts}.
+
+The function returns zero in case the operation was successful, a
+non-zero value otherwise.
@end deftypefun
-@comment fenv.h
-@comment ISO
-@deftypefun void fesetexceptflag (const fexcept_t *@var{flagp}, int
-@var{excepts})
+@deftypefun int fesetexceptflag (const fexcept_t *@var{flagp}, int @var{excepts})
+@standards{ISO, fenv.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
This function restores the flags for the exceptions indicated by
@var{excepts} to the values stored in the variable pointed to by
@var{flagp}.
+
+The function returns zero in case the operation was successful, a
+non-zero value otherwise.
@end deftypefun
Note that the value stored in @code{fexcept_t} bears no resemblance to
the bit mask returned by @code{fetestexcept}. The type may not even be
an integer. Do not attempt to modify an @code{fexcept_t} variable.
+@deftypefun int fetestexceptflag (const fexcept_t *@var{flagp}, int @var{excepts})
+@standards{ISO, fenv.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
+Test whether the exception flags indicated by the parameter
+@var{excepts} are set in the variable pointed to by @var{flagp}. If
+any of them are, a nonzero value is returned which specifies which
+exceptions are set. Otherwise the result is zero.
+@code{fetestexceptflag} is from TS 18661-1:2014.
+@end deftypefun
+
@node Math Error Reporting
@subsection Error Reporting by Mathematical Functions
@cindex errors, mathematical
Many of the math functions are defined only over a subset of the real or
complex numbers. Even if they are mathematically defined, their result
may be larger or smaller than the range representable by their return
-type. These are known as @dfn{domain errors}, @dfn{overflows}, and
+type without loss of accuracy. These are known as @dfn{domain errors},
+@dfn{overflows}, and
@dfn{underflows}, respectively. Math functions do several things when
one of these errors occurs. In this manual we will refer to the
complete response as @dfn{signalling} a domain error, overflow, or
exception and returns NaN. It also sets @var{errno} to @code{EDOM};
this is for compatibility with old systems that do not support @w{IEEE
754} exception handling. Likewise, when overflow occurs, math
-functions raise the overflow exception and return @math{@infinity{}} or
-@math{-@infinity{}} as appropriate. They also set @var{errno} to
-@code{ERANGE}. When underflow occurs, the underflow exception is
-raised, and zero (appropriately signed) is returned. @var{errno} may be
-set to @code{ERANGE}, but this is not guaranteed.
+functions raise the overflow exception and, in the default rounding
+mode, return @math{@infinity{}} or @math{-@infinity{}} as appropriate
+(in other rounding modes, the largest finite value of the appropriate
+sign is returned when appropriate for that rounding mode). They also
+set @var{errno} to @code{ERANGE} if returning @math{@infinity{}} or
+@math{-@infinity{}}; @var{errno} may or may not be set to
+@code{ERANGE} when a finite value is returned on overflow. When
+underflow occurs, the underflow exception is raised, and zero
+(appropriately signed) or a subnormal value, as appropriate for the
+mathematical result of the function and the rounding mode, is
+returned. @var{errno} may be set to @code{ERANGE}, but this is not
+guaranteed; it is intended that @theglibc{} should set it when the
+underflow is to an appropriately signed zero, but not necessarily for
+other underflows.
+
+When a math function has an argument that is a signaling NaN,
+@theglibc{} does not consider this a domain error, so @code{errno} is
+unchanged, but the invalid exception is still raised (except for a few
+functions that are specified to handle signaling NaNs differently).
Some of the math functions are defined mathematically to result in a
complex value over parts of their domains. The most familiar example of
largest representable number). @file{math.h} defines macros you can use
to test for overflow on both old and new hardware.
-@comment math.h
-@comment ISO
@deftypevr Macro double HUGE_VAL
-@comment math.h
-@comment ISO
@deftypevrx Macro float HUGE_VALF
-@comment math.h
-@comment ISO
@deftypevrx Macro {long double} HUGE_VALL
+@deftypevrx Macro _FloatN HUGE_VAL_FN
+@deftypevrx Macro _FloatNx HUGE_VAL_FNx
+@standards{ISO, math.h}
+@standardsx{HUGE_VAL_FN, TS 18661-3:2015, math.h}
+@standardsx{HUGE_VAL_FNx, TS 18661-3:2015, math.h}
An expression representing a particular very large number. On machines
that use @w{IEEE 754} floating point format, @code{HUGE_VAL} is infinity.
On other machines, it's typically the largest positive number that can
various rounding modes. Each one will be defined if and only if the FPU
supports the corresponding rounding mode.
-@table @code
-@comment fenv.h
-@comment ISO
-@vindex FE_TONEAREST
+@vtable @code
@item FE_TONEAREST
+@standards{ISO, fenv.h}
Round to nearest.
-@comment fenv.h
-@comment ISO
-@vindex FE_UPWARD
@item FE_UPWARD
+@standards{ISO, fenv.h}
Round toward @math{+@infinity{}}.
-@comment fenv.h
-@comment ISO
-@vindex FE_DOWNWARD
@item FE_DOWNWARD
+@standards{ISO, fenv.h}
Round toward @math{-@infinity{}}.
-@comment fenv.h
-@comment ISO
-@vindex FE_TOWARDZERO
@item FE_TOWARDZERO
+@standards{ISO, fenv.h}
Round toward zero.
-@end table
+@end vtable
Underflow is an unusual case. Normally, @w{IEEE 754} floating point
numbers are always normalized (@pxref{Floating Point Concepts}).
is rounded to zero. However, the sign of the result is preserved; if
the calculation was negative, the result is @dfn{negative zero}.
Negative zero can also result from some operations on infinity, such as
-@math{4/-@infinity{}}. Negative zero behaves identically to zero except
-when the @code{copysign} or @code{signbit} functions are used to check
-the sign bit directly.
+@math{4/-@infinity{}}.
-At any time one of the above four rounding modes is selected. You can
+At any time, one of the above four rounding modes is selected. You can
find out which one with this function:
-@comment fenv.h
-@comment ISO
@deftypefun int fegetround (void)
+@standards{ISO, fenv.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
Returns the currently selected rounding mode, represented by one of the
values of the defined rounding mode macros.
@end deftypefun
@noindent
To change the rounding mode, use this function:
-@comment fenv.h
-@comment ISO
@deftypefun int fesetround (int @var{round})
+@standards{ISO, fenv.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
Changes the currently selected rounding mode to @var{round}. If
@var{round} does not correspond to one of the supported rounding modes
-nothing is changed. @code{fesetround} returns a nonzero value if it
-changed the rounding mode, zero if the mode is not supported.
+nothing is changed. @code{fesetround} returns zero if it changed the
+rounding mode, or a nonzero value if the mode is not supported.
@end deftypefun
You should avoid changing the rounding mode if possible. It can be an
bits in the @dfn{control word}. In C, traps result in the program
receiving the @code{SIGFPE} signal; see @ref{Signal Handling}.
-@strong{Note:} @w{IEEE 754} says that trap handlers are given details of
+@strong{NB:} @w{IEEE 754} says that trap handlers are given details of
the exceptional situation, and can set the result value. C signals do
not provide any mechanism to pass this information back and forth.
Trapping exceptions in C is therefore not very useful.
To save the state of the FPU, use one of these functions:
-@comment fenv.h
-@comment ISO
-@deftypefun void fegetenv (fenv_t *@var{envp})
+@deftypefun int fegetenv (fenv_t *@var{envp})
+@standards{ISO, fenv.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
Store the floating-point environment in the variable pointed to by
@var{envp}.
+
+The function returns zero in case the operation was successful, a
+non-zero value otherwise.
@end deftypefun
-@comment fenv.h
-@comment ISO
@deftypefun int feholdexcept (fenv_t *@var{envp})
+@standards{ISO, fenv.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
Store the current floating-point environment in the object pointed to by
@var{envp}. Then clear all exception flags, and set the FPU to trap no
exceptions. Not all FPUs support trapping no exceptions; if
-@code{feholdexcept} cannot set this mode, it returns zero. If it
-succeeds, it returns a nonzero value.
+@code{feholdexcept} cannot set this mode, it returns nonzero value. If it
+succeeds, it returns zero.
@end deftypefun
-The functions which restore the floating-point environment can take two
+The functions which restore the floating-point environment can take these
kinds of arguments:
@itemize @bullet
The special macro @code{FE_DFL_ENV} which represents the floating-point
environment as it was available at program start.
@item
-Implementation defined macros with names starting with @code{FE_}.
+Implementation defined macros with names starting with @code{FE_} and
+having type @code{fenv_t *}.
@vindex FE_NOMASK_ENV
-If possible, the GNU C Library defines a macro @code{FE_NOMASK_ENV}
+If possible, @theglibc{} defines a macro @code{FE_NOMASK_ENV}
which represents an environment where every exception raised causes a
trap to occur. You can test for this macro using @code{#ifdef}. It is
only defined if @code{_GNU_SOURCE} is defined.
To set the floating-point environment, you can use either of these
functions:
-@comment fenv.h
-@comment ISO
-@deftypefun void fesetenv (const fenv_t *@var{envp})
+@deftypefun int fesetenv (const fenv_t *@var{envp})
+@standards{ISO, fenv.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
Set the floating-point environment to that described by @var{envp}.
+
+The function returns zero in case the operation was successful, a
+non-zero value otherwise.
@end deftypefun
-@comment fenv.h
-@comment ISO
-@deftypefun void feupdateenv (const fenv_t *@var{envp})
+@deftypefun int feupdateenv (const fenv_t *@var{envp})
+@standards{ISO, fenv.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
Like @code{fesetenv}, this function sets the floating-point environment
to that described by @var{envp}. However, if any exceptions were
flagged in the status word before @code{feupdateenv} was called, they
remain flagged after the call. In other words, after @code{feupdateenv}
is called, the status word is the bitwise OR of the previous status word
and the one saved in @var{envp}.
+
+The function returns zero in case the operation was successful, a
+non-zero value otherwise.
+@end deftypefun
+
+@noindent
+TS 18661-1:2014 defines additional functions to save and restore
+floating-point control modes (such as the rounding mode and whether
+traps are enabled) while leaving other status (such as raised flags)
+unchanged.
+
+@vindex FE_DFL_MODE
+The special macro @code{FE_DFL_MODE} may be passed to
+@code{fesetmode}. It represents the floating-point control modes at
+program start.
+
+@deftypefun int fegetmode (femode_t *@var{modep})
+@standards{ISO, fenv.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
+Store the floating-point control modes in the variable pointed to by
+@var{modep}.
+
+The function returns zero in case the operation was successful, a
+non-zero value otherwise.
+@end deftypefun
+
+@deftypefun int fesetmode (const femode_t *@var{modep})
+@standards{ISO, fenv.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
+Set the floating-point control modes to those described by
+@var{modep}.
+
+The function returns zero in case the operation was successful, a
+non-zero value otherwise.
+@end deftypefun
+
+@noindent
+To control for individual exceptions if raising them causes a trap to
+occur, you can use the following two functions.
+
+@strong{Portability Note:} These functions are all GNU extensions.
+
+@deftypefun int feenableexcept (int @var{excepts})
+@standards{GNU, fenv.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
+This function enables traps for each of the exceptions as indicated by
+the parameter @var{excepts}. The individual exceptions are described in
+@ref{Status bit operations}. Only the specified exceptions are
+enabled, the status of the other exceptions is not changed.
+
+The function returns the previous enabled exceptions in case the
+operation was successful, @code{-1} otherwise.
+@end deftypefun
+
+@deftypefun int fedisableexcept (int @var{excepts})
+@standards{GNU, fenv.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
+This function disables traps for each of the exceptions as indicated by
+the parameter @var{excepts}. The individual exceptions are described in
+@ref{Status bit operations}. Only the specified exceptions are
+disabled, the status of the other exceptions is not changed.
+
+The function returns the previous enabled exceptions in case the
+operation was successful, @code{-1} otherwise.
+@end deftypefun
+
+@deftypefun int fegetexcept (void)
+@standards{GNU, fenv.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
+The function returns a bitmask of all currently enabled exceptions. It
+returns @code{-1} in case of failure.
@end deftypefun
@node Arithmetic Functions
@pindex stdlib.h
Prototypes for @code{abs}, @code{labs} and @code{llabs} are in @file{stdlib.h};
@code{imaxabs} is declared in @file{inttypes.h};
-@code{fabs}, @code{fabsf} and @code{fabsl} are declared in @file{math.h}.
-@code{cabs}, @code{cabsf} and @code{cabsl} are declared in @file{complex.h}.
+the @code{fabs} functions are declared in @file{math.h};
+the @code{cabs} functions are declared in @file{complex.h}.
-@comment stdlib.h
-@comment ISO
@deftypefun int abs (int @var{number})
-@comment stdlib.h
-@comment ISO
@deftypefunx {long int} labs (long int @var{number})
-@comment stdlib.h
-@comment ISO
@deftypefunx {long long int} llabs (long long int @var{number})
-@comment inttypes.h
-@comment ISO
@deftypefunx intmax_t imaxabs (intmax_t @var{number})
+@standards{ISO, stdlib.h}
+@standardsx{imaxabs, ISO, inttypes.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
These functions return 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, @w{@code{abs (INT_MIN)}} is not defined.
-@code{llabs} and @code{imaxdiv} are new to @w{ISO C 9x}.
+@code{llabs} and @code{imaxdiv} are new to @w{ISO C99}.
+
+See @ref{Integers} for a description of the @code{intmax_t} type.
+
@end deftypefun
-@comment math.h
-@comment ISO
@deftypefun double fabs (double @var{number})
-@comment math.h
-@comment ISO
@deftypefunx float fabsf (float @var{number})
-@comment math.h
-@comment ISO
@deftypefunx {long double} fabsl (long double @var{number})
+@deftypefunx _FloatN fabsfN (_Float@var{N} @var{number})
+@deftypefunx _FloatNx fabsfNx (_Float@var{N}x @var{number})
+@standards{ISO, math.h}
+@standardsx{fabsfN, TS 18661-3:2015, math.h}
+@standardsx{fabsfNx, TS 18661-3:2015, math.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
This function returns the absolute value of the floating-point number
@var{number}.
@end deftypefun
-@comment complex.h
-@comment ISO
@deftypefun double cabs (complex double @var{z})
-@comment complex.h
-@comment ISO
@deftypefunx float cabsf (complex float @var{z})
-@comment complex.h
-@comment ISO
@deftypefunx {long double} cabsl (complex long double @var{z})
+@deftypefunx _FloatN cabsfN (complex _Float@var{N} @var{z})
+@deftypefunx _FloatNx cabsfNx (complex _Float@var{N}x @var{z})
+@standards{ISO, complex.h}
+@standardsx{cabsfN, TS 18661-3:2015, complex.h}
+@standardsx{cabsfNx, TS 18661-3:2015, complex.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
These functions return the absolute value of the complex number @var{z}
(@pxref{Complex Numbers}). The absolute value of a complex number is:
This function should always be used instead of the direct formula
because it takes special care to avoid losing precision. It may also
-take advantage of hardware support for this operation. See @code{hypot}
+take advantage of hardware support for this operation. See @code{hypot}
in @ref{Exponents and Logarithms}.
@end deftypefun
@pindex math.h
All these functions are declared in @file{math.h}.
-@comment math.h
-@comment ISO
@deftypefun double frexp (double @var{value}, int *@var{exponent})
-@comment math.h
-@comment ISO
@deftypefunx float frexpf (float @var{value}, int *@var{exponent})
-@comment math.h
-@comment ISO
@deftypefunx {long double} frexpl (long double @var{value}, int *@var{exponent})
+@deftypefunx _FloatN frexpfN (_Float@var{N} @var{value}, int *@var{exponent})
+@deftypefunx _FloatNx frexpfNx (_Float@var{N}x @var{value}, int *@var{exponent})
+@standards{ISO, math.h}
+@standardsx{frexpfN, TS 18661-3:2015, math.h}
+@standardsx{frexpfNx, TS 18661-3:2015, math.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
These functions are used to split the number @var{value}
into a normalized fraction and an exponent.
If the argument @var{value} is not zero, the return value is @var{value}
-times a power of two, and is always in the range 1/2 (inclusive) to 1
-(exclusive). The corresponding exponent is stored in
+times a power of two, and its magnitude is always in the range 1/2
+(inclusive) to 1 (exclusive). The corresponding exponent is stored in
@code{*@var{exponent}}; the return value multiplied by 2 raised to this
exponent equals the original number @var{value}.
zero is stored in @code{*@var{exponent}}.
@end deftypefun
-@comment math.h
-@comment ISO
@deftypefun double ldexp (double @var{value}, int @var{exponent})
-@comment math.h
-@comment ISO
@deftypefunx float ldexpf (float @var{value}, int @var{exponent})
-@comment math.h
-@comment ISO
@deftypefunx {long double} ldexpl (long double @var{value}, int @var{exponent})
+@deftypefunx _FloatN ldexpfN (_Float@var{N} @var{value}, int @var{exponent})
+@deftypefunx _FloatNx ldexpfNx (_Float@var{N}x @var{value}, int @var{exponent})
+@standards{ISO, math.h}
+@standardsx{ldexpfN, TS 18661-3:2015, math.h}
+@standardsx{ldexpfNx, TS 18661-3:2015, math.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
These functions return 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
@end deftypefun
The following functions, which come from BSD, provide facilities
-equivalent to those of @code{ldexp} and @code{frexp}.
-
-@comment math.h
-@comment BSD
-@deftypefun double logb (double @var{x})
-@comment math.h
-@comment BSD
-@deftypefunx float logbf (float @var{x})
-@comment math.h
-@comment BSD
-@deftypefunx {long double} logbl (long double @var{x})
-These functions return 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}. The sign of
-@var{x} is ignored. For example, @code{logb (3.5)} is @code{1.0} and
-@code{logb (4.0)} is @code{2.0}.
-
-When @code{2} raised to this power is divided into @var{x}, it gives a
-quotient between @code{1} (inclusive) and @code{2} (exclusive).
-
-If @var{x} is zero, the return value is minus infinity if the machine
-supports infinities, and a very small number if it does not. If @var{x}
-is infinity, the return value is infinity.
-
-For finite @var{x}, the value returned by @code{logb} is one less than
-the value that @code{frexp} would store into @code{*@var{exponent}}.
-@end deftypefun
-
-@comment math.h
-@comment BSD
-@deftypefun double scalb (double @var{value}, int @var{exponent})
-@comment math.h
-@comment BSD
-@deftypefunx float scalbf (float @var{value}, int @var{exponent})
-@comment math.h
-@comment BSD
-@deftypefunx {long double} scalbl (long double @var{value}, int @var{exponent})
+equivalent to those of @code{ldexp} and @code{frexp}. See also the
+@w{ISO C} function @code{logb} which originally also appeared in BSD.
+The @code{_Float@var{N}} and @code{_Float@var{N}} variants of the
+following functions come from TS 18661-3:2015.
+
+@deftypefun double scalb (double @var{value}, double @var{exponent})
+@deftypefunx float scalbf (float @var{value}, float @var{exponent})
+@deftypefunx {long double} scalbl (long double @var{value}, long double @var{exponent})
+@standards{BSD, math.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
The @code{scalb} function is the BSD name for @code{ldexp}.
@end deftypefun
-@comment math.h
-@comment BSD
-@deftypefun {long long int} scalbn (double @var{x}, int n)
-@comment math.h
-@comment BSD
-@deftypefunx {long long int} scalbnf (float @var{x}, int n)
-@comment math.h
-@comment BSD
-@deftypefunx {long long int} scalbnl (long double @var{x}, int n)
+@deftypefun double scalbn (double @var{x}, int @var{n})
+@deftypefunx float scalbnf (float @var{x}, int @var{n})
+@deftypefunx {long double} scalbnl (long double @var{x}, int @var{n})
+@deftypefunx _FloatN scalbnfN (_Float@var{N} @var{x}, int @var{n})
+@deftypefunx _FloatNx scalbnfNx (_Float@var{N}x @var{x}, int @var{n})
+@standards{BSD, math.h}
+@standardsx{scalbnfN, TS 18661-3:2015, math.h}
+@standardsx{scalbnfNx, TS 18661-3:2015, math.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
@code{scalbn} is identical to @code{scalb}, except that the exponent
@var{n} is an @code{int} instead of a floating-point number.
@end deftypefun
-@comment math.h
-@comment BSD
-@deftypefun {long long int} scalbln (double @var{x}, long int n)
-@comment math.h
-@comment BSD
-@deftypefunx {long long int} scalblnf (float @var{x}, long int n)
-@comment math.h
-@comment BSD
-@deftypefunx {long long int} scalblnl (long double @var{x}, long int n)
+@deftypefun double scalbln (double @var{x}, long int @var{n})
+@deftypefunx float scalblnf (float @var{x}, long int @var{n})
+@deftypefunx {long double} scalblnl (long double @var{x}, long int @var{n})
+@deftypefunx _FloatN scalblnfN (_Float@var{N} @var{x}, long int @var{n})
+@deftypefunx _FloatNx scalblnfNx (_Float@var{N}x @var{x}, long int @var{n})
+@standards{BSD, math.h}
+@standardsx{scalblnfN, TS 18661-3:2015, math.h}
+@standardsx{scalblnfNx, TS 18661-3:2015, math.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
@code{scalbln} is identical to @code{scalb}, except that the exponent
@var{n} is a @code{long int} instead of a floating-point number.
@end deftypefun
-@comment math.h
-@comment BSD
-@deftypefun {long long int} significand (double @var{x})
-@comment math.h
-@comment BSD
-@deftypefunx {long long int} significandf (float @var{x})
-@comment math.h
-@comment BSD
-@deftypefunx {long long int} significandl (long double @var{x})
+@deftypefun double significand (double @var{x})
+@deftypefunx float significandf (float @var{x})
+@deftypefunx {long double} significandl (long double @var{x})
+@standards{BSD, math.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
@code{significand} returns the mantissa of @var{x} scaled to the range
@math{[1, 2)}.
It is equivalent to @w{@code{scalb (@var{x}, (double) -ilogb (@var{x}))}}.
@pindex math.h
The functions listed here perform operations such as rounding and
-truncation of floating-point values. Some of these functions convert
+truncation of floating-point values. Some of these functions convert
floating point numbers to integer values. They are all declared in
@file{math.h}.
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 ISO
+The @code{fromfp} functions use the following macros, from TS
+18661-1:2014, to specify the direction of rounding. These correspond
+to the rounding directions defined in IEEE 754-2008.
+
+@vtable @code
+@item FP_INT_UPWARD
+@standards{ISO, math.h}
+Round toward @math{+@infinity{}}.
+
+@item FP_INT_DOWNWARD
+@standards{ISO, math.h}
+Round toward @math{-@infinity{}}.
+
+@item FP_INT_TOWARDZERO
+@standards{ISO, math.h}
+Round toward zero.
+
+@item FP_INT_TONEARESTFROMZERO
+@standards{ISO, math.h}
+Round to nearest, ties round away from zero.
+
+@item FP_INT_TONEAREST
+@standards{ISO, math.h}
+Round to nearest, ties round to even.
+@end vtable
+
@deftypefun double ceil (double @var{x})
-@comment math.h
-@comment ISO
@deftypefunx float ceilf (float @var{x})
-@comment math.h
-@comment ISO
@deftypefunx {long double} ceill (long double @var{x})
+@deftypefunx _FloatN ceilfN (_Float@var{N} @var{x})
+@deftypefunx _FloatNx ceilfNx (_Float@var{N}x @var{x})
+@standards{ISO, math.h}
+@standardsx{ceilfN, TS 18661-3:2015, math.h}
+@standardsx{ceilfNx, TS 18661-3:2015, math.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
These functions round @var{x} upwards to the nearest integer,
returning that value as a @code{double}. Thus, @code{ceil (1.5)}
is @code{2.0}.
@end deftypefun
-@comment math.h
-@comment ISO
@deftypefun double floor (double @var{x})
-@comment math.h
-@comment ISO
@deftypefunx float floorf (float @var{x})
-@comment math.h
-@comment ISO
@deftypefunx {long double} floorl (long double @var{x})
+@deftypefunx _FloatN floorfN (_Float@var{N} @var{x})
+@deftypefunx _FloatNx floorfNx (_Float@var{N}x @var{x})
+@standards{ISO, math.h}
+@standardsx{floorfN, TS 18661-3:2015, math.h}
+@standardsx{floorfNx, TS 18661-3:2015, math.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
These functions round @var{x} downwards to the nearest
integer, returning that value as a @code{double}. Thus, @code{floor
(1.5)} is @code{1.0} and @code{floor (-1.5)} is @code{-2.0}.
@end deftypefun
-@comment math.h
-@comment ISO
@deftypefun double trunc (double @var{x})
-@comment math.h
-@comment ISO
@deftypefunx float truncf (float @var{x})
-@comment math.h
-@comment ISO
@deftypefunx {long double} truncl (long double @var{x})
-@code{trunc} is another name for @code{floor}
+@deftypefunx _FloatN truncfN (_Float@var{N} @var{x})
+@deftypefunx _FloatNx truncfNx (_Float@var{N}x @var{x})
+@standards{ISO, math.h}
+@standardsx{truncfN, TS 18661-3:2015, math.h}
+@standardsx{truncfNx, TS 18661-3:2015, math.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
+The @code{trunc} functions round @var{x} towards zero to the nearest
+integer (returned in floating-point format). Thus, @code{trunc (1.5)}
+is @code{1.0} and @code{trunc (-1.5)} is @code{-1.0}.
@end deftypefun
-@comment math.h
-@comment ISO
@deftypefun double rint (double @var{x})
-@comment math.h
-@comment ISO
@deftypefunx float rintf (float @var{x})
-@comment math.h
-@comment ISO
@deftypefunx {long double} rintl (long double @var{x})
+@deftypefunx _FloatN rintfN (_Float@var{N} @var{x})
+@deftypefunx _FloatNx rintfNx (_Float@var{N}x @var{x})
+@standards{ISO, math.h}
+@standardsx{rintfN, TS 18661-3:2015, math.h}
+@standardsx{rintfNx, TS 18661-3:2015, math.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
These functions round @var{x} to an integer value according to the
current rounding mode. @xref{Floating Point Parameters}, for
information about the various rounding modes. The default
inexact exception.
@end deftypefun
-@comment math.h
-@comment ISO
@deftypefun double nearbyint (double @var{x})
-@comment math.h
-@comment ISO
@deftypefunx float nearbyintf (float @var{x})
-@comment math.h
-@comment ISO
@deftypefunx {long double} nearbyintl (long double @var{x})
+@deftypefunx _FloatN nearbyintfN (_Float@var{N} @var{x})
+@deftypefunx _FloatNx nearbyintfNx (_Float@var{N}x @var{x})
+@standards{ISO, math.h}
+@standardsx{nearbyintfN, TS 18661-3:2015, math.h}
+@standardsx{nearbyintfNx, TS 18661-3:2015, math.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
These functions return the same value as the @code{rint} functions, but
do not raise the inexact exception if @var{x} is not an integer.
@end deftypefun
-@comment math.h
-@comment ISO
@deftypefun double round (double @var{x})
-@comment math.h
-@comment ISO
@deftypefunx float roundf (float @var{x})
-@comment math.h
-@comment ISO
@deftypefunx {long double} roundl (long double @var{x})
+@deftypefunx _FloatN roundfN (_Float@var{N} @var{x})
+@deftypefunx _FloatNx roundfNx (_Float@var{N}x @var{x})
+@standards{ISO, math.h}
+@standardsx{roundfN, TS 18661-3:2015, math.h}
+@standardsx{roundfNx, TS 18661-3:2015, math.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
These functions are similar to @code{rint}, but they round halfway
-cases away from zero instead of to the nearest even integer.
+cases away from zero instead of to the nearest integer (or other
+current rounding mode).
+@end deftypefun
+
+@deftypefun double roundeven (double @var{x})
+@deftypefunx float roundevenf (float @var{x})
+@deftypefunx {long double} roundevenl (long double @var{x})
+@deftypefunx _FloatN roundevenfN (_Float@var{N} @var{x})
+@deftypefunx _FloatNx roundevenfNx (_Float@var{N}x @var{x})
+@standards{ISO, math.h}
+@standardsx{roundevenfN, TS 18661-3:2015, math.h}
+@standardsx{roundevenfNx, TS 18661-3:2015, math.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
+These functions, from TS 18661-1:2014 and TS 18661-3:2015, are similar
+to @code{round}, but they round halfway cases to even instead of away
+from zero.
@end deftypefun
-@comment math.h
-@comment ISO
@deftypefun {long int} lrint (double @var{x})
-@comment math.h
-@comment ISO
@deftypefunx {long int} lrintf (float @var{x})
-@comment math.h
-@comment ISO
@deftypefunx {long int} lrintl (long double @var{x})
+@deftypefunx {long int} lrintfN (_Float@var{N} @var{x})
+@deftypefunx {long int} lrintfNx (_Float@var{N}x @var{x})
+@standards{ISO, math.h}
+@standardsx{lrintfN, TS 18661-3:2015, math.h}
+@standardsx{lrintfNx, TS 18661-3:2015, math.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
These functions are just like @code{rint}, but they return a
@code{long int} instead of a floating-point number.
@end deftypefun
-@comment math.h
-@comment ISO
@deftypefun {long long int} llrint (double @var{x})
-@comment math.h
-@comment ISO
@deftypefunx {long long int} llrintf (float @var{x})
-@comment math.h
-@comment ISO
@deftypefunx {long long int} llrintl (long double @var{x})
+@deftypefunx {long long int} llrintfN (_Float@var{N} @var{x})
+@deftypefunx {long long int} llrintfNx (_Float@var{N}x @var{x})
+@standards{ISO, math.h}
+@standardsx{llrintfN, TS 18661-3:2015, math.h}
+@standardsx{llrintfNx, TS 18661-3:2015, math.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
These functions are just like @code{rint}, but they return a
@code{long long int} instead of a floating-point number.
@end deftypefun
-@comment math.h
-@comment ISO
@deftypefun {long int} lround (double @var{x})
-@comment math.h
-@comment ISO
@deftypefunx {long int} lroundf (float @var{x})
-@comment math.h
-@comment ISO
@deftypefunx {long int} lroundl (long double @var{x})
+@deftypefunx {long int} lroundfN (_Float@var{N} @var{x})
+@deftypefunx {long int} lroundfNx (_Float@var{N}x @var{x})
+@standards{ISO, math.h}
+@standardsx{lroundfN, TS 18661-3:2015, math.h}
+@standardsx{lroundfNx, TS 18661-3:2015, math.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
These functions are just like @code{round}, but they return a
@code{long int} instead of a floating-point number.
@end deftypefun
-@comment math.h
-@comment ISO
@deftypefun {long long int} llround (double @var{x})
-@comment math.h
-@comment ISO
@deftypefunx {long long int} llroundf (float @var{x})
-@comment math.h
-@comment ISO
@deftypefunx {long long int} llroundl (long double @var{x})
+@deftypefunx {long long int} llroundfN (_Float@var{N} @var{x})
+@deftypefunx {long long int} llroundfNx (_Float@var{N}x @var{x})
+@standards{ISO, math.h}
+@standardsx{llroundfN, TS 18661-3:2015, math.h}
+@standardsx{llroundfNx, TS 18661-3:2015, math.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
These functions are just like @code{round}, but they return a
@code{long long int} instead of a floating-point number.
@end deftypefun
+@deftypefun intmax_t fromfp (double @var{x}, int @var{round}, unsigned int @var{width})
+@deftypefunx intmax_t fromfpf (float @var{x}, int @var{round}, unsigned int @var{width})
+@deftypefunx intmax_t fromfpl (long double @var{x}, int @var{round}, unsigned int @var{width})
+@deftypefunx intmax_t fromfpfN (_Float@var{N} @var{x}, int @var{round}, unsigned int @var{width})
+@deftypefunx intmax_t fromfpfNx (_Float@var{N}x @var{x}, int @var{round}, unsigned int @var{width})
+@deftypefunx uintmax_t ufromfp (double @var{x}, int @var{round}, unsigned int @var{width})
+@deftypefunx uintmax_t ufromfpf (float @var{x}, int @var{round}, unsigned int @var{width})
+@deftypefunx uintmax_t ufromfpl (long double @var{x}, int @var{round}, unsigned int @var{width})
+@deftypefunx uintmax_t ufromfpfN (_Float@var{N} @var{x}, int @var{round}, unsigned int @var{width})
+@deftypefunx uintmax_t ufromfpfNx (_Float@var{N}x @var{x}, int @var{round}, unsigned int @var{width})
+@deftypefunx intmax_t fromfpx (double @var{x}, int @var{round}, unsigned int @var{width})
+@deftypefunx intmax_t fromfpxf (float @var{x}, int @var{round}, unsigned int @var{width})
+@deftypefunx intmax_t fromfpxl (long double @var{x}, int @var{round}, unsigned int @var{width})
+@deftypefunx intmax_t fromfpxfN (_Float@var{N} @var{x}, int @var{round}, unsigned int @var{width})
+@deftypefunx intmax_t fromfpxfNx (_Float@var{N}x @var{x}, int @var{round}, unsigned int @var{width})
+@deftypefunx uintmax_t ufromfpx (double @var{x}, int @var{round}, unsigned int @var{width})
+@deftypefunx uintmax_t ufromfpxf (float @var{x}, int @var{round}, unsigned int @var{width})
+@deftypefunx uintmax_t ufromfpxl (long double @var{x}, int @var{round}, unsigned int @var{width})
+@deftypefunx uintmax_t ufromfpxfN (_Float@var{N} @var{x}, int @var{round}, unsigned int @var{width})
+@deftypefunx uintmax_t ufromfpxfNx (_Float@var{N}x @var{x}, int @var{round}, unsigned int @var{width})
+@standards{ISO, math.h}
+@standardsx{fromfpfN, TS 18661-3:2015, math.h}
+@standardsx{fromfpfNx, TS 18661-3:2015, math.h}
+@standardsx{ufromfpfN, TS 18661-3:2015, math.h}
+@standardsx{ufromfpfNx, TS 18661-3:2015, math.h}
+@standardsx{fromfpxfN, TS 18661-3:2015, math.h}
+@standardsx{fromfpxfNx, TS 18661-3:2015, math.h}
+@standardsx{ufromfpxfN, TS 18661-3:2015, math.h}
+@standardsx{ufromfpxfNx, TS 18661-3:2015, math.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
+These functions, from TS 18661-1:2014 and TS 18661-3:2015, convert a
+floating-point number to an integer according to the rounding direction
+@var{round} (one of the @code{FP_INT_*} macros). If the integer is
+outside the range of a signed or unsigned (depending on the return type
+of the function) type of width @var{width} bits (or outside the range of
+the return type, if @var{width} is larger), or if @var{x} is infinite or
+NaN, or if @var{width} is zero, a domain error occurs and an unspecified
+value is returned. The functions with an @samp{x} in their names raise
+the inexact exception when a domain error does not occur and the
+argument is not an integer; the other functions do not raise the inexact
+exception.
+@end deftypefun
+
-@comment math.h
-@comment ISO
@deftypefun double modf (double @var{value}, double *@var{integer-part})
-@comment math.h
-@comment ISO
@deftypefunx float modff (float @var{value}, float *@var{integer-part})
-@comment math.h
-@comment ISO
@deftypefunx {long double} modfl (long double @var{value}, long double *@var{integer-part})
+@deftypefunx _FloatN modffN (_Float@var{N} @var{value}, _Float@var{N} *@var{integer-part})
+@deftypefunx _FloatNx modffNx (_Float@var{N}x @var{value}, _Float@var{N}x *@var{integer-part})
+@standards{ISO, math.h}
+@standardsx{modffN, TS 18661-3:2015, math.h}
+@standardsx{modffNx, TS 18661-3:2015, math.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
These functions break the argument @var{value} into an integer part and a
fractional part (between @code{-1} and @code{1}, exclusive). Their sum
equals @var{value}. Each of the parts has the same sign as @var{value},
floating-point numbers. Each is a little different; pick the one that
suits your problem.
-@comment math.h
-@comment ISO
@deftypefun double fmod (double @var{numerator}, double @var{denominator})
-@comment math.h
-@comment ISO
@deftypefunx float fmodf (float @var{numerator}, float @var{denominator})
-@comment math.h
-@comment ISO
@deftypefunx {long double} fmodl (long double @var{numerator}, long double @var{denominator})
+@deftypefunx _FloatN fmodfN (_Float@var{N} @var{numerator}, _Float@var{N} @var{denominator})
+@deftypefunx _FloatNx fmodfNx (_Float@var{N}x @var{numerator}, _Float@var{N}x @var{denominator})
+@standards{ISO, math.h}
+@standardsx{fmodfN, TS 18661-3:2015, math.h}
+@standardsx{fmodfNx, TS 18661-3:2015, math.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
These functions compute the remainder from the division of
@var{numerator} by @var{denominator}. Specifically, the return value is
@code{@var{numerator} - @w{@var{n} * @var{denominator}}}, where @var{n}
If @var{denominator} is zero, @code{fmod} signals a domain error.
@end deftypefun
-@comment math.h
-@comment BSD
-@deftypefun double drem (double @var{numerator}, double @var{denominator})
-@comment math.h
-@comment BSD
-@deftypefunx float dremf (float @var{numerator}, float @var{denominator})
-@comment math.h
-@comment BSD
-@deftypefunx {long double} dreml (long double @var{numerator}, long double @var{denominator})
-These functions are like @code{fmod} except that they rounds the
+@deftypefun double remainder (double @var{numerator}, double @var{denominator})
+@deftypefunx float remainderf (float @var{numerator}, float @var{denominator})
+@deftypefunx {long double} remainderl (long double @var{numerator}, long double @var{denominator})
+@deftypefunx _FloatN remainderfN (_Float@var{N} @var{numerator}, _Float@var{N} @var{denominator})
+@deftypefunx _FloatNx remainderfNx (_Float@var{N}x @var{numerator}, _Float@var{N}x @var{denominator})
+@standards{ISO, math.h}
+@standardsx{remainderfN, TS 18661-3:2015, math.h}
+@standardsx{remainderfNx, TS 18661-3:2015, math.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
+These functions are like @code{fmod} except that they round the
internal quotient @var{n} to the nearest integer instead of towards zero
-to an integer. For example, @code{drem (6.5, 2.3)} returns @code{-0.4},
-which is @code{6.5} minus @code{6.9}.
+to an integer. For example, @code{remainder (6.5, 2.3)} returns
+@code{-0.4}, which is @code{6.5} minus @code{6.9}.
The absolute value of the result is less than or equal to half the
absolute value of the @var{denominator}. The difference between
-@code{fmod (@var{numerator}, @var{denominator})} and @code{drem
+@code{fmod (@var{numerator}, @var{denominator})} and @code{remainder
(@var{numerator}, @var{denominator})} is always either
@var{denominator}, minus @var{denominator}, or zero.
-If @var{denominator} is zero, @code{drem} signals a domain error.
+If @var{denominator} is zero, @code{remainder} signals a domain error.
@end deftypefun
-@comment math.h
-@comment BSD
-@deftypefun double remainder (double @var{numerator}, double @var{denominator})
-@comment math.h
-@comment BSD
-@deftypefunx float remainderf (float @var{numerator}, float @var{denominator})
-@comment math.h
-@comment BSD
-@deftypefunx {long double} remainderl (long double @var{numerator}, long double @var{denominator})
-This function is another name for @code{drem}.
+@deftypefun double drem (double @var{numerator}, double @var{denominator})
+@deftypefunx float dremf (float @var{numerator}, float @var{denominator})
+@deftypefunx {long double} dreml (long double @var{numerator}, long double @var{denominator})
+@standards{BSD, math.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
+This function is another name for @code{remainder}.
@end deftypefun
@node FP Bit Twiddling
@cindex FP arithmetic
There are some operations that are too complicated or expensive to
-perform by hand on floating-point numbers. @w{ISO C 9x} defines
+perform by hand on floating-point numbers. @w{ISO C99} defines
functions to do these operations, which mostly involve changing single
bits.
-@comment math.h
-@comment ISO
@deftypefun double copysign (double @var{x}, double @var{y})
-@comment math.h
-@comment ISO
@deftypefunx float copysignf (float @var{x}, float @var{y})
-@comment math.h
-@comment ISO
@deftypefunx {long double} copysignl (long double @var{x}, long double @var{y})
+@deftypefunx _FloatN copysignfN (_Float@var{N} @var{x}, _Float@var{N} @var{y})
+@deftypefunx _FloatNx copysignfNx (_Float@var{N}x @var{x}, _Float@var{N}x @var{y})
+@standards{ISO, math.h}
+@standardsx{copysignfN, TS 18661-3:2015, math.h}
+@standardsx{copysignfNx, TS 18661-3:2015, math.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
These functions return @var{x} but with the sign of @var{y}. They work
even if @var{x} or @var{y} are NaN or zero. Both of these can carry a
sign (although not all implementations support it) and this is one of
recommended functions in @w{IEEE 754}/@w{IEEE 854}).
@end deftypefun
-@comment math.h
-@comment ISO
@deftypefun int signbit (@emph{float-type} @var{x})
+@standards{ISO, math.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
@code{signbit} is a generic macro which can work on all floating-point
types. It returns a nonzero value if the value of @var{x} has its sign
bit set.
false, but @code{signbit (-0.0)} will return a nonzero value.
@end deftypefun
-@comment math.h
-@comment ISO
@deftypefun double nextafter (double @var{x}, double @var{y})
-@comment math.h
-@comment ISO
@deftypefunx float nextafterf (float @var{x}, float @var{y})
-@comment math.h
-@comment ISO
@deftypefunx {long double} nextafterl (long double @var{x}, long double @var{y})
+@deftypefunx _FloatN nextafterfN (_Float@var{N} @var{x}, _Float@var{N} @var{y})
+@deftypefunx _FloatNx nextafterfNx (_Float@var{N}x @var{x}, _Float@var{N}x @var{y})
+@standards{ISO, math.h}
+@standardsx{nextafterfN, TS 18661-3:2015, math.h}
+@standardsx{nextafterfNx, TS 18661-3:2015, math.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
The @code{nextafter} function returns the next representable neighbor of
@var{x} in the direction towards @var{y}. The size of the step between
@var{x} and the result depends on the type of the result. If
-@math{@var{x} = @var{y}} the function simply returns @var{x}. If either
+@math{@var{x} = @var{y}} the function simply returns @var{y}. If either
value is @code{NaN}, @code{NaN} is returned. Otherwise
a value corresponding to the value of the least significant bit in the
mantissa is added or subtracted, depending on the direction.
recommended functions in @w{IEEE 754}/@w{IEEE 854}).
@end deftypefun
-@comment math.h
-@comment ISO
@deftypefun double nexttoward (double @var{x}, long double @var{y})
-@comment math.h
-@comment ISO
@deftypefunx float nexttowardf (float @var{x}, long double @var{y})
-@comment math.h
-@comment ISO
@deftypefunx {long double} nexttowardl (long double @var{x}, long double @var{y})
+@standards{ISO, math.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
These functions are identical to the corresponding versions of
@code{nextafter} except that their second argument is a @code{long
double}.
@end deftypefun
+@deftypefun double nextup (double @var{x})
+@deftypefunx float nextupf (float @var{x})
+@deftypefunx {long double} nextupl (long double @var{x})
+@deftypefunx _FloatN nextupfN (_Float@var{N} @var{x})
+@deftypefunx _FloatNx nextupfNx (_Float@var{N}x @var{x})
+@standards{ISO, math.h}
+@standardsx{nextupfN, TS 18661-3:2015, math.h}
+@standardsx{nextupfNx, TS 18661-3:2015, math.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
+The @code{nextup} function returns the next representable neighbor of @var{x}
+in the direction of positive infinity. If @var{x} is the smallest negative
+subnormal number in the type of @var{x} the function returns @code{-0}. If
+@math{@var{x} = @code{0}} the function returns the smallest positive subnormal
+number in the type of @var{x}. If @var{x} is NaN, NaN is returned.
+If @var{x} is @math{+@infinity{}}, @math{+@infinity{}} is returned.
+@code{nextup} is from TS 18661-1:2014 and TS 18661-3:2015.
+@code{nextup} never raises an exception except for signaling NaNs.
+@end deftypefun
+
+@deftypefun double nextdown (double @var{x})
+@deftypefunx float nextdownf (float @var{x})
+@deftypefunx {long double} nextdownl (long double @var{x})
+@deftypefunx _FloatN nextdownfN (_Float@var{N} @var{x})
+@deftypefunx _FloatNx nextdownfNx (_Float@var{N}x @var{x})
+@standards{ISO, math.h}
+@standardsx{nextdownfN, TS 18661-3:2015, math.h}
+@standardsx{nextdownfNx, TS 18661-3:2015, math.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
+The @code{nextdown} function returns the next representable neighbor of @var{x}
+in the direction of negative infinity. If @var{x} is the smallest positive
+subnormal number in the type of @var{x} the function returns @code{+0}. If
+@math{@var{x} = @code{0}} the function returns the smallest negative subnormal
+number in the type of @var{x}. If @var{x} is NaN, NaN is returned.
+If @var{x} is @math{-@infinity{}}, @math{-@infinity{}} is returned.
+@code{nextdown} is from TS 18661-1:2014 and TS 18661-3:2015.
+@code{nextdown} never raises an exception except for signaling NaNs.
+@end deftypefun
+
@cindex NaN
-@comment math.h
-@comment ISO
@deftypefun double nan (const char *@var{tagp})
-@comment math.h
-@comment ISO
@deftypefunx float nanf (const char *@var{tagp})
-@comment math.h
-@comment ISO
@deftypefunx {long double} nanl (const char *@var{tagp})
+@deftypefunx _FloatN nanfN (const char *@var{tagp})
+@deftypefunx _FloatNx nanfNx (const char *@var{tagp})
+@standards{ISO, math.h}
+@standardsx{nanfN, TS 18661-3:2015, math.h}
+@standardsx{nanfNx, TS 18661-3:2015, math.h}
+@safety{@prelim{}@mtsafe{@mtslocale{}}@assafe{}@acsafe{}}
+@c The unsafe-but-ruled-safe locale use comes from strtod.
The @code{nan} function returns a representation of NaN, provided that
NaN is supported by the target platform.
@code{nan ("@var{n-char-sequence}")} is equivalent to
selects one. On other systems it may do nothing.
@end deftypefun
+@deftypefun int canonicalize (double *@var{cx}, const double *@var{x})
+@deftypefunx int canonicalizef (float *@var{cx}, const float *@var{x})
+@deftypefunx int canonicalizel (long double *@var{cx}, const long double *@var{x})
+@deftypefunx int canonicalizefN (_Float@var{N} *@var{cx}, const _Float@var{N} *@var{x})
+@deftypefunx int canonicalizefNx (_Float@var{N}x *@var{cx}, const _Float@var{N}x *@var{x})
+@standards{ISO, math.h}
+@standardsx{canonicalizefN, TS 18661-3:2015, math.h}
+@standardsx{canonicalizefNx, TS 18661-3:2015, math.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
+In some floating-point formats, some values have canonical (preferred)
+and noncanonical encodings (for IEEE interchange binary formats, all
+encodings are canonical). These functions, defined by TS
+18661-1:2014 and TS 18661-3:2015, attempt to produce a canonical version
+of the floating-point value pointed to by @var{x}; if that value is a
+signaling NaN, they raise the invalid exception and produce a quiet
+NaN. If a canonical value is produced, it is stored in the object
+pointed to by @var{cx}, and these functions return zero. Otherwise
+(if a canonical value could not be produced because the object pointed
+to by @var{x} is not a valid representation of any floating-point
+value), the object pointed to by @var{cx} is unchanged and a nonzero
+value is returned.
+
+Note that some formats have multiple encodings of a value which are
+all equally canonical; when such an encoding is used as an input to
+this function, any such encoding of the same value (or of the
+corresponding quiet NaN, if that value is a signaling NaN) may be
+produced as output.
+@end deftypefun
+
+@deftypefun double getpayload (const double *@var{x})
+@deftypefunx float getpayloadf (const float *@var{x})
+@deftypefunx {long double} getpayloadl (const long double *@var{x})
+@deftypefunx _FloatN getpayloadfN (const _Float@var{N} *@var{x})
+@deftypefunx _FloatNx getpayloadfNx (const _Float@var{N}x *@var{x})
+@standards{ISO, math.h}
+@standardsx{getpayloadfN, TS 18661-3:2015, math.h}
+@standardsx{getpayloadfNx, TS 18661-3:2015, math.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
+IEEE 754 defines the @dfn{payload} of a NaN to be an integer value
+encoded in the representation of the NaN. Payloads are typically
+propagated from NaN inputs to the result of a floating-point
+operation. These functions, defined by TS 18661-1:2014 and TS
+18661-3:2015, return the payload of the NaN pointed to by @var{x}
+(returned as a positive integer, or positive zero, represented as a
+floating-point number); if @var{x} is not a NaN, they return an
+unspecified value. They raise no floating-point exceptions even for
+signaling NaNs.
+@end deftypefun
+
+@deftypefun int setpayload (double *@var{x}, double @var{payload})
+@deftypefunx int setpayloadf (float *@var{x}, float @var{payload})
+@deftypefunx int setpayloadl (long double *@var{x}, long double @var{payload})
+@deftypefunx int setpayloadfN (_Float@var{N} *@var{x}, _Float@var{N} @var{payload})
+@deftypefunx int setpayloadfNx (_Float@var{N}x *@var{x}, _Float@var{N}x @var{payload})
+@standards{ISO, math.h}
+@standardsx{setpayloadfN, TS 18661-3:2015, math.h}
+@standardsx{setpayloadfNx, TS 18661-3:2015, math.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
+These functions, defined by TS 18661-1:2014 and TS 18661-3:2015, set the
+object pointed to by @var{x} to a quiet NaN with payload @var{payload}
+and a zero sign bit and return zero. If @var{payload} is not a
+positive-signed integer that is a valid payload for a quiet NaN of the
+given type, the object pointed to by @var{x} is set to positive zero and
+a nonzero value is returned. They raise no floating-point exceptions.
+@end deftypefun
+
+@deftypefun int setpayloadsig (double *@var{x}, double @var{payload})
+@deftypefunx int setpayloadsigf (float *@var{x}, float @var{payload})
+@deftypefunx int setpayloadsigl (long double *@var{x}, long double @var{payload})
+@deftypefunx int setpayloadsigfN (_Float@var{N} *@var{x}, _Float@var{N} @var{payload})
+@deftypefunx int setpayloadsigfNx (_Float@var{N}x *@var{x}, _Float@var{N}x @var{payload})
+@standards{ISO, math.h}
+@standardsx{setpayloadsigfN, TS 18661-3:2015, math.h}
+@standardsx{setpayloadsigfNx, TS 18661-3:2015, math.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
+These functions, defined by TS 18661-1:2014 and TS 18661-3:2015, set the
+object pointed to by @var{x} to a signaling NaN with payload
+@var{payload} and a zero sign bit and return zero. If @var{payload} is
+not a positive-signed integer that is a valid payload for a signaling
+NaN of the given type, the object pointed to by @var{x} is set to
+positive zero and a nonzero value is returned. They raise no
+floating-point exceptions.
+@end deftypefun
+
@node FP Comparison Functions
@subsection Floating-Point Comparison Functions
@cindex unordered comparison
will raise an exception if @var{a} is NaN. (This does @emph{not}
happen with @code{==} and @code{!=}; those merely return false and true,
respectively, when NaN is examined.) Frequently this exception is
-undesirable. @w{ISO C 9x} therefore defines comparison functions that
+undesirable. @w{ISO C99} therefore defines comparison functions that
do not raise exceptions when NaN is examined. All of the functions are
implemented as macros which allow their arguments to be of any
floating-point type. The macros are guaranteed to evaluate their
-arguments only once.
+arguments only once. TS 18661-1:2014 adds such a macro for an
+equality comparison that @emph{does} raise an exception for a NaN
+argument; it also adds functions that provide a total ordering on all
+floating-point values, including NaNs, without raising any exceptions
+even for signaling NaNs.
-@comment math.h
-@comment ISO
@deftypefn Macro int isgreater (@emph{real-floating} @var{x}, @emph{real-floating} @var{y})
+@standards{ISO, math.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
This macro determines whether the argument @var{x} is greater than
@var{y}. It is equivalent to @code{(@var{x}) > (@var{y})}, but no
exception is raised if @var{x} or @var{y} are NaN.
@end deftypefn
-@comment math.h
-@comment ISO
@deftypefn Macro int isgreaterequal (@emph{real-floating} @var{x}, @emph{real-floating} @var{y})
+@standards{ISO, math.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
This macro determines whether the argument @var{x} is greater than or
equal to @var{y}. It is equivalent to @code{(@var{x}) >= (@var{y})}, but no
exception is raised if @var{x} or @var{y} are NaN.
@end deftypefn
-@comment math.h
-@comment ISO
@deftypefn Macro int isless (@emph{real-floating} @var{x}, @emph{real-floating} @var{y})
+@standards{ISO, math.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
This macro determines whether the argument @var{x} is less than @var{y}.
It is equivalent to @code{(@var{x}) < (@var{y})}, but no exception is
raised if @var{x} or @var{y} are NaN.
@end deftypefn
-@comment math.h
-@comment ISO
@deftypefn Macro int islessequal (@emph{real-floating} @var{x}, @emph{real-floating} @var{y})
+@standards{ISO, math.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
This macro determines whether the argument @var{x} is less than or equal
to @var{y}. It is equivalent to @code{(@var{x}) <= (@var{y})}, but no
exception is raised if @var{x} or @var{y} are NaN.
@end deftypefn
-@comment math.h
-@comment ISO
@deftypefn Macro int islessgreater (@emph{real-floating} @var{x}, @emph{real-floating} @var{y})
+@standards{ISO, math.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
This macro determines whether the argument @var{x} is less or greater
than @var{y}. It is equivalent to @code{(@var{x}) < (@var{y}) ||
(@var{x}) > (@var{y})} (although it only evaluates @var{x} and @var{y}
expression is true if @var{x} or @var{y} are NaN.
@end deftypefn
-@comment math.h
-@comment ISO
@deftypefn Macro int isunordered (@emph{real-floating} @var{x}, @emph{real-floating} @var{y})
+@standards{ISO, math.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
This macro determines whether its arguments are unordered. In other
words, it is true if @var{x} or @var{y} are NaN, and false otherwise.
@end deftypefn
+@deftypefn Macro int iseqsig (@emph{real-floating} @var{x}, @emph{real-floating} @var{y})
+@standards{ISO, math.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
+This macro determines whether its arguments are equal. It is
+equivalent to @code{(@var{x}) == (@var{y})}, but it raises the invalid
+exception and sets @code{errno} to @code{EDOM} if either argument is a
+NaN.
+@end deftypefn
+
+@deftypefun int totalorder (double @var{x}, double @var{y})
+@deftypefunx int totalorderf (float @var{x}, float @var{y})
+@deftypefunx int totalorderl (long double @var{x}, long double @var{y})
+@deftypefunx int totalorderfN (_Float@var{N} @var{x}, _Float@var{N} @var{y})
+@deftypefunx int totalorderfNx (_Float@var{N}x @var{x}, _Float@var{N}x @var{y})
+@standards{TS 18661-1:2014, math.h}
+@standardsx{totalorderfN, TS 18661-3:2015, math.h}
+@standardsx{totalorderfNx, TS 18661-3:2015, math.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
+These functions determine whether the total order relationship,
+defined in IEEE 754-2008, is true for @var{x} and @var{y}, returning
+nonzero if it is true and zero if it is false. No exceptions are
+raised even for signaling NaNs. The relationship is true if they are
+the same floating-point value (including sign for zero and NaNs, and
+payload for NaNs), or if @var{x} comes before @var{y} in the following
+order: negative quiet NaNs, in order of decreasing payload; negative
+signaling NaNs, in order of decreasing payload; negative infinity;
+finite numbers, in ascending order, with negative zero before positive
+zero; positive infinity; positive signaling NaNs, in order of
+increasing payload; positive quiet NaNs, in order of increasing
+payload.
+@end deftypefun
+
+@deftypefun int totalordermag (double @var{x}, double @var{y})
+@deftypefunx int totalordermagf (float @var{x}, float @var{y})
+@deftypefunx int totalordermagl (long double @var{x}, long double @var{y})
+@deftypefunx int totalordermagfN (_Float@var{N} @var{x}, _Float@var{N} @var{y})
+@deftypefunx int totalordermagfNx (_Float@var{N}x @var{x}, _Float@var{N}x @var{y})
+@standards{TS 18661-1:2014, math.h}
+@standardsx{totalordermagfN, TS 18661-3:2015, math.h}
+@standardsx{totalordermagfNx, TS 18661-3:2015, math.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
+These functions determine whether the total order relationship,
+defined in IEEE 754-2008, is true for the absolute values of @var{x}
+and @var{y}, returning nonzero if it is true and zero if it is false.
+No exceptions are raised even for signaling NaNs.
+@end deftypefun
+
Not all machines provide hardware support for these operations. On
machines that don't, the macros can be very slow. Therefore, you should
not use these functions when NaN is not a concern.
-@strong{Note:} There are no macros @code{isequal} or @code{isunequal}.
+@strong{NB:} There are no macros @code{isequal} or @code{isunequal}.
They are unnecessary, because the @code{==} and @code{!=} operators do
@emph{not} throw an exception if one or both of the operands are NaN.
processors these functions can use special machine instructions to
perform these operations faster than the equivalent C code.
-@comment math.h
-@comment ISO
@deftypefun double fmin (double @var{x}, double @var{y})
-@comment math.h
-@comment ISO
@deftypefunx float fminf (float @var{x}, float @var{y})
-@comment math.h
-@comment ISO
@deftypefunx {long double} fminl (long double @var{x}, long double @var{y})
+@deftypefunx _FloatN fminfN (_Float@var{N} @var{x}, _Float@var{N} @var{y})
+@deftypefunx _FloatNx fminfNx (_Float@var{N}x @var{x}, _Float@var{N}x @var{y})
+@standards{ISO, math.h}
+@standardsx{fminfN, TS 18661-3:2015, math.h}
+@standardsx{fminfNx, TS 18661-3:2015, math.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
The @code{fmin} function returns the lesser of the two values @var{x}
and @var{y}. It is similar to the expression
@smallexample
are NaN, NaN is returned.
@end deftypefun
-@comment math.h
-@comment ISO
@deftypefun double fmax (double @var{x}, double @var{y})
-@comment math.h
-@comment ISO
@deftypefunx float fmaxf (float @var{x}, float @var{y})
-@comment math.h
-@comment ISO
@deftypefunx {long double} fmaxl (long double @var{x}, long double @var{y})
+@deftypefunx _FloatN fmaxfN (_Float@var{N} @var{x}, _Float@var{N} @var{y})
+@deftypefunx _FloatNx fmaxfNx (_Float@var{N}x @var{x}, _Float@var{N}x @var{y})
+@standards{ISO, math.h}
+@standardsx{fmaxfN, TS 18661-3:2015, math.h}
+@standardsx{fmaxfNx, TS 18661-3:2015, math.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
The @code{fmax} function returns the greater of the two values @var{x}
and @var{y}.
are NaN, NaN is returned.
@end deftypefun
-@comment math.h
-@comment ISO
+@deftypefun double fminmag (double @var{x}, double @var{y})
+@deftypefunx float fminmagf (float @var{x}, float @var{y})
+@deftypefunx {long double} fminmagl (long double @var{x}, long double @var{y})
+@deftypefunx _FloatN fminmagfN (_Float@var{N} @var{x}, _Float@var{N} @var{y})
+@deftypefunx _FloatNx fminmagfNx (_Float@var{N}x @var{x}, _Float@var{N}x @var{y})
+@standards{ISO, math.h}
+@standardsx{fminmagfN, TS 18661-3:2015, math.h}
+@standardsx{fminmagfNx, TS 18661-3:2015, math.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
+These functions, from TS 18661-1:2014 and TS 18661-3:2015, return
+whichever of the two values @var{x} and @var{y} has the smaller absolute
+value. If both have the same absolute value, or either is NaN, they
+behave the same as the @code{fmin} functions.
+@end deftypefun
+
+@deftypefun double fmaxmag (double @var{x}, double @var{y})
+@deftypefunx float fmaxmagf (float @var{x}, float @var{y})
+@deftypefunx {long double} fmaxmagl (long double @var{x}, long double @var{y})
+@deftypefunx _FloatN fmaxmagfN (_Float@var{N} @var{x}, _Float@var{N} @var{y})
+@deftypefunx _FloatNx fmaxmagfNx (_Float@var{N}x @var{x}, _Float@var{N}x @var{y})
+@standards{ISO, math.h}
+@standardsx{fmaxmagfN, TS 18661-3:2015, math.h}
+@standardsx{fmaxmagfNx, TS 18661-3:2015, math.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
+These functions, from TS 18661-1:2014, return whichever of the two
+values @var{x} and @var{y} has the greater absolute value. If both
+have the same absolute value, or either is NaN, they behave the same
+as the @code{fmax} functions.
+@end deftypefun
+
@deftypefun double fdim (double @var{x}, double @var{y})
-@comment math.h
-@comment ISO
@deftypefunx float fdimf (float @var{x}, float @var{y})
-@comment math.h
-@comment ISO
@deftypefunx {long double} fdiml (long double @var{x}, long double @var{y})
+@deftypefunx _FloatN fdimfN (_Float@var{N} @var{x}, _Float@var{N} @var{y})
+@deftypefunx _FloatNx fdimfNx (_Float@var{N}x @var{x}, _Float@var{N}x @var{y})
+@standards{ISO, math.h}
+@standardsx{fdimfN, TS 18661-3:2015, math.h}
+@standardsx{fdimfNx, TS 18661-3:2015, math.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
The @code{fdim} function returns the positive difference between
@var{x} and @var{y}. The positive difference is @math{@var{x} -
@var{y}} if @var{x} is greater than @var{y}, and @math{0} otherwise.
If @var{x}, @var{y}, or both are NaN, NaN is returned.
@end deftypefun
-@comment math.h
-@comment ISO
@deftypefun double fma (double @var{x}, double @var{y}, double @var{z})
-@comment math.h
-@comment ISO
@deftypefunx float fmaf (float @var{x}, float @var{y}, float @var{z})
-@comment math.h
-@comment ISO
@deftypefunx {long double} fmal (long double @var{x}, long double @var{y}, long double @var{z})
+@deftypefunx _FloatN fmafN (_Float@var{N} @var{x}, _Float@var{N} @var{y}, _Float@var{N} @var{z})
+@deftypefunx _FloatNx fmafNx (_Float@var{N}x @var{x}, _Float@var{N}x @var{y}, _Float@var{N}x @var{z})
+@standards{ISO, math.h}
+@standardsx{fmafN, TS 18661-3:2015, math.h}
+@standardsx{fmafNx, TS 18661-3:2015, math.h}
@cindex butterfly
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
The @code{fma} function performs floating-point multiply-add. This is
the operation @math{(@var{x} @mul{} @var{y}) + @var{z}}, but the
intermediate result is not rounded to the destination type. This can
@file{math.h} defines the symbols @code{FP_FAST_FMA},
@code{FP_FAST_FMAF}, and @code{FP_FAST_FMAL} when the corresponding
version of @code{fma} is no slower than the expression @samp{x*y + z}.
-In the GNU C library, this always means the operation is implemented in
+In @theglibc{}, this always means the operation is implemented in
hardware.
@end deftypefun
+@deftypefun float fadd (double @var{x}, double @var{y})
+@deftypefunx float faddl (long double @var{x}, long double @var{y})
+@deftypefunx double daddl (long double @var{x}, long double @var{y})
+@deftypefunx _FloatM fMaddfN (_Float@var{N} @var{x}, _Float@var{N} @var{y})
+@deftypefunx _FloatM fMaddfNx (_Float@var{N}x @var{x}, _Float@var{N}x @var{y})
+@deftypefunx _FloatMx fMxaddfN (_Float@var{N} @var{x}, _Float@var{N} @var{y})
+@deftypefunx _FloatMx fMxaddfNx (_Float@var{N}x @var{x}, _Float@var{N}x @var{y})
+@standards{TS 18661-1:2014, math.h}
+@standardsx{fMaddfN, TS 18661-3:2015, math.h}
+@standardsx{fMaddfNx, TS 18661-3:2015, math.h}
+@standardsx{fMxaddfN, TS 18661-3:2015, math.h}
+@standardsx{fMxaddfNx, TS 18661-3:2015, math.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
+These functions, from TS 18661-1:2014 and TS 18661-3:2015, return
+@math{@var{x} + @var{y}}, rounded once to the return type of the
+function without any intermediate rounding to the type of the
+arguments.
+@end deftypefun
+
+@deftypefun float fsub (double @var{x}, double @var{y})
+@deftypefunx float fsubl (long double @var{x}, long double @var{y})
+@deftypefunx double dsubl (long double @var{x}, long double @var{y})
+@deftypefunx _FloatM fMsubfN (_Float@var{N} @var{x}, _Float@var{N} @var{y})
+@deftypefunx _FloatM fMsubfNx (_Float@var{N}x @var{x}, _Float@var{N}x @var{y})
+@deftypefunx _FloatMx fMxsubfN (_Float@var{N} @var{x}, _Float@var{N} @var{y})
+@deftypefunx _FloatMx fMxsubfNx (_Float@var{N}x @var{x}, _Float@var{N}x @var{y})
+@standards{TS 18661-1:2014, math.h}
+@standardsx{fMsubfN, TS 18661-3:2015, math.h}
+@standardsx{fMsubfNx, TS 18661-3:2015, math.h}
+@standardsx{fMxsubfN, TS 18661-3:2015, math.h}
+@standardsx{fMxsubfNx, TS 18661-3:2015, math.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
+These functions, from TS 18661-1:2014 and TS 18661-3:2015, return
+@math{@var{x} - @var{y}}, rounded once to the return type of the
+function without any intermediate rounding to the type of the
+arguments.
+@end deftypefun
+
+@deftypefun float fmul (double @var{x}, double @var{y})
+@deftypefunx float fmull (long double @var{x}, long double @var{y})
+@deftypefunx double dmull (long double @var{x}, long double @var{y})
+@deftypefunx _FloatM fMmulfN (_Float@var{N} @var{x}, _Float@var{N} @var{y})
+@deftypefunx _FloatM fMmulfNx (_Float@var{N}x @var{x}, _Float@var{N}x @var{y})
+@deftypefunx _FloatMx fMxmulfN (_Float@var{N} @var{x}, _Float@var{N} @var{y})
+@deftypefunx _FloatMx fMxmulfNx (_Float@var{N}x @var{x}, _Float@var{N}x @var{y})
+@standards{TS 18661-1:2014, math.h}
+@standardsx{fMmulfN, TS 18661-3:2015, math.h}
+@standardsx{fMmulfNx, TS 18661-3:2015, math.h}
+@standardsx{fMxmulfN, TS 18661-3:2015, math.h}
+@standardsx{fMxmulfNx, TS 18661-3:2015, math.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
+These functions, from TS 18661-1:2014 and TS 18661-3:2015, return
+@math{@var{x} * @var{y}}, rounded once to the return type of the
+function without any intermediate rounding to the type of the
+arguments.
+@end deftypefun
+
+@deftypefun float fdiv (double @var{x}, double @var{y})
+@deftypefunx float fdivl (long double @var{x}, long double @var{y})
+@deftypefunx double ddivl (long double @var{x}, long double @var{y})
+@deftypefunx _FloatM fMdivfN (_Float@var{N} @var{x}, _Float@var{N} @var{y})
+@deftypefunx _FloatM fMdivfNx (_Float@var{N}x @var{x}, _Float@var{N}x @var{y})
+@deftypefunx _FloatMx fMxdivfN (_Float@var{N} @var{x}, _Float@var{N} @var{y})
+@deftypefunx _FloatMx fMxdivfNx (_Float@var{N}x @var{x}, _Float@var{N}x @var{y})
+@standards{TS 18661-1:2014, math.h}
+@standardsx{fMdivfN, TS 18661-3:2015, math.h}
+@standardsx{fMdivfNx, TS 18661-3:2015, math.h}
+@standardsx{fMxdivfN, TS 18661-3:2015, math.h}
+@standardsx{fMxdivfNx, TS 18661-3:2015, math.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
+These functions, from TS 18661-1:2014 and TS 18661-3:2015, return
+@math{@var{x} / @var{y}}, rounded once to the return type of the
+function without any intermediate rounding to the type of the
+arguments.
+@end deftypefun
+
@node Complex Numbers
@section Complex Numbers
@pindex complex.h
@cindex complex numbers
-@w{ISO C 9x} introduces support for complex numbers in C. This is done
+@w{ISO C99} introduces support for complex numbers in C. This is done
with a new type qualifier, @code{complex}. It is a keyword if and only
if @file{complex.h} has been included. There are three complex types,
corresponding to the three real types: @code{float complex},
@code{double complex}, and @code{long double complex}.
+Likewise, on machines that have support for @code{_Float@var{N}} or
+@code{_Float@var{N}x} enabled, the complex types @code{_Float@var{N}
+complex} and @code{_Float@var{N}x complex} are also available if
+@file{complex.h} has been included; @pxref{Mathematics}.
+
To construct complex numbers you need a way to indicate the imaginary
part of a number. There is no standard notation for an imaginary
floating point constant. Instead, @file{complex.h} defines two macros
that can be used to create complex numbers.
@deftypevr Macro {const float complex} _Complex_I
+@standards{C99, complex.h}
This macro is a representation of the complex number ``@math{0+1i}''.
Multiplying a real floating-point value by @code{_Complex_I} gives a
complex number whose value is purely imaginary. You can use this to
a shorter name for the same constant.
@deftypevr Macro {const float complex} I
+@standards{C99, complex.h}
This macro has exactly the same value as @code{_Complex_I}. Most of the
time it is preferable. However, it causes problems if you want to use
the identifier @code{I} for something else. You can safely write
@cindex decompose complex numbers
@pindex complex.h
-@w{ISO C 9x} also defines functions that perform basic operations on
+@w{ISO C99} also defines functions that perform basic operations on
complex numbers, such as decomposition and conjugation. The prototypes
for all these functions are in @file{complex.h}. All functions are
available in three variants, one for each of the three complex types.
-@comment complex.h
-@comment ISO
@deftypefun double creal (complex double @var{z})
-@comment complex.h
-@comment ISO
@deftypefunx float crealf (complex float @var{z})
-@comment complex.h
-@comment ISO
@deftypefunx {long double} creall (complex long double @var{z})
+@deftypefunx _FloatN crealfN (complex _Float@var{N} @var{z})
+@deftypefunx _FloatNx crealfNx (complex _Float@var{N}x @var{z})
+@standards{ISO, complex.h}
+@standardsx{crealfN, TS 18661-3:2015, complex.h}
+@standardsx{crealfNx, TS 18661-3:2015, complex.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
These functions return the real part of the complex number @var{z}.
@end deftypefun
-@comment complex.h
-@comment ISO
@deftypefun double cimag (complex double @var{z})
-@comment complex.h
-@comment ISO
@deftypefunx float cimagf (complex float @var{z})
-@comment complex.h
-@comment ISO
@deftypefunx {long double} cimagl (complex long double @var{z})
+@deftypefunx _FloatN cimagfN (complex _Float@var{N} @var{z})
+@deftypefunx _FloatNx cimagfNx (complex _Float@var{N}x @var{z})
+@standards{ISO, complex.h}
+@standardsx{cimagfN, TS 18661-3:2015, complex.h}
+@standardsx{cimagfNx, TS 18661-3:2015, complex.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
These functions return the imaginary part of the complex number @var{z}.
@end deftypefun
-@comment complex.h
-@comment ISO
@deftypefun {complex double} conj (complex double @var{z})
-@comment complex.h
-@comment ISO
@deftypefunx {complex float} conjf (complex float @var{z})
-@comment complex.h
-@comment ISO
@deftypefunx {complex long double} conjl (complex long double @var{z})
+@deftypefunx {complex _FloatN} conjfN (complex _Float@var{N} @var{z})
+@deftypefunx {complex _FloatNx} conjfNx (complex _Float@var{N}x @var{z})
+@standards{ISO, complex.h}
+@standardsx{conjfN, TS 18661-3:2015, complex.h}
+@standardsx{conjfNx, TS 18661-3:2015, complex.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
These functions return the conjugate value of the complex number
@var{z}. The conjugate of a complex number has the same real part and a
negated imaginary part. In other words, @samp{conj(a + bi) = a + -bi}.
@end deftypefun
-@comment complex.h
-@comment ISO
@deftypefun double carg (complex double @var{z})
-@comment complex.h
-@comment ISO
@deftypefunx float cargf (complex float @var{z})
-@comment complex.h
-@comment ISO
@deftypefunx {long double} cargl (complex long double @var{z})
+@deftypefunx _FloatN cargfN (complex _Float@var{N} @var{z})
+@deftypefunx _FloatNx cargfNx (complex _Float@var{N}x @var{z})
+@standards{ISO, complex.h}
+@standardsx{cargfN, TS 18661-3:2015, complex.h}
+@standardsx{cargfNx, TS 18661-3:2015, complex.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
These functions return the argument of the complex number @var{z}.
The argument of a complex number is the angle in the complex plane
between the positive real axis and a line passing through zero and the
-number. This angle is measured in the usual fashion and ranges from @math{0}
-to @math{2@pi{}}.
+number. This angle is measured in the usual fashion and ranges from
+@math{-@pi{}} to @math{@pi{}}.
-@code{carg} has a branch cut along the positive real axis.
+@code{carg} has a branch cut along the negative real axis.
@end deftypefun
-@comment complex.h
-@comment ISO
@deftypefun {complex double} cproj (complex double @var{z})
-@comment complex.h
-@comment ISO
@deftypefunx {complex float} cprojf (complex float @var{z})
-@comment complex.h
-@comment ISO
@deftypefunx {complex long double} cprojl (complex long double @var{z})
+@deftypefunx {complex _FloatN} cprojfN (complex _Float@var{N} @var{z})
+@deftypefunx {complex _FloatNx} cprojfNx (complex _Float@var{N}x @var{z})
+@standards{ISO, complex.h}
+@standardsx{cprojfN, TS 18661-3:2015, complex.h}
+@standardsx{cprojfNx, TS 18661-3:2015, complex.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
These functions return the projection of the complex value @var{z} onto
-the Riemann sphere. Values with a infinite imaginary part are projected
+the Riemann sphere. Values with an infinite imaginary part are projected
to positive infinity on the real axis, even if the real part is NaN. If
the real part is infinite, the result is equivalent to
@end smallexample
@end deftypefun
-@node Integer Division
-@section Integer Division
-@cindex integer division functions
-
-This section describes functions for performing integer division. These
-functions are redundant when GNU CC is used, because 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: towards zero. The remainder has the same sign as the
-numerator.
-
-These functions are specified to return a result @var{r} such that the value
-@code{@var{r}.quot*@var{denominator} + @var{r}.rem} equals
-@var{numerator}.
-
-@pindex stdlib.h
-To use these facilities, you should include the header file
-@file{stdlib.h} in your program.
-
-@comment stdlib.h
-@comment ISO
-@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 ISO
-@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.
-
-Here is an example, albeit not a very useful one.
-
-@smallexample
-div_t result;
-result = div (20, -6);
-@end smallexample
-
-@noindent
-Now @code{result.quot} is @code{-3} and @code{result.rem} is @code{2}.
-@end deftypefun
-
-@comment stdlib.h
-@comment ISO
-@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 @code{div_t} except that the components are of
-type @code{long int} rather than @code{int}.)
-@end deftp
-
-@comment stdlib.h
-@comment ISO
-@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_t}.
-@end deftypefun
-
-@comment stdlib.h
-@comment ISO
-@deftp {Data Type} lldiv_t
-This is a structure type used to hold the result returned by the @code{lldiv}
-function. It has the following members:
-
-@table @code
-@item long long int quot
-The quotient from the division.
-
-@item long long int rem
-The remainder from the division.
-@end table
-
-(This is identical to @code{div_t} except that the components are of
-type @code{long long int} rather than @code{int}.)
-@end deftp
-
-@comment stdlib.h
-@comment ISO
-@deftypefun lldiv_t lldiv (long long int @var{numerator}, long long int @var{denominator})
-The @code{lldiv} function is like the @code{div} function, but the
-arguments are of type @code{long long int} and the result is returned as
-a structure of type @code{lldiv_t}.
-
-The @code{lldiv} function was added in @w{ISO C 9x}.
-@end deftypefun
-
-@comment inttypes.h
-@comment ISO
-@deftp {Data Type} imaxdiv_t
-This is a structure type used to hold the result returned by the @code{imaxdiv}
-function. It has the following members:
-
-@table @code
-@item intmax_t quot
-The quotient from the division.
-
-@item intmax_t rem
-The remainder from the division.
-@end table
-
-(This is identical to @code{div_t} except that the components are of
-type @code{intmax_t} rather than @code{int}.)
-@end deftp
-
-@comment inttypes.h
-@comment ISO
-@deftypefun imaxdiv_t imaxdiv (intmax_t @var{numerator}, intmax_t @var{denominator})
-The @code{imaxdiv} function is like the @code{div} function, but the
-arguments are of type @code{intmax_t} and the result is returned as
-a structure of type @code{imaxdiv_t}.
-
-The @code{imaxdiv} function was added in @w{ISO C 9x}.
-@end deftypefun
-
-
@node Parsing of Numbers
@section Parsing of Numbers
@cindex parsing numbers (in formatted input)
@subsection Parsing of Integers
@pindex stdlib.h
-These functions are declared in @file{stdlib.h}.
-
-@comment stdlib.h
-@comment ISO
-@deftypefun {long int} strtol (const char *@var{string}, char **@var{tailptr}, int @var{base})
+@pindex wchar.h
+The @samp{str} functions are declared in @file{stdlib.h} and those
+beginning with @samp{wcs} are declared in @file{wchar.h}. One might
+wonder about the use of @code{restrict} in the prototypes of the
+functions in this section. It is seemingly useless but the @w{ISO C}
+standard uses it (for the functions defined there) so we have to do it
+as well.
+
+@deftypefun {long int} strtol (const char *restrict @var{string}, char **restrict @var{tailptr}, int @var{base})
+@standards{ISO, stdlib.h}
+@safety{@prelim{}@mtsafe{@mtslocale{}}@assafe{}@acsafe{}}
+@c strtol uses the thread-local pointer to the locale in effect, and
+@c strtol_l loads the LC_NUMERIC locale data from it early on and once,
+@c but if the locale is the global locale, and another thread calls
+@c setlocale in a way that modifies the pointer to the LC_CTYPE locale
+@c category, the behavior of e.g. IS*, TOUPPER will vary throughout the
+@c execution of the function, because they re-read the locale data from
+@c the given locale pointer. We solved this by documenting setlocale as
+@c MT-Unsafe.
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}.
@samp{0X} (specifying hexadecimal radix); in other words, the same
syntax used for integer constants in C.
-Otherwise @var{base} must have a value between @code{2} and @code{35}.
+Otherwise @var{base} must have a value between @code{2} and @code{36}.
If @var{base} is @code{16}, the digits may optionally be preceded by
@samp{0x} or @samp{0X}. If base has no legal value the value returned
is @code{0l} and the global variable @code{errno} is set to @code{EINVAL}.
There is an example at the end of this section.
@end deftypefun
-@comment stdlib.h
-@comment ISO
-@deftypefun {unsigned long int} strtoul (const char *@var{string}, char **@var{tailptr}, int @var{base})
+@deftypefun {long int} wcstol (const wchar_t *restrict @var{string}, wchar_t **restrict @var{tailptr}, int @var{base})
+@standards{ISO, wchar.h}
+@safety{@prelim{}@mtsafe{@mtslocale{}}@assafe{}@acsafe{}}
+The @code{wcstol} function is equivalent to the @code{strtol} function
+in nearly all aspects but handles wide character strings.
+
+The @code{wcstol} function was introduced in @w{Amendment 1} of @w{ISO C90}.
+@end deftypefun
+
+@deftypefun {unsigned long int} strtoul (const char *restrict @var{string}, char **restrict @var{tailptr}, int @var{base})
+@standards{ISO, stdlib.h}
+@safety{@prelim{}@mtsafe{@mtslocale{}}@assafe{}@acsafe{}}
The @code{strtoul} (``string-to-unsigned-long'') function is like
-@code{strtol} except it returns an @code{unsigned long int} value. If
-the number has a leading @samp{-} sign, the return value is negated.
+@code{strtol} except it converts to an @code{unsigned long int} value.
The syntax is the same as described above for @code{strtol}. The value
-returned on overflow is @code{ULONG_MAX} (@pxref{Range of
-Type}).
+returned on overflow is @code{ULONG_MAX} (@pxref{Range of Type}).
+
+If @var{string} depicts a negative number, @code{strtoul} acts the same
+as @var{strtol} but casts the result to an unsigned integer. That means
+for example that @code{strtoul} on @code{"-1"} returns @code{ULONG_MAX}
+and an input more negative than @code{LONG_MIN} returns
+(@code{ULONG_MAX} + 1) / 2.
@code{strtoul} sets @var{errno} to @code{EINVAL} if @var{base} is out of
range, or @code{ERANGE} on overflow.
@end deftypefun
-@comment stdlib.h
-@comment ISO
-@deftypefun {long long int} strtoll (const char *@var{string}, char **@var{tailptr}, int @var{base})
+@deftypefun {unsigned long int} wcstoul (const wchar_t *restrict @var{string}, wchar_t **restrict @var{tailptr}, int @var{base})
+@standards{ISO, wchar.h}
+@safety{@prelim{}@mtsafe{@mtslocale{}}@assafe{}@acsafe{}}
+The @code{wcstoul} function is equivalent to the @code{strtoul} function
+in nearly all aspects but handles wide character strings.
+
+The @code{wcstoul} function was introduced in @w{Amendment 1} of @w{ISO C90}.
+@end deftypefun
+
+@deftypefun {long long int} strtoll (const char *restrict @var{string}, char **restrict @var{tailptr}, int @var{base})
+@standards{ISO, stdlib.h}
+@safety{@prelim{}@mtsafe{@mtslocale{}}@assafe{}@acsafe{}}
The @code{strtoll} function is like @code{strtol} except that it returns
a @code{long long int} value, and accepts numbers with a correspondingly
larger range.
If the string has valid syntax for an integer but the value is not
representable because of overflow, @code{strtoll} returns either
-@code{LONG_LONG_MAX} or @code{LONG_LONG_MIN} (@pxref{Range of Type}), as
+@code{LLONG_MAX} or @code{LLONG_MIN} (@pxref{Range of Type}), as
appropriate for the sign of the value. It also sets @code{errno} to
@code{ERANGE} to indicate there was overflow.
-The @code{strtoll} function was introduced in @w{ISO C 9x}.
+The @code{strtoll} function was introduced in @w{ISO C99}.
+@end deftypefun
+
+@deftypefun {long long int} wcstoll (const wchar_t *restrict @var{string}, wchar_t **restrict @var{tailptr}, int @var{base})
+@standards{ISO, wchar.h}
+@safety{@prelim{}@mtsafe{@mtslocale{}}@assafe{}@acsafe{}}
+The @code{wcstoll} function is equivalent to the @code{strtoll} function
+in nearly all aspects but handles wide character strings.
+
+The @code{wcstoll} function was introduced in @w{Amendment 1} of @w{ISO C90}.
@end deftypefun
-@comment stdlib.h
-@comment BSD
-@deftypefun {long long int} strtoq (const char *@var{string}, char **@var{tailptr}, int @var{base})
+@deftypefun {long long int} strtoq (const char *restrict @var{string}, char **restrict @var{tailptr}, int @var{base})
+@standards{BSD, stdlib.h}
+@safety{@prelim{}@mtsafe{@mtslocale{}}@assafe{}@acsafe{}}
@code{strtoq} (``string-to-quad-word'') is the BSD name for @code{strtoll}.
@end deftypefun
-@comment stdlib.h
-@comment ISO
-@deftypefun {unsigned long long int} strtoull (const char *@var{string}, char **@var{tailptr}, int @var{base})
-The @code{strtoull} function is like @code{strtoul} except that it
-returns an @code{unsigned long long int}. The value returned on overflow
-is @code{ULONG_LONG_MAX} (@pxref{Range of Type}).
+@deftypefun {long long int} wcstoq (const wchar_t *restrict @var{string}, wchar_t **restrict @var{tailptr}, int @var{base})
+@standards{GNU, wchar.h}
+@safety{@prelim{}@mtsafe{@mtslocale{}}@assafe{}@acsafe{}}
+The @code{wcstoq} function is equivalent to the @code{strtoq} function
+in nearly all aspects but handles wide character strings.
+
+The @code{wcstoq} function is a GNU extension.
+@end deftypefun
+
+@deftypefun {unsigned long long int} strtoull (const char *restrict @var{string}, char **restrict @var{tailptr}, int @var{base})
+@standards{ISO, stdlib.h}
+@safety{@prelim{}@mtsafe{@mtslocale{}}@assafe{}@acsafe{}}
+The @code{strtoull} function is related to @code{strtoll} the same way
+@code{strtoul} is related to @code{strtol}.
-The @code{strtoull} function was introduced in @w{ISO C 9x}.
+The @code{strtoull} function was introduced in @w{ISO C99}.
@end deftypefun
-@comment stdlib.h
-@comment BSD
-@deftypefun {unsigned long long int} strtouq (const char *@var{string}, char **@var{tailptr}, int @var{base})
+@deftypefun {unsigned long long int} wcstoull (const wchar_t *restrict @var{string}, wchar_t **restrict @var{tailptr}, int @var{base})
+@standards{ISO, wchar.h}
+@safety{@prelim{}@mtsafe{@mtslocale{}}@assafe{}@acsafe{}}
+The @code{wcstoull} function is equivalent to the @code{strtoull} function
+in nearly all aspects but handles wide character strings.
+
+The @code{wcstoull} function was introduced in @w{Amendment 1} of @w{ISO C90}.
+@end deftypefun
+
+@deftypefun {unsigned long long int} strtouq (const char *restrict @var{string}, char **restrict @var{tailptr}, int @var{base})
+@standards{BSD, stdlib.h}
+@safety{@prelim{}@mtsafe{@mtslocale{}}@assafe{}@acsafe{}}
@code{strtouq} is the BSD name for @code{strtoull}.
@end deftypefun
-@comment stdlib.h
-@comment ISO
+@deftypefun {unsigned long long int} wcstouq (const wchar_t *restrict @var{string}, wchar_t **restrict @var{tailptr}, int @var{base})
+@standards{GNU, wchar.h}
+@safety{@prelim{}@mtsafe{@mtslocale{}}@assafe{}@acsafe{}}
+The @code{wcstouq} function is equivalent to the @code{strtouq} function
+in nearly all aspects but handles wide character strings.
+
+The @code{wcstouq} function is a GNU extension.
+@end deftypefun
+
+@deftypefun intmax_t strtoimax (const char *restrict @var{string}, char **restrict @var{tailptr}, int @var{base})
+@standards{ISO, inttypes.h}
+@safety{@prelim{}@mtsafe{@mtslocale{}}@assafe{}@acsafe{}}
+The @code{strtoimax} function is like @code{strtol} except that it returns
+a @code{intmax_t} value, and accepts numbers of a corresponding range.
+
+If the string has valid syntax for an integer but the value is not
+representable because of overflow, @code{strtoimax} returns either
+@code{INTMAX_MAX} or @code{INTMAX_MIN} (@pxref{Integers}), as
+appropriate for the sign of the value. It also sets @code{errno} to
+@code{ERANGE} to indicate there was overflow.
+
+See @ref{Integers} for a description of the @code{intmax_t} type. The
+@code{strtoimax} function was introduced in @w{ISO C99}.
+@end deftypefun
+
+@deftypefun intmax_t wcstoimax (const wchar_t *restrict @var{string}, wchar_t **restrict @var{tailptr}, int @var{base})
+@standards{ISO, wchar.h}
+@safety{@prelim{}@mtsafe{@mtslocale{}}@assafe{}@acsafe{}}
+The @code{wcstoimax} function is equivalent to the @code{strtoimax} function
+in nearly all aspects but handles wide character strings.
+
+The @code{wcstoimax} function was introduced in @w{ISO C99}.
+@end deftypefun
+
+@deftypefun uintmax_t strtoumax (const char *restrict @var{string}, char **restrict @var{tailptr}, int @var{base})
+@standards{ISO, inttypes.h}
+@safety{@prelim{}@mtsafe{@mtslocale{}}@assafe{}@acsafe{}}
+The @code{strtoumax} function is related to @code{strtoimax}
+the same way that @code{strtoul} is related to @code{strtol}.
+
+See @ref{Integers} for a description of the @code{intmax_t} type. The
+@code{strtoumax} function was introduced in @w{ISO C99}.
+@end deftypefun
+
+@deftypefun uintmax_t wcstoumax (const wchar_t *restrict @var{string}, wchar_t **restrict @var{tailptr}, int @var{base})
+@standards{ISO, wchar.h}
+@safety{@prelim{}@mtsafe{@mtslocale{}}@assafe{}@acsafe{}}
+The @code{wcstoumax} function is equivalent to the @code{strtoumax} function
+in nearly all aspects but handles wide character strings.
+
+The @code{wcstoumax} function was introduced in @w{ISO C99}.
+@end deftypefun
+
@deftypefun {long int} atol (const char *@var{string})
+@standards{ISO, stdlib.h}
+@safety{@prelim{}@mtsafe{@mtslocale{}}@assafe{}@acsafe{}}
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 ISO
@deftypefun int atoi (const char *@var{string})
+@standards{ISO, stdlib.h}
+@safety{@prelim{}@mtsafe{@mtslocale{}}@assafe{}@acsafe{}}
This function is like @code{atol}, except that it returns an @code{int}.
The @code{atoi} function is also considered obsolete; use @code{strtol}
instead.
@end deftypefun
-@comment stdlib.h
-@comment ISO
@deftypefun {long long int} atoll (const char *@var{string})
+@standards{ISO, stdlib.h}
+@safety{@prelim{}@mtsafe{@mtslocale{}}@assafe{}@acsafe{}}
This function is similar to @code{atol}, except it returns a @code{long
long int}.
-The @code{atoll} function was introduced in @w{ISO C 9x}. It too is
+The @code{atoll} function was introduced in @w{ISO C99}. It too is
obsolete (despite having just been added); use @code{strtoll} instead.
@end deftypefun
-@c !!! please fact check this paragraph -zw
-@findex strtol_l
-@findex strtoul_l
-@findex strtoll_l
-@findex strtoull_l
-@cindex parsing numbers and locales
-@cindex locales, parsing numbers and
-Some locales specify a printed syntax for numbers other than the one
-that these functions understand. If you need to read numbers formatted
-in some other locale, you can use the @code{strtoX_l} functions. Each
-of the @code{strtoX} functions has a counterpart with @samp{_l} added to
-its name. The @samp{_l} counterparts take an additional argument: a
-pointer to an @code{locale_t} structure, which describes how the numbers
-to be read are formatted. @xref{Locales}.
-
-@strong{Portability Note:} These functions are all GNU extensions. You
-can also use @code{scanf} or its relatives, which have the @samp{'} flag
-for parsing numeric input according to the current locale
-(@pxref{Numeric Input Conversions}). This feature is standard.
+All the functions mentioned in this section so far do not handle
+alternative representations of characters as described in the locale
+data. Some locales specify thousands separator and the way they have to
+be used which can help to make large numbers more readable. To read
+such numbers one has to use the @code{scanf} functions with the @samp{'}
+flag.
Here is a function which parses a string as a sequence of integers and
returns the sum of them:
@subsection Parsing of Floats
@pindex stdlib.h
-These functions are declared in @file{stdlib.h}.
-
-@comment stdlib.h
-@comment ISO
-@deftypefun double strtod (const char *@var{string}, char **@var{tailptr})
+The @samp{str} functions are declared in @file{stdlib.h} and those
+beginning with @samp{wcs} are declared in @file{wchar.h}. One might
+wonder about the use of @code{restrict} in the prototypes of the
+functions in this section. It is seemingly useless but the @w{ISO C}
+standard uses it (for the functions defined there) so we have to do it
+as well.
+
+@deftypefun double strtod (const char *restrict @var{string}, char **restrict @var{tailptr})
+@standards{ISO, stdlib.h}
+@safety{@prelim{}@mtsafe{@mtslocale{}}@assafe{}@acsafe{}}
+@c Besides the unsafe-but-ruled-safe locale uses, this uses a lot of
+@c mpn, but it's all safe.
+@c
+@c round_and_return
+@c get_rounding_mode ok
+@c mpn_add_1 ok
+@c mpn_rshift ok
+@c MPN_ZERO ok
+@c MPN2FLOAT -> mpn_construct_(float|double|long_double) ok
+@c str_to_mpn
+@c mpn_mul_1 -> umul_ppmm ok
+@c mpn_add_1 ok
+@c mpn_lshift_1 -> mpn_lshift ok
+@c STRTOF_INTERNAL
+@c MPN_VAR ok
+@c SET_NAN_PAYLOAD ok
+@c STRNCASECMP ok, wide and narrow
+@c round_and_return ok
+@c mpn_mul ok
+@c mpn_addmul_1 ok
+@c ... mpn_sub
+@c mpn_lshift ok
+@c udiv_qrnnd ok
+@c count_leading_zeros ok
+@c add_ssaaaa ok
+@c sub_ddmmss ok
+@c umul_ppmm ok
+@c mpn_submul_1 ok
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}.
@item
An optional plus or minus sign (@samp{+} or @samp{-}).
+@item A floating point number in decimal or hexadecimal format. The
+decimal format is:
+@itemize @minus
+
@item
A nonempty sequence of digits optionally containing a decimal-point
character---normally @samp{.}, but it depends on the locale
An optional exponent part, consisting of a character @samp{e} or
@samp{E}, an optional sign, and a sequence of digits.
+@end itemize
+
+The hexadecimal format is as follows:
+@itemize @minus
+
+@item
+A 0x or 0X followed by a nonempty sequence of hexadecimal digits
+optionally containing a decimal-point character---normally @samp{.}, but
+it depends on the locale (@pxref{General Numeric}).
+
+@item
+An optional binary-exponent part, consisting of a character @samp{p} or
+@samp{P}, an optional sign, and a sequence of digits.
+
+@end itemize
+
@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
doesn't support infinities. You can prepend a @code{"+"} or @code{"-"}
to specify the sign. Case is ignored when scanning these strings.
-The strings @code{"nan"} and @code{"nan(@var{chars...})"} are converted
-to NaN. Again, case is ignored. If @var{chars...} are provided, they
+The strings @code{"nan"} and @code{"nan(@var{chars@dots{}})"} are converted
+to NaN. Again, case is ignored. If @var{chars@dots{}} are provided, they
are used in some unspecified fashion to select a particular
representation of NaN (there can be several).
examining @var{errno} and @var{tailptr}.
@end deftypefun
-@comment stdlib.h
-@comment GNU
@deftypefun float strtof (const char *@var{string}, char **@var{tailptr})
-@comment stdlib.h
-@comment GNU
@deftypefunx {long double} strtold (const char *@var{string}, char **@var{tailptr})
+@standards{ISO, stdlib.h}
+@safety{@prelim{}@mtsafe{@mtslocale{}}@assafe{}@acsafe{}}
+@comment See safety comments for strtod.
These functions are analogous to @code{strtod}, but return @code{float}
and @code{long double} values respectively. They report errors in the
same way as @code{strtod}. @code{strtof} can be substantially faster
can be much slower but has more precision (on systems where @code{long
double} is a separate type).
-These functions are GNU extensions.
+These functions have been GNU extensions and are new to @w{ISO C99}.
+@end deftypefun
+
+@deftypefun _FloatN strtofN (const char *@var{string}, char **@var{tailptr})
+@deftypefunx _FloatNx strtofNx (const char *@var{string}, char **@var{tailptr})
+@standards{ISO/IEC TS 18661-3, stdlib.h}
+@safety{@prelim{}@mtsafe{@mtslocale{}}@assafe{}@acsafe{}}
+@comment See safety comments for strtod.
+These functions are like @code{strtod}, except for the return type.
+
+They were introduced in @w{ISO/IEC TS 18661-3} and are available on machines
+that support the related types; @pxref{Mathematics}.
+@end deftypefun
+
+@deftypefun double wcstod (const wchar_t *restrict @var{string}, wchar_t **restrict @var{tailptr})
+@deftypefunx float wcstof (const wchar_t *@var{string}, wchar_t **@var{tailptr})
+@deftypefunx {long double} wcstold (const wchar_t *@var{string}, wchar_t **@var{tailptr})
+@deftypefunx _FloatN wcstofN (const wchar_t *@var{string}, wchar_t **@var{tailptr})
+@deftypefunx _FloatNx wcstofNx (const wchar_t *@var{string}, wchar_t **@var{tailptr})
+@standards{ISO, wchar.h}
+@standardsx{wcstofN, GNU, wchar.h}
+@standardsx{wcstofNx, GNU, wchar.h}
+@safety{@prelim{}@mtsafe{@mtslocale{}}@assafe{}@acsafe{}}
+@comment See safety comments for strtod.
+The @code{wcstod}, @code{wcstof}, @code{wcstol}, @code{wcstof@var{N}},
+and @code{wcstof@var{N}x} functions are equivalent in nearly all aspects
+to the @code{strtod}, @code{strtof}, @code{strtold},
+@code{strtof@var{N}}, and @code{strtof@var{N}x} functions, but they
+handle wide character strings.
+
+The @code{wcstod} function was introduced in @w{Amendment 1} of @w{ISO
+C90}. The @code{wcstof} and @code{wcstold} functions were introduced in
+@w{ISO C99}.
+
+The @code{wcstof@var{N}} and @code{wcstof@var{N}x} functions are not in
+any standard, but are added to provide completeness for the
+non-deprecated interface of wide character string to floating-point
+conversion functions. They are only available on machines that support
+the related types; @pxref{Mathematics}.
@end deftypefun
-@comment stdlib.h
-@comment ISO
@deftypefun double atof (const char *@var{string})
+@standards{ISO, stdlib.h}
+@safety{@prelim{}@mtsafe{@mtslocale{}}@assafe{}@acsafe{}}
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
-The GNU C library also provides @samp{_l} versions of thse functions,
+@Theglibc{} also provides @samp{_l} versions of these functions,
which take an additional argument, the locale to use in conversion.
-@xref{Parsing of Integers}.
+
+See also @ref{Parsing of Integers}.
+
+@node Printing of Floats
+@section Printing of Floats
+
+@pindex stdlib.h
+The @samp{strfrom} functions are declared in @file{stdlib.h}.
+
+@deftypefun int strfromd (char *restrict @var{string}, size_t @var{size}, const char *restrict @var{format}, double @var{value})
+@deftypefunx int strfromf (char *restrict @var{string}, size_t @var{size}, const char *restrict @var{format}, float @var{value})
+@deftypefunx int strfroml (char *restrict @var{string}, size_t @var{size}, const char *restrict @var{format}, long double @var{value})
+@standards{ISO/IEC TS 18661-1, stdlib.h}
+@safety{@prelim{}@mtsafe{@mtslocale{}}@asunsafe{@ascuheap{}}@acunsafe{@acsmem{}}}
+@comment All these functions depend on both __printf_fp and __printf_fphex,
+@comment which are both AS-unsafe (ascuheap) and AC-unsafe (acsmem).
+The functions @code{strfromd} (``string-from-double''), @code{strfromf}
+(``string-from-float''), and @code{strfroml} (``string-from-long-double'')
+convert the floating-point number @var{value} to a string of characters and
+stores them into the area pointed to by @var{string}. The conversion
+writes at most @var{size} characters and respects the format specified by
+@var{format}.
+
+The format string must start with the character @samp{%}. An optional
+precision follows, which starts with a period, @samp{.}, and may be
+followed by a decimal integer, representing the precision. If a decimal
+integer is not specified after the period, the precision is taken to be
+zero. The character @samp{*} is not allowed. Finally, the format string
+ends with one of the following conversion specifiers: @samp{a}, @samp{A},
+@samp{e}, @samp{E}, @samp{f}, @samp{F}, @samp{g} or @samp{G} (@pxref{Table
+of Output Conversions}). Invalid format strings result in undefined
+behavior.
+
+These functions return the number of characters that would have been
+written to @var{string} had @var{size} been sufficiently large, not
+counting the terminating null character. Thus, the null-terminated output
+has been completely written if and only if the returned value is less than
+@var{size}.
+
+These functions were introduced by ISO/IEC TS 18661-1.
+@end deftypefun
+
+@deftypefun int strfromfN (char *restrict @var{string}, size_t @var{size}, const char *restrict @var{format}, _Float@var{N} @var{value})
+@deftypefunx int strfromfNx (char *restrict @var{string}, size_t @var{size}, const char *restrict @var{format}, _Float@var{N}x @var{value})
+@standards{ISO/IEC TS 18661-3, stdlib.h}
+@safety{@prelim{}@mtsafe{@mtslocale{}}@asunsafe{@ascuheap{}}@acunsafe{@acsmem{}}}
+@comment See safety comments for strfromd.
+These functions are like @code{strfromd}, except for the type of
+@code{value}.
+
+They were introduced in @w{ISO/IEC TS 18661-3} and are available on machines
+that support the related types; @pxref{Mathematics}.
+@end deftypefun
@node System V Number Conversion
@section Old-fashioned System V number-to-string functions
The old @w{System V} C library provided three functions to convert
-numbers to strings, with unusual and hard-to-use semantics. The GNU C
-library also provides these functions and some natural extensions.
+numbers to strings, with unusual and hard-to-use semantics. @Theglibc{}
+also provides these functions and some natural extensions.
-These functions are only available in glibc and on systems descended
+These functions are only available in @theglibc{} and on systems descended
from AT&T Unix. Therefore, unless these functions do precisely what you
need, it is better to use @code{sprintf}, which is standard.
All these functions are defined in @file{stdlib.h}.
-@comment stdlib.h
-@comment SVID, Unix98
@deftypefun {char *} ecvt (double @var{value}, int @var{ndigit}, int *@var{decpt}, int *@var{neg})
+@standards{SVID, stdlib.h}
+@standards{Unix98, stdlib.h}
+@safety{@prelim{}@mtunsafe{@mtasurace{:ecvt}}@asunsafe{}@acsafe{}}
The function @code{ecvt} converts the floating-point number @var{value}
-to a string with at most @var{ndigit} decimal digits.
-The returned string contains no decimal point or sign. The first
-digit of the string is non-zero (unless @var{value} is actually zero)
-and the last digit is rounded to nearest. @var{decpt} is set to the
+to a string with at most @var{ndigit} decimal digits. The
+returned string contains no decimal point or sign. The first digit of
+the string is non-zero (unless @var{value} is actually zero) and the
+last digit is rounded to nearest. @code{*@var{decpt}} is set to the
index in the string of the first digit after the decimal point.
-@var{neg} is set to a nonzero value if @var{value} is negative, zero
-otherwise.
+@code{*@var{neg}} is set to a nonzero value if @var{value} is negative,
+zero otherwise.
If @var{ndigit} decimal digits would exceed the precision of a
@code{double} it is reduced to a system-specific value.
The returned string is statically allocated and overwritten by each call
to @code{ecvt}.
-If @var{value} is zero, it's implementation defined whether @var{decpt} is
-@code{0} or @code{1}.
+If @var{value} is zero, it is implementation defined whether
+@code{*@var{decpt}} is @code{0} or @code{1}.
-For example: @code{ecvt (12.3, 5, &decpt, &neg)} returns @code{"12300"}
-and sets @var{decpt} to @code{2} and @var{neg} to @code{0}.
+For example: @code{ecvt (12.3, 5, &d, &n)} returns @code{"12300"}
+and sets @var{d} to @code{2} and @var{n} to @code{0}.
@end deftypefun
-@comment stdlib.h
-@comment SVID, Unix98
-@deftypefun {char *} fcvt (double @var{value}, int @var{ndigit}, int @var{decpt}, int *@var{neg})
+@deftypefun {char *} fcvt (double @var{value}, int @var{ndigit}, int *@var{decpt}, int *@var{neg})
+@standards{SVID, stdlib.h}
+@standards{Unix98, stdlib.h}
+@safety{@prelim{}@mtunsafe{@mtasurace{:fcvt}}@asunsafe{@ascuheap{}}@acunsafe{@acsmem{}}}
The function @code{fcvt} is like @code{ecvt}, but @var{ndigit} specifies
the number of digits after the decimal point. If @var{ndigit} is less
than zero, @var{value} is rounded to the @math{@var{ndigit}+1}'th place to the
to @code{fcvt}.
@end deftypefun
-@comment stdlib.h
-@comment SVID, Unix98
@deftypefun {char *} gcvt (double @var{value}, int @var{ndigit}, char *@var{buf})
+@standards{SVID, stdlib.h}
+@standards{Unix98, stdlib.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
+@c gcvt calls sprintf, that ultimately calls vfprintf, which malloc()s
+@c args_value if it's too large, but gcvt never exercises this path.
@code{gcvt} is functionally equivalent to @samp{sprintf(buf, "%*g",
ndigit, value}. It is provided only for compatibility's sake. It
returns @var{buf}.
@code{double} it is reduced to a system-specific value.
@end deftypefun
-As extensions, the GNU C library provides versions of these three
+As extensions, @theglibc{} provides versions of these three
functions that take @code{long double} arguments.
-@comment stdlib.h
-@comment GNU
@deftypefun {char *} qecvt (long double @var{value}, int @var{ndigit}, int *@var{decpt}, int *@var{neg})
+@standards{GNU, stdlib.h}
+@safety{@prelim{}@mtunsafe{@mtasurace{:qecvt}}@asunsafe{}@acsafe{}}
This function is equivalent to @code{ecvt} except that it takes a
@code{long double} for the first parameter and that @var{ndigit} is
restricted by the precision of a @code{long double}.
@end deftypefun
-@comment stdlib.h
-@comment GNU
-@deftypefun {char *} qfcvt (long double @var{value}, int @var{ndigit}, int @var{decpt}, int *@var{neg})
+@deftypefun {char *} qfcvt (long double @var{value}, int @var{ndigit}, int *@var{decpt}, int *@var{neg})
+@standards{GNU, stdlib.h}
+@safety{@prelim{}@mtunsafe{@mtasurace{:qfcvt}}@asunsafe{@ascuheap{}}@acunsafe{@acsmem{}}}
This function is equivalent to @code{fcvt} except that it
takes a @code{long double} for the first parameter and that @var{ndigit} is
restricted by the precision of a @code{long double}.
@end deftypefun
-@comment stdlib.h
-@comment GNU
@deftypefun {char *} qgcvt (long double @var{value}, int @var{ndigit}, char *@var{buf})
+@standards{GNU, stdlib.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
This function is equivalent to @code{gcvt} except that it takes a
@code{long double} for the first parameter and that @var{ndigit} is
restricted by the precision of a @code{long double}.
@cindex gcvt_r
The @code{ecvt} and @code{fcvt} functions, and their @code{long double}
equivalents, all return a string located in a static buffer which is
-overwritten by the next call to the function. The GNU C library
+overwritten by the next call to the function. @Theglibc{}
provides another set of extended functions which write the converted
string into a user-supplied buffer. These have the conventional
@code{_r} suffix.
@code{gcvt_r} is not necessary, because @code{gcvt} already uses a
user-supplied buffer.
-@comment stdlib.h
-@comment GNU
-@deftypefun {char *} ecvt_r (double @var{value}, int @var{ndigit}, int *@var{decpt}, int *@var{neg}, char *@var{buf}, size_t @var{len})
+@deftypefun int ecvt_r (double @var{value}, int @var{ndigit}, int *@var{decpt}, int *@var{neg}, char *@var{buf}, size_t @var{len})
+@standards{GNU, stdlib.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
The @code{ecvt_r} function is the same as @code{ecvt}, except
that it places its result into the user-specified buffer pointed to by
-@var{buf}, with length @var{len}.
+@var{buf}, with length @var{len}. The return value is @code{-1} in
+case of an error and zero otherwise.
This function is a GNU extension.
@end deftypefun
-@comment stdlib.h
-@comment SVID, Unix98
-@deftypefun {char *} fcvt_r (double @var{value}, int @var{ndigit}, int @var{decpt}, int *@var{neg}, char *@var{buf}, size_t @var{len})
-The @code{fcvt_r} function is the same as @code{fcvt}, except
-that it places its result into the user-specified buffer pointed to by
-@var{buf}, with length @var{len}.
+@deftypefun int fcvt_r (double @var{value}, int @var{ndigit}, int *@var{decpt}, int *@var{neg}, char *@var{buf}, size_t @var{len})
+@standards{SVID, stdlib.h}
+@standards{Unix98, stdlib.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
+The @code{fcvt_r} function is the same as @code{fcvt}, except that it
+places its result into the user-specified buffer pointed to by
+@var{buf}, with length @var{len}. The return value is @code{-1} in
+case of an error and zero otherwise.
This function is a GNU extension.
@end deftypefun
-@comment stdlib.h
-@comment GNU
-@deftypefun {char *} qecvt_r (long double @var{value}, int @var{ndigit}, int *@var{decpt}, int *@var{neg}, char *@var{buf}, size_t @var{len})
+@deftypefun int qecvt_r (long double @var{value}, int @var{ndigit}, int *@var{decpt}, int *@var{neg}, char *@var{buf}, size_t @var{len})
+@standards{GNU, stdlib.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
The @code{qecvt_r} function is the same as @code{qecvt}, except
that it places its result into the user-specified buffer pointed to by
-@var{buf}, with length @var{len}.
+@var{buf}, with length @var{len}. The return value is @code{-1} in
+case of an error and zero otherwise.
This function is a GNU extension.
@end deftypefun
-@comment stdlib.h
-@comment GNU
-@deftypefun {char *} qfcvt_r (long double @var{value}, int @var{ndigit}, int @var{decpt}, int *@var{neg}, char *@var{buf}, size_t @var{len})
+@deftypefun int qfcvt_r (long double @var{value}, int @var{ndigit}, int *@var{decpt}, int *@var{neg}, char *@var{buf}, size_t @var{len})
+@standards{GNU, stdlib.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
The @code{qfcvt_r} function is the same as @code{qfcvt}, except
that it places its result into the user-specified buffer pointed to by
-@var{buf}, with length @var{len}.
+@var{buf}, with length @var{len}. The return value is @code{-1} in
+case of an error and zero otherwise.
This function is a GNU extension.
@end deftypefun
projects / thirdparty / glibc.git / blobdiff