@c We need some definitions here.
@ifclear mult
@ifhtml
-@set mult ·
-@set infty ∞
-@set pie π
+@set mult @U{00B7}
+@set infty @U{221E}
+@set pie @U{03C0}
@end ifhtml
@iftex
@set mult @cdot
Not all machines have a distinct @code{long double} type; it may be the
same as @code{double}.
+@Theglibc{} also provides @code{_Float@var{N}} and
+@code{_Float@var{N}x} types. These types are defined in @w{ISO/IEC TS
+18661-3}, which extends @w{ISO C} and defines floating-point types that
+are not machine-dependent. When such a type, such as @code{_Float128},
+is supported by @theglibc{}, extra variants for most of the mathematical
+functions provided for @code{double}, @code{float}, and @code{long
+double} are also provided for the supported type. Throughout this
+manual, the @code{_Float@var{N}} and @code{_Float@var{N}x} variants of
+these functions are described along with the @code{double},
+@code{float}, and @code{long double} variants and they come from
+@w{ISO/IEC TS 18661-3}, unless explicitly stated otherwise.
+
+Support for @code{_Float@var{N}} or @code{_Float@var{N}x} types is
+provided for @code{_Float32}, @code{_Float64} and @code{_Float32x} on
+all platforms.
+It is also provided for @code{_Float128} and @code{_Float64x} on
+powerpc64le (PowerPC 64-bits little-endian), x86_64, x86, ia64,
+aarch64, alpha, mips64, riscv, s390 and sparc.
+
@menu
* Mathematical Constants:: Precise numeric values for often-used
constants.
@end vtable
These constants come from the Unix98 standard and were also available in
-4.4BSD; therefore they are only defined if @code{_BSD_SOURCE} or
+4.4BSD; therefore they are only defined if
@code{_XOPEN_SOURCE=500}, or a more general feature select macro, is
defined. The default set of features includes these constants.
@xref{Feature Test Macros}.
-All values are of type @code{double}. As an extension, the GNU C
-library also defines these constants with type @code{long double}. The
-@code{long double} macros have a lowercase @samp{l} appended to their
-names: @code{M_El}, @code{M_PIl}, and so forth. These are only
+All values are of type @code{double}. As an extension, @theglibc{}
+also defines these constants with type @code{long double} and
+@code{float}. The @code{long double} macros have a lowercase @samp{l}
+while the @code{float} macros have a lowercase @samp{f} appended to
+their names: @code{M_El}, @code{M_PIl}, and so forth. These are only
available if @code{_GNU_SOURCE} is defined.
+Likewise, @theglibc{} also defines these constants with the types
+@code{_Float@var{N}} and @code{_Float@var{N}x} for the machines that
+have support for such types enabled (@pxref{Mathematics}) and if
+@code{_GNU_SOURCE} is defined. When available, the macros names are
+appended with @samp{f@var{N}} or @samp{f@var{N}x}, such as @samp{f128}
+for the type @code{_Float128}.
+
@vindex PI
@emph{Note:} Some programs use a constant named @code{PI} which has the
same value as @code{M_PI}. This constant is not standard; it may have
appeared in some old AT&T headers, and is mentioned in Stroustrup's book
-on C++. It infringes on the user's name space, so the GNU C library
+on C++. It infringes on the user's name space, so @theglibc{}
does not define it. Fixing programs written to expect it is simple:
replace @code{PI} with @code{M_PI} throughout, or put @samp{-DPI=M_PI}
on the compiler command line.
You can also compute the value of pi with the expression @code{acos
(-1.0)}.
-@comment math.h
-@comment ISO
@deftypefun double sin (double @var{x})
-@comment math.h
-@comment ISO
@deftypefunx float sinf (float @var{x})
-@comment math.h
-@comment ISO
@deftypefunx {long double} sinl (long double @var{x})
+@deftypefunx _FloatN sinfN (_Float@var{N} @var{x})
+@deftypefunx _FloatNx sinfNx (_Float@var{N}x @var{x})
+@standards{ISO, math.h}
+@standardsx{sinfN, TS 18661-3:2015, math.h}
+@standardsx{sinfNx, TS 18661-3:2015, math.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
These functions return the sine of @var{x}, where @var{x} is given in
radians. The return value is in the range @code{-1} to @code{1}.
@end deftypefun
-@comment math.h
-@comment ISO
@deftypefun double cos (double @var{x})
-@comment math.h
-@comment ISO
@deftypefunx float cosf (float @var{x})
-@comment math.h
-@comment ISO
@deftypefunx {long double} cosl (long double @var{x})
+@deftypefunx _FloatN cosfN (_Float@var{N} @var{x})
+@deftypefunx _FloatNx cosfNx (_Float@var{N}x @var{x})
+@standards{ISO, math.h}
+@standardsx{cosfN, TS 18661-3:2015, math.h}
+@standardsx{cosfNx, TS 18661-3:2015, math.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
These functions return the cosine of @var{x}, where @var{x} is given in
radians. The return value is in the range @code{-1} to @code{1}.
@end deftypefun
-@comment math.h
-@comment ISO
@deftypefun double tan (double @var{x})
-@comment math.h
-@comment ISO
@deftypefunx float tanf (float @var{x})
-@comment math.h
-@comment ISO
@deftypefunx {long double} tanl (long double @var{x})
+@deftypefunx _FloatN tanfN (_Float@var{N} @var{x})
+@deftypefunx _FloatNx tanfNx (_Float@var{N}x @var{x})
+@standards{ISO, math.h}
+@standardsx{tanfN, TS 18661-3:2015, math.h}
+@standardsx{tanfNx, TS 18661-3:2015, math.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
These functions return the tangent of @var{x}, where @var{x} is given in
radians.
efficient to compute them simultaneously, so the library provides a
function to do that.
-@comment math.h
-@comment GNU
@deftypefun void sincos (double @var{x}, double *@var{sinx}, double *@var{cosx})
-@comment math.h
-@comment GNU
@deftypefunx void sincosf (float @var{x}, float *@var{sinx}, float *@var{cosx})
-@comment math.h
-@comment GNU
@deftypefunx void sincosl (long double @var{x}, long double *@var{sinx}, long double *@var{cosx})
+@deftypefunx _FloatN sincosfN (_Float@var{N} @var{x}, _Float@var{N} *@var{sinx}, _Float@var{N} *@var{cosx})
+@deftypefunx _FloatNx sincosfNx (_Float@var{N}x @var{x}, _Float@var{N}x *@var{sinx}, _Float@var{N}x *@var{cosx})
+@standards{GNU, math.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
These functions return the sine of @var{x} in @code{*@var{sinx}} and the
-cosine of @var{x} in @code{*@var{cos}}, where @var{x} is given in
+cosine of @var{x} in @code{*@var{cosx}}, where @var{x} is given in
radians. Both values, @code{*@var{sinx}} and @code{*@var{cosx}}, are in
the range of @code{-1} to @code{1}.
-This function is a GNU extension. Portable programs should be prepared
-to cope with its absence.
+All these functions, including the @code{_Float@var{N}} and
+@code{_Float@var{N}x} variants, are GNU extensions. Portable programs
+should be prepared to cope with their absence.
@end deftypefun
@cindex complex trigonometric functions
@w{ISO C99} defines variants of the trig functions which work on
-complex numbers. The GNU C library provides these functions, but they
+complex numbers. @Theglibc{} provides these functions, but they
are only useful if your compiler supports the new complex types defined
by the standard.
@c XXX Change this when gcc is fixed. -zw
(As of this writing GCC supports complex numbers, but there are bugs in
the implementation.)
-@comment complex.h
-@comment ISO
@deftypefun {complex double} csin (complex double @var{z})
-@comment complex.h
-@comment ISO
@deftypefunx {complex float} csinf (complex float @var{z})
-@comment complex.h
-@comment ISO
@deftypefunx {complex long double} csinl (complex long double @var{z})
+@deftypefunx {complex _FloatN} csinfN (complex _Float@var{N} @var{z})
+@deftypefunx {complex _FloatNx} csinfNx (complex _Float@var{N}x @var{z})
+@standards{ISO, complex.h}
+@standardsx{csinfN, TS 18661-3:2015, complex.h}
+@standardsx{csinfNx, TS 18661-3:2015, complex.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
+@c There are calls to nan* that could trigger @mtslocale if they didn't get
+@c empty strings.
These functions return the complex sine of @var{z}.
The mathematical definition of the complex sine is
-@ifinfo
+@ifnottex
@math{sin (z) = 1/(2*i) * (exp (z*i) - exp (-z*i))}.
-@end ifinfo
+@end ifnottex
@tex
$$\sin(z) = {1\over 2i} (e^{zi} - e^{-zi})$$
@end tex
@end deftypefun
-@comment complex.h
-@comment ISO
@deftypefun {complex double} ccos (complex double @var{z})
-@comment complex.h
-@comment ISO
@deftypefunx {complex float} ccosf (complex float @var{z})
-@comment complex.h
-@comment ISO
@deftypefunx {complex long double} ccosl (complex long double @var{z})
+@deftypefunx {complex _FloatN} ccosfN (complex _Float@var{N} @var{z})
+@deftypefunx {complex _FloatNx} ccosfNx (complex _Float@var{N}x @var{z})
+@standards{ISO, complex.h}
+@standardsx{ccosfN, TS 18661-3:2015, complex.h}
+@standardsx{ccosfNx, TS 18661-3:2015, complex.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
These functions return the complex cosine of @var{z}.
The mathematical definition of the complex cosine is
-@ifinfo
+@ifnottex
@math{cos (z) = 1/2 * (exp (z*i) + exp (-z*i))}
-@end ifinfo
+@end ifnottex
@tex
$$\cos(z) = {1\over 2} (e^{zi} + e^{-zi})$$
@end tex
@end deftypefun
-@comment complex.h
-@comment ISO
@deftypefun {complex double} ctan (complex double @var{z})
-@comment complex.h
-@comment ISO
@deftypefunx {complex float} ctanf (complex float @var{z})
-@comment complex.h
-@comment ISO
@deftypefunx {complex long double} ctanl (complex long double @var{z})
+@deftypefunx {complex _FloatN} ctanfN (complex _Float@var{N} @var{z})
+@deftypefunx {complex _FloatNx} ctanfNx (complex _Float@var{N}x @var{z})
+@standards{ISO, complex.h}
+@standardsx{ctanfN, TS 18661-3:2015, complex.h}
+@standardsx{ctanfNx, TS 18661-3:2015, complex.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
These functions return the complex tangent of @var{z}.
The mathematical definition of the complex tangent is
-@ifinfo
+@ifnottex
@math{tan (z) = -i * (exp (z*i) - exp (-z*i)) / (exp (z*i) + exp (-z*i))}
-@end ifinfo
+@end ifnottex
@tex
$$\tan(z) = -i \cdot {e^{zi} - e^{-zi}\over e^{zi} + e^{-zi}}$$
@end tex
@section Inverse Trigonometric Functions
@cindex inverse trigonometric functions
-These are the usual arc sine, arc cosine and arc tangent functions,
+These are the usual arcsine, arccosine and arctangent functions,
which are the inverses of the sine, cosine and tangent functions
respectively.
-@comment math.h
-@comment ISO
@deftypefun double asin (double @var{x})
-@comment math.h
-@comment ISO
@deftypefunx float asinf (float @var{x})
-@comment math.h
-@comment ISO
@deftypefunx {long double} asinl (long double @var{x})
-These functions compute the arc sine of @var{x}---that is, the value whose
+@deftypefunx _FloatN asinfN (_Float@var{N} @var{x})
+@deftypefunx _FloatNx asinfNx (_Float@var{N}x @var{x})
+@standards{ISO, math.h}
+@standardsx{asinfN, TS 18661-3:2015, math.h}
+@standardsx{asinfNx, TS 18661-3:2015, math.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
+These functions compute the arcsine of @var{x}---that is, the value whose
sine is @var{x}. The value is in units of radians. Mathematically,
there are infinitely many such values; the one actually returned is the
one between @code{-pi/2} and @code{pi/2} (inclusive).
-The arc sine function is defined mathematically only
+The arcsine function is defined mathematically only
over the domain @code{-1} to @code{1}. If @var{x} is outside the
domain, @code{asin} signals a domain error.
@end deftypefun
-@comment math.h
-@comment ISO
@deftypefun double acos (double @var{x})
-@comment math.h
-@comment ISO
@deftypefunx float acosf (float @var{x})
-@comment math.h
-@comment ISO
@deftypefunx {long double} acosl (long double @var{x})
-These functions compute the arc cosine of @var{x}---that is, the value
+@deftypefunx _FloatN acosfN (_Float@var{N} @var{x})
+@deftypefunx _FloatNx acosfNx (_Float@var{N}x @var{x})
+@standards{ISO, math.h}
+@standardsx{acosfN, TS 18661-3:2015, math.h}
+@standardsx{acosfNx, TS 18661-3:2015, math.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
+These functions compute the arccosine of @var{x}---that is, the value
whose cosine is @var{x}. The value is in units of radians.
Mathematically, there are infinitely many such values; the one actually
returned is the one between @code{0} and @code{pi} (inclusive).
-The arc cosine function is defined mathematically only
+The arccosine function is defined mathematically only
over the domain @code{-1} to @code{1}. If @var{x} is outside the
domain, @code{acos} signals a domain error.
@end deftypefun
-@comment math.h
-@comment ISO
@deftypefun double atan (double @var{x})
-@comment math.h
-@comment ISO
@deftypefunx float atanf (float @var{x})
-@comment math.h
-@comment ISO
@deftypefunx {long double} atanl (long double @var{x})
-These functions compute the arc tangent of @var{x}---that is, the value
+@deftypefunx _FloatN atanfN (_Float@var{N} @var{x})
+@deftypefunx _FloatNx atanfNx (_Float@var{N}x @var{x})
+@standards{ISO, math.h}
+@standardsx{atanfN, TS 18661-3:2015, math.h}
+@standardsx{atanfNx, TS 18661-3:2015, math.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
+These functions compute the arctangent of @var{x}---that is, the value
whose tangent is @var{x}. The value is in units of radians.
Mathematically, there are infinitely many such values; the one actually
returned is the one between @code{-pi/2} and @code{pi/2} (inclusive).
@end deftypefun
-@comment math.h
-@comment ISO
@deftypefun double atan2 (double @var{y}, double @var{x})
-@comment math.h
-@comment ISO
@deftypefunx float atan2f (float @var{y}, float @var{x})
-@comment math.h
-@comment ISO
@deftypefunx {long double} atan2l (long double @var{y}, long double @var{x})
-This function computes the arc tangent of @var{y}/@var{x}, but the signs
+@deftypefunx _FloatN atan2fN (_Float@var{N} @var{y}, _Float@var{N} @var{x})
+@deftypefunx _FloatNx atan2fNx (_Float@var{N}x @var{y}, _Float@var{N}x @var{x})
+@standards{ISO, math.h}
+@standardsx{atan2fN, TS 18661-3:2015, math.h}
+@standardsx{atan2fNx, TS 18661-3:2015, math.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
+This function computes the arctangent of @var{y}/@var{x}, but the signs
of both arguments are used to determine the quadrant of the result, and
@var{x} is permitted to be zero. The return value is given in radians
and is in the range @code{-pi} to @code{pi}, inclusive.
@cindex inverse complex trigonometric functions
@w{ISO C99} defines complex versions of the inverse trig functions.
-@comment complex.h
-@comment ISO
@deftypefun {complex double} casin (complex double @var{z})
-@comment complex.h
-@comment ISO
@deftypefunx {complex float} casinf (complex float @var{z})
-@comment complex.h
-@comment ISO
@deftypefunx {complex long double} casinl (complex long double @var{z})
-These functions compute the complex arc sine of @var{z}---that is, the
+@deftypefunx {complex _FloatN} casinfN (complex _Float@var{N} @var{z})
+@deftypefunx {complex _FloatNx} casinfNx (complex _Float@var{N}x @var{z})
+@standards{ISO, complex.h}
+@standardsx{casinfN, TS 18661-3:2015, complex.h}
+@standardsx{casinfNx, TS 18661-3:2015, complex.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
+These functions compute the complex arcsine of @var{z}---that is, the
value whose sine is @var{z}. The value returned is in radians.
Unlike the real-valued functions, @code{casin} is defined for all
values of @var{z}.
@end deftypefun
-@comment complex.h
-@comment ISO
@deftypefun {complex double} cacos (complex double @var{z})
-@comment complex.h
-@comment ISO
@deftypefunx {complex float} cacosf (complex float @var{z})
-@comment complex.h
-@comment ISO
@deftypefunx {complex long double} cacosl (complex long double @var{z})
-These functions compute the complex arc cosine of @var{z}---that is, the
+@deftypefunx {complex _FloatN} cacosfN (complex _Float@var{N} @var{z})
+@deftypefunx {complex _FloatNx} cacosfNx (complex _Float@var{N}x @var{z})
+@standards{ISO, complex.h}
+@standardsx{cacosfN, TS 18661-3:2015, complex.h}
+@standardsx{cacosfNx, TS 18661-3:2015, complex.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
+These functions compute the complex arccosine of @var{z}---that is, the
value whose cosine is @var{z}. The value returned is in radians.
Unlike the real-valued functions, @code{cacos} is defined for all
@end deftypefun
-@comment complex.h
-@comment ISO
@deftypefun {complex double} catan (complex double @var{z})
-@comment complex.h
-@comment ISO
@deftypefunx {complex float} catanf (complex float @var{z})
-@comment complex.h
-@comment ISO
@deftypefunx {complex long double} catanl (complex long double @var{z})
-These functions compute the complex arc tangent of @var{z}---that is,
+@deftypefunx {complex _FloatN} catanfN (complex _Float@var{N} @var{z})
+@deftypefunx {complex _FloatNx} catanfNx (complex _Float@var{N}x @var{z})
+@standards{ISO, complex.h}
+@standardsx{catanfN, TS 18661-3:2015, complex.h}
+@standardsx{catanfNx, TS 18661-3:2015, complex.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
+These functions compute the complex arctangent of @var{z}---that is,
the value whose tangent is @var{z}. The value is in units of radians.
@end deftypefun
@cindex power functions
@cindex logarithm functions
-@comment math.h
-@comment ISO
@deftypefun double exp (double @var{x})
-@comment math.h
-@comment ISO
@deftypefunx float expf (float @var{x})
-@comment math.h
-@comment ISO
@deftypefunx {long double} expl (long double @var{x})
+@deftypefunx _FloatN expfN (_Float@var{N} @var{x})
+@deftypefunx _FloatNx expfNx (_Float@var{N}x @var{x})
+@standards{ISO, math.h}
+@standardsx{expfN, TS 18661-3:2015, math.h}
+@standardsx{expfNx, TS 18661-3:2015, math.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
These functions compute @code{e} (the base of natural logarithms) raised
to the power @var{x}.
@code{exp} signals overflow.
@end deftypefun
-@comment math.h
-@comment ISO
@deftypefun double exp2 (double @var{x})
-@comment math.h
-@comment ISO
@deftypefunx float exp2f (float @var{x})
-@comment math.h
-@comment ISO
@deftypefunx {long double} exp2l (long double @var{x})
+@deftypefunx _FloatN exp2fN (_Float@var{N} @var{x})
+@deftypefunx _FloatNx exp2fNx (_Float@var{N}x @var{x})
+@standards{ISO, math.h}
+@standardsx{exp2fN, TS 18661-3:2015, math.h}
+@standardsx{exp2fNx, TS 18661-3:2015, math.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
These functions compute @code{2} raised to the power @var{x}.
Mathematically, @code{exp2 (x)} is the same as @code{exp (x * log (2))}.
@end deftypefun
-@comment math.h
-@comment GNU
@deftypefun double exp10 (double @var{x})
-@comment math.h
-@comment GNU
@deftypefunx float exp10f (float @var{x})
-@comment math.h
-@comment GNU
@deftypefunx {long double} exp10l (long double @var{x})
-@comment math.h
-@comment GNU
-@deftypefunx double pow10 (double @var{x})
-@comment math.h
-@comment GNU
-@deftypefunx float pow10f (float @var{x})
-@comment math.h
-@comment GNU
-@deftypefunx {long double} pow10l (long double @var{x})
+@deftypefunx _FloatN exp10fN (_Float@var{N} @var{x})
+@deftypefunx _FloatNx exp10fNx (_Float@var{N}x @var{x})
+@standards{ISO, math.h}
+@standardsx{exp10fN, TS 18661-4:2015, math.h}
+@standardsx{exp10fNx, TS 18661-4:2015, math.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
These functions compute @code{10} raised to the power @var{x}.
Mathematically, @code{exp10 (x)} is the same as @code{exp (x * log (10))}.
-These functions are GNU extensions. The name @code{exp10} is
-preferred, since it is analogous to @code{exp} and @code{exp2}.
+The @code{exp10} functions are from TS 18661-4:2015.
@end deftypefun
-@comment math.h
-@comment ISO
@deftypefun double log (double @var{x})
-@comment math.h
-@comment ISO
@deftypefunx float logf (float @var{x})
-@comment math.h
-@comment ISO
@deftypefunx {long double} logl (long double @var{x})
+@deftypefunx _FloatN logfN (_Float@var{N} @var{x})
+@deftypefunx _FloatNx logfNx (_Float@var{N}x @var{x})
+@standards{ISO, math.h}
+@standardsx{logfN, TS 18661-3:2015, math.h}
+@standardsx{logfNx, TS 18661-3:2015, math.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
These functions compute the natural logarithm of @var{x}. @code{exp (log
(@var{x}))} equals @var{x}, exactly in mathematics and approximately in
C.
it may signal overflow.
@end deftypefun
-@comment math.h
-@comment ISO
@deftypefun double log10 (double @var{x})
-@comment math.h
-@comment ISO
@deftypefunx float log10f (float @var{x})
-@comment math.h
-@comment ISO
@deftypefunx {long double} log10l (long double @var{x})
+@deftypefunx _FloatN log10fN (_Float@var{N} @var{x})
+@deftypefunx _FloatNx log10fNx (_Float@var{N}x @var{x})
+@standards{ISO, math.h}
+@standardsx{log10fN, TS 18661-3:2015, math.h}
+@standardsx{log10fNx, TS 18661-3:2015, math.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
These functions return the base-10 logarithm of @var{x}.
@code{log10 (@var{x})} equals @code{log (@var{x}) / log (10)}.
@end deftypefun
-@comment math.h
-@comment ISO
@deftypefun double log2 (double @var{x})
-@comment math.h
-@comment ISO
@deftypefunx float log2f (float @var{x})
-@comment math.h
-@comment ISO
@deftypefunx {long double} log2l (long double @var{x})
+@deftypefunx _FloatN log2fN (_Float@var{N} @var{x})
+@deftypefunx _FloatNx log2fNx (_Float@var{N}x @var{x})
+@standards{ISO, math.h}
+@standardsx{log2fN, TS 18661-3:2015, math.h}
+@standardsx{log2fNx, TS 18661-3:2015, math.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
These functions return the base-2 logarithm of @var{x}.
@code{log2 (@var{x})} equals @code{log (@var{x}) / log (2)}.
@end deftypefun
-@comment math.h
-@comment ISO
@deftypefun double logb (double @var{x})
-@comment math.h
-@comment ISO
@deftypefunx float logbf (float @var{x})
-@comment math.h
-@comment ISO
@deftypefunx {long double} logbl (long double @var{x})
+@deftypefunx _FloatN logbfN (_Float@var{N} @var{x})
+@deftypefunx _FloatNx logbfNx (_Float@var{N}x @var{x})
+@standards{ISO, math.h}
+@standardsx{logbfN, TS 18661-3:2015, math.h}
+@standardsx{logbfNx, TS 18661-3:2015, math.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
These functions extract the exponent of @var{x} and return it as a
floating-point value. If @code{FLT_RADIX} is two, @code{logb} is equal
to @code{floor (log2 (x))}, except it's probably faster.
@code{logb} returns @math{@infinity{}}. It does not signal.
@end deftypefun
-@comment math.h
-@comment ISO
@deftypefun int ilogb (double @var{x})
-@comment math.h
-@comment ISO
@deftypefunx int ilogbf (float @var{x})
-@comment math.h
-@comment ISO
@deftypefunx int ilogbl (long double @var{x})
+@deftypefunx int ilogbfN (_Float@var{N} @var{x})
+@deftypefunx int ilogbfNx (_Float@var{N}x @var{x})
+@deftypefunx {long int} llogb (double @var{x})
+@deftypefunx {long int} llogbf (float @var{x})
+@deftypefunx {long int} llogbl (long double @var{x})
+@deftypefunx {long int} llogbfN (_Float@var{N} @var{x})
+@deftypefunx {long int} llogbfNx (_Float@var{N}x @var{x})
+@standards{ISO, math.h}
+@standardsx{ilogbfN, TS 18661-3:2015, math.h}
+@standardsx{ilogbfNx, TS 18661-3:2015, math.h}
+@standardsx{llogbfN, TS 18661-3:2015, math.h}
+@standardsx{llogbfNx, TS 18661-3:2015, math.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
These functions are equivalent to the corresponding @code{logb}
-functions except that they return signed integer values.
+functions except that they return signed integer values. The
+@code{ilogb}, @code{ilogbf}, and @code{ilogbl} functions are from ISO
+C99; the @code{llogb}, @code{llogbf}, @code{llogbl} functions are from
+TS 18661-1:2014; the @code{ilogbfN}, @code{ilogbfNx}, @code{llogbfN},
+and @code{llogbfNx} functions are from TS 18661-3:2015.
@end deftypefun
@noindent
returns an integer that can't be the exponent of a normal floating-point
number. @file{math.h} defines constants so you can check for this.
-@comment math.h
-@comment ISO
@deftypevr Macro int FP_ILOGB0
+@standards{ISO, math.h}
@code{ilogb} returns this value if its argument is @code{0}. The
numeric value is either @code{INT_MIN} or @code{-INT_MAX}.
This macro is defined in @w{ISO C99}.
@end deftypevr
-@comment math.h
-@comment ISO
+@deftypevr Macro {long int} FP_LLOGB0
+@standards{ISO, math.h}
+@code{llogb} returns this value if its argument is @code{0}. The
+numeric value is either @code{LONG_MIN} or @code{-LONG_MAX}.
+
+This macro is defined in TS 18661-1:2014.
+@end deftypevr
+
@deftypevr Macro int FP_ILOGBNAN
+@standards{ISO, math.h}
@code{ilogb} returns this value if its argument is @code{NaN}. The
numeric value is either @code{INT_MIN} or @code{INT_MAX}.
This macro is defined in @w{ISO C99}.
@end deftypevr
+@deftypevr Macro {long int} FP_LLOGBNAN
+@standards{ISO, math.h}
+@code{llogb} returns this value if its argument is @code{NaN}. The
+numeric value is either @code{LONG_MIN} or @code{LONG_MAX}.
+
+This macro is defined in TS 18661-1:2014.
+@end deftypevr
+
These values are system specific. They might even be the same. The
proper way to test the result of @code{ilogb} is as follows:
@}
@end smallexample
-@comment math.h
-@comment ISO
@deftypefun double pow (double @var{base}, double @var{power})
-@comment math.h
-@comment ISO
@deftypefunx float powf (float @var{base}, float @var{power})
-@comment math.h
-@comment ISO
@deftypefunx {long double} powl (long double @var{base}, long double @var{power})
+@deftypefunx _FloatN powfN (_Float@var{N} @var{base}, _Float@var{N} @var{power})
+@deftypefunx _FloatNx powfNx (_Float@var{N}x @var{base}, _Float@var{N}x @var{power})
+@standards{ISO, math.h}
+@standardsx{powfN, TS 18661-3:2015, math.h}
+@standardsx{powfNx, TS 18661-3:2015, math.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
These are general exponentiation functions, returning @var{base} raised
to @var{power}.
@end deftypefun
@cindex square root function
-@comment math.h
-@comment ISO
@deftypefun double sqrt (double @var{x})
-@comment math.h
-@comment ISO
@deftypefunx float sqrtf (float @var{x})
-@comment math.h
-@comment ISO
@deftypefunx {long double} sqrtl (long double @var{x})
+@deftypefunx _FloatN sqrtfN (_Float@var{N} @var{x})
+@deftypefunx _FloatNx sqrtfNx (_Float@var{N}x @var{x})
+@standards{ISO, math.h}
+@standardsx{sqrtfN, TS 18661-3:2015, math.h}
+@standardsx{sqrtfNx, TS 18661-3:2015, math.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
These functions return the nonnegative square root of @var{x}.
If @var{x} is negative, @code{sqrt} signals a domain error.
@end deftypefun
@cindex cube root function
-@comment math.h
-@comment BSD
@deftypefun double cbrt (double @var{x})
-@comment math.h
-@comment BSD
@deftypefunx float cbrtf (float @var{x})
-@comment math.h
-@comment BSD
@deftypefunx {long double} cbrtl (long double @var{x})
+@deftypefunx _FloatN cbrtfN (_Float@var{N} @var{x})
+@deftypefunx _FloatNx cbrtfNx (_Float@var{N}x @var{x})
+@standards{BSD, math.h}
+@standardsx{cbrtfN, TS 18661-3:2015, math.h}
+@standardsx{cbrtfNx, TS 18661-3:2015, math.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
These functions return the cube root of @var{x}. They cannot
fail; every representable real value has a representable real cube root.
@end deftypefun
-@comment math.h
-@comment ISO
@deftypefun double hypot (double @var{x}, double @var{y})
-@comment math.h
-@comment ISO
@deftypefunx float hypotf (float @var{x}, float @var{y})
-@comment math.h
-@comment ISO
@deftypefunx {long double} hypotl (long double @var{x}, long double @var{y})
+@deftypefunx _FloatN hypotfN (_Float@var{N} @var{x}, _Float@var{N} @var{y})
+@deftypefunx _FloatNx hypotfNx (_Float@var{N}x @var{x}, _Float@var{N}x @var{y})
+@standards{ISO, math.h}
+@standardsx{hypotfN, TS 18661-3:2015, math.h}
+@standardsx{hypotfNx, TS 18661-3:2015, math.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
These functions return @code{sqrt (@var{x}*@var{x} +
@var{y}*@var{y})}. This is the length of the hypotenuse of a right
triangle with sides of length @var{x} and @var{y}, or the distance
much smaller. See also the function @code{cabs} in @ref{Absolute Value}.
@end deftypefun
-@comment math.h
-@comment ISO
@deftypefun double expm1 (double @var{x})
-@comment math.h
-@comment ISO
@deftypefunx float expm1f (float @var{x})
-@comment math.h
-@comment ISO
@deftypefunx {long double} expm1l (long double @var{x})
+@deftypefunx _FloatN expm1fN (_Float@var{N} @var{x})
+@deftypefunx _FloatNx expm1fNx (_Float@var{N}x @var{x})
+@standards{ISO, math.h}
+@standardsx{expm1fN, TS 18661-3:2015, math.h}
+@standardsx{expm1fNx, TS 18661-3:2015, math.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
These functions return a value equivalent to @code{exp (@var{x}) - 1}.
They are computed in a way that is accurate even if @var{x} is
near zero---a case where @code{exp (@var{x}) - 1} would be inaccurate owing
to subtraction of two numbers that are nearly equal.
@end deftypefun
-@comment math.h
-@comment ISO
@deftypefun double log1p (double @var{x})
-@comment math.h
-@comment ISO
@deftypefunx float log1pf (float @var{x})
-@comment math.h
-@comment ISO
@deftypefunx {long double} log1pl (long double @var{x})
-These functions returns a value equivalent to @w{@code{log (1 + @var{x})}}.
+@deftypefunx _FloatN log1pfN (_Float@var{N} @var{x})
+@deftypefunx _FloatNx log1pfNx (_Float@var{N}x @var{x})
+@standards{ISO, math.h}
+@standardsx{log1pfN, TS 18661-3:2015, math.h}
+@standardsx{log1pfNx, TS 18661-3:2015, math.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
+These functions return a value equivalent to @w{@code{log (1 + @var{x})}}.
They are computed in a way that is accurate even if @var{x} is
near zero.
@end deftypefun
@w{ISO C99} defines complex variants of some of the exponentiation and
logarithm functions.
-@comment complex.h
-@comment ISO
@deftypefun {complex double} cexp (complex double @var{z})
-@comment complex.h
-@comment ISO
@deftypefunx {complex float} cexpf (complex float @var{z})
-@comment complex.h
-@comment ISO
@deftypefunx {complex long double} cexpl (complex long double @var{z})
+@deftypefunx {complex _FloatN} cexpfN (complex _Float@var{N} @var{z})
+@deftypefunx {complex _FloatNx} cexpfNx (complex _Float@var{N}x @var{z})
+@standards{ISO, complex.h}
+@standardsx{cexpfN, TS 18661-3:2015, complex.h}
+@standardsx{cexpfNx, TS 18661-3:2015, complex.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
These functions return @code{e} (the base of natural
logarithms) raised to the power of @var{z}.
Mathematically, this corresponds to the value
-@ifinfo
+@ifnottex
@math{exp (z) = exp (creal (z)) * (cos (cimag (z)) + I * sin (cimag (z)))}
-@end ifinfo
+@end ifnottex
@tex
$$\exp(z) = e^z = e^{{\rm Re}\,z} (\cos ({\rm Im}\,z) + i \sin ({\rm Im}\,z))$$
@end tex
@end deftypefun
-@comment complex.h
-@comment ISO
@deftypefun {complex double} clog (complex double @var{z})
-@comment complex.h
-@comment ISO
@deftypefunx {complex float} clogf (complex float @var{z})
-@comment complex.h
-@comment ISO
@deftypefunx {complex long double} clogl (complex long double @var{z})
+@deftypefunx {complex _FloatN} clogfN (complex _Float@var{N} @var{z})
+@deftypefunx {complex _FloatNx} clogfNx (complex _Float@var{N}x @var{z})
+@standards{ISO, complex.h}
+@standardsx{clogfN, TS 18661-3:2015, complex.h}
+@standardsx{clogfNx, TS 18661-3:2015, complex.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
These functions return the natural logarithm of @var{z}.
Mathematically, this corresponds to the value
-@ifinfo
+@ifnottex
@math{log (z) = log (cabs (z)) + I * carg (z)}
-@end ifinfo
+@end ifnottex
@tex
$$\log(z) = \log |z| + i \arg z$$
@end tex
@end deftypefun
-@comment complex.h
-@comment GNU
@deftypefun {complex double} clog10 (complex double @var{z})
-@comment complex.h
-@comment GNU
@deftypefunx {complex float} clog10f (complex float @var{z})
-@comment complex.h
-@comment GNU
@deftypefunx {complex long double} clog10l (complex long double @var{z})
+@deftypefunx {complex _FloatN} clog10fN (complex _Float@var{N} @var{z})
+@deftypefunx {complex _FloatNx} clog10fNx (complex _Float@var{N}x @var{z})
+@standards{GNU, complex.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
These functions return the base 10 logarithm of the complex value
-@var{z}. Mathematically, this corresponds to the value
+@var{z}. Mathematically, this corresponds to the value
-@ifinfo
-@math{log (z) = log10 (cabs (z)) + I * carg (z)}
-@end ifinfo
+@ifnottex
+@math{log10 (z) = log10 (cabs (z)) + I * carg (z) / log (10)}
+@end ifnottex
@tex
-$$\log_{10}(z) = \log_{10}|z| + i \arg z$$
+$$\log_{10}(z) = \log_{10}|z| + i \arg z / \log (10)$$
@end tex
-These functions are GNU extensions.
+All these functions, including the @code{_Float@var{N}} and
+@code{_Float@var{N}x} variants, are GNU extensions.
@end deftypefun
-@comment complex.h
-@comment ISO
@deftypefun {complex double} csqrt (complex double @var{z})
-@comment complex.h
-@comment ISO
@deftypefunx {complex float} csqrtf (complex float @var{z})
-@comment complex.h
-@comment ISO
@deftypefunx {complex long double} csqrtl (complex long double @var{z})
+@deftypefunx {complex _FloatN} csqrtfN (_Float@var{N} @var{z})
+@deftypefunx {complex _FloatNx} csqrtfNx (complex _Float@var{N}x @var{z})
+@standards{ISO, complex.h}
+@standardsx{csqrtfN, TS 18661-3:2015, complex.h}
+@standardsx{csqrtfNx, TS 18661-3:2015, complex.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
These functions return the complex square root of the argument @var{z}. Unlike
the real-valued functions, they are defined for all values of @var{z}.
@end deftypefun
-@comment complex.h
-@comment ISO
@deftypefun {complex double} cpow (complex double @var{base}, complex double @var{power})
-@comment complex.h
-@comment ISO
@deftypefunx {complex float} cpowf (complex float @var{base}, complex float @var{power})
-@comment complex.h
-@comment ISO
@deftypefunx {complex long double} cpowl (complex long double @var{base}, complex long double @var{power})
+@deftypefunx {complex _FloatN} cpowfN (complex _Float@var{N} @var{base}, complex _Float@var{N} @var{power})
+@deftypefunx {complex _FloatNx} cpowfNx (complex _Float@var{N}x @var{base}, complex _Float@var{N}x @var{power})
+@standards{ISO, complex.h}
+@standardsx{cpowfN, TS 18661-3:2015, complex.h}
+@standardsx{cpowfNx, TS 18661-3:2015, complex.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
These functions return @var{base} raised to the power of
@var{power}. This is equivalent to @w{@code{cexp (y * clog (x))}}
@end deftypefun
The functions in this section are related to the exponential functions;
see @ref{Exponents and Logarithms}.
-@comment math.h
-@comment ISO
@deftypefun double sinh (double @var{x})
-@comment math.h
-@comment ISO
@deftypefunx float sinhf (float @var{x})
-@comment math.h
-@comment ISO
@deftypefunx {long double} sinhl (long double @var{x})
+@deftypefunx _FloatN sinhfN (_Float@var{N} @var{x})
+@deftypefunx _FloatNx sinhfNx (_Float@var{N}x @var{x})
+@standards{ISO, math.h}
+@standardsx{sinhfN, TS 18661-3:2015, math.h}
+@standardsx{sinhfNx, TS 18661-3:2015, math.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
These functions return the hyperbolic sine of @var{x}, defined
mathematically as @w{@code{(exp (@var{x}) - exp (-@var{x})) / 2}}. They
may signal overflow if @var{x} is too large.
@end deftypefun
-@comment math.h
-@comment ISO
@deftypefun double cosh (double @var{x})
-@comment math.h
-@comment ISO
@deftypefunx float coshf (float @var{x})
-@comment math.h
-@comment ISO
@deftypefunx {long double} coshl (long double @var{x})
-These function return the hyperbolic cosine of @var{x},
+@deftypefunx _FloatN coshfN (_Float@var{N} @var{x})
+@deftypefunx _FloatNx coshfNx (_Float@var{N}x @var{x})
+@standards{ISO, math.h}
+@standardsx{coshfN, TS 18661-3:2015, math.h}
+@standardsx{coshfNx, TS 18661-3:2015, math.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
+These functions return the hyperbolic cosine of @var{x},
defined mathematically as @w{@code{(exp (@var{x}) + exp (-@var{x})) / 2}}.
They may signal overflow if @var{x} is too large.
@end deftypefun
-@comment math.h
-@comment ISO
@deftypefun double tanh (double @var{x})
-@comment math.h
-@comment ISO
@deftypefunx float tanhf (float @var{x})
-@comment math.h
-@comment ISO
@deftypefunx {long double} tanhl (long double @var{x})
+@deftypefunx _FloatN tanhfN (_Float@var{N} @var{x})
+@deftypefunx _FloatNx tanhfNx (_Float@var{N}x @var{x})
+@standards{ISO, math.h}
+@standardsx{tanhfN, TS 18661-3:2015, math.h}
+@standardsx{tanhfNx, TS 18661-3:2015, math.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
These functions return the hyperbolic tangent of @var{x},
defined mathematically as @w{@code{sinh (@var{x}) / cosh (@var{x})}}.
They may signal overflow if @var{x} is too large.
There are counterparts for the hyperbolic functions which take
complex arguments.
-@comment complex.h
-@comment ISO
@deftypefun {complex double} csinh (complex double @var{z})
-@comment complex.h
-@comment ISO
@deftypefunx {complex float} csinhf (complex float @var{z})
-@comment complex.h
-@comment ISO
@deftypefunx {complex long double} csinhl (complex long double @var{z})
+@deftypefunx {complex _FloatN} csinhfN (complex _Float@var{N} @var{z})
+@deftypefunx {complex _FloatNx} csinhfNx (complex _Float@var{N}x @var{z})
+@standards{ISO, complex.h}
+@standardsx{csinhfN, TS 18661-3:2015, complex.h}
+@standardsx{csinhfNx, TS 18661-3:2015, complex.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
These functions return the complex hyperbolic sine of @var{z}, defined
mathematically as @w{@code{(exp (@var{z}) - exp (-@var{z})) / 2}}.
@end deftypefun
-@comment complex.h
-@comment ISO
@deftypefun {complex double} ccosh (complex double @var{z})
-@comment complex.h
-@comment ISO
@deftypefunx {complex float} ccoshf (complex float @var{z})
-@comment complex.h
-@comment ISO
@deftypefunx {complex long double} ccoshl (complex long double @var{z})
+@deftypefunx {complex _FloatN} ccoshfN (complex _Float@var{N} @var{z})
+@deftypefunx {complex _FloatNx} ccoshfNx (complex _Float@var{N}x @var{z})
+@standards{ISO, complex.h}
+@standardsx{ccoshfN, TS 18661-3:2015, complex.h}
+@standardsx{ccoshfNx, TS 18661-3:2015, complex.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
These functions return the complex hyperbolic cosine of @var{z}, defined
mathematically as @w{@code{(exp (@var{z}) + exp (-@var{z})) / 2}}.
@end deftypefun
-@comment complex.h
-@comment ISO
@deftypefun {complex double} ctanh (complex double @var{z})
-@comment complex.h
-@comment ISO
@deftypefunx {complex float} ctanhf (complex float @var{z})
-@comment complex.h
-@comment ISO
@deftypefunx {complex long double} ctanhl (complex long double @var{z})
+@deftypefunx {complex _FloatN} ctanhfN (complex _Float@var{N} @var{z})
+@deftypefunx {complex _FloatNx} ctanhfNx (complex _Float@var{N}x @var{z})
+@standards{ISO, complex.h}
+@standardsx{ctanhfN, TS 18661-3:2015, complex.h}
+@standardsx{ctanhfNx, TS 18661-3:2015, complex.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
These functions return the complex hyperbolic tangent of @var{z},
defined mathematically as @w{@code{csinh (@var{z}) / ccosh (@var{z})}}.
@end deftypefun
@cindex inverse hyperbolic functions
-@comment math.h
-@comment ISO
@deftypefun double asinh (double @var{x})
-@comment math.h
-@comment ISO
@deftypefunx float asinhf (float @var{x})
-@comment math.h
-@comment ISO
@deftypefunx {long double} asinhl (long double @var{x})
+@deftypefunx _FloatN asinhfN (_Float@var{N} @var{x})
+@deftypefunx _FloatNx asinhfNx (_Float@var{N}x @var{x})
+@standards{ISO, math.h}
+@standardsx{asinhfN, TS 18661-3:2015, math.h}
+@standardsx{asinhfNx, TS 18661-3:2015, math.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
These functions return the inverse hyperbolic sine of @var{x}---the
value whose hyperbolic sine is @var{x}.
@end deftypefun
-@comment math.h
-@comment ISO
@deftypefun double acosh (double @var{x})
-@comment math.h
-@comment ISO
@deftypefunx float acoshf (float @var{x})
-@comment math.h
-@comment ISO
@deftypefunx {long double} acoshl (long double @var{x})
+@deftypefunx _FloatN acoshfN (_Float@var{N} @var{x})
+@deftypefunx _FloatNx acoshfNx (_Float@var{N}x @var{x})
+@standards{ISO, math.h}
+@standardsx{acoshfN, TS 18661-3:2015, math.h}
+@standardsx{acoshfNx, TS 18661-3:2015, math.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
These functions return the inverse hyperbolic cosine of @var{x}---the
value whose hyperbolic cosine is @var{x}. If @var{x} is less than
@code{1}, @code{acosh} signals a domain error.
@end deftypefun
-@comment math.h
-@comment ISO
@deftypefun double atanh (double @var{x})
-@comment math.h
-@comment ISO
@deftypefunx float atanhf (float @var{x})
-@comment math.h
-@comment ISO
@deftypefunx {long double} atanhl (long double @var{x})
+@deftypefunx _FloatN atanhfN (_Float@var{N} @var{x})
+@deftypefunx _FloatNx atanhfNx (_Float@var{N}x @var{x})
+@standards{ISO, math.h}
+@standardsx{atanhfN, TS 18661-3:2015, math.h}
+@standardsx{atanhfNx, TS 18661-3:2015, math.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
These functions return the inverse hyperbolic tangent of @var{x}---the
value whose hyperbolic tangent is @var{x}. If the absolute value of
@var{x} is greater than @code{1}, @code{atanh} signals a domain error;
@cindex inverse complex hyperbolic functions
-@comment complex.h
-@comment ISO
@deftypefun {complex double} casinh (complex double @var{z})
-@comment complex.h
-@comment ISO
@deftypefunx {complex float} casinhf (complex float @var{z})
-@comment complex.h
-@comment ISO
@deftypefunx {complex long double} casinhl (complex long double @var{z})
+@deftypefunx {complex _FloatN} casinhfN (complex _Float@var{N} @var{z})
+@deftypefunx {complex _FloatNx} casinhfNx (complex _Float@var{N}x @var{z})
+@standards{ISO, complex.h}
+@standardsx{casinhfN, TS 18661-3:2015, complex.h}
+@standardsx{casinhfNx, TS 18661-3:2015, complex.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
These functions return the inverse complex hyperbolic sine of
@var{z}---the value whose complex hyperbolic sine is @var{z}.
@end deftypefun
-@comment complex.h
-@comment ISO
@deftypefun {complex double} cacosh (complex double @var{z})
-@comment complex.h
-@comment ISO
@deftypefunx {complex float} cacoshf (complex float @var{z})
-@comment complex.h
-@comment ISO
@deftypefunx {complex long double} cacoshl (complex long double @var{z})
+@deftypefunx {complex _FloatN} cacoshfN (complex _Float@var{N} @var{z})
+@deftypefunx {complex _FloatNx} cacoshfNx (complex _Float@var{N}x @var{z})
+@standards{ISO, complex.h}
+@standardsx{cacoshfN, TS 18661-3:2015, complex.h}
+@standardsx{cacoshfNx, TS 18661-3:2015, complex.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
These functions return the inverse complex hyperbolic cosine of
@var{z}---the value whose complex hyperbolic cosine is @var{z}. Unlike
the real-valued functions, there are no restrictions on the value of @var{z}.
@end deftypefun
-@comment complex.h
-@comment ISO
@deftypefun {complex double} catanh (complex double @var{z})
-@comment complex.h
-@comment ISO
@deftypefunx {complex float} catanhf (complex float @var{z})
-@comment complex.h
-@comment ISO
@deftypefunx {complex long double} catanhl (complex long double @var{z})
+@deftypefunx {complex _FloatN} catanhfN (complex _Float@var{N} @var{z})
+@deftypefunx {complex _FloatNx} catanhfNx (complex _Float@var{N}x @var{z})
+@standards{ISO, complex.h}
+@standardsx{catanhfN, TS 18661-3:2015, complex.h}
+@standardsx{catanhfNx, TS 18661-3:2015, complex.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
These functions return the inverse complex hyperbolic tangent of
@var{z}---the value whose complex hyperbolic tangent is @var{z}. Unlike
the real-valued functions, there are no restrictions on the value of
These are some more exotic mathematical functions which are sometimes
useful. Currently they only have real-valued versions.
-@comment math.h
-@comment SVID
@deftypefun double erf (double @var{x})
-@comment math.h
-@comment SVID
@deftypefunx float erff (float @var{x})
-@comment math.h
-@comment SVID
@deftypefunx {long double} erfl (long double @var{x})
+@deftypefunx _FloatN erffN (_Float@var{N} @var{x})
+@deftypefunx _FloatNx erffNx (_Float@var{N}x @var{x})
+@standards{SVID, math.h}
+@standardsx{erffN, TS 18661-3:2015, math.h}
+@standardsx{erffNx, TS 18661-3:2015, math.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
@code{erf} returns the error function of @var{x}. The error
function is defined as
@tex
@end ifnottex
@end deftypefun
-@comment math.h
-@comment SVID
@deftypefun double erfc (double @var{x})
-@comment math.h
-@comment SVID
@deftypefunx float erfcf (float @var{x})
-@comment math.h
-@comment SVID
@deftypefunx {long double} erfcl (long double @var{x})
+@deftypefunx _FloatN erfcfN (_Float@var{N} @var{x})
+@deftypefunx _FloatNx erfcfNx (_Float@var{N}x @var{x})
+@standards{SVID, math.h}
+@standardsx{erfcfN, TS 18661-3:2015, math.h}
+@standardsx{erfcfNx, TS 18661-3:2015, math.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
@code{erfc} returns @code{1.0 - erf(@var{x})}, but computed in a
fashion that avoids round-off error when @var{x} is large.
@end deftypefun
-@comment math.h
-@comment SVID
@deftypefun double lgamma (double @var{x})
-@comment math.h
-@comment SVID
@deftypefunx float lgammaf (float @var{x})
-@comment math.h
-@comment SVID
@deftypefunx {long double} lgammal (long double @var{x})
+@deftypefunx _FloatN lgammafN (_Float@var{N} @var{x})
+@deftypefunx _FloatNx lgammafNx (_Float@var{N}x @var{x})
+@standards{SVID, math.h}
+@standardsx{lgammafN, TS 18661-3:2015, math.h}
+@standardsx{lgammafNx, TS 18661-3:2015, math.h}
+@safety{@prelim{}@mtunsafe{@mtasurace{:signgam}}@asunsafe{}@acsafe{}}
@code{lgamma} returns the natural logarithm of the absolute value of
the gamma function of @var{x}. The gamma function is defined as
@tex
singularity.
@end deftypefun
-@comment math.h
-@comment XPG
@deftypefun double lgamma_r (double @var{x}, int *@var{signp})
-@comment math.h
-@comment XPG
@deftypefunx float lgammaf_r (float @var{x}, int *@var{signp})
-@comment math.h
-@comment XPG
@deftypefunx {long double} lgammal_r (long double @var{x}, int *@var{signp})
+@deftypefunx _FloatN lgammafN_r (_Float@var{N} @var{x}, int *@var{signp})
+@deftypefunx _FloatNx lgammafNx_r (_Float@var{N}x @var{x}, int *@var{signp})
+@standards{XPG, math.h}
+@standardsx{lgammafN_r, GNU, math.h}
+@standardsx{lgammafNx_r, GNU, math.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
@code{lgamma_r} is just like @code{lgamma}, but it stores the sign of
the intermediate result in the variable pointed to by @var{signp}
instead of in the @var{signgam} global. This means it is reentrant.
+
+The @code{lgammaf@var{N}_r} and @code{lgammaf@var{N}x_r} functions are
+GNU extensions.
@end deftypefun
-@comment math.h
-@comment SVID
@deftypefun double gamma (double @var{x})
-@comment math.h
-@comment SVID
@deftypefunx float gammaf (float @var{x})
-@comment math.h
-@comment SVID
@deftypefunx {long double} gammal (long double @var{x})
+@standards{SVID, math.h}
+@safety{@prelim{}@mtunsafe{@mtasurace{:signgam}}@asunsafe{}@acsafe{}}
These functions exist for compatibility reasons. They are equivalent to
@code{lgamma} etc. It is better to use @code{lgamma} since for one the
-name reflects better the actual computation, moreover @code{lgamma} is
+name reflects better the actual computation, and moreover @code{lgamma} is
standardized in @w{ISO C99} while @code{gamma} is not.
@end deftypefun
-@comment math.h
-@comment XPG, ISO
@deftypefun double tgamma (double @var{x})
-@comment math.h
-@comment XPG, ISO
@deftypefunx float tgammaf (float @var{x})
-@comment math.h
-@comment XPG, ISO
@deftypefunx {long double} tgammal (long double @var{x})
+@deftypefunx _FloatN tgammafN (_Float@var{N} @var{x})
+@deftypefunx _FloatNx tgammafNx (_Float@var{N}x @var{x})
+@standardsx{tgamma, XPG, math.h}
+@standardsx{tgamma, ISO, math.h}
+@standardsx{tgammaf, XPG, math.h}
+@standardsx{tgammaf, ISO, math.h}
+@standardsx{tgammal, XPG, math.h}
+@standardsx{tgammal, ISO, math.h}
+@standardsx{tgammafN, TS 18661-3:2015, math.h}
+@standardsx{tgammafNx, TS 18661-3:2015, math.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
@code{tgamma} applies the gamma function to @var{x}. The gamma
function is defined as
@tex
@end smallexample
@end ifnottex
-This function was introduced in @w{ISO C99}.
+This function was introduced in @w{ISO C99}. The @code{_Float@var{N}}
+and @code{_Float@var{N}x} variants were introduced in @w{ISO/IEC TS
+18661-3}.
@end deftypefun
-@comment math.h
-@comment SVID
@deftypefun double j0 (double @var{x})
-@comment math.h
-@comment SVID
@deftypefunx float j0f (float @var{x})
-@comment math.h
-@comment SVID
@deftypefunx {long double} j0l (long double @var{x})
+@deftypefunx _FloatN j0fN (_Float@var{N} @var{x})
+@deftypefunx _FloatNx j0fNx (_Float@var{N}x @var{x})
+@standards{SVID, math.h}
+@standardsx{j0fN, GNU, math.h}
+@standardsx{j0fNx, GNU, math.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
@code{j0} returns the Bessel function of the first kind of order 0 of
@var{x}. It may signal underflow if @var{x} is too large.
+
+The @code{_Float@var{N}} and @code{_Float@var{N}x} variants are GNU
+extensions.
@end deftypefun
-@comment math.h
-@comment SVID
@deftypefun double j1 (double @var{x})
-@comment math.h
-@comment SVID
@deftypefunx float j1f (float @var{x})
-@comment math.h
-@comment SVID
@deftypefunx {long double} j1l (long double @var{x})
+@deftypefunx _FloatN j1fN (_Float@var{N} @var{x})
+@deftypefunx _FloatNx j1fNx (_Float@var{N}x @var{x})
+@standards{SVID, math.h}
+@standardsx{j1fN, GNU, math.h}
+@standardsx{j1fNx, GNU, math.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
@code{j1} returns the Bessel function of the first kind of order 1 of
@var{x}. It may signal underflow if @var{x} is too large.
+
+The @code{_Float@var{N}} and @code{_Float@var{N}x} variants are GNU
+extensions.
@end deftypefun
-@comment math.h
-@comment SVID
-@deftypefun double jn (int n, double @var{x})
-@comment math.h
-@comment SVID
-@deftypefunx float jnf (int n, float @var{x})
-@comment math.h
-@comment SVID
-@deftypefunx {long double} jnl (int n, long double @var{x})
+@deftypefun double jn (int @var{n}, double @var{x})
+@deftypefunx float jnf (int @var{n}, float @var{x})
+@deftypefunx {long double} jnl (int @var{n}, long double @var{x})
+@deftypefunx _FloatN jnfN (int @var{n}, _Float@var{N} @var{x})
+@deftypefunx _FloatNx jnfNx (int @var{n}, _Float@var{N}x @var{x})
+@standards{SVID, math.h}
+@standardsx{jnfN, GNU, math.h}
+@standardsx{jnfNx, GNU, math.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
@code{jn} returns the Bessel function of the first kind of order
@var{n} of @var{x}. It may signal underflow if @var{x} is too large.
+
+The @code{_Float@var{N}} and @code{_Float@var{N}x} variants are GNU
+extensions.
@end deftypefun
-@comment math.h
-@comment SVID
@deftypefun double y0 (double @var{x})
-@comment math.h
-@comment SVID
@deftypefunx float y0f (float @var{x})
-@comment math.h
-@comment SVID
@deftypefunx {long double} y0l (long double @var{x})
+@deftypefunx _FloatN y0fN (_Float@var{N} @var{x})
+@deftypefunx _FloatNx y0fNx (_Float@var{N}x @var{x})
+@standards{SVID, math.h}
+@standardsx{y0fN, GNU, math.h}
+@standardsx{y0fNx, GNU, math.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
@code{y0} returns the Bessel function of the second kind of order 0 of
@var{x}. It may signal underflow if @var{x} is too large. If @var{x}
is negative, @code{y0} signals a domain error; if it is zero,
@code{y0} signals overflow and returns @math{-@infinity}.
+
+The @code{_Float@var{N}} and @code{_Float@var{N}x} variants are GNU
+extensions.
@end deftypefun
-@comment math.h
-@comment SVID
@deftypefun double y1 (double @var{x})
-@comment math.h
-@comment SVID
@deftypefunx float y1f (float @var{x})
-@comment math.h
-@comment SVID
@deftypefunx {long double} y1l (long double @var{x})
+@deftypefunx _FloatN y1fN (_Float@var{N} @var{x})
+@deftypefunx _FloatNx y1fNx (_Float@var{N}x @var{x})
+@standards{SVID, math.h}
+@standardsx{y1fN, GNU, math.h}
+@standardsx{y1fNx, GNU, math.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
@code{y1} returns the Bessel function of the second kind of order 1 of
@var{x}. It may signal underflow if @var{x} is too large. If @var{x}
is negative, @code{y1} signals a domain error; if it is zero,
@code{y1} signals overflow and returns @math{-@infinity}.
+
+The @code{_Float@var{N}} and @code{_Float@var{N}x} variants are GNU
+extensions.
@end deftypefun
-@comment math.h
-@comment SVID
-@deftypefun double yn (int n, double @var{x})
-@comment math.h
-@comment SVID
-@deftypefunx float ynf (int n, float @var{x})
-@comment math.h
-@comment SVID
-@deftypefunx {long double} ynl (int n, long double @var{x})
+@deftypefun double yn (int @var{n}, double @var{x})
+@deftypefunx float ynf (int @var{n}, float @var{x})
+@deftypefunx {long double} ynl (int @var{n}, long double @var{x})
+@deftypefunx _FloatN ynfN (int @var{n}, _Float@var{N} @var{x})
+@deftypefunx _FloatNx ynfNx (int @var{n}, _Float@var{N}x @var{x})
+@standards{SVID, math.h}
+@standardsx{ynfN, GNU, math.h}
+@standardsx{ynfNx, GNU, math.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
@code{yn} returns the Bessel function of the second kind of order @var{n} of
@var{x}. It may signal underflow if @var{x} is too large. If @var{x}
is negative, @code{yn} signals a domain error; if it is zero,
@code{yn} signals overflow and returns @math{-@infinity}.
+
+The @code{_Float@var{N}} and @code{_Float@var{N}x} variants are GNU
+extensions.
@end deftypefun
@node Errors in Math Functions
@noindent
where @math{p} is the number of bits in the mantissa of the
floating-point number representation. Ideally the error for all
-functions is always less than 0.5ulps. Using rounding bits this is also
-possible and normally implemented for the basic operations. To achieve
-the same for the complex math functions requires a lot more work and
-this was not spend so far.
+functions is always less than 0.5ulps in round-to-nearest mode. Using
+rounding bits this is also
+possible and normally implemented for the basic operations. Except
+for certain functions such as @code{sqrt}, @code{fma} and @code{rint}
+whose results are fully specified by reference to corresponding IEEE
+754 floating-point operations, and conversions between strings and
+floating point, @theglibc{} does not aim for correctly rounded results
+for functions in the math library, and does not aim for correctness in
+whether ``inexact'' exceptions are raised. Instead, the goals for
+accuracy of functions without fully specified results are as follows;
+some functions have bugs meaning they do not meet these goals in all
+cases. In the future, @theglibc{} may provide some other correctly
+rounding functions under the names such as @code{crsin} proposed for
+an extension to ISO C.
+
+@itemize @bullet
+
+@item
+Each function with a floating-point result behaves as if it computes
+an infinite-precision result that is within a few ulp (in both real
+and complex parts, for functions with complex results) of the
+mathematically correct value of the function (interpreted together
+with ISO C or POSIX semantics for the function in question) at the
+exact value passed as the input. Exceptions are raised appropriately
+for this value and in accordance with IEEE 754 / ISO C / POSIX
+semantics, and it is then rounded according to the current rounding
+direction to the result that is returned to the user. @code{errno}
+may also be set (@pxref{Math Error Reporting}). (The ``inexact''
+exception may be raised, or not raised, even if this is inconsistent
+with the infinite-precision value.)
+
+@item
+For the IBM @code{long double} format, as used on PowerPC GNU/Linux,
+the accuracy goal is weaker for input values not exactly representable
+in 106 bits of precision; it is as if the input value is some value
+within 0.5ulp of the value actually passed, where ``ulp'' is
+interpreted in terms of a fixed-precision 106-bit mantissa, but not
+necessarily the exact value actually passed with discontiguous
+mantissa bits.
+
+@item
+For the IBM @code{long double} format, functions whose results are
+fully specified by reference to corresponding IEEE 754 floating-point
+operations have the same accuracy goals as other functions, but with
+the error bound being the same as that for division (3ulp).
+Furthermore, ``inexact'' and ``underflow'' exceptions may be raised
+for all functions for any inputs, even where such exceptions are
+inconsistent with the returned value, since the underlying
+floating-point arithmetic has that property.
+
+@item
+Functions behave as if the infinite-precision result computed is zero,
+infinity or NaN if and only if that is the mathematically correct
+infinite-precision result. They behave as if the infinite-precision
+result computed always has the same sign as the mathematically correct
+result.
+
+@item
+If the mathematical result is more than a few ulp above the overflow
+threshold for the current rounding direction, the value returned is
+the appropriate overflow value for the current rounding direction,
+with the overflow exception raised.
+
+@item
+If the mathematical result has magnitude well below half the least
+subnormal magnitude, the returned value is either zero or the least
+subnormal (in each case, with the correct sign), according to the
+current rounding direction and with the underflow exception raised.
+
+@item
+Where the mathematical result underflows (before rounding) and is not
+exactly representable as a floating-point value, the function does not
+behave as if the computed infinite-precision result is an exact value
+in the subnormal range. This means that the underflow exception is
+raised other than possibly for cases where the mathematical result is
+very close to the underflow threshold and the function behaves as if
+it computes an infinite-precision result that does not underflow. (So
+there may be spurious underflow exceptions in cases where the
+underflowing result is exact, but not missing underflow exceptions in
+cases where it is inexact.)
+
+@item
+@Theglibc{} does not aim for functions to satisfy other properties of
+the underlying mathematical function, such as monotonicity, where not
+implied by the above goals.
+
+@item
+All the above applies to both real and complex parts, for complex
+functions.
+
+@end itemize
Therefore many of the functions in the math library have errors. The
table lists the maximum error for each function which is exposed by one
-of the existing tests in the test suite. It is tried to cover as much
-as possible and really list the maximum error (or at least a ballpark
+of the existing tests in the test suite. The table tries to cover as much
+as possible and list the actual maximum error (or at least a ballpark
figure) but this is often not achieved due to the large search space.
The table lists the ULP values for different architectures. Different
architectures have different results since their hardware support for
floating-point operations varies and also the existing hardware support
-is different.
+is different. Only the round-to-nearest rounding mode is covered by
+this table. Functions not listed do not have known errors. Vector
+versions of functions in the x86_64 libmvec library have a maximum error
+of 4 ulps.
+@page
+@c This multitable does not fit on a single page
@include libm-err.texi
@node Pseudo-Random Numbers
you want the program to behave unpredictably. If you want a different
pseudo-random series each time your program runs, you must specify a
different seed each time. For ordinary purposes, basing the seed on the
-current time works well.
+current time works well. For random numbers in cryptography,
+@pxref{Unpredictable Bytes}.
You can obtain repeatable sequences of numbers on a particular machine type
by specifying the same initial seed value for the random number
the same seed, used in different C libraries or on different CPU types,
will give you different random numbers.
-The GNU library supports the standard @w{ISO C} random number functions
+@Theglibc{} supports the standard @w{ISO C} random number functions
plus two other sets derived from BSD and SVID. The BSD and @w{ISO C}
functions provide identical, somewhat limited functionality. If only a
small number of random bits are required, we recommend you use the
@file{stdlib.h} in your program.
@pindex stdlib.h
-@comment stdlib.h
-@comment ISO
@deftypevr Macro int RAND_MAX
+@standards{ISO, stdlib.h}
The value of this macro is an integer constant representing the largest
-value the @code{rand} function can return. In the GNU library, it is
+value the @code{rand} function can return. In @theglibc{}, it is
@code{2147483647}, which is the largest signed integer representable in
32 bits. In other libraries, it may be as low as @code{32767}.
@end deftypevr
-@comment stdlib.h
-@comment ISO
@deftypefun int rand (void)
+@standards{ISO, stdlib.h}
+@safety{@prelim{}@mtsafe{}@asunsafe{@asulock{}}@acunsafe{@aculock{}}}
+@c Just calls random.
The @code{rand} function returns the next pseudo-random number in the
series. The value ranges from @code{0} to @code{RAND_MAX}.
@end deftypefun
-@comment stdlib.h
-@comment ISO
@deftypefun void srand (unsigned int @var{seed})
+@standards{ISO, stdlib.h}
+@safety{@prelim{}@mtsafe{}@asunsafe{@asulock{}}@acunsafe{@aculock{}}}
+@c Alias to srandom.
This function establishes @var{seed} as the seed for a new series of
pseudo-random numbers. If you call @code{rand} before a seed has been
established with @code{srand}, it uses the value @code{1} as a default
numbers in multi-threaded programs. However, the extension is badly
designed and unsuitable for serious work.
-@comment stdlib.h
-@comment POSIX.1
@deftypefun int rand_r (unsigned int *@var{seed})
+@standards{POSIX.1, stdlib.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
This function returns a random number in the range 0 to @code{RAND_MAX}
just as @code{rand} does. However, all its state is stored in the
@var{seed} argument. This means the RNG's state can only have as many
This section describes a set of random number generation functions that
are derived from BSD. There is no advantage to using these functions
-with the GNU C library; we support them for BSD compatibility only.
+with @theglibc{}; we support them for BSD compatibility only.
The prototypes for these functions are in @file{stdlib.h}.
@pindex stdlib.h
-@comment stdlib.h
-@comment BSD
@deftypefun {long int} random (void)
+@standards{BSD, stdlib.h}
+@safety{@prelim{}@mtsafe{}@asunsafe{@asulock{}}@acunsafe{@aculock{}}}
+@c Takes a lock and calls random_r with an automatic variable and the
+@c global state, while holding a lock.
This function returns the next pseudo-random number in the sequence.
-The value returned ranges from @code{0} to @code{RAND_MAX}.
+The value returned ranges from @code{0} to @code{2147483647}.
-@strong{Note:} Temporarily this function was defined to return a
+@strong{NB:} Temporarily this function was defined to return a
@code{int32_t} value to indicate that the return value always contains
32 bits even if @code{long int} is wider. The standard demands it
differently. Users must always be aware of the 32-bit limitation,
though.
@end deftypefun
-@comment stdlib.h
-@comment BSD
@deftypefun void srandom (unsigned int @var{seed})
+@standards{BSD, stdlib.h}
+@safety{@prelim{}@mtsafe{}@asunsafe{@asulock{}}@acunsafe{@aculock{}}}
+@c Takes a lock and calls srandom_r with an automatic variable and a
+@c static buffer. There's no MT-safety issue because the static buffer
+@c is internally protected by a lock, although other threads may modify
+@c the set state before it is used.
The @code{srandom} function sets the state of the random number
generator based on the integer @var{seed}. If you supply a @var{seed} value
of @code{1}, this will cause @code{random} to reproduce the default set
program runs, do @code{srandom (time (0))}.
@end deftypefun
-@comment stdlib.h
-@comment BSD
-@deftypefun {void *} initstate (unsigned int @var{seed}, void *@var{state}, size_t @var{size})
+@deftypefun {char *} initstate (unsigned int @var{seed}, char *@var{state}, size_t @var{size})
+@standards{BSD, stdlib.h}
+@safety{@prelim{}@mtsafe{}@asunsafe{@asulock{}}@acunsafe{@aculock{}}}
The @code{initstate} function is used to initialize the random number
generator state. The argument @var{state} is an array of @var{size}
bytes, used to hold the state information. It is initialized based on
restore that state.
@end deftypefun
-@comment stdlib.h
-@comment BSD
-@deftypefun {void *} setstate (void *@var{state})
+@deftypefun {char *} setstate (char *@var{state})
+@standards{BSD, stdlib.h}
+@safety{@prelim{}@mtsafe{}@asunsafe{@asulock{}}@acunsafe{@aculock{}}}
The @code{setstate} function restores the random number state
information @var{state}. The argument must have been the result of
a previous call to @var{initstate} or @var{setstate}.
If the function fails the return value is @code{NULL}.
@end deftypefun
+The four functions described so far in this section all work on a state
+which is shared by all threads. The state is not directly accessible to
+the user and can only be modified by these functions. This makes it
+hard to deal with situations where each thread should have its own
+pseudo-random number generator.
+
+@Theglibc{} contains four additional functions which contain the
+state as an explicit parameter and therefore make it possible to handle
+thread-local PRNGs. Besides this there is no difference. In fact, the
+four functions already discussed are implemented internally using the
+following interfaces.
+
+The @file{stdlib.h} header contains a definition of the following type:
+
+@deftp {Data Type} {struct random_data}
+@standards{GNU, stdlib.h}
+
+Objects of type @code{struct random_data} contain the information
+necessary to represent the state of the PRNG. Although a complete
+definition of the type is present the type should be treated as opaque.
+@end deftp
+
+The functions modifying the state follow exactly the already described
+functions.
+
+@deftypefun int random_r (struct random_data *restrict @var{buf}, int32_t *restrict @var{result})
+@standards{GNU, stdlib.h}
+@safety{@prelim{}@mtsafe{@mtsrace{:buf}}@assafe{}@acunsafe{@acucorrupt{}}}
+The @code{random_r} function behaves exactly like the @code{random}
+function except that it uses and modifies the state in the object
+pointed to by the first parameter instead of the global state.
+@end deftypefun
+
+@deftypefun int srandom_r (unsigned int @var{seed}, struct random_data *@var{buf})
+@standards{GNU, stdlib.h}
+@safety{@prelim{}@mtsafe{@mtsrace{:buf}}@assafe{}@acunsafe{@acucorrupt{}}}
+The @code{srandom_r} function behaves exactly like the @code{srandom}
+function except that it uses and modifies the state in the object
+pointed to by the second parameter instead of the global state.
+@end deftypefun
+
+@deftypefun int initstate_r (unsigned int @var{seed}, char *restrict @var{statebuf}, size_t @var{statelen}, struct random_data *restrict @var{buf})
+@standards{GNU, stdlib.h}
+@safety{@prelim{}@mtsafe{@mtsrace{:buf}}@assafe{}@acunsafe{@acucorrupt{}}}
+The @code{initstate_r} function behaves exactly like the @code{initstate}
+function except that it uses and modifies the state in the object
+pointed to by the fourth parameter instead of the global state.
+@end deftypefun
+
+@deftypefun int setstate_r (char *restrict @var{statebuf}, struct random_data *restrict @var{buf})
+@standards{GNU, stdlib.h}
+@safety{@prelim{}@mtsafe{@mtsrace{:buf}}@assafe{}@acunsafe{@acucorrupt{}}}
+The @code{setstate_r} function behaves exactly like the @code{setstate}
+function except that it uses and modifies the state in the object
+pointed to by the first parameter instead of the global state.
+@end deftypefun
+
@node SVID Random
@subsection SVID Random Number Function
but they can also be changed by the user. @code{m} is of course 2^48
since the state consists of a 48-bit array.
+The prototypes for these functions are in @file{stdlib.h}.
+@pindex stdlib.h
+
-@comment stdlib.h
-@comment SVID
@deftypefun double drand48 (void)
+@standards{SVID, stdlib.h}
+@safety{@prelim{}@mtunsafe{@mtasurace{:drand48}}@asunsafe{}@acunsafe{@acucorrupt{}}}
+@c Uses of the static state buffer are not guarded by a lock (thus
+@c @mtasurace:drand48), so they may be found or left at a
+@c partially-updated state in case of calls from within signal handlers
+@c or cancellation. None of this will break safety rules or invoke
+@c undefined behavior, but it may affect randomness.
This function returns a @code{double} value in the range of @code{0.0}
to @code{1.0} (exclusive). The random bits are determined by the global
state of the random number generator in the C library.
bits and they are initialized to @code{0}.
@end deftypefun
-@comment stdlib.h
-@comment SVID
@deftypefun double erand48 (unsigned short int @var{xsubi}[3])
+@standards{SVID, stdlib.h}
+@safety{@prelim{}@mtunsafe{@mtasurace{:drand48}}@asunsafe{}@acunsafe{@acucorrupt{}}}
+@c The static buffer is just initialized with default parameters, which
+@c are later read to advance the state held in xsubi.
This function returns a @code{double} value in the range of @code{0.0}
to @code{1.0} (exclusive), similarly to @code{drand48}. The argument is
an array describing the state of the random number generator.
initial use to obtain reproducible results.
@end deftypefun
-@comment stdlib.h
-@comment SVID
@deftypefun {long int} lrand48 (void)
+@standards{SVID, stdlib.h}
+@safety{@prelim{}@mtunsafe{@mtasurace{:drand48}}@asunsafe{}@acunsafe{@acucorrupt{}}}
The @code{lrand48} function returns an integer value in the range of
@code{0} to @code{2^31} (exclusive). Even if the size of the @code{long
int} type can take more than 32 bits, no higher numbers are returned.
generator in the C library.
@end deftypefun
-@comment stdlib.h
-@comment SVID
@deftypefun {long int} nrand48 (unsigned short int @var{xsubi}[3])
+@standards{SVID, stdlib.h}
+@safety{@prelim{}@mtunsafe{@mtasurace{:drand48}}@asunsafe{}@acunsafe{@acucorrupt{}}}
This function is similar to the @code{lrand48} function in that it
returns a number in the range of @code{0} to @code{2^31} (exclusive) but
the state of the random number generator used to produce the random bits
first call to obtain reproducible results.
@end deftypefun
-@comment stdlib.h
-@comment SVID
@deftypefun {long int} mrand48 (void)
+@standards{SVID, stdlib.h}
+@safety{@prelim{}@mtunsafe{@mtasurace{:drand48}}@asunsafe{}@acunsafe{@acucorrupt{}}}
The @code{mrand48} function is similar to @code{lrand48}. The only
difference is that the numbers returned are in the range @code{-2^31} to
@code{2^31} (exclusive).
@end deftypefun
-@comment stdlib.h
-@comment SVID
@deftypefun {long int} jrand48 (unsigned short int @var{xsubi}[3])
+@standards{SVID, stdlib.h}
+@safety{@prelim{}@mtunsafe{@mtasurace{:drand48}}@asunsafe{}@acunsafe{@acucorrupt{}}}
The @code{jrand48} function is similar to @code{nrand48}. The only
difference is that the numbers returned are in the range @code{-2^31} to
@code{2^31} (exclusive). For the @code{xsubi} parameter the same
several ways. The methods differ in the completeness of the
information provided.
-@comment stdlib.h
-@comment SVID
@deftypefun void srand48 (long int @var{seedval})
+@standards{SVID, stdlib.h}
+@safety{@prelim{}@mtunsafe{@mtasurace{:drand48}}@asunsafe{}@acunsafe{@acucorrupt{}}}
The @code{srand48} function sets the most significant 32 bits of the
internal state of the random number generator to the least
significant 32 bits of the @var{seedval} parameter. The lower 16 bits
the user has called the @code{lcong48} function (see below).
@end deftypefun
-@comment stdlib.h
-@comment SVID
@deftypefun {unsigned short int *} seed48 (unsigned short int @var{seed16v}[3])
+@standards{SVID, stdlib.h}
+@safety{@prelim{}@mtunsafe{@mtasurace{:drand48}}@asunsafe{}@acunsafe{@acucorrupt{}}}
The @code{seed48} function initializes all 48 bits of the state of the
internal random number generator from the contents of the parameter
@var{seed16v}. Here the lower 16 bits of the first element of
-@var{see16v} initialize the least significant 16 bits of the internal
+@var{seed16v} initialize the least significant 16 bits of the internal
state, the lower 16 bits of @code{@var{seed16v}[1]} initialize the mid-order
16 bits of the state and the 16 lower bits of @code{@var{seed16v}[2]}
initialize the most significant 16 bits of the state.
which enables you to specify even more information by allowing you to
change the parameters in the congruential formula.
-@comment stdlib.h
-@comment SVID
@deftypefun void lcong48 (unsigned short int @var{param}[7])
+@standards{SVID, stdlib.h}
+@safety{@prelim{}@mtunsafe{@mtasurace{:drand48}}@asunsafe{}@acunsafe{@acucorrupt{}}}
The @code{lcong48} function allows the user to change the complete state
of the random number generator. Unlike @code{srand48} and
@code{seed48}, this function also changes the constants in the
The user-supplied buffer must be of type @code{struct drand48_data}.
This type should be regarded as opaque and not manipulated directly.
-@comment stdlib.h
-@comment GNU
@deftypefun int drand48_r (struct drand48_data *@var{buffer}, double *@var{result})
+@standards{GNU, stdlib.h}
+@safety{@prelim{}@mtsafe{@mtsrace{:buffer}}@assafe{}@acunsafe{@acucorrupt{}}}
This function is equivalent to the @code{drand48} function with the
difference that it does not modify the global random number generator
parameters but instead the parameters in the buffer supplied through the
pointed to by @var{result}.
The return value of the function indicates whether the call succeeded.
-If the value is less than @code{0} an error occurred and @var{errno} is
+If the value is less than @code{0} an error occurred and @code{errno} is
set to indicate the problem.
This function is a GNU extension and should not be used in portable
programs.
@end deftypefun
-@comment stdlib.h
-@comment GNU
@deftypefun int erand48_r (unsigned short int @var{xsubi}[3], struct drand48_data *@var{buffer}, double *@var{result})
+@standards{GNU, stdlib.h}
+@safety{@prelim{}@mtsafe{@mtsrace{:buffer}}@assafe{}@acunsafe{@acucorrupt{}}}
The @code{erand48_r} function works like @code{erand48}, but in addition
it takes an argument @var{buffer} which describes the random number
generator. The state of the random number generator is taken from the
programs.
@end deftypefun
-@comment stdlib.h
-@comment GNU
-@deftypefun int lrand48_r (struct drand48_data *@var{buffer}, double *@var{result})
+@deftypefun int lrand48_r (struct drand48_data *@var{buffer}, long int *@var{result})
+@standards{GNU, stdlib.h}
+@safety{@prelim{}@mtsafe{@mtsrace{:buffer}}@assafe{}@acunsafe{@acucorrupt{}}}
This function is similar to @code{lrand48}, but in addition it takes a
pointer to a buffer describing the state of the random number generator
just like @code{drand48}.
programs.
@end deftypefun
-@comment stdlib.h
-@comment GNU
@deftypefun int nrand48_r (unsigned short int @var{xsubi}[3], struct drand48_data *@var{buffer}, long int *@var{result})
+@standards{GNU, stdlib.h}
+@safety{@prelim{}@mtsafe{@mtsrace{:buffer}}@assafe{}@acunsafe{@acucorrupt{}}}
The @code{nrand48_r} function works like @code{nrand48} in that it
produces a random number in the range @code{0} to @code{2^31}. But instead
of using the global parameters for the congruential formula it uses the
programs.
@end deftypefun
-@comment stdlib.h
-@comment GNU
-@deftypefun int mrand48_r (struct drand48_data *@var{buffer}, double *@var{result})
+@deftypefun int mrand48_r (struct drand48_data *@var{buffer}, long int *@var{result})
+@standards{GNU, stdlib.h}
+@safety{@prelim{}@mtsafe{@mtsrace{:buffer}}@assafe{}@acunsafe{@acucorrupt{}}}
This function is similar to @code{mrand48} but like the other reentrant
functions it uses the random number generator described by the value in
the buffer pointed to by @var{buffer}.
programs.
@end deftypefun
-@comment stdlib.h
-@comment GNU
@deftypefun int jrand48_r (unsigned short int @var{xsubi}[3], struct drand48_data *@var{buffer}, long int *@var{result})
+@standards{GNU, stdlib.h}
+@safety{@prelim{}@mtsafe{@mtsrace{:buffer}}@assafe{}@acunsafe{@acucorrupt{}}}
The @code{jrand48_r} function is similar to @code{jrand48}. Like the
other reentrant functions of this function family it uses the
congruential formula parameters from the buffer pointed to by
recommended to use these functions since the result might not always be
what you expect.
-@comment stdlib.h
-@comment GNU
@deftypefun int srand48_r (long int @var{seedval}, struct drand48_data *@var{buffer})
+@standards{GNU, stdlib.h}
+@safety{@prelim{}@mtsafe{@mtsrace{:buffer}}@assafe{}@acunsafe{@acucorrupt{}}}
The description of the random number generator represented by the
information in @var{buffer} is initialized similarly to what the function
@code{srand48} does. The state is initialized from the parameter
programs.
@end deftypefun
-@comment stdlib.h
-@comment GNU
@deftypefun int seed48_r (unsigned short int @var{seed16v}[3], struct drand48_data *@var{buffer})
+@standards{GNU, stdlib.h}
+@safety{@prelim{}@mtsafe{@mtsrace{:buffer}}@assafe{}@acunsafe{@acucorrupt{}}}
This function is similar to @code{srand48_r} but like @code{seed48} it
initializes all 48 bits of the state from the parameter @var{seed16v}.
programs.
@end deftypefun
-@comment stdlib.h
-@comment GNU
@deftypefun int lcong48_r (unsigned short int @var{param}[7], struct drand48_data *@var{buffer})
+@standards{GNU, stdlib.h}
+@safety{@prelim{}@mtsafe{@mtsrace{:buffer}}@assafe{}@acunsafe{@acucorrupt{}}}
This function initializes all aspects of the random number generator
described in @var{buffer} with the data in @var{param}. Here it is
especially true that the function does more than just copying the
Modern processors can often execute the operations themselves
very fast, but the function call disrupts the instruction pipeline.
-For this reason the GNU C Library provides optimizations for many of the
+For this reason @theglibc{} provides optimizations for many of the
frequently-used math functions. When GNU CC is used and the user
activates the optimizer, several new inline functions and macros are
defined. These new functions and macros have the same names as the
can increase the speed of generated code significantly. The drawback is
that code size will increase, and the increase is not always negligible.
-There are two kind of inline functions: Those that give the same result
+There are two kinds of inline functions: those that give the same result
as the library functions and others that might not set @code{errno} and
might have a reduced precision and/or argument range in comparison with
the library functions. The latter inline functions are only available
if the flag @code{-ffast-math} is given to GNU CC.
-In cases where the inline functions and macros are not wanted the symbol
-@code{__NO_MATH_INLINES} should be defined before any system header is
-included. This will ensure that only library functions are used. Of
-course, it can be determined for each file in the project whether
-giving this option is preferable or not.
-
Not all hardware implements the entire @w{IEEE 754} standard, and even
if it does there may be a substantial performance penalty for using some
of its features. For example, enabling traps on some processors forces
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