Document _FloatN and _FloatNx versions of math functions

The functions defined in ISO/IEC TS 18661-3 take floating-point arguments
and return floating-point numbers of _FloatN and _FloatNx types.  Apart
from the type, these functions behave the same as their float, double, and
long double counterparts.  This patch adds the newer functions to the
manual.

	* manual/arith.texi (Infinity and NaN): Document SNANFN and SNANFNx.
	(Error Reporting by Mathematical Functions): Document HUGE_VAL_FN
	and HUGE_VAL_FNx.
	(Absolute Value): Document fabsfN, fabsfNx, cabsfN, cabsfNx.
	Rephrase the paragraph that mentions that fabs, fabsf, and fabsl
	are in math.h, to avoid having to list the _FloatN and _FloatNx
	variants as well.  Likewise for the cabs functions.
	(Normalization Functions): Document frexpfN, frexpfNx, ldexpfN,
	ldexpfNx, scalbnfN, scalbnfNx, scalblnfN, scalblnfNx.
	Mention that _FloatN and _FloatNx variants of scalbn and scalbln
	come from TS 18661-3, since this section explicitly states that
	these functions come from BSD.
	(Rounding Functions): Document ceilfN, ceilfNx, floorfN, floorfNx,
	truncfN, truncfNx, rintfN, rintfNx, nearbyintfN, nearbyintfNx,
	roundfN, roundfNx, roundevenfN, roundevenfNx, lrintfN, lrintfNx,
	llrintfN, llrintfNx, lroundfN, lroundfNx, llroundfN, llroundfNx,
	fromfpfN, fromfpfNx, ufromfpfN, ufromfpfNx, fromfpxfN, fromfpxfNx,
	ufromfpxfN, ufromfpxfNx, modffN, modffNx.
	(Remainder Functions): Document fmodfN, fmodfNx, remainderfN,
	remainderfNx.
	(Setting and modifying single bits of FP values): Document
	copysignfN, copysignfNx, nextafterfN, nextafterfNx, nextupfN,
	nextupfNx, nextdownfN, nextdownfNx, nanfN, nanfNx, canonicalizefN,
	canonicalizefNx, getpayloadfN, getpayloadfNx, setpayloadfN,
	setpayloadfNx, setpayloadsigfN, setpayloadsigfNx.
	(Floating-Point Comparison Functions): Document totalorderfN,
	totalorderfNx, totalordermagfN, totalordermagfNx.
	(Miscellaneous FP arithmetic functions): Document fminfN, fminfNx,
	fmaxfN, fmaxfNx, fminmagfN, fminmagfNx, fmaxmagfN, fmaxmagfNx,
	fdimfN, fdimfNx, fmafN, fmafNx.
	(Complex Numbers): Document the complex types: _FloatN complex and
	_FloatNx complex.
	(rojections, Conjugates, and Decomposing of Complex Numbers):
	Document crealfN, crealfNx, cimagfN, cimagfNx, conjfN, conjfNx,
	cargfN, cargfNx, cprojfN, cprojfNx.
	* manual/math.texi (Mathematics): Mention that the _FloatN and
	_FloatNx variants of the math functions come from TS 18661-3,
	unless otherwise stated.
	(Predefined Mathematical Constants): Document the _FloatN and
	_FloatNx variants of the macros prefixed with M_.
	(Trigonometric Functions): Document sinfN, sinfNx, cosfN, cosfNx,
	tanfN, tanfNx, sincosfN, sincosfNx, csinfN, csinfNx, ccosfN,
	ccosfNx, ctanfN, ctanfNx.
	(Inverse Trigonometric Functions): Document asinfN, asinfNx,
	acosfN, acosfNx, atanfN, atanfNx, atan2fN, atan2fNx.
	(Exponentiation and Logarithms): Document expfN, expfNx, exp2fN,
	exp2fNx, exp10fN, exp10fNx, logfN, logfNx, log10fN, log10fNx,
	log2fN, log2fNx, logbfN, logbfNx, ilogbfN, ilogbfNx, llogbfN,
	llogbfNx, powfN, powfNx, sqrtfN, sqrtfNx, cbrtfN, cbrtfNx, hypotfN,
	hypotfNx, expm1fN, expm1fNx, log1pfN, log1pfNx, cexpfN, cexpfNx,
	clogfN, clogfNx, clog10fN, clog10fNx, csqrtfN, csqrtfNx, cpowfN,
	cpowfNx.
	(Hyperbolic Functions): sinhfN, sinhfNx, coshfN, coshfNx, tanhfN,
	tanhfNx, csinhfN, csinhfNx, ccoshfN, ccoshfNx, ctanhfN, ctanhfNx,
	asinhfN, asinhfNx, acoshfN, acoshfNx, atanhfN, atanhfNx, casinhfN,
	casinhfNx, cacoshfN, cacoshfNx, catanhfN, catanhfNx.
	(Special Functions): Document erffN, erffNx, erfcfN, erfcfNx,
	lgammafN, lgammafNx, lgammarfN_r, lgammafNx_r, tgammafN, tgammafNx,
	j0fN, j0fNx, j1fN, j1fNx, jnfN, jnfNx, y0fN, y0fNx, y1fN, y1fNx,
	ynfN, ynfNx.

1 files changed, 269 insertions, 7 deletions

diff --git a/manual/math.texi b/manual/math.texi
index 912e74009f..cad9e5e88b 100644
--- a/manual/math.texi
+++ b/manual/math.texi
@@ -59,7 +59,11 @@ On some machines, @theglibc{} also provides @code{_Float@var{N}} and
 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.
+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.
 
 Currently, support for @code{_Float@var{N}} or @code{_Float@var{N}x}
 types is not provided for any machine.
@@ -128,6 +132,13 @@ also defines these constants with type @code{long double}.  The
 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
@@ -162,7 +173,11 @@ You can also compute the value of pi with the expression @code{acos
 @deftypefun double sin (double @var{x})
 @deftypefunx float sinf (float @var{x})
 @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}.
@@ -171,7 +186,11 @@ radians.  The return value is in the range @code{-1} to @code{1}.
 @deftypefun double cos (double @var{x})
 @deftypefunx float cosf (float @var{x})
 @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}.
@@ -180,7 +199,11 @@ radians.  The return value is in the range @code{-1} to @code{1}.
 @deftypefun double tan (double @var{x})
 @deftypefunx float tanf (float @var{x})
 @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.
@@ -198,6 +221,8 @@ function to do that.
 @deftypefun void sincos (double @var{x}, double *@var{sinx}, double *@var{cosx})
 @deftypefunx void sincosf (float @var{x}, float *@var{sinx}, float *@var{cosx})
 @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
@@ -205,8 +230,9 @@ 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 its absence.
 @end deftypefun
 
 @cindex complex trigonometric functions
@@ -222,7 +248,11 @@ the implementation.)
 @deftypefun {complex double} csin (complex double @var{z})
 @deftypefunx {complex float} csinf (complex float @var{z})
 @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.
@@ -240,7 +270,11 @@ $$\sin(z) = {1\over 2i} (e^{zi} - e^{-zi})$$
 @deftypefun {complex double} ccos (complex double @var{z})
 @deftypefunx {complex float} ccosf (complex float @var{z})
 @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
@@ -256,7 +290,11 @@ $$\cos(z) = {1\over 2} (e^{zi} + e^{-zi})$$
 @deftypefun {complex double} ctan (complex double @var{z})
 @deftypefunx {complex float} ctanf (complex float @var{z})
 @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
@@ -286,7 +324,11 @@ respectively.
 @deftypefun double asin (double @var{x})
 @deftypefunx float asinf (float @var{x})
 @deftypefunx {long double} asinl (long double @var{x})
+@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,
@@ -301,7 +343,11 @@ domain, @code{asin} signals a domain error.
 @deftypefun double acos (double @var{x})
 @deftypefunx float acosf (float @var{x})
 @deftypefunx {long double} acosl (long double @var{x})
+@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.
@@ -316,7 +362,11 @@ domain, @code{acos} signals a domain error.
 @deftypefun double atan (double @var{x})
 @deftypefunx float atanf (float @var{x})
 @deftypefunx {long double} atanl (long double @var{x})
+@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.
@@ -327,7 +377,11 @@ returned is the one between @code{-pi/2} and @code{pi/2} (inclusive).
 @deftypefun double atan2 (double @var{y}, double @var{x})
 @deftypefunx float atan2f (float @var{y}, float @var{x})
 @deftypefunx {long double} atan2l (long double @var{y}, long double @var{x})
+@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
@@ -351,7 +405,11 @@ If both @var{x} and @var{y} are zero, @code{atan2} returns zero.
 @deftypefun {complex double} casin (complex double @var{z})
 @deftypefunx {complex float} casinf (complex float @var{z})
 @deftypefunx {complex long double} casinl (complex long double @var{z})
+@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.
@@ -363,7 +421,11 @@ values of @var{z}.
 @deftypefun {complex double} cacos (complex double @var{z})
 @deftypefunx {complex float} cacosf (complex float @var{z})
 @deftypefunx {complex long double} cacosl (complex long double @var{z})
+@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.
@@ -376,7 +438,11 @@ values of @var{z}.
 @deftypefun {complex double} catan (complex double @var{z})
 @deftypefunx {complex float} catanf (complex float @var{z})
 @deftypefunx {complex long double} catanl (complex long double @var{z})
+@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.
@@ -392,7 +458,11 @@ the value whose tangent is @var{z}.  The value is in units of radians.
 @deftypefun double exp (double @var{x})
 @deftypefunx float expf (float @var{x})
 @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}.
@@ -404,7 +474,11 @@ If the magnitude of the result is too large to be representable,
 @deftypefun double exp2 (double @var{x})
 @deftypefunx float exp2f (float @var{x})
 @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))}.
@@ -413,10 +487,14 @@ Mathematically, @code{exp2 (x)} is the same as @code{exp (x * log (2))}.
 @deftypefun double exp10 (double @var{x})
 @deftypefunx float exp10f (float @var{x})
 @deftypefunx {long double} exp10l (long double @var{x})
+@deftypefunx _FloatN exp10fN (_Float@var{N} @var{x})
+@deftypefunx _FloatNx exp10fNx (_Float@var{N}x @var{x})
 @deftypefunx double pow10 (double @var{x})
 @deftypefunx float pow10f (float @var{x})
 @deftypefunx {long double} pow10l (long double @var{x})
 @standards{ISO, math.h}
+@standardsx{exp10fN, TS 18661-4:2015, math.h}
+@standardsx{exp10fNx, TS 18661-4:2015, math.h}
 @standardsx{pow10, GNU, math.h}
 @standardsx{pow10f, GNU, math.h}
 @standardsx{pow10l, GNU, math.h}
@@ -433,7 +511,11 @@ preferred, since it is analogous to @code{exp} and @code{exp2}.
 @deftypefun double log (double @var{x})
 @deftypefunx float logf (float @var{x})
 @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
@@ -447,7 +529,11 @@ it may signal overflow.
 @deftypefun double log10 (double @var{x})
 @deftypefunx float log10f (float @var{x})
 @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)}.
@@ -457,7 +543,11 @@ These functions return the base-10 logarithm of @var{x}.
 @deftypefun double log2 (double @var{x})
 @deftypefunx float log2f (float @var{x})
 @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)}.
@@ -466,7 +556,11 @@ These functions return the base-2 logarithm of @var{x}.
 @deftypefun double logb (double @var{x})
 @deftypefunx float logbf (float @var{x})
 @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
@@ -481,15 +575,25 @@ negative), @code{logb} returns @math{@infinity{}}.  If @var{x} is zero,
 @deftypefun int ilogb (double @var{x})
 @deftypefunx int ilogbf (float @var{x})
 @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.  The
-@code{ilogb} functions are from ISO C99; the @code{llogb} functions
-are from TS 18661-1:2014.
+@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
@@ -555,7 +659,11 @@ if (i == FP_ILOGB0 || i == FP_ILOGBNAN)
 @deftypefun double pow (double @var{base}, double @var{power})
 @deftypefunx float powf (float @var{base}, float @var{power})
 @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}.
@@ -570,7 +678,11 @@ underflow or overflow the destination type.
 @deftypefun double sqrt (double @var{x})
 @deftypefunx float sqrtf (float @var{x})
 @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}.
 
@@ -582,7 +694,11 @@ Mathematically, it should return a complex number.
 @deftypefun double cbrt (double @var{x})
 @deftypefunx float cbrtf (float @var{x})
 @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.
@@ -591,7 +707,11 @@ fail; every representable real value has a representable real cube root.
 @deftypefun double hypot (double @var{x}, double @var{y})
 @deftypefunx float hypotf (float @var{x}, float @var{y})
 @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
@@ -604,7 +724,11 @@ much smaller.  See also the function @code{cabs} in @ref{Absolute Value}.
 @deftypefun double expm1 (double @var{x})
 @deftypefunx float expm1f (float @var{x})
 @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
@@ -615,7 +739,11 @@ to subtraction of two numbers that are nearly equal.
 @deftypefun double log1p (double @var{x})
 @deftypefunx float log1pf (float @var{x})
 @deftypefunx {long double} log1pl (long double @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
@@ -631,7 +759,11 @@ logarithm functions.
 @deftypefun {complex double} cexp (complex double @var{z})
 @deftypefunx {complex float} cexpf (complex float @var{z})
 @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}.
@@ -648,7 +780,11 @@ $$\exp(z) = e^z = e^{{\rm Re}\,z} (\cos ({\rm Im}\,z) + i \sin ({\rm Im}\,z))$$
 @deftypefun {complex double} clog (complex double @var{z})
 @deftypefunx {complex float} clogf (complex float @var{z})
 @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
@@ -670,6 +806,8 @@ or is very close to 0.  It is well-defined for all other values of
 @deftypefun {complex double} clog10 (complex double @var{z})
 @deftypefunx {complex float} clog10f (complex float @var{z})
 @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
@@ -682,13 +820,18 @@ These functions return the base 10 logarithm of the complex value
 $$\log_{10}(z) = \log_{10}|z| + i \arg z / \log (10)$$
 @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
 
 @deftypefun {complex double} csqrt (complex double @var{z})
 @deftypefunx {complex float} csqrtf (complex float @var{z})
 @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}.
@@ -697,7 +840,11 @@ the real-valued functions, they are defined for all values of @var{z}.
 @deftypefun {complex double} cpow (complex double @var{base}, complex double @var{power})
 @deftypefunx {complex float} cpowf (complex float @var{base}, complex float @var{power})
 @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))}}
@@ -713,7 +860,11 @@ see @ref{Exponents and Logarithms}.
 @deftypefun double sinh (double @var{x})
 @deftypefunx float sinhf (float @var{x})
 @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
@@ -723,7 +874,11 @@ may signal overflow if @var{x} is too large.
 @deftypefun double cosh (double @var{x})
 @deftypefunx float coshf (float @var{x})
 @deftypefunx {long double} coshl (long double @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}}.
@@ -733,7 +888,11 @@ They may signal overflow if @var{x} is too large.
 @deftypefun double tanh (double @var{x})
 @deftypefunx float tanhf (float @var{x})
 @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})}}.
@@ -748,7 +907,11 @@ complex arguments.
 @deftypefun {complex double} csinh (complex double @var{z})
 @deftypefunx {complex float} csinhf (complex float @var{z})
 @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}}.
@@ -757,7 +920,11 @@ mathematically as @w{@code{(exp (@var{z}) - exp (-@var{z})) / 2}}.
 @deftypefun {complex double} ccosh (complex double @var{z})
 @deftypefunx {complex float} ccoshf (complex float @var{z})
 @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}}.
@@ -766,7 +933,11 @@ mathematically as @w{@code{(exp (@var{z}) + exp (-@var{z})) / 2}}.
 @deftypefun {complex double} ctanh (complex double @var{z})
 @deftypefunx {complex float} ctanhf (complex float @var{z})
 @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})}}.
@@ -778,7 +949,11 @@ defined mathematically as @w{@code{csinh (@var{z}) / ccosh (@var{z})}}.
 @deftypefun double asinh (double @var{x})
 @deftypefunx float asinhf (float @var{x})
 @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}.
@@ -787,7 +962,11 @@ value whose hyperbolic sine is @var{x}.
 @deftypefun double acosh (double @var{x})
 @deftypefunx float acoshf (float @var{x})
 @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
@@ -797,7 +976,11 @@ value whose hyperbolic cosine is @var{x}.  If @var{x} is less than
 @deftypefun double atanh (double @var{x})
 @deftypefunx float atanhf (float @var{x})
 @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
@@ -810,7 +993,11 @@ if it is equal to 1, @code{atanh} returns infinity.
 @deftypefun {complex double} casinh (complex double @var{z})
 @deftypefunx {complex float} casinhf (complex float @var{z})
 @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}.
@@ -819,7 +1006,11 @@ These functions return the inverse complex hyperbolic sine of
 @deftypefun {complex double} cacosh (complex double @var{z})
 @deftypefunx {complex float} cacoshf (complex float @var{z})
 @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
@@ -829,7 +1020,11 @@ the real-valued functions, there are no restrictions on the value of @var{z}.
 @deftypefun {complex double} catanh (complex double @var{z})
 @deftypefunx {complex float} catanhf (complex float @var{z})
 @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
@@ -849,7 +1044,11 @@ useful.  Currently they only have real-valued versions.
 @deftypefun double erf (double @var{x})
 @deftypefunx float erff (float @var{x})
 @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
@@ -866,7 +1065,11 @@ erf (x) = 2/sqrt(pi) * integral from 0 to x of exp(-t^2) dt
 @deftypefun double erfc (double @var{x})
 @deftypefunx float erfcf (float @var{x})
 @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.
@@ -875,7 +1078,11 @@ fashion that avoids round-off error when @var{x} is large.
 @deftypefun double lgamma (double @var{x})
 @deftypefunx float lgammaf (float @var{x})
 @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
@@ -909,11 +1116,18 @@ singularity.
 @deftypefun double lgamma_r (double @var{x}, int *@var{signp})
 @deftypefunx float lgammaf_r (float @var{x}, int *@var{signp})
 @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
 
 @deftypefun double gamma (double @var{x})
@@ -930,12 +1144,16 @@ standardized in @w{ISO C99} while @code{gamma} is not.
 @deftypefun double tgamma (double @var{x})
 @deftypefunx float tgammaf (float @var{x})
 @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
@@ -948,67 +1166,111 @@ gamma (x) = integral from 0 to @infinity{} of t^(x-1) e^-t dt
 @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
 
 @deftypefun double j0 (double @var{x})
 @deftypefunx float j0f (float @var{x})
 @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
 
 @deftypefun double j1 (double @var{x})
 @deftypefunx float j1f (float @var{x})
 @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
 
 @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
 
 @deftypefun double y0 (double @var{x})
 @deftypefunx float y0f (float @var{x})
 @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
 
 @deftypefun double y1 (double @var{x})
 @deftypefunx float y1f (float @var{x})
 @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
 
 @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