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.

2 files changed, 513 insertions, 49 deletions

diff --git a/manual/arith.texi b/manual/arith.texi
index e403cb51cd..28a0e134d5 100644
--- a/manual/arith.texi
+++ b/manual/arith.texi
@@ -686,9 +686,13 @@ such as by defining @code{_GNU_SOURCE}, and then you must include
 @deftypevr Macro float SNANF
 @deftypevrx Macro double SNAN
 @deftypevrx Macro {long double} SNANL
+@deftypevrx Macro _FloatN SNANFN
+@deftypevrx Macro _FloatNx SNANFNx
 @standards{TS 18661-1:2014, math.h}
-These macros, defined by TS 18661-1:2014, are constant expressions for
-signaling NaNs.
+@standardsx{SNANFN, TS 18661-3:2015, math.h}
+@standardsx{SNANFNx, TS 18661-3:2015, math.h}
+These macros, defined by TS 18661-1:2014 and TS 18661-3:2015, are
+constant expressions for signaling NaNs.
 @end deftypevr
 
 @deftypevr Macro int FE_SNANS_ALWAYS_SIGNAL
@@ -917,7 +921,11 @@ to test for overflow on both old and new hardware.
 @deftypevr Macro double HUGE_VAL
 @deftypevrx Macro float HUGE_VALF
 @deftypevrx Macro {long double} HUGE_VALL
+@deftypevrx Macro _FloatN HUGE_VAL_FN
+@deftypevrx Macro _FloatNx HUGE_VAL_FNx
 @standards{ISO, math.h}
+@standardsx{HUGE_VAL_FN, TS 18661-3:2015, math.h}
+@standardsx{HUGE_VAL_FNx, TS 18661-3:2015, math.h}
 An expression representing a particular very large number.  On machines
 that use @w{IEEE 754} floating point format, @code{HUGE_VAL} is infinity.
 On other machines, it's typically the largest positive number that can
@@ -1229,8 +1237,8 @@ whose imaginary part is @var{y}, the absolute value is @w{@code{sqrt
 @pindex stdlib.h
 Prototypes for @code{abs}, @code{labs} and @code{llabs} are in @file{stdlib.h};
 @code{imaxabs} is declared in @file{inttypes.h};
-@code{fabs}, @code{fabsf} and @code{fabsl} are declared in @file{math.h}.
-@code{cabs}, @code{cabsf} and @code{cabsl} are declared in @file{complex.h}.
+the @code{fabs} functions are declared in @file{math.h};
+the @code{cabs} functions are declared in @file{complex.h}.
 
 @deftypefun int abs (int @var{number})
 @deftypefunx {long int} labs (long int @var{number})
@@ -1254,7 +1262,11 @@ See @ref{Integers} for a description of the @code{intmax_t} type.
 @deftypefun double fabs (double @var{number})
 @deftypefunx float fabsf (float @var{number})
 @deftypefunx {long double} fabsl (long double @var{number})
+@deftypefunx _FloatN fabsfN (_Float@var{N} @var{number})
+@deftypefunx _FloatNx fabsfNx (_Float@var{N}x @var{number})
 @standards{ISO, math.h}
+@standardsx{fabsfN, TS 18661-3:2015, math.h}
+@standardsx{fabsfNx, TS 18661-3:2015, math.h}
 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
 This function returns the absolute value of the floating-point number
 @var{number}.
@@ -1263,7 +1275,11 @@ This function returns the absolute value of the floating-point number
 @deftypefun double cabs (complex double @var{z})
 @deftypefunx float cabsf (complex float @var{z})
 @deftypefunx {long double} cabsl (complex long double @var{z})
+@deftypefunx _FloatN cabsfN (complex _Float@var{N} @var{z})
+@deftypefunx _FloatNx cabsfNx (complex _Float@var{N}x @var{z})
 @standards{ISO, complex.h}
+@standardsx{cabsfN, TS 18661-3:2015, complex.h}
+@standardsx{cabsfNx, TS 18661-3:2015, complex.h}
 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
 These functions return the absolute  value of the complex number @var{z}
 (@pxref{Complex Numbers}).  The absolute value of a complex number is:
@@ -1296,7 +1312,11 @@ All these functions are declared in @file{math.h}.
 @deftypefun double frexp (double @var{value}, int *@var{exponent})
 @deftypefunx float frexpf (float @var{value}, int *@var{exponent})
 @deftypefunx {long double} frexpl (long double @var{value}, int *@var{exponent})
+@deftypefunx _FloatN frexpfN (_Float@var{N} @var{value}, int *@var{exponent})
+@deftypefunx _FloatNx frexpfNx (_Float@var{N}x @var{value}, int *@var{exponent})
 @standards{ISO, math.h}
+@standardsx{frexpfN, TS 18661-3:2015, math.h}
+@standardsx{frexpfNx, TS 18661-3:2015, math.h}
 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
 These functions are used to split the number @var{value}
 into a normalized fraction and an exponent.
@@ -1317,7 +1337,11 @@ zero is stored in @code{*@var{exponent}}.
 @deftypefun double ldexp (double @var{value}, int @var{exponent})
 @deftypefunx float ldexpf (float @var{value}, int @var{exponent})
 @deftypefunx {long double} ldexpl (long double @var{value}, int @var{exponent})
+@deftypefunx _FloatN ldexpfN (_Float@var{N} @var{value}, int @var{exponent})
+@deftypefunx _FloatNx ldexpfNx (_Float@var{N}x @var{value}, int @var{exponent})
 @standards{ISO, math.h}
+@standardsx{ldexpfN, TS 18661-3:2015, math.h}
+@standardsx{ldexpfNx, TS 18661-3:2015, math.h}
 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
 These functions return the result of multiplying the floating-point
 number @var{value} by 2 raised to the power @var{exponent}.  (It can
@@ -1330,6 +1354,8 @@ For example, @code{ldexp (0.8, 4)} returns @code{12.8}.
 The following functions, which come from BSD, provide facilities
 equivalent to those of @code{ldexp} and @code{frexp}.  See also the
 @w{ISO C} function @code{logb} which originally also appeared in BSD.
+The @code{_Float@var{N}} and @code{_Float@var{N}} variants of the
+following functions come from TS 18661-3:2015.
 
 @deftypefun double scalb (double @var{value}, double @var{exponent})
 @deftypefunx float scalbf (float @var{value}, float @var{exponent})
@@ -1342,7 +1368,11 @@ The @code{scalb} function is the BSD name for @code{ldexp}.
 @deftypefun double scalbn (double @var{x}, int @var{n})
 @deftypefunx float scalbnf (float @var{x}, int @var{n})
 @deftypefunx {long double} scalbnl (long double @var{x}, int @var{n})
+@deftypefunx _FloatN scalbnfN (_Float@var{N} @var{x}, int @var{n})
+@deftypefunx _FloatNx scalbnfNx (_Float@var{N}x @var{x}, int @var{n})
 @standards{BSD, math.h}
+@standardsx{scalbnfN, TS 18661-3:2015, math.h}
+@standardsx{scalbnfNx, TS 18661-3:2015, math.h}
 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
 @code{scalbn} is identical to @code{scalb}, except that the exponent
 @var{n} is an @code{int} instead of a floating-point number.
@@ -1351,7 +1381,11 @@ The @code{scalb} function is the BSD name for @code{ldexp}.
 @deftypefun double scalbln (double @var{x}, long int @var{n})
 @deftypefunx float scalblnf (float @var{x}, long int @var{n})
 @deftypefunx {long double} scalblnl (long double @var{x}, long int @var{n})
+@deftypefunx _FloatN scalblnfN (_Float@var{N} @var{x}, long int @var{n})
+@deftypefunx _FloatNx scalblnfNx (_Float@var{N}x @var{x}, long int @var{n})
 @standards{BSD, math.h}
+@standardsx{scalblnfN, TS 18661-3:2015, math.h}
+@standardsx{scalblnfNx, TS 18661-3:2015, math.h}
 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
 @code{scalbln} is identical to @code{scalb}, except that the exponent
 @var{n} is a @code{long int} instead of a floating-point number.
@@ -1416,7 +1450,11 @@ Round to nearest, ties round to even.
 @deftypefun double ceil (double @var{x})
 @deftypefunx float ceilf (float @var{x})
 @deftypefunx {long double} ceill (long double @var{x})
+@deftypefunx _FloatN ceilfN (_Float@var{N} @var{x})
+@deftypefunx _FloatNx ceilfNx (_Float@var{N}x @var{x})
 @standards{ISO, math.h}
+@standardsx{ceilfN, TS 18661-3:2015, math.h}
+@standardsx{ceilfNx, TS 18661-3:2015, math.h}
 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
 These functions round @var{x} upwards to the nearest integer,
 returning that value as a @code{double}.  Thus, @code{ceil (1.5)}
@@ -1426,7 +1464,11 @@ is @code{2.0}.
 @deftypefun double floor (double @var{x})
 @deftypefunx float floorf (float @var{x})
 @deftypefunx {long double} floorl (long double @var{x})
+@deftypefunx _FloatN floorfN (_Float@var{N} @var{x})
+@deftypefunx _FloatNx floorfNx (_Float@var{N}x @var{x})
 @standards{ISO, math.h}
+@standardsx{floorfN, TS 18661-3:2015, math.h}
+@standardsx{floorfNx, TS 18661-3:2015, math.h}
 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
 These functions round @var{x} downwards to the nearest
 integer, returning that value as a @code{double}.  Thus, @code{floor
@@ -1436,7 +1478,11 @@ integer, returning that value as a @code{double}.  Thus, @code{floor
 @deftypefun double trunc (double @var{x})
 @deftypefunx float truncf (float @var{x})
 @deftypefunx {long double} truncl (long double @var{x})
+@deftypefunx _FloatN truncfN (_Float@var{N} @var{x})
+@deftypefunx _FloatNx truncfNx (_Float@var{N}x @var{x})
 @standards{ISO, math.h}
+@standardsx{truncfN, TS 18661-3:2015, math.h}
+@standardsx{truncfNx, TS 18661-3:2015, math.h}
 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
 The @code{trunc} functions round @var{x} towards zero to the nearest
 integer (returned in floating-point format).  Thus, @code{trunc (1.5)}
@@ -1446,7 +1492,11 @@ is @code{1.0} and @code{trunc (-1.5)} is @code{-1.0}.
 @deftypefun double rint (double @var{x})
 @deftypefunx float rintf (float @var{x})
 @deftypefunx {long double} rintl (long double @var{x})
+@deftypefunx _FloatN rintfN (_Float@var{N} @var{x})
+@deftypefunx _FloatNx rintfNx (_Float@var{N}x @var{x})
 @standards{ISO, math.h}
+@standardsx{rintfN, TS 18661-3:2015, math.h}
+@standardsx{rintfNx, TS 18661-3:2015, math.h}
 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
 These functions round @var{x} to an integer value according to the
 current rounding mode.  @xref{Floating Point Parameters}, for
@@ -1462,7 +1512,11 @@ inexact exception.
 @deftypefun double nearbyint (double @var{x})
 @deftypefunx float nearbyintf (float @var{x})
 @deftypefunx {long double} nearbyintl (long double @var{x})
+@deftypefunx _FloatN nearbyintfN (_Float@var{N} @var{x})
+@deftypefunx _FloatNx nearbyintfNx (_Float@var{N}x @var{x})
 @standards{ISO, math.h}
+@standardsx{nearbyintfN, TS 18661-3:2015, math.h}
+@standardsx{nearbyintfNx, TS 18661-3:2015, math.h}
 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
 These functions return the same value as the @code{rint} functions, but
 do not raise the inexact exception if @var{x} is not an integer.
@@ -1471,7 +1525,11 @@ do not raise the inexact exception if @var{x} is not an integer.
 @deftypefun double round (double @var{x})
 @deftypefunx float roundf (float @var{x})
 @deftypefunx {long double} roundl (long double @var{x})
+@deftypefunx _FloatN roundfN (_Float@var{N} @var{x})
+@deftypefunx _FloatNx roundfNx (_Float@var{N}x @var{x})
 @standards{ISO, math.h}
+@standardsx{roundfN, TS 18661-3:2015, math.h}
+@standardsx{roundfNx, TS 18661-3:2015, math.h}
 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
 These functions are similar to @code{rint}, but they round halfway
 cases away from zero instead of to the nearest integer (or other
@@ -1481,16 +1539,25 @@ current rounding mode).
 @deftypefun double roundeven (double @var{x})
 @deftypefunx float roundevenf (float @var{x})
 @deftypefunx {long double} roundevenl (long double @var{x})
+@deftypefunx _FloatN roundevenfN (_Float@var{N} @var{x})
+@deftypefunx _FloatNx roundevenfNx (_Float@var{N}x @var{x})
 @standards{ISO, math.h}
+@standardsx{roundevenfN, TS 18661-3:2015, math.h}
+@standardsx{roundevenfNx, TS 18661-3:2015, math.h}
 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
-These functions, from TS 18661-1:2014, are similar to @code{round},
-but they round halfway cases to even instead of away from zero.
+These functions, from TS 18661-1:2014 and TS 18661-3:2015, are similar
+to @code{round}, but they round halfway cases to even instead of away
+from zero.
 @end deftypefun
 
 @deftypefun {long int} lrint (double @var{x})
 @deftypefunx {long int} lrintf (float @var{x})
 @deftypefunx {long int} lrintl (long double @var{x})
+@deftypefunx {long int} lrintfN (_Float@var{N} @var{x})
+@deftypefunx {long int} lrintfNx (_Float@var{N}x @var{x})
 @standards{ISO, math.h}
+@standardsx{lrintfN, TS 18661-3:2015, math.h}
+@standardsx{lrintfNx, TS 18661-3:2015, math.h}
 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
 These functions are just like @code{rint}, but they return a
 @code{long int} instead of a floating-point number.
@@ -1499,7 +1566,11 @@ These functions are just like @code{rint}, but they return a
 @deftypefun {long long int} llrint (double @var{x})
 @deftypefunx {long long int} llrintf (float @var{x})
 @deftypefunx {long long int} llrintl (long double @var{x})
+@deftypefunx {long long int} llrintfN (_Float@var{N} @var{x})
+@deftypefunx {long long int} llrintfNx (_Float@var{N}x @var{x})
 @standards{ISO, math.h}
+@standardsx{llrintfN, TS 18661-3:2015, math.h}
+@standardsx{llrintfNx, TS 18661-3:2015, math.h}
 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
 These functions are just like @code{rint}, but they return a
 @code{long long int} instead of a floating-point number.
@@ -1508,7 +1579,11 @@ These functions are just like @code{rint}, but they return a
 @deftypefun {long int} lround (double @var{x})
 @deftypefunx {long int} lroundf (float @var{x})
 @deftypefunx {long int} lroundl (long double @var{x})
+@deftypefunx {long int} lroundfN (_Float@var{N} @var{x})
+@deftypefunx {long int} lroundfNx (_Float@var{N}x @var{x})
 @standards{ISO, math.h}
+@standardsx{lroundfN, TS 18661-3:2015, math.h}
+@standardsx{lroundfNx, TS 18661-3:2015, math.h}
 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
 These functions are just like @code{round}, but they return a
 @code{long int} instead of a floating-point number.
@@ -1517,7 +1592,11 @@ These functions are just like @code{round}, but they return a
 @deftypefun {long long int} llround (double @var{x})
 @deftypefunx {long long int} llroundf (float @var{x})
 @deftypefunx {long long int} llroundl (long double @var{x})
+@deftypefunx {long long int} llroundfN (_Float@var{N} @var{x})
+@deftypefunx {long long int} llroundfNx (_Float@var{N}x @var{x})
 @standards{ISO, math.h}
+@standardsx{llroundfN, TS 18661-3:2015, math.h}
+@standardsx{llroundfNx, TS 18661-3:2015, math.h}
 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
 These functions are just like @code{round}, but they return a
 @code{long long int} instead of a floating-point number.
@@ -1526,27 +1605,43 @@ These functions are just like @code{round}, but they return a
 @deftypefun intmax_t fromfp (double @var{x}, int @var{round}, unsigned int @var{width})
 @deftypefunx intmax_t fromfpf (float @var{x}, int @var{round}, unsigned int @var{width})
 @deftypefunx intmax_t fromfpl (long double @var{x}, int @var{round}, unsigned int @var{width})
+@deftypefunx intmax_t fromfpfN (_Float@var{N} @var{x}, int @var{round}, unsigned int @var{width})
+@deftypefunx intmax_t fromfpfNx (_Float@var{N}x @var{x}, int @var{round}, unsigned int @var{width})
 @deftypefunx uintmax_t ufromfp (double @var{x}, int @var{round}, unsigned int @var{width})
 @deftypefunx uintmax_t ufromfpf (float @var{x}, int @var{round}, unsigned int @var{width})
 @deftypefunx uintmax_t ufromfpl (long double @var{x}, int @var{round}, unsigned int @var{width})
+@deftypefunx uintmax_t ufromfpfN (_Float@var{N} @var{x}, int @var{round}, unsigned int @var{width})
+@deftypefunx uintmax_t ufromfpfNx (_Float@var{N}x @var{x}, int @var{round}, unsigned int @var{width})
 @deftypefunx intmax_t fromfpx (double @var{x}, int @var{round}, unsigned int @var{width})
 @deftypefunx intmax_t fromfpxf (float @var{x}, int @var{round}, unsigned int @var{width})
 @deftypefunx intmax_t fromfpxl (long double @var{x}, int @var{round}, unsigned int @var{width})
+@deftypefunx intmax_t fromfpxfN (_Float@var{N} @var{x}, int @var{round}, unsigned int @var{width})
+@deftypefunx intmax_t fromfpxfNx (_Float@var{N}x @var{x}, int @var{round}, unsigned int @var{width})
 @deftypefunx uintmax_t ufromfpx (double @var{x}, int @var{round}, unsigned int @var{width})
 @deftypefunx uintmax_t ufromfpxf (float @var{x}, int @var{round}, unsigned int @var{width})
 @deftypefunx uintmax_t ufromfpxl (long double @var{x}, int @var{round}, unsigned int @var{width})
+@deftypefunx uintmax_t ufromfpxfN (_Float@var{N} @var{x}, int @var{round}, unsigned int @var{width})
+@deftypefunx uintmax_t ufromfpxfNx (_Float@var{N}x @var{x}, int @var{round}, unsigned int @var{width})
 @standards{ISO, math.h}
-@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
-These functions, from TS 18661-1:2014, convert a floating-point number
-to an integer according to the rounding direction @var{round} (one of
-the @code{FP_INT_*} macros).  If the integer is outside the range of a
-signed or unsigned (depending on the return type of the function) type
-of width @var{width} bits (or outside the range of the return type, if
-@var{width} is larger), or if @var{x} is infinite or NaN, or if
-@var{width} is zero, a domain error occurs and an unspecified value is
-returned.  The functions with an @samp{x} in their names raise the
-inexact exception when a domain error does not occur and the argument
-is not an integer; the other functions do not raise the inexact
+@standardsx{fromfpfN, TS 18661-3:2015, math.h}
+@standardsx{fromfpfNx, TS 18661-3:2015, math.h}
+@standardsx{ufromfpfN, TS 18661-3:2015, math.h}
+@standardsx{ufromfpfNx, TS 18661-3:2015, math.h}
+@standardsx{fromfpxfN, TS 18661-3:2015, math.h}
+@standardsx{fromfpxfNx, TS 18661-3:2015, math.h}
+@standardsx{ufromfpxfN, TS 18661-3:2015, math.h}
+@standardsx{ufromfpxfNx, TS 18661-3:2015, math.h}
+@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
+These functions, from TS 18661-1:2014 and TS 18661-3:2015, convert a
+floating-point number to an integer according to the rounding direction
+@var{round} (one of the @code{FP_INT_*} macros).  If the integer is
+outside the range of a signed or unsigned (depending on the return type
+of the function) type of width @var{width} bits (or outside the range of
+the return type, if @var{width} is larger), or if @var{x} is infinite or
+NaN, or if @var{width} is zero, a domain error occurs and an unspecified
+value is returned.  The functions with an @samp{x} in their names raise
+the inexact exception when a domain error does not occur and the
+argument is not an integer; the other functions do not raise the inexact
 exception.
 @end deftypefun
 
@@ -1554,7 +1649,11 @@ exception.
 @deftypefun double modf (double @var{value}, double *@var{integer-part})
 @deftypefunx float modff (float @var{value}, float *@var{integer-part})
 @deftypefunx {long double} modfl (long double @var{value}, long double *@var{integer-part})
+@deftypefunx _FloatN modffN (_Float@var{N} @var{value}, _Float@var{N} *@var{integer-part})
+@deftypefunx _FloatNx modffNx (_Float@var{N}x @var{value}, _Float@var{N}x *@var{integer-part})
 @standards{ISO, math.h}
+@standardsx{modffN, TS 18661-3:2015, math.h}
+@standardsx{modffNx, TS 18661-3:2015, math.h}
 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
 These functions break the argument @var{value} into an integer part and a
 fractional part (between @code{-1} and @code{1}, exclusive).  Their sum
@@ -1576,7 +1675,11 @@ suits your problem.
 @deftypefun double fmod (double @var{numerator}, double @var{denominator})
 @deftypefunx float fmodf (float @var{numerator}, float @var{denominator})
 @deftypefunx {long double} fmodl (long double @var{numerator}, long double @var{denominator})
+@deftypefunx _FloatN fmodfN (_Float@var{N} @var{numerator}, _Float@var{N} @var{denominator})
+@deftypefunx _FloatNx fmodfNx (_Float@var{N}x @var{numerator}, _Float@var{N}x @var{denominator})
 @standards{ISO, math.h}
+@standardsx{fmodfN, TS 18661-3:2015, math.h}
+@standardsx{fmodfNx, TS 18661-3:2015, math.h}
 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
 These functions compute the remainder from the division of
 @var{numerator} by @var{denominator}.  Specifically, the return value is
@@ -1594,7 +1697,11 @@ If @var{denominator} is zero, @code{fmod} signals a domain error.
 @deftypefun double remainder (double @var{numerator}, double @var{denominator})
 @deftypefunx float remainderf (float @var{numerator}, float @var{denominator})
 @deftypefunx {long double} remainderl (long double @var{numerator}, long double @var{denominator})
+@deftypefunx _FloatN remainderfN (_Float@var{N} @var{numerator}, _Float@var{N} @var{denominator})
+@deftypefunx _FloatNx remainderfNx (_Float@var{N}x @var{numerator}, _Float@var{N}x @var{denominator})
 @standards{ISO, math.h}
+@standardsx{remainderfN, TS 18661-3:2015, math.h}
+@standardsx{remainderfNx, TS 18661-3:2015, math.h}
 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
 These functions are like @code{fmod} except that they round the
 internal quotient @var{n} to the nearest integer instead of towards zero
@@ -1630,7 +1737,11 @@ bits.
 @deftypefun double copysign (double @var{x}, double @var{y})
 @deftypefunx float copysignf (float @var{x}, float @var{y})
 @deftypefunx {long double} copysignl (long double @var{x}, long double @var{y})
+@deftypefunx _FloatN copysignfN (_Float@var{N} @var{x}, _Float@var{N} @var{y})
+@deftypefunx _FloatNx copysignfNx (_Float@var{N}x @var{x}, _Float@var{N}x @var{y})
 @standards{ISO, math.h}
+@standardsx{copysignfN, TS 18661-3:2015, math.h}
+@standardsx{copysignfNx, TS 18661-3:2015, math.h}
 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
 These functions return @var{x} but with the sign of @var{y}.  They work
 even if @var{x} or @var{y} are NaN or zero.  Both of these can carry a
@@ -1659,7 +1770,11 @@ false, but @code{signbit (-0.0)} will return a nonzero value.
 @deftypefun double nextafter (double @var{x}, double @var{y})
 @deftypefunx float nextafterf (float @var{x}, float @var{y})
 @deftypefunx {long double} nextafterl (long double @var{x}, long double @var{y})
+@deftypefunx _FloatN nextafterfN (_Float@var{N} @var{x}, _Float@var{N} @var{y})
+@deftypefunx _FloatNx nextafterfNx (_Float@var{N}x @var{x}, _Float@var{N}x @var{y})
 @standards{ISO, math.h}
+@standardsx{nextafterfN, TS 18661-3:2015, math.h}
+@standardsx{nextafterfNx, TS 18661-3:2015, math.h}
 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
 The @code{nextafter} function returns the next representable neighbor of
 @var{x} in the direction towards @var{y}.  The size of the step between
@@ -1688,7 +1803,11 @@ double}.
 @deftypefun double nextup (double @var{x})
 @deftypefunx float nextupf (float @var{x})
 @deftypefunx {long double} nextupl (long double @var{x})
+@deftypefunx _FloatN nextupfN (_Float@var{N} @var{x})
+@deftypefunx _FloatNx nextupfNx (_Float@var{N}x @var{x})
 @standards{ISO, math.h}
+@standardsx{nextupfN, TS 18661-3:2015, math.h}
+@standardsx{nextupfNx, TS 18661-3:2015, math.h}
 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
 The @code{nextup} function returns the next representable neighbor of @var{x}
 in the direction of positive infinity.  If @var{x} is the smallest negative
@@ -1696,14 +1815,18 @@ subnormal number in the type of @var{x} the function returns @code{-0}.  If
 @math{@var{x} = @code{0}} the function returns the smallest positive subnormal
 number in the type of @var{x}.  If @var{x} is NaN, NaN is returned.
 If @var{x} is @math{+@infinity{}}, @math{+@infinity{}} is returned.
-@code{nextup} is from TS 18661-1:2014.
+@code{nextup} is from TS 18661-1:2014 and TS 18661-3:2015.
 @code{nextup} never raises an exception except for signaling NaNs.
 @end deftypefun
 
 @deftypefun double nextdown (double @var{x})
 @deftypefunx float nextdownf (float @var{x})
 @deftypefunx {long double} nextdownl (long double @var{x})
+@deftypefunx _FloatN nextdownfN (_Float@var{N} @var{x})
+@deftypefunx _FloatNx nextdownfNx (_Float@var{N}x @var{x})
 @standards{ISO, math.h}
+@standardsx{nextdownfN, TS 18661-3:2015, math.h}
+@standardsx{nextdownfNx, TS 18661-3:2015, math.h}
 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
 The @code{nextdown} function returns the next representable neighbor of @var{x}
 in the direction of negative infinity.  If @var{x} is the smallest positive
@@ -1711,7 +1834,7 @@ subnormal number in the type of @var{x} the function returns @code{+0}.  If
 @math{@var{x} = @code{0}} the function returns the smallest negative subnormal
 number in the type of @var{x}.  If @var{x} is NaN, NaN is returned.
 If @var{x} is @math{-@infinity{}}, @math{-@infinity{}} is returned.
-@code{nextdown} is from TS 18661-1:2014.
+@code{nextdown} is from TS 18661-1:2014 and TS 18661-3:2015.
 @code{nextdown} never raises an exception except for signaling NaNs.
 @end deftypefun
 
@@ -1719,7 +1842,11 @@ If @var{x} is @math{-@infinity{}}, @math{-@infinity{}} is returned.
 @deftypefun double nan (const char *@var{tagp})
 @deftypefunx float nanf (const char *@var{tagp})
 @deftypefunx {long double} nanl (const char *@var{tagp})
+@deftypefunx _FloatN nanfN (const char *@var{tagp})
+@deftypefunx _FloatNx nanfNx (const char *@var{tagp})
 @standards{ISO, math.h}
+@standardsx{nanfN, TS 18661-3:2015, math.h}
+@standardsx{nanfNx, TS 18661-3:2015, math.h}
 @safety{@prelim{}@mtsafe{@mtslocale{}}@assafe{}@acsafe{}}
 @c The unsafe-but-ruled-safe locale use comes from strtod.
 The @code{nan} function returns a representation of NaN, provided that
@@ -1735,13 +1862,17 @@ selects one.  On other systems it may do nothing.
 @deftypefun int canonicalize (double *@var{cx}, const double *@var{x})
 @deftypefunx int canonicalizef (float *@var{cx}, const float *@var{x})
 @deftypefunx int canonicalizel (long double *@var{cx}, const long double *@var{x})
+@deftypefunx int canonicalizefN (_Float@var{N} *@var{cx}, const _Float@var{N} *@var{x})
+@deftypefunx int canonicalizefNx (_Float@var{N}x *@var{cx}, const _Float@var{N}x *@var{x})
 @standards{ISO, math.h}
+@standardsx{canonicalizefN, TS 18661-3:2015, math.h}
+@standardsx{canonicalizefNx, TS 18661-3:2015, math.h}
 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
 In some floating-point formats, some values have canonical (preferred)
 and noncanonical encodings (for IEEE interchange binary formats, all
 encodings are canonical).  These functions, defined by TS
-18661-1:2014, attempt to produce a canonical version of the
-floating-point value pointed to by @var{x}; if that value is a
+18661-1:2014 and TS 18661-3:2015, attempt to produce a canonical version
+of the floating-point value pointed to by @var{x}; if that value is a
 signaling NaN, they raise the invalid exception and produce a quiet
 NaN.  If a canonical value is produced, it is stored in the object
 pointed to by @var{cx}, and these functions return zero.  Otherwise
@@ -1760,42 +1891,56 @@ produced as output.
 @deftypefun double getpayload (const double *@var{x})
 @deftypefunx float getpayloadf (const float *@var{x})
 @deftypefunx {long double} getpayloadl (const long double *@var{x})
+@deftypefunx _FloatN getpayloadfN (const _Float@var{N} *@var{x})
+@deftypefunx _FloatNx getpayloadfNx (const _Float@var{N}x *@var{x})
 @standards{ISO, math.h}
+@standardsx{getpayloadfN, TS 18661-3:2015, math.h}
+@standardsx{getpayloadfNx, TS 18661-3:2015, math.h}
 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
 IEEE 754 defines the @dfn{payload} of a NaN to be an integer value
 encoded in the representation of the NaN.  Payloads are typically
 propagated from NaN inputs to the result of a floating-point
-operation.  These functions, defined by TS 18661-1:2014, return the
-payload of the NaN pointed to by @var{x} (returned as a positive
-integer, or positive zero, represented as a floating-point number); if
-@var{x} is not a NaN, they return an unspecified value.  They raise no
-floating-point exceptions even for signaling NaNs.
+operation.  These functions, defined by TS 18661-1:2014 and TS
+18661-3:2015, return the payload of the NaN pointed to by @var{x}
+(returned as a positive integer, or positive zero, represented as a
+floating-point number); if @var{x} is not a NaN, they return an
+unspecified value.  They raise no floating-point exceptions even for
+signaling NaNs.
 @end deftypefun
 
 @deftypefun int setpayload (double *@var{x}, double @var{payload})
 @deftypefunx int setpayloadf (float *@var{x}, float @var{payload})
 @deftypefunx int setpayloadl (long double *@var{x}, long double @var{payload})
+@deftypefunx int setpayloadfN (_Float@var{N} *@var{x}, _Float@var{N} @var{payload})
+@deftypefunx int setpayloadfNx (_Float@var{N}x *@var{x}, _Float@var{N}x @var{payload})
 @standards{ISO, math.h}
+@standardsx{setpayloadfN, TS 18661-3:2015, math.h}
+@standardsx{setpayloadfNx, TS 18661-3:2015, math.h}
 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
-These functions, defined by TS 18661-1:2014, set the object pointed to
-by @var{x} to a quiet NaN with payload @var{payload} and a zero sign
-bit and return zero.  If @var{payload} is not a positive-signed
-integer that is a valid payload for a quiet NaN of the given type, the
-object pointed to by @var{x} is set to positive zero and a nonzero
-value is returned.  They raise no floating-point exceptions.
+These functions, defined by TS 18661-1:2014 and TS 18661-3:2015, set the
+object pointed to by @var{x} to a quiet NaN with payload @var{payload}
+and a zero sign bit and return zero.  If @var{payload} is not a
+positive-signed integer that is a valid payload for a quiet NaN of the
+given type, the object pointed to by @var{x} is set to positive zero and
+a nonzero value is returned.  They raise no floating-point exceptions.
 @end deftypefun
 
 @deftypefun int setpayloadsig (double *@var{x}, double @var{payload})
 @deftypefunx int setpayloadsigf (float *@var{x}, float @var{payload})
 @deftypefunx int setpayloadsigl (long double *@var{x}, long double @var{payload})
+@deftypefunx int setpayloadsigfN (_Float@var{N} *@var{x}, _Float@var{N} @var{payload})
+@deftypefunx int setpayloadsigfNx (_Float@var{N}x *@var{x}, _Float@var{N}x @var{payload})
 @standards{ISO, math.h}
+@standardsx{setpayloadsigfN, TS 18661-3:2015, math.h}
+@standardsx{setpayloadsigfNx, TS 18661-3:2015, math.h}
 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
-These functions, defined by TS 18661-1:2014, set the object pointed to
-by @var{x} to a signaling NaN with payload @var{payload} and a zero
-sign bit and return zero.  If @var{payload} is not a positive-signed
-integer that is a valid payload for a signaling NaN of the given type,
-the object pointed to by @var{x} is set to positive zero and a nonzero
-value is returned.  They raise no floating-point exceptions.
+These functions, defined by TS 18661-1:2014 and TS 18661-3:2015, set the
+object pointed to by @var{x} to a signaling NaN with payload
+@var{payload} and a zero sign bit and return zero.  If @var{payload} is
+not a positive-signed integer that is a valid payload for a signaling
+NaN of the given type, the object pointed to by @var{x} is set to
+positive zero and a nonzero value is returned.  They raise no
+floating-point exceptions.
 @end deftypefun
 
 @node FP Comparison Functions
@@ -1886,7 +2031,11 @@ NaN.
 @deftypefun int totalorder (double @var{x}, double @var{y})
 @deftypefunx int totalorderf (float @var{x}, float @var{y})
 @deftypefunx int totalorderl (long double @var{x}, long double @var{y})
+@deftypefunx int totalorderfN (_Float@var{N} @var{x}, _Float@var{N} @var{y})
+@deftypefunx int totalorderfNx (_Float@var{N}x @var{x}, _Float@var{N}x @var{y})
 @standards{TS 18661-1:2014, math.h}
+@standardsx{totalorderfN, TS 18661-3:2015, math.h}
+@standardsx{totalorderfNx, TS 18661-3:2015, math.h}
 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
 These functions determine whether the total order relationship,
 defined in IEEE 754-2008, is true for @var{x} and @var{y}, returning
@@ -1905,7 +2054,11 @@ payload.
 @deftypefun int totalordermag (double @var{x}, double @var{y})
 @deftypefunx int totalordermagf (float @var{x}, float @var{y})
 @deftypefunx int totalordermagl (long double @var{x}, long double @var{y})
+@deftypefunx int totalordermagfN (_Float@var{N} @var{x}, _Float@var{N} @var{y})
+@deftypefunx int totalordermagfNx (_Float@var{N}x @var{x}, _Float@var{N}x @var{y})
 @standards{TS 18661-1:2014, math.h}
+@standardsx{totalordermagfN, TS 18661-3:2015, math.h}
+@standardsx{totalordermagfNx, TS 18661-3:2015, math.h}
 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
 These functions determine whether the total order relationship,
 defined in IEEE 754-2008, is true for the absolute values of @var{x}
@@ -1936,7 +2089,11 @@ perform these operations faster than the equivalent C code.
 @deftypefun double fmin (double @var{x}, double @var{y})
 @deftypefunx float fminf (float @var{x}, float @var{y})
 @deftypefunx {long double} fminl (long double @var{x}, long double @var{y})
+@deftypefunx _FloatN fminfN (_Float@var{N} @var{x}, _Float@var{N} @var{y})
+@deftypefunx _FloatNx fminfNx (_Float@var{N}x @var{x}, _Float@var{N}x @var{y})
 @standards{ISO, math.h}
+@standardsx{fminfN, TS 18661-3:2015, math.h}
+@standardsx{fminfNx, TS 18661-3:2015, math.h}
 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
 The @code{fmin} function returns the lesser of the two values @var{x}
 and @var{y}.  It is similar to the expression
@@ -1952,7 +2109,11 @@ are NaN, NaN is returned.
 @deftypefun double fmax (double @var{x}, double @var{y})
 @deftypefunx float fmaxf (float @var{x}, float @var{y})
 @deftypefunx {long double} fmaxl (long double @var{x}, long double @var{y})
+@deftypefunx _FloatN fmaxfN (_Float@var{N} @var{x}, _Float@var{N} @var{y})
+@deftypefunx _FloatNx fmaxfNx (_Float@var{N}x @var{x}, _Float@var{N}x @var{y})
 @standards{ISO, math.h}
+@standardsx{fmaxfN, TS 18661-3:2015, math.h}
+@standardsx{fmaxfNx, TS 18661-3:2015, math.h}
 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
 The @code{fmax} function returns the greater of the two values @var{x}
 and @var{y}.
@@ -1964,18 +2125,26 @@ are NaN, NaN is returned.
 @deftypefun double fminmag (double @var{x}, double @var{y})
 @deftypefunx float fminmagf (float @var{x}, float @var{y})
 @deftypefunx {long double} fminmagl (long double @var{x}, long double @var{y})
+@deftypefunx _FloatN fminmagfN (_Float@var{N} @var{x}, _Float@var{N} @var{y})
+@deftypefunx _FloatNx fminmagfNx (_Float@var{N}x @var{x}, _Float@var{N}x @var{y})
 @standards{ISO, math.h}
+@standardsx{fminmagfN, TS 18661-3:2015, math.h}
+@standardsx{fminmagfNx, TS 18661-3:2015, math.h}
 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
-These functions, from TS 18661-1:2014, return whichever of the two
-values @var{x} and @var{y} has the smaller absolute value.  If both
-have the same absolute value, or either is NaN, they behave the same
-as the @code{fmin} functions.
+These functions, from TS 18661-1:2014 and TS 18661-3:2015, return
+whichever of the two values @var{x} and @var{y} has the smaller absolute
+value.  If both have the same absolute value, or either is NaN, they
+behave the same as the @code{fmin} functions.
 @end deftypefun
 
 @deftypefun double fmaxmag (double @var{x}, double @var{y})
 @deftypefunx float fmaxmagf (float @var{x}, float @var{y})
 @deftypefunx {long double} fmaxmagl (long double @var{x}, long double @var{y})
+@deftypefunx _FloatN fmaxmagfN (_Float@var{N} @var{x}, _Float@var{N} @var{y})
+@deftypefunx _FloatNx fmaxmagfNx (_Float@var{N}x @var{x}, _Float@var{N}x @var{y})
 @standards{ISO, math.h}
+@standardsx{fmaxmagfN, TS 18661-3:2015, math.h}
+@standardsx{fmaxmagfNx, TS 18661-3:2015, math.h}
 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
 These functions, from TS 18661-1:2014, return whichever of the two
 values @var{x} and @var{y} has the greater absolute value.  If both
@@ -1986,7 +2155,11 @@ as the @code{fmax} functions.
 @deftypefun double fdim (double @var{x}, double @var{y})
 @deftypefunx float fdimf (float @var{x}, float @var{y})
 @deftypefunx {long double} fdiml (long double @var{x}, long double @var{y})
+@deftypefunx _FloatN fdimfN (_Float@var{N} @var{x}, _Float@var{N} @var{y})
+@deftypefunx _FloatNx fdimfNx (_Float@var{N}x @var{x}, _Float@var{N}x @var{y})
 @standards{ISO, math.h}
+@standardsx{fdimfN, TS 18661-3:2015, math.h}
+@standardsx{fdimfNx, TS 18661-3:2015, math.h}
 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
 The @code{fdim} function returns the positive difference between
 @var{x} and @var{y}.  The positive difference is @math{@var{x} -
@@ -1998,7 +2171,11 @@ If @var{x}, @var{y}, or both are NaN, NaN is returned.
 @deftypefun double fma (double @var{x}, double @var{y}, double @var{z})
 @deftypefunx float fmaf (float @var{x}, float @var{y}, float @var{z})
 @deftypefunx {long double} fmal (long double @var{x}, long double @var{y}, long double @var{z})
+@deftypefunx _FloatN fmafN (_Float@var{N} @var{x}, _Float@var{N} @var{y}, _Float@var{N} @var{z})
+@deftypefunx _FloatNx fmafNx (_Float@var{N}x @var{x}, _Float@var{N}x @var{y}, _Float@var{N}x @var{z})
 @standards{ISO, math.h}
+@standardsx{fmafN, TS 18661-3:2015, math.h}
+@standardsx{fmafNx, TS 18661-3:2015, math.h}
 @cindex butterfly
 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
 The @code{fma} function performs floating-point multiply-add.  This is
@@ -2033,6 +2210,11 @@ if @file{complex.h} has been included.  There are three complex types,
 corresponding to the three real types:  @code{float complex},
 @code{double complex}, and @code{long double complex}.
 
+Likewise, on machines that have support for @code{_Float@var{N}} or
+@code{_Float@var{N}x} enabled, the complex types @code{_Float@var{N}
+complex} and @code{_Float@var{N}x complex} are also available if
+@file{complex.h} has been included; @pxref{Mathematics}.
+
 To construct complex numbers you need a way to indicate the imaginary
 part of a number.  There is no standard notation for an imaginary
 floating point constant.  Instead, @file{complex.h} defines two macros
@@ -2126,7 +2308,11 @@ available in three variants, one for each of the three complex types.
 @deftypefun double creal (complex double @var{z})
 @deftypefunx float crealf (complex float @var{z})
 @deftypefunx {long double} creall (complex long double @var{z})
+@deftypefunx _FloatN crealfN (complex _Float@var{N} @var{z})
+@deftypefunx _FloatNx crealfNx (complex _Float@var{N}x @var{z})
 @standards{ISO, complex.h}
+@standardsx{crealfN, TS 18661-3:2015, complex.h}
+@standardsx{crealfNx, TS 18661-3:2015, complex.h}
 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
 These functions return the real part of the complex number @var{z}.
 @end deftypefun
@@ -2134,7 +2320,11 @@ These functions return the real part of the complex number @var{z}.
 @deftypefun double cimag (complex double @var{z})
 @deftypefunx float cimagf (complex float @var{z})
 @deftypefunx {long double} cimagl (complex long double @var{z})
+@deftypefunx _FloatN cimagfN (complex _Float@var{N} @var{z})
+@deftypefunx _FloatNx cimagfNx (complex _Float@var{N}x @var{z})
 @standards{ISO, complex.h}
+@standardsx{cimagfN, TS 18661-3:2015, complex.h}
+@standardsx{cimagfNx, TS 18661-3:2015, complex.h}
 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
 These functions return the imaginary part of the complex number @var{z}.
 @end deftypefun
@@ -2142,7 +2332,11 @@ These functions return the imaginary part of the complex number @var{z}.
 @deftypefun {complex double} conj (complex double @var{z})
 @deftypefunx {complex float} conjf (complex float @var{z})
 @deftypefunx {complex long double} conjl (complex long double @var{z})
+@deftypefunx {complex _FloatN} conjfN (complex _Float@var{N} @var{z})
+@deftypefunx {complex _FloatNx} conjfNx (complex _Float@var{N}x @var{z})
 @standards{ISO, complex.h}
+@standardsx{conjfN, TS 18661-3:2015, complex.h}
+@standardsx{conjfNx, TS 18661-3:2015, complex.h}
 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
 These functions return the conjugate value of the complex number
 @var{z}.  The conjugate of a complex number has the same real part and a
@@ -2152,7 +2346,11 @@ negated imaginary part.  In other words, @samp{conj(a + bi) = a + -bi}.
 @deftypefun double carg (complex double @var{z})
 @deftypefunx float cargf (complex float @var{z})
 @deftypefunx {long double} cargl (complex long double @var{z})
+@deftypefunx _FloatN cargfN (complex _Float@var{N} @var{z})
+@deftypefunx _FloatNx cargfNx (complex _Float@var{N}x @var{z})
 @standards{ISO, complex.h}
+@standardsx{cargfN, TS 18661-3:2015, complex.h}
+@standardsx{cargfNx, TS 18661-3:2015, complex.h}
 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
 These functions return the argument of the complex number @var{z}.
 The argument of a complex number is the angle in the complex plane
@@ -2166,7 +2364,11 @@ number.  This angle is measured in the usual fashion and ranges from
 @deftypefun {complex double} cproj (complex double @var{z})
 @deftypefunx {complex float} cprojf (complex float @var{z})
 @deftypefunx {complex long double} cprojl (complex long double @var{z})
+@deftypefunx {complex _FloatN} cprojfN (complex _Float@var{N} @var{z})
+@deftypefunx {complex _FloatNx} cprojfNx (complex _Float@var{N}x @var{z})
 @standards{ISO, complex.h}
+@standardsx{cprojfN, TS 18661-3:2015, complex.h}
+@standardsx{cprojfNx, TS 18661-3:2015, complex.h}
 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
 These functions return the projection of the complex value @var{z} onto
 the Riemann sphere.  Values with an infinite imaginary part are projected
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