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Diffstat (limited to 'manual/math.texi')
| -rw-r--r-- | manual/math.texi | 276 |
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 |