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Diffstat (limited to 'manual/math.texi')
| -rw-r--r-- | manual/math.texi | 234 |
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diff --git a/manual/math.texi b/manual/math.texi index 2b804300f2..8520de4835 100644 --- a/manual/math.texi +++ b/manual/math.texi @@ -150,7 +150,11 @@ You can also compute the value of pi with the expression @code{acos @comment math.h @comment ISO @deftypefun double sin (double @var{x}) +@comment math.h +@comment ISO @deftypefunx float sinf (float @var{x}) +@comment math.h +@comment ISO @deftypefunx {long double} sinl (long double @var{x}) 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}. @@ -159,7 +163,11 @@ radians. The return value is in the range @code{-1} to @code{1}. @comment math.h @comment ISO @deftypefun double cos (double @var{x}) +@comment math.h +@comment ISO @deftypefunx float cosf (float @var{x}) +@comment math.h +@comment ISO @deftypefunx {long double} cosl (long double @var{x}) 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}. @@ -168,7 +176,11 @@ radians. The return value is in the range @code{-1} to @code{1}. @comment math.h @comment ISO @deftypefun double tan (double @var{x}) +@comment math.h +@comment ISO @deftypefunx float tanf (float @var{x}) +@comment math.h +@comment ISO @deftypefunx {long double} tanl (long double @var{x}) These functions return the tangent of @var{x}, where @var{x} is given in radians. @@ -186,7 +198,11 @@ function to do that. @comment math.h @comment GNU @deftypefun void sincos (double @var{x}, double *@var{sinx}, double *@var{cosx}) +@comment math.h +@comment GNU @deftypefunx void sincosf (float @var{x}, float *@var{sinx}, float *@var{cosx}) +@comment math.h +@comment GNU @deftypefunx void sincosl (long double @var{x}, long double *@var{sinx}, long double *@var{cosx}) These functions return the sine of @var{x} in @code{*@var{sinx}} and the cosine of @var{x} in @code{*@var{cos}}, where @var{x} is given in @@ -210,7 +226,11 @@ the implementation.) @comment complex.h @comment ISO @deftypefun {complex double} csin (complex double @var{z}) +@comment complex.h +@comment ISO @deftypefunx {complex float} csinf (complex float @var{z}) +@comment complex.h +@comment ISO @deftypefunx {complex long double} csinl (complex long double @var{z}) These functions return the complex sine of @var{z}. The mathematical definition of the complex sine is @@ -226,7 +246,11 @@ $$\sin(z) = {1\over 2i} (e^{zi} - e^{-zi})$$ @comment complex.h @comment ISO @deftypefun {complex double} ccos (complex double @var{z}) +@comment complex.h +@comment ISO @deftypefunx {complex float} ccosf (complex float @var{z}) +@comment complex.h +@comment ISO @deftypefunx {complex long double} ccosl (complex long double @var{z}) These functions return the complex cosine of @var{z}. The mathematical definition of the complex cosine is @@ -242,7 +266,11 @@ $$\cos(z) = {1\over 2} (e^{zi} + e^{-zi})$$ @comment complex.h @comment ISO @deftypefun {complex double} ctan (complex double @var{z}) +@comment complex.h +@comment ISO @deftypefunx {complex float} ctanf (complex float @var{z}) +@comment complex.h +@comment ISO @deftypefunx {complex long double} ctanl (complex long double @var{z}) These functions return the complex tangent of @var{z}. The mathematical definition of the complex tangent is @@ -272,7 +300,11 @@ respectively. @comment math.h @comment ISO @deftypefun double asin (double @var{x}) +@comment math.h +@comment ISO @deftypefunx float asinf (float @var{x}) +@comment math.h +@comment ISO @deftypefunx {long double} asinl (long double @var{x}) These functions compute the arc sine of @var{x}---that is, the value whose sine is @var{x}. The value is in units of radians. Mathematically, @@ -287,7 +319,11 @@ domain, @code{asin} signals a domain error. @comment math.h @comment ISO @deftypefun double acos (double @var{x}) +@comment math.h +@comment ISO @deftypefunx float acosf (float @var{x}) +@comment math.h +@comment ISO @deftypefunx {long double} acosl (long double @var{x}) These functions compute the arc cosine of @var{x}---that is, the value whose cosine is @var{x}. The value is in units of radians. @@ -302,7 +338,11 @@ domain, @code{acos} signals a domain error. @comment math.h @comment ISO @deftypefun double atan (double @var{x}) +@comment math.h +@comment ISO @deftypefunx float atanf (float @var{x}) +@comment math.h +@comment ISO @deftypefunx {long double} atanl (long double @var{x}) These functions compute the arc tangent of @var{x}---that is, the value whose tangent is @var{x}. The value is in units of radians. @@ -313,7 +353,11 @@ returned is the one between @code{-pi/2} and @code{pi/2} (inclusive). @comment math.h @comment ISO @deftypefun double atan2 (double @var{y}, double @var{x}) +@comment math.h +@comment ISO @deftypefunx float atan2f (float @var{y}, float @var{x}) +@comment math.h +@comment ISO @deftypefunx {long double} atan2l (long double @var{y}, long double @var{x}) This function computes the arc tangent of @var{y}/@var{x}, but the signs of both arguments are used to determine the quadrant of the result, and @@ -337,7 +381,11 @@ If both @var{x} and @var{y} are zero, @code{atan2} returns zero. @comment complex.h @comment ISO @deftypefun {complex double} casin (complex double @var{z}) +@comment complex.h +@comment ISO @deftypefunx {complex float} casinf (complex float @var{z}) +@comment complex.h +@comment ISO @deftypefunx {complex long double} casinl (complex long double @var{z}) These functions compute the complex arc sine of @var{z}---that is, the value whose sine is @var{z}. The value returned is in radians. @@ -349,7 +397,11 @@ values of @var{z}. @comment complex.h @comment ISO @deftypefun {complex double} cacos (complex double @var{z}) +@comment complex.h +@comment ISO @deftypefunx {complex float} cacosf (complex float @var{z}) +@comment complex.h +@comment ISO @deftypefunx {complex long double} cacosl (complex long double @var{z}) These functions compute the complex arc cosine of @var{z}---that is, the value whose cosine is @var{z}. The value returned is in radians. @@ -362,7 +414,11 @@ values of @var{z}. @comment complex.h @comment ISO @deftypefun {complex double} catan (complex double @var{z}) +@comment complex.h +@comment ISO @deftypefunx {complex float} catanf (complex float @var{z}) +@comment complex.h +@comment ISO @deftypefunx {complex long double} catanl (complex long double @var{z}) These functions compute the complex arc tangent of @var{z}---that is, the value whose tangent is @var{z}. The value is in units of radians. @@ -378,7 +434,11 @@ the value whose tangent is @var{z}. The value is in units of radians. @comment math.h @comment ISO @deftypefun double exp (double @var{x}) +@comment math.h +@comment ISO @deftypefunx float expf (float @var{x}) +@comment math.h +@comment ISO @deftypefunx {long double} expl (long double @var{x}) These functions compute @code{e} (the base of natural logarithms) raised to the power @var{x}. @@ -390,7 +450,11 @@ If the magnitude of the result is too large to be representable, @comment math.h @comment ISO @deftypefun double exp2 (double @var{x}) +@comment math.h +@comment ISO @deftypefunx float exp2f (float @var{x}) +@comment math.h +@comment ISO @deftypefunx {long double} exp2l (long double @var{x}) These functions compute @code{2} raised to the power @var{x}. Mathematically, @code{exp2 (x)} is the same as @code{exp (x * log (2))}. @@ -399,10 +463,20 @@ Mathematically, @code{exp2 (x)} is the same as @code{exp (x * log (2))}. @comment math.h @comment GNU @deftypefun double exp10 (double @var{x}) +@comment math.h +@comment GNU @deftypefunx float exp10f (float @var{x}) +@comment math.h +@comment GNU @deftypefunx {long double} exp10l (long double @var{x}) +@comment math.h +@comment GNU @deftypefunx double pow10 (double @var{x}) +@comment math.h +@comment GNU @deftypefunx float pow10f (float @var{x}) +@comment math.h +@comment GNU @deftypefunx {long double} pow10l (long double @var{x}) These functions compute @code{10} raised to the power @var{x}. Mathematically, @code{exp10 (x)} is the same as @code{exp (x * log (10))}. @@ -415,7 +489,11 @@ preferred, since it is analogous to @code{exp} and @code{exp2}. @comment math.h @comment ISO @deftypefun double log (double @var{x}) +@comment math.h +@comment ISO @deftypefunx float logf (float @var{x}) +@comment math.h +@comment ISO @deftypefunx {long double} logl (long double @var{x}) These functions compute the natural logarithm of @var{x}. @code{exp (log (@var{x}))} equals @var{x}, exactly in mathematics and approximately in @@ -429,7 +507,11 @@ it may signal overflow. @comment math.h @comment ISO @deftypefun double log10 (double @var{x}) +@comment math.h +@comment ISO @deftypefunx float log10f (float @var{x}) +@comment math.h +@comment ISO @deftypefunx {long double} log10l (long double @var{x}) These functions return the base-10 logarithm of @var{x}. @code{log10 (@var{x})} equals @code{log (@var{x}) / log (10)}. @@ -439,7 +521,11 @@ These functions return the base-10 logarithm of @var{x}. @comment math.h @comment ISO @deftypefun double log2 (double @var{x}) +@comment math.h +@comment ISO @deftypefunx float log2f (float @var{x}) +@comment math.h +@comment ISO @deftypefunx {long double} log2l (long double @var{x}) These functions return the base-2 logarithm of @var{x}. @code{log2 (@var{x})} equals @code{log (@var{x}) / log (2)}. @@ -448,7 +534,11 @@ These functions return the base-2 logarithm of @var{x}. @comment math.h @comment ISO @deftypefun double logb (double @var{x}) +@comment math.h +@comment ISO @deftypefunx float logbf (float @var{x}) +@comment math.h +@comment ISO @deftypefunx {long double} logbl (long double @var{x}) 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 @@ -463,7 +553,11 @@ negative), @code{logb} returns @math{@infinity{}}. If @var{x} is zero, @comment math.h @comment ISO @deftypefun int ilogb (double @var{x}) +@comment math.h +@comment ISO @deftypefunx int ilogbf (float @var{x}) +@comment math.h +@comment ISO @deftypefunx int ilogbl (long double @var{x}) These functions are equivalent to the corresponding @code{logb} functions except that they return signed integer values. @@ -518,7 +612,11 @@ if (i == FP_ILOGB0 || i == FP_ILOGBNAN) @comment math.h @comment ISO @deftypefun double pow (double @var{base}, double @var{power}) +@comment math.h +@comment ISO @deftypefunx float powf (float @var{base}, float @var{power}) +@comment math.h +@comment ISO @deftypefunx {long double} powl (long double @var{base}, long double @var{power}) These are general exponentiation functions, returning @var{base} raised to @var{power}. @@ -533,7 +631,11 @@ underflow or overflow the destination type. @comment math.h @comment ISO @deftypefun double sqrt (double @var{x}) +@comment math.h +@comment ISO @deftypefunx float sqrtf (float @var{x}) +@comment math.h +@comment ISO @deftypefunx {long double} sqrtl (long double @var{x}) These functions return the nonnegative square root of @var{x}. @@ -545,7 +647,11 @@ Mathematically, it should return a complex number. @comment math.h @comment BSD @deftypefun double cbrt (double @var{x}) +@comment math.h +@comment BSD @deftypefunx float cbrtf (float @var{x}) +@comment math.h +@comment BSD @deftypefunx {long double} cbrtl (long double @var{x}) These functions return the cube root of @var{x}. They cannot fail; every representable real value has a representable real cube root. @@ -554,7 +660,11 @@ fail; every representable real value has a representable real cube root. @comment math.h @comment ISO @deftypefun double hypot (double @var{x}, double @var{y}) +@comment math.h +@comment ISO @deftypefunx float hypotf (float @var{x}, float @var{y}) +@comment math.h +@comment ISO @deftypefunx {long double} hypotl (long double @var{x}, long double @var{y}) These functions return @code{sqrt (@var{x}*@var{x} + @var{y}*@var{y})}. This is the length of the hypotenuse of a right @@ -567,7 +677,11 @@ much smaller. See also the function @code{cabs} in @ref{Absolute Value}. @comment math.h @comment ISO @deftypefun double expm1 (double @var{x}) +@comment math.h +@comment ISO @deftypefunx float expm1f (float @var{x}) +@comment math.h +@comment ISO @deftypefunx {long double} expm1l (long double @var{x}) 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 @@ -578,7 +692,11 @@ to subtraction of two numbers that are nearly equal. @comment math.h @comment ISO @deftypefun double log1p (double @var{x}) +@comment math.h +@comment ISO @deftypefunx float log1pf (float @var{x}) +@comment math.h +@comment ISO @deftypefunx {long double} log1pl (long double @var{x}) These functions returns a value equivalent to @w{@code{log (1 + @var{x})}}. They are computed in a way that is accurate even if @var{x} is @@ -594,7 +712,11 @@ logarithm functions. @comment complex.h @comment ISO @deftypefun {complex double} cexp (complex double @var{z}) +@comment complex.h +@comment ISO @deftypefunx {complex float} cexpf (complex float @var{z}) +@comment complex.h +@comment ISO @deftypefunx {complex long double} cexpl (complex long double @var{z}) These functions return @code{e} (the base of natural logarithms) raised to the power of @var{z}. @@ -611,7 +733,11 @@ $$\exp(z) = e^z = e^{{\rm Re}\,z} (\cos ({\rm Im}\,z) + i \sin ({\rm Im}\,z))$$ @comment complex.h @comment ISO @deftypefun {complex double} clog (complex double @var{z}) +@comment complex.h +@comment ISO @deftypefunx {complex float} clogf (complex float @var{z}) +@comment complex.h +@comment ISO @deftypefunx {complex long double} clogl (complex long double @var{z}) These functions return the natural logarithm of @var{z}. Mathematically this corresponds to the value @@ -633,7 +759,11 @@ or is very close to 0. It is well-defined for all other values of @comment complex.h @comment GNU @deftypefun {complex double} clog10 (complex double @var{z}) +@comment complex.h +@comment GNU @deftypefunx {complex float} clog10f (complex float @var{z}) +@comment complex.h +@comment GNU @deftypefunx {complex long double} clog10l (complex long double @var{z}) These functions return the base 10 logarithm of the complex value @var{z}. Mathematically this corresponds to the value @@ -651,7 +781,11 @@ These functions are GNU extensions. @comment complex.h @comment ISO @deftypefun {complex double} csqrt (complex double @var{z}) +@comment complex.h +@comment ISO @deftypefunx {complex float} csqrtf (complex float @var{z}) +@comment complex.h +@comment ISO @deftypefunx {complex long double} csqrtl (complex long double @var{z}) 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}. @@ -660,7 +794,11 @@ the real-valued functions, they are defined for all values of @var{z}. @comment complex.h @comment ISO @deftypefun {complex double} cpow (complex double @var{base}, complex double @var{power}) +@comment complex.h +@comment ISO @deftypefunx {complex float} cpowf (complex float @var{base}, complex float @var{power}) +@comment complex.h +@comment ISO @deftypefunx {complex long double} cpowl (complex long double @var{base}, complex long double @var{power}) These functions return @var{base} raised to the power of @var{power}. This is equivalent to @w{@code{cexp (y * clog (x))}} @@ -676,7 +814,11 @@ see @ref{Exponents and Logarithms}. @comment math.h @comment ISO @deftypefun double sinh (double @var{x}) +@comment math.h +@comment ISO @deftypefunx float sinhf (float @var{x}) +@comment math.h +@comment ISO @deftypefunx {long double} sinhl (long double @var{x}) These functions return the hyperbolic sine of @var{x}, defined mathematically as @w{@code{(exp (@var{x}) - exp (-@var{x})) / 2}}. They @@ -686,7 +828,11 @@ may signal overflow if @var{x} is too large. @comment math.h @comment ISO @deftypefun double cosh (double @var{x}) +@comment math.h +@comment ISO @deftypefunx float coshf (float @var{x}) +@comment math.h +@comment ISO @deftypefunx {long double} coshl (long double @var{x}) These function return the hyperbolic cosine of @var{x}, defined mathematically as @w{@code{(exp (@var{x}) + exp (-@var{x})) / 2}}. @@ -696,7 +842,11 @@ They may signal overflow if @var{x} is too large. @comment math.h @comment ISO @deftypefun double tanh (double @var{x}) +@comment math.h +@comment ISO @deftypefunx float tanhf (float @var{x}) +@comment math.h +@comment ISO @deftypefunx {long double} tanhl (long double @var{x}) These functions return the hyperbolic tangent of @var{x}, defined mathematically as @w{@code{sinh (@var{x}) / cosh (@var{x})}}. @@ -711,7 +861,11 @@ complex arguments. @comment complex.h @comment ISO @deftypefun {complex double} csinh (complex double @var{z}) +@comment complex.h +@comment ISO @deftypefunx {complex float} csinhf (complex float @var{z}) +@comment complex.h +@comment ISO @deftypefunx {complex long double} csinhl (complex long double @var{z}) These functions return the complex hyperbolic sine of @var{z}, defined mathematically as @w{@code{(exp (@var{z}) - exp (-@var{z})) / 2}}. @@ -720,7 +874,11 @@ mathematically as @w{@code{(exp (@var{z}) - exp (-@var{z})) / 2}}. @comment complex.h @comment ISO @deftypefun {complex double} ccosh (complex double @var{z}) +@comment complex.h +@comment ISO @deftypefunx {complex float} ccoshf (complex float @var{z}) +@comment complex.h +@comment ISO @deftypefunx {complex long double} ccoshl (complex long double @var{z}) These functions return the complex hyperbolic cosine of @var{z}, defined mathematically as @w{@code{(exp (@var{z}) + exp (-@var{z})) / 2}}. @@ -729,7 +887,11 @@ mathematically as @w{@code{(exp (@var{z}) + exp (-@var{z})) / 2}}. @comment complex.h @comment ISO @deftypefun {complex double} ctanh (complex double @var{z}) +@comment complex.h +@comment ISO @deftypefunx {complex float} ctanhf (complex float @var{z}) +@comment complex.h +@comment ISO @deftypefunx {complex long double} ctanhl (complex long double @var{z}) These functions return the complex hyperbolic tangent of @var{z}, defined mathematically as @w{@code{csinh (@var{z}) / ccosh (@var{z})}}. @@ -741,7 +903,11 @@ defined mathematically as @w{@code{csinh (@var{z}) / ccosh (@var{z})}}. @comment math.h @comment ISO @deftypefun double asinh (double @var{x}) +@comment math.h +@comment ISO @deftypefunx float asinhf (float @var{x}) +@comment math.h +@comment ISO @deftypefunx {long double} asinhl (long double @var{x}) These functions return the inverse hyperbolic sine of @var{x}---the value whose hyperbolic sine is @var{x}. @@ -750,7 +916,11 @@ value whose hyperbolic sine is @var{x}. @comment math.h @comment ISO @deftypefun double acosh (double @var{x}) +@comment math.h +@comment ISO @deftypefunx float acoshf (float @var{x}) +@comment math.h +@comment ISO @deftypefunx {long double} acoshl (long double @var{x}) These functions return the inverse hyperbolic cosine of @var{x}---the value whose hyperbolic cosine is @var{x}. If @var{x} is less than @@ -760,7 +930,11 @@ value whose hyperbolic cosine is @var{x}. If @var{x} is less than @comment math.h @comment ISO @deftypefun double atanh (double @var{x}) +@comment math.h +@comment ISO @deftypefunx float atanhf (float @var{x}) +@comment math.h +@comment ISO @deftypefunx {long double} atanhl (long double @var{x}) These functions return the inverse hyperbolic tangent of @var{x}---the value whose hyperbolic tangent is @var{x}. If the absolute value of @@ -773,7 +947,11 @@ if it is equal to 1, @code{atanh} returns infinity. @comment complex.h @comment ISO @deftypefun {complex double} casinh (complex double @var{z}) +@comment complex.h +@comment ISO @deftypefunx {complex float} casinhf (complex float @var{z}) +@comment complex.h +@comment ISO @deftypefunx {complex long double} casinhl (complex long double @var{z}) These functions return the inverse complex hyperbolic sine of @var{z}---the value whose complex hyperbolic sine is @var{z}. @@ -782,7 +960,11 @@ These functions return the inverse complex hyperbolic sine of @comment complex.h @comment ISO @deftypefun {complex double} cacosh (complex double @var{z}) +@comment complex.h +@comment ISO @deftypefunx {complex float} cacoshf (complex float @var{z}) +@comment complex.h +@comment ISO @deftypefunx {complex long double} cacoshl (complex long double @var{z}) These functions return the inverse complex hyperbolic cosine of @var{z}---the value whose complex hyperbolic cosine is @var{z}. Unlike @@ -792,7 +974,11 @@ the real-valued functions, there are no restrictions on the value of @var{z}. @comment complex.h @comment ISO @deftypefun {complex double} catanh (complex double @var{z}) +@comment complex.h +@comment ISO @deftypefunx {complex float} catanhf (complex float @var{z}) +@comment complex.h +@comment ISO @deftypefunx {complex long double} catanhl (complex long double @var{z}) These functions return the inverse complex hyperbolic tangent of @var{z}---the value whose complex hyperbolic tangent is @var{z}. Unlike @@ -812,7 +998,11 @@ useful. Currently they only have real-valued versions. @comment math.h @comment SVID @deftypefun double erf (double @var{x}) +@comment math.h +@comment SVID @deftypefunx float erff (float @var{x}) +@comment math.h +@comment SVID @deftypefunx {long double} erfl (long double @var{x}) @code{erf} returns the error function of @var{x}. The error function is defined as @@ -829,7 +1019,11 @@ erf (x) = 2/sqrt(pi) * integral from 0 to x of exp(-t^2) dt @comment math.h @comment SVID @deftypefun double erfc (double @var{x}) +@comment math.h +@comment SVID @deftypefunx float erfcf (float @var{x}) +@comment math.h +@comment SVID @deftypefunx {long double} erfcl (long double @var{x}) @code{erfc} returns @code{1.0 - erf(@var{x})}, but computed in a fashion that avoids round-off error when @var{x} is large. @@ -838,7 +1032,11 @@ fashion that avoids round-off error when @var{x} is large. @comment math.h @comment SVID @deftypefun double lgamma (double @var{x}) +@comment math.h +@comment SVID @deftypefunx float lgammaf (float @var{x}) +@comment math.h +@comment SVID @deftypefunx {long double} lgammal (long double @var{x}) @code{lgamma} returns the natural logarithm of the absolute value of the gamma function of @var{x}. The gamma function is defined as @@ -872,7 +1070,11 @@ singularity. @comment math.h @comment XPG @deftypefun double lgamma_r (double @var{x}, int *@var{signp}) +@comment math.h +@comment XPG @deftypefunx float lgammaf_r (float @var{x}, int *@var{signp}) +@comment math.h +@comment XPG @deftypefunx {long double} lgammal_r (long double @var{x}, int *@var{signp}) @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} @@ -882,7 +1084,11 @@ instead of in the @var{signgam} global. @comment math.h @comment SVID @deftypefun double gamma (double @var{x}) +@comment math.h +@comment SVID @deftypefunx float gammaf (float @var{x}) +@comment math.h +@comment SVID @deftypefunx {long double} gammal (long double @var{x}) These functions exist for compatibility reasons. They are equivalent to @code{lgamma} etc. It is better to use @code{lgamma} since for one the @@ -893,7 +1099,11 @@ standardized in @w{ISO C 9x} while @code{gamma} is not. @comment math.h @comment XPG @deftypefun double tgamma (double @var{x}) +@comment math.h +@comment XPG @deftypefunx float tgammaf (float @var{x}) +@comment math.h +@comment XPG @deftypefunx {long double} tgammal (long double @var{x}) @code{tgamma} applies the gamma function to @var{x}. The gamma function is defined as @@ -912,7 +1122,11 @@ This function was introduced in @w{ISO C 9x}. @comment math.h @comment SVID @deftypefun double j0 (double @var{x}) +@comment math.h +@comment SVID @deftypefunx float j0f (float @var{x}) +@comment math.h +@comment SVID @deftypefunx {long double} j0l (long double @var{x}) @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. @@ -921,7 +1135,11 @@ This function was introduced in @w{ISO C 9x}. @comment math.h @comment SVID @deftypefun double j1 (double @var{x}) +@comment math.h +@comment SVID @deftypefunx float j1f (float @var{x}) +@comment math.h +@comment SVID @deftypefunx {long double} j1l (long double @var{x}) @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. @@ -930,7 +1148,11 @@ This function was introduced in @w{ISO C 9x}. @comment math.h @comment SVID @deftypefun double jn (int n, double @var{x}) +@comment math.h +@comment SVID @deftypefunx float jnf (int n, float @var{x}) +@comment math.h +@comment SVID @deftypefunx {long double} jnl (int n, long double @var{x}) @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. @@ -939,7 +1161,11 @@ This function was introduced in @w{ISO C 9x}. @comment math.h @comment SVID @deftypefun double y0 (double @var{x}) +@comment math.h +@comment SVID @deftypefunx float y0f (float @var{x}) +@comment math.h +@comment SVID @deftypefunx {long double} y0l (long double @var{x}) @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} @@ -950,7 +1176,11 @@ is negative, @code{y0} signals a domain error; if it is zero, @comment math.h @comment SVID @deftypefun double y1 (double @var{x}) +@comment math.h +@comment SVID @deftypefunx float y1f (float @var{x}) +@comment math.h +@comment SVID @deftypefunx {long double} y1l (long double @var{x}) @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} @@ -961,7 +1191,11 @@ is negative, @code{y1} signals a domain error; if it is zero, @comment math.h @comment SVID @deftypefun double yn (int n, double @var{x}) +@comment math.h +@comment SVID @deftypefunx float ynf (int n, float @var{x}) +@comment math.h +@comment SVID @deftypefunx {long double} ynl (int n, long double @var{x}) @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} |