| @cindex trigonometric functions |
| |
| The library includes its own trigonometric functions in order to provide |
| consistency across platforms and reliable error estimates. These |
| functions are declared in the header file @file{gsl_sf_trig.h}. |
| |
| @menu |
| * Circular Trigonometric Functions:: |
| * Trigonometric Functions for Complex Arguments:: |
| * Hyperbolic Trigonometric Functions:: |
| * Conversion Functions:: |
| * Restriction Functions:: |
| * Trigonometric Functions With Error Estimates:: |
| @end menu |
| |
| @node Circular Trigonometric Functions |
| @subsection Circular Trigonometric Functions |
| |
| @deftypefun double gsl_sf_sin (double @var{x}) |
| @deftypefunx int gsl_sf_sin_e (double @var{x}, gsl_sf_result * @var{result}) |
| @cindex sine function, special functions |
| These routines compute the sine function @math{\sin(x)}. |
| @comment Exceptional Return Values: |
| @end deftypefun |
| |
| @deftypefun double gsl_sf_cos (double @var{x}) |
| @deftypefunx int gsl_sf_cos_e (double @var{x}, gsl_sf_result * @var{result}) |
| @cindex cosine function, special functions |
| These routines compute the cosine function @math{\cos(x)}. |
| @comment Exceptional Return Values: |
| @end deftypefun |
| |
| @deftypefun double gsl_sf_hypot (double @var{x}, double @var{y}) |
| @deftypefunx int gsl_sf_hypot_e (double @var{x}, double @var{y}, gsl_sf_result * @var{result}) |
| @cindex hypot function, special functions |
| These routines compute the hypotenuse function @c{$\sqrt{x^2 + y^2}$} |
| @math{\sqrt@{x^2 + y^2@}} avoiding overflow and underflow. |
| @comment Exceptional Return Values: |
| @end deftypefun |
| |
| @deftypefun double gsl_sf_sinc (double @var{x}) |
| @deftypefunx int gsl_sf_sinc_e (double @var{x}, gsl_sf_result * @var{result}) |
| @cindex complex sinc function, special functions |
| These routines compute @math{\sinc(x) = \sin(\pi x) / (\pi x)} for any |
| value of @var{x}. |
| @comment Exceptional Return Values: none |
| @end deftypefun |
| |
| @node Trigonometric Functions for Complex Arguments |
| @subsection Trigonometric Functions for Complex Arguments |
| |
| @deftypefun int gsl_sf_complex_sin_e (double @var{zr}, double @var{zi}, gsl_sf_result * @var{szr}, gsl_sf_result * @var{szi}) |
| @cindex complex sine function, special functions |
| This function computes the complex sine, @math{\sin(z_r + i z_i)} storing |
| the real and imaginary parts in @var{szr}, @var{szi}. |
| @comment Exceptional Return Values: GSL_EOVRFLW |
| @end deftypefun |
| |
| @deftypefun int gsl_sf_complex_cos_e (double @var{zr}, double @var{zi}, gsl_sf_result * @var{czr}, gsl_sf_result * @var{czi}) |
| @cindex complex cosine function, special functions |
| This function computes the complex cosine, @math{\cos(z_r + i z_i)} storing |
| the real and imaginary parts in @var{szr}, @var{szi}. |
| @comment Exceptional Return Values: GSL_EOVRFLW |
| @end deftypefun |
| |
| @deftypefun int gsl_sf_complex_logsin_e (double @var{zr}, double @var{zi}, gsl_sf_result * @var{lszr}, gsl_sf_result * @var{lszi}) |
| @cindex complex log sine function, special functions |
| This function computes the logarithm of the complex sine, |
| @math{\log(\sin(z_r + i z_i))} storing the real and imaginary parts in |
| @var{szr}, @var{szi}. |
| @comment Exceptional Return Values: GSL_EDOM, GSL_ELOSS |
| @end deftypefun |
| |
| @node Hyperbolic Trigonometric Functions |
| @subsection Hyperbolic Trigonometric Functions |
| |
| @deftypefun double gsl_sf_lnsinh (double @var{x}) |
| @deftypefunx int gsl_sf_lnsinh_e (double @var{x}, gsl_sf_result * @var{result}) |
| @cindex logarithm of sinh function, special functions |
| These routines compute @math{\log(\sinh(x))} for @math{x > 0}. |
| @comment Domain: x > 0 |
| @comment Exceptional Return Values: GSL_EDOM |
| @end deftypefun |
| |
| @deftypefun double gsl_sf_lncosh (double @var{x}) |
| @deftypefunx int gsl_sf_lncosh_e (double @var{x}, gsl_sf_result * @var{result}) |
| @cindex logarithm of cosh function, special functions |
| These routines compute @math{\log(\cosh(x))} for any @var{x}. |
| @comment Exceptional Return Values: none |
| @end deftypefun |
| |
| |
| @node Conversion Functions |
| @subsection Conversion Functions |
| @cindex polar to rectangular conversion |
| @cindex rectangular to polar conversion |
| |
| @deftypefun int gsl_sf_polar_to_rect (double @var{r}, double @var{theta}, gsl_sf_result * @var{x}, gsl_sf_result * @var{y}); |
| This function converts the polar coordinates (@var{r},@var{theta}) to |
| rectilinear coordinates (@var{x},@var{y}), @math{x = r\cos(\theta)}, |
| @math{y = r\sin(\theta)}. |
| @comment Exceptional Return Values: GSL_ELOSS |
| @end deftypefun |
| |
| @deftypefun int gsl_sf_rect_to_polar (double @var{x}, double @var{y}, gsl_sf_result * @var{r}, gsl_sf_result * @var{theta}) |
| This function converts the rectilinear coordinates (@var{x},@var{y}) to |
| polar coordinates (@var{r},@var{theta}), such that @math{x = |
| r\cos(\theta)}, @math{y = r\sin(\theta)}. The argument @var{theta} |
| lies in the range @math{[-\pi, \pi]}. |
| @comment Exceptional Return Values: GSL_EDOM |
| @end deftypefun |
| |
| @node Restriction Functions |
| @subsection Restriction Functions |
| @cindex angular reduction |
| @cindex reduction of angular variables |
| |
| @deftypefun double gsl_sf_angle_restrict_symm (double @var{theta}) |
| @deftypefunx int gsl_sf_angle_restrict_symm_e (double * @var{theta}) |
| These routines force the angle @var{theta} to lie in the range |
| @math{(-\pi,\pi]}. |
| |
| Note that the mathematical value of @math{\pi} is slightly greater |
| than @code{M_PI}, so the machine numbers @code{M_PI} and @code{-M_PI} |
| are included in the range. |
| @comment Exceptional Return Values: GSL_ELOSS |
| @end deftypefun |
| |
| @deftypefun double gsl_sf_angle_restrict_pos (double @var{theta}) |
| @deftypefunx int gsl_sf_angle_restrict_pos_e (double * @var{theta}) |
| These routines force the angle @var{theta} to lie in the range @math{[0, |
| 2\pi)}. |
| |
| Note that the mathematical value of @math{2\pi} is slightly greater |
| than @code{2*M_PI}, so the machine number @code{2*M_PI} is included in |
| the range. |
| |
| @comment Exceptional Return Values: GSL_ELOSS |
| @end deftypefun |
| |
| |
| @node Trigonometric Functions With Error Estimates |
| @subsection Trigonometric Functions With Error Estimates |
| |
| @deftypefun int gsl_sf_sin_err_e (double @var{x}, double @var{dx}, gsl_sf_result * @var{result}) |
| This routine computes the sine of an angle @var{x} with an associated |
| absolute error @var{dx}, |
| @c{$\sin(x \pm dx)$} |
| @math{\sin(x \pm dx)}. Note that this function is provided in the error-handling form only since |
| its purpose is to compute the propagated error. |
| @end deftypefun |
| |
| @deftypefun int gsl_sf_cos_err_e (double @var{x}, double @var{dx}, gsl_sf_result * @var{result}) |
| This routine computes the cosine of an angle @var{x} with an associated |
| absolute error @var{dx}, |
| @c{$\cos(x \pm dx)$} |
| @math{\cos(x \pm dx)}. Note that this function is provided in the error-handling form only since |
| its purpose is to compute the propagated error. |
| @end deftypefun |
| |
