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diff --git a/gsl-1.9/doc/specfunc-trig.texi b/gsl-1.9/doc/specfunc-trig.texi new file mode 100644 index 0000000..547b2a1 --- /dev/null +++ b/gsl-1.9/doc/specfunc-trig.texi @@ -0,0 +1,160 @@ +@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 + |