GSL-Functions(3)

NAME
GSL-Functions - GSL Function Reference

SYNOPSIS
gsl_thread_wakeup (thread);
gsl_thread_abort (thread);
gsl_thread_queue_abort (thread);
gsl_thread_aborted ();
gsl_thread_sleep (max_msec);
gsl_thread_awake_after (tick_stamp);
gsl_thread_awake_before (tick_stamp);
gsl_tick_stamp ();
gsl_data_find_block (handle, n_values, values, epsilon);
gsl_module_tick_stamp (module);
gsl_job_integrate (module);
gsl_job_discard (module);
gsl_job_connect (src_module, src_ostream, dest_module, dest_istream);
gsl_job_disconnect (dest_module, dest_istream);
GslAccessFunc (module, data);
gsl_job_access (module, access_func, data, free_func);
gsl_flow_job_access (module, tick_stamp, access_func, data, free_func);
GslPollFunc (data, n_values, timeout_p, n_fds, fds, revents_filled);
gsl_job_add_poll (poll_func, data, free_func, n_fds, fds);
gsl_job_remove_poll (poll_func, data);
gsl_job_debug (debug);
gsl_trans_open ();
gsl_trans_add (trans, job);
gsl_trans_commit (trans);
gsl_trans_dismiss (trans);
gsl_transact (job, ...);
gsl_engine_init (run_threaded, block_size, sample_freq, sub_sample_mask);
gsl_engine_wait_on_trans ();
gsl_power2_fftac (n_values, ri_values_in, ri_values_out);
gsl_power2_fftsc (n_values, ri_values_in, ri_values_out);
gsl_power2_fftar (n_values, r_values_in, ri_values_out);
gsl_power2_fftsr (n_values, ri_values_in, r_values_out);
gsl_filter_tscheb2_steepness_db (iorder, c_freq, epsilon, stopband_db);
gsl_filter_tscheb2_steepness (iorder, c_freq, epsilon, residue);
gsl_filter_butter_lp (iorder, freq, epsilon, a, b);
gsl_filter_tscheb1_lp (iorder, freq, epsilon, a, b);
gsl_filter_tscheb2_lp (iorder, freq, steepness, epsilon, a, b);
gsl_filter_butter_hp (iorder, freq, epsilon, a, b);
gsl_filter_tscheb1_hp (iorder, freq, epsilon, a, b);
gsl_filter_tscheb2_hp (iorder, freq, steepness, epsilon, a, b);
gsl_filter_butter_bp (iorder, freq1, freq2, epsilon, a, b);
gsl_filter_tscheb1_bp (iorder, freq1, freq2, epsilon, a, b);
gsl_filter_tscheb2_bp (iorder, freq1, freq2, steepness, epsilon, a, b);
gsl_filter_butter_bs (iorder, freq1, freq2, epsilon, a, b);
gsl_filter_tscheb1_bs (iorder, freq1, freq2, epsilon, a, b);
gsl_filter_tscheb2_bs (iorder, freq1, freq2, steepness, epsilon, a, b);
gsl_filter_fir_approx (iorder, freq, value);
gsl_filter_sine_scan (order, a, b, freq, n_values);
gsl_engine_garbage_collect ();
gsl_signal_exp2 ();
gsl_approx_exp2 (ex);
gsl_approx_atan1 (x);
gsl_approx_atan1_prescale (boost_amount);
gsl_approx_qcircle1 (x);
gsl_approx_qcircle2 (x);
gsl_approx_qcircle3 (x);
gsl_approx_qcircle4 (x);

DESCRIPTION

  gsl_thread_wakeup (thread);
GslThread* thread
    thread to wake up

Wake up a currently sleeping thread. In practice, this function simply causes the next call to gsl_thread_sleep() within thread to last for 0 seconds.

  gsl_thread_abort (thread);
GslThread* thread
    thread to abort

Abort a currently running thread. This function does not return until the thread in question terminated execution. Note that the thread handle gets invalidated with invocation of gsl_thread_abort() or gsl_thread_queue_abort().

  gsl_thread_queue_abort (thread);
GslThread* thread
    thread to abort

Same as gsl_thread_abort(), but returns as soon as possible, even if thread hasn't stopped execution yet. Note that the thread handle gets invalidated with invocation of gsl_thread_abort() or gsl_thread_queue_abort().

  gsl_thread_aborted ();
RETURNS:
    TRUE if the thread should abort execution

Find out if the currently running thread should be aborted (the thread is supposed to return from its main thread function).

  gsl_thread_sleep (max_msec);
glong  max_msec
    maximum amount of milli seconds to sleep (-1 for infinite time)
RETURNS:
    TRUE if the thread should continue execution

Sleep for the amount of time given. This function may get interrupted by wakeup or abort requests, it returns whether the thread is supposed to continue execution after waking up.

  gsl_thread_awake_after (tick_stamp);
guint64  tick_stamp
    tick stamp update to trigger wakeup

Wakeup the currently running thread after the global tick stamp (see gsl_tick_stamp()) has been updated to tick_stamp. (If the moment of wakeup has already passed by, the thread is woken up at the next global tick stamp update.)

  gsl_thread_awake_before (tick_stamp);
guint64  tick_stamp
    tick stamp update to trigger wakeup

Wakeup the currently running thread upon the last global tick stamp update (see gsl_tick_stamp()) that happens prior to updating the global tick stamp to tick_stamp. (If the moment of wakeup has already passed by, the thread is woken up at the next global tick stamp update.)

  gsl_tick_stamp ();
RETURNS:
    GSL's execution tick stamp as unsigned 64bit integer

Retrive the GSL global tick stamp. GSL increments its global tick stamp at certain intervals, by specific amounts (refer to gsl_engine_init() for further details). The tick stamp is a non-wrapping, unsigned 64bit integer greater than 0. Threads can schedule sleep interruptions at certain tick stamps with gsl_thread_awake_after() and gsl_thread_awake_before(). Tick stamp updating occours at GSL engine block processing boundaries, so code that can guarantee to not run across those boundaries (for instance GslProcessFunc() functions) may use the macro GSL_TICK_STAMP to retrive the current tick in a faster manner (not involving mutex locking). See also gsl_module_tick_stamp().

  gsl_data_find_block (handle, n_values, values, epsilon);
GslDataHandle* handle
    an open GslDataHandle
guint          n_values
    amount of values to look for
const gfloat*  values
    values to find
gfloat         epsilon
    maximum difference upon comparisions
RETURNS:
    position of values in data handle or -1

Find the position of a block of values within a data handle, where all values compare to the reference values with a delta smaller than epsilon.

  gsl_module_tick_stamp (module);
GslModule* module
    a GSL engine module
RETURNS:
    the module's tick stamp, indicating its process status

Any thread may call this function on a valid engine module. The module specific tick stamp is updated to gsl_tick_stamp() + n_values every time its GslProcessFunc() function was called. See also gsl_tick_stamp().

  gsl_job_integrate (module);
GslModule* module
    The module to integrate
RETURNS:
    New job suitable for gsl_trans_add()

Create a new transaction job to integrate module into the engine.

  gsl_job_discard (module);
GslModule* module
    The module to discard
RETURNS:
    New job suitable for gsl_trans_add()

Create a new transaction job which removes module from the engine and destroys it.

  gsl_job_connect (src_module, src_ostream, dest_module, dest_istream);
GslModule* src_module
    Module with output stream
guint      src_ostream
    Index of output stream of src_module
GslModule* dest_module
    Module with unconnected input stream
guint      dest_istream
    Index of input stream of dest_module
RETURNS:
    New job suitable for gsl_trans_add()

Create a new transaction job which connects the ouput stream src_ostream of module src_module to the input stream dest_istream of module dest_module (it is an error if the input stream is already connected by the time the job is executed).

  gsl_job_disconnect (dest_module, dest_istream);
GslModule* dest_module
    Module with connected input stream
guint      dest_istream
    Index of input stream of dest_module
RETURNS:
    New job suitable for gsl_trans_add()

Create a new transaction job which causes the input stream dest_istream of dest_module to be disconnected (it is an error if the input stream isn't connected by the time the job is executed).

  GslAccessFunc (module, data);
module
    Module to operate on
data
    Accessor data

The GslAccessFunc is a user supplied callback function which can access a module in times it is not processing. Accessors are usually used to either read out a module's current state, or to modify its state. An accessor may only operate on the data and the module passed in to it.

  gsl_job_access (module, access_func, data, free_func);
GslModule*     module
    The module to access
GslAccessFunc  access_func
    The accessor function
gpointer       data
    Data passed in to the accessor
GslFreeFunc    free_func
    Function to free data
RETURNS:
    New job suitable for gsl_trans_add()

Create a new transaction job which will invoke access_func on module with data when the transaction queue is processed to modify the module's state.

  gsl_flow_job_access (module, tick_stamp, access_func, data, free_func);
GslModule*     module
guint64        tick_stamp
GslAccessFunc  access_func
gpointer       data
GslFreeFunc    free_func

  GslPollFunc (data, n_values, timeout_p, n_fds, fds, revents_filled);
data
    Data of poll function
n_values
    Minimum number of values the engine wants to process
timeout_p
    Location of timeout value
n_fds
    Number of file descriptors used for polling
fds File descriptors to be used for polling
revents_filled
    Indicates whether fds actually have their ->revents field filled with valid data.
RETURNS:
    A boolean value indicating whether the engine should process data right now

The GslPollFunc is a user supplied callback function which can be hooked into the GSL engine. The engine uses the poll functions to determine whether processing of n_values in its module network is necessary. In order for the poll functions to react to extern events, such as device driver status changes, the engine will poll(2) the fds of the poll function and invoke the callback with revents_filled==TRUE if any of its fds changed state. The callback may also be invoked at other random times with revents_filled=FALSE. It is supposed to return TRUE if network processing is currently necessary, and FALSE if not. If FALSE is returned, timeout_p may be filled with the number of milliseconds the engine should use for polling at maximum.

  gsl_job_add_poll (poll_func, data, free_func, n_fds, fds);
GslPollFunc      poll_func
    Poll function to add
gpointer         data
    Data of poll function
GslFreeFunc      free_func
    Function to free data
guint            n_fds
    Number of poll file descriptors
const GslPollFD* fds
    File descriptors to select(2) or poll(2) on
RETURNS:
    New job suitable for gsl_trans_add()

Create a new transaction job which adds a poll function to the engine. The poll function is used by the engine to determine whether processing is currently necessary.

  gsl_job_remove_poll (poll_func, data);
GslPollFunc  poll_func
    Poll function to remove
gpointer     data
    Data of poll function
RETURNS:
    New job suitable for gsl_trans_add()

Create a new transaction job which removes a previously inserted poll function from the engine.

  gsl_job_debug (debug);
const gchar* debug
    Debug message
RETURNS:
    New job suitable for gsl_trans_add()

Create a new transaction job which issues debug message when the job is executed. This function is meant for debugging purposes during development phase only and shouldn't be used in production code.

  gsl_trans_open ();
RETURNS:
    Newly opened empty transaction

Open up a new transaction to commit jobs to the GSL engine. This function may cause garbage collection (see gsl_engine_garbage_collect()).

  gsl_trans_add (trans, job);
GslTrans* trans
    Opened transaction
GslJob*   job
    Job to add

Append a job to an opened transaction.

  gsl_trans_commit (trans);
GslTrans* trans
    Opened transaction

Close the transaction and commit it to the engine. The engine will execute the jobs contained in this transaction as soon as it has completed its current processing cycle. The jobs will be executed in the exact order they were added to the transaction.

  gsl_trans_dismiss (trans);
GslTrans* trans
    Opened transaction

Close and discard the transaction, destroy all jobs currently contained in it and do not execute them. This function may cause garbage collection (see gsl_engine_garbage_collect()).

  gsl_transact (job, ...);
job First job
... NULL terminated job list

Convenience function which openes up a new transaction, collects the NULL terminated job list passed to the function, and commits the transaction.

  gsl_engine_init (run_threaded, block_size, sample_freq, sub_sample_mask);
gboolean  run_threaded
guint     block_size
    number of values to process block wise
guint     sample_freq
guint     sub_sample_mask

Initialize the GSL engine, this function must be called prior to any other engine related function and can only be invoked once. The block_size determines the amount by which the global tick stamp (see gsl_tick_stamp()) is updated everytime the whole module network completed processing block_size values.

  gsl_engine_wait_on_trans ();

Wait until all pending transactions have been processed by the GSL Engine. This function may cause garbage collection (see gsl_engine_garbage_collect()).

  gsl_power2_fftac (n_values, ri_values_in, ri_values_out);
n_values
    Number of complex values
ri_values_in
    Complex sample values [0..n_values*2-1]
ri_values_out
    Complex frequency values [0..n_values*2-1]

This function performs a decimation in time fourier transformation in forward direction, where the input values are equidistant sampled data, and the output values contain the frequency proportions of the input. The input and output arrays are complex values with real and imaginery portions interleaved, adressable in the range [0..2*n_values-1], where n_values must be a power of two. Frequencies are stored in-order, the K-th output corresponds to the frequency K/n_values. (If you want to interpret negative frequencies, note that the frequencies -K/n_values and (n_values-K)/n_values are equivalent). Note that the transformation is performed out of place, the input array is not modified, and may not overlap with the output array.

  gsl_power2_fftsc (n_values, ri_values_in, ri_values_out);
n_values
    Number of complex values
ri_values_in
    Complex frequency values [0..n_values*2-1]
ri_values_out
    Complex sample values [0..n_values*2-1]

This function performs a decimation in time fourier transformation in backwards direction with normalization. As such, this function represents the counterpart to gsl_power2_fftac(), that is, a value array which is transformed into the frequency domain with gsl_power2_fftac() can be reconstructed by issuing gsl_power2_fftsc() on the transform. Note that the transformation is performed out of place, the input array is not modified, and may not overlap with the output array.

  gsl_power2_fftar (n_values, r_values_in, ri_values_out);
n_values
    Number of complex values
r_values_in
    Real sample values [0..n_values-1]
ri_values_out
    Complex frequency values [0..n_values-1]

Real valued variant of gsl_power2_fftac(), the input array contains real valued equidistant sampled data [0..n_values-1], and the output array contains the positive frequency half of the complex valued fourier transform. Note, that the complex valued fourier transform H of a purely real valued set of data, satisfies H(-f) = Conj(H(f)), where Conj() denotes the complex conjugate, so that just the positive frequency half suffices to describe the entire frequency spectrum. Even so, the resulting n_values/2 complex frequencies are one value off in storage size, but the resulting frequencies H(0) and H(n_values/2) are both real valued, so the real portion of H(n_values/2) is stored in ri_values_out[1] (the imaginery part of H(0)), so that both r_values_in and ri_values_out can be of size n_values. Note that the transformation is performed out of place, the input array is not modified, and may not overlap with the output array.

  gsl_power2_fftsr (n_values, ri_values_in, r_values_out);
n_values
    Number of complex values
ri_values_in
    Complex frequency values [0..n_values-1]
r_values_out
    Real sample values [0..n_values-1]

Real valued variant of gsl_power2_fftsc(), counterpart to gsl_power2_fftar(), using the same frequency storage format. A real valued data set transformed into the frequency domain with gsl_power2_fftar() can be reconstructed using this function. Note that the transformation is performed out of place, the input array is not modified, and may not overlap with the output array.

  gsl_filter_tscheb2_steepness_db (iorder, c_freq, epsilon, stopband_db);
unsigned int  iorder
    filter order
double        c_freq
    passband cutoff frequency (0..pi)
double        epsilon
    fall off at passband frequency (0..1)
double        stopband_db
    reduction in stopband in dB (>= 0)

Calculates the steepness parameter for Tschebyscheff type 2 lowpass filter, based on the ripple residue in the stop band.

  gsl_filter_tscheb2_steepness (iorder, c_freq, epsilon, residue);
unsigned int  iorder
    filter order
double        c_freq
    passband cutoff frequency (0..pi)
double        epsilon
    fall off at passband frequency (0..1)
double        residue
    maximum of transfer function in stopband (0..1)

Calculates the steepness parameter for Tschebyscheff type 2 lowpass filter, based on ripple residue in the stop band.

  gsl_filter_butter_lp (iorder, freq, epsilon, a, b);
iorder
    filter order
freq
    cutoff frequency (0..pi)
epsilon
    fall off at cutoff frequency (0..1)
a   root polynomial coefficients a[0..iorder]
b   pole polynomial coefficients b[0..iorder]

Butterworth lowpass filter.

  gsl_filter_tscheb1_lp (iorder, freq, epsilon, a, b);
iorder
    filter order
freq
    cutoff frequency (0..pi)
epsilon
    fall off at cutoff frequency (0..1)
a   root polynomial coefficients a[0..iorder]
b   pole polynomial coefficients b[0..iorder]

Tschebyscheff type 1 lowpass filter.

  gsl_filter_tscheb2_lp (iorder, freq, steepness, epsilon, a, b);
iorder
    filter order
freq
    passband cutoff frequency (0..pi)
steepness
    frequency steepness (c_freq * steepness < pi)
epsilon
    fall off at passband frequency (0..1)
a   root polynomial coefficients a[0..iorder]
b   pole polynomial coefficients b[0..iorder]

Tschebyscheff type 2 lowpass filter. To gain a transition band between freq1 and freq2, pass arguements freq=freq1 and steepness=freq2/freq1. To specify the transition band width in fractions of octaves, pass steepness=2^octave_fraction.

  gsl_filter_butter_hp (iorder, freq, epsilon, a, b);
iorder
    filter order
freq
    passband frequency (0..pi)
epsilon
    fall off at passband frequency (0..1)
a   root polynomial coefficients a[0..iorder]
b   pole polynomial coefficients b[0..iorder]

Butterworth highpass filter.

  gsl_filter_tscheb1_hp (iorder, freq, epsilon, a, b);
iorder
    filter order
freq
    passband frequency (0..pi)
epsilon
    fall off at passband frequency (0..1)
a   root polynomial coefficients a[0..iorder]
b   pole polynomial coefficients b[0..iorder]

Tschebyscheff type 1 highpass filter.

  gsl_filter_tscheb2_hp (iorder, freq, steepness, epsilon, a, b);
iorder
    filter order
freq
    stopband frequency (0..pi)
steepness
    frequency steepness
epsilon
    fall off at passband frequency (0..1)
a   root polynomial coefficients a[0..iorder]
b   pole polynomial coefficients b[0..iorder]

Tschebyscheff type 2 highpass filter.

  gsl_filter_butter_bp (iorder, freq1, freq2, epsilon, a, b);
iorder
    filter order (must be even)
freq1
    stopband end frequency (0..pi)
freq2
    passband end frequency (0..pi)
epsilon
    fall off at passband frequency (0..1)
a   root polynomial coefficients a[0..iorder]
b   pole polynomial coefficients b[0..iorder]

Butterworth bandpass filter.

  gsl_filter_tscheb1_bp (iorder, freq1, freq2, epsilon, a, b);
iorder
    filter order (must be even)
freq1
    stopband end frequency (0..pi)
freq2
    passband end frequency (0..pi)
epsilon
    fall off at passband frequency (0..1)
a   root polynomial coefficients a[0..iorder]
b   pole polynomial coefficients b[0..iorder]

Tschebyscheff type 1 bandpass filter.

  gsl_filter_tscheb2_bp (iorder, freq1, freq2, steepness, epsilon, a, b);
iorder
    filter order (must be even)
freq1
    stopband end frequency (0..pi)
freq2
    passband end frequency (0..pi)
steepness
    frequency steepness factor
epsilon
    fall off at passband frequency (0..1)
a   root polynomial coefficients a[0..iorder]
b   pole polynomial coefficients b[0..iorder]

Tschebyscheff type 2 bandpass filter.

  gsl_filter_butter_bs (iorder, freq1, freq2, epsilon, a, b);
iorder
    filter order (must be even)
freq1
    passband end frequency (0..pi)
freq2
    stopband end frequency (0..pi)
epsilon
    fall off at passband frequency (0..1)
a   root polynomial coefficients a[0..iorder]
b   pole polynomial coefficients b[0..iorder]

Butterworth bandstop filter.

  gsl_filter_tscheb1_bs (iorder, freq1, freq2, epsilon, a, b);
iorder
    filter order (must be even)
freq1
    passband end frequency (0..pi)
freq2
    stopband end frequency (0..pi)
epsilon
    fall off at passband frequency (0..1)
a   root polynomial coefficients a[0..iorder]
b   pole polynomial coefficients b[0..iorder]

Tschebyscheff type 1 bandstop filter.

  gsl_filter_tscheb2_bs (iorder, freq1, freq2, steepness, epsilon, a, b);
iorder
    filter order (must be even)
freq1
    passband end frequency (0..pi)
freq2
    stopband end frequency (0..pi)
steepness
    frequency steepness factor
epsilon
    fall off at passband frequency (0..1)
a   root polynomial coefficients a[0..iorder]
b   pole polynomial coefficients b[0..iorder]

Tschebyscheff type 2 bandstop filter.

  gsl_filter_fir_approx (iorder, freq, value);
iorder
    order of the filter (must be oven, >= 2)
freq
    the frequencies of the transfer function
value
    the desired value of the transfer function

Approximates a given transfer function with an iorder-coefficient FIR filter. It is recommended to provide enough frequency values, so that n_points >= iorder.

  gsl_filter_sine_scan (order, a, b, freq, n_values);
guint          order
    order of the iir filter
const gdouble* a
    root polynomial coefficients of the filter a[0..order]
const gdouble* b
    pole polynomial coefficients of the filter b[0..order]
gdouble        freq
    frequency to test
guint          n_values
    number of samples

This function sends a sine signal of the desired frequency through an IIR filter, to test the value of the transfer function at a given point. It uses gsl_iir_filter_eval to do so. Compared to a "mathematical approach" of finding the transfer function, this function makes it possible to see the effects of finite arithmetic during filter evaluation. The first half of the output signal is not considered, since a lot of IIR filters have a transient phase where also overshoot is possible. For n_values, you should specify a reasonable large value. It should be a lot larger than the filter order, and large enough to let the input signal become (close to) 1.0 multiple times.

  gsl_engine_garbage_collect ();

GSL Engine user thread function. Collects processed jobs and transactions from the engine and frees them, this involves callback invocation of GslFreeFunc() functions, e.g. from gsl_job_access() or gsl_flow_job_access() jobs. This function may only be called from the user thread, as GslFreeFunc() functions are guranteed to be executed in the user thread.

  gsl_signal_exp2 ();

Deprecated in favour of gsl_approx_exp2().

  gsl_approx_exp2 (ex);
float  ex
    exponent within [-127..127]
RETURNS:
    y approximating 2^x

Fast approximation of 2 raised to the power of x. Multiplicative error stays below 8e-6 and aproaches zero for integer values of x (i.e. x - floor (x) = 0).

  gsl_approx_atan1 (x);
register double  x

Fast atan(x)/(PI/2) approximation, with maximum error < 0.01 and gsl_approx_atan1(0)==0, according to the formula: n1 = -0.41156875521951602506487246309908; n2 = -1.0091272542790025586079663559158; d1 = 0.81901156857081841441890603235599; d2 = 1.0091272542790025586079663559158; positive_atan1(x) = 1 + (n1 * x + n2) / ((1 + d1 * x) * x + d2);

  gsl_approx_atan1_prescale (boost_amount);
boost_amount
    boost amount between [0..1]
RETURNS:
    prescale factor for gsl_approx_atan1()

Calculate the prescale factor for gsl_approx_atan1(x*prescale) from a linear boost factor, where 0.5 amounts to prescale=1.0, 1.0 results in maximum boost and 0.0 results in maximum attenuation.

  gsl_approx_qcircle1 (x);
register double  x
    x within [0..1]
RETURNS:
    y for circle approximation within [0..1]

Fast approximation of the upper right quadrant of a circle. Errors at x=0 and x=1 are zero, for the rest of the curve, the error wasn't minimized, but distributed to best fit the curverture of a quarter circle. The maximum error is below 0.092.

  gsl_approx_qcircle2 (x);
register double  x
    x within [0..1]
RETURNS:
    y for circle approximation within [0..1]

Fast approximation of the upper left quadrant of a circle. Errors at x=0 and x=1 are zero, for the rest of the curve, the error wasn't minimized, but distributed to best fit the curverture of a quarter circle. The maximum error is below 0.092.

  gsl_approx_qcircle3 (x);
register double  x
    x within [0..1]
RETURNS:
    y for circle approximation within [0..1]

Fast approximation of the lower left quadrant of a circle. Errors at x=0 and x=1 are zero, for the rest of the curve, the error wasn't minimized, but distributed to best fit the curverture of a quarter circle. The maximum error is below 0.092.

  gsl_approx_qcircle4 (x);
register double  x
    x within [0..1]
RETURNS:
    y for circle approximation within [0..1]

Fast approximation of the lower right quadrant of a circle. Errors at x=0 and x=1 are zero, for the rest of the curve, the error wasn't minimized, but distributed to best fit the curverture of a quarter circle. The maximum error is below 0.092.