3 * Copyright (C) 2007 Sebastian Dröge <slomo@circular-chaos.org>
5 * This library is free software; you can redistribute it and/or
6 * modify it under the terms of the GNU Library General Public
7 * License as published by the Free Software Foundation; either
8 * version 2 of the License, or (at your option) any later version.
10 * This library is distributed in the hope that it will be useful,
11 * but WITHOUT ANY WARRANTY; without even the implied warranty of
12 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
13 * Library General Public License for more details.
15 * You should have received a copy of the GNU Library General Public
16 * License along with this library; if not, write to the
17 * Free Software Foundation, Inc., 59 Temple Place - Suite 330,
18 * Boston, MA 02111-1307, USA.
22 * Chebyshev type 1 filter design based on
23 * "The Scientist and Engineer's Guide to DSP", Chapter 20.
24 * http://www.dspguide.com/
26 * For type 2 and Chebyshev filters in general read
27 * http://en.wikipedia.org/wiki/Chebyshev_filter
32 * SECTION:element-audiochebyshevfreqlimit
33 * @short_description: Chebyshev low pass and high pass filter
37 * Attenuates all frequencies above the cutoff frequency (low-pass) or all frequencies below the
38 * cutoff frequency (high-pass). The number of poles and the ripple parameter control the rolloff.
41 * For type 1 the ripple parameter specifies how much ripple in dB is allowed in the passband, i.e.
42 * some frequencies in the passband will be amplified by that value. A higher ripple value will allow
46 * For type 2 the ripple parameter specifies the stopband attenuation. In the stopband the gain will
47 * be at most this value. A lower ripple value will allow a faster rolloff.
50 * As a special case, a Chebyshev type 1 filter with no ripple is a Butterworth filter.
53 * Be warned that a too large number of poles can produce noise. The most poles are possible with
54 * a cutoff frequency at a quarter of the sampling rate.
56 * <title>Example launch line</title>
59 * gst-launch audiotestsrc freq=1500 ! audioconvert ! audiochebyshevfreqlimit mode=low-pass cutoff=1000 poles=4 ! audioconvert ! alsasink
60 * gst-launch filesrc location="melo1.ogg" ! oggdemux ! vorbisdec ! audioconvert ! audiochebyshevfreqlimit mode=high-pass cutoff=400 ripple=0.2 ! audioconvert ! alsasink
61 * gst-launch audiotestsrc wave=white-noise ! audioconvert ! audiochebyshevfreqlimit mode=low-pass cutoff=800 type=2 ! audioconvert ! alsasink
72 #include <gst/base/gstbasetransform.h>
73 #include <gst/audio/audio.h>
74 #include <gst/audio/gstaudiofilter.h>
75 #include <gst/controller/gstcontroller.h>
79 #include "audiochebyshevfreqlimit.h"
81 #define GST_CAT_DEFAULT gst_audio_chebyshev_freq_limit_debug
82 GST_DEBUG_CATEGORY_STATIC (GST_CAT_DEFAULT);
84 static const GstElementDetails element_details =
85 GST_ELEMENT_DETAILS ("AudioChebyshevFreqLimit",
86 "Filter/Effect/Audio",
87 "Chebyshev low pass and high pass filter",
88 "Sebastian Dröge <slomo@circular-chaos.org>");
90 /* Filter signals and args */
107 #define ALLOWED_CAPS \
108 "audio/x-raw-float," \
109 " width = (int) { 32, 64 }, " \
110 " endianness = (int) BYTE_ORDER," \
111 " rate = (int) [ 1, MAX ]," \
112 " channels = (int) [ 1, MAX ]"
114 #define DEBUG_INIT(bla) \
115 GST_DEBUG_CATEGORY_INIT (gst_audio_chebyshev_freq_limit_debug, "audiochebyshevfreqlimit", 0, "audiochebyshevfreqlimit element");
117 GST_BOILERPLATE_FULL (GstAudioChebyshevFreqLimit,
118 gst_audio_chebyshev_freq_limit, GstAudioFilter, GST_TYPE_AUDIO_FILTER,
121 static void gst_audio_chebyshev_freq_limit_set_property (GObject * object,
122 guint prop_id, const GValue * value, GParamSpec * pspec);
123 static void gst_audio_chebyshev_freq_limit_get_property (GObject * object,
124 guint prop_id, GValue * value, GParamSpec * pspec);
126 static gboolean gst_audio_chebyshev_freq_limit_setup (GstAudioFilter * filter,
127 GstRingBufferSpec * format);
129 gst_audio_chebyshev_freq_limit_transform_ip (GstBaseTransform * base,
131 static gboolean gst_audio_chebyshev_freq_limit_start (GstBaseTransform * base);
133 static void process_64 (GstAudioChebyshevFreqLimit * filter,
134 gdouble * data, guint num_samples);
135 static void process_32 (GstAudioChebyshevFreqLimit * filter,
136 gfloat * data, guint num_samples);
144 #define GST_TYPE_AUDIO_CHEBYSHEV_FREQ_LIMIT_MODE (gst_audio_chebyshev_freq_limit_mode_get_type ())
146 gst_audio_chebyshev_freq_limit_mode_get_type (void)
148 static GType gtype = 0;
151 static const GEnumValue values[] = {
152 {MODE_LOW_PASS, "Low pass (default)",
154 {MODE_HIGH_PASS, "High pass",
159 gtype = g_enum_register_static ("GstAudioChebyshevFreqLimitMode", values);
164 /* GObject vmethod implementations */
167 gst_audio_chebyshev_freq_limit_base_init (gpointer klass)
169 GstElementClass *element_class = GST_ELEMENT_CLASS (klass);
172 gst_element_class_set_details (element_class, &element_details);
174 caps = gst_caps_from_string (ALLOWED_CAPS);
175 gst_audio_filter_class_add_pad_templates (GST_AUDIO_FILTER_CLASS (klass),
177 gst_caps_unref (caps);
181 gst_audio_chebyshev_freq_limit_dispose (GObject * object)
183 GstAudioChebyshevFreqLimit *filter = GST_AUDIO_CHEBYSHEV_FREQ_LIMIT (object);
195 if (filter->channels) {
196 GstAudioChebyshevFreqLimitChannelCtx *ctx;
197 gint i, channels = GST_AUDIO_FILTER (filter)->format.channels;
199 for (i = 0; i < channels; i++) {
200 ctx = &filter->channels[i];
205 g_free (filter->channels);
206 filter->channels = NULL;
209 G_OBJECT_CLASS (parent_class)->dispose (object);
213 gst_audio_chebyshev_freq_limit_class_init (GstAudioChebyshevFreqLimitClass *
216 GObjectClass *gobject_class;
217 GstBaseTransformClass *trans_class;
218 GstAudioFilterClass *filter_class;
220 gobject_class = (GObjectClass *) klass;
221 trans_class = (GstBaseTransformClass *) klass;
222 filter_class = (GstAudioFilterClass *) klass;
224 gobject_class->set_property = gst_audio_chebyshev_freq_limit_set_property;
225 gobject_class->get_property = gst_audio_chebyshev_freq_limit_get_property;
226 gobject_class->dispose = gst_audio_chebyshev_freq_limit_dispose;
228 g_object_class_install_property (gobject_class, PROP_MODE,
229 g_param_spec_enum ("mode", "Mode",
230 "Low pass or high pass mode",
231 GST_TYPE_AUDIO_CHEBYSHEV_FREQ_LIMIT_MODE, MODE_LOW_PASS,
232 G_PARAM_READWRITE | GST_PARAM_CONTROLLABLE));
233 g_object_class_install_property (gobject_class, PROP_TYPE,
234 g_param_spec_int ("type", "Type", "Type of the chebychev filter", 1, 2, 1,
235 G_PARAM_READWRITE | GST_PARAM_CONTROLLABLE));
237 /* FIXME: Don't use the complete possible range but restrict the upper boundary
238 * so automatically generated UIs can use a slider without */
239 g_object_class_install_property (gobject_class, PROP_CUTOFF,
240 g_param_spec_float ("cutoff", "Cutoff", "Cut off frequency (Hz)", 0.0,
241 100000.0, 0.0, G_PARAM_READWRITE | GST_PARAM_CONTROLLABLE));
242 g_object_class_install_property (gobject_class, PROP_RIPPLE,
243 g_param_spec_float ("ripple", "Ripple", "Amount of ripple (dB)", 0.0,
244 200.0, 0.25, G_PARAM_READWRITE | GST_PARAM_CONTROLLABLE));
246 /* FIXME: What to do about this upper boundary? With a cutoff frequency of
247 * rate/4 32 poles are completely possible, with a cutoff frequency very low
248 * or very high 16 poles already produces only noise */
249 g_object_class_install_property (gobject_class, PROP_POLES,
250 g_param_spec_int ("poles", "Poles",
251 "Number of poles to use, will be rounded up to the next even number",
252 2, 32, 4, G_PARAM_READWRITE | GST_PARAM_CONTROLLABLE));
254 filter_class->setup =
255 GST_DEBUG_FUNCPTR (gst_audio_chebyshev_freq_limit_setup);
256 trans_class->transform_ip =
257 GST_DEBUG_FUNCPTR (gst_audio_chebyshev_freq_limit_transform_ip);
258 trans_class->start = GST_DEBUG_FUNCPTR (gst_audio_chebyshev_freq_limit_start);
262 gst_audio_chebyshev_freq_limit_init (GstAudioChebyshevFreqLimit * filter,
263 GstAudioChebyshevFreqLimitClass * klass)
265 filter->cutoff = 0.0;
266 filter->mode = MODE_LOW_PASS;
269 filter->ripple = 0.25;
270 gst_base_transform_set_in_place (GST_BASE_TRANSFORM (filter), TRUE);
272 filter->have_coeffs = FALSE;
275 filter->channels = NULL;
279 generate_biquad_coefficients (GstAudioChebyshevFreqLimit * filter,
280 gint p, gdouble * a0, gdouble * a1, gdouble * a2,
281 gdouble * b1, gdouble * b2)
283 gint np = filter->poles;
284 gdouble ripple = filter->ripple;
286 /* pole location in s-plane */
289 /* zero location in s-plane */
290 gdouble rz = 0.0, iz = 0.0;
292 /* transfer function coefficients for the z-plane */
293 gdouble x0, x1, x2, y1, y2;
294 gint type = filter->type;
296 /* Calculate pole location for lowpass at frequency 1 */
298 gdouble angle = (M_PI / 2.0) * (2.0 * p - 1) / np;
304 /* If we allow ripple, move the pole from the unit
305 * circle to an ellipse and keep cutoff at frequency 1 */
306 if (ripple > 0 && type == 1) {
309 es = sqrt (pow (10.0, ripple / 10.0) - 1.0);
311 vx = (1.0 / np) * asinh (1.0 / es);
314 } else if (type == 2) {
317 es = sqrt (pow (10.0, ripple / 10.0) - 1.0);
318 vx = (1.0 / np) * asinh (es);
323 /* Calculate inverse of the pole location to convert from
324 * type I to type II */
326 gdouble mag2 = rp * rp + ip * ip;
332 /* Calculate zero location for frequency 1 on the
333 * unit circle for type 2 */
335 gdouble angle = M_PI / (np * 2.0) + ((p - 1) * M_PI) / (np);
340 mag2 = rz * rz + iz * iz;
345 /* Convert from s-domain to z-domain by
346 * using the bilinear Z-transform, i.e.
347 * substitute s by (2/t)*((z-1)/(z+1))
348 * with t = 2 * tan(0.5).
354 m = rp * rp + ip * ip;
355 d = 4.0 - 4.0 * rp * t + m * t * t;
360 y1 = (8.0 - 2.0 * m * t * t) / d;
361 y2 = (-4.0 - 4.0 * rp * t - m * t * t) / d;
366 m = rp * rp + ip * ip;
367 d = 4.0 - 4.0 * rp * t + m * t * t;
369 x0 = (t * t * iz * iz + 4.0) / d;
370 x1 = (-8.0 + 2.0 * iz * iz * t * t) / d;
372 y1 = (8.0 - 2.0 * m * t * t) / d;
373 y2 = (-4.0 - 4.0 * rp * t - m * t * t) / d;
376 /* Convert from lowpass at frequency 1 to either lowpass
379 * For lowpass substitute z^(-1) with:
386 * k = sin((1-w)/2) / sin((1+w)/2)
388 * For highpass substitute z^(-1) with:
396 * k = -cos((1+w)/2) / cos((1-w)/2)
402 2.0 * M_PI * (filter->cutoff / GST_AUDIO_FILTER (filter)->format.rate);
404 if (filter->mode == MODE_LOW_PASS)
405 k = sin ((1.0 - omega) / 2.0) / sin ((1.0 + omega) / 2.0);
407 k = -cos ((omega + 1.0) / 2.0) / cos ((omega - 1.0) / 2.0);
409 d = 1.0 + y1 * k - y2 * k * k;
410 *a0 = (x0 + k * (-x1 + k * x2)) / d;
411 *a1 = (x1 + k * k * x1 - 2.0 * k * (x0 + x2)) / d;
412 *a2 = (x0 * k * k - x1 * k + x2) / d;
413 *b1 = (2.0 * k + y1 + y1 * k * k - 2.0 * y2 * k) / d;
414 *b2 = (-k * k - y1 * k + y2) / d;
416 if (filter->mode == MODE_HIGH_PASS) {
423 /* Evaluate the transfer function that corresponds to the IIR
424 * coefficients at zr + zi*I and return the magnitude */
426 calculate_gain (gdouble * a, gdouble * b, gint num_a, gint num_b, gdouble zr,
429 gdouble sum_ar, sum_ai;
430 gdouble sum_br, sum_bi;
431 gdouble gain_r, gain_i;
440 for (i = num_a; i >= 0; i--) {
444 sum_ar = (sum_r_old * zr - sum_i_old * zi) + a[i];
445 sum_ai = (sum_r_old * zi + sum_i_old * zr) + 0.0;
450 for (i = num_b; i >= 0; i--) {
454 sum_br = (sum_r_old * zr - sum_i_old * zi) - b[i];
455 sum_bi = (sum_r_old * zi + sum_i_old * zr) - 0.0;
461 (sum_ar * sum_br + sum_ai * sum_bi) / (sum_br * sum_br + sum_bi * sum_bi);
463 (sum_ai * sum_br - sum_ar * sum_bi) / (sum_br * sum_br + sum_bi * sum_bi);
465 return (sqrt (gain_r * gain_r + gain_i * gain_i));
469 generate_coefficients (GstAudioChebyshevFreqLimit * filter)
471 gint channels = GST_AUDIO_FILTER (filter)->format.channels;
483 if (filter->channels) {
484 GstAudioChebyshevFreqLimitChannelCtx *ctx;
487 for (i = 0; i < channels; i++) {
488 ctx = &filter->channels[i];
493 g_free (filter->channels);
494 filter->channels = NULL;
497 if (GST_AUDIO_FILTER (filter)->format.rate == 0) {
499 filter->a = g_new0 (gdouble, 1);
502 filter->channels = g_new0 (GstAudioChebyshevFreqLimitChannelCtx, channels);
503 GST_LOG_OBJECT (filter, "rate was not set yet");
507 filter->have_coeffs = TRUE;
509 if (filter->cutoff >= GST_AUDIO_FILTER (filter)->format.rate / 2.0) {
511 filter->a = g_new0 (gdouble, 1);
512 filter->a[0] = (filter->mode == MODE_LOW_PASS) ? 1.0 : 0.0;
514 filter->channels = g_new0 (GstAudioChebyshevFreqLimitChannelCtx, channels);
515 GST_LOG_OBJECT (filter, "cutoff was higher than nyquist frequency");
517 } else if (filter->cutoff <= 0.0) {
519 filter->a = g_new0 (gdouble, 1);
520 filter->a[0] = (filter->mode == MODE_LOW_PASS) ? 0.0 : 1.0;
522 filter->channels = g_new0 (GstAudioChebyshevFreqLimitChannelCtx, channels);
523 GST_LOG_OBJECT (filter, "cutoff is lower than zero");
527 /* Calculate coefficients for the chebyshev filter */
529 gint np = filter->poles;
533 filter->num_a = np + 1;
534 filter->a = a = g_new0 (gdouble, np + 3);
535 filter->num_b = np + 1;
536 filter->b = b = g_new0 (gdouble, np + 3);
538 filter->channels = g_new0 (GstAudioChebyshevFreqLimitChannelCtx, channels);
539 for (i = 0; i < channels; i++) {
540 GstAudioChebyshevFreqLimitChannelCtx *ctx = &filter->channels[i];
542 ctx->x = g_new0 (gdouble, np + 1);
543 ctx->y = g_new0 (gdouble, np + 1);
546 /* Calculate transfer function coefficients */
550 for (p = 1; p <= np / 2; p++) {
551 gdouble a0, a1, a2, b1, b2;
552 gdouble *ta = g_new0 (gdouble, np + 3);
553 gdouble *tb = g_new0 (gdouble, np + 3);
555 generate_biquad_coefficients (filter, p, &a0, &a1, &a2, &b1, &b2);
557 memcpy (ta, a, sizeof (gdouble) * (np + 3));
558 memcpy (tb, b, sizeof (gdouble) * (np + 3));
560 /* add the new coefficients for the new two poles
561 * to the cascade by multiplication of the transfer
563 for (i = 2; i < np + 3; i++) {
564 a[i] = a0 * ta[i] + a1 * ta[i - 1] + a2 * ta[i - 2];
565 b[i] = tb[i] - b1 * tb[i - 1] - b2 * tb[i - 2];
571 /* Move coefficients to the beginning of the array
572 * and multiply the b coefficients with -1 to move from
573 * the transfer function's coefficients to the difference
574 * equation's coefficients */
576 for (i = 0; i <= np; i++) {
581 /* Normalize to unity gain at frequency 0 for lowpass
582 * and frequency 0.5 for highpass */
586 if (filter->mode == MODE_LOW_PASS)
587 gain = calculate_gain (a, b, np, np, 1.0, 0.0);
589 gain = calculate_gain (a, b, np, np, -1.0, 0.0);
591 for (i = 0; i <= np; i++) {
596 GST_LOG_OBJECT (filter,
597 "Generated IIR coefficients for the Chebyshev filter");
598 GST_LOG_OBJECT (filter,
599 "mode: %s, type: %d, poles: %d, cutoff: %.2f Hz, ripple: %.2f dB",
600 (filter->mode == MODE_LOW_PASS) ? "low-pass" : "high-pass",
601 filter->type, filter->poles, filter->cutoff, filter->ripple);
602 GST_LOG_OBJECT (filter, "%.2f dB gain @ 0 Hz",
603 20.0 * log10 (calculate_gain (a, b, np, np, 1.0, 0.0)));
606 2.0 * M_PI * (filter->cutoff /
607 GST_AUDIO_FILTER (filter)->format.rate);
608 gdouble zr = cos (wc), zi = sin (wc);
610 GST_LOG_OBJECT (filter, "%.2f dB gain @ %d Hz",
611 20.0 * log10 (calculate_gain (a, b, np, np, zr, zi)),
612 (int) filter->cutoff);
614 GST_LOG_OBJECT (filter, "%.2f dB gain @ %d Hz",
615 20.0 * log10 (calculate_gain (a, b, np, np, -1.0, 0.0)),
616 GST_AUDIO_FILTER (filter)->format.rate / 2);
621 gst_audio_chebyshev_freq_limit_set_property (GObject * object, guint prop_id,
622 const GValue * value, GParamSpec * pspec)
624 GstAudioChebyshevFreqLimit *filter = GST_AUDIO_CHEBYSHEV_FREQ_LIMIT (object);
628 GST_BASE_TRANSFORM_LOCK (filter);
629 filter->mode = g_value_get_enum (value);
630 generate_coefficients (filter);
631 GST_BASE_TRANSFORM_UNLOCK (filter);
634 GST_BASE_TRANSFORM_LOCK (filter);
635 filter->type = g_value_get_int (value);
636 generate_coefficients (filter);
637 GST_BASE_TRANSFORM_UNLOCK (filter);
640 GST_BASE_TRANSFORM_LOCK (filter);
641 filter->cutoff = g_value_get_float (value);
642 generate_coefficients (filter);
643 GST_BASE_TRANSFORM_UNLOCK (filter);
646 GST_BASE_TRANSFORM_LOCK (filter);
647 filter->ripple = g_value_get_float (value);
648 generate_coefficients (filter);
649 GST_BASE_TRANSFORM_UNLOCK (filter);
652 GST_BASE_TRANSFORM_LOCK (filter);
653 filter->poles = GST_ROUND_UP_2 (g_value_get_int (value));
654 generate_coefficients (filter);
655 GST_BASE_TRANSFORM_UNLOCK (filter);
658 G_OBJECT_WARN_INVALID_PROPERTY_ID (object, prop_id, pspec);
664 gst_audio_chebyshev_freq_limit_get_property (GObject * object, guint prop_id,
665 GValue * value, GParamSpec * pspec)
667 GstAudioChebyshevFreqLimit *filter = GST_AUDIO_CHEBYSHEV_FREQ_LIMIT (object);
671 g_value_set_enum (value, filter->mode);
674 g_value_set_int (value, filter->type);
677 g_value_set_float (value, filter->cutoff);
680 g_value_set_float (value, filter->ripple);
683 g_value_set_int (value, filter->poles);
686 G_OBJECT_WARN_INVALID_PROPERTY_ID (object, prop_id, pspec);
691 /* GstAudioFilter vmethod implementations */
694 gst_audio_chebyshev_freq_limit_setup (GstAudioFilter * base,
695 GstRingBufferSpec * format)
697 GstAudioChebyshevFreqLimit *filter = GST_AUDIO_CHEBYSHEV_FREQ_LIMIT (base);
700 if (format->width == 32)
701 filter->process = (GstAudioChebyshevFreqLimitProcessFunc)
703 else if (format->width == 64)
704 filter->process = (GstAudioChebyshevFreqLimitProcessFunc)
709 filter->have_coeffs = FALSE;
714 static inline gdouble
715 process (GstAudioChebyshevFreqLimit * filter,
716 GstAudioChebyshevFreqLimitChannelCtx * ctx, gdouble x0)
718 gdouble val = filter->a[0] * x0;
721 for (i = 1, j = ctx->x_pos; i < filter->num_a; i++) {
722 val += filter->a[i] * ctx->x[j];
725 j = filter->num_a - 1;
728 for (i = 1, j = ctx->y_pos; i < filter->num_b; i++) {
729 val += filter->b[i] * ctx->y[j];
732 j = filter->num_b - 1;
737 if (ctx->x_pos > filter->num_a - 1)
739 ctx->x[ctx->x_pos] = x0;
744 if (ctx->y_pos > filter->num_b - 1)
747 ctx->y[ctx->y_pos] = val;
753 #define DEFINE_PROCESS_FUNC(width,ctype) \
755 process_##width (GstAudioChebyshevFreqLimit * filter, \
756 g##ctype * data, guint num_samples) \
758 gint i, j, channels = GST_AUDIO_FILTER (filter)->format.channels; \
761 for (i = 0; i < num_samples / channels; i++) { \
762 for (j = 0; j < channels; j++) { \
763 val = process (filter, &filter->channels[j], *data); \
769 DEFINE_PROCESS_FUNC (32, float);
770 DEFINE_PROCESS_FUNC (64, double);
772 #undef DEFINE_PROCESS_FUNC
774 /* GstBaseTransform vmethod implementations */
776 gst_audio_chebyshev_freq_limit_transform_ip (GstBaseTransform * base,
779 GstAudioChebyshevFreqLimit *filter = GST_AUDIO_CHEBYSHEV_FREQ_LIMIT (base);
781 GST_BUFFER_SIZE (buf) / (GST_AUDIO_FILTER (filter)->format.width / 8);
783 if (!gst_buffer_is_writable (buf))
786 if (GST_CLOCK_TIME_IS_VALID (GST_BUFFER_TIMESTAMP (buf)))
787 gst_object_sync_values (G_OBJECT (filter), GST_BUFFER_TIMESTAMP (buf));
789 if (!filter->have_coeffs)
790 generate_coefficients (filter);
792 filter->process (filter, GST_BUFFER_DATA (buf), num_samples);
799 gst_audio_chebyshev_freq_limit_start (GstBaseTransform * base)
801 GstAudioChebyshevFreqLimit *filter = GST_AUDIO_CHEBYSHEV_FREQ_LIMIT (base);
802 gint channels = GST_AUDIO_FILTER (filter)->format.channels;
803 GstAudioChebyshevFreqLimitChannelCtx *ctx;
806 /* Reset the history of input and output values if
807 * already existing */
808 if (channels && filter->channels) {
809 for (i = 0; i < channels; i++) {
810 ctx = &filter->channels[i];
812 memset (ctx->x, 0, (filter->poles + 1) * sizeof (gdouble));
814 memset (ctx->y, 0, (filter->poles + 1) * sizeof (gdouble));