Line data Source code
1 : /********************************************************************
2 : * *
3 : * THIS FILE IS PART OF THE OggVorbis SOFTWARE CODEC SOURCE CODE. *
4 : * USE, DISTRIBUTION AND REPRODUCTION OF THIS LIBRARY SOURCE IS *
5 : * GOVERNED BY A BSD-STYLE SOURCE LICENSE INCLUDED WITH THIS SOURCE *
6 : * IN 'COPYING'. PLEASE READ THESE TERMS BEFORE DISTRIBUTING. *
7 : * *
8 : * THE OggVorbis SOURCE CODE IS (C) COPYRIGHT 1994-2009 *
9 : * by the Xiph.Org Foundation http://www.xiph.org/ *
10 : * *
11 : ********************************************************************
12 :
13 : function: LSP (also called LSF) conversion routines
14 : last mod: $Id$
15 :
16 : The LSP generation code is taken (with minimal modification and a
17 : few bugfixes) from "On the Computation of the LSP Frequencies" by
18 : Joseph Rothweiler (see http://www.rothweiler.us for contact info).
19 : The paper is available at:
20 :
21 : http://www.myown1.com/joe/lsf
22 :
23 : ********************************************************************/
24 :
25 : /* Note that the lpc-lsp conversion finds the roots of polynomial with
26 : an iterative root polisher (CACM algorithm 283). It *is* possible
27 : to confuse this algorithm into not converging; that should only
28 : happen with absurdly closely spaced roots (very sharp peaks in the
29 : LPC f response) which in turn should be impossible in our use of
30 : the code. If this *does* happen anyway, it's a bug in the floor
31 : finder; find the cause of the confusion (probably a single bin
32 : spike or accidental near-float-limit resolution problems) and
33 : correct it. */
34 :
35 : #include <math.h>
36 : #include <string.h>
37 : #include <stdlib.h>
38 : #include "lsp.h"
39 : #include "os.h"
40 : #include "misc.h"
41 : #include "lookup.h"
42 : #include "scales.h"
43 :
44 : /* three possible LSP to f curve functions; the exact computation
45 : (float), a lookup based float implementation, and an integer
46 : implementation. The float lookup is likely the optimal choice on
47 : any machine with an FPU. The integer implementation is *not* fixed
48 : point (due to the need for a large dynamic range and thus a
49 : separately tracked exponent) and thus much more complex than the
50 : relatively simple float implementations. It's mostly for future
51 : work on a fully fixed point implementation for processors like the
52 : ARM family. */
53 :
54 : /* define either of these (preferably FLOAT_LOOKUP) to have faster
55 : but less precise implementation. */
56 : #undef FLOAT_LOOKUP
57 : #undef INT_LOOKUP
58 :
59 : #ifdef FLOAT_LOOKUP
60 : #include "vorbis_lookup.c" /* catch this in the build system; we #include for
61 : compilers (like gcc) that can't inline across
62 : modules */
63 :
64 : /* side effect: changes *lsp to cosines of lsp */
65 : void vorbis_lsp_to_curve(float *curve,int *map,int n,int ln,float *lsp,int m,
66 : float amp,float ampoffset){
67 : int i;
68 : float wdel=M_PI/ln;
69 : vorbis_fpu_control fpu;
70 :
71 : vorbis_fpu_setround(&fpu);
72 : for(i=0;i<m;i++)lsp[i]=vorbis_coslook(lsp[i]);
73 :
74 : i=0;
75 : while(i<n){
76 : int k=map[i];
77 : int qexp;
78 : float p=.7071067812f;
79 : float q=.7071067812f;
80 : float w=vorbis_coslook(wdel*k);
81 : float *ftmp=lsp;
82 : int c=m>>1;
83 :
84 : while(c--){
85 : q*=ftmp[0]-w;
86 : p*=ftmp[1]-w;
87 : ftmp+=2;
88 : }
89 :
90 : if(m&1){
91 : /* odd order filter; slightly assymetric */
92 : /* the last coefficient */
93 : q*=ftmp[0]-w;
94 : q*=q;
95 : p*=p*(1.f-w*w);
96 : }else{
97 : /* even order filter; still symmetric */
98 : q*=q*(1.f+w);
99 : p*=p*(1.f-w);
100 : }
101 :
102 : q=frexp(p+q,&qexp);
103 : q=vorbis_fromdBlook(amp*
104 : vorbis_invsqlook(q)*
105 : vorbis_invsq2explook(qexp+m)-
106 : ampoffset);
107 :
108 : do{
109 : curve[i++]*=q;
110 : }while(map[i]==k);
111 : }
112 : vorbis_fpu_restore(fpu);
113 : }
114 :
115 : #else
116 :
117 : #ifdef INT_LOOKUP
118 : #include "vorbis_lookup.c" /* catch this in the build system; we #include for
119 : compilers (like gcc) that can't inline across
120 : modules */
121 :
122 : static const int MLOOP_1[64]={
123 : 0,10,11,11, 12,12,12,12, 13,13,13,13, 13,13,13,13,
124 : 14,14,14,14, 14,14,14,14, 14,14,14,14, 14,14,14,14,
125 : 15,15,15,15, 15,15,15,15, 15,15,15,15, 15,15,15,15,
126 : 15,15,15,15, 15,15,15,15, 15,15,15,15, 15,15,15,15,
127 : };
128 :
129 : static const int MLOOP_2[64]={
130 : 0,4,5,5, 6,6,6,6, 7,7,7,7, 7,7,7,7,
131 : 8,8,8,8, 8,8,8,8, 8,8,8,8, 8,8,8,8,
132 : 9,9,9,9, 9,9,9,9, 9,9,9,9, 9,9,9,9,
133 : 9,9,9,9, 9,9,9,9, 9,9,9,9, 9,9,9,9,
134 : };
135 :
136 : static const int MLOOP_3[8]={0,1,2,2,3,3,3,3};
137 :
138 :
139 : /* side effect: changes *lsp to cosines of lsp */
140 : void vorbis_lsp_to_curve(float *curve,int *map,int n,int ln,float *lsp,int m,
141 : float amp,float ampoffset){
142 :
143 : /* 0 <= m < 256 */
144 :
145 : /* set up for using all int later */
146 : int i;
147 : int ampoffseti=rint(ampoffset*4096.f);
148 : int ampi=rint(amp*16.f);
149 : long *ilsp=alloca(m*sizeof(*ilsp));
150 : for(i=0;i<m;i++)ilsp[i]=vorbis_coslook_i(lsp[i]/M_PI*65536.f+.5f);
151 :
152 : i=0;
153 : while(i<n){
154 : int j,k=map[i];
155 : unsigned long pi=46341; /* 2**-.5 in 0.16 */
156 : unsigned long qi=46341;
157 : int qexp=0,shift;
158 : long wi=vorbis_coslook_i(k*65536/ln);
159 :
160 : qi*=labs(ilsp[0]-wi);
161 : pi*=labs(ilsp[1]-wi);
162 :
163 : for(j=3;j<m;j+=2){
164 : if(!(shift=MLOOP_1[(pi|qi)>>25]))
165 : if(!(shift=MLOOP_2[(pi|qi)>>19]))
166 : shift=MLOOP_3[(pi|qi)>>16];
167 : qi=(qi>>shift)*labs(ilsp[j-1]-wi);
168 : pi=(pi>>shift)*labs(ilsp[j]-wi);
169 : qexp+=shift;
170 : }
171 : if(!(shift=MLOOP_1[(pi|qi)>>25]))
172 : if(!(shift=MLOOP_2[(pi|qi)>>19]))
173 : shift=MLOOP_3[(pi|qi)>>16];
174 :
175 : /* pi,qi normalized collectively, both tracked using qexp */
176 :
177 : if(m&1){
178 : /* odd order filter; slightly assymetric */
179 : /* the last coefficient */
180 : qi=(qi>>shift)*labs(ilsp[j-1]-wi);
181 : pi=(pi>>shift)<<14;
182 : qexp+=shift;
183 :
184 : if(!(shift=MLOOP_1[(pi|qi)>>25]))
185 : if(!(shift=MLOOP_2[(pi|qi)>>19]))
186 : shift=MLOOP_3[(pi|qi)>>16];
187 :
188 : pi>>=shift;
189 : qi>>=shift;
190 : qexp+=shift-14*((m+1)>>1);
191 :
192 : pi=((pi*pi)>>16);
193 : qi=((qi*qi)>>16);
194 : qexp=qexp*2+m;
195 :
196 : pi*=(1<<14)-((wi*wi)>>14);
197 : qi+=pi>>14;
198 :
199 : }else{
200 : /* even order filter; still symmetric */
201 :
202 : /* p*=p(1-w), q*=q(1+w), let normalization drift because it isn't
203 : worth tracking step by step */
204 :
205 : pi>>=shift;
206 : qi>>=shift;
207 : qexp+=shift-7*m;
208 :
209 : pi=((pi*pi)>>16);
210 : qi=((qi*qi)>>16);
211 : qexp=qexp*2+m;
212 :
213 : pi*=(1<<14)-wi;
214 : qi*=(1<<14)+wi;
215 : qi=(qi+pi)>>14;
216 :
217 : }
218 :
219 :
220 : /* we've let the normalization drift because it wasn't important;
221 : however, for the lookup, things must be normalized again. We
222 : need at most one right shift or a number of left shifts */
223 :
224 : if(qi&0xffff0000){ /* checks for 1.xxxxxxxxxxxxxxxx */
225 : qi>>=1; qexp++;
226 : }else
227 : while(qi && !(qi&0x8000)){ /* checks for 0.0xxxxxxxxxxxxxxx or less*/
228 : qi<<=1; qexp--;
229 : }
230 :
231 : amp=vorbis_fromdBlook_i(ampi* /* n.4 */
232 : vorbis_invsqlook_i(qi,qexp)-
233 : /* m.8, m+n<=8 */
234 : ampoffseti); /* 8.12[0] */
235 :
236 : curve[i]*=amp;
237 : while(map[++i]==k)curve[i]*=amp;
238 : }
239 : }
240 :
241 : #else
242 :
243 : /* old, nonoptimized but simple version for any poor sap who needs to
244 : figure out what the hell this code does, or wants the other
245 : fraction of a dB precision */
246 :
247 : /* side effect: changes *lsp to cosines of lsp */
248 0 : void vorbis_lsp_to_curve(float *curve,int *map,int n,int ln,float *lsp,int m,
249 : float amp,float ampoffset){
250 : int i;
251 0 : float wdel=M_PI/ln;
252 0 : for(i=0;i<m;i++)lsp[i]=2.f*cos(lsp[i]);
253 :
254 0 : i=0;
255 0 : while(i<n){
256 0 : int j,k=map[i];
257 0 : float p=.5f;
258 0 : float q=.5f;
259 0 : float w=2.f*cos(wdel*k);
260 0 : for(j=1;j<m;j+=2){
261 0 : q *= w-lsp[j-1];
262 0 : p *= w-lsp[j];
263 : }
264 0 : if(j==m){
265 : /* odd order filter; slightly assymetric */
266 : /* the last coefficient */
267 0 : q*=w-lsp[j-1];
268 0 : p*=p*(4.f-w*w);
269 0 : q*=q;
270 : }else{
271 : /* even order filter; still symmetric */
272 0 : p*=p*(2.f-w);
273 0 : q*=q*(2.f+w);
274 : }
275 :
276 0 : q=fromdB(amp/sqrt(p+q)-ampoffset);
277 :
278 0 : curve[i]*=q;
279 0 : while(map[++i]==k)curve[i]*=q;
280 : }
281 0 : }
282 :
283 : #endif
284 : #endif
285 :
286 0 : static void cheby(float *g, int ord) {
287 : int i, j;
288 :
289 0 : g[0] *= .5f;
290 0 : for(i=2; i<= ord; i++) {
291 0 : for(j=ord; j >= i; j--) {
292 0 : g[j-2] -= g[j];
293 0 : g[j] += g[j];
294 : }
295 : }
296 0 : }
297 :
298 0 : static int comp(const void *a,const void *b){
299 0 : return (*(float *)a<*(float *)b)-(*(float *)a>*(float *)b);
300 : }
301 :
302 : /* Newton-Raphson-Maehly actually functioned as a decent root finder,
303 : but there are root sets for which it gets into limit cycles
304 : (exacerbated by zero suppression) and fails. We can't afford to
305 : fail, even if the failure is 1 in 100,000,000, so we now use
306 : Laguerre and later polish with Newton-Raphson (which can then
307 : afford to fail) */
308 :
309 : #define EPSILON 10e-7
310 0 : static int Laguerre_With_Deflation(float *a,int ord,float *r){
311 : int i,m;
312 0 : double *defl=alloca(sizeof(*defl)*(ord+1));
313 0 : for(i=0;i<=ord;i++)defl[i]=a[i];
314 :
315 0 : for(m=ord;m>0;m--){
316 0 : double new=0.f,delta;
317 :
318 : /* iterate a root */
319 0 : while(1){
320 0 : double p=defl[m],pp=0.f,ppp=0.f,denom;
321 :
322 : /* eval the polynomial and its first two derivatives */
323 0 : for(i=m;i>0;i--){
324 0 : ppp = new*ppp + pp;
325 0 : pp = new*pp + p;
326 0 : p = new*p + defl[i-1];
327 : }
328 :
329 : /* Laguerre's method */
330 0 : denom=(m-1) * ((m-1)*pp*pp - m*p*ppp);
331 0 : if(denom<0)
332 0 : return(-1); /* complex root! The LPC generator handed us a bad filter */
333 :
334 0 : if(pp>0){
335 0 : denom = pp + sqrt(denom);
336 0 : if(denom<EPSILON)denom=EPSILON;
337 : }else{
338 0 : denom = pp - sqrt(denom);
339 0 : if(denom>-(EPSILON))denom=-(EPSILON);
340 : }
341 :
342 0 : delta = m*p/denom;
343 0 : new -= delta;
344 :
345 0 : if(delta<0.f)delta*=-1;
346 :
347 0 : if(fabs(delta/new)<10e-12)break;
348 : }
349 :
350 0 : r[m-1]=new;
351 :
352 : /* forward deflation */
353 :
354 0 : for(i=m;i>0;i--)
355 0 : defl[i-1]+=new*defl[i];
356 0 : defl++;
357 :
358 : }
359 0 : return(0);
360 : }
361 :
362 :
363 : /* for spit-and-polish only */
364 0 : static int Newton_Raphson(float *a,int ord,float *r){
365 0 : int i, k, count=0;
366 0 : double error=1.f;
367 0 : double *root=alloca(ord*sizeof(*root));
368 :
369 0 : for(i=0; i<ord;i++) root[i] = r[i];
370 :
371 0 : while(error>1e-20){
372 0 : error=0;
373 :
374 0 : for(i=0; i<ord; i++) { /* Update each point. */
375 0 : double pp=0.,delta;
376 0 : double rooti=root[i];
377 0 : double p=a[ord];
378 0 : for(k=ord-1; k>= 0; k--) {
379 :
380 0 : pp= pp* rooti + p;
381 0 : p = p * rooti + a[k];
382 : }
383 :
384 0 : delta = p/pp;
385 0 : root[i] -= delta;
386 0 : error+= delta*delta;
387 : }
388 :
389 0 : if(count>40)return(-1);
390 :
391 0 : count++;
392 : }
393 :
394 : /* Replaced the original bubble sort with a real sort. With your
395 : help, we can eliminate the bubble sort in our lifetime. --Monty */
396 :
397 0 : for(i=0; i<ord;i++) r[i] = root[i];
398 0 : return(0);
399 : }
400 :
401 :
402 : /* Convert lpc coefficients to lsp coefficients */
403 0 : int vorbis_lpc_to_lsp(float *lpc,float *lsp,int m){
404 0 : int order2=(m+1)>>1;
405 : int g1_order,g2_order;
406 0 : float *g1=alloca(sizeof(*g1)*(order2+1));
407 0 : float *g2=alloca(sizeof(*g2)*(order2+1));
408 0 : float *g1r=alloca(sizeof(*g1r)*(order2+1));
409 0 : float *g2r=alloca(sizeof(*g2r)*(order2+1));
410 : int i;
411 :
412 : /* even and odd are slightly different base cases */
413 0 : g1_order=(m+1)>>1;
414 0 : g2_order=(m) >>1;
415 :
416 : /* Compute the lengths of the x polynomials. */
417 : /* Compute the first half of K & R F1 & F2 polynomials. */
418 : /* Compute half of the symmetric and antisymmetric polynomials. */
419 : /* Remove the roots at +1 and -1. */
420 :
421 0 : g1[g1_order] = 1.f;
422 0 : for(i=1;i<=g1_order;i++) g1[g1_order-i] = lpc[i-1]+lpc[m-i];
423 0 : g2[g2_order] = 1.f;
424 0 : for(i=1;i<=g2_order;i++) g2[g2_order-i] = lpc[i-1]-lpc[m-i];
425 :
426 0 : if(g1_order>g2_order){
427 0 : for(i=2; i<=g2_order;i++) g2[g2_order-i] += g2[g2_order-i+2];
428 : }else{
429 0 : for(i=1; i<=g1_order;i++) g1[g1_order-i] -= g1[g1_order-i+1];
430 0 : for(i=1; i<=g2_order;i++) g2[g2_order-i] += g2[g2_order-i+1];
431 : }
432 :
433 : /* Convert into polynomials in cos(alpha) */
434 0 : cheby(g1,g1_order);
435 0 : cheby(g2,g2_order);
436 :
437 : /* Find the roots of the 2 even polynomials.*/
438 0 : if(Laguerre_With_Deflation(g1,g1_order,g1r) ||
439 0 : Laguerre_With_Deflation(g2,g2_order,g2r))
440 0 : return(-1);
441 :
442 0 : Newton_Raphson(g1,g1_order,g1r); /* if it fails, it leaves g1r alone */
443 0 : Newton_Raphson(g2,g2_order,g2r); /* if it fails, it leaves g2r alone */
444 :
445 0 : qsort(g1r,g1_order,sizeof(*g1r),comp);
446 0 : qsort(g2r,g2_order,sizeof(*g2r),comp);
447 :
448 0 : for(i=0;i<g1_order;i++)
449 0 : lsp[i*2] = acos(g1r[i]);
450 :
451 0 : for(i=0;i<g2_order;i++)
452 0 : lsp[i*2+1] = acos(g2r[i]);
453 0 : return(0);
454 : }
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