vrshoot
view libs/vorbis/lsp.c @ 0:b2f14e535253
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| author | John Tsiombikas <nuclear@member.fsf.org> |
|---|---|
| date | Sat, 01 Feb 2014 19:58:19 +0200 |
| parents | |
| children |
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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 ********************************************************************
13 function: LSP (also called LSF) conversion routines
14 last mod: $Id: lsp.c 17538 2010-10-15 02:52:29Z tterribe $
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:
21 http://www.myown1.com/joe/lsf
23 ********************************************************************/
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. */
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"
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. */
54 /* define either of these (preferably FLOAT_LOOKUP) to have faster
55 but less precise implementation. */
56 #undef FLOAT_LOOKUP
57 #undef INT_LOOKUP
59 #ifdef FLOAT_LOOKUP
60 #include "lookup.c" /* catch this in the build system; we #include for
61 compilers (like gcc) that can't inline across
62 modules */
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;
71 vorbis_fpu_setround(&fpu);
72 for(i=0;i<m;i++)lsp[i]=vorbis_coslook(lsp[i]);
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;
84 while(c--){
85 q*=ftmp[0]-w;
86 p*=ftmp[1]-w;
87 ftmp+=2;
88 }
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 }
102 q=frexp(p+q,&qexp);
103 q=vorbis_fromdBlook(amp*
104 vorbis_invsqlook(q)*
105 vorbis_invsq2explook(qexp+m)-
106 ampoffset);
108 do{
109 curve[i++]*=q;
110 }while(map[i]==k);
111 }
112 vorbis_fpu_restore(fpu);
113 }
115 #else
117 #ifdef INT_LOOKUP
118 #include "lookup.c" /* catch this in the build system; we #include for
119 compilers (like gcc) that can't inline across
120 modules */
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 };
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 };
136 static const int MLOOP_3[8]={0,1,2,2,3,3,3,3};
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){
143 /* 0 <= m < 256 */
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);
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);
160 qi*=labs(ilsp[0]-wi);
161 pi*=labs(ilsp[1]-wi);
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];
175 /* pi,qi normalized collectively, both tracked using qexp */
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;
184 if(!(shift=MLOOP_1[(pi|qi)>>25]))
185 if(!(shift=MLOOP_2[(pi|qi)>>19]))
186 shift=MLOOP_3[(pi|qi)>>16];
188 pi>>=shift;
189 qi>>=shift;
190 qexp+=shift-14*((m+1)>>1);
192 pi=((pi*pi)>>16);
193 qi=((qi*qi)>>16);
194 qexp=qexp*2+m;
196 pi*=(1<<14)-((wi*wi)>>14);
197 qi+=pi>>14;
199 }else{
200 /* even order filter; still symmetric */
202 /* p*=p(1-w), q*=q(1+w), let normalization drift because it isn't
203 worth tracking step by step */
205 pi>>=shift;
206 qi>>=shift;
207 qexp+=shift-7*m;
209 pi=((pi*pi)>>16);
210 qi=((qi*qi)>>16);
211 qexp=qexp*2+m;
213 pi*=(1<<14)-wi;
214 qi*=(1<<14)+wi;
215 qi=(qi+pi)>>14;
217 }
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 */
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 }
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] */
236 curve[i]*=amp;
237 while(map[++i]==k)curve[i]*=amp;
238 }
239 }
241 #else
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 */
247 /* side effect: changes *lsp to cosines of lsp */
248 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 float wdel=M_PI/ln;
252 for(i=0;i<m;i++)lsp[i]=2.f*cos(lsp[i]);
254 i=0;
255 while(i<n){
256 int j,k=map[i];
257 float p=.5f;
258 float q=.5f;
259 float w=2.f*cos(wdel*k);
260 for(j=1;j<m;j+=2){
261 q *= w-lsp[j-1];
262 p *= w-lsp[j];
263 }
264 if(j==m){
265 /* odd order filter; slightly assymetric */
266 /* the last coefficient */
267 q*=w-lsp[j-1];
268 p*=p*(4.f-w*w);
269 q*=q;
270 }else{
271 /* even order filter; still symmetric */
272 p*=p*(2.f-w);
273 q*=q*(2.f+w);
274 }
276 q=fromdB(amp/sqrt(p+q)-ampoffset);
278 curve[i]*=q;
279 while(map[++i]==k)curve[i]*=q;
280 }
281 }
283 #endif
284 #endif
286 static void cheby(float *g, int ord) {
287 int i, j;
289 g[0] *= .5f;
290 for(i=2; i<= ord; i++) {
291 for(j=ord; j >= i; j--) {
292 g[j-2] -= g[j];
293 g[j] += g[j];
294 }
295 }
296 }
298 static int comp(const void *a,const void *b){
299 return (*(float *)a<*(float *)b)-(*(float *)a>*(float *)b);
300 }
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) */
309 #define EPSILON 10e-7
310 static int Laguerre_With_Deflation(float *a,int ord,float *r){
311 int i,m;
312 double *defl=alloca(sizeof(*defl)*(ord+1));
313 for(i=0;i<=ord;i++)defl[i]=a[i];
315 for(m=ord;m>0;m--){
316 double new=0.f,delta;
318 /* iterate a root */
319 while(1){
320 double p=defl[m],pp=0.f,ppp=0.f,denom;
322 /* eval the polynomial and its first two derivatives */
323 for(i=m;i>0;i--){
324 ppp = new*ppp + pp;
325 pp = new*pp + p;
326 p = new*p + defl[i-1];
327 }
329 /* Laguerre's method */
330 denom=(m-1) * ((m-1)*pp*pp - m*p*ppp);
331 if(denom<0)
332 return(-1); /* complex root! The LPC generator handed us a bad filter */
334 if(pp>0){
335 denom = pp + sqrt(denom);
336 if(denom<EPSILON)denom=EPSILON;
337 }else{
338 denom = pp - sqrt(denom);
339 if(denom>-(EPSILON))denom=-(EPSILON);
340 }
342 delta = m*p/denom;
343 new -= delta;
345 if(delta<0.f)delta*=-1;
347 if(fabs(delta/new)<10e-12)break;
348 }
350 r[m-1]=new;
352 /* forward deflation */
354 for(i=m;i>0;i--)
355 defl[i-1]+=new*defl[i];
356 defl++;
358 }
359 return(0);
360 }
363 /* for spit-and-polish only */
364 static int Newton_Raphson(float *a,int ord,float *r){
365 int i, k, count=0;
366 double error=1.f;
367 double *root=alloca(ord*sizeof(*root));
369 for(i=0; i<ord;i++) root[i] = r[i];
371 while(error>1e-20){
372 error=0;
374 for(i=0; i<ord; i++) { /* Update each point. */
375 double pp=0.,delta;
376 double rooti=root[i];
377 double p=a[ord];
378 for(k=ord-1; k>= 0; k--) {
380 pp= pp* rooti + p;
381 p = p * rooti + a[k];
382 }
384 delta = p/pp;
385 root[i] -= delta;
386 error+= delta*delta;
387 }
389 if(count>40)return(-1);
391 count++;
392 }
394 /* Replaced the original bubble sort with a real sort. With your
395 help, we can eliminate the bubble sort in our lifetime. --Monty */
397 for(i=0; i<ord;i++) r[i] = root[i];
398 return(0);
399 }
402 /* Convert lpc coefficients to lsp coefficients */
403 int vorbis_lpc_to_lsp(float *lpc,float *lsp,int m){
404 int order2=(m+1)>>1;
405 int g1_order,g2_order;
406 float *g1=alloca(sizeof(*g1)*(order2+1));
407 float *g2=alloca(sizeof(*g2)*(order2+1));
408 float *g1r=alloca(sizeof(*g1r)*(order2+1));
409 float *g2r=alloca(sizeof(*g2r)*(order2+1));
410 int i;
412 /* even and odd are slightly different base cases */
413 g1_order=(m+1)>>1;
414 g2_order=(m) >>1;
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. */
421 g1[g1_order] = 1.f;
422 for(i=1;i<=g1_order;i++) g1[g1_order-i] = lpc[i-1]+lpc[m-i];
423 g2[g2_order] = 1.f;
424 for(i=1;i<=g2_order;i++) g2[g2_order-i] = lpc[i-1]-lpc[m-i];
426 if(g1_order>g2_order){
427 for(i=2; i<=g2_order;i++) g2[g2_order-i] += g2[g2_order-i+2];
428 }else{
429 for(i=1; i<=g1_order;i++) g1[g1_order-i] -= g1[g1_order-i+1];
430 for(i=1; i<=g2_order;i++) g2[g2_order-i] += g2[g2_order-i+1];
431 }
433 /* Convert into polynomials in cos(alpha) */
434 cheby(g1,g1_order);
435 cheby(g2,g2_order);
437 /* Find the roots of the 2 even polynomials.*/
438 if(Laguerre_With_Deflation(g1,g1_order,g1r) ||
439 Laguerre_With_Deflation(g2,g2_order,g2r))
440 return(-1);
442 Newton_Raphson(g1,g1_order,g1r); /* if it fails, it leaves g1r alone */
443 Newton_Raphson(g2,g2_order,g2r); /* if it fails, it leaves g2r alone */
445 qsort(g1r,g1_order,sizeof(*g1r),comp);
446 qsort(g2r,g2_order,sizeof(*g2r),comp);
448 for(i=0;i<g1_order;i++)
449 lsp[i*2] = acos(g1r[i]);
451 for(i=0;i<g2_order;i++)
452 lsp[i*2+1] = acos(g2r[i]);
453 return(0);
454 }