ref: 099da8cb824ee60bf3f55e9e69380660f167b216
dir: /sys/src/cmd/audio/libvorbis/res0.c/
/******************************************************************** * * * THIS FILE IS PART OF THE OggVorbis SOFTWARE CODEC SOURCE CODE. * * USE, DISTRIBUTION AND REPRODUCTION OF THIS LIBRARY SOURCE IS * * GOVERNED BY A BSD-STYLE SOURCE LICENSE INCLUDED WITH THIS SOURCE * * IN 'COPYING'. PLEASE READ THESE TERMS BEFORE DISTRIBUTING. * * * * THE OggVorbis SOURCE CODE IS (C) COPYRIGHT 1994-2010 * * by the Xiph.Org Foundation http://www.xiph.org/ * * * ******************************************************************** function: residue backend 0, 1 and 2 implementation last mod: $Id: res0.c 19441 2015-01-21 01:17:41Z xiphmont $ ********************************************************************/ /* Slow, slow, slow, simpleminded and did I mention it was slow? The encode/decode loops are coded for clarity and performance is not yet even a nagging little idea lurking in the shadows. Oh and BTW, it's slow. */ #include <stdlib.h> #include <string.h> #include <math.h> #include <ogg/ogg.h> #include "vorbis/codec.h" #include "codec_internal.h" #include "registry.h" #include "codebook.h" #include "misc.h" #include "os.h" //#define TRAIN_RES 1 //#define TRAIN_RESAUX 1 #if defined(TRAIN_RES) || defined (TRAIN_RESAUX) #include <stdio.h> #endif typedef struct { vorbis_info_residue0 *info; int parts; int stages; codebook *fullbooks; codebook *phrasebook; codebook ***partbooks; int partvals; int **decodemap; long postbits; long phrasebits; long frames; #if defined(TRAIN_RES) || defined(TRAIN_RESAUX) int train_seq; long *training_data[8][64]; float training_max[8][64]; float training_min[8][64]; float tmin; float tmax; int submap; #endif } vorbis_look_residue0; void res0_free_info(vorbis_info_residue *i){ vorbis_info_residue0 *info=(vorbis_info_residue0 *)i; if(info){ memset(info,0,sizeof(*info)); _ogg_free(info); } } void res0_free_look(vorbis_look_residue *i){ int j; if(i){ vorbis_look_residue0 *look=(vorbis_look_residue0 *)i; #ifdef TRAIN_RES { int j,k,l; for(j=0;j<look->parts;j++){ /*fprintf(stderr,"partition %d: ",j);*/ for(k=0;k<8;k++) if(look->training_data[k][j]){ char buffer[80]; FILE *of; codebook *statebook=look->partbooks[j][k]; /* long and short into the same bucket by current convention */ sprintf(buffer,"res_sub%d_part%d_pass%d.vqd",look->submap,j,k); of=fopen(buffer,"a"); for(l=0;l<statebook->entries;l++) fprintf(of,"%d:%ld\n",l,look->training_data[k][j][l]); fclose(of); /*fprintf(stderr,"%d(%.2f|%.2f) ",k, look->training_min[k][j],look->training_max[k][j]);*/ _ogg_free(look->training_data[k][j]); look->training_data[k][j]=NULL; } /*fprintf(stderr,"\n");*/ } } fprintf(stderr,"min/max residue: %g::%g\n",look->tmin,look->tmax); /*fprintf(stderr,"residue bit usage %f:%f (%f total)\n", (float)look->phrasebits/look->frames, (float)look->postbits/look->frames, (float)(look->postbits+look->phrasebits)/look->frames);*/ #endif /*vorbis_info_residue0 *info=look->info; fprintf(stderr, "%ld frames encoded in %ld phrasebits and %ld residue bits " "(%g/frame) \n",look->frames,look->phrasebits, look->resbitsflat, (look->phrasebits+look->resbitsflat)/(float)look->frames); for(j=0;j<look->parts;j++){ long acc=0; fprintf(stderr,"\t[%d] == ",j); for(k=0;k<look->stages;k++) if((info->secondstages[j]>>k)&1){ fprintf(stderr,"%ld,",look->resbits[j][k]); acc+=look->resbits[j][k]; } fprintf(stderr,":: (%ld vals) %1.2fbits/sample\n",look->resvals[j], acc?(float)acc/(look->resvals[j]*info->grouping):0); } fprintf(stderr,"\n");*/ for(j=0;j<look->parts;j++) if(look->partbooks[j])_ogg_free(look->partbooks[j]); _ogg_free(look->partbooks); for(j=0;j<look->partvals;j++) _ogg_free(look->decodemap[j]); _ogg_free(look->decodemap); memset(look,0,sizeof(*look)); _ogg_free(look); } } static int icount(unsigned int v){ int ret=0; while(v){ ret+=v&1; v>>=1; } return(ret); } void res0_pack(vorbis_info_residue *vr,oggpack_buffer *opb){ vorbis_info_residue0 *info=(vorbis_info_residue0 *)vr; int j,acc=0; oggpack_write(opb,info->begin,24); oggpack_write(opb,info->end,24); oggpack_write(opb,info->grouping-1,24); /* residue vectors to group and code with a partitioned book */ oggpack_write(opb,info->partitions-1,6); /* possible partition choices */ oggpack_write(opb,info->groupbook,8); /* group huffman book */ /* secondstages is a bitmask; as encoding progresses pass by pass, a bitmask of one indicates this partition class has bits to write this pass */ for(j=0;j<info->partitions;j++){ if(ov_ilog(info->secondstages[j])>3){ /* yes, this is a minor hack due to not thinking ahead */ oggpack_write(opb,info->secondstages[j],3); oggpack_write(opb,1,1); oggpack_write(opb,info->secondstages[j]>>3,5); }else oggpack_write(opb,info->secondstages[j],4); /* trailing zero */ acc+=icount(info->secondstages[j]); } for(j=0;j<acc;j++) oggpack_write(opb,info->booklist[j],8); } /* vorbis_info is for range checking */ vorbis_info_residue *res0_unpack(vorbis_info *vi,oggpack_buffer *opb){ int j,acc=0; vorbis_info_residue0 *info=_ogg_calloc(1,sizeof(*info)); codec_setup_info *ci=vi->codec_setup; info->begin=oggpack_read(opb,24); info->end=oggpack_read(opb,24); info->grouping=oggpack_read(opb,24)+1; info->partitions=oggpack_read(opb,6)+1; info->groupbook=oggpack_read(opb,8); /* check for premature EOP */ if(info->groupbook<0)goto errout; for(j=0;j<info->partitions;j++){ int cascade=oggpack_read(opb,3); int cflag=oggpack_read(opb,1); if(cflag<0) goto errout; if(cflag){ int c=oggpack_read(opb,5); if(c<0) goto errout; cascade|=(c<<3); } info->secondstages[j]=cascade; acc+=icount(cascade); } for(j=0;j<acc;j++){ int book=oggpack_read(opb,8); if(book<0) goto errout; info->booklist[j]=book; } if(info->groupbook>=ci->books)goto errout; for(j=0;j<acc;j++){ if(info->booklist[j]>=ci->books)goto errout; if(ci->book_param[info->booklist[j]]->maptype==0)goto errout; } /* verify the phrasebook is not specifying an impossible or inconsistent partitioning scheme. */ /* modify the phrasebook ranging check from r16327; an early beta encoder had a bug where it used an oversized phrasebook by accident. These files should continue to be playable, but don't allow an exploit */ { int entries = ci->book_param[info->groupbook]->entries; int dim = ci->book_param[info->groupbook]->dim; int partvals = 1; if (dim<1) goto errout; while(dim>0){ partvals *= info->partitions; if(partvals > entries) goto errout; dim--; } info->partvals = partvals; } return(info); errout: res0_free_info(info); return(NULL); } vorbis_look_residue *res0_look(vorbis_dsp_state *vd, vorbis_info_residue *vr){ vorbis_info_residue0 *info=(vorbis_info_residue0 *)vr; vorbis_look_residue0 *look=_ogg_calloc(1,sizeof(*look)); codec_setup_info *ci=vd->vi->codec_setup; int j,k,acc=0; int dim; int maxstage=0; look->info=info; look->parts=info->partitions; look->fullbooks=ci->fullbooks; look->phrasebook=ci->fullbooks+info->groupbook; dim=look->phrasebook->dim; look->partbooks=_ogg_calloc(look->parts,sizeof(*look->partbooks)); for(j=0;j<look->parts;j++){ int stages=ov_ilog(info->secondstages[j]); if(stages){ if(stages>maxstage)maxstage=stages; look->partbooks[j]=_ogg_calloc(stages,sizeof(*look->partbooks[j])); for(k=0;k<stages;k++) if(info->secondstages[j]&(1<<k)){ look->partbooks[j][k]=ci->fullbooks+info->booklist[acc++]; #ifdef TRAIN_RES look->training_data[k][j]=_ogg_calloc(look->partbooks[j][k]->entries, sizeof(***look->training_data)); #endif } } } look->partvals=1; for(j=0;j<dim;j++) look->partvals*=look->parts; look->stages=maxstage; look->decodemap=_ogg_malloc(look->partvals*sizeof(*look->decodemap)); for(j=0;j<look->partvals;j++){ long val=j; long mult=look->partvals/look->parts; look->decodemap[j]=_ogg_malloc(dim*sizeof(*look->decodemap[j])); for(k=0;k<dim;k++){ long deco=val/mult; val-=deco*mult; mult/=look->parts; look->decodemap[j][k]=deco; } } #if defined(TRAIN_RES) || defined (TRAIN_RESAUX) { static int train_seq=0; look->train_seq=train_seq++; } #endif return(look); } /* break an abstraction and copy some code for performance purposes */ static int local_book_besterror(codebook *book,int *a){ int dim=book->dim; int i,j,o; int minval=book->minval; int del=book->delta; int qv=book->quantvals; int ze=(qv>>1); int index=0; /* assumes integer/centered encoder codebook maptype 1 no more than dim 8 */ int p[8]={0,0,0,0,0,0,0,0}; if(del!=1){ for(i=0,o=dim;i<dim;i++){ int v = (a[--o]-minval+(del>>1))/del; int m = (v<ze ? ((ze-v)<<1)-1 : ((v-ze)<<1)); index = index*qv+ (m<0?0:(m>=qv?qv-1:m)); p[o]=v*del+minval; } }else{ for(i=0,o=dim;i<dim;i++){ int v = a[--o]-minval; int m = (v<ze ? ((ze-v)<<1)-1 : ((v-ze)<<1)); index = index*qv+ (m<0?0:(m>=qv?qv-1:m)); p[o]=v*del+minval; } } if(book->c->lengthlist[index]<=0){ const static_codebook *c=book->c; int best=-1; /* assumes integer/centered encoder codebook maptype 1 no more than dim 8 */ int e[8]={0,0,0,0,0,0,0,0}; int maxval = book->minval + book->delta*(book->quantvals-1); for(i=0;i<book->entries;i++){ if(c->lengthlist[i]>0){ int this=0; for(j=0;j<dim;j++){ int val=(e[j]-a[j]); this+=val*val; } if(best==-1 || this<best){ memcpy(p,e,sizeof(p)); best=this; index=i; } } /* assumes the value patterning created by the tools in vq/ */ j=0; while(e[j]>=maxval) e[j++]=0; if(e[j]>=0) e[j]+=book->delta; e[j]= -e[j]; } } if(index>-1){ for(i=0;i<dim;i++) *a++ -= p[i]; } return(index); } #ifdef TRAIN_RES static int _encodepart(oggpack_buffer *opb,int *vec, int n, codebook *book,long *acc){ #else static int _encodepart(oggpack_buffer *opb,int *vec, int n, codebook *book){ #endif int i,bits=0; int dim=book->dim; int step=n/dim; for(i=0;i<step;i++){ int entry=local_book_besterror(book,vec+i*dim); #ifdef TRAIN_RES if(entry>=0) acc[entry]++; #endif bits+=vorbis_book_encode(book,entry,opb); } return(bits); } static long **_01class(vorbis_block *vb,vorbis_look_residue *vl, int **in,int ch){ long i,j,k; vorbis_look_residue0 *look=(vorbis_look_residue0 *)vl; vorbis_info_residue0 *info=look->info; /* move all this setup out later */ int samples_per_partition=info->grouping; int possible_partitions=info->partitions; int n=info->end-info->begin; int partvals=n/samples_per_partition; long **partword=_vorbis_block_alloc(vb,ch*sizeof(*partword)); float scale=100./samples_per_partition; /* we find the partition type for each partition of each channel. We'll go back and do the interleaved encoding in a bit. For now, clarity */ for(i=0;i<ch;i++){ partword[i]=_vorbis_block_alloc(vb,n/samples_per_partition*sizeof(*partword[i])); memset(partword[i],0,n/samples_per_partition*sizeof(*partword[i])); } for(i=0;i<partvals;i++){ int offset=i*samples_per_partition+info->begin; for(j=0;j<ch;j++){ int max=0; int ent=0; for(k=0;k<samples_per_partition;k++){ if(abs(in[j][offset+k])>max)max=abs(in[j][offset+k]); ent+=abs(in[j][offset+k]); } ent*=scale; for(k=0;k<possible_partitions-1;k++) if(max<=info->classmetric1[k] && (info->classmetric2[k]<0 || ent<info->classmetric2[k])) break; partword[j][i]=k; } } #ifdef TRAIN_RESAUX { FILE *of; char buffer[80]; for(i=0;i<ch;i++){ sprintf(buffer,"resaux_%d.vqd",look->train_seq); of=fopen(buffer,"a"); for(j=0;j<partvals;j++) fprintf(of,"%ld, ",partword[i][j]); fprintf(of,"\n"); fclose(of); } } #endif look->frames++; return(partword); } /* designed for stereo or other modes where the partition size is an integer multiple of the number of channels encoded in the current submap */ static long **_2class(vorbis_block *vb,vorbis_look_residue *vl,int **in, int ch){ long i,j,k,l; vorbis_look_residue0 *look=(vorbis_look_residue0 *)vl; vorbis_info_residue0 *info=look->info; /* move all this setup out later */ int samples_per_partition=info->grouping; int possible_partitions=info->partitions; int n=info->end-info->begin; int partvals=n/samples_per_partition; long **partword=_vorbis_block_alloc(vb,sizeof(*partword)); #if defined(TRAIN_RES) || defined (TRAIN_RESAUX) FILE *of; char buffer[80]; #endif partword[0]=_vorbis_block_alloc(vb,partvals*sizeof(*partword[0])); memset(partword[0],0,partvals*sizeof(*partword[0])); for(i=0,l=info->begin/ch;i<partvals;i++){ int magmax=0; int angmax=0; for(j=0;j<samples_per_partition;j+=ch){ if(abs(in[0][l])>magmax)magmax=abs(in[0][l]); for(k=1;k<ch;k++) if(abs(in[k][l])>angmax)angmax=abs(in[k][l]); l++; } for(j=0;j<possible_partitions-1;j++) if(magmax<=info->classmetric1[j] && angmax<=info->classmetric2[j]) break; partword[0][i]=j; } #ifdef TRAIN_RESAUX sprintf(buffer,"resaux_%d.vqd",look->train_seq); of=fopen(buffer,"a"); for(i=0;i<partvals;i++) fprintf(of,"%ld, ",partword[0][i]); fprintf(of,"\n"); fclose(of); #endif look->frames++; return(partword); } static int _01forward(oggpack_buffer *opb, vorbis_look_residue *vl, int **in,int ch, long **partword, #ifdef TRAIN_RES int (*encode)(oggpack_buffer *,int *,int, codebook *,long *), int submap #else int (*encode)(oggpack_buffer *,int *,int, codebook *) #endif ){ long i,j,k,s; vorbis_look_residue0 *look=(vorbis_look_residue0 *)vl; vorbis_info_residue0 *info=look->info; #ifdef TRAIN_RES look->submap=submap; #endif /* move all this setup out later */ int samples_per_partition=info->grouping; int possible_partitions=info->partitions; int partitions_per_word=look->phrasebook->dim; int n=info->end-info->begin; int partvals=n/samples_per_partition; long resbits[128]; long resvals[128]; #ifdef TRAIN_RES for(i=0;i<ch;i++) for(j=info->begin;j<info->end;j++){ if(in[i][j]>look->tmax)look->tmax=in[i][j]; if(in[i][j]<look->tmin)look->tmin=in[i][j]; } #endif memset(resbits,0,sizeof(resbits)); memset(resvals,0,sizeof(resvals)); /* we code the partition words for each channel, then the residual words for a partition per channel until we've written all the residual words for that partition word. Then write the next partition channel words... */ for(s=0;s<look->stages;s++){ for(i=0;i<partvals;){ /* first we encode a partition codeword for each channel */ if(s==0){ for(j=0;j<ch;j++){ long val=partword[j][i]; for(k=1;k<partitions_per_word;k++){ val*=possible_partitions; if(i+k<partvals) val+=partword[j][i+k]; } /* training hack */ if(val<look->phrasebook->entries) look->phrasebits+=vorbis_book_encode(look->phrasebook,val,opb); #if 0 /*def TRAIN_RES*/ else fprintf(stderr,"!"); #endif } } /* now we encode interleaved residual values for the partitions */ for(k=0;k<partitions_per_word && i<partvals;k++,i++){ long offset=i*samples_per_partition+info->begin; for(j=0;j<ch;j++){ if(s==0)resvals[partword[j][i]]+=samples_per_partition; if(info->secondstages[partword[j][i]]&(1<<s)){ codebook *statebook=look->partbooks[partword[j][i]][s]; if(statebook){ int ret; #ifdef TRAIN_RES long *accumulator=NULL; accumulator=look->training_data[s][partword[j][i]]; { int l; int *samples=in[j]+offset; for(l=0;l<samples_per_partition;l++){ if(samples[l]<look->training_min[s][partword[j][i]]) look->training_min[s][partword[j][i]]=samples[l]; if(samples[l]>look->training_max[s][partword[j][i]]) look->training_max[s][partword[j][i]]=samples[l]; } } ret=encode(opb,in[j]+offset,samples_per_partition, statebook,accumulator); #else ret=encode(opb,in[j]+offset,samples_per_partition, statebook); #endif look->postbits+=ret; resbits[partword[j][i]]+=ret; } } } } } } return(0); } /* a truncated packet here just means 'stop working'; it's not an error */ static int _01inverse(vorbis_block *vb,vorbis_look_residue *vl, float **in,int ch, long (*decodepart)(codebook *, float *, oggpack_buffer *,int)){ long i,j,k,l,s; vorbis_look_residue0 *look=(vorbis_look_residue0 *)vl; vorbis_info_residue0 *info=look->info; /* move all this setup out later */ int samples_per_partition=info->grouping; int partitions_per_word=look->phrasebook->dim; int max=vb->pcmend>>1; int end=(info->end<max?info->end:max); int n=end-info->begin; if(n>0){ int partvals=n/samples_per_partition; int partwords=(partvals+partitions_per_word-1)/partitions_per_word; int ***partword=malloc(ch*sizeof(*partword)); for(j=0;j<ch;j++) partword[j]=_vorbis_block_alloc(vb,partwords*sizeof(*partword[j])); for(s=0;s<look->stages;s++){ /* each loop decodes on partition codeword containing partitions_per_word partitions */ for(i=0,l=0;i<partvals;l++){ if(s==0){ /* fetch the partition word for each channel */ for(j=0;j<ch;j++){ int temp=vorbis_book_decode(look->phrasebook,&vb->opb); if(temp==-1 || temp>=info->partvals)goto eopbreak; partword[j][l]=look->decodemap[temp]; if(partword[j][l]==NULL)goto errout; } } /* now we decode residual values for the partitions */ for(k=0;k<partitions_per_word && i<partvals;k++,i++) for(j=0;j<ch;j++){ long offset=info->begin+i*samples_per_partition; if(info->secondstages[partword[j][l][k]]&(1<<s)){ codebook *stagebook=look->partbooks[partword[j][l][k]][s]; if(stagebook){ if(decodepart(stagebook,in[j]+offset,&vb->opb, samples_per_partition)==-1)goto eopbreak; } } } } } free(partword); } errout: eopbreak: return(0); } int res0_inverse(vorbis_block *vb,vorbis_look_residue *vl, float **in,int *nonzero,int ch){ int i,used=0; for(i=0;i<ch;i++) if(nonzero[i]) in[used++]=in[i]; if(used) return(_01inverse(vb,vl,in,used,vorbis_book_decodevs_add)); else return(0); } int res1_forward(oggpack_buffer *opb,vorbis_block *vb,vorbis_look_residue *vl, int **in,int *nonzero,int ch, long **partword, int submap){ int i,used=0; (void)vb; for(i=0;i<ch;i++) if(nonzero[i]) in[used++]=in[i]; if(used){ #ifdef TRAIN_RES return _01forward(opb,vl,in,used,partword,_encodepart,submap); #else (void)submap; return _01forward(opb,vl,in,used,partword,_encodepart); #endif }else{ return(0); } } long **res1_class(vorbis_block *vb,vorbis_look_residue *vl, int **in,int *nonzero,int ch){ int i,used=0; for(i=0;i<ch;i++) if(nonzero[i]) in[used++]=in[i]; if(used) return(_01class(vb,vl,in,used)); else return(0); } int res1_inverse(vorbis_block *vb,vorbis_look_residue *vl, float **in,int *nonzero,int ch){ int i,used=0; for(i=0;i<ch;i++) if(nonzero[i]) in[used++]=in[i]; if(used) return(_01inverse(vb,vl,in,used,vorbis_book_decodev_add)); else return(0); } long **res2_class(vorbis_block *vb,vorbis_look_residue *vl, int **in,int *nonzero,int ch){ int i,used=0; for(i=0;i<ch;i++) if(nonzero[i])used++; if(used) return(_2class(vb,vl,in,ch)); else return(0); } /* res2 is slightly more different; all the channels are interleaved into a single vector and encoded. */ int res2_forward(oggpack_buffer *opb, vorbis_block *vb,vorbis_look_residue *vl, int **in,int *nonzero,int ch, long **partword,int submap){ long i,j,k,n=vb->pcmend/2,used=0; /* don't duplicate the code; use a working vector hack for now and reshape ourselves into a single channel res1 */ /* ugly; reallocs for each coupling pass :-( */ int *work=_vorbis_block_alloc(vb,ch*n*sizeof(*work)); for(i=0;i<ch;i++){ int *pcm=in[i]; if(nonzero[i])used++; for(j=0,k=i;j<n;j++,k+=ch) work[k]=pcm[j]; } if(used){ #ifdef TRAIN_RES return _01forward(opb,vl,&work,1,partword,_encodepart,submap); #else (void)submap; return _01forward(opb,vl,&work,1,partword,_encodepart); #endif }else{ return(0); } } /* duplicate code here as speed is somewhat more important */ int res2_inverse(vorbis_block *vb,vorbis_look_residue *vl, float **in,int *nonzero,int ch){ long i,k,l,s; vorbis_look_residue0 *look=(vorbis_look_residue0 *)vl; vorbis_info_residue0 *info=look->info; /* move all this setup out later */ int samples_per_partition=info->grouping; int partitions_per_word=look->phrasebook->dim; int max=(vb->pcmend*ch)>>1; int end=(info->end<max?info->end:max); int n=end-info->begin; if(n>0){ int partvals=n/samples_per_partition; int partwords=(partvals+partitions_per_word-1)/partitions_per_word; int **partword=_vorbis_block_alloc(vb,partwords*sizeof(*partword)); for(i=0;i<ch;i++)if(nonzero[i])break; if(i==ch)return(0); /* no nonzero vectors */ for(s=0;s<look->stages;s++){ for(i=0,l=0;i<partvals;l++){ if(s==0){ /* fetch the partition word */ int temp=vorbis_book_decode(look->phrasebook,&vb->opb); if(temp==-1 || temp>=info->partvals)goto eopbreak; partword[l]=look->decodemap[temp]; if(partword[l]==NULL)goto errout; } /* now we decode residual values for the partitions */ for(k=0;k<partitions_per_word && i<partvals;k++,i++) if(info->secondstages[partword[l][k]]&(1<<s)){ codebook *stagebook=look->partbooks[partword[l][k]][s]; if(stagebook){ if(vorbis_book_decodevv_add(stagebook,in, i*samples_per_partition+info->begin,ch, &vb->opb,samples_per_partition)==-1) goto eopbreak; } } } } } errout: eopbreak: return(0); } const vorbis_func_residue residue0_exportbundle={ NULL, &res0_unpack, &res0_look, &res0_free_info, &res0_free_look, NULL, NULL, &res0_inverse }; const vorbis_func_residue residue1_exportbundle={ &res0_pack, &res0_unpack, &res0_look, &res0_free_info, &res0_free_look, &res1_class, &res1_forward, &res1_inverse }; const vorbis_func_residue residue2_exportbundle={ &res0_pack, &res0_unpack, &res0_look, &res0_free_info, &res0_free_look, &res2_class, &res2_forward, &res2_inverse };