src/libgsm/rpe.c - vcbox/third_party/libsox - Git at Google

 /*
  * Copyright 1992 by Jutta Degener and Carsten Bormann, Technische
  * Universitaet Berlin.  See the accompanying file "COPYRIGHT" for
  * details.  THERE IS ABSOLUTELY NO WARRANTY FOR THIS SOFTWARE.
  */

 /* $Header: /cvsroot/sox/sox/libgsm/rpe.c,v 1.2 2007/11/04 16:32:36 robs Exp $ */

 #include <stdio.h>
 #include <assert.h>

 #include "third_party/sox/src/libgsm/private.h"

 #include "third_party/sox/src/libgsm/gsm.h"

 /*  4.2.13 .. 4.2.17  RPE ENCODING SECTION
  */

 /* 4.2.13 */

 static void Weighting_filter (
 	register word	* e,		/* signal [-5..0.39.44]	IN  */
 	word		* x		/* signal [0..39]	OUT */
 )
 /*
  *  The coefficients of the weighting filter are stored in a table
  *  (see table 4.4).  The following scaling is used:
  *
  *	H[0..10] = integer( real_H[ 0..10] * 8192 );
  */
 {
 	/* word			wt[ 50 ]; */

 	register longword	L_result;
 	register int		k /* , i */ ;

 	/*  Initialization of a temporary working array wt[0...49]
 	 */

 	/* for (k =  0; k <=  4; k++) wt[k] = 0;
 	 * for (k =  5; k <= 44; k++) wt[k] = *e++;
 	 * for (k = 45; k <= 49; k++) wt[k] = 0;
 	 *
 	 *  (e[-5..-1] and e[40..44] are allocated by the caller,
 	 *  are initially zero and are not written anywhere.)
 	 */
 	e -= 5;

 	/*  Compute the signal x[0..39]
 	 */
 	for (k = 0; k <= 39; k++) {

 		L_result = 8192 >> 1;

 		/* for (i = 0; i <= 10; i++) {
 		 *	L_temp   = GSM_L_MULT( wt[k+i], gsm_H[i] );
 		 *	L_result = GSM_L_ADD( L_result, L_temp );
 		 * }
 		 */

 #undef	STEP
 #define	STEP( i, H )	(e[ k + i ] * (longword)H)

 		/*  Every one of these multiplications is done twice --
 		 *  but I don't see an elegant way to optimize this.
 		 *  Do you?
 		 */

 #ifdef	STUPID_COMPILER
 		L_result += STEP(	0, 	-134 ) ;
 		L_result += STEP(	1, 	-374 )  ;
 	               /* + STEP(	2, 	0    )  */
 		L_result += STEP(	3, 	2054 ) ;
 		L_result += STEP(	4, 	5741 ) ;
 		L_result += STEP(	5, 	8192 ) ;
 		L_result += STEP(	6, 	5741 ) ;
 		L_result += STEP(	7, 	2054 ) ;
 	 	       /* + STEP(	8, 	0    )  */
 		L_result += STEP(	9, 	-374 ) ;
 		L_result += STEP(	10, 	-134 ) ;
 #else
 		L_result +=
 		  STEP(	0, 	-134 )
 		+ STEP(	1, 	-374 )
 	     /* + STEP(	2, 	0    )  */
 		+ STEP(	3, 	2054 )
 		+ STEP(	4, 	5741 )
 		+ STEP(	5, 	8192 )
 		+ STEP(	6, 	5741 )
 		+ STEP(	7, 	2054 )
 	     /* + STEP(	8, 	0    )  */
 		+ STEP(	9, 	-374 )
 		+ STEP(10, 	-134 )
 		;
 #endif

 		/* L_result = GSM_L_ADD( L_result, L_result ); (* scaling(x2) *)
 		 * L_result = GSM_L_ADD( L_result, L_result ); (* scaling(x4) *)
 		 *
 		 * x[k] = SASR( L_result, 16 );
 		 */

 		/* 2 adds vs. >>16 => 14, minus one shift to compensate for
 		 * those we lost when replacing L_MULT by '*'.
 		 */

 		L_result = SASR( L_result, 13 );
 		x[k] =  (  L_result < MIN_WORD ? MIN_WORD
 			: (L_result > MAX_WORD ? MAX_WORD : L_result ));
 	}
 }

 /* 4.2.14 */

 static void RPE_grid_selection (
 	word		* x,		/* [0..39]		IN  */
 	word		* xM,		/* [0..12]		OUT */
 	word		* Mc_out	/*			OUT */
 )
 /*
  *  The signal x[0..39] is used to select the RPE grid which is
  *  represented by Mc.
  */
 {
 	/* register word	temp1;	*/
 	register int		/* m, */  i;
 	register longword	L_result, L_temp;
 	longword		EM;	/* xxx should be L_EM? */
 	word			Mc;

 	longword		L_common_0_3;

 	EM = 0;
 	Mc = 0;

 	/* for (m = 0; m <= 3; m++) {
 	 *	L_result = 0;
 	 *
 	 *
 	 *	for (i = 0; i <= 12; i++) {
 	 *
 	 *		temp1    = SASR( x[m + 3*i], 2 );
 	 *
 	 *		assert(temp1 != MIN_WORD);
 	 *
 	 *		L_temp   = GSM_L_MULT( temp1, temp1 );
 	 *		L_result = GSM_L_ADD( L_temp, L_result );
 	 *	}
 	 *
 	 *	if (L_result > EM) {
 	 *		Mc = m;
 	 *		EM = L_result;
 	 *	}
 	 * }
 	 */

 #undef	STEP
 #define	STEP( m, i )		L_temp = SASR( x[m + 3 * i], 2 );	\
 				L_result += L_temp * L_temp;

 	/* common part of 0 and 3 */

 	L_result = 0;
 	STEP( 0, 1 ); STEP( 0, 2 ); STEP( 0, 3 ); STEP( 0, 4 );
 	STEP( 0, 5 ); STEP( 0, 6 ); STEP( 0, 7 ); STEP( 0, 8 );
 	STEP( 0, 9 ); STEP( 0, 10); STEP( 0, 11); STEP( 0, 12);
 	L_common_0_3 = L_result;

 	/* i = 0 */

 	STEP( 0, 0 );
 	L_result <<= 1;	/* implicit in L_MULT */
 	EM = L_result;

 	/* i = 1 */

 	L_result = 0;
 	STEP( 1, 0 );
 	STEP( 1, 1 ); STEP( 1, 2 ); STEP( 1, 3 ); STEP( 1, 4 );
 	STEP( 1, 5 ); STEP( 1, 6 ); STEP( 1, 7 ); STEP( 1, 8 );
 	STEP( 1, 9 ); STEP( 1, 10); STEP( 1, 11); STEP( 1, 12);
 	L_result <<= 1;
 	if (L_result > EM) {
 		Mc = 1;
 	 	EM = L_result;
 	}

 	/* i = 2 */

 	L_result = 0;
 	STEP( 2, 0 );
 	STEP( 2, 1 ); STEP( 2, 2 ); STEP( 2, 3 ); STEP( 2, 4 );
 	STEP( 2, 5 ); STEP( 2, 6 ); STEP( 2, 7 ); STEP( 2, 8 );
 	STEP( 2, 9 ); STEP( 2, 10); STEP( 2, 11); STEP( 2, 12);
 	L_result <<= 1;
 	if (L_result > EM) {
 		Mc = 2;
 	 	EM = L_result;
 	}

 	/* i = 3 */

 	L_result = L_common_0_3;
 	STEP( 3, 12 );
 	L_result <<= 1;
 	if (L_result > EM) {
 		Mc = 3;
 	 	EM = L_result;
 	}

 	/**/

 	/*  Down-sampling by a factor 3 to get the selected xM[0..12]
 	 *  RPE sequence.
 	 */
 	for (i = 0; i <= 12; i ++) xM[i] = x[Mc + 3*i];
 	*Mc_out = Mc;
 }

 /* 4.12.15 */

 static void APCM_quantization_xmaxc_to_exp_mant (
 	word		xmaxc,		/* IN 	*/
 	word		* exp_out,	/* OUT	*/
 	word		* mant_out )	/* OUT  */
 {
 	word	exp, mant;

 	/* Compute exponent and mantissa of the decoded version of xmaxc
 	 */

 	exp = 0;
 	if (xmaxc > 15) exp = SASR(xmaxc, 3) - 1;
 	mant = xmaxc - (exp << 3);

 	if (mant == 0) {
 		exp  = -4;
 		mant = 7;
 	}
 	else {
 		while (mant <= 7) {
 			mant = mant << 1 | 1;
 			exp--;
 		}
 		mant -= 8;
 	}

 	assert( exp  >= -4 && exp <= 6 );
 	assert( mant >= 0 && mant <= 7 );

 	*exp_out  = exp;
 	*mant_out = mant;
 }

 static void APCM_quantization (
 	word		* xM,		/* [0..12]		IN	*/

 	word		* xMc,		/* [0..12]		OUT	*/
 	word		* mant_out,	/* 			OUT	*/
 	word		* exp_out,	/*			OUT	*/
 	word		* xmaxc_out	/*			OUT	*/
 )
 {
 	int	i, itest;

 	word	xmax, xmaxc, temp, temp1, temp2;
 	word	exp, mant;


 	/*  Find the maximum absolute value xmax of xM[0..12].
 	 */

 	xmax = 0;
 	for (i = 0; i <= 12; i++) {
 		temp = xM[i];
 		temp = GSM_ABS(temp);
 		if (temp > xmax) xmax = temp;
 	}

 	/*  Qantizing and coding of xmax to get xmaxc.
 	 */

 	exp   = 0;
 	temp  = SASR( xmax, 9 );
 	itest = 0;

 	for (i = 0; i <= 5; i++) {

 		itest |= (temp <= 0);
 		temp = SASR( temp, 1 );

 		assert(exp <= 5);
 		if (itest == 0) exp++;		/* exp = add (exp, 1) */
 	}

 	assert(exp <= 6 && exp >= 0);
 	temp = exp + 5;

 	assert(temp <= 11 && temp >= 0);
 	xmaxc = gsm_add( SASR(xmax, temp), exp << 3 );

 	/*   Quantizing and coding of the xM[0..12] RPE sequence
 	 *   to get the xMc[0..12]
 	 */

 	APCM_quantization_xmaxc_to_exp_mant( xmaxc, &exp, &mant );

 	/*  This computation uses the fact that the decoded version of xmaxc
 	 *  can be calculated by using the exponent and the mantissa part of
 	 *  xmaxc (logarithmic table).
 	 *  So, this method avoids any division and uses only a scaling
 	 *  of the RPE samples by a function of the exponent.  A direct
 	 *  multiplication by the inverse of the mantissa (NRFAC[0..7]
 	 *  found in table 4.5) gives the 3 bit coded version xMc[0..12]
 	 *  of the RPE samples.
 	 */


 	/* Direct computation of xMc[0..12] using table 4.5
 	 */

 	assert( exp <= 4096 && exp >= -4096);
 	assert( mant >= 0 && mant <= 7 );

 	temp1 = 6 - exp;		/* normalization by the exponent */
 	temp2 = gsm_NRFAC[ mant ];  	/* inverse mantissa 		 */

 	for (i = 0; i <= 12; i++) {

 		assert(temp1 >= 0 && temp1 < 16);

 		temp = xM[i] << temp1;
 		temp = GSM_MULT( temp, temp2 );
 		temp = SASR(temp, 12);
 		xMc[i] = temp + 4;		/* see note below */
 	}

 	/*  NOTE: This equation is used to make all the xMc[i] positive.
 	 */

 	*mant_out  = mant;
 	*exp_out   = exp;
 	*xmaxc_out = xmaxc;
 }

 /* 4.2.16 */

 static void APCM_inverse_quantization (
 	register word	* xMc,	/* [0..12]			IN 	*/
 	word		mant,
 	word		exp,
 	register word	* xMp)	/* [0..12]			OUT 	*/
 /*
  *  This part is for decoding the RPE sequence of coded xMc[0..12]
  *  samples to obtain the xMp[0..12] array.  Table 4.6 is used to get
  *  the mantissa of xmaxc (FAC[0..7]).
  */
 {
 	int	i;
 	word	temp, temp1, temp2, temp3;
 	longword	ltmp;

 	assert( mant >= 0 && mant <= 7 );

 	temp1 = gsm_FAC[ mant ];	/* see 4.2-15 for mant */
 	temp2 = gsm_sub( 6, exp );	/* see 4.2-15 for exp  */
 	temp3 = gsm_asl( 1, gsm_sub( temp2, 1 ));

 	for (i = 13; i--;) {

 		assert( *xMc <= 7 && *xMc >= 0 ); 	/* 3 bit unsigned */

 		/* temp = gsm_sub( *xMc++ << 1, 7 ); */
 		temp = (*xMc++ << 1) - 7;	        /* restore sign   */
 		assert( temp <= 7 && temp >= -7 ); 	/* 4 bit signed   */

 		temp <<= 12;				/* 16 bit signed  */
 		temp = GSM_MULT_R( temp1, temp );
 		temp = GSM_ADD( temp, temp3 );
 		*xMp++ = gsm_asr( temp, temp2 );
 	}
 }

 /* 4.2.17 */

 static void RPE_grid_positioning (
 	word		Mc,		/* grid position	IN	*/
 	register word	* xMp,		/* [0..12]		IN	*/
 	register word	* ep		/* [0..39]		OUT	*/
 )
 /*
  *  This procedure computes the reconstructed long term residual signal
  *  ep[0..39] for the LTP analysis filter.  The inputs are the Mc
  *  which is the grid position selection and the xMp[0..12] decoded
  *  RPE samples which are upsampled by a factor of 3 by inserting zero
  *  values.
  */
 {
 	int	i = 13;

 	assert(0 <= Mc && Mc <= 3);

         switch (Mc) {
                 case 3: *ep++ = 0;
                 case 2:  do {
                                 *ep++ = 0;
                 case 1:         *ep++ = 0;
                 case 0:         *ep++ = *xMp++;
                          } while (--i);
         }
         while (++Mc < 4) *ep++ = 0;

 	/*

 	int i, k;
 	for (k = 0; k <= 39; k++) ep[k] = 0;
 	for (i = 0; i <= 12; i++) {
 		ep[ Mc + (3*i) ] = xMp[i];
 	}
 	*/
 }

 /* 4.2.18 */

 /*  This procedure adds the reconstructed long term residual signal
  *  ep[0..39] to the estimated signal dpp[0..39] from the long term
  *  analysis filter to compute the reconstructed short term residual
  *  signal dp[-40..-1]; also the reconstructed short term residual
  *  array dp[-120..-41] is updated.
  */

 #if 0	/* Has been inlined in code.c */
 void Gsm_Update_of_reconstructed_short_time_residual_signal P3((dpp, ep, dp),
 	word	* dpp,		/* [0...39]	IN	*/
 	word	* ep,		/* [0...39]	IN	*/
 	word	* dp)		/* [-120...-1]  IN/OUT 	*/
 {
 	int 		k;

 	for (k = 0; k <= 79; k++)
 		dp[ -120 + k ] = dp[ -80 + k ];

 	for (k = 0; k <= 39; k++)
 		dp[ -40 + k ] = gsm_add( ep[k], dpp[k] );
 }
 #endif	/* Has been inlined in code.c */

 void Gsm_RPE_Encoding (

 	struct gsm_state * S,

 	word	* e,		/* -5..-1][0..39][40..44	IN/OUT  */
 	word	* xmaxc,	/* 				OUT */
 	word	* Mc,		/* 			  	OUT */
 	word	* xMc)		/* [0..12]			OUT */
 {
 	word	x[40];
 	word	xM[13], xMp[13];
 	word	mant, exp;

   (void)S; /* Denotes intentionally unused */
 	Weighting_filter(e, x);
 	RPE_grid_selection(x, xM, Mc);

 	APCM_quantization(	xM, xMc, &mant, &exp, xmaxc);
 	APCM_inverse_quantization(  xMc,  mant,  exp, xMp);

 	RPE_grid_positioning( *Mc, xMp, e );

 }

 void Gsm_RPE_Decoding (
 	struct gsm_state	* S,

 	word 		xmaxcr,
 	word		Mcr,
 	word		* xMcr,  /* [0..12], 3 bits 		IN	*/
 	word		* erp	 /* [0..39]			OUT 	*/
 )
 {
 	word	exp, mant;
 	word	xMp[ 13 ];

   (void)S; /* Denotes intentionally unused */
 	APCM_quantization_xmaxc_to_exp_mant( xmaxcr, &exp, &mant );
 	APCM_inverse_quantization( xMcr, mant, exp, xMp );
 	RPE_grid_positioning( Mcr, xMp, erp );

 }
	/*
	* Copyright 1992 by Jutta Degener and Carsten Bormann, Technische
	* Universitaet Berlin. See the accompanying file "COPYRIGHT" for
	* details. THERE IS ABSOLUTELY NO WARRANTY FOR THIS SOFTWARE.
	*/

	/* $Header: /cvsroot/sox/sox/libgsm/rpe.c,v 1.2 2007/11/04 16:32:36 robs Exp $ */

	#include <stdio.h>
	#include <assert.h>

	#include "third_party/sox/src/libgsm/private.h"

	#include "third_party/sox/src/libgsm/gsm.h"

	/* 4.2.13 .. 4.2.17 RPE ENCODING SECTION
	*/

	/* 4.2.13 */

	static void Weighting_filter (
	register word * e, /* signal [-5..0.39.44] IN */
	word * x /* signal [0..39] OUT */
	)
	/*
	* The coefficients of the weighting filter are stored in a table
	* (see table 4.4). The following scaling is used:
	*
	* H[0..10] = integer( real_H[ 0..10] * 8192 );
	*/
	{
	/* word wt[ 50 ]; */

	register longword L_result;
	register int k /* , i */ ;

	/* Initialization of a temporary working array wt[0...49]
	*/

	/* for (k = 0; k <= 4; k++) wt[k] = 0;
	* for (k = 5; k <= 44; k++) wt[k] = *e++;
	* for (k = 45; k <= 49; k++) wt[k] = 0;
	*
	* (e[-5..-1] and e[40..44] are allocated by the caller,
	* are initially zero and are not written anywhere.)
	*/
	e -= 5;

	/* Compute the signal x[0..39]
	*/
	for (k = 0; k <= 39; k++) {

	L_result = 8192 >> 1;

	/* for (i = 0; i <= 10; i++) {
	* L_temp = GSM_L_MULT( wt[k+i], gsm_H[i] );
	* L_result = GSM_L_ADD( L_result, L_temp );
	* }
	*/

	#undef STEP
	#define STEP( i, H ) (e[ k + i ] * (longword)H)

	/* Every one of these multiplications is done twice --
	* but I don't see an elegant way to optimize this.
	* Do you?
	*/

	#ifdef STUPID_COMPILER
	L_result += STEP( 0, -134 ) ;
	L_result += STEP( 1, -374 ) ;
	/* + STEP( 2, 0 ) */
	L_result += STEP( 3, 2054 ) ;
	L_result += STEP( 4, 5741 ) ;
	L_result += STEP( 5, 8192 ) ;
	L_result += STEP( 6, 5741 ) ;
	L_result += STEP( 7, 2054 ) ;
	/* + STEP( 8, 0 ) */
	L_result += STEP( 9, -374 ) ;
	L_result += STEP( 10, -134 ) ;
	#else
	L_result +=
	STEP( 0, -134 )
	+ STEP( 1, -374 )
	/* + STEP( 2, 0 ) */
	+ STEP( 3, 2054 )
	+ STEP( 4, 5741 )
	+ STEP( 5, 8192 )
	+ STEP( 6, 5741 )
	+ STEP( 7, 2054 )
	/* + STEP( 8, 0 ) */
	+ STEP( 9, -374 )
	+ STEP(10, -134 )
	;
	#endif

	/* L_result = GSM_L_ADD( L_result, L_result ); (* scaling(x2) *)
	* L_result = GSM_L_ADD( L_result, L_result ); (* scaling(x4) *)
	*
	* x[k] = SASR( L_result, 16 );
	*/

	/* 2 adds vs. >>16 => 14, minus one shift to compensate for
	* those we lost when replacing L_MULT by '*'.
	*/

	L_result = SASR( L_result, 13 );
	x[k] = ( L_result < MIN_WORD ? MIN_WORD
	: (L_result > MAX_WORD ? MAX_WORD : L_result ));
	}
	}

	/* 4.2.14 */

	static void RPE_grid_selection (
	word * x, /* [0..39] IN */
	word * xM, /* [0..12] OUT */
	word * Mc_out /* OUT */
	)
	/*
	* The signal x[0..39] is used to select the RPE grid which is
	* represented by Mc.
	*/
	{
	/* register word temp1; */
	register int /* m, */ i;
	register longword L_result, L_temp;
	longword EM; /* xxx should be L_EM? */
	word Mc;

	longword L_common_0_3;

	EM = 0;
	Mc = 0;

	/* for (m = 0; m <= 3; m++) {
	* L_result = 0;
	*
	*
	* for (i = 0; i <= 12; i++) {
	*
	* temp1 = SASR( x[m + 3*i], 2 );
	*
	* assert(temp1 != MIN_WORD);
	*
	* L_temp = GSM_L_MULT( temp1, temp1 );
	* L_result = GSM_L_ADD( L_temp, L_result );
	* }
	*
	* if (L_result > EM) {
	* Mc = m;
	* EM = L_result;
	* }
	* }
	*/

	#undef STEP
	#define STEP( m, i ) L_temp = SASR( x[m + 3 * i], 2 ); \
	L_result += L_temp * L_temp;

	/* common part of 0 and 3 */

	L_result = 0;
	STEP( 0, 1 ); STEP( 0, 2 ); STEP( 0, 3 ); STEP( 0, 4 );
	STEP( 0, 5 ); STEP( 0, 6 ); STEP( 0, 7 ); STEP( 0, 8 );
	STEP( 0, 9 ); STEP( 0, 10); STEP( 0, 11); STEP( 0, 12);
	L_common_0_3 = L_result;

	/* i = 0 */

	STEP( 0, 0 );
	L_result <<= 1; /* implicit in L_MULT */
	EM = L_result;

	/* i = 1 */

	L_result = 0;
	STEP( 1, 0 );
	STEP( 1, 1 ); STEP( 1, 2 ); STEP( 1, 3 ); STEP( 1, 4 );
	STEP( 1, 5 ); STEP( 1, 6 ); STEP( 1, 7 ); STEP( 1, 8 );
	STEP( 1, 9 ); STEP( 1, 10); STEP( 1, 11); STEP( 1, 12);
	L_result <<= 1;
	if (L_result > EM) {
	Mc = 1;
	EM = L_result;
	}

	/* i = 2 */

	L_result = 0;
	STEP( 2, 0 );
	STEP( 2, 1 ); STEP( 2, 2 ); STEP( 2, 3 ); STEP( 2, 4 );
	STEP( 2, 5 ); STEP( 2, 6 ); STEP( 2, 7 ); STEP( 2, 8 );
	STEP( 2, 9 ); STEP( 2, 10); STEP( 2, 11); STEP( 2, 12);
	L_result <<= 1;
	if (L_result > EM) {
	Mc = 2;
	EM = L_result;
	}

	/* i = 3 */

	L_result = L_common_0_3;
	STEP( 3, 12 );
	L_result <<= 1;
	if (L_result > EM) {
	Mc = 3;
	EM = L_result;
	}

	/**/

	/* Down-sampling by a factor 3 to get the selected xM[0..12]
	* RPE sequence.
	*/
	for (i = 0; i <= 12; i ++) xM[i] = x[Mc + 3*i];
	*Mc_out = Mc;
	}

	/* 4.12.15 */

	static void APCM_quantization_xmaxc_to_exp_mant (
	word xmaxc, /* IN */
	word * exp_out, /* OUT */
	word * mant_out ) /* OUT */
	{
	word exp, mant;

	/* Compute exponent and mantissa of the decoded version of xmaxc
	*/

	exp = 0;
	if (xmaxc > 15) exp = SASR(xmaxc, 3) - 1;
	mant = xmaxc - (exp << 3);

	if (mant == 0) {
	exp = -4;
	mant = 7;
	}
	else {
	while (mant <= 7) {
	mant = mant << 1 \| 1;
	exp--;
	}
	mant -= 8;
	}

	assert( exp >= -4 && exp <= 6 );
	assert( mant >= 0 && mant <= 7 );

	*exp_out = exp;
	*mant_out = mant;
	}

	static void APCM_quantization (
	word * xM, /* [0..12] IN */

	word * xMc, /* [0..12] OUT */
	word * mant_out, /* OUT */
	word * exp_out, /* OUT */
	word * xmaxc_out /* OUT */
	)
	{
	int i, itest;

	word xmax, xmaxc, temp, temp1, temp2;
	word exp, mant;


	/* Find the maximum absolute value xmax of xM[0..12].
	*/

	xmax = 0;
	for (i = 0; i <= 12; i++) {
	temp = xM[i];
	temp = GSM_ABS(temp);
	if (temp > xmax) xmax = temp;
	}

	/* Qantizing and coding of xmax to get xmaxc.
	*/

	exp = 0;
	temp = SASR( xmax, 9 );
	itest = 0;

	for (i = 0; i <= 5; i++) {

	itest \|= (temp <= 0);
	temp = SASR( temp, 1 );

	assert(exp <= 5);
	if (itest == 0) exp++; /* exp = add (exp, 1) */
	}

	assert(exp <= 6 && exp >= 0);
	temp = exp + 5;

	assert(temp <= 11 && temp >= 0);
	xmaxc = gsm_add( SASR(xmax, temp), exp << 3 );

	/* Quantizing and coding of the xM[0..12] RPE sequence
	* to get the xMc[0..12]
	*/

	APCM_quantization_xmaxc_to_exp_mant( xmaxc, &exp, &mant );

	/* This computation uses the fact that the decoded version of xmaxc
	* can be calculated by using the exponent and the mantissa part of
	* xmaxc (logarithmic table).
	* So, this method avoids any division and uses only a scaling
	* of the RPE samples by a function of the exponent. A direct
	* multiplication by the inverse of the mantissa (NRFAC[0..7]
	* found in table 4.5) gives the 3 bit coded version xMc[0..12]
	* of the RPE samples.
	*/


	/* Direct computation of xMc[0..12] using table 4.5
	*/

	assert( exp <= 4096 && exp >= -4096);
	assert( mant >= 0 && mant <= 7 );

	temp1 = 6 - exp; /* normalization by the exponent */
	temp2 = gsm_NRFAC[ mant ]; /* inverse mantissa */

	for (i = 0; i <= 12; i++) {

	assert(temp1 >= 0 && temp1 < 16);

	temp = xM[i] << temp1;
	temp = GSM_MULT( temp, temp2 );
	temp = SASR(temp, 12);
	xMc[i] = temp + 4; /* see note below */
	}

	/* NOTE: This equation is used to make all the xMc[i] positive.
	*/

	*mant_out = mant;
	*exp_out = exp;
	*xmaxc_out = xmaxc;
	}

	/* 4.2.16 */

	static void APCM_inverse_quantization (
	register word * xMc, /* [0..12] IN */
	word mant,
	word exp,
	register word * xMp) /* [0..12] OUT */
	/*
	* This part is for decoding the RPE sequence of coded xMc[0..12]
	* samples to obtain the xMp[0..12] array. Table 4.6 is used to get
	* the mantissa of xmaxc (FAC[0..7]).
	*/
	{
	int i;
	word temp, temp1, temp2, temp3;
	longword ltmp;

	assert( mant >= 0 && mant <= 7 );

	temp1 = gsm_FAC[ mant ]; /* see 4.2-15 for mant */
	temp2 = gsm_sub( 6, exp ); /* see 4.2-15 for exp */
	temp3 = gsm_asl( 1, gsm_sub( temp2, 1 ));

	for (i = 13; i--;) {

	assert( xMc <= 7 && xMc >= 0 ); /* 3 bit unsigned */

	/* temp = gsm_sub( xMc++ << 1, 7 ); /
	temp = (xMc++ << 1) - 7; / restore sign */
	assert( temp <= 7 && temp >= -7 ); /* 4 bit signed */

	temp <<= 12; /* 16 bit signed */
	temp = GSM_MULT_R( temp1, temp );
	temp = GSM_ADD( temp, temp3 );
	*xMp++ = gsm_asr( temp, temp2 );
	}
	}

	/* 4.2.17 */

	static void RPE_grid_positioning (
	word Mc, /* grid position IN */
	register word * xMp, /* [0..12] IN */
	register word * ep /* [0..39] OUT */
	)
	/*
	* This procedure computes the reconstructed long term residual signal
	* ep[0..39] for the LTP analysis filter. The inputs are the Mc
	* which is the grid position selection and the xMp[0..12] decoded
	* RPE samples which are upsampled by a factor of 3 by inserting zero
	* values.
	*/
	{
	int i = 13;

	assert(0 <= Mc && Mc <= 3);

	switch (Mc) {
	case 3: *ep++ = 0;
	case 2: do {
	*ep++ = 0;
	case 1: *ep++ = 0;
	case 0: ep++ = xMp++;
	} while (--i);
	}
	while (++Mc < 4) *ep++ = 0;

	/*

	int i, k;
	for (k = 0; k <= 39; k++) ep[k] = 0;
	for (i = 0; i <= 12; i++) {
	ep[ Mc + (3*i) ] = xMp[i];
	}
	*/
	}

	/* 4.2.18 */

	/* This procedure adds the reconstructed long term residual signal
	* ep[0..39] to the estimated signal dpp[0..39] from the long term
	* analysis filter to compute the reconstructed short term residual
	* signal dp[-40..-1]; also the reconstructed short term residual
	* array dp[-120..-41] is updated.
	*/

	#if 0 /* Has been inlined in code.c */
	void Gsm_Update_of_reconstructed_short_time_residual_signal P3((dpp, ep, dp),
	word * dpp, /* [0...39] IN */
	word * ep, /* [0...39] IN */
	word * dp) /* [-120...-1] IN/OUT */
	{
	int k;

	for (k = 0; k <= 79; k++)
	dp[ -120 + k ] = dp[ -80 + k ];

	for (k = 0; k <= 39; k++)
	dp[ -40 + k ] = gsm_add( ep[k], dpp[k] );
	}
	#endif /* Has been inlined in code.c */

	void Gsm_RPE_Encoding (

	struct gsm_state * S,

	word * e, /* -5..-1][0..39][40..44 IN/OUT */
	word * xmaxc, /* OUT */
	word * Mc, /* OUT */
	word * xMc) /* [0..12] OUT */
	{
	word x[40];
	word xM[13], xMp[13];
	word mant, exp;

	(void)S; /* Denotes intentionally unused */
	Weighting_filter(e, x);
	RPE_grid_selection(x, xM, Mc);

	APCM_quantization( xM, xMc, &mant, &exp, xmaxc);
	APCM_inverse_quantization( xMc, mant, exp, xMp);

	RPE_grid_positioning( *Mc, xMp, e );

	}

	void Gsm_RPE_Decoding (
	struct gsm_state * S,

	word xmaxcr,
	word Mcr,
	word * xMcr, /* [0..12], 3 bits IN */
	word * erp /* [0..39] OUT */
	)
	{
	word exp, mant;
	word xMp[ 13 ];

	(void)S; /* Denotes intentionally unused */
	APCM_quantization_xmaxc_to_exp_mant( xmaxcr, &exp, &mant );
	APCM_inverse_quantization( xMcr, mant, exp, xMp );
	RPE_grid_positioning( Mcr, xMp, erp );

	}