math_lib.c

MELPe 1200 bps, fixed point

/*

2.4 kbps MELP Proposed Federal Standard speech coder

Fixed-point C code, version 1.0

Copyright (c) 1998, Texas Instruments, Inc.

Texas Instruments has intellectual property rights on the MELP
algorithm.	The Texas Instruments contact for licensing issues for
commercial and non-government use is William Gordon, Director,
Government Contracts, Texas Instruments Incorporated, Semiconductor
Group (phone [phone]).

The fixed-point version of the voice codec Mixed Excitation Linear
Prediction (MELP) is based on specifications on the C-language software
simulation contained in GSM 06.06 which is protected by copyright and
is the property of the European Telecommunications Standards Institute
(ETSI). This standard is available from the ETSI publication office
tel. [phone]. ETSI has granted a license to United States
Department of Defense to use the C-language software simulation contained
in GSM 06.06 for the purposes of the development of a fixed-point
version of the voice codec Mixed Excitation Linear Prediction (MELP).
Requests for authorization to make other use of the GSM 06.06 or
otherwise distribute or modify them need to be addressed to the ETSI
Secretariat fax: [phone].

*/

#include <assert.h>

#include "sc1200.h"
#include "mathhalf.h"
#include "mathdp31.h"
#include "math_lib.h"
#include "constant.h"
#include "global.h"
#include "macro.h"

/* log_table[] is Q13, and log_table[i] = log(i+1) * 2^11. */
static const Shortword	log_table[256] = {
		0,  2466,  3908,  4932,  5725,  6374,  6923,  7398,  7817,  8192,
	 8531,  8840,  9125,  9389,  9634,  9864, 10079, 10283, 10475, 10658,
	10831, 10997, 11155, 11306, 11451, 11591, 11725, 11855, 11979, 12100,
	12217, 12330, 12439, 12545, 12649, 12749, 12846, 12941, 13034, 13124,
	13211, 13297, 13381, 13463, 13543, 13621, 13697, 13772, 13846, 13917,
	13988, 14057, 14125, 14191, 14257, 14321, 14384, 14446, 14506, 14566,
	14625, 14683, 14740, 14796, 14851, 14905, 14959, 15011, 15063, 15115,
	15165, 15215, 15264, 15312, 15360, 15407, 15454, 15500, 15545, 15590,
	15634, 15677, 15721, 15763, 15805, 15847, 15888, 15929, 15969, 16009,
	16048, 16087, 16125, 16163, 16201, 16238, 16275, 16312, 16348, 16384,
	16419, 16454, 16489, 16523, 16557, 16591, 16624, 16657, 16690, 16723,
	16755, 16787, 16818, 16850, 16881, 16912, 16942, 16972, 17002, 17032,
	17062, 17091, 17120, 17149, 17177, 17206, 17234, 17262, 17289, 17317,
	17344, 17371, 17398, 17425, 17451, 17477, 17504, 17529, 17555, 17581,
	17606, 17631, 17656, 17681, 17705, 17730, 17754, 17778, 17802, 17826,
	17850, 17873, 17896, 17920, 17943, 17966, 17988, 18011, 18033, 18056,
	18078, 18100, 18122, 18144, 18165, 18187, 18208, 18229, 18250, 18271,
	18292, 18313, 18334, 18354, 18374, 18395, 18415, 18435, 18455, 18475,
	18494, 18514, 18533, 18553, 18572, 18591, 18610, 18629, 18648, 18667,
	18686, 18704, 18723, 18741, 18759, 18778, 18796, 18814, 18832, 18850,
	18867, 18885, 18903, 18920, 18937, 18955, 18972, 18989, 19006, 19023,
	19040, 19057, 19074, 19090, 19107, 19123, 19140, 19156, 19172, 19189,
	19205, 19221, 19237, 19253, 19269, 19284, 19300, 19316, 19331, 19347,
	19362, 19378, 19393, 19408, 19423, 19438, 19453, 19468, 19483, 19498,
	19513, 19528, 19542, 19557, 19572, 19586, 19600, 19615, 19629, 19643,
	19658, 19672, 19686, 19700, 19714, 19728
};


/***************************************************************************
 *
 *	 FUNCTION NAME: L_divider2
 *
 *	 PURPOSE:
 *
 *	   Divide numer by denom.  If numer is bigger than denom, a warning
 *	   is given and a zero is returned.
 *
 *
 *	 INPUTS:
 *
 *	   numer
 *					   32 bit long signed integer (Longword).
 *	   denom
 *					   32 bit long signed integer (Longword).
 *	   numer_shift
 *					   16 bit short signed integer (Shortword) represents
 *					   number of right shifts for numer.
 *	   denom_shift
 *					   16 bit short signed integer (Shortword) represents
 *					   number of left shifts for denom.
 *
 *	 OUTPUTS:
 *
 *	   none
 *
 *	 RETURN VALUE:
 *
 *	   result
 *					   16 bit short signed integer (Shortword).
 *
 *************************************************************************/
Shortword L_divider2(Longword numer, Longword denom, Shortword numer_shift,
					 Shortword denom_shift)
{
	Shortword	result;
	Shortword	sign = 0;
	Shortword	short_shift = 0;
	Longword	L_temp;


	assert(denom != 0);

	if (numer < 0)
		sign = (Shortword) (!sign);
	if (denom < 0)
		sign = (Shortword) (!sign);

	L_temp = L_shl(denom, denom_shift);
	denom = L_abs(L_temp);
	L_temp = L_shr(numer, numer_shift);
	numer = L_abs(L_temp);

	while (denom > (Longword) SW_MAX){
		denom = L_shr(denom,1);
		short_shift = add(short_shift, 1);
	}
	numer = L_shr(numer, short_shift);

	assert(numer <= denom);

	result = divide_s(extract_l(numer), extract_l(denom));

	if (sign){
		result = negate(result);
	}

	return(result);
}


/***************************************************************************
 *
 *	 FUNCTION NAME: log10_fxp
 *
 *	 PURPOSE:
 *
 *	   Compute the logarithm to the base 10 of x.
 *
 *
 *	 INPUTS:
 *
 *	   x
 *					   16 bit short signed integer (Shortword).
 *	   Q
 *					   16 bit short signed integer (Shortword) represents
 *					   Q value of x.
 *
 *	 OUTPUTS:
 *
 *	   none
 *
 *	 RETURN VALUE:
 *
 *	   y
 *					   16 bit short signed integer (Shortword) in Q12.
 *
 *************************************************************************/
Shortword log10_fxp(Shortword x, Shortword Q)
{
	Shortword	y, interp_factor, interp_component;
	Shortword	index1, index2;
	Shortword	shift;
	Shortword	temp1, temp2;
	Longword	L_temp;


	/* Treat x as if it is a fixed-point number with Q7.  Use "shift" to      */
	/* record the exponent required for adjustment.                           */

	shift = sub(7, Q);

	/* If x is 0, stop and return minus infinity. */
	if (!x)
		return(-SW_MAX);

	/* Keep multiplying x by 2 until x is larger than 1 in Q7.  x in Q7 will  */
	/* now lie between the two integers index1 and index2.                    */

	index2 = shr(x, 7);
	while ((!index2) && x){
		x = shl(x, 1);
		shift = sub(shift, 1);
		index2 = shr(x, 7);
	}
	index1 = sub(index2, 1);

	/* interpolation */

	interp_factor = shl((Shortword) (x & 127), 8);
	temp1 = sub(log_table[index2], log_table[index1]);
	interp_component = mult(temp1, interp_factor);

	/* return a Q12 */

	L_temp = L_mult(log_table[1], shift);
	L_temp = L_shr(L_temp, 2);
	temp1 = shr(log_table[index1], 1);
	temp1 = add(temp1, extract_l(L_temp));
	temp2 = shr(interp_component, 1);
	y = add(temp1, temp2);

	return(y);
}


/***************************************************************************
 *
 *	 FUNCTION NAME: L_log10_fxp
 *
 *	 PURPOSE:
 *
 *	   Compute the logarithm to the base 10 of x.
 *
 *
 *	 INPUTS:
 *
 *	   x
 *					   32 bit long signed integer (Longword).
 *	   Q
 *					   16 bit short signed integer (Shortword) represents
 *					   Q value of x.
 *
 *	 OUTPUTS:
 *
 *	   none
 *
 *	 RETURN VALUE:
 *
 *	   y
 *					   16 bit short signed integer (Shortword) in Q11.
 *
 *************************************************************************/
Shortword L_log10_fxp(Longword x, Shortword Q)
{
	Shortword	y, interp_component;
	Longword	interp_factor;
	Shortword	index1, index2;
	Shortword	shift;
	Shortword	temp1, temp2;
	Longword	L_temp;


	shift = sub(23, Q);
	if (!x)
		return((Shortword) -SW_MAX);

	index2 = extract_l(L_shr(x, 23));
	while ((!index2) && x){
		x = L_shl(x, 1);
		shift = sub(shift, 1);
		index2 = extract_l(L_shr(x, 23));
	}
	index1 = sub(index2, 1);

	/* interpolation */

	interp_factor = L_shl(x & (Longword) 0x7fffff, 8);
	temp1 = sub(log_table[index2], log_table[index1]);
	interp_component = extract_h(L_mpy_ls(interp_factor, temp1));

	/* return a Q11 */

	L_temp = L_mult(log_table[1], shift);                   /* log10(2^shift) */
	L_temp = L_shr(L_temp, 3);
	temp1 = shr(log_table[index1], 2);
	temp1 = add(temp1, extract_l(L_temp));
	temp2 = shr(interp_component, 2);
	y = add(temp1, temp2);

	return(y);
}


/***************************************************************************
 *
 *	 FUNCTION NAME: pow10_fxp
 *
 *	 PURPOSE:
 *
 *	   Compute 10 raised to the power x.
 *
 *
 *	 INPUTS:
 *
 *	   x
 *					   16 bit short signed integer (Shortword) in Q12.
 *	   Q
 *					   16 bit short signed integer (Shortword) represents
 *					   required Q value of returned result.
 *
 *	 OUTPUTS:
 *
 *	   none
 *
 *	 RETURN VALUE:
 *
 *	   y
 *					   16 bit short signed integer (Shortword).
 *
 *************************************************************************/
Shortword pow10_fxp(Shortword x, Shortword Q)
{
	/* table in Q11 */
	static const Shortword	table[257] = {
		 2048,  2066,  2085,  2104,  2123,  2142,  2161,  2181,  2200,  2220,
		 2240,  2260,  2281,  2302,  2322,  2343,  2364,  2386,  2407,  2429,
		 2451,  2473,  2496,  2518,  2541,  2564,  2587,  2610,  2634,  2658,
		 2682,  2706,  2731,  2755,  2780,  2805,  2831,  2856,  2882,  2908,
		 2934,  2961,  2988,  3015,  3042,  3069,  3097,  3125,  3153,  3182,
		 3211,  3240,  3269,  3298,  3328,  3358,  3389,  3419,  3450,  3481,
		 3513,  3544,  3576,  3609,  3641,  3674,  3708,  3741,  3775,  3809,
		 3843,  3878,  3913,  3948,  3984,  4020,  4056,  4093,  4130,  4167,
		 4205,  4243,  4281,  4320,  4359,  4399,  4438,  4478,  4519,  4560,
		 4601,  4643,  4684,  4727,  4769,  4813,  4856,  4900,  4944,  4989,
		 5034,  5079,  5125,  5172,  5218,  5266,  5313,  5361,  5410,  5458,
		 5508,  5558,  5608,  5658,  5710,  5761,  5813,  5866,  5919,  5972,
		 6026,  6081,  6136,  6191,  6247,  6303,  6360,  6418,  6476,  6534,
		 6593,  6653,  6713,  6774,  6835,  6897,  6959,  7022,  7085,  7149,
		 7214,  7279,  7345,  7411,  7478,  7546,  7614,  7683,  7752,  7822,
		 7893,  7964,  8036,  8109,  8182,  8256,  8331,  8406,  8482,  8559,
		 8636,  8714,  8793,  8872,  8952,  9033,  9115,  9197,  9280,  9364,
		 9449,  9534,  9620,  9707,  9795,  9883,  9973, 10063, 10154, 10245,
		10338, 10431, 10526, 10621, 10717, 10813, 10911, 11010, 11109, 11210,
		11311, 11413, 11516, 11620, 11725, 11831, 11938, 12046, 12155, 12265,
		12375, 12487, 12600, 12714, 12829, 12945, 13062, 13180, 13299, 13419,
		13540, 13663, 13786, 13911, 14036, 14163, 14291, 14420, 14550, 14682,
		14815, 14948, 15084, 15220, 15357, 15496, 15636, 15777, 15920, 16064,
		16209, 16355, 16503, 16652, 16803, 16955, 17108, 17262, 17418, 17576,
		17734, 17895, 18056, 18220, 18384, 18550, 18718, 18887, 19058, 19230,
		19404, 19579, 19756, 19934, 20114, 20296, 20480
	};

	static const Shortword	tens_table[9] = {
		26844, 16777, 20972, 26214, 1, 10, 100, 1000, 10000
	};

	static const Shortword	Q_table[4] = {
		28, 24, 21, 18
	};

	Shortword	y, interp_factor, interp_component;
	Shortword	index1, index2;
	Shortword	ten_multiple;
	Longword	L_y;
	Shortword	temp1, temp2;


	ten_multiple = shr(x, 12);      /* ten_multiple is the integral part of x */
	if (ten_multiple < -4)
		return((Shortword) 0);
	else if (ten_multiple > 4){
		inc_saturation();
		return((Shortword) SW_MAX);
	}

	index1 = shr((Shortword) (x & (Shortword) 0x0ff0), 4);
						/* index1 is the most significant 8 bits of the */
                          /* fractional part of x, Q8 */
	index2 = add(index1, 1);

	/* interpolation */
	/* shift by 11 to make it a number between 0 & 1 in Q15 */

	interp_factor = shl((Shortword)(x & (Shortword) 0x000f), 11);
				       /* interp_factor is the least significant 4 bits of the */
					                              /* fractional part of x, Q15 */
	temp1 = sub(table[index2], table[index1]);        /* Q0, at most 8 digits */
	interp_component = mult(temp1, interp_factor);                      /* Q0 */

	/* L_y in Q12 if x >= 0 and in Q_table[temp2] + 12 if x < 0 */
	temp1 = add(table[index1], interp_component);                       /* Q0 */
	temp2 = add(ten_multiple, 4);
	L_y = L_mult(tens_table[temp2], temp1);

	if (ten_multiple >= 0){
		temp1 = sub(12, Q);
		L_y = L_shr(L_y, temp1);
		y = extract_l(L_y);
		if (extract_h(L_y)){
			y = SW_MAX;
			inc_saturation();
		}
	} else {
		temp1 = add(Q_table[temp2], 12);
		temp1 = sub(temp1, Q);
		y = extract_l(L_shr(L_y, temp1));
	}

	return(y);
}


/***************************************************************************
 *
 *	 FUNCTION NAME: sqrt_fxp