/* ------------------------------------------------------------------ * Copyright (C) 1998-2009 PacketVideo * * Licensed under the Apache License, Version 2.0 (the "License"); * you may not use this file except in compliance with the License. * You may obtain a copy of the License at * * http://www.apache.org/licenses/LICENSE-2.0 * * Unless required by applicable law or agreed to in writing, software * distributed under the License is distributed on an "AS IS" BASIS, * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either * express or implied. * See the License for the specific language governing permissions * and limitations under the License. * ------------------------------------------------------------------- */ /**************************************************************************************** Portions of this file are derived from the following 3GPP standard: 3GPP TS 26.073 ANSI-C code for the Adaptive Multi-Rate (AMR) speech codec Available from http://www.3gpp.org (C) 2004, 3GPP Organizational Partners (ARIB, ATIS, CCSA, ETSI, TTA, TTC) Permission to distribute, modify and use this file under the standard license terms listed above has been obtained from the copyright holder. ****************************************************************************************/ /* Pathname: ./audio/gsm-amr/c/src/sqrt_l.c ------------------------------------------------------------------------------ REVISION HISTORY Description: Updated template. Changed function interface to pass in a pointer to overflow flag into the function instead of using a global flag. Changed name of an input pointer from "exp" to "pExp" for clarity. Removed inclusion of unwanted header files. Description: Removed inclusion of sqrt_l.tab file. Changed the array name "table" to "sqrt_l_tbl". Fixed typos. Who: Date: Description: ------------------------------------------------------------------------------ */ /*---------------------------------------------------------------------------- ; INCLUDES ----------------------------------------------------------------------------*/ #include "sqrt_l.h" #include "typedef.h" #include "basic_op.h" /*---------------------------------------------------------------------------- ; MACROS ; Define module specific macros here ----------------------------------------------------------------------------*/ /*---------------------------------------------------------------------------- ; DEFINES ; Include all pre-processor statements here. Include conditional ; compile variables also. ----------------------------------------------------------------------------*/ /*---------------------------------------------------------------------------- ; LOCAL FUNCTION DEFINITIONS ; Function Prototype declaration ----------------------------------------------------------------------------*/ /*---------------------------------------------------------------------------- ; LOCAL STORE/BUFFER/POINTER DEFINITIONS ; Variable declaration - defined here and used outside this module ----------------------------------------------------------------------------*/ /* ------------------------------------------------------------------------------ FUNCTION NAME: sqrt_l_exp ------------------------------------------------------------------------------ INPUT AND OUTPUT DEFINITIONS Inputs: L_x = input value (Word32) pExp = pointer to right shift to be applied to result pOverflow = pointer to overflow flag Outputs: pOverflow -> if the Inv_sqrt operation resulted in an overflow. Returns: L_y = squareroot of L_x (Word32) Global Variables Used: None. Local Variables Needed: None. ------------------------------------------------------------------------------ FUNCTION DESCRIPTION This function computes sqrt(L_x), where L_x is positive. If L_var is negative or zero, the result is 0 The function sqrt(L_x) is approximated by a table and linear interpolation. The square root is computed using the following steps: 1- Normalization of L_x. 2- If exponent is even then shift right once. 3- exponent = exponent/2 4- i = bit25-b31 of L_x; 16<=i<=63 because of normalization. 5- a = bit10-b24 6- i -=16 7- L_y = table[i]<<16 - (table[i] - table[i+1]) * a * 2 8- return L_y and exponent so caller can do denormalization ------------------------------------------------------------------------------ REQUIREMENTS None. ------------------------------------------------------------------------------ REFERENCES sqrt_l.c, UMTS GSM AMR speech codec, R99 - Version 3.2.0, March 2, 2001 ------------------------------------------------------------------------------ PSEUDO-CODE Word32 sqrt_l_exp ( // o : output value Word32 L_x, // i : input value Word16 *exp // o : right shift to be applied to result ) { // y = sqrt(x) // x = f * 2^-e, 0.5 <= f < 1 (normalization) // y = sqrt(f) * 2^(-e/2) // // a) e = 2k --> y = sqrt(f) * 2^-k (k = e div 2, // 0.707 <= sqrt(f) < 1) // b) e = 2k+1 --> y = sqrt(f/2) * 2^-k (k = e div 2, 0.5 <= sqrt(f/2) < 0.707) Word16 e, i, a, tmp; Word32 L_y; if (L_x <= (Word32) 0) { *exp = 0; return (Word32) 0; } * The reference ETSI code uses a global Overflow flag. In the actual * implementation a pointer to the overflow flag is passed into the function. * This pointer is in turn passed into the basic math functions such as add(), * L_shl(), L_shr(), sub() called by this module. e = norm_l (L_x) & 0xFFFE; // get next lower EVEN norm. exp L_x = L_shl (L_x, e); // L_x is normalized to [0.25..1) *exp = e; // return 2*exponent (or Q1) L_x = L_shr (L_x, 9); i = extract_h (L_x); // Extract b25-b31, 16 <= i <= 63 because of normalization L_x = L_shr (L_x, 1); a = extract_l (L_x); // Extract b10-b24 a = a & (Word16) 0x7fff; i = sub (i, 16); // 0 <= i <= 47 L_y = L_deposit_h (table[i]); // table[i] << 16 tmp = sub (table[i], table[i + 1]); // table[i] - table[i+1]) L_y = L_msu (L_y, tmp, a); // L_y -= tmp*a*2 return (L_y); } ------------------------------------------------------------------------------ RESOURCES USED [optional] When the code is written for a specific target processor the the resources used should be documented below. HEAP MEMORY USED: x bytes STACK MEMORY USED: x bytes CLOCK CYCLES: (cycle count equation for this function) + (variable used to represent cycle count for each subroutine called) where: (cycle count variable) = cycle count for [subroutine name] ------------------------------------------------------------------------------ CAUTION [optional] [State any special notes, constraints or cautions for users of this function] ------------------------------------------------------------------------------ */ Word32 sqrt_l_exp( /* o : output value, Q31 */ Word32 L_x, /* i : input value, Q31 */ Word16 *pExp, /* o : right shift to be applied to result, Q1 */ Flag *pOverflow /* i : pointer to overflow flag */ ) { Word16 e; Word16 i; Word16 a; Word16 tmp; Word32 L_y; /* y = sqrt(x) x = f * 2^-e, 0.5 <= f < 1 (normalization) y = sqrt(f) * 2^(-e/2) a) e = 2k --> y = sqrt(f) * 2^-k (k = e div 2, 0.707 <= sqrt(f) < 1) b) e = 2k+1 --> y = sqrt(f/2) * 2^-k (k = e div 2, 0.5 <= sqrt(f/2) < 0.707) */ if (L_x <= (Word32) 0) { *pExp = 0; return (Word32) 0; } e = norm_l(L_x) & 0xFFFE; /* get next lower EVEN norm. exp */ L_x = L_shl(L_x, e, pOverflow); /* L_x is normalized to [0.25..1) */ *pExp = e; /* return 2*exponent (or Q1) */ L_x >>= 10; i = (Word16)(L_x >> 15) & 63; /* Extract b25-b31, 16<= i <=63 */ /* because of normalization */ a = (Word16)(L_x); /* Extract b10-b24 */ a &= (Word16) 0x7fff; if (i > 15) { i -= 16; /* 0 <= i <= 47 */ } L_y = L_deposit_h(sqrt_l_tbl[i]); /* sqrt_l_tbl[i] << 16 */ /* sqrt_l_tbl[i] - sqrt_l_tbl[i+1]) */ tmp = sub(sqrt_l_tbl[i], sqrt_l_tbl[i + 1], pOverflow); L_y = L_msu(L_y, tmp, a, pOverflow); /* L_y -= tmp*a*2 */ /* L_y = L_shr (L_y, *exp); */ /* denormalization done by caller */ return (L_y); }