1/* ------------------------------------------------------------------
2 * Copyright (C) 1998-2009 PacketVideo
3 *
4 * Licensed under the Apache License, Version 2.0 (the "License");
5 * you may not use this file except in compliance with the License.
6 * You may obtain a copy of the License at
7 *
8 *      http://www.apache.org/licenses/LICENSE-2.0
9 *
10 * Unless required by applicable law or agreed to in writing, software
11 * distributed under the License is distributed on an "AS IS" BASIS,
12 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either
13 * express or implied.
14 * See the License for the specific language governing permissions
15 * and limitations under the License.
16 * -------------------------------------------------------------------
17 */
18/****************************************************************************************
19Portions of this file are derived from the following 3GPP standard:
20
21    3GPP TS 26.073
22    ANSI-C code for the Adaptive Multi-Rate (AMR) speech codec
23    Available from http://www.3gpp.org
24
25(C) 2004, 3GPP Organizational Partners (ARIB, ATIS, CCSA, ETSI, TTA, TTC)
26Permission to distribute, modify and use this file under the standard license
27terms listed above has been obtained from the copyright holder.
28****************************************************************************************/
29/*
30
31 Pathname: ./audio/gsm-amr/c/src/sqrt_l.c
32
33------------------------------------------------------------------------------
34 REVISION HISTORY
35
36
37 Description: Updated template. Changed function interface to pass in a
38              pointer to overflow flag into the function instead of using a
39              global flag. Changed name of an input pointer from "exp" to "pExp"
40              for clarity. Removed inclusion of unwanted header files.
41
42 Description: Removed inclusion of sqrt_l.tab file. Changed the array name
43              "table" to "sqrt_l_tbl". Fixed typos.
44
45 Who:                           Date:
46 Description:
47
48------------------------------------------------------------------------------
49*/
50
51/*----------------------------------------------------------------------------
52; INCLUDES
53----------------------------------------------------------------------------*/
54#include    "sqrt_l.h"
55#include    "typedef.h"
56#include    "basic_op.h"
57
58/*----------------------------------------------------------------------------
59; MACROS
60; Define module specific macros here
61----------------------------------------------------------------------------*/
62
63
64/*----------------------------------------------------------------------------
65; DEFINES
66; Include all pre-processor statements here. Include conditional
67; compile variables also.
68----------------------------------------------------------------------------*/
69
70
71/*----------------------------------------------------------------------------
72; LOCAL FUNCTION DEFINITIONS
73; Function Prototype declaration
74----------------------------------------------------------------------------*/
75
76
77/*----------------------------------------------------------------------------
78; LOCAL STORE/BUFFER/POINTER DEFINITIONS
79; Variable declaration - defined here and used outside this module
80----------------------------------------------------------------------------*/
81
82
83/*
84------------------------------------------------------------------------------
85 FUNCTION NAME: sqrt_l_exp
86------------------------------------------------------------------------------
87 INPUT AND OUTPUT DEFINITIONS
88
89 Inputs:
90    L_x = input value (Word32)
91    pExp = pointer to right shift to be applied to result
92    pOverflow = pointer to overflow flag
93
94 Outputs:
95    pOverflow -> if the Inv_sqrt operation resulted in an overflow.
96
97 Returns:
98    L_y = squareroot of L_x (Word32)
99
100 Global Variables Used:
101    None.
102
103 Local Variables Needed:
104    None.
105
106------------------------------------------------------------------------------
107 FUNCTION DESCRIPTION
108
109 This function computes sqrt(L_x),  where  L_x is positive.
110 If L_var is negative or zero, the result is 0
111
112 The function sqrt(L_x) is approximated by a table and linear
113 interpolation. The square root is computed using the
114 following steps:
115    1- Normalization of L_x.
116    2- If exponent is even then shift right once.
117    3- exponent = exponent/2
118    4- i = bit25-b31 of L_x;  16<=i<=63  because of normalization.
119    5- a = bit10-b24
120    6- i -=16
121    7- L_y = table[i]<<16 - (table[i] - table[i+1]) * a * 2
122    8- return L_y and exponent so caller can do denormalization
123
124------------------------------------------------------------------------------
125 REQUIREMENTS
126
127 None.
128
129------------------------------------------------------------------------------
130 REFERENCES
131
132 sqrt_l.c, UMTS GSM AMR speech codec, R99 - Version 3.2.0, March 2, 2001
133
134------------------------------------------------------------------------------
135 PSEUDO-CODE
136
137Word32 sqrt_l_exp (     // o : output value
138    Word32 L_x,         // i : input value
139    Word16 *exp         // o : right shift to be applied to result
140)
141{
142
143//          y = sqrt(x)
144//          x = f * 2^-e,   0.5 <= f < 1   (normalization)
145//          y = sqrt(f) * 2^(-e/2)
146//
147//          a) e = 2k   --> y = sqrt(f)   * 2^-k  (k = e div 2,
148//                                                 0.707 <= sqrt(f) < 1)
149//          b) e = 2k+1 --> y = sqrt(f/2) * 2^-k  (k = e div 2,
150                                                 0.5 <= sqrt(f/2) < 0.707)
151
152
153    Word16 e, i, a, tmp;
154    Word32 L_y;
155
156    if (L_x <= (Word32) 0)
157    {
158        *exp = 0;
159        return (Word32) 0;
160    }
161
162* The reference ETSI code uses a global Overflow flag. In the actual
163* implementation a pointer to the overflow flag is passed into the function.
164* This pointer is in turn passed into the basic math functions such as add(),
165* L_shl(), L_shr(), sub() called by this module.
166
167    e = norm_l (L_x) & 0xFFFE;              // get next lower EVEN norm. exp
168    L_x = L_shl (L_x, e);                   // L_x is normalized to [0.25..1)
169    *exp = e;                               // return 2*exponent (or Q1)
170
171    L_x = L_shr (L_x, 9);
172    i = extract_h (L_x);                    // Extract b25-b31, 16 <= i <= 63
173                                                because of normalization
174    L_x = L_shr (L_x, 1);
175    a = extract_l (L_x);                    // Extract b10-b24
176    a = a & (Word16) 0x7fff;
177
178    i = sub (i, 16);                        // 0 <= i <= 47
179
180    L_y = L_deposit_h (table[i]);           // table[i] << 16
181    tmp = sub (table[i], table[i + 1]);     // table[i] - table[i+1])
182    L_y = L_msu (L_y, tmp, a);              // L_y -= tmp*a*2
183
184    return (L_y);
185}
186
187------------------------------------------------------------------------------
188 RESOURCES USED [optional]
189
190 When the code is written for a specific target processor the
191 the resources used should be documented below.
192
193 HEAP MEMORY USED: x bytes
194
195 STACK MEMORY USED: x bytes
196
197 CLOCK CYCLES: (cycle count equation for this function) + (variable
198                used to represent cycle count for each subroutine
199                called)
200     where: (cycle count variable) = cycle count for [subroutine
201                                     name]
202
203------------------------------------------------------------------------------
204 CAUTION [optional]
205 [State any special notes, constraints or cautions for users of this function]
206
207------------------------------------------------------------------------------
208*/
209
210Word32 sqrt_l_exp(      /* o : output value,                          Q31 */
211    Word32 L_x,         /* i : input value,                           Q31 */
212    Word16 *pExp,       /* o : right shift to be applied to result,   Q1  */
213    Flag   *pOverflow   /* i : pointer to overflow flag */
214)
215
216{
217    Word16 e;
218    Word16 i;
219    Word16 a;
220    Word16 tmp;
221    Word32 L_y;
222
223    /*
224          y = sqrt(x)
225          x = f * 2^-e,   0.5 <= f < 1   (normalization)
226          y = sqrt(f) * 2^(-e/2)
227          a) e = 2k   --> y = sqrt(f)   * 2^-k  (k = e div 2,
228                                                 0.707 <= sqrt(f) < 1)
229          b) e = 2k+1 --> y = sqrt(f/2) * 2^-k  (k = e div 2,
230                                                 0.5 <= sqrt(f/2) < 0.707)
231     */
232
233    if (L_x <= (Word32) 0)
234    {
235        *pExp = 0;
236        return (Word32) 0;
237    }
238
239    e = norm_l(L_x) & 0xFFFE;               /* get next lower EVEN norm. exp  */
240    L_x = L_shl(L_x, e, pOverflow);         /* L_x is normalized to [0.25..1) */
241    *pExp = e;                              /* return 2*exponent (or Q1)      */
242
243    L_x >>= 10;
244    i = (Word16)(L_x >> 15) & 63;            /* Extract b25-b31, 16<= i <=63  */
245    /* because of normalization       */
246
247    a = (Word16)(L_x);                      /* Extract b10-b24 */
248    a &= (Word16) 0x7fff;
249
250    if (i > 15)
251    {
252        i -= 16;                              /* 0 <= i <= 47                   */
253    }
254
255    L_y = L_deposit_h(sqrt_l_tbl[i]);       /* sqrt_l_tbl[i] << 16            */
256
257    /* sqrt_l_tbl[i] - sqrt_l_tbl[i+1]) */
258    tmp = sub(sqrt_l_tbl[i], sqrt_l_tbl[i + 1], pOverflow);
259
260    L_y = L_msu(L_y, tmp, a, pOverflow);    /* L_y -= tmp*a*2                 */
261
262    /* L_y = L_shr (L_y, *exp); */          /* denormalization done by caller */
263
264    return (L_y);
265}
266
267