1 /*
2 * Copyright (c) 2011 The WebRTC project authors. All Rights Reserved.
3 *
4 * Use of this source code is governed by a BSD-style license
5 * that can be found in the LICENSE file in the root of the source
6 * tree. An additional intellectual property rights grant can be found
7 * in the file PATENTS. All contributing project authors may
8 * be found in the AUTHORS file in the root of the source tree.
9 */
10
11
12 /*
13 * This file contains the function WebRtcSpl_Sqrt().
14 * The description header can be found in signal_processing_library.h
15 *
16 */
17
18 #include "rtc_base/checks.h"
19 #include "common_audio/signal_processing/include/signal_processing_library.h"
20
21 int32_t WebRtcSpl_SqrtLocal(int32_t in);
22
WebRtcSpl_SqrtLocal(int32_t in)23 int32_t WebRtcSpl_SqrtLocal(int32_t in)
24 {
25
26 int16_t x_half, t16;
27 int32_t A, B, x2;
28
29 /* The following block performs:
30 y=in/2
31 x=y-2^30
32 x_half=x/2^31
33 t = 1 + (x_half) - 0.5*((x_half)^2) + 0.5*((x_half)^3) - 0.625*((x_half)^4)
34 + 0.875*((x_half)^5)
35 */
36
37 B = in / 2;
38
39 B = B - ((int32_t)0x40000000); // B = in/2 - 1/2
40 x_half = (int16_t)(B >> 16); // x_half = x/2 = (in-1)/2
41 B = B + ((int32_t)0x40000000); // B = 1 + x/2
42 B = B + ((int32_t)0x40000000); // Add 0.5 twice (since 1.0 does not exist in Q31)
43
44 x2 = ((int32_t)x_half) * ((int32_t)x_half) * 2; // A = (x/2)^2
45 A = -x2; // A = -(x/2)^2
46 B = B + (A >> 1); // B = 1 + x/2 - 0.5*(x/2)^2
47
48 A >>= 16;
49 A = A * A * 2; // A = (x/2)^4
50 t16 = (int16_t)(A >> 16);
51 B += -20480 * t16 * 2; // B = B - 0.625*A
52 // After this, B = 1 + x/2 - 0.5*(x/2)^2 - 0.625*(x/2)^4
53
54 A = x_half * t16 * 2; // A = (x/2)^5
55 t16 = (int16_t)(A >> 16);
56 B += 28672 * t16 * 2; // B = B + 0.875*A
57 // After this, B = 1 + x/2 - 0.5*(x/2)^2 - 0.625*(x/2)^4 + 0.875*(x/2)^5
58
59 t16 = (int16_t)(x2 >> 16);
60 A = x_half * t16 * 2; // A = x/2^3
61
62 B = B + (A >> 1); // B = B + 0.5*A
63 // After this, B = 1 + x/2 - 0.5*(x/2)^2 + 0.5*(x/2)^3 - 0.625*(x/2)^4 + 0.875*(x/2)^5
64
65 B = B + ((int32_t)32768); // Round off bit
66
67 return B;
68 }
69
WebRtcSpl_Sqrt(int32_t value)70 int32_t WebRtcSpl_Sqrt(int32_t value)
71 {
72 /*
73 Algorithm:
74
75 Six term Taylor Series is used here to compute the square root of a number
76 y^0.5 = (1+x)^0.5 where x = y-1
77 = 1+(x/2)-0.5*((x/2)^2+0.5*((x/2)^3-0.625*((x/2)^4+0.875*((x/2)^5)
78 0.5 <= x < 1
79
80 Example of how the algorithm works, with ut=sqrt(in), and
81 with in=73632 and ut=271 (even shift value case):
82
83 in=73632
84 y= in/131072
85 x=y-1
86 t = 1 + (x/2) - 0.5*((x/2)^2) + 0.5*((x/2)^3) - 0.625*((x/2)^4) + 0.875*((x/2)^5)
87 ut=t*(1/sqrt(2))*512
88
89 or:
90
91 in=73632
92 in2=73632*2^14
93 y= in2/2^31
94 x=y-1
95 t = 1 + (x/2) - 0.5*((x/2)^2) + 0.5*((x/2)^3) - 0.625*((x/2)^4) + 0.875*((x/2)^5)
96 ut=t*(1/sqrt(2))
97 ut2=ut*2^9
98
99 which gives:
100
101 in = 73632
102 in2 = 1206386688
103 y = 0.56176757812500
104 x = -0.43823242187500
105 t = 0.74973506527313
106 ut = 0.53014274874797
107 ut2 = 2.714330873589594e+002
108
109 or:
110
111 in=73632
112 in2=73632*2^14
113 y=in2/2
114 x=y-2^30
115 x_half=x/2^31
116 t = 1 + (x_half) - 0.5*((x_half)^2) + 0.5*((x_half)^3) - 0.625*((x_half)^4)
117 + 0.875*((x_half)^5)
118 ut=t*(1/sqrt(2))
119 ut2=ut*2^9
120
121 which gives:
122
123 in = 73632
124 in2 = 1206386688
125 y = 603193344
126 x = -470548480
127 x_half = -0.21911621093750
128 t = 0.74973506527313
129 ut = 0.53014274874797
130 ut2 = 2.714330873589594e+002
131
132 */
133
134 int16_t x_norm, nshift, t16, sh;
135 int32_t A;
136
137 int16_t k_sqrt_2 = 23170; // 1/sqrt2 (==5a82)
138
139 A = value;
140
141 // The convention in this function is to calculate sqrt(abs(A)). Negate the
142 // input if it is negative.
143 if (A < 0) {
144 if (A == WEBRTC_SPL_WORD32_MIN) {
145 // This number cannot be held in an int32_t after negating.
146 // Map it to the maximum positive value.
147 A = WEBRTC_SPL_WORD32_MAX;
148 } else {
149 A = -A;
150 }
151 } else if (A == 0) {
152 return 0; // sqrt(0) = 0
153 }
154
155 sh = WebRtcSpl_NormW32(A); // # shifts to normalize A
156 A = WEBRTC_SPL_LSHIFT_W32(A, sh); // Normalize A
157 if (A < (WEBRTC_SPL_WORD32_MAX - 32767))
158 {
159 A = A + ((int32_t)32768); // Round off bit
160 } else
161 {
162 A = WEBRTC_SPL_WORD32_MAX;
163 }
164
165 x_norm = (int16_t)(A >> 16); // x_norm = AH
166
167 nshift = (sh / 2);
168 RTC_DCHECK_GE(nshift, 0);
169
170 A = (int32_t)WEBRTC_SPL_LSHIFT_W32((int32_t)x_norm, 16);
171 A = WEBRTC_SPL_ABS_W32(A); // A = abs(x_norm<<16)
172 A = WebRtcSpl_SqrtLocal(A); // A = sqrt(A)
173
174 if (2 * nshift == sh) {
175 // Even shift value case
176
177 t16 = (int16_t)(A >> 16); // t16 = AH
178
179 A = k_sqrt_2 * t16 * 2; // A = 1/sqrt(2)*t16
180 A = A + ((int32_t)32768); // Round off
181 A = A & ((int32_t)0x7fff0000); // Round off
182
183 A >>= 15; // A = A>>16
184
185 } else
186 {
187 A >>= 16; // A = A>>16
188 }
189
190 A = A & ((int32_t)0x0000ffff);
191 A >>= nshift; // De-normalize the result.
192
193 return A;
194 }
195