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