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/*
* Copyright (c) 2011 The WebRTC project authors. All Rights Reserved.
*
* Use of this source code is governed by a BSD-style license
* that can be found in the LICENSE file in the root of the source
* tree. An additional intellectual property rights grant can be found
* in the file PATENTS. All contributing project authors may
* be found in the AUTHORS file in the root of the source tree.
*/
/*
* This file contains the function WebRtcSpl_Sqrt().
* The description header can be found in signal_processing_library.h
*
*/
#include "signal_processing_library.h"
WebRtc_Word32 WebRtcSpl_SqrtLocal(WebRtc_Word32 in);
WebRtc_Word32 WebRtcSpl_SqrtLocal(WebRtc_Word32 in)
{
WebRtc_Word16 x_half, t16;
WebRtc_Word32 A, B, x2;
/* The following block performs:
y=in/2
x=y-2^30
x_half=x/2^31
t = 1 + (x_half) - 0.5*((x_half)^2) + 0.5*((x_half)^3) - 0.625*((x_half)^4)
+ 0.875*((x_half)^5)
*/
B = in;
B = WEBRTC_SPL_RSHIFT_W32(B, 1); // B = in/2
B = B - ((WebRtc_Word32)0x40000000); // B = in/2 - 1/2
x_half = (WebRtc_Word16)WEBRTC_SPL_RSHIFT_W32(B, 16);// x_half = x/2 = (in-1)/2
B = B + ((WebRtc_Word32)0x40000000); // B = 1 + x/2
B = B + ((WebRtc_Word32)0x40000000); // Add 0.5 twice (since 1.0 does not exist in Q31)
x2 = ((WebRtc_Word32)x_half) * ((WebRtc_Word32)x_half) * 2; // A = (x/2)^2
A = -x2; // A = -(x/2)^2
B = B + (A >> 1); // B = 1 + x/2 - 0.5*(x/2)^2
A = WEBRTC_SPL_RSHIFT_W32(A, 16);
A = A * A * 2; // A = (x/2)^4
t16 = (WebRtc_Word16)WEBRTC_SPL_RSHIFT_W32(A, 16);
B = B + WEBRTC_SPL_MUL_16_16(-20480, t16) * 2; // B = B - 0.625*A
// After this, B = 1 + x/2 - 0.5*(x/2)^2 - 0.625*(x/2)^4
t16 = (WebRtc_Word16)WEBRTC_SPL_RSHIFT_W32(A, 16);
A = WEBRTC_SPL_MUL_16_16(x_half, t16) * 2; // A = (x/2)^5
t16 = (WebRtc_Word16)WEBRTC_SPL_RSHIFT_W32(A, 16);
B = B + WEBRTC_SPL_MUL_16_16(28672, t16) * 2; // B = B + 0.875*A
// After this, B = 1 + x/2 - 0.5*(x/2)^2 - 0.625*(x/2)^4 + 0.875*(x/2)^5
t16 = (WebRtc_Word16)WEBRTC_SPL_RSHIFT_W32(x2, 16);
A = WEBRTC_SPL_MUL_16_16(x_half, t16) * 2; // A = x/2^3
B = B + (A >> 1); // B = B + 0.5*A
// 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
B = B + ((WebRtc_Word32)32768); // Round off bit
return B;
}
WebRtc_Word32 WebRtcSpl_Sqrt(WebRtc_Word32 value)
{
/*
Algorithm:
Six term Taylor Series is used here to compute the square root of a number
y^0.5 = (1+x)^0.5 where x = y-1
= 1+(x/2)-0.5*((x/2)^2+0.5*((x/2)^3-0.625*((x/2)^4+0.875*((x/2)^5)
0.5 <= x < 1
Example of how the algorithm works, with ut=sqrt(in), and
with in=73632 and ut=271 (even shift value case):
in=73632
y= in/131072
x=y-1
t = 1 + (x/2) - 0.5*((x/2)^2) + 0.5*((x/2)^3) - 0.625*((x/2)^4) + 0.875*((x/2)^5)
ut=t*(1/sqrt(2))*512
or:
in=73632
in2=73632*2^14
y= in2/2^31
x=y-1
t = 1 + (x/2) - 0.5*((x/2)^2) + 0.5*((x/2)^3) - 0.625*((x/2)^4) + 0.875*((x/2)^5)
ut=t*(1/sqrt(2))
ut2=ut*2^9
which gives:
in = 73632
in2 = 1206386688
y = 0.56176757812500
x = -0.43823242187500
t = 0.74973506527313
ut = 0.53014274874797
ut2 = 2.714330873589594e+002
or:
in=73632
in2=73632*2^14
y=in2/2
x=y-2^30
x_half=x/2^31
t = 1 + (x_half) - 0.5*((x_half)^2) + 0.5*((x_half)^3) - 0.625*((x_half)^4)
+ 0.875*((x_half)^5)
ut=t*(1/sqrt(2))
ut2=ut*2^9
which gives:
in = 73632
in2 = 1206386688
y = 603193344
x = -470548480
x_half = -0.21911621093750
t = 0.74973506527313
ut = 0.53014274874797
ut2 = 2.714330873589594e+002
*/
WebRtc_Word16 x_norm, nshift, t16, sh;
WebRtc_Word32 A;
WebRtc_Word16 k_sqrt_2 = 23170; // 1/sqrt2 (==5a82)
A = value;
if (A == 0)
return (WebRtc_Word32)0; // sqrt(0) = 0
sh = WebRtcSpl_NormW32(A); // # shifts to normalize A
A = WEBRTC_SPL_LSHIFT_W32(A, sh); // Normalize A
if (A < (WEBRTC_SPL_WORD32_MAX - 32767))
{
A = A + ((WebRtc_Word32)32768); // Round off bit
} else
{
A = WEBRTC_SPL_WORD32_MAX;
}
x_norm = (WebRtc_Word16)WEBRTC_SPL_RSHIFT_W32(A, 16); // x_norm = AH
nshift = WEBRTC_SPL_RSHIFT_W16(sh, 1); // nshift = sh>>1
nshift = -nshift; // Negate the power for later de-normalization
A = (WebRtc_Word32)WEBRTC_SPL_LSHIFT_W32((WebRtc_Word32)x_norm, 16);
A = WEBRTC_SPL_ABS_W32(A); // A = abs(x_norm<<16)
A = WebRtcSpl_SqrtLocal(A); // A = sqrt(A)
if ((-2 * nshift) == sh)
{ // Even shift value case
t16 = (WebRtc_Word16)WEBRTC_SPL_RSHIFT_W32(A, 16); // t16 = AH
A = WEBRTC_SPL_MUL_16_16(k_sqrt_2, t16) * 2; // A = 1/sqrt(2)*t16
A = A + ((WebRtc_Word32)32768); // Round off
A = A & ((WebRtc_Word32)0x7fff0000); // Round off
A = WEBRTC_SPL_RSHIFT_W32(A, 15); // A = A>>16
} else
{
A = WEBRTC_SPL_RSHIFT_W32(A, 16); // A = A>>16
}
A = A & ((WebRtc_Word32)0x0000ffff);
A = (WebRtc_Word32)WEBRTC_SPL_SHIFT_W32(A, nshift); // De-normalize the result
return A;
}
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