Rollback to working sqrt version.
git-svn-id: http://webrtc.googlecode.com/svn/trunk@154 4adac7df-926f-26a2-2b94-8c16560cd09d
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henrika@google.com
parent
d0159d8eb0
commit
dcdf311b6c
@ -53,6 +53,7 @@ LOCAL_SRC_FILES := add_sat_w16.c \
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resample_fractional.c \
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sin_table.c \
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sin_table_1024.c \
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spl_sqrt.c \
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spl_version.c \
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splitting_filter.c \
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sqrt_of_one_minus_x_squared.c \
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@ -60,14 +61,6 @@ LOCAL_SRC_FILES := add_sat_w16.c \
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sub_sat_w32.c \
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vector_scaling_operations.c
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ifeq ($(TARGET_ARCH), arm)
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LOCAL_SRC_FILES += \
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spl_sqrt.s
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else
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LOCAL_SRC_FILES += \
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spl_sqrt.c
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endif
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# Flags passed to both C and C++ files.
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MY_CFLAGS :=
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MY_CFLAGS_C :=
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@ -8,6 +8,7 @@
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* be found in the AUTHORS file in the root of the source tree.
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*/
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/*
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* This file contains the function WebRtcSpl_Sqrt().
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* The description header can be found in signal_processing_library.h
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@ -16,23 +17,168 @@
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#include "signal_processing_library.h"
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#define iter1(N) \
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try1 = root + (1 << (N)); \
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if (value >= try1 << (N)) \
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{ \
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value -= try1 << (N); \
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root |= 2 << (N); \
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}
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WebRtc_Word32 WebRtcSpl_SqrtLocal(WebRtc_Word32 in);
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// (out) Square root of input parameter
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WebRtc_Word32 WebRtcSpl_Sqrt(WebRtc_Word32 value) {
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// new routine for performance, 4 cycles/bit in ARM
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// output precision is 16 bits
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WebRtc_Word32 WebRtcSpl_SqrtLocal(WebRtc_Word32 in)
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{
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WebRtc_Word32 root = 0, try1;
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iter1 (15); iter1 (14); iter1 (13); iter1 (12);
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iter1 (11); iter1 (10); iter1 ( 9); iter1 ( 8);
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iter1 ( 7); iter1 ( 6); iter1 ( 5); iter1 ( 4);
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iter1 ( 3); iter1 ( 2); iter1 ( 1); iter1 ( 0);
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return root >> 1;
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WebRtc_Word16 x_half, t16;
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WebRtc_Word32 A, B, x2;
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/* The following block performs:
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y=in/2
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x=y-2^30
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x_half=x/2^31
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t = 1 + (x_half) - 0.5*((x_half)^2) + 0.5*((x_half)^3) - 0.625*((x_half)^4)
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+ 0.875*((x_half)^5)
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*/
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B = in;
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B = WEBRTC_SPL_RSHIFT_W32(B, 1); // B = in/2
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B = B - ((WebRtc_Word32)0x40000000); // B = in/2 - 1/2
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x_half = (WebRtc_Word16)WEBRTC_SPL_RSHIFT_W32(B, 16);// x_half = x/2 = (in-1)/2
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B = B + ((WebRtc_Word32)0x40000000); // B = 1 + x/2
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B = B + ((WebRtc_Word32)0x40000000); // Add 0.5 twice (since 1.0 does not exist in Q31)
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x2 = ((WebRtc_Word32)x_half) * ((WebRtc_Word32)x_half) * 2; // A = (x/2)^2
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A = -x2; // A = -(x/2)^2
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B = B + (A >> 1); // B = 1 + x/2 - 0.5*(x/2)^2
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A = WEBRTC_SPL_RSHIFT_W32(A, 16);
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A = A * A * 2; // A = (x/2)^4
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t16 = (WebRtc_Word16)WEBRTC_SPL_RSHIFT_W32(A, 16);
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B = B + WEBRTC_SPL_MUL_16_16(-20480, t16) * 2; // B = B - 0.625*A
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// After this, B = 1 + x/2 - 0.5*(x/2)^2 - 0.625*(x/2)^4
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t16 = (WebRtc_Word16)WEBRTC_SPL_RSHIFT_W32(A, 16);
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A = WEBRTC_SPL_MUL_16_16(x_half, t16) * 2; // A = (x/2)^5
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t16 = (WebRtc_Word16)WEBRTC_SPL_RSHIFT_W32(A, 16);
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B = B + WEBRTC_SPL_MUL_16_16(28672, t16) * 2; // B = B + 0.875*A
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// After this, B = 1 + x/2 - 0.5*(x/2)^2 - 0.625*(x/2)^4 + 0.875*(x/2)^5
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t16 = (WebRtc_Word16)WEBRTC_SPL_RSHIFT_W32(x2, 16);
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A = WEBRTC_SPL_MUL_16_16(x_half, t16) * 2; // A = x/2^3
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B = B + (A >> 1); // B = B + 0.5*A
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// 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
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B = B + ((WebRtc_Word32)32768); // Round off bit
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return B;
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}
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WebRtc_Word32 WebRtcSpl_Sqrt(WebRtc_Word32 value)
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{
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/*
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Algorithm:
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Six term Taylor Series is used here to compute the square root of a number
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y^0.5 = (1+x)^0.5 where x = y-1
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= 1+(x/2)-0.5*((x/2)^2+0.5*((x/2)^3-0.625*((x/2)^4+0.875*((x/2)^5)
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0.5 <= x < 1
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Example of how the algorithm works, with ut=sqrt(in), and
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with in=73632 and ut=271 (even shift value case):
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in=73632
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y= in/131072
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x=y-1
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t = 1 + (x/2) - 0.5*((x/2)^2) + 0.5*((x/2)^3) - 0.625*((x/2)^4) + 0.875*((x/2)^5)
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ut=t*(1/sqrt(2))*512
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or:
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in=73632
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in2=73632*2^14
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y= in2/2^31
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x=y-1
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t = 1 + (x/2) - 0.5*((x/2)^2) + 0.5*((x/2)^3) - 0.625*((x/2)^4) + 0.875*((x/2)^5)
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ut=t*(1/sqrt(2))
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ut2=ut*2^9
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which gives:
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in = 73632
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in2 = 1206386688
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y = 0.56176757812500
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x = -0.43823242187500
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t = 0.74973506527313
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ut = 0.53014274874797
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ut2 = 2.714330873589594e+002
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or:
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in=73632
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in2=73632*2^14
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y=in2/2
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x=y-2^30
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x_half=x/2^31
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t = 1 + (x_half) - 0.5*((x_half)^2) + 0.5*((x_half)^3) - 0.625*((x_half)^4)
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+ 0.875*((x_half)^5)
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ut=t*(1/sqrt(2))
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ut2=ut*2^9
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which gives:
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in = 73632
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in2 = 1206386688
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y = 603193344
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x = -470548480
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x_half = -0.21911621093750
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t = 0.74973506527313
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ut = 0.53014274874797
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ut2 = 2.714330873589594e+002
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*/
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WebRtc_Word16 x_norm, nshift, t16, sh;
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WebRtc_Word32 A;
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WebRtc_Word16 k_sqrt_2 = 23170; // 1/sqrt2 (==5a82)
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A = value;
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if (A == 0)
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return (WebRtc_Word32)0; // sqrt(0) = 0
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sh = WebRtcSpl_NormW32(A); // # shifts to normalize A
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A = WEBRTC_SPL_LSHIFT_W32(A, sh); // Normalize A
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if (A < (WEBRTC_SPL_WORD32_MAX - 32767))
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{
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A = A + ((WebRtc_Word32)32768); // Round off bit
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} else
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{
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A = WEBRTC_SPL_WORD32_MAX;
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}
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x_norm = (WebRtc_Word16)WEBRTC_SPL_RSHIFT_W32(A, 16); // x_norm = AH
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nshift = WEBRTC_SPL_RSHIFT_W16(sh, 1); // nshift = sh>>1
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nshift = -nshift; // Negate the power for later de-normalization
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A = (WebRtc_Word32)WEBRTC_SPL_LSHIFT_W32((WebRtc_Word32)x_norm, 16);
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A = WEBRTC_SPL_ABS_W32(A); // A = abs(x_norm<<16)
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A = WebRtcSpl_SqrtLocal(A); // A = sqrt(A)
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if ((-2 * nshift) == sh)
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{ // Even shift value case
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t16 = (WebRtc_Word16)WEBRTC_SPL_RSHIFT_W32(A, 16); // t16 = AH
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A = WEBRTC_SPL_MUL_16_16(k_sqrt_2, t16) * 2; // A = 1/sqrt(2)*t16
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A = A + ((WebRtc_Word32)32768); // Round off
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A = A & ((WebRtc_Word32)0x7fff0000); // Round off
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A = WEBRTC_SPL_RSHIFT_W32(A, 15); // A = A>>16
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} else
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{
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A = WEBRTC_SPL_RSHIFT_W32(A, 16); // A = A>>16
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}
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A = A & ((WebRtc_Word32)0x0000ffff);
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A = (WebRtc_Word32)WEBRTC_SPL_SHIFT_W32(A, nshift); // De-normalize the result
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return A;
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}
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@ -1,93 +0,0 @@
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@
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@ Copyright (c) 2011 The WebRTC project authors. All Rights Reserved.
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@
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@ Use of this source code is governed by a BSD-style license
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@ that can be found in the LICENSE file in the root of the source
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@ tree. An additional intellectual property rights grant can be found
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@ in the file PATENTS. All contributing project authors may
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@ be found in the AUTHORS file in the root of the source tree.
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@ sqrt() routine. 3 cycles/bit, total 51 cycles.
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@ IN : r0 32 bit unsigned integer
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@ OUT: r0 = INT (SQRT (r0)), precision is 16 bits
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@ TMP: r1, r2
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.global WebRtcSpl_Sqrt
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.align 2
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.section .text.WebRtcSpl_Sqrt:
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WebRtcSpl_Sqrt:
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.fnstart
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MOV r1, #3 << 30
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MOV r2, #1 << 30
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@ unroll for i = 0 .. 15
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CMP r0, r2, ROR #2 * 0
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SUBHS r0, r0, r2, ROR #2 * 0
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ADC r2, r1, r2, LSL #1
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CMP r0, r2, ROR #2 * 1
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SUBHS r0, r0, r2, ROR #2 * 1
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ADC r2, r1, r2, LSL #1
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CMP r0, r2, ROR #2 * 2
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SUBHS r0, r0, r2, ROR #2 * 2
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ADC r2, r1, r2, LSL #1
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CMP r0, r2, ROR #2 * 3
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SUBHS r0, r0, r2, ROR #2 * 3
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ADC r2, r1, r2, LSL #1
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CMP r0, r2, ROR #2 * 4
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SUBHS r0, r0, r2, ROR #2 * 4
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ADC r2, r1, r2, LSL #1
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CMP r0, r2, ROR #2 * 5
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SUBHS r0, r0, r2, ROR #2 * 5
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ADC r2, r1, r2, LSL #1
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CMP r0, r2, ROR #2 * 6
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SUBHS r0, r0, r2, ROR #2 * 6
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ADC r2, r1, r2, LSL #1
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CMP r0, r2, ROR #2 * 7
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SUBHS r0, r0, r2, ROR #2 * 7
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ADC r2, r1, r2, LSL #1
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CMP r0, r2, ROR #2 * 8
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SUBHS r0, r0, r2, ROR #2 * 8
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ADC r2, r1, r2, LSL #1
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CMP r0, r2, ROR #2 * 9
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SUBHS r0, r0, r2, ROR #2 * 9
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ADC r2, r1, r2, LSL #1
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CMP r0, r2, ROR #2 * 10
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SUBHS r0, r0, r2, ROR #2 * 10
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ADC r2, r1, r2, LSL #1
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CMP r0, r2, ROR #2 * 11
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SUBHS r0, r0, r2, ROR #2 * 11
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ADC r2, r1, r2, LSL #1
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CMP r0, r2, ROR #2 * 12
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SUBHS r0, r0, r2, ROR #2 * 12
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ADC r2, r1, r2, LSL #1
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CMP r0, r2, ROR #2 * 13
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SUBHS r0, r0, r2, ROR #2 * 13
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ADC r2, r1, r2, LSL #1
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CMP r0, r2, ROR #2 * 14
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SUBHS r0, r0, r2, ROR #2 * 14
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ADC r2, r1, r2, LSL #1
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CMP r0, r2, ROR #2 * 15
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SUBHS r0, r0, r2, ROR #2 * 15
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ADC r2, r1, r2, LSL #1
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BIC r0, r2, #3 << 30 @ for rounding add: CMP r0, r2 ADC r2, #1
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.fnend
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