📄 cfftr2.asm
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*===============================================================================
*
* TEXAS INSTRUMENTS, INC.
*
* RADIX-2 FFT (DIT)
*
* Revision Date: 5/21/98
*
* USAGE
*
* This routine is C Callable and can be called as:
*
* void cfftr2_dit( float *x, const float *w, short N)
*
* x Pointer to Array of Dimension 2*N elements holding
* Input to and Outputs from function cfftr2_dit()
* w Pointer to an array holding the coefficient (Dimension
* n/2 complex numbers)
* N Number of complex points in x
*
* If routine is not to be used as a C callable function then
* you need to initialize values for all of the values passed
* as these are assumed to be in registers as defined by the
* calling convention of the compiler, (refer to the C compiler
* reference guide).
*
* ARGUMENTS PASSED -> REGISTER
* ---------------------------------
* x -> A4
* w -> B4
* N -> A6
*
* C CODE
*
* This is the C equivalent of the assembly code. Note that
* the assembly code is hand optimized and restrictions may
* apply.
*
* void cfftr2_dit(float* x, float* w, short n)
* {
* short n2, ie, ia, i, j, k, m;
* float rtemp, itemp, c, s;
*
* n2 = n;
* ie = 1;
*
* for(k=n; k > 1; k >>= 1)
* {
* n2 >>= 1;
* ia = 0;
* for(j=0; j < ie; j++)
* {
* c = w[2*j];
* s = w[2*j+1];
* for(i=0; i < n2; i++)
* {
* m = ia + n2;
* rtemp = c * x[2*m] + s * x[2*m+1];
* itemp = c * x[2*m+1] - s * x[2*m];
* x[2*m] = x[2*ia] - rtemp;
* x[2*m+1] = x[2*ia+1] - itemp;
* x[2*ia] = x[2*ia] + rtemp;
* x[2*ia+1] = x[2*ia+1] + itemp;
* ia++;
* }
* ia += n2;
* }
* ie <<= 1;
* }
* }
*
*
* DESCRIPTION
*
* This routine performs the Decimation-in-Time (DIT) Radix-2 FFT
* of the input array x.
* x has N complex floating point numbers arranged as successive
* real and imaginary number pairs. Input array x contains N
* complex points (N*2 elements). The coefficients for the
* FFT are passed to the function in array w which contains
* N/2 complex numbers (N elements) as successive real and
* imaginary number pairs.
* The FFT Coefficients w are in N/2 bit-reversed order
* The elements of input array x are in normal order
* The assembly routine performs 4 output samples (2 real and 2
* imaginary) for a pass through inner loop.
*
* Note that (bit-reversed) coefficients for higher order FFT (1024
* point) can be used unchanged as coefficients for a lower order
* FFT (512, 256, 128 ... ,2)
*
* The routine can be used to implement Inverse-FFT by any ONE of
* the following methods:
*
* 1.Inputs (x) are replaced by their Complex-conjugate values
* Output values are divided by N
* 2.FFT Coefficients (w) are replaced by their Complex-conjugates
* Output values are divided by N
* 3.Swap Real and Imaginary values of input
* 4.Swap Real and Imaginary values of output
*
* TECHNIQUES
*
* 1. The inner two loops are combined into one inner loop whose
* loop count is N/2.
* 2. The first 4 cycles of inner loop prolog are scheduled in
* parallel with the outer loop.
* 3. Load counter is not used, so extreneous loads are performed
* 4. Variables n and c share the register A6 and variables w and
* nsave share the register B4.
*
* ASSUMPTIONS
*
* N is a integral power of 2 (4, 8,16,32 ...) and the FFT
* dimension (N) must atleast be 4.
* The FFT Coefficients w are in bit-reversed order
* The elements of input array x are in normal order
* The imaginary coefficients of w are negated as {cos(d*0),
* sin(d*0), cos(d*1), sin(d*1) ...} as opposed to the normal
* sequence of {cos(d*0), -sin(d*0), cos(d*1), -sin(d*1) ...}
* where d = 2*PI/N.
*
* MEMORY NOTE
*
* Arrays x (data) and w (coefficients) must reside in
* different memory banks to avoid memory conflicts. If Data and
* Coefficents do reside in the same memory bank, add (N/2) + log2(N) + 1
* cycles to the cycles equation below. The memory bank hits are due to
* scheduling of assembly code and also due to extreneous loads
* causing bank hits.
*
* Data and Coefficents must be aligned on an 8 byte boundary.
*
* CYCLES
*
* ((2*N) + 23)*log2(N) + 6
*
* For N=1024, Cycles = 20716
*
* NOTATIONS
*
* f = Function Prolog or Epilog
* o = Outer Loop
* p = Inner Loop Prolog
*
*===============================================================================
.global _cfftr2_dit
.text
_cfftr2_dit:
STW .D2T2 B14,*B15--(48)
STW .D2T2 B3,*+B15(4)
STW .D2T1 A10,*+B15(8)
STW .D2T1 A11,*+B15(12)
STW .D2T1 A12,*+B15(16)
STW .D2T1 A13,*+B15(20)
STW .D2T1 A14,*+B15(24)
STW .D2T1 A15,*+B15(28)
STW .D2T2 B10,*+B15(32)
STW .D2T2 B11,*+B15(36)
STW .D2T2 B12,*+B15(40)
STW .D2T2 B13,*+B15(44)
* Begin Benchmark Timing
ADDAW .D1 A4,A6,A3 ; f xx2 = x + n*4
|| MV .L2 B4,B12 ; f wsave = w
|| SHRU .S2X A6,1,B4 ; f nsave = n>>1
|| MV .L1X B4,A5 ; f w1 = w
|| MVK .S1 1,A14 ; f onea = 1
MV .S2X A3,B8 ; f xx1 = xx2
|| MV .L2 B4,B0 ; f i = nsave
|| SHL .S1 A6,2,A10 ; f k1 = n<<2
LDDW .D2 *B8++,B7:B6 ; p @ t2_1:t2_0 = *xx1++
|| LDDW .D1 *A5++,A7:A6 ; p @ s:c = *w1
|| MPY .M2 B0,1,B13 ; f ireset = i*1
|| ADD .L2X A6,1,B9 ; f bk = n+1
|| MV .S2 B8,B5 ; f xx3 = xx1
MV .L1 A4,A11 ; f xx4 = x
|| SHL .S2X A6,2,B1 ; f k = n * 4
MV .L1X B9,A0 ; f bk1 = bk
||[B0] SUB .L2 B0,1,B0 ; p if (i) i = i-1
|| MV .S1 A4,A3 ; f xx2 = x
|| MVK .S2 1,B14 ; f oneb = 1
[!B0] ADD .L2 B8,B1,B8 ; p if (!i) xx1 = xx1 + k
|| MV .S2 B13,B2 ; f t3_ctr = ireset
|| MV .L1X B13,A1 ; f st_ctr = ireset
oloop:
LDDW .D2 *B8++,B7:B6 ; p @@ t2_1:t2_0 = *xx1++
||[!B0] LDDW .D1 *A5++,A7:A6 ; p @@ if (!i) s:c = *w1
||[!B0] MPY .M2 B14,B13,B0 ; p if (!i) i = ireset*1
MPYSP .M1X A6,B6,A13 ; p rtemp2 = c*t2_0
|| MPYSP .M2X A6,B7,B11 ; p itemp2 = c*t2_1
[B0] SUB .S2 B0,1,B0 ; p if (i) i = i-1
|| SUB .L1X B4,1,A2 ; f l = nsave - 1
MPYSP .M1X A7,B7,A15 ; p rtemp3 = s*t2_1
|| MPYSP .M2X A7,B6,B3 ; p itemp3 = s*t2_0
||[!B0] ADD .L2 B8,B1,B8 ; p if (!i) xx1 = xx1 + k
LDDW .D2 *B8++,B7:B6 ; p @@@ t2_1:t2_0 = *xx1++
||[!B0] LDDW .D1 *A5++,A7:A6 ; p @@@ if (!i) s:c = *w1
||[!B0] MPY .M2 B14,B13,B0 ; p if (!i) i = ireset*1
MPYSP .M1X A6,B6,A13 ; p rtemp2 = c*t2_0
|| MPYSP .M2X A6,B7,B11 ; p itemp2 = c*t2_1
[B0] SUB .S2 B0,1,B0 ; p if (i) i = i-1
LDDW .D1 *A3++,A9:A8 ; p @ t3_1:t3_0 = *xx2++
|| MPYSP .M1X A7,B7,A15 ; p rtemp3 = s*t2_1
|| MPYSP .M2X A7,B6,B3 ; p itemp3 = s*t2_0
||[!B0] ADD .D2 B8,B1,B8 ; p if (!i) xx1 = xx1 + k
|| ADDSP .L1 A13,A15,A12 ; p rtemp1 = rtemp2 + rtemp3
|| SUBSP .L2 B11,B3,B10 ; p itemp1 = itemp2 - itemp3
LDDW .D2 *B8++,B7:B6 ; p @@@@ t2_1:t2_0 = *xx1++
||[!B0] LDDW .D1 *A5++,A7:A6 ; p @@@@ if (!i) s:c = *w1
||[!B0] MPY .M2 B14,B13,B0 ; p if (!i) i = ireset*1
||[B2] SUB .S2 B2,1,B2 ; p if (t3_ctr) t3_ctr -= 1
MPYSP .M1X A6,B6,A13 ; p rtemp2 = c*t2_0
|| MPYSP .M2X A6,B7,B11 ; p itemp2 = c*t2_1
||[!B2] ADD .S1 A3,A10,A3 ; p if (!t3_ctr) xx2 = xx2 + k1
[B0] SUB .S2 B0,1,B0 ; p if (i) i = i-1
||[!B2] MPY .M2 B14,B13,B2 ; p if (!t3_ctr) t3_ctr = ireset*1
LDDW .D1 *A3++,A9:A8 ; p @@ t3_1:t3_0 = *xx2++
|| MPYSP .M1X A7,B7,A15 ; p rtemp3 = s*t2_1
|| MPYSP .M2X A7,B6,B3 ; p itemp3 = s*t2_0
||[!B0] ADD .D2 B8,B1,B8 ; p if (!i) xx1 = xx1 + k
|| ADDSP .L1 A13,A15,A12 ; p rtemp1 = rtemp2 + rtemp3
|| SUBSP .L2 B11,B3,B10 ; p itemp1 = itemp2 - itemp3
LDDW .D2 *B8++,B7:B6 ; p @@@@@ t2_1:t2_0 = *xx1++
||[!B0] LDDW .D1 *A5++,A7:A6 ; p @@@@@ if (!i) s:c = *w1
||[!B0] MPY .M2 B14,B13,B0 ; p if (!i) i = ireset*1
||[B2] SUB .S2 B2,1,B2 ; p if (t3_ctr) t3_ctr -= 1
|| SUBSP .L1 A8,A12,A15 ; p rtemp3 = t3_0 - rtemp1
|| SUBSP .L2X A9,B10,B3 ; p itemp3 = t3_1 - itemp1
MPYSP .M1X A6,B6,A13 ; p rtemp2 = c*t2_0
|| MPYSP .M2X A6,B7,B11 ; p itemp2 = c*t2_1
||[!B2] ADD .S1 A3,A10,A3 ; p if (!t3_ctr) xx2 = xx2 + k1
|| B .S2 iloop
[B0] SUB .S2 B0,1,B0 ; p if (i) i = i-1
||[!B2] MPY .M2 B14,B13,B2 ; p if (!t3_ctr) t3_ctr =ireset*1
|| ADDSP .L1 A8,A12,A15 ; p rtemp3 = t3_0 + rtemp1
|| ADDSP .L2X A9,B10,B3 ; p itemp3 = t3_1 + itemp1
; Kernel Loop Begins
iloop:
LDDW .D1 *A3++,A9:A8 ; @@@ t3_1:t3_0 = *xx2++
|| MPYSP .M1X A7,B7,A15 ; rtemp3 = s*t2_1
|| MPYSP .M2X A7,B6,B3 ; itemp3 = s*t2_0
||[!B0] ADD .D2 B8,B1,B8 ; if (!i) xx1 = xx1 + k
|| ADDSP .L1 A13,A15,A12 ; rtemp1 = rtemp2 + rtemp3
|| SUBSP .L2 B11,B3,B10 ; itemp1 = itemp2 - itemp3
||[!A1] ADD .S2 B5,B1,B5 ; if (!st_ctr) xx3 = xx3 + k
||[!A1] ADD .S1 A11,A10,A11 ; if (!st_ctr) xx4 = xx4 + k1
LDDW .D2 *B8++,B7:B6 ; @@@@@@ t2_1:t2_0 = *xx1++
||[!B0] LDDW .D1 *A5++,A7:A6 ; @@@@@@ if (!i) s:c = *w1
||[!B0] MPY .M2 B14,B13,B0 ; if (!i) i = ireset*1
||[B2] SUB .S2 B2,1,B2 ; if (t3_ctr) t3_ctr -= 1
|| SUBSP .L1 A8,A12,A15 ; rtemp3 = t3_0 - rtemp1
|| SUBSP .L2X A9,B10,B3 ; itemp3 = t3_1 - itemp1
||[A2] SUB .S1 A2,1,A2 ; if (l) l = l-1
||[!A1] MPY .M1X A14,B13,A1 ; if (!st_ctr) st_ctr = ireset*1
MPYSP .M1X A6,B6,A13 ; rtemp2 = c*t2_0
|| MPYSP .M2X A6,B7,B11 ; itemp2 = c*t2_1
||[!B2] ADD .S1 A3,A10,A3 ; if (!t3_ctr) xx2 = xx2 + k1
||[A2] B .S2 iloop ; Branch iloop
|| STW .D2T1 A15,*B5++[2] ; *xx3++[2] = rtemp3
|| STW .D1T2 B3,*+A11[A0] ; *+xx4[bk1] = itemp3
[B0] SUB .S2 B0,1,B0 ; if (i) i = i-1
||[!B2] MPY .M2 B14,B13,B2 ; if (!t3_ctr) t3_ctr = ireset*1
|| ADDSP .L1 A8,A12,A15 ; rtemp3 = t3_0 + rtemp1
|| ADDSP .L2X A9,B10,B3 ; itemp3 = t3_1 + itemp1
|| STW .D1 A15,*A11++[2] ; *xx4++[2] = rtemp3
|| STW .D2 B3,*-B5[B9] ; *-xx3[bk] = itemp3
||[A1] SUB .S1 A1,1,A1 ; if (st_ctr) st_ctr=st_ctr-1
; Kernel Loop Ends
MV .S2 B13,B1 ; o k = ireset
|| MV .S1X B13,A2 ; o l = ireset
SUB .S1X B1,1,A2 ; o l = k - 1
|| SHRU .S2 B13,1,B0 ; o i = ireset>>1
|| ADDAW .D1 A4,A2,A3 ; o xx2 = x + 4*l
[A2] B .S1 oloop
||[!A2] LDW .D2 *+B15(4),B3 ; o if (!l) pop B3
|| MV .S2X A3,B8 ; o xx1 = xx2
MV .L1X B12,A5 ; o w1 = wsave
||[!A2] LDDW .D2T1 *+B15(8),A11:A10; o if (!l) pop A11:A10
[A2] LDDW .D2 *B8++,B7:B6 ; p @ if (l) t2_1:t2_0 = *xx1++
||[A2] LDDW .D1 *A5++,A7:A6 ; p @ if (l) s:c = *w1
|| SHL .S1X B1,2,A10 ; f k1 = k<<2
|| MPY .M2 B0,1,B13 ; f ireset = i*1
|| ADD .L2 B1,1,B9 ; f bk = k + 1
MV .L1 A4,A11 ; f xx4 = x
|| SHL .S2 B1,2,B1 ; f k = k<<2
|| MV .L2X A3,B5 ; f xx3 = xx2
||[!A2] LDDW .D2T1 *+B15(16),A13:A12; o if (!l) pop A13:A12
MV .L1X B9,A0 ; f bk1 = bk
||[B0] SUB .L2 B0,1,B0 ; p if (i) i = i - 1
|| MV .S1 A4,A3 ; f xx2 = x
||[!A2] LDDW .D2T1 *+B15(24),A15:A14; o if (!l) pop A15:A14
[!B0] ADD .L2 B8,B1,B8 ; p if (!i) xx1 = xx1 + k
|| MV .S2 B13,B2 ; f t3_ctr = ireset
|| MV .L1X B13,A1 ; f st_ctr = ireset
||[!A2] LDDW .D2T2 *+B15(32),B11:B10; o if (!l) pop B11:B10
;-----------------------------------------------
* End Benchmark Timing
LDDW .D2T2 *+B15(40),B13:B12
|| B .S2 B3
LDW .D2T2 *++B15(48),B14
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