Fixed-point IIR Filter Code Generator for ARM

Jordan November 30, 2010 Coded in ASM for the ARM

This is a fixed-point IIR filtering routine written in ARM assembly. We also provide an online tool that takes a Matlab coefficient file as input and generates a source file, header file, and example code as output. The code generator also works on FIR filters.

Detailed writeup and tutorial: http://ieee.ucsd.edu/wiki/tutorials:fixed_point_filtering_library

Online Code Generator: http://ieee.ucsd.edu/projects/qfilt/

Note that while the example below has a lowpass filter response, the code can be used with any filter response by changing the coefficients.

The detailed writeup also contains flavors written in C and C++. The C version is the most versatile, but uses more memory and instructions than the C++ or ARM version. The C++ version uses templates to eliminate a few pointers and constants by evaluating them at compile time. The hand-written ARM assembly version is the fastest and most memory efficient, and leverages the smlal 64-bit single cycle multiply accumulate instruction.

/* 
 * fixedp lowpass_iir(fixedp *w, fixedp x);
 *
 * Fixed point IIR filtering routine for ARM. Computes output y for
 * input x. The output will have the same fracbits as the input.
 *  w: caller-allocated array for state storage. Should be length 2*L.
 *  x: sample to filter
 * 
 * Required data:
 *   LENGTH: number of sections
 *   .sos: sos matrix
 *   SOS_FRACBITS: sos fracbits
 *   .gain: scale values array
 *   G_FRACBITS: scale values fracbits
 *   
 * Register usage:
 *   r0: address of internal state array (w)
 *   r1: x
 *   r2: address of SOS array
 *   r3: address of gain array
 *   r4: w0
 *   r5: w1
 *   r6: y
 *   r7: long multiply lo word
 *   r8: long multiply hi word
 *   r9:  B1
 *   r10: B2
 *   r11: A1
 *   r12: A2
 *   r14: loop counter
 */

.set LENGTH,  3
.set SOS_FRACBITS,  30
.set G_FRACBITS,  31

.section .rodata
.align 4

.sos:
    .word 0x49be7eaf, 0x40000000, 0xc4c9d93a, 0x251f228c
    .word 0x1d81c8a5, 0x40000000, 0xdaa0b600, 0x37cef3c1
    .word 0x40000000, 0x00000000, 0xd87b730c, 0x00000000

.gain:

    .word 0x06b1dbb5, 0x42fe27a0, 0x613d5d5a

.text
.arm

.global	lowpass_iir
.func   lowpass_iir
lowpass_iir:
	push {r4-r11, lr}

	mov  r14, #0								/* i = 0 */
	ldr  r2, =.sos								/* load address of SOS matrix */
	ldr  r3, =.gain								/* load address of gain coefficient array */

	cmp  r14, #LENGTH
	bge  .endloop

.loop:
	/* load all the SOS coefficients we need into r8-r12 and increment the SOS pointer */
	ldmia r2!, {r9-r12}							/* B1, B2, A1, A2 */

	/* x = gain[i]*x */
	ldr    r6, [r3], #4							/* load current element of gain array into r6 and increment by 4 */
	smull  r7, r8, r1, r6						/* 64-bit multiply: r5:r4 = x*gain[i]; */
	mov    r1, r7, lsr#G_FRACBITS				/* shift lo word to the right by G_FRACBITS */
	orr    r1, r1, r8, lsl#(32 - G_FRACBITS)		/* shift hi word to the right by G_FRACBITS  and OR with lo word*/

	/* load w0 and w1 into r4, r5, but do NOT increment */
	ldm    r0, {r4-r5}

	/* y(r6) = x(r1) + w[W0](r4)*/
	add r6, r1, r4

	/* w0(r4) = .sos[B1](r9)*x(r1) - .sos[A1](r11)*y(r6) + w[W1](r5); */
	rsb    r11, r11, #0							/* .sos[A1] = -sos[A1] */
	smull  r7, r8, r9, r1						/* r8:r7 = sos[B1]*x */
	smlal  r7, r8, r11, r6						/* r8:r7 += -sos[A1]*y */
	mov    r4, r7, lsr#SOS_FRACBITS				/* shift lo word to the right by SOS_FRACBITS */
	orr    r4, r4, r8, lsl#(32 - SOS_FRACBITS)	/* shift hi word to the right by SOS_FRACBITS and OR with lo word*/
	add    r4, r4, r5							/* add w1 */

	/* w2 = sos[B2]*x(r1) - .sos[A2](r12)*y(r6); */
	rsb    r12, r12, #0							/* .sos[A2] = -sos[A2] */
	smull  r7, r8, r10, r1                      /* r8:r7 = sos[B2](r10)*x(r1) */
	smlal  r7, r8, r12, r6						/* r8:r7 += -sos[A2](r12)*y(r6) */
	mov    r5, r7, lsr#SOS_FRACBITS				/* shift lo word to the right by SOS_FRACBITS */
	orr    r5, r5, r8, lsl#(32 - SOS_FRACBITS)	/* shift hi word to the right by SOS_FRACBITS and OR with lo word*/

	/* need to store w0, w1 back to memory and increment */
	stmia r0!, {r4-r5}

	/* x = y */
	mov    r1, r6

	/* increment pointer and branch to top of loop */
	add r14, r14, #1
	cmp r14, #LENGTH
	blt   .loop

.endloop:
	/* set return val, restore stack, and return */
	mov r0, r6
	pop {r4-r11, lr}
	bx  lr

.endfunc
.end

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