~ chicken-core (chicken-5) a2eee7ac4fa8053a0c444b4b94cf97f6ae997628
commit a2eee7ac4fa8053a0c444b4b94cf97f6ae997628
Author: unknown <felix@.(none)>
AuthorDate: Wed Nov 4 13:08:02 2009 +0100
Commit: unknown <felix@.(none)>
CommitDate: Wed Nov 4 13:08:02 2009 +0100
added Brad Luciers fft benchmark to test suite
diff --git a/tests/fft.scm b/tests/fft.scm
new file mode 100644
index 00000000..726ec292
--- /dev/null
+++ b/tests/fft.scm
@@ -0,0 +1,2071 @@
+(declare (standard-bindings)
+ (extended-bindings)
+ (block)
+ (not safe)
+ )
+
+;;; All the following redefinitions are *ignored* by the Gambit compiler
+;;; because of the declarations above.
+
+(cond-expand
+ (chicken
+ (begin
+ (use srfi-4)
+ (define-syntax defalias
+ (syntax-rules ()
+ ((_ one two)
+ (define-syntax one
+ (syntax-rules ()
+ ((_ . args) (two . args)))))))
+ (defalias fixnum->flonum exact->inexact)
+ (defalias fxodd? odd?)
+ (defalias fxeven? even?)
+ (defalias fxarithmetic-shift-right fxshr)
+ (defalias fxarithmetic-shift-left fxshl)
+ (defalias fl* fp*)
+ (defalias fl/ fp/)
+ (defalias fl+ fp+)
+ (defalias fl- fp-)
+ (defalias flsqrt sqrt)))
+ (else))
+
+(cond-expand
+ ((and chicken (not unboxed))
+ (begin
+ (defalias make-f64vector make-vector)
+ (defalias f64vector vector)
+ (defalias f64vector-set! vector-set!)
+ (defalias f64vector-ref vector-ref)
+ (defalias list->f64vector list->vector)
+ (defalias f64vector-length vector-length)) )
+ (else) )
+
+;;; end of *ignored* definitions
+
+(define lut-table-size 512)
+(define lut-table-size^2 262144)
+(define lut-table-size^3 134217728)
+(define log-lut-table-size 9)
+
+(define low-lut
+ (list->f64vector '(1. 0.
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+ .9999999999830838 5.816562283133429e-6
+ .9999999999830157 5.8282656277673675e-6
+ .9999999999829474 5.839968972401306e-6
+ .9999999999828789 5.851672317035243e-6
+ .9999999999828104 5.86337566166918e-6
+ .9999999999827417 5.875079006303115e-6
+ .9999999999826729 5.88678235093705e-6
+ .9999999999826039 5.898485695570985e-6
+ .9999999999825349 5.910189040204917e-6
+ .9999999999824656 5.92189238483885e-6
+ .9999999999823962 5.933595729472782e-6
+ .9999999999823267 5.945299074106713e-6
+ .9999999999822571 5.957002418740643e-6
+ .9999999999821872 5.9687057633745715e-6
+ .9999999999821173 5.9804091080085e-6
+ )))
+
+(define (make-w log-n)
+ (let ((n (expt 2 log-n))) ;; number of complexes
+ (if (fx<= n lut-table-size)
+ low-lut
+ (let ((result (make-f64vector (fx* 2 n))))
+
+ (define (copy-low-lut)
+ (do ((i 0 (fx+ i 1)))
+ ((fx= i lut-table-size))
+ (let ((index (fx* i 2)))
+ (f64vector-set!
+ result
+ index
+ (f64vector-ref low-lut index))
+ (f64vector-set!
+ result
+ (fx+ index 1)
+ (f64vector-ref low-lut (fx+ index 1))))))
+
+ (define (extend-lut multiplier-lut bit-reverse-size bit-reverse-multiplier start end)
+
+ (define (bit-reverse x n)
+ (declare (not interrupts-enabled))
+ (do ((i 0 (fx+ i 1))
+ (x x (fxarithmetic-shift-right x 1))
+ (result 0 (fx+ (fx* result 2)
+ (bitwise-and x 1))))
+ ((fx= i n) result)))
+
+ (let loop ((i start)
+ (j 1))
+ (if (fx< i end)
+ (let* ((multiplier-index
+ (fx* 2
+ (fx* (bit-reverse j bit-reverse-size)
+ bit-reverse-multiplier)))
+ (multiplier-real
+ (f64vector-ref multiplier-lut multiplier-index))
+ (multiplier-imag
+ (f64vector-ref multiplier-lut (fx+ multiplier-index 1))))
+ (let inner ((i i)
+ (k 0))
+ ;; we copy complex multiples of all entries below
+ ;; start to entries starting at start
+ (if (fx< k start)
+ (let* ((index
+ (fx* k 2))
+ (real
+ (f64vector-ref result index))
+ (imag
+ (f64vector-ref result (fx+ index 1)))
+ (result-real
+ (fl- (fl* multiplier-real real)
+ (fl* multiplier-imag imag)))
+ (result-imag
+ (fl+ (fl* multiplier-real imag)
+ (fl* multiplier-imag real)))
+ (result-index (fx* i 2)))
+ (f64vector-set! result result-index result-real)
+ (f64vector-set! result (fx+ result-index 1) result-imag)
+ (inner (fx+ i 1)
+ (fx+ k 1)))
+ (loop i
+ (fx+ j 1)))))
+ result)))
+
+ (cond ((fx<= n lut-table-size^2)
+ (copy-low-lut)
+ (extend-lut med-lut
+ (fx- log-n log-lut-table-size)
+ (fxarithmetic-shift-left 1 (fx- (fx* 2 log-lut-table-size) log-n))
+ lut-table-size
+ n))
+ ((fx<= n lut-table-size^3)
+ (copy-low-lut)
+ (extend-lut med-lut
+ log-lut-table-size
+ 1
+ lut-table-size
+ lut-table-size^2)
+ (extend-lut high-lut
+ (fx- log-n (fx* 2 log-lut-table-size))
+ (fxarithmetic-shift-left 1 (fx- (fx* 3 log-lut-table-size) log-n))
+ lut-table-size^2
+ n))
+ (else
+ (error "asking for too large a table")))))))
+
+(define (direct-fft-recursive-4 a W-table)
+
+ ;; This is a direcct complex fft, using a decimation-in-time
+ ;; algorithm with inputs in natural order and outputs in
+ ;; bit-reversed order. The table of "twiddle" factors is in
+ ;; bit-reversed order.
+
+ ;; this is from page 66 of Chu and George, except that we have
+ ;; combined passes in pairs to cut the number of passes through
+ ;; the vector a
+
+ (let ((W (f64vector 0. 0. 0. 0.)))
+
+ (define (main-loop M N K SizeOfGroup)
+
+ (let inner-loop ((K K)
+ (JFirst M))
+
+ (if (fx< JFirst N)
+
+ (let* ((JLast (fx+ JFirst SizeOfGroup)))
+
+ (if (fxeven? K)
+ (begin
+ (f64vector-set! W 0 (f64vector-ref W-table K))
+ (f64vector-set! W 1 (f64vector-ref W-table (fx+ K 1))))
+ (begin
+ (f64vector-set! W 0 (fl- 0. (f64vector-ref W-table K)))
+ (f64vector-set! W 1 (f64vector-ref W-table (fx- K 1)))))
+
+ ;; we know the that the next two complex roots of
+ ;; unity have index 2K and 2K+1 so that the 2K+1
+ ;; index root can be gotten from the 2K index root
+ ;; in the same way that we get W_0 and W_1 from the
+ ;; table depending on whether K is even or not
+
+ (f64vector-set! W 2 (f64vector-ref W-table (fx* K 2)))
+ (f64vector-set! W 3 (f64vector-ref W-table (fx+ (fx* K 2) 1)))
+
+ (let J-loop ((J0 JFirst))
+ (if (fx< J0 JLast)
+
+ (let* ((J0 J0)
+ (J1 (fx+ J0 1))
+ (J2 (fx+ J0 SizeOfGroup))
+ (J3 (fx+ J2 1))
+ (J4 (fx+ J2 SizeOfGroup))
+ (J5 (fx+ J4 1))
+ (J6 (fx+ J4 SizeOfGroup))
+ (J7 (fx+ J6 1)))
+
+ (let ((W_0 (f64vector-ref W 0))
+ (W_1 (f64vector-ref W 1))
+ (W_2 (f64vector-ref W 2))
+ (W_3 (f64vector-ref W 3))
+ (a_J0 (f64vector-ref a J0))
+ (a_J1 (f64vector-ref a J1))
+ (a_J2 (f64vector-ref a J2))
+ (a_J3 (f64vector-ref a J3))
+ (a_J4 (f64vector-ref a J4))
+ (a_J5 (f64vector-ref a J5))
+ (a_J6 (f64vector-ref a J6))
+ (a_J7 (f64vector-ref a J7)))
+
+ ;; first we do the (overlapping) pairs of
+ ;; butterflies with entries 2*SizeOfGroup
+ ;; apart.
+
+ (let ((Temp_0 (fl- (fl* W_0 a_J4)
+ (fl* W_1 a_J5)))
+ (Temp_1 (fl+ (fl* W_0 a_J5)
+ (fl* W_1 a_J4)))
+ (Temp_2 (fl- (fl* W_0 a_J6)
+ (fl* W_1 a_J7)))
+ (Temp_3 (fl+ (fl* W_0 a_J7)
+ (fl* W_1 a_J6))))
+
+ (let ((a_J0 (fl+ a_J0 Temp_0))
+ (a_J1 (fl+ a_J1 Temp_1))
+ (a_J2 (fl+ a_J2 Temp_2))
+ (a_J3 (fl+ a_J3 Temp_3))
+ (a_J4 (fl- a_J0 Temp_0))
+ (a_J5 (fl- a_J1 Temp_1))
+ (a_J6 (fl- a_J2 Temp_2))
+ (a_J7 (fl- a_J3 Temp_3)))
+
+ ;; now we do the two (disjoint) pairs
+ ;; of butterflies distance SizeOfGroup
+ ;; apart, the first pair with W2+W3i,
+ ;; the second with -W3+W2i
+
+ ;; we rewrite the multipliers so I
+ ;; don't hurt my head too much when
+ ;; thinking about them.
+
+ (let ((W_0 W_2)
+ (W_1 W_3)
+ (W_2 (fl- 0. W_3))
+ (W_3 W_2))
+
+ (let ((Temp_0
+ (fl- (fl* W_0 a_J2)
+ (fl* W_1 a_J3)))
+ (Temp_1
+ (fl+ (fl* W_0 a_J3)
+ (fl* W_1 a_J2)))
+ (Temp_2
+ (fl- (fl* W_2 a_J6)
+ (fl* W_3 a_J7)))
+ (Temp_3
+ (fl+ (fl* W_2 a_J7)
+ (fl* W_3 a_J6))))
+
+ (let ((a_J0 (fl+ a_J0 Temp_0))
+ (a_J1 (fl+ a_J1 Temp_1))
+ (a_J2 (fl- a_J0 Temp_0))
+ (a_J3 (fl- a_J1 Temp_1))
+ (a_J4 (fl+ a_J4 Temp_2))
+ (a_J5 (fl+ a_J5 Temp_3))
+ (a_J6 (fl- a_J4 Temp_2))
+ (a_J7 (fl- a_J5 Temp_3)))
+
+ (f64vector-set! a J0 a_J0)
+ (f64vector-set! a J1 a_J1)
+ (f64vector-set! a J2 a_J2)
+ (f64vector-set! a J3 a_J3)
+ (f64vector-set! a J4 a_J4)
+ (f64vector-set! a J5 a_J5)
+ (f64vector-set! a J6 a_J6)
+ (f64vector-set! a J7 a_J7)
+
+ (J-loop (fx+ J0 2)))))))))
+ (inner-loop (fx+ K 1)
+ (fx+ JFirst (fx* SizeOfGroup 4)))))))))
+
+ (define (recursive-bit M N K SizeOfGroup)
+ (if (fx<= 2 SizeOfGroup)
+ (begin
+ (main-loop M N K SizeOfGroup)
+ (if (fx< 2048 (fx- N M))
+ (let ((new-size (fxarithmetic-shift-right (fx- N M) 2)))
+ (recursive-bit M
+ (fx+ M new-size)
+ (fx* K 4)
+ (fxarithmetic-shift-right SizeOfGroup 2))
+ (recursive-bit (fx+ M new-size)
+ (fx+ M (fx* new-size 2))
+ (fx+ (fx* K 4) 1)
+ (fxarithmetic-shift-right SizeOfGroup 2))
+ (recursive-bit (fx+ M (fx* new-size 2))
+ (fx+ M (fx* new-size 3))
+ (fx+ (fx* K 4) 2)
+ (fxarithmetic-shift-right SizeOfGroup 2))
+ (recursive-bit (fx+ M (fx* new-size 3))
+ N
+ (fx+ (fx* K 4) 3)
+ (fxarithmetic-shift-right SizeOfGroup 2)))
+ (recursive-bit M
+ N
+ (fx* K 4)
+ (fxarithmetic-shift-right SizeOfGroup 2))))))
+
+ (define (radix-2-pass a)
+
+ ;; If we're here, the size of our (conceptually complex)
+ ;; array is not a power of 4, so we need to do a basic radix
+ ;; two pass with w=1 (so W[0]=1.0 and W[1] = 0.) and then
+ ;; call recursive-bit appropriately on the two half arrays.
+
+ (declare (not interrupts-enabled))
+
+ (let ((SizeOfGroup
+ (fxarithmetic-shift-right (f64vector-length a) 1)))
+ (let loop ((J0 0))
+ (if (fx< J0 SizeOfGroup)
+ (let ((J0 J0)
+ (J2 (fx+ J0 SizeOfGroup)))
+ (let ((J1 (fx+ J0 1))
+ (J3 (fx+ J2 1)))
+ (let ((a_J0 (f64vector-ref a J0))
+ (a_J1 (f64vector-ref a J1))
+ (a_J2 (f64vector-ref a J2))
+ (a_J3 (f64vector-ref a J3)))
+ (let ((a_J0 (fl+ a_J0 a_J2))
+ (a_J1 (fl+ a_J1 a_J3))
+ (a_J2 (fl- a_J0 a_J2))
+ (a_J3 (fl- a_J1 a_J3)))
+ (f64vector-set! a J0 a_J0)
+ (f64vector-set! a J1 a_J1)
+ (f64vector-set! a J2 a_J2)
+ (f64vector-set! a J3 a_J3)
+ (loop (fx+ J0 2))))))))))
+
+ (let* ((n (f64vector-length a))
+ (log_n (two^p>=m n)))
+
+ ;; there are n/2 complex entries in a; if n/2 is not a power
+ ;; of 4, then do a single radix-2 pass and do the rest of
+ ;; the passes as radix-4 passes
+
+ (if (fxodd? log_n)
+ (recursive-bit 0 n 0 (fxarithmetic-shift-right n 2))
+ (let ((n/2 (fxarithmetic-shift-right n 1))
+ (n/8 (fxarithmetic-shift-right n 3)))
+ (radix-2-pass a)
+ (recursive-bit 0 n/2 0 n/8)
+ (recursive-bit n/2 n 1 n/8))))))
+
+(define (inverse-fft-recursive-4 a W-table)
+
+ ;; This is an complex fft, using a decimation-in-frequency algorithm
+ ;; with inputs in bit-reversed order and outputs in natural order.
+
+ ;; The organization of the algorithm has little to do with the the
+ ;; associated algorithm on page 41 of Chu and George,
+ ;; I just reversed the operations of the direct algorithm given
+ ;; above (without dividing by 2 each time, so that this has to
+ ;; be "normalized" by dividing by N/2 at the end.
+
+ ;; The table of "twiddle" factors is in bit-reversed order.
+
+ (let ((W (f64vector 0. 0. 0. 0.)))
+
+ (define (main-loop M N K SizeOfGroup)
+ (let inner-loop ((K K)
+ (JFirst M))
+ (if (fx< JFirst N)
+ (let* ((JLast (fx+ JFirst SizeOfGroup)))
+ (if (fxeven? K)
+ (begin
+ (f64vector-set! W 0 (f64vector-ref W-table K))
+ (f64vector-set! W 1 (f64vector-ref W-table (fx+ K 1))))
+ (begin
+ (f64vector-set! W 0 (fl- 0. (f64vector-ref W-table K)))
+ (f64vector-set! W 1 (f64vector-ref W-table (fx- K 1)))))
+ (f64vector-set! W 2 (f64vector-ref W-table (fx* K 2)))
+ (f64vector-set! W 3 (f64vector-ref W-table (fx+ (fx* K 2) 1)))
+ (let J-loop ((J0 JFirst))
+ (if (fx< J0 JLast)
+ (let* ((J0 J0)
+ (J1 (fx+ J0 1))
+ (J2 (fx+ J0 SizeOfGroup))
+ (J3 (fx+ J2 1))
+ (J4 (fx+ J2 SizeOfGroup))
+ (J5 (fx+ J4 1))
+ (J6 (fx+ J4 SizeOfGroup))
+ (J7 (fx+ J6 1)))
+ (let ((W_0 (f64vector-ref W 0))
+ (W_1 (f64vector-ref W 1))
+ (W_2 (f64vector-ref W 2))
+ (W_3 (f64vector-ref W 3))
+ (a_J0 (f64vector-ref a J0))
+ (a_J1 (f64vector-ref a J1))
+ (a_J2 (f64vector-ref a J2))
+ (a_J3 (f64vector-ref a J3))
+ (a_J4 (f64vector-ref a J4))
+ (a_J5 (f64vector-ref a J5))
+ (a_J6 (f64vector-ref a J6))
+ (a_J7 (f64vector-ref a J7)))
+ (let ((W_00 W_2)
+ (W_01 W_3)
+ (W_02 (fl- 0. W_3))
+ (W_03 W_2))
+ (let ((Temp_0 (fl- a_J0 a_J2))
+ (Temp_1 (fl- a_J1 a_J3))
+ (Temp_2 (fl- a_J4 a_J6))
+ (Temp_3 (fl- a_J5 a_J7)))
+ (let ((a_J0 (fl+ a_J0 a_J2))
+ (a_J1 (fl+ a_J1 a_J3))
+ (a_J4 (fl+ a_J4 a_J6))
+ (a_J5 (fl+ a_J5 a_J7))
+ (a_J2 (fl+ (fl* W_00 Temp_0)
+ (fl* W_01 Temp_1)))
+ (a_J3 (fl- (fl* W_00 Temp_1)
+ (fl* W_01 Temp_0)))
+ (a_J6 (fl+ (fl* W_02 Temp_2)
+ (fl* W_03 Temp_3)))
+ (a_J7 (fl- (fl* W_02 Temp_3)
+ (fl* W_03 Temp_2))))
+ (let ((Temp_0 (fl- a_J0 a_J4))
+ (Temp_1 (fl- a_J1 a_J5))
+ (Temp_2 (fl- a_J2 a_J6))
+ (Temp_3 (fl- a_J3 a_J7)))
+ (let ((a_J0 (fl+ a_J0 a_J4))
+ (a_J1 (fl+ a_J1 a_J5))
+ (a_J2 (fl+ a_J2 a_J6))
+ (a_J3 (fl+ a_J3 a_J7))
+ (a_J4 (fl+ (fl* W_0 Temp_0)
+ (fl* W_1 Temp_1)))
+ (a_J5 (fl- (fl* W_0 Temp_1)
+ (fl* W_1 Temp_0)))
+ (a_J6 (fl+ (fl* W_0 Temp_2)
+ (fl* W_1 Temp_3)))
+ (a_J7 (fl- (fl* W_0 Temp_3)
+ (fl* W_1 Temp_2))))
+ (f64vector-set! a J0 a_J0)
+ (f64vector-set! a J1 a_J1)
+ (f64vector-set! a J2 a_J2)
+ (f64vector-set! a J3 a_J3)
+ (f64vector-set! a J4 a_J4)
+ (f64vector-set! a J5 a_J5)
+ (f64vector-set! a J6 a_J6)
+ (f64vector-set! a J7 a_J7)
+ (J-loop (fx+ J0 2)))))))))
+ (inner-loop (fx+ K 1)
+ (fx+ JFirst (fx* SizeOfGroup 4)))))))))
+
+ (define (recursive-bit M N K SizeOfGroup)
+ (if (fx<= 2 SizeOfGroup)
+ (begin
+ (if (fx< 2048 (fx- N M))
+ (let ((new-size (fxarithmetic-shift-right (fx- N M) 2)))
+ (recursive-bit M
+ (fx+ M new-size)
+ (fx* K 4)
+ (fxarithmetic-shift-right SizeOfGroup 2))
+ (recursive-bit (fx+ M new-size)
+ (fx+ M (fx* new-size 2))
+ (fx+ (fx* K 4) 1)
+ (fxarithmetic-shift-right SizeOfGroup 2))
+ (recursive-bit (fx+ M (fx* new-size 2))
+ (fx+ M (fx* new-size 3))
+ (fx+ (fx* K 4) 2)
+ (fxarithmetic-shift-right SizeOfGroup 2))
+ (recursive-bit (fx+ M (fx* new-size 3))
+ N
+ (fx+ (fx* K 4) 3)
+ (fxarithmetic-shift-right SizeOfGroup 2)))
+ (recursive-bit M
+ N
+ (fx* K 4)
+ (fxarithmetic-shift-right SizeOfGroup 2)))
+ (main-loop M N K SizeOfGroup))))
+
+ (define (radix-2-pass a)
+ (declare (not interrupts-enabled))
+ (let ((SizeOfGroup
+ (fxarithmetic-shift-right (f64vector-length a) 1)))
+ (let loop ((J0 0))
+ (if (fx< J0 SizeOfGroup)
+ (let ((J0 J0)
+ (J2 (fx+ J0 SizeOfGroup)))
+ (let ((J1 (fx+ J0 1))
+ (J3 (fx+ J2 1)))
+ (let ((a_J0 (f64vector-ref a J0))
+ (a_J1 (f64vector-ref a J1))
+ (a_J2 (f64vector-ref a J2))
+ (a_J3 (f64vector-ref a J3)))
+ (let ((a_J0 (fl+ a_J0 a_J2))
+ (a_J1 (fl+ a_J1 a_J3))
+ (a_J2 (fl- a_J0 a_J2))
+ (a_J3 (fl- a_J1 a_J3)))
+ (f64vector-set! a J0 a_J0)
+ (f64vector-set! a J1 a_J1)
+ (f64vector-set! a J2 a_J2)
+ (f64vector-set! a J3 a_J3)
+ (loop (fx+ J0 2))))))))))
+
+ (let* ((n (f64vector-length a))
+ (log_n (two^p>=m n)))
+ (if (fxodd? log_n)
+ (recursive-bit 0 n 0 (fxarithmetic-shift-right n 2))
+ (let ((n/2 (fxarithmetic-shift-right n 1))
+ (n/8 (fxarithmetic-shift-right n 3)))
+ (recursive-bit 0 n/2 0 n/8)
+ (recursive-bit n/2 n 1 n/8)
+ (radix-2-pass a))))))
+
+(define (two^p>=m m)
+ ;; returns smallest p, assumes fixnum m >= 0
+ (do ((p 0 (fx+ p 1))
+ (two^p 1 (fx* two^p 2)))
+ ((fx<= m two^p) p)))
+
+(define (test iters n)
+ (let ((two^n
+ (expt 2 n))
+ (table
+ (make-w (fx- n 1))))
+ (display (fx* two^n 2))(newline)
+ (let ((a
+ (make-f64vector (fx* two^n 2) 0.)))
+ (do ((i 0 (fx+ i 1)))
+ ((fx= i iters))
+ (direct-fft-recursive-4 a table)
+ (inverse-fft-recursive-4 a table)))))
+
+(test 2000 11)
diff --git a/tests/runtests.sh b/tests/runtests.sh
index 95f9fb7e..84af3fc1 100644
--- a/tests/runtests.sh
+++ b/tests/runtests.sh
@@ -210,4 +210,8 @@ $compile -e embedded2.scm
echo "======================================== timing compilation ..."
time $compile silex.scm -t -S -O3
+echo "======================================== running floating-point benchmark ..."
+$compile fft.scm -O4 -d0 -disable-interrupts -unsafe-libraries
+time ./a.out
+
echo "======================================== done."
Trap