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;;; complex timings
(unless (defined? 'complex-vector)
(define complex-vector vector)
(define* (make-complex-vector len (init 0.0)) (make-vector len init complex?))
(define complex-vector-ref vector-ref)
(define complex-vector-set! vector-set!)
(define complex-vector? vector?)
(set! *#readers* (cons (cons #\c (lambda (s) (apply vector (read)))) *#readers*)))
(define size 1000)
(define tries 1000)
(define cv (make-complex-vector size 1.0+i))
(define (c1)
(do ((i 0 (+ i 1)))
((= i tries))
(copy cv)))
;(c1) ; 7 copy_source_no_dest -> s7_vector_copy_1
(define (c2a)
(let ((val 1+i))
(do ((i 0 (+ i 1)))
((= i tries))
(fill! cv val))))
;(c2a) ; 3 complex_vector_fill
(define (c2)
(let* ((len (length cv))
(cv1 (make-complex-vector len))
(val 1+i))
(do ((j 0 (+ j 1)))
((= j tries))
(do ((i 0 (+ i 1)))
((= i len) cv1)
(complex-vector-set! cv1 i val)))))
;(c2) ; 100 univect_set(70) opt_p_call_sss g_complex_vector_set opt_do_step_i
; 36 complex_vector_set_p_pip_direct(15) opt_p_pip_sss opt_do_step_i
(define (c3)
(let* ((len (length cv))
(cv1 (make-complex-vector len)))
(do ((j 0 (+ j 1)))
((= j tries))
(do ((i 0 (+ i 1)))
((= i len))
(complex-vector-set! cv1 i (complex-vector-ref cv i))))))
;(c3) ; 161 univect_set + complex_vector_ref_p_pp + opt_p_call_ssf->g_complex_vector_set(74)
; needs complex_vector_set_pip_direct? and complex_vector_ref_p_pi and complex_vector_ref signature car is (complex? complex-vector?) which 65615 doesn't like
; 113 complex_vector_ref_p_pp complex_vector_set_p_ppp opt_p_ppp_ssf -- why not the pi/pip cases (68367)? 65011--needs p_pi 65655
; removed pointless cv1 return val -> opt_do_very_simple 113
; 83 complex_vector_ref_p_pi opt_do_very_simple complex_vector_set_p_pip_direct
; 68 after bugfix in p_pi_ok but not copy yet, and (set! (cv1 i) (cv i)) is also not copy
(define (c4)
(let* ((len (length cv))
(cv1 (make-complex-vector len)))
(do ((j 0 (+ j 1)))
((= j tries))
(do ((i 0 (+ i 1)))
((= i len))
(complex-vector-set! cv1 i (complex i (- i)))))))
;(c4) ; 129 complex_vector_set_p_ppp complex_p_ii etc
; 109 same but complex_p_ii_wrapped and less gc
(define (c4a)
(let* ((len (length cv))
(cv1 (make-complex-vector len)))
(do ((j 0 (+ j 1))
(d 1.0 (+ d 1.0)))
((= j tries))
(do ((i 0 (+ i 1)))
((= i len))
(complex-vector-set! cv1 i (complex d d))))))
;(c4a) ; hits complex_p_pp_wrapped, 93, complex_vector_set_p_ppp 36, complex_p_pp_wrapped 16
(define (c4b)
(let* ((len (length cv))
(cv1 (make-complex-vector len)))
(do ((j 0 (+ j 1))
(d 1.0 (+ d 1.0)))
((= j tries))
(do ((i 0 (+ i 1)))
((= i len))
(complex-vector-set! cv1 i (complex d 1.0))))))
;(c4b) ; hits complex_p_dd_wrapped, 94, complex_vector_set_p_ppp 36, complex_p_dd_wrapped 8
(define (c5)
(let* ((len (length cv))
(cv1 (copy cv))
(magmore (lambda (a b) (> (magnitude a) (magnitude b)))))
(do ((j 0 (+ j 1)))
((= j tries))
(do ((i 0 (+ i 1)))
((= i len))
(complex-vector-set! cv1 i (complex i (- i))))
(sort! cv1 magmore)
;; (let-temporarily (((*s7* 'print-length) 10)) (display cv1) (newline))
(do ((i 0 (+ i 1)))
((= i (- len 1)))
(if (<= (magnitude (complex-vector-ref cv1 i)) (magnitude (complex-vector-ref cv1 (+ i 1))))
(display 'oops))))))
;(c5) ; 1481: 508 magnitude_p_p, 125 qsort, 117 gc, 116 opt_b_7pp_ffo, 80 opt_bool_sort_0, 76 complex_vector_ref_p_pi, 66 gt_b_7pp etc
; 1460 complex_p_ii_wrapped
; maybe specialized sort_func for each data type (to avoid make_real etc)
; 1383 complex_vector_ref_p_pi_wrapped
; 1340 with opt_p_z_magnitude
(define (c6)
(let ((cv1 (make-complex-vector size))
(cv2 (make-complex-vector size))
(cv3 (make-complex-vector size)))
(do ((j 0 (+ j 1)))
((= j tries))
(do ((i 0 (+ i 1)))
((= i size))
(complex-vector-set! cv1 i (complex i i))
(complex-vector-set! cv2 i (complex i (- i)))
(complex-vector-set! cv3 i (* (complex-vector-ref cv1 i) (complex-vector-ref cv2 i)))
(unless (zero? (imag-part (cv3 i)))
(format *stderr* "(cv3 ~D): ~S~%" i (cv3 i)))))))
;(c6) ; 579: 99 complex-vector-set_p_ppp, 76 complex_vector_ref_p_pi, 57 opt_p_ppp_ssf, 52 complex_p_ii etc
; 535: complex_p_ii_wrapped
(define* (cfft data n (dir 1)) ; complex data
(unless n (set! n (length data)))
(do ((i 0 (+ i 1))
(j 0))
((= i n))
(if (> j i)
(let ((temp (data j)))
(set! (data j) (data i))
(set! (data i) temp)))
(do ((m (/ n 2) (/ m 2)))
((or (< m 2)
(< j m))
(set! j (+ j m)))
(set! j (- j m))))
(do ((ipow (floor (log n 2)))
(prev 1)
(lg 0 (+ lg 1))
(mmax 2 (* mmax 2))
(pow (/ n 2) (/ pow 2))
(theta (complex 0.0 (* pi dir)) (* theta 0.5)))
((= lg ipow))
(do ((wpc (exp theta))
(wc 1.0)
(ii 0 (+ ii 1)))
((= ii prev)
(set! prev mmax))
(do ((jj 0 (+ jj 1))
(i ii (+ i mmax))
(j (+ ii prev) (+ j mmax)))
((>= jj pow))
(let ((tc (* wc (data j))))
(set! (data j) (- (data i) tc))
(set! (data i) (+ (data i) tc))))
(set! wc (* wc wpc))))
data)
(define (c7)
(let ((cv1 (make-complex-vector 128 1+i)))
(do ((i 0 (+ i 1)))
((= i tries))
(cfft cv1 128))))
;(c7) ; 807: 300 eval, 56 lookup, 50 op_dox, 46 add_p_pp, 35 fx_s, 34 complex_vector_getter, 34 complex_vector_set_p_ppp etc
(define z-transform
(let ((+documentation+ "(z-transform data n z) performs a Z transform on data; if z=e^2*pi*j/n you get a Fourier transform"))
(lambda (f n z)
(let ((res (make-complex-vector n)))
(do ((w 0 (+ 1 w)))
((= w n))
(do ((sum 0.0)
(t 1.0)
(m (expt z w))
(k 0 (+ k 1)))
((= k n)
(set! (res w) sum))
(set! sum (+ sum (* (f k) t)))
(set! t (* t m))))
res))))
(define (compare-cfft-and-z-transform)
(let ((size 128))
(let ((cv1 (make-complex-vector size 0.0)))
(do ((i 0 (+ i 1)))
((= i size))
(set! (cv1 i) (complex (- 1.0 (random 2.0)) (- 1.0 (random 2.0)))))
(let ((cv2 (copy cv1)))
(let ((cf (cfft cv1 size))
(zf (z-transform cv2 size (exp (/ (* 2 pi 0+i) size)))))
(let-temporarily (((*s7* 'equivalent-float-epsilon) 1e-10))
(unless (equivalent? cf zf)
(format *stderr* "~S~%~S~%" cf zf))))))))
(define (cx)
(let ((n (/ tries 10)))
(do ((i 0 (+ i 1)))
((= i n))
(compare-cfft-and-z-transform))))
;(cx) ; 1160: 550 eval, 153 multiply_p_pp, 68 add_p_pp etc (42 for complex_vector_getter!)
(define (dolph N gamma)
(let ((vals (make-complex-vector N)))
(let ((alpha (cosh (/ (acosh (expt 10.0 gamma)) N))))
(do ((den (/ 1.0 (cosh (* N (acosh alpha)))))
(freq (/ pi N))
(mult -1 (- mult))
(i 0 (+ i 1))
(phase (* -0.5 pi)))
((= i N))
(set! (vals i) (* mult den (cos (* N (acos (* alpha (cos phase)))))))
(set! phase (+ phase freq))))
(let ((pk 0.0)
(w (make-float-vector N)))
(do ((i 0 (+ i 1))
(sum 0.0 0.0))
((= i N))
(do ((k 0 (+ k 1))
(cin (/ (* 2.0 0+1.0i pi i) N)))
((= k N))
(set! sum (+ sum (* (vals k) (exp (* cin k))))))
(set! (w i) (magnitude sum))
(set! pk (max pk (w i))))
(do ((i 0 (+ i 1)))
((= i N))
(set! (w i) (/ (w i) pk)))
w)))
(define (c8)
(let ((v (dolph 16 2.5))
(vr #r(0.097 0.113 0.221 0.366 0.536 0.709 0.860 0.963 1.000 0.963 0.860 0.709 0.536 0.366 0.221 0.113)))
(let-temporarily (((*s7* 'equivalent-float-epsilon) 1e-3))
(unless (equivalent? v vr)
(let ((pk 0.0))
(do ((i 0 (+ i 1)))
((= i 16)
(format *stderr* "dolph pk: ~S~%" pk))
(let ((mx (magnitude (- (v i) (vr i)))))
(if (> mx pk)
(set! pk mx)))))))))
(define (c9)
(let* ((len (length cv))
(cv1 (make-complex-vector len))
(cv2 #f))
(do ((i 0 (+ i 1)))
((= i len))
(complex-vector-set! cv1 i (complex i (- i))))
(set! cv2 (copy cv1))
(do ((j 0 (+ j 1)))
((= j tries))
(set! cv1 (reverse! (reverse! cv1)))
(set! cv1 (reverse (reverse cv1)))
(unless (equivalent? cv2 cv1)
(display cv1)))))
;(c9) ; 36: 12 g_reverse_in_place, 11 vector_equivalent, 9 reverse_p_p
; 36: complex_p_ii (too insignificant)
;;; append+float etc, iterate, map/for-each, object->string?
(define (test-all)
(c1)
(c2)
(c2a)
(c3)
(c4)
(c4a)
(c4b)
(c5)
(c6)
(c7)
(cx)
(c8)
(c9)
)
(test-all) ; 4306 6-Sep
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