# spectral-norm Lisp SBCL #3 program

## source code

```;;    The Computer Language Benchmarks Game
;;    https://salsa.debian.org/benchmarksgame-team/benchmarksgame/
;;
;;    Adapted from the C (gcc) code by Sebastien Loisel
;;
;;    Contributed by Christopher Neufeld
;;    Modified by Juho Snellman 2005-10-26
;;      * Use SIMPLE-ARRAY instead of ARRAY in declarations
;;      * Use TRUNCATE instead of / for fixnum division
;;      * Rearrange EVAL-A to make it more readable and a bit faster
;;    Modified by Andy Hefner 2008-09-18
;;      * Eliminate array consing
;;      * Clean up type declarations in eval-A
;;      * Distribute work across multiple cores on SBCL
;;    Modified by Witali Kusnezow 2008-12-02
;;      * use right shift instead of truncate for division in eval-A
;;      * redefine eval-A as a macro

;; This is our most expensive function.  Optimized with the knowledge
;; that 'n' will never be "huge".  This will break if 'n' exceeds
;; approximately half of the square root of the largest fixnum
;; supported by the implementation.  On 32-bit sbcl,
;; 'most-positive-fixnum' is 536870911, and we can support values of
;; 'n' above 11000.

(defmacro eval-A (i j)
`(let* ((n (+ ,i ,j))
(n+1 (1+ n)))
(declare (type (integer 0 22000) n n+1))
(/ (float (+ (ash (* n n+1) -1) ,i 1) 0d0))))

(defun eval-At-times-u (u n Au start end)
(declare (type fixnum n start end)
(type (simple-array double-float) u Au))
(loop for i from start below end do
(setf (aref Au i)
(loop for j below n
summing (* (aref u j) (eval-A j i))
of-type double-float))))

(defun eval-A-times-u (u n Au start end)
(declare (type fixnum n start end)
(type (simple-array double-float) u Au))
(loop for i from start below end do
(setf (aref Au i)
(loop for j below n
summing (* (aref u j) (eval-A i j))
of-type double-float))))

(defun execute-parallel (start end function)
(declare (optimize (speed 0)))
(loop with step = (truncate (- end start) num-threads)
for index from start below end by step
collecting (let ((start index)
(end (min end (+ index step))))
(lambda () (funcall function start end))))

(defun execute-parallel (start end function )
(funcall function start end))

(defun eval-AtA-times-u (u AtAu v n start end)
(execute-parallel start end
(lambda (start end)
(eval-A-times-u u n v start end)))
(execute-parallel start end
(lambda (start end)
(eval-At-times-u v n AtAu start end))))

(defun main (&optional n-supplied)
(let ((n (or n-supplied
(parse-integer (or (car (last #+sbcl sb-ext:*posix-argv*
#+clisp ext:*args*
#+cmu extensions:*command-line-strings*
#+gcl  si::*command-args*))
"2000")))))
(declare (type fixnum n))
(or (typep (* (- (* 2 n) 1) (- (* 2 n) 2)) 'fixnum)
(error "The supplied value of 'n' breaks the optimizations in EVAL-A"))
(let ((u (make-array n :element-type 'double-float :initial-element 1.0d0))
(v (make-array n :element-type 'double-float))
(tmp (make-array n :element-type 'double-float)))
(declare (type (simple-array double-float) U V))
(dotimes (i 10)
(eval-AtA-times-u u v tmp n 0 n)
(eval-AtA-times-u v u tmp n 0 n))
(let ((vBv 0.0d0)
(vv 0.0d0))
(dotimes (i n)
(incf vBv (* (aref u i) (aref v i)))
(incf vv (* (aref v i) (aref v i))))
(format t "~11,9F~%" (sqrt (the (double-float 0d0) (/ vBv vv))))))))
```

## notes, command-line, and program output

```NOTES:
64-bit Ubuntu quad core
SBCL 2.2.4

Thu, 05 May 2022 01:32:05 GMT

MAKE:
cp: 'spectralnorm.sbcl-3.sbcl' and './spectralnorm.sbcl-3.sbcl' are the same file
SBCL built with: /opt/src/sbcl-2.2.4/bin/sbcl --userinit /dev/null --batch --eval '(load "spectralnorm.sbcl-3.sbcl_compile")'
### START spectralnorm.sbcl-3.sbcl_compile
(handler-bind ((sb-ext:defconstant-uneql      (lambda (c) (abort c))))      (require :sb-concurrency)      (load (compile-file "spectralnorm.sbcl-3.sbcl" ))) (save-lisp-and-die "sbcl.core" :purify t)
### END spectralnorm.sbcl-3.sbcl_compile

; compiling file "/home/dunham/all-benchmarksgame/benchmarksgame_i53330/spectralnorm/tmp/spectralnorm.sbcl-3.sbcl" (written 26 APR 2018 12:50:14 PM):

; wrote /home/dunham/all-benchmarksgame/benchmarksgame_i53330/spectralnorm/tmp/spectralnorm.sbcl-3.fasl
; compilation finished in 0:00:00.100
### START spectralnorm.sbcl-3.sbcl_run
(main) (quit)
### END spectralnorm.sbcl-3.sbcl_run

2.61s to complete and log all make actions

COMMAND LINE:
/opt/src/sbcl-2.2.4/bin/sbcl --dynamic-space-size 500 --noinform --core sbcl.core --userinit /dev/null --load spectralnorm.sbcl-3.sbcl_run 5500

PROGRAM OUTPUT:
1.274224153
```