# publicpkhuong/rational-simplex

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278 279 280 281 282 283 `(defvar *points*)(defun eval-poly (coefs)  (let ((max 0)        (poly (make-poly coefs t)))    (map nil (lambda (point)               (let ((error (abs (- (funcall poly (point-loc point))                                    (point-value point)))))                 (setf max (max max error))))         *points*)    max))(defstruct approx  coefs  error  lg-error  degree  non-zero  non-one  non-two  constant  id)(defun find-non-dominated (approxs)  (let ((good (make-array (length approxs)                          :fill-pointer 0)))    (map nil (lambda (x)               (unless (or (null x)                           (some (lambda (y)                                   (and (not (eql x y)) y                                        (let ((cmp                                                (list (- (approx-error y)                                                         (approx-error x))                                                      (- (approx-degree y)                                                         (approx-degree x))                                                      (- (approx-non-zero y)                                                         (approx-non-zero x))                                                      (- (approx-non-one y)                                                         (approx-non-one x))                                                      (- (approx-non-two y)                                                         (approx-non-two x))                                                      (- (approx-constant y)                                                         (approx-constant x)))))                                          (or (and (notany #'plusp cmp)                                                   (some #'minusp cmp))                                              (and (every #'zerop cmp)                                                   (< (approx-id y)                                                      (approx-id x)))))))                                 approxs))                 (vector-push-extend x good)))         approxs)    (coerce good 'simple-vector)))(defun coefs-pareto (coefs from to npoints function)  (let* ((*loc-value* function)         (*points* (chebyshev-nodes from to npoints))         (seen (make-hash-table :test #'equalp)))    (find-non-dominated     (map 'simple-vector          (lambda (coefs)            (let* ((coefs (car coefs))                   (constant (if (plusp (length coefs))                                 (elt coefs 0)                                 0))                   (start (if (plusp (length coefs)) 1 0))                   (key (map '(simple-array double-float 1)                               (lambda (x) (float x 1d0)) coefs)))              (unless (gethash key seen)                (setf (gethash key seen) t)                (let ((error (float (eval-poly coefs) 1d0)))                  (make-approx                   :coefs coefs                   :error error                   :lg-error (if (zerop error)                                 sb-ext:double-float-positive-infinity                                 (floor (- (log error 2d0))))                   :degree (coefs-degree coefs)                   :non-zero (count 0 coefs :test-not #'eql                                    :start start)                   :non-one (count-if-not (lambda (x)                                             (member x '(-1 0 1)))                                           coefs                                           :start start)                   :non-two (count-if-not (lambda (x)                                             (member x '(-2 -1 0 1 2)))                                           coefs                                           :start start)                   :constant (case (abs constant)                               (0 0)                               (1 1)                               (2 2)                               (t 3))                   :id (hash-table-count seen))))))          coefs))))(defun sort-by (values &rest accessors)  (let ((values (if (simple-vector-p values)                    (copy-seq values)                    (coerce values 'simple-vector))))    (dolist (accessor (reverse accessors) values)      (setf values (stable-sort values #'< :key accessor)))))(defvar *accessors* (list (cons #'approx-error "error")                          (cons (lambda (x)                                  (- (approx-lg-error x)))                                "lb_error")                          (cons (lambda (x)                                  (1- (approx-degree x)))                                "degree")                          (cons #'approx-non-zero "non_zero")                          (cons #'approx-non-one "non_one")                          (cons #'approx-non-two "non_two")                          (cons #'approx-constant "constant")))(defvar *default-accessors* (list (cons (lambda (x)                                          (- (approx-lg-error x)))                                        "lb_error")                                  (cons (lambda (x)                                          (1- (approx-degree x)))                                        "degree")                                  (cons #'approx-error "error")                                  (cons #'approx-non-zero "non_zero")                                  (cons #'approx-non-one "non_one")                                  (cons #'approx-non-two "non_two")                                  (cons #'approx-constant "constant")))(defvar *default-accessors2* (list (cons (lambda (x)                                           (1- (approx-degree x)))                                         "degree")                                   (cons (lambda (x)                                           (- (approx-lg-error x)))                                         "lb_error")                                   (cons #'approx-non-zero "non_zero")                                   (cons #'approx-non-one "non_one")                                   (cons #'approx-non-two "non_two")                                   (cons #'approx-constant "constant")                                   (cons #'approx-error "error")))(defun md5 (x)  #+sbcl  (let ((sum (sb-md5:md5sum-string x)))    (format nil "~{~2,'0X~}" (coerce sum 'list)))  #-sbcl  (sxhash x))(defun md5-coefs (coefs)  #+sbcl  (ecase *float-mode*    (double-float     (let* ((coefs (map '(simple-array double-float 1) (lambda (x)                                                         (float x 1d0))                        coefs))            (nbytes (* 8 (length coefs)))            (bytes (make-array nbytes :element-type '(unsigned-byte 8))))       (sb-impl::ub8-bash-copy coefs 0 bytes 0 nbytes)       (let ((sum (sb-md5:md5sum-sequence bytes)))         (format nil "~{~2,'0X~}" (coerce sum 'list)))))    (single-float     (let* ((coefs (map '(simple-array single-float 1) (lambda (x)                                                         (float x 1s0))                        coefs))            (nbytes (* 4 (length coefs)))            (bytes (make-array nbytes :element-type '(unsigned-byte 8))))       (sb-impl::ub8-bash-copy coefs 0 bytes 0 nbytes)       (let ((sum (sb-md5:md5sum-sequence bytes)))         (format nil "~{~2,'0X~}" (coerce sum 'list))))))  #-sbcl  (sxhash coefs))(defun print-index (function long-description approx accessors)  (let ((approx (apply 'sort-by approx (mapcar #'car accessors)))        (accessors (mapcar #'car accessors))        (names (mapcar #'cdr accessors))        (*read-default-float-format* *float-mode*)        (error-width (ecase *float-mode*                        (single-float 14)                        (double-float 24))))    (with-open-file (s (format nil "~A~{-~A~}"                               function names)                       :direction :output                       :if-exists :supersede)      (format s "~A ~A~%" function long-description)      (dolist (name names)        (if (equal name "error")            (format s "~V,A " error-width "error")            (format s "~8,A " name)))      (format s "| coefficients | rationals | hash~%")      (map nil (lambda (approx)                 (loop for accessor in accessors                       for name in names                       do (let ((x (funcall accessor approx)))                            (when (equal name "lb_error")                              (setf x (- x)))                            (cond ((eql x sb-ext:double-float-positive-infinity)                                   (format s "~V,A " error-width "inf"))                                  ((floatp x)                                   (format s "~V,E " error-width (coerce x *float-mode*)))                                  (t                                   (format s "~8,A " x)))))                 (let ((coefs (approx-coefs approx)))                   (setf coefs (subseq coefs 0 (coefs-degree coefs)))                   (format s "| ~{~W ~}| ~{~A ~}| ~A-~A~%"                           (map 'list (lambda (x)                                        (floatify x))                                coefs)                           (coerce coefs 'list)                           function                           (md5-coefs coefs))))           approx))))(defun print-all-indices (approx function long-description                          &key (max-error sb-ext:double-float-positive-infinity))  (let ((approx (remove-if (lambda (x)                             (> (approx-error x) max-error))                           approx))        (seen (make-hash-table :test #'equalp)))    (let ((error (car *accessors*)))      (alexandria:map-permutations       (lambda (accessors)         (let* ((split (1+ (position error accessors)))                (first (subseq accessors 0 split))                (second (subseq accessors split)))           (setf second                 (sort second #'<                       :key (lambda (x)                              (position x *accessors*))))           (let* ((accessors (append first second))                  (key (mapcar #'cdr accessors)))             (unless (gethash key seen)               (setf (gethash key seen) t)               (print-index                function long-description                approx accessors)))))       *accessors*))))(defun print-default-index (approx function long-description                            &key (max-error                                  sb-ext:double-float-positive-infinity))  (let ((approx (remove-if (lambda (x)                             (> (approx-error x) max-error))                           approx)))    (print-index function long-description                 approx *default-accessors*)    (print-index function long-description                 approx *default-accessors2*)))(defun print-indices ()  (mapc (lambda (x)          (destructuring-bind (file from to approximatee                               name long-description)              x            (print-default-index             (coefs-pareto (with-open-file (s file)                             (read s))                           from to (ash 1 13)                           (coerce approximatee 'function))             name long-description :max-error 0.1d0)            (format t "~A done~%" name)            (force-output)))        `(          ("arctan-16" 0 1 ,#'computable-reals:atan-r "atan" "over [0, 1], degree at most 16, error at most 0.1")          ("arctan-wide-16" -1 1 ,#'computable-reals:atan-r "wider-atan" "over [-1, 1], degree at most 16, error at most 0.1")          ("cos-narrow-16" ,(- (float-from-bits (float-bits (/ pi 2)) 2))                           ,(float-from-bits (float-bits (/ pi 2)) 2)                           ,#'computable-reals:cos-r                           "cos" "over [-pi/2, pi/2], degree at most 16, error at most 0.1")          ("sin-narrow-16" ,(- (float-from-bits (float-bits (/ pi 2)) 2))                           ,(float-from-bits (float-bits (/ pi 2)) 2)                           ,#'computable-reals:sin-r                           "sin" "over [-pi/2, pi/2], degree at most 16, error at most 0.1")          ("exp-16" 0 1 ,#'computable-reals:exp-r "exp" "over [0, 1], degree at most 16, error at most 0.1")          ("exp-wide-16" -1 1 ,#'computable-reals:exp-r "wider-exp" "over [-1, 1], degree at most 16, error at most 0.1")          ("lg1px-16" 0 1 ,(lambda (x)                             (computable-reals:log-r (computable-reals:+r 1 x) 2))                      "lg1px" "(log_2 1+x) over [0, 1], degree at most 16, error at most 0.1")          ("log1px-16" 0 1 ,(lambda (x)                              (computable-reals:log-r (computable-reals:+r 1 x)))                       "log1px" "(log 1+x) over [0, 1], degree at most 16, error at most 0.1")          ("log-16" 1 2 ,(lambda (x)                           (computable-reals:log-r x))                    "log" "over [1, 2], degree at most 16, error at most 0.1")          )))`
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