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;;;; Copyright (c) 2007, 2008, 2011 Raymond Toy
;;;;
;;;; Permission is hereby granted, free of charge, to any person
;;;; obtaining a copy of this software and associated documentation
;;;; files (the "Software"), to deal in the Software without
;;;; restriction, including without limitation the rights to use,
;;;; copy, modify, merge, publish, distribute, sublicense, and/or sell
;;;; copies of the Software, and to permit persons to whom the
;;;; Software is furnished to do so, subject to the following
;;;; conditions:
;;;;
;;;; The above copyright notice and this permission notice shall be
;;;; included in all copies or substantial portions of the Software.
;;;;
;;;; THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
;;;; EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
;;;; OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
;;;; NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
;;;; HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
;;;; WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
;;;; FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
;;;; OTHER DEALINGS IN THE SOFTWARE.
(in-package #:octi)
;; Smallest exponent for a double-float.
(eval-when (:compile-toplevel :load-toplevel :execute)
(defconstant +double-float-min-e+
-1073)
(defconstant +digits+
"0123456789")
) ; eval-when
(defun qd-to-digits (v &optional position relativep)
;; V is the number to be printed. If RELATIVEP is NIL, POSITION is
;; the number of digits to the left of the decimal point where we
;; want to stop printing. If RELATIVEP is non-NIL, POSITION is the
;; total number of digits we want printed.
;;
;; Two values are returned: k, and the digit string, without a
;; decimal point. k is the index into the string, before which the
;; decimal point would go.
(let ((print-base 10) ; B
(float-radix 2) ; b
(float-digits (cl:* 4 53)) ; p
(min-e +double-float-min-e+))
(multiple-value-bind (f e)
(integer-decode-qd v)
(let ( ;; FIXME: these even tests assume normal IEEE rounding
;; mode. I wonder if we should cater for non-normal?
(high-ok (evenp f))
(low-ok (evenp f))
(result (make-array 50 :element-type 'base-char
:fill-pointer 0 :adjustable t)))
(labels ((scale (r s m+ m-)
;; Keep increasing k until it's big enough
(do ((k 0 (1+ k))
(s s (cl:* s print-base)))
((not (let ((test (cl:+ r m+)))
(or (> test s)
(and high-ok (= test s)))))
;; k is too big. Decrease until
(do ((k k (1- k))
(r r (cl:* r print-base))
(m+ m+ (cl:* m+ print-base))
(m- m- (cl:* m- print-base)))
((not (let ((test (cl:* (cl:+ r m+) print-base)))
(or (< test s)
(and (not high-ok) (= test s)))))
;; k is correct. Generate the digits.
(values k (generate r s m+ m-)))))))
(generate (r s m+ m-)
(multiple-value-bind (d r)
(truncate (cl:* r print-base) s)
(let ((m+ (cl:* m+ print-base))
(m- (cl:* m- print-base)))
(let ((tc1 (or (< r m-) (and low-ok (= r m-))))
(or (> test s)
(and high-ok (= test s))))))
(cond
((and (not tc1) (not tc2))
(vector-push-extend (char +digits+ d) result)
;; FIXME sucky tail recursion. This whole
;; kaboodle should be DO*/LOOPified.
(generate r s m+ m-))
;; pedantically keeping all the conditions
;; in so that we can move them around.
((and (not tc1) tc2)
(vector-push-extend (char +digits+ (1+ d)) result)
(vector-push-extend (char +digits+ d) result)
(vector-push-extend (char +digits+
(if (< (cl:* r 2) s) d (1+ d)))
result)
result)))))))
(let (r s m+ m-)
(if (>= e 0)
(let* ((be (expt float-radix e))
(if (/= f (expt float-radix (1-
float-digits)))
(setf r (cl:* f be1 2)
s (cl:* float-radix 2)
m+ be1
m- be)))
(if (or (= e min-e)
(/= f (expt float-radix (1-
float-digits))))
(setf r (cl:* f 2)
s (cl:* (expt float-radix (cl:- e)) 2)
(setf r (cl:* f float-radix 2)
s (cl:* (expt float-radix (cl:- 1 e)) 2)
m+ float-radix
m- 1)))
(when position
(when relativep
;;(aver (> position 0))
(do ((k 0 (1+ k))
;; running out of letters here
(l 1 (cl:* l print-base)))
((>= (cl:* s l) (cl:+ r m+))
(if (< (cl:+ r (cl:* s (cl:/ (expt print-base (cl:- k
(cl:* s (expt print-base k)))
(setf position (cl:- k position))
(setf position (cl:- k position 1))))))
(let ((low (max m- (cl:/ (cl:* s (expt print-base
(high (max m+ (cl:/ (cl:* s (expt print-base
position)) 2))))
(when (<= m- low)
(setf m- low)
(setf low-ok t))
(when (<= m+ high)
(setf m+ high)
(setf high-ok t))))
(scale r s m+ m-)))))))
(defun qd-print-exponent (x exp stream)
(let ((*print-radix* nil))
(format stream "q~D" exp)))
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(defun qd-to-string (x &optional width fdigits scale fmin)
(setf x (abs-qd x))
(cond ((zerop-qd x)
;;zero is a special case which float-string cannot handle
(if fdigits
(let ((s (make-string (1+ fdigits) :initial-element #\0)))
(setf (schar s 0) #\.)
(values s (length s) t (zerop fdigits) 0))
(values "." 1 t t 0)))
(t
(multiple-value-bind (e string)
(if fdigits
(qd-to-digits x (min (- (+ fdigits (or scale 0)))
(- (or fmin 0))))
(if (and width (> width 1))
(let ((w (multiple-value-list
(qd-to-digits x
(max 0
(+ (1- width)
(if (and scale (minusp scale))
scale 0)))
t)))
(f (multiple-value-list
(qd-to-digits x (- (+ (or fmin 0)
(if scale scale 0)))))))
(cond
((>= (length (cadr w)) (length (cadr f)))
(values-list w))
(t (values-list f))))
(qd-to-digits x)))
(let ((e (+ e (or scale 0)))
(stream (make-string-output-stream)))
(if (plusp e)
(progn
(write-string string stream :end (min (length string)
e))
(dotimes (i (- e (length string)))
(write-char #\0 stream))
(write-char #\. stream)
(write-string string stream :start (min (length string)
e))
(when fdigits
(dotimes (i (- fdigits
(- (length string)
(min (length string) e))))
(write-char #\0 stream))))
(progn
(write-string "." stream)
(dotimes (i (- e))
(write-char #\0 stream))
;; If we're out of room (because fdigits is too
;; small), don't print out our string. This fixes
;; things like (format nil "~,2f" 0.001). We should
;; print ".00", not ".001".
(when (or (null fdigits)
(plusp (+ e fdigits)))
(write-string string stream))
(when fdigits
(dotimes (i (+ fdigits e (- (length string))))
(write-char #\0 stream)))))
(let ((string (get-output-stream-string stream)))
(values string (length string)
(char= (char string 0) #\.)
(char= (char string (1- (length string))) #\.)
(position #\. string))))))))
(defun qd-output-aux (x &optional (stream *standard-output*))
(write-string (if (minusp (float-sign (qd-0 x)))
"-0.0q0"
"0.0q0")
stream)
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(multiple-value-bind (e string)
(qd-to-digits x)
(when (minusp (float-sign (qd-0 x)))
(write-char #\- stream))
(cond ((< -3 e 8)
;; Free format
(cond ((plusp e)
(write-string string stream :end (min (length string) e))
(dotimes (i (cl:- e (length string)))
(write-char #\0 stream))
(write-char #\. stream)
(write-string string stream :start (min (length string) e))
(when (<= (length string) e)
(write-char #\0 stream))
(qd-print-exponent x 0 stream))
(t
(write-string "0." stream)
(dotimes (i (cl:- e))
(write-char #\0 stream))
(write-string string stream)
(qd-print-exponent x 0 stream))))
(t
;; Exponential format
(write-string string stream :end 1)
(write-char #\. stream)
(write-string string stream :start 1)
;; CLHS 22.1.3.1.3 says at least one digit must be printed
;; after the decimal point.
(when (= (length string) 1)
(write-char #\0 stream))
(qd-print-exponent x (1- e) stream))))))
;; Function that can be used with FORMAT ~/
(defun qd-format (stream arg colon-p at-sign-p &rest par)
;; We should do something with colon-p and at-sign-p
(declare (ignore colon-p at-sign-p par))
(write-string "#q" stream)
#+cmu
(defun qd-output-infinity (x stream)
(cond (*read-eval*
(write-string "#." stream))
(*print-readably*
(error 'print-not-readable :object x))
(t
(write-string "#<" stream)))
(write-string "QD:+QUAD-DOUBLE-FLOAT" stream)
(write-string (if (plusp (qd-0 x))
"-POSITIVE-"
"-NEGATIVE-")
stream)
(write-string "INFINITY+" stream)
(unless *read-eval*
(write-string ">" stream)))
#+cmu
(defun qd-output-nan (x stream)
(print-unreadable-object (x stream)
(write-string "QUAD-DOUBLE-FLOAT" stream)
(write-string (if (float-trapping-nan-p (qd-0 x)) " Trapping" " Quiet") stream)
(write-string " NaN" stream)))
#+cmu
(defun qd-format (stream arg colon-p at-sign-p &rest par)
(declare (type %quad-double arg)
(stream stream))
;; We should do something with colon-p and at-sign-p
(declare (ignore colon-p at-sign-p par))
(cond ((float-infinity-p (qd-0 arg))
(qd-output-infinity arg stream))
((ext:float-nan-p (qd-0 arg))
(qd-output-nan arg stream))
(write-string "#q" stream)
(qd-output-aux arg stream))))
;; This version has problems with roundoff.
#+nil
(defun make-float (sign int-part frac-part scale exp)
(declare (type (member -1 1) sign)
(type unsigned-byte int-part frac-part)
(fixnum scale exp))
(progn
(format t "sign = ~A~%" sign)
(format t "int-part = ~A~%" int-part)
(format t "frac-part = ~A~%" frac-part)
(format t "scale = ~A~%" scale)
(format t "exp = ~A~%" exp))
(let ((int (cl:+ (cl:* int-part (expt 10 scale))
frac-part))
(power (cl:- exp scale)))
(format t "~A * ~A * 10^(~A)~%" sign int power)
(let* ((len (integer-length int)))
#+(or)
(format t "len = ~A~%" len)
(cond ((<= len 53)
(let ((xx (make-qd-d (float int 1d0)))
(yy (npow (make-qd-d 10d0)
power)))
#+(or)
(progn
(format t "int = ~A~%" int)
(format t "fl = ~A~%" (float int 1w0))
(format t "s = ~A~%" sign)
(format t "sint = ~A~%" (cl:* sign (float int 1w0)))
(format t "~A~%" xx)
(format t "npow = ~A~%" yy))
(if (minusp sign)
(neg-qd (mul-qd xx yy))
(mul-qd xx yy))))
(t
(let*
((q0 (ldb (byte 53 (cl:- len 53)) int))
(q1 (ldb (byte 53 (cl:- len (* 2 53))) int))
(q2 (ldb (byte 53 (cl:- len (* 3 53))) int))
(q3 (ldb (byte 53 (cl:- len (* 4 53))) int))
(q4 (ldb (byte 53 (cl:- len (* 5 53))) int))
(xx (multiple-value-call #'%make-qd-d
(renorm-5 (scale-float (float q0 1d0)
(cl:- len 53))
(scale-float (float q1 1d0)
(cl:- len (* 2 53)))
(scale-float (float q2 1d0)
(cl:- len (* 3 53)))
(scale-float (float q3 1d0)
(cl:- len (* 4 53)))
(scale-float (float q4 1d0)
(cl:- len (* 5 53))))))
(yy (npow (make-qd-d 10d0)
power)))
#+(or)
(progn
(format t "xx = ~A~%" xx)
#+(or)
(format t " = ~/qd::qd-format/~%" xx)
(format t "yy = ~A~%" yy)
#+(or)
(format t " = ~/qd::qd-format/~%" yy)
(format t "q0 = ~X (~A)~%" q0
(scale-float (float q0 1d0)
(cl:- len 53)))
(format t "q1 = ~X (~A)~%" q1
(scale-float (float q1 1d0)
(cl:- len (* 2 53))))
#+(or)
(format t "~/octi::qd-format/~%" (mul-qd xx yy)))
(if (minusp sign)
(neg-qd (mul-qd xx yy))
(mul-qd xx yy))))))))
;; This is a slightly modified version of Richard Fateman's code to
;; convert bignums to qd. This supports converting rationals to qd
;; too.
(defun rational-to-qd (rat)
"Convert a rational number RAT to a %QUAD-DOUBLE number"
(declare (rational rat))
(let* ((p (coerce rat 'double-float))
(ans (make-qd-d p))
(remainder rat))
(declare (double-float p)
(rational remainder)
(type %quad-double ans))
(dotimes (k 3 ans)
(decf remainder (rational p))
(setf p (coerce remainder 'double-float))
(setf ans (add-qd-d ans p)))))
(defun make-float (sign int-part frac-part scale exp)
(declare (type (member -1 1) sign)
(type unsigned-byte int-part frac-part)
(fixnum scale exp))
(let ((qd (rational-to-qd (* (+ int-part (/ frac-part (expt 10 scale)))
(expt 10 exp)))))
(if (minusp sign)
(neg-qd qd)
qd)))
;; This seems to work, but really needs to be rewritten!
"Read a %QUAD-DOUBLE number from the stream STREAM. The format of the number
should be like a float, but with extra significant digits allowed. An exponent
marker of Q is allowed."
;; Read a sequence of digits and return the decimal
;; value, the character that terminated the sequence, and
;; how many characters were read.
(let ((val 0)
(ch nil)
(count 0))
(loop
(setf ch (peek-char nil s nil :eof))
(cond ((eq ch :eof)
(return))
((digit-char-p ch)
(read-char s)
(incf count)
(setf val (cl:+ (digit-char-p ch)
(cl:* 10 val))))
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(t
(return))))
(values ch val count)))
(read-sign (s)
(let ((maybe-sign (peek-char t s nil :eof)))
(cond ((eql maybe-sign #\-)
(read-char s)
-1
)
((eql maybe-sign #\+)
(read-char s)
+1)
((and (characterp maybe-sign)
(digit-char-p maybe-sign))
+1)
((eql maybe-sign #\.)
+1)
(t
maybe-sign))))
(read-exp (s)
(let ((exp-sign (read-sign s)))
(when (eq :eof exp-sign)
(return-from read-exp 0))
(when (eq :eof (peek-char t s nil :eof))
(error "Sign of exponent, but no value"))
(multiple-value-bind (char expo)
(read-digits s)
(declare (ignore char))
(let ((sign (read-sign stream))
(int-part 0)
(frac-part 0)
(exp 0)
(scale 0))
(when (eq :eof (peek-char t stream nil :eof))
(error "Sign, but no value"))
(multiple-value-bind (char int)
(read-digits stream)
(setf int-part int)
(cond ((eql :eof char)
)
((eql char #\.)
(read-char stream)
(multiple-value-bind (char val scale-val)
(read-digits stream)
(declare (ignore char))
(setf frac-part val)
(setf scale scale-val)
(let ((next (peek-char nil stream nil :eof)))
(when (equalp next #\q)
(read-char stream)
(let ((exp-sign (read-sign stream)))
(setf exp (read-exp stream))
(setf exp (cl:* exp exp-sign)))))))
((equalp char #\q)
(read-char stream)
(setf exp (read-exp stream))
))
(make-float sign int-part frac-part scale exp)))))
(defun qd-reader (stream subchar arg)
(defun qd-from-string (string)
(cl::with-input-from-string (s string)
(read-qd s)))
(set-dispatch-macro-character #\# #\Q #'qd-reader)