- (cond ((zerop 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 (sig exp) (integer-decode-float x)
- (let* ((precision (float-precision x))
- (digits (float-digits x))
- (fudge (- digits precision))
- (width (if width (max width 1) nil)))
- (float-string (ash sig (- fudge)) (+ exp fudge) precision width
- fdigits scale fmin))))))
-
-(defun float-string (fraction exponent precision width fdigits scale fmin)
- (let ((r fraction) (s 1) (m- 1) (m+ 1) (k 0)
- (digits 0) (decpnt 0) (cutoff nil) (roundup nil) u low high
- (digit-string (make-array 50
- :element-type 'base-char
- :fill-pointer 0
- :adjustable t)))
- ;; Represent fraction as r/s, error bounds as m+/s and m-/s.
- ;; Rational arithmetic avoids loss of precision in subsequent
- ;; calculations.
- (cond ((> exponent 0)
- (setq r (ash fraction exponent))
- (setq m- (ash 1 exponent))
- (setq m+ m-))
- ((< exponent 0)
- (setq s (ash 1 (- exponent)))))
- ;; Adjust the error bounds m+ and m- for unequal gaps.
- (when (= fraction (ash 1 precision))
- (setq m+ (ash m+ 1))
- (setq r (ash r 1))
- (setq s (ash s 1)))
- ;; Scale value by requested amount, and update error bounds.
- (when scale
- (if (minusp scale)
- (let ((scale-factor (expt 10 (- scale))))
- (setq s (* s scale-factor)))
- (let ((scale-factor (expt 10 scale)))
- (setq r (* r scale-factor))
- (setq m+ (* m+ scale-factor))
- (setq m- (* m- scale-factor)))))
- ;; Scale r and s and compute initial k, the base 10 logarithm of r.
- (do ()
- ((>= r (ceiling s 10)))
- (decf k)
- (setq r (* r 10))
- (setq m- (* m- 10))
- (setq m+ (* m+ 10)))
- (do ()(nil)
- (do ()
- ((< (+ (ash r 1) m+) (ash s 1)))
- (setq s (* s 10))
- (incf k))
- ;; Determine number of fraction digits to generate.
- (cond (fdigits
- ;; Use specified number of fraction digits.
- (setq cutoff (- fdigits))
- ;;don't allow less than fmin fraction digits
- (if (and fmin (> cutoff (- fmin))) (setq cutoff (- fmin))))
- (width
- ;; Use as many fraction digits as width will permit but
- ;; force at least fmin digits even if width will be
- ;; exceeded.
- (if (< k 0)
- (setq cutoff (- 1 width))
- (setq cutoff (1+ (- k width))))
- (if (and fmin (> cutoff (- fmin))) (setq cutoff (- fmin)))))
- ;; If we decided to cut off digit generation before precision
- ;; has been exhausted, rounding the last digit may cause a carry
- ;; propagation. We can prevent this, preserving left-to-right
- ;; digit generation, with a few magical adjustments to m- and
- ;; m+. Of course, correct rounding is also preserved.
- (when (or fdigits width)
- (let ((a (- cutoff k))
- (y s))
- (if (>= a 0)
- (dotimes (i a) (setq y (* y 10)))
- (dotimes (i (- a)) (setq y (ceiling y 10))))
- (setq m- (max y m-))
- (setq m+ (max y m+))
- (when (= m+ y) (setq roundup t))))
- (when (< (+ (ash r 1) m+) (ash s 1)) (return)))
- ;; Zero-fill before fraction if no integer part.
- (when (< k 0)
- (setq decpnt digits)
- (vector-push-extend #\. digit-string)
- (dotimes (i (- k))
- (incf digits) (vector-push-extend #\0 digit-string)))
- ;; Generate the significant digits.
- (do ()(nil)
- (decf k)
- (when (= k -1)
- (vector-push-extend #\. digit-string)
- (setq decpnt digits))
- (multiple-value-setq (u r) (truncate (* r 10) s))
- (setq m- (* m- 10))
- (setq m+ (* m+ 10))
- (setq low (< (ash r 1) m-))
- (if roundup
- (setq high (>= (ash r 1) (- (ash s 1) m+)))
- (setq high (> (ash r 1) (- (ash s 1) m+))))
- ;; Stop when either precision is exhausted or we have printed as
- ;; many fraction digits as permitted.
- (when (or low high (and cutoff (<= k cutoff))) (return))
- (vector-push-extend (char *digits* u) digit-string)
- (incf digits))
- ;; If cutoff occurred before first digit, then no digits are
- ;; generated at all.
- (when (or (not cutoff) (>= k cutoff))
- ;; Last digit may need rounding
- (vector-push-extend (char *digits*
- (cond ((and low (not high)) u)
- ((and high (not low)) (1+ u))
- (t (if (<= (ash r 1) s) u (1+ u)))))
- digit-string)
- (incf digits))
- ;; Zero-fill after integer part if no fraction.
- (when (>= k 0)
- (dotimes (i k) (incf digits) (vector-push-extend #\0 digit-string))
- (vector-push-extend #\. digit-string)
- (setq decpnt digits))
- ;; Add trailing zeroes to pad fraction if fdigits specified.
- (when fdigits
- (dotimes (i (- fdigits (- digits decpnt)))
- (incf digits)
- (vector-push-extend #\0 digit-string)))
- ;; all done
- (values digit-string (1+ digits) (= decpnt 0) (= decpnt digits) decpnt)))
-
+ (declare (type float x))
+ ;; FIXME: I think only FORMAT-DOLLARS calls FLONUM-TO-STRING with
+ ;; possibly-negative X.
+ (setf x (abs x))
+ (multiple-value-bind (e string)
+ (if fdigits
+ (flonum-to-digits x (min (- (+ fdigits (or scale 0)))
+ (- (or fmin 0))))
+ (if (and width (> width 1))
+ (let ((w (multiple-value-list
+ (flonum-to-digits x
+ (max 1
+ (+ (1- width)
+ (if (and scale (minusp scale))
+ scale 0)))
+ t)))
+ (f (multiple-value-list
+ (flonum-to-digits x (- (+ (or fmin 0)
+ (if scale scale 0)))))))
+ (cond
+ ((>= (length (cadr w)) (length (cadr f)))
+ (values-list w))
+ (t (values-list f))))
+ (flonum-to-digits x)))
+ (let ((e (if (zerop x)
+ 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))
+ (write-string string stream :end (when fdigits
+ (min (length string)
+ (max (or fmin 0)
+ (+ fdigits e)))))
+ (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))))))
+
+;;; implementation of figure 1 from Burger and Dybvig, 1996. It is
+;;; extended in order to handle rounding.
+;;;
+;;; As the implementation of the Dragon from Classic CMUCL (and
+;;; previously in SBCL above FLONUM-TO-STRING) says: "DO NOT EVEN
+;;; THINK OF ATTEMPTING TO UNDERSTAND THIS CODE WITHOUT READING THE
+;;; PAPER!", and in this case we have to add that even reading the
+;;; paper might not bring immediate illumination as CSR has attempted
+;;; to turn idiomatic Scheme into idiomatic Lisp.
+;;;
+;;; FIXME: figure 1 from Burger and Dybvig is the unoptimized
+;;; algorithm, noticeably slow at finding the exponent. Figure 2 has
+;;; an improved algorithm, but CSR ran out of energy.
+;;;
+;;; possible extension for the enthusiastic: printing floats in bases
+;;; other than base 10.
+(defconstant single-float-min-e
+ (- 2 sb!vm:single-float-bias sb!vm:single-float-digits))
+(defconstant double-float-min-e
+ (- 2 sb!vm:double-float-bias sb!vm:double-float-digits))
+#!+long-float
+(defconstant long-float-min-e
+ (nth-value 1 (decode-float least-positive-long-float)))
+
+(defun flonum-to-digits (v &optional position relativep)
+ (let ((print-base 10) ; B
+ (float-radix 2) ; b
+ (float-digits (float-digits v)) ; p
+ (digit-characters "0123456789")
+ (min-e
+ (etypecase v
+ (single-float single-float-min-e)
+ (double-float double-float-min-e)
+ #!+long-float
+ (long-float long-float-min-e))))
+ (multiple-value-bind (f e)
+ (integer-decode-float 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)))
+ (with-push-char (:element-type base-char)
+ (labels ((scale (r s m+ m-)
+ (do ((k 0 (1+ k))
+ (s s (* s print-base)))
+ ((not (or (> (+ r m+) s)
+ (and high-ok (= (+ r m+) s))))
+ (do ((k k (1- k))
+ (r r (* r print-base))
+ (m+ m+ (* m+ print-base))
+ (m- m- (* m- print-base)))
+ ((not (and (plusp (- r m-)) ; Extension to handle zero
+ (or (< (* (+ r m+) print-base) s)
+ (and (not high-ok)
+ (= (* (+ r m+) print-base) s)))))
+ (values k (generate r s m+ m-)))))))
+ (generate (r s m+ m-)
+ (let (d tc1 tc2)
+ (tagbody
+ loop
+ (setf (values d r) (truncate (* r print-base) s))
+ (setf m+ (* m+ print-base))
+ (setf m- (* m- print-base))
+ (setf tc1 (or (< r m-) (and low-ok (= r m-))))
+ (setf tc2 (or (> (+ r m+) s)
+ (and high-ok (= (+ r m+) s))))
+ (when (or tc1 tc2)
+ (go end))
+ (push-char (char digit-characters d))
+ (go loop)
+ end
+ (let ((d (cond
+ ((and (not tc1) tc2) (1+ d))
+ ((and tc1 (not tc2)) d)
+ (t ; (and tc1 tc2)
+ (if (< (* r 2) s) d (1+ d))))))
+ (push-char (char digit-characters d))
+ (return-from generate (get-pushed-string))))))
+ (initialize ()
+ (let (r s m+ m-)
+ (if (>= e 0)
+ (let* ((be (expt float-radix e))
+ (be1 (* be float-radix)))
+ (if (/= f (expt float-radix (1- float-digits)))
+ (setf r (* f be 2)
+ s 2
+ m+ be
+ m- be)
+ (setf r (* f be1 2)
+ s (* float-radix 2)
+ m+ be1
+ m- be)))
+ (if (or (= e min-e)
+ (/= f (expt float-radix (1- float-digits))))
+ (setf r (* f 2)
+ s (* (expt float-radix (- e)) 2)
+ m+ 1
+ m- 1)
+ (setf r (* f float-radix 2)
+ s (* (expt float-radix (- 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 (* l print-base)))
+ ((>= (* s l) (+ r m+))
+ ;; k is now \hat{k}
+ (if (< (+ r (* s (/ (expt print-base (- k position)) 2)))
+ (* s (expt print-base k)))
+ (setf position (- k position))
+ (setf position (- k position 1))))))
+ (let ((low (max m- (/ (* s (expt print-base position)) 2)))
+ (high (max m+ (/ (* 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))))
+ (values r s m+ m-))))
+ (multiple-value-bind (r s m+ m-) (initialize)
+ (scale r s m+ m-))))))))
+\f
projects / sbcl.git / blobdiff