;;;; float printing
;;; FLONUM-TO-STRING (and its subsidiary function FLOAT-STRING) does
-;;; most of the work for all printing of floating point numbers in the
-;;; printer and in FORMAT. It converts a floating point number to a
-;;; string in a free or fixed format with no exponent. The
-;;; interpretation of the arguments is as follows:
+;;; most of the work for all printing of floating point numbers in
+;;; FORMAT. It converts a floating point number to a string in a free
+;;; or fixed format with no exponent. The interpretation of the
+;;; arguments is as follows:
;;;
;;; X - The floating point number to convert, which must not be
;;; negative.
;;; significance in the printed value due to a bogus choice of
;;; scale factor.
;;;
-;;; Most of the optional arguments are for the benefit for FORMAT and are not
-;;; used by the printer.
-;;;
;;; Returns:
;;; (VALUES DIGIT-STRING DIGIT-LENGTH LEADING-POINT TRAILING-POINT DECPNT)
;;; where the results have the following interpretation:
;;; representation. Furthermore, only as many digits as necessary to
;;; satisfy this condition will be printed.
;;;
-;;; FLOAT-STRING actually generates the digits for positive numbers.
-;;; The algorithm is essentially that of algorithm Dragon4 in "How to
-;;; Print Floating-Point Numbers Accurately" by Steele and White. The
-;;; current (draft) version of this paper may be found in
-;;; [CMUC]<steele>tradix.press. DO NOT EVEN THINK OF ATTEMPTING TO
-;;; UNDERSTAND THIS CODE WITHOUT READING THE PAPER!
+;;; FLOAT-DIGITS actually generates the digits for positive numbers;
+;;; see below for comments.
(defun flonum-to-string (x &optional width fdigits scale fmin)
+ (declare (type float x))
+ ;; FIXME: I think only FORMAT-DOLLARS calls FLONUM-TO-STRING with
+ ;; possibly-negative X.
+ (setf x (abs x))
(cond ((zerop x)
;; Zero is a special case which FLOAT-STRING cannot handle.
(if fdigits
(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-characters "0123456789")
- (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 digit-characters 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 digit-characters
- (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)))
+ (multiple-value-bind (e string)
+ (if fdigits
+ (flonum-to-digits x (min (- fdigits) (- (or fmin 0))))
+ (if (and width (> width 1))
+ (let ((w (multiple-value-list (flonum-to-digits x (1- width) t)))
+ (f (multiple-value-list (flonum-to-digits x (- (or fmin 0))))))
+ (cond
+ ((>= (length (cadr w)) (length (cadr f)))
+ (values-list w))
+ (t (values-list f))))
+ (flonum-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))
+ (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))))))))
;;; implementation of figure 1 from Burger and Dybvig, 1996. As the
-;;; implementation of the Dragon from Classic CMUCL (and 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.
+;;; 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
-;;;
-;;; FIXME: Burger and Dybvig also provide an algorithm for
-;;; fixed-format floating point printing. If it were implemented,
-;;; then we could delete the Dragon altogether (see FLONUM-TO-STRING).
+;;; an improved algorithm, but CSR ran out of energy.
;;;
;;; possible extension for the enthusiastic: printing floats in bases
;;; other than base 10.
(defconstant long-float-min-e
(nth-value 1 (decode-float least-positive-long-float)))
-(defun flonum-to-digits (v)
+(defun flonum-to-digits (v &optional position relativep)
(let ((print-base 10) ; B
(float-radix 2) ; b
(float-digits (float-digits v)) ; p
(t ; (and tc1 tc2)
(if (< (* r 2) s) d (1+ d))))))
(vector-push-extend (char digit-characters d) result)
- (return-from generate result))))))
- (if (>= e 0)
- (if (/= f (expt float-radix (1- float-digits)))
- (let ((be (expt float-radix e)))
- (scale (* f be 2) 2 be be))
- (let* ((be (expt float-radix e))
- (be1 (* be float-radix)))
- (scale (* f be1 2) (* float-radix 2) be1 be)))
- (if (or (= e min-e) (/= f (expt float-radix (1- float-digits))))
- (scale (* f 2) (* (expt float-radix (- e)) 2) 1 1)
- (scale (* f float-radix 2)
- (* (expt float-radix (- 1 e)) 2) float-radix 1))))))))
+ (return-from generate result)))))
+ (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
;;; Given a non-negative floating point number, SCALE-EXPONENT returns
;;; a new floating point number Z in the range (0.1, 1.0] and an
;;; We return true if we overflowed, so that ~G can output the overflow char
;;; instead of spaces.
(defun format-fixed-aux (stream number w d k ovf pad atsign)
+ (declare (type float number))
(cond
- ((or (not (or w d))
- (and (floatp number)
- (or (float-infinity-p number)
- (float-nan-p number))))
+ ((and (floatp number)
+ (or (float-infinity-p number)
+ (float-nan-p number)))
(prin1 number stream)
nil)
(t
(let ((spaceleft w))
- (when (and w (or atsign (minusp number))) (decf spaceleft))
+ (when (and w (or atsign (minusp (float-sign number))))
+ (decf spaceleft))
(multiple-value-bind (str len lpoint tpoint)
(sb!impl::flonum-to-string (abs number) spaceleft d k)
;;if caller specifically requested no fraction digits, suppress the
t)
(t
(when w (dotimes (i spaceleft) (write-char pad stream)))
- (if (minusp number)
+ (if (minusp (float-sign number))
(write-char #\- stream)
(if atsign (write-char #\+ stream)))
(when lpoint (write-char #\0 stream))
;;; silent here, so let's just print out infinities and NaN's instead
;;; of causing an error.
(defun format-exp-aux (stream number w d e k ovf pad marker atsign)
- (if (and (floatp number)
- (or (float-infinity-p number)
- (float-nan-p number)))
+ (declare (type float number))
+ (if (or (float-infinity-p number)
+ (float-nan-p number))
(prin1 number stream)
(multiple-value-bind (num expt) (sb!impl::scale-exponent (abs number))
(let* ((expt (- expt k))
(fmin (if (minusp k) (- 1 k) nil))
(spaceleft (if w
(- w 2 elen
- (if (or atsign (minusp number))
+ (if (or atsign (minusp (float-sign number)))
1 0))
nil)))
(if (and w ovf e (> elen e)) ;exponent overflow
(dotimes (i w) (write-char ovf stream))
- (multiple-value-bind (fstr flen lpoint)
+ (multiple-value-bind (fstr flen lpoint tpoint)
(sb!impl::flonum-to-string num spaceleft fdig k fmin)
+ (when (and d (zerop d)) (setq tpoint nil))
(when w
(decf spaceleft flen)
(when lpoint
+ (if (or (> spaceleft 0) tpoint)
+ (decf spaceleft)
+ (setq lpoint nil)))
+ (when tpoint
(if (> spaceleft 0)
(decf spaceleft)
- (setq lpoint nil))))
+ (setq tpoint nil))))
(cond ((and w (< spaceleft 0) ovf)
;;significand overflow
(dotimes (i w) (write-char ovf stream)))
(t (when w
(dotimes (i spaceleft) (write-char pad stream)))
- (if (minusp number)
+ (if (minusp (float-sign number))
(write-char #\- stream)
(if atsign (write-char #\+ stream)))
(when lpoint (write-char #\0 stream))
(write-string fstr stream)
+ (when tpoint (write-char #\0 stream))
(write-char (if marker
marker
(format-exponent-marker number))
;;; Raymond Toy writes: same change as for format-exp-aux
(defun format-general-aux (stream number w d e k ovf pad marker atsign)
- (if (and (floatp number)
- (or (float-infinity-p number)
- (float-nan-p number)))
+ (declare (type float number))
+ (if (or (float-infinity-p number)
+ (float-nan-p number))
(prin1 number stream)
(multiple-value-bind (ignore n) (sb!impl::scale-exponent (abs number))
(declare (ignore ignore))
;; thing, and at least the user shouldn't be surprised.
(setq number (coerce number 'single-float)))
(if (floatp number)
- (let* ((signstr (if (minusp number) "-" (if atsign "+" "")))
+ (let* ((signstr (if (minusp (float-sign number))
+ "-"
+ (if atsign "+" "")))
(signlen (length signstr)))
(multiple-value-bind (str strlen ig2 ig3 pointplace)
(sb!impl::flonum-to-string number nil d nil)
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