-;;;; This file contains the definitions of float specific number
+;;;; This file contains the definitions of float-specific number
;;;; support (other than irrational stuff, which is in irrat.) There is
;;;; code in here that assumes there are only two float formats: IEEE
-;;;; single and double. (Long-float support has been added, but bugs
+;;;; single and double. (LONG-FLOAT support has been added, but bugs
;;;; may still remain due to old code which assumes this dichotomy.)
;;;; This software is part of the SBCL system. See the README file for
(in-package "SB!KERNEL")
\f
-;;;; utilities
-
-(eval-when (:compile-toplevel :load-toplevel :execute)
-
-;;; These functions let us create floats from bits with the
-;;; significand uniformly represented as an integer. This is less
-;;; efficient for double floats, but is more convenient when making
-;;; special values, etc.
-(defun single-from-bits (sign exp sig)
- (declare (type bit sign) (type (unsigned-byte 24) sig)
- (type (unsigned-byte 8) exp))
- (make-single-float
- (dpb exp sb!vm:single-float-exponent-byte
- (dpb sig sb!vm:single-float-significand-byte
- (if (zerop sign) 0 -1)))))
-(defun double-from-bits (sign exp sig)
- (declare (type bit sign) (type (unsigned-byte 53) sig)
- (type (unsigned-byte 11) exp))
- (make-double-float (dpb exp sb!vm:double-float-exponent-byte
- (dpb (ash sig -32) sb!vm:double-float-significand-byte
- (if (zerop sign) 0 -1)))
- (ldb (byte 32 0) sig)))
-#!+(and long-float x86)
-(defun long-from-bits (sign exp sig)
- (declare (type bit sign) (type (unsigned-byte 64) sig)
- (type (unsigned-byte 15) exp))
- (make-long-float (logior (ash sign 15) exp)
- (ldb (byte 32 32) sig)
- (ldb (byte 32 0) sig)))
-
-) ; EVAL-WHEN
-\f
-;;;; float parameters
-
-(defconstant least-positive-single-float (single-from-bits 0 0 1))
-(defconstant least-positive-short-float least-positive-single-float)
-(defconstant least-negative-single-float (single-from-bits 1 0 1))
-(defconstant least-negative-short-float least-negative-single-float)
-(defconstant least-positive-double-float (double-from-bits 0 0 1))
-#!-long-float
-(defconstant least-positive-long-float least-positive-double-float)
-#!+(and long-float x86)
-(defconstant least-positive-long-float (long-from-bits 0 0 1))
-(defconstant least-negative-double-float (double-from-bits 1 0 1))
-#!-long-float
-(defconstant least-negative-long-float least-negative-double-float)
-#!+(and long-float x86)
-(defconstant least-negative-long-float (long-from-bits 1 0 1))
-
-(defconstant least-positive-normalized-single-float
- (single-from-bits 0 sb!vm:single-float-normal-exponent-min 0))
-(defconstant least-positive-normalized-short-float
- least-positive-normalized-single-float)
-(defconstant least-negative-normalized-single-float
- (single-from-bits 1 sb!vm:single-float-normal-exponent-min 0))
-(defconstant least-negative-normalized-short-float
- least-negative-normalized-single-float)
-(defconstant least-positive-normalized-double-float
- (double-from-bits 0 sb!vm:double-float-normal-exponent-min 0))
-#!-long-float
-(defconstant least-positive-normalized-long-float
- least-positive-normalized-double-float)
-#!+(and long-float x86)
-(defconstant least-positive-normalized-long-float
- (long-from-bits 0 sb!vm:long-float-normal-exponent-min
- (ash sb!vm:long-float-hidden-bit 32)))
-(defconstant least-negative-normalized-double-float
- (double-from-bits 1 sb!vm:double-float-normal-exponent-min 0))
-#!-long-float
-(defconstant least-negative-normalized-long-float
- least-negative-normalized-double-float)
-#!+(and long-float x86)
-(defconstant least-negative-normalized-long-float
- (long-from-bits 1 sb!vm:long-float-normal-exponent-min
- (ash sb!vm:long-float-hidden-bit 32)))
-
-(defconstant most-positive-single-float
- (single-from-bits 0 sb!vm:single-float-normal-exponent-max
- (ldb sb!vm:single-float-significand-byte -1)))
-(defconstant most-positive-short-float most-positive-single-float)
-(defconstant most-negative-single-float
- (single-from-bits 1 sb!vm:single-float-normal-exponent-max
- (ldb sb!vm:single-float-significand-byte -1)))
-(defconstant most-negative-short-float most-negative-single-float)
-(defconstant most-positive-double-float
- (double-from-bits 0 sb!vm:double-float-normal-exponent-max
- (ldb (byte sb!vm:double-float-digits 0) -1)))
-#!-long-float
-(defconstant most-positive-long-float most-positive-double-float)
-#!+(and long-float x86)
-(defconstant most-positive-long-float
- (long-from-bits 0 sb!vm:long-float-normal-exponent-max
- (ldb (byte sb!vm:long-float-digits 0) -1)))
-(defconstant most-negative-double-float
- (double-from-bits 1 sb!vm:double-float-normal-exponent-max
- (ldb (byte sb!vm:double-float-digits 0) -1)))
-#!-long-float
-(defconstant most-negative-long-float most-negative-double-float)
-#!+(and long-float x86)
-(defconstant most-negative-long-float
- (long-from-bits 1 sb!vm:long-float-normal-exponent-max
- (ldb (byte sb!vm:long-float-digits 0) -1)))
-
-;;; We don't want to do these DEFCONSTANTs at cross-compilation time,
-;;; because the cross-compilation host might not support floating
-;;; point infinities. Putting them inside a LET removes
-;;; toplevel-formness, so that any EVAL-WHEN trickiness in the
-;;; DEFCONSTANT forms is suppressed.
-(let ()
-(defconstant single-float-positive-infinity
- (single-from-bits 0 (1+ sb!vm:single-float-normal-exponent-max) 0))
-(defconstant short-float-positive-infinity single-float-positive-infinity)
-(defconstant single-float-negative-infinity
- (single-from-bits 1 (1+ sb!vm:single-float-normal-exponent-max) 0))
-(defconstant short-float-negative-infinity single-float-negative-infinity)
-(defconstant double-float-positive-infinity
- (double-from-bits 0 (1+ sb!vm:double-float-normal-exponent-max) 0))
-#!+(not long-float)
-(defconstant long-float-positive-infinity double-float-positive-infinity)
-#!+(and long-float x86)
-(defconstant long-float-positive-infinity
- (long-from-bits 0 (1+ sb!vm:long-float-normal-exponent-max)
- (ash sb!vm:long-float-hidden-bit 32)))
-(defconstant double-float-negative-infinity
- (double-from-bits 1 (1+ sb!vm:double-float-normal-exponent-max) 0))
-#!+(not long-float)
-(defconstant long-float-negative-infinity double-float-negative-infinity)
-#!+(and long-float x86)
-(defconstant long-float-negative-infinity
- (long-from-bits 1 (1+ sb!vm:long-float-normal-exponent-max)
- (ash sb!vm:long-float-hidden-bit 32)))
-) ; LET-to-suppress-possible-EVAL-WHENs
-
-(defconstant single-float-epsilon
- (single-from-bits 0 (- sb!vm:single-float-bias
- (1- sb!vm:single-float-digits)) 1))
-(defconstant short-float-epsilon single-float-epsilon)
-(defconstant single-float-negative-epsilon
- (single-from-bits 0 (- sb!vm:single-float-bias sb!vm:single-float-digits) 1))
-(defconstant short-float-negative-epsilon single-float-negative-epsilon)
-(defconstant double-float-epsilon
- (double-from-bits 0 (- sb!vm:double-float-bias
- (1- sb!vm:double-float-digits)) 1))
-#!-long-float
-(defconstant long-float-epsilon double-float-epsilon)
-#!+(and long-float x86)
-(defconstant long-float-epsilon
- (long-from-bits 0 (- sb!vm:long-float-bias (1- sb!vm:long-float-digits))
- (+ 1 (ash sb!vm:long-float-hidden-bit 32))))
-(defconstant double-float-negative-epsilon
- (double-from-bits 0 (- sb!vm:double-float-bias sb!vm:double-float-digits) 1))
-#!-long-float
-(defconstant long-float-negative-epsilon double-float-negative-epsilon)
-#!+(and long-float x86)
-(defconstant long-float-negative-epsilon
- (long-from-bits 0 (- sb!vm:long-float-bias sb!vm:long-float-digits)
- (+ 1 (ash sb!vm:long-float-hidden-bit 32))))
-\f
;;;; float predicates and environment query
#!-sb-fluid
(declaim (maybe-inline float-denormalized-p float-infinity-p float-nan-p
- float-trapping-nan-p))
+ float-trapping-nan-p))
(defun float-denormalized-p (x)
#!+sb-doc
(number-dispatch ((x float))
((single-float)
(and (zerop (ldb sb!vm:single-float-exponent-byte (single-float-bits x)))
- (not (zerop x))))
+ (not (zerop x))))
((double-float)
(and (zerop (ldb sb!vm:double-float-exponent-byte
- (double-float-high-bits x)))
- (not (zerop x))))
+ (double-float-high-bits x)))
+ (not (zerop x))))
#!+(and long-float x86)
((long-float)
(and (zerop (ldb sb!vm:long-float-exponent-byte (long-float-exp-bits x)))
- (not (zerop x))))))
-
-(macrolet ((def (name doc single double #!+(and long-float x86) long)
- `(defun ,name (x)
- ,doc
- (number-dispatch ((x float))
- ((single-float)
- (let ((bits (single-float-bits x)))
- (and (> (ldb sb!vm:single-float-exponent-byte bits)
- sb!vm:single-float-normal-exponent-max)
- ,single)))
- ((double-float)
- (let ((hi (double-float-high-bits x))
- (lo (double-float-low-bits x)))
- (declare (ignorable lo))
- (and (> (ldb sb!vm:double-float-exponent-byte hi)
- sb!vm:double-float-normal-exponent-max)
- ,double)))
- #!+(and long-float x86)
- ((long-float)
- (let ((exp (long-float-exp-bits x))
- (hi (long-float-high-bits x))
- (lo (long-float-low-bits x)))
- (declare (ignorable lo))
- (and (> (ldb sb!vm:long-float-exponent-byte exp)
- sb!vm:long-float-normal-exponent-max)
- ,long)))))))
-
- (def float-infinity-p
- "Return true if the float X is an infinity (+ or -)."
- (zerop (ldb sb!vm:single-float-significand-byte bits))
- (and (zerop (ldb sb!vm:double-float-significand-byte hi))
- (zerop lo))
- #!+(and long-float x86)
- (and (zerop (ldb sb!vm:long-float-significand-byte hi))
- (zerop lo)))
-
- (def float-nan-p
- "Return true if the float X is a NaN (Not a Number)."
- (not (zerop (ldb sb!vm:single-float-significand-byte bits)))
- (or (not (zerop (ldb sb!vm:double-float-significand-byte hi)))
- (not (zerop lo)))
- #!+(and long-float x86)
- (or (not (zerop (ldb sb!vm:long-float-significand-byte hi)))
- (not (zerop lo))))
-
- (def float-trapping-nan-p
- "Return true if the float X is a trapping NaN (Not a Number)."
- (zerop (logand (ldb sb!vm:single-float-significand-byte bits)
- sb!vm:single-float-trapping-nan-bit))
- (zerop (logand (ldb sb!vm:double-float-significand-byte hi)
- sb!vm:double-float-trapping-nan-bit))
- #!+(and long-float x86)
- (zerop (logand (ldb sb!vm:long-float-significand-byte hi)
- sb!vm:long-float-trapping-nan-bit))))
+ (not (zerop x))))))
+
+(defmacro !define-float-dispatching-function
+ (name doc single double #!+(and long-float x86) long)
+ `(defun ,name (x)
+ ,doc
+ (number-dispatch ((x float))
+ ((single-float)
+ (let ((bits (single-float-bits x)))
+ (and (> (ldb sb!vm:single-float-exponent-byte bits)
+ sb!vm:single-float-normal-exponent-max)
+ ,single)))
+ ((double-float)
+ (let ((hi (double-float-high-bits x))
+ (lo (double-float-low-bits x)))
+ (declare (ignorable lo))
+ (and (> (ldb sb!vm:double-float-exponent-byte hi)
+ sb!vm:double-float-normal-exponent-max)
+ ,double)))
+ #!+(and long-float x86)
+ ((long-float)
+ (let ((exp (long-float-exp-bits x))
+ (hi (long-float-high-bits x))
+ (lo (long-float-low-bits x)))
+ (declare (ignorable lo))
+ (and (> (ldb sb!vm:long-float-exponent-byte exp)
+ sb!vm:long-float-normal-exponent-max)
+ ,long))))))
+
+(!define-float-dispatching-function float-infinity-p
+ "Return true if the float X is an infinity (+ or -)."
+ (zerop (ldb sb!vm:single-float-significand-byte bits))
+ (and (zerop (ldb sb!vm:double-float-significand-byte hi))
+ (zerop lo))
+ #!+(and long-float x86)
+ (and (zerop (ldb sb!vm:long-float-significand-byte hi))
+ (zerop lo)))
+
+(!define-float-dispatching-function float-nan-p
+ "Return true if the float X is a NaN (Not a Number)."
+ (not (zerop (ldb sb!vm:single-float-significand-byte bits)))
+ (or (not (zerop (ldb sb!vm:double-float-significand-byte hi)))
+ (not (zerop lo)))
+ #!+(and long-float x86)
+ (or (not (zerop (ldb sb!vm:long-float-significand-byte hi)))
+ (not (zerop lo))))
+
+(!define-float-dispatching-function float-trapping-nan-p
+ "Return true if the float X is a trapping NaN (Not a Number)."
+ (zerop (logand (ldb sb!vm:single-float-significand-byte bits)
+ sb!vm:single-float-trapping-nan-bit))
+ (zerop (logand (ldb sb!vm:double-float-significand-byte hi)
+ sb!vm:double-float-trapping-nan-bit))
+ #!+(and long-float x86)
+ (zerop (logand (ldb sb!vm:long-float-significand-byte hi)
+ sb!vm:long-float-trapping-nan-bit)))
;;; If denormalized, use a subfunction from INTEGER-DECODE-FLOAT to find the
;;; actual exponent (and hence how denormalized it is), otherwise we just
"Return a non-negative number of significant digits in its float argument.
Will be less than FLOAT-DIGITS if denormalized or zero."
(macrolet ((frob (digits bias decode)
- `(cond ((zerop f) 0)
- ((float-denormalized-p f)
- (multiple-value-bind (ignore exp) (,decode f)
- (declare (ignore ignore))
- (truly-the fixnum
- (+ ,digits (1- ,digits) ,bias exp))))
- (t
- ,digits))))
+ `(cond ((zerop f) 0)
+ ((float-denormalized-p f)
+ (multiple-value-bind (ignore exp) (,decode f)
+ (declare (ignore ignore))
+ (truly-the fixnum
+ (+ ,digits (1- ,digits) ,bias exp))))
+ (t
+ ,digits))))
(number-dispatch ((f float))
((single-float)
(frob sb!vm:single-float-digits sb!vm:single-float-bias
- integer-decode-single-denorm))
+ integer-decode-single-denorm))
((double-float)
(frob sb!vm:double-float-digits sb!vm:double-float-bias
- integer-decode-double-denorm))
+ integer-decode-double-denorm))
#!+long-float
((long-float)
(frob sb!vm:long-float-digits sb!vm:long-float-bias
- integer-decode-long-denorm)))))
+ integer-decode-long-denorm)))))
(defun float-sign (float1 &optional (float2 (float 1 float1)))
#!+sb-doc
"Return a floating-point number that has the same sign as
- float1 and, if float2 is given, has the same absolute value
- as float2."
+ FLOAT1 and, if FLOAT2 is given, has the same absolute value
+ as FLOAT2."
(declare (float float1 float2))
(* (if (etypecase float1
- (single-float (minusp (single-float-bits float1)))
- (double-float (minusp (double-float-high-bits float1)))
- #!+long-float
- (long-float (minusp (long-float-exp-bits float1))))
- (float -1 float1)
- (float 1 float1))
+ (single-float (minusp (single-float-bits float1)))
+ (double-float (minusp (double-float-high-bits float1)))
+ #!+long-float
+ (long-float (minusp (long-float-exp-bits float1))))
+ (float -1 float1)
+ (float 1 float1))
(abs float2)))
(defun float-format-digits (format)
(defun float-radix (x)
#!+sb-doc
"Return (as an integer) the radix b of its floating-point argument."
- ;; ANSI says this function "should signal an error if [..] argument
- ;; is not a float". Since X is otherwise ignored, Python doesn't
- ;; check the type by default, so we have to do it ourself:
- (unless (floatp x)
- (error 'type-error :datum x :expected-type 'float))
+ (declare (ignore x))
2)
\f
;;;; INTEGER-DECODE-FLOAT and DECODE-FLOAT
#!-sb-fluid
(declaim (maybe-inline integer-decode-single-float
- integer-decode-double-float))
+ integer-decode-double-float))
;;; Handle the denormalized case of INTEGER-DECODE-FLOAT for SINGLE-FLOAT.
(defun integer-decode-single-denorm (x)
(declare (type single-float x))
(let* ((bits (single-float-bits (abs x)))
- (sig (ash (ldb sb!vm:single-float-significand-byte bits) 1))
- (extra-bias 0))
+ (sig (ash (ldb sb!vm:single-float-significand-byte bits) 1))
+ (extra-bias 0))
(declare (type (unsigned-byte 24) sig)
- (type (integer 0 23) extra-bias))
+ (type (integer 0 23) extra-bias))
(loop
(unless (zerop (logand sig sb!vm:single-float-hidden-bit))
- (return))
+ (return))
(setq sig (ash sig 1))
(incf extra-bias))
(values sig
- (- (- sb!vm:single-float-bias)
- sb!vm:single-float-digits
- extra-bias)
- (if (minusp (float-sign x)) -1 1))))
+ (- (- sb!vm:single-float-bias)
+ sb!vm:single-float-digits
+ extra-bias)
+ (if (minusp (float-sign x)) -1 1))))
;;; Handle the single-float case of INTEGER-DECODE-FLOAT. If an infinity or
;;; NaN, error. If a denorm, call i-d-s-DENORM to handle it.
(defun integer-decode-single-float (x)
(declare (single-float x))
(let* ((bits (single-float-bits (abs x)))
- (exp (ldb sb!vm:single-float-exponent-byte bits))
- (sig (ldb sb!vm:single-float-significand-byte bits))
- (sign (if (minusp (float-sign x)) -1 1))
- (biased (- exp sb!vm:single-float-bias sb!vm:single-float-digits)))
+ (exp (ldb sb!vm:single-float-exponent-byte bits))
+ (sig (ldb sb!vm:single-float-significand-byte bits))
+ (sign (if (minusp (float-sign x)) -1 1))
+ (biased (- exp sb!vm:single-float-bias sb!vm:single-float-digits)))
(declare (fixnum biased))
(unless (<= exp sb!vm:single-float-normal-exponent-max)
(error "can't decode NaN or infinity: ~S" x))
(cond ((and (zerop exp) (zerop sig))
- (values 0 biased sign))
- ((< exp sb!vm:single-float-normal-exponent-min)
- (integer-decode-single-denorm x))
- (t
- (values (logior sig sb!vm:single-float-hidden-bit) biased sign)))))
+ (values 0 biased sign))
+ ((< exp sb!vm:single-float-normal-exponent-min)
+ (integer-decode-single-denorm x))
+ (t
+ (values (logior sig sb!vm:single-float-hidden-bit) biased sign)))))
-;;; Like INTEGER-DECODE-SINGLE-DENORM, only doubly so.
+;;; like INTEGER-DECODE-SINGLE-DENORM, only doubly so
(defun integer-decode-double-denorm (x)
(declare (type double-float x))
(let* ((high-bits (double-float-high-bits (abs x)))
- (sig-high (ldb sb!vm:double-float-significand-byte high-bits))
- (low-bits (double-float-low-bits x))
- (sign (if (minusp (float-sign x)) -1 1))
- (biased (- (- sb!vm:double-float-bias) sb!vm:double-float-digits)))
+ (sig-high (ldb sb!vm:double-float-significand-byte high-bits))
+ (low-bits (double-float-low-bits x))
+ (sign (if (minusp (float-sign x)) -1 1))
+ (biased (- (- sb!vm:double-float-bias) sb!vm:double-float-digits)))
(if (zerop sig-high)
- (let ((sig low-bits)
- (extra-bias (- sb!vm:double-float-digits 33))
- (bit (ash 1 31)))
- (declare (type (unsigned-byte 32) sig) (fixnum extra-bias))
- (loop
- (unless (zerop (logand sig bit)) (return))
- (setq sig (ash sig 1))
- (incf extra-bias))
- (values (ash sig (- sb!vm:double-float-digits 32))
- (truly-the fixnum (- biased extra-bias))
- sign))
- (let ((sig (ash sig-high 1))
- (extra-bias 0))
- (declare (type (unsigned-byte 32) sig) (fixnum extra-bias))
- (loop
- (unless (zerop (logand sig sb!vm:double-float-hidden-bit))
- (return))
- (setq sig (ash sig 1))
- (incf extra-bias))
- (values (logior (ash sig 32) (ash low-bits (1- extra-bias)))
- (truly-the fixnum (- biased extra-bias))
- sign)))))
-
-;;; Like INTEGER-DECODE-SINGLE-FLOAT, only doubly so.
+ (let ((sig low-bits)
+ (extra-bias (- sb!vm:double-float-digits 33))
+ (bit (ash 1 31)))
+ (declare (type (unsigned-byte 32) sig) (fixnum extra-bias))
+ (loop
+ (unless (zerop (logand sig bit)) (return))
+ (setq sig (ash sig 1))
+ (incf extra-bias))
+ (values (ash sig (- sb!vm:double-float-digits 32))
+ (truly-the fixnum (- biased extra-bias))
+ sign))
+ (let ((sig (ash sig-high 1))
+ (extra-bias 0))
+ (declare (type (unsigned-byte 32) sig) (fixnum extra-bias))
+ (loop
+ (unless (zerop (logand sig sb!vm:double-float-hidden-bit))
+ (return))
+ (setq sig (ash sig 1))
+ (incf extra-bias))
+ (values (logior (ash sig 32) (ash low-bits (1- extra-bias)))
+ (truly-the fixnum (- biased extra-bias))
+ sign)))))
+
+;;; like INTEGER-DECODE-SINGLE-FLOAT, only doubly so
(defun integer-decode-double-float (x)
(declare (double-float x))
(let* ((abs (abs x))
- (hi (double-float-high-bits abs))
- (lo (double-float-low-bits abs))
- (exp (ldb sb!vm:double-float-exponent-byte hi))
- (sig (ldb sb!vm:double-float-significand-byte hi))
- (sign (if (minusp (float-sign x)) -1 1))
- (biased (- exp sb!vm:double-float-bias sb!vm:double-float-digits)))
+ (hi (double-float-high-bits abs))
+ (lo (double-float-low-bits abs))
+ (exp (ldb sb!vm:double-float-exponent-byte hi))
+ (sig (ldb sb!vm:double-float-significand-byte hi))
+ (sign (if (minusp (float-sign x)) -1 1))
+ (biased (- exp sb!vm:double-float-bias sb!vm:double-float-digits)))
(declare (fixnum biased))
(unless (<= exp sb!vm:double-float-normal-exponent-max)
(error "Can't decode NaN or infinity: ~S." x))
(cond ((and (zerop exp) (zerop sig) (zerop lo))
- (values 0 biased sign))
- ((< exp sb!vm:double-float-normal-exponent-min)
- (integer-decode-double-denorm x))
- (t
- (values
- (logior (ash (logior (ldb sb!vm:double-float-significand-byte hi)
- sb!vm:double-float-hidden-bit)
- 32)
- lo)
- biased sign)))))
+ (values 0 biased sign))
+ ((< exp sb!vm:double-float-normal-exponent-min)
+ (integer-decode-double-denorm x))
+ (t
+ (values
+ (logior (ash (logior (ldb sb!vm:double-float-significand-byte hi)
+ sb!vm:double-float-hidden-bit)
+ 32)
+ lo)
+ biased sign)))))
#!+(and long-float x86)
(defun integer-decode-long-denorm (x)
(declare (type long-float x))
(let* ((high-bits (long-float-high-bits (abs x)))
- (sig-high (ldb sb!vm:long-float-significand-byte high-bits))
- (low-bits (long-float-low-bits x))
- (sign (if (minusp (float-sign x)) -1 1))
- (biased (- (- sb!vm:long-float-bias) sb!vm:long-float-digits)))
+ (sig-high (ldb sb!vm:long-float-significand-byte high-bits))
+ (low-bits (long-float-low-bits x))
+ (sign (if (minusp (float-sign x)) -1 1))
+ (biased (- (- sb!vm:long-float-bias) sb!vm:long-float-digits)))
(if (zerop sig-high)
- (let ((sig low-bits)
- (extra-bias (- sb!vm:long-float-digits 33))
- (bit (ash 1 31)))
- (declare (type (unsigned-byte 32) sig) (fixnum extra-bias))
- (loop
- (unless (zerop (logand sig bit)) (return))
- (setq sig (ash sig 1))
- (incf extra-bias))
- (values (ash sig (- sb!vm:long-float-digits 32))
- (truly-the fixnum (- biased extra-bias))
- sign))
- (let ((sig (ash sig-high 1))
- (extra-bias 0))
- (declare (type (unsigned-byte 32) sig) (fixnum extra-bias))
- (loop
- (unless (zerop (logand sig sb!vm:long-float-hidden-bit))
- (return))
- (setq sig (ash sig 1))
- (incf extra-bias))
- (values (logior (ash sig 32) (ash low-bits (1- extra-bias)))
- (truly-the fixnum (- biased extra-bias))
- sign)))))
+ (let ((sig low-bits)
+ (extra-bias (- sb!vm:long-float-digits 33))
+ (bit (ash 1 31)))
+ (declare (type (unsigned-byte 32) sig) (fixnum extra-bias))
+ (loop
+ (unless (zerop (logand sig bit)) (return))
+ (setq sig (ash sig 1))
+ (incf extra-bias))
+ (values (ash sig (- sb!vm:long-float-digits 32))
+ (truly-the fixnum (- biased extra-bias))
+ sign))
+ (let ((sig (ash sig-high 1))
+ (extra-bias 0))
+ (declare (type (unsigned-byte 32) sig) (fixnum extra-bias))
+ (loop
+ (unless (zerop (logand sig sb!vm:long-float-hidden-bit))
+ (return))
+ (setq sig (ash sig 1))
+ (incf extra-bias))
+ (values (logior (ash sig 32) (ash low-bits (1- extra-bias)))
+ (truly-the fixnum (- biased extra-bias))
+ sign)))))
#!+(and long-float x86)
(defun integer-decode-long-float (x)
(declare (long-float x))
(let* ((hi (long-float-high-bits x))
- (lo (long-float-low-bits x))
- (exp-bits (long-float-exp-bits x))
- (exp (ldb sb!vm:long-float-exponent-byte exp-bits))
- (sign (if (minusp exp-bits) -1 1))
- (biased (- exp sb!vm:long-float-bias sb!vm:long-float-digits)))
+ (lo (long-float-low-bits x))
+ (exp-bits (long-float-exp-bits x))
+ (exp (ldb sb!vm:long-float-exponent-byte exp-bits))
+ (sign (if (minusp exp-bits) -1 1))
+ (biased (- exp sb!vm:long-float-bias sb!vm:long-float-digits)))
(declare (fixnum biased))
(unless (<= exp sb!vm:long-float-normal-exponent-max)
(error "can't decode NaN or infinity: ~S" x))
(cond ((and (zerop exp) (zerop hi) (zerop lo))
- (values 0 biased sign))
- ((< exp sb!vm:long-float-normal-exponent-min)
- (integer-decode-long-denorm x))
- (t
- (values (logior (ash hi 32) lo) biased sign)))))
+ (values 0 biased sign))
+ ((< exp sb!vm:long-float-normal-exponent-min)
+ (integer-decode-long-denorm x))
+ (t
+ (values (logior (ash hi 32) lo) biased sign)))))
;;; Dispatch to the correct type-specific i-d-f function.
(defun integer-decode-float (x)
(declare (type single-float x))
(multiple-value-bind (sig exp sign) (integer-decode-single-denorm x)
(values (make-single-float
- (dpb sig sb!vm:single-float-significand-byte
- (dpb sb!vm:single-float-bias
- sb!vm:single-float-exponent-byte
- 0)))
- (truly-the fixnum (+ exp sb!vm:single-float-digits))
- (float sign x))))
+ (dpb sig sb!vm:single-float-significand-byte
+ (dpb sb!vm:single-float-bias
+ sb!vm:single-float-exponent-byte
+ 0)))
+ (truly-the fixnum (+ exp sb!vm:single-float-digits))
+ (float sign x))))
;;; Handle the single-float case of DECODE-FLOAT. If an infinity or NaN,
;;; error. If a denorm, call d-s-DENORM to handle it.
(defun decode-single-float (x)
(declare (single-float x))
(let* ((bits (single-float-bits (abs x)))
- (exp (ldb sb!vm:single-float-exponent-byte bits))
- (sign (float-sign x))
- (biased (truly-the single-float-exponent
- (- exp sb!vm:single-float-bias))))
+ (exp (ldb sb!vm:single-float-exponent-byte bits))
+ (sign (float-sign x))
+ (biased (truly-the single-float-exponent
+ (- exp sb!vm:single-float-bias))))
(unless (<= exp sb!vm:single-float-normal-exponent-max)
(error "can't decode NaN or infinity: ~S" x))
(cond ((zerop x)
- (values 0.0f0 biased sign))
- ((< exp sb!vm:single-float-normal-exponent-min)
- (decode-single-denorm x))
- (t
- (values (make-single-float
- (dpb sb!vm:single-float-bias
- sb!vm:single-float-exponent-byte
- bits))
- biased sign)))))
-
-;;; Like DECODE-SINGLE-DENORM, only doubly so.
+ (values 0.0f0 biased sign))
+ ((< exp sb!vm:single-float-normal-exponent-min)
+ (decode-single-denorm x))
+ (t
+ (values (make-single-float
+ (dpb sb!vm:single-float-bias
+ sb!vm:single-float-exponent-byte
+ bits))
+ biased sign)))))
+
+;;; like DECODE-SINGLE-DENORM, only doubly so
(defun decode-double-denorm (x)
(declare (double-float x))
(multiple-value-bind (sig exp sign) (integer-decode-double-denorm x)
(values (make-double-float
- (dpb (logand (ash sig -32) (lognot sb!vm:double-float-hidden-bit))
- sb!vm:double-float-significand-byte
- (dpb sb!vm:double-float-bias
- sb!vm:double-float-exponent-byte 0))
- (ldb (byte 32 0) sig))
- (truly-the fixnum (+ exp sb!vm:double-float-digits))
- (float sign x))))
-
-;;; Like DECODE-SINGLE-FLOAT, only doubly so.
+ (dpb (logand (ash sig -32) (lognot sb!vm:double-float-hidden-bit))
+ sb!vm:double-float-significand-byte
+ (dpb sb!vm:double-float-bias
+ sb!vm:double-float-exponent-byte 0))
+ (ldb (byte 32 0) sig))
+ (truly-the fixnum (+ exp sb!vm:double-float-digits))
+ (float sign x))))
+
+;;; like DECODE-SINGLE-FLOAT, only doubly so
(defun decode-double-float (x)
(declare (double-float x))
(let* ((abs (abs x))
- (hi (double-float-high-bits abs))
- (lo (double-float-low-bits abs))
- (exp (ldb sb!vm:double-float-exponent-byte hi))
- (sign (float-sign x))
- (biased (truly-the double-float-exponent
- (- exp sb!vm:double-float-bias))))
+ (hi (double-float-high-bits abs))
+ (lo (double-float-low-bits abs))
+ (exp (ldb sb!vm:double-float-exponent-byte hi))
+ (sign (float-sign x))
+ (biased (truly-the double-float-exponent
+ (- exp sb!vm:double-float-bias))))
(unless (<= exp sb!vm:double-float-normal-exponent-max)
(error "can't decode NaN or infinity: ~S" x))
(cond ((zerop x)
- (values 0.0d0 biased sign))
- ((< exp sb!vm:double-float-normal-exponent-min)
- (decode-double-denorm x))
- (t
- (values (make-double-float
- (dpb sb!vm:double-float-bias
- sb!vm:double-float-exponent-byte hi)
- lo)
- biased sign)))))
+ (values 0.0d0 biased sign))
+ ((< exp sb!vm:double-float-normal-exponent-min)
+ (decode-double-denorm x))
+ (t
+ (values (make-double-float
+ (dpb sb!vm:double-float-bias
+ sb!vm:double-float-exponent-byte hi)
+ lo)
+ biased sign)))))
#!+(and long-float x86)
(defun decode-long-denorm (x)
(declare (long-float x))
(multiple-value-bind (sig exp sign) (integer-decode-long-denorm x)
(values (make-long-float sb!vm:long-float-bias (ash sig -32)
- (ldb (byte 32 0) sig))
- (truly-the fixnum (+ exp sb!vm:long-float-digits))
- (float sign x))))
+ (ldb (byte 32 0) sig))
+ (truly-the fixnum (+ exp sb!vm:long-float-digits))
+ (float sign x))))
#!+(and long-float x86)
(defun decode-long-float (x)
(declare (long-float x))
(let* ((hi (long-float-high-bits x))
- (lo (long-float-low-bits x))
- (exp-bits (long-float-exp-bits x))
- (exp (ldb sb!vm:long-float-exponent-byte exp-bits))
- (sign (if (minusp exp-bits) -1l0 1l0))
- (biased (truly-the long-float-exponent
- (- exp sb!vm:long-float-bias))))
+ (lo (long-float-low-bits x))
+ (exp-bits (long-float-exp-bits x))
+ (exp (ldb sb!vm:long-float-exponent-byte exp-bits))
+ (sign (if (minusp exp-bits) -1l0 1l0))
+ (biased (truly-the long-float-exponent
+ (- exp sb!vm:long-float-bias))))
(unless (<= exp sb!vm:long-float-normal-exponent-max)
(error "can't decode NaN or infinity: ~S" x))
(cond ((zerop x)
- (values 0.0l0 biased sign))
- ((< exp sb!vm:long-float-normal-exponent-min)
- (decode-long-denorm x))
- (t
- (values (make-long-float
- (dpb sb!vm:long-float-bias sb!vm:long-float-exponent-byte
- exp-bits)
- hi
- lo)
- biased sign)))))
+ (values 0.0l0 biased sign))
+ ((< exp sb!vm:long-float-normal-exponent-min)
+ (decode-long-denorm x))
+ (t
+ (values (make-long-float
+ (dpb sb!vm:long-float-bias sb!vm:long-float-exponent-byte
+ exp-bits)
+ hi
+ lo)
+ biased sign)))))
;;; Dispatch to the appropriate type-specific function.
(defun decode-float (f)
(defun scale-float-maybe-underflow (x exp)
(multiple-value-bind (sig old-exp) (integer-decode-float x)
(let* ((digits (float-digits x))
- (new-exp (+ exp old-exp digits
- (etypecase x
- (single-float sb!vm:single-float-bias)
- (double-float sb!vm:double-float-bias))))
- (sign (if (minusp (float-sign x)) 1 0)))
+ (new-exp (+ exp old-exp digits
+ (etypecase x
+ (single-float sb!vm:single-float-bias)
+ (double-float sb!vm:double-float-bias))))
+ (sign (if (minusp (float-sign x)) 1 0)))
(cond
((< new-exp
- (etypecase x
- (single-float sb!vm:single-float-normal-exponent-min)
- (double-float sb!vm:double-float-normal-exponent-min)))
- (when (sb!vm:current-float-trap :inexact)
- (error 'floating-point-inexact :operation 'scale-float
- :operands (list x exp)))
- (when (sb!vm:current-float-trap :underflow)
- (error 'floating-point-underflow :operation 'scale-float
- :operands (list x exp)))
- (let ((shift (1- new-exp)))
- (if (< shift (- (1- digits)))
- (float-sign x 0.0)
- (etypecase x
- (single-float (single-from-bits sign 0 (ash sig shift)))
- (double-float (double-from-bits sign 0 (ash sig shift)))))))
+ (etypecase x
+ (single-float sb!vm:single-float-normal-exponent-min)
+ (double-float sb!vm:double-float-normal-exponent-min)))
+ (when (sb!vm:current-float-trap :inexact)
+ (error 'floating-point-inexact :operation 'scale-float
+ :operands (list x exp)))
+ (when (sb!vm:current-float-trap :underflow)
+ (error 'floating-point-underflow :operation 'scale-float
+ :operands (list x exp)))
+ (let ((shift (1- new-exp)))
+ (if (< shift (- (1- digits)))
+ (float-sign x 0.0)
+ (etypecase x
+ (single-float (single-from-bits sign 0 (ash sig shift)))
+ (double-float (double-from-bits sign 0 (ash sig shift)))))))
(t
- (etypecase x
- (single-float (single-from-bits sign new-exp sig))
- (double-float (double-from-bits sign new-exp sig))))))))
+ (etypecase x
+ (single-float (single-from-bits sign new-exp sig))
+ (double-float (double-from-bits sign new-exp sig))))))))
;;; Called when scaling a float overflows, or the original float was a
;;; NaN or infinity. If overflow errors are trapped, then error,
x)
((float-nan-p x)
(when (and (float-trapping-nan-p x)
- (sb!vm:current-float-trap :invalid))
+ (sb!vm:current-float-trap :invalid))
(error 'floating-point-invalid-operation :operation 'scale-float
- :operands (list x exp)))
+ :operands (list x exp)))
x)
(t
(when (sb!vm:current-float-trap :overflow)
(error 'floating-point-overflow :operation 'scale-float
- :operands (list x exp)))
+ :operands (list x exp)))
(when (sb!vm:current-float-trap :inexact)
(error 'floating-point-inexact :operation 'scale-float
- :operands (list x exp)))
+ :operands (list x exp)))
(* (float-sign x)
(etypecase x
- (single-float single-float-positive-infinity)
- (double-float double-float-positive-infinity))))))
+ (single-float
+ ;; SINGLE-FLOAT-POSITIVE-INFINITY
+ (single-from-bits 0 (1+ sb!vm:single-float-normal-exponent-max) 0))
+ (double-float
+ ;; DOUBLE-FLOAT-POSITIVE-INFINITY
+ (double-from-bits 0 (1+ sb!vm:double-float-normal-exponent-max) 0)))))))
;;; Scale a single or double float, calling the correct over/underflow
;;; functions.
(defun scale-single-float (x exp)
- (declare (single-float x) (fixnum exp))
- (let* ((bits (single-float-bits x))
- (old-exp (ldb sb!vm:single-float-exponent-byte bits))
- (new-exp (+ old-exp exp)))
- (cond
- ((zerop x) x)
- ((or (< old-exp sb!vm:single-float-normal-exponent-min)
- (< new-exp sb!vm:single-float-normal-exponent-min))
- (scale-float-maybe-underflow x exp))
- ((or (> old-exp sb!vm:single-float-normal-exponent-max)
- (> new-exp sb!vm:single-float-normal-exponent-max))
- (scale-float-maybe-overflow x exp))
- (t
- (make-single-float (dpb new-exp
- sb!vm:single-float-exponent-byte
- bits))))))
+ (declare (single-float x) (integer exp))
+ (etypecase exp
+ (fixnum
+ (let* ((bits (single-float-bits x))
+ (old-exp (ldb sb!vm:single-float-exponent-byte bits))
+ (new-exp (+ old-exp exp)))
+ (cond
+ ((zerop x) x)
+ ((or (< old-exp sb!vm:single-float-normal-exponent-min)
+ (< new-exp sb!vm:single-float-normal-exponent-min))
+ (scale-float-maybe-underflow x exp))
+ ((or (> old-exp sb!vm:single-float-normal-exponent-max)
+ (> new-exp sb!vm:single-float-normal-exponent-max))
+ (scale-float-maybe-overflow x exp))
+ (t
+ (make-single-float (dpb new-exp
+ sb!vm:single-float-exponent-byte
+ bits))))))
+ (unsigned-byte (scale-float-maybe-overflow x exp))
+ ((integer * 0) (scale-float-maybe-underflow x exp))))
(defun scale-double-float (x exp)
- (declare (double-float x) (fixnum exp))
- (let* ((hi (double-float-high-bits x))
- (lo (double-float-low-bits x))
- (old-exp (ldb sb!vm:double-float-exponent-byte hi))
- (new-exp (+ old-exp exp)))
- (cond
- ((zerop x) x)
- ((or (< old-exp sb!vm:double-float-normal-exponent-min)
- (< new-exp sb!vm:double-float-normal-exponent-min))
- (scale-float-maybe-underflow x exp))
- ((or (> old-exp sb!vm:double-float-normal-exponent-max)
- (> new-exp sb!vm:double-float-normal-exponent-max))
- (scale-float-maybe-overflow x exp))
- (t
- (make-double-float (dpb new-exp sb!vm:double-float-exponent-byte hi)
- lo)))))
+ (declare (double-float x) (integer exp))
+ (etypecase exp
+ (fixnum
+ (let* ((hi (double-float-high-bits x))
+ (lo (double-float-low-bits x))
+ (old-exp (ldb sb!vm:double-float-exponent-byte hi))
+ (new-exp (+ old-exp exp)))
+ (cond
+ ((zerop x) x)
+ ((or (< old-exp sb!vm:double-float-normal-exponent-min)
+ (< new-exp sb!vm:double-float-normal-exponent-min))
+ (scale-float-maybe-underflow x exp))
+ ((or (> old-exp sb!vm:double-float-normal-exponent-max)
+ (> new-exp sb!vm:double-float-normal-exponent-max))
+ (scale-float-maybe-overflow x exp))
+ (t
+ (make-double-float (dpb new-exp sb!vm:double-float-exponent-byte hi)
+ lo)))))
+ (unsigned-byte (scale-float-maybe-overflow x exp))
+ ((integer * 0) (scale-float-maybe-underflow x exp))))
#!+(and x86 long-float)
(defun scale-long-float (x exp)
- (declare (long-float x) (fixnum exp))
+ (declare (long-float x) (integer exp))
(scale-float x exp))
;;; Dispatch to the correct type-specific scale-float function.
result is the same float format as OTHER."
(if otherp
(number-dispatch ((number real) (other float))
- (((foreach rational single-float double-float #!+long-float long-float)
- (foreach single-float double-float #!+long-float long-float))
- (coerce number '(dispatch-type other))))
+ (((foreach rational single-float double-float #!+long-float long-float)
+ (foreach single-float double-float #!+long-float long-float))
+ (coerce number '(dispatch-type other))))
(if (floatp number)
- number
- (coerce number 'single-float))))
+ number
+ (coerce number 'single-float))))
(macrolet ((frob (name type)
- `(defun ,name (x)
- (number-dispatch ((x real))
- (((foreach single-float double-float #!+long-float long-float
- fixnum))
- (coerce x ',type))
- ((bignum)
- (bignum-to-float x ',type))
- ((ratio)
- (float-ratio x ',type))))))
+ `(defun ,name (x)
+ (number-dispatch ((x real))
+ (((foreach single-float double-float #!+long-float long-float
+ fixnum))
+ (coerce x ',type))
+ ((bignum)
+ (bignum-to-float x ',type))
+ ((ratio)
+ (float-ratio x ',type))))))
(frob %single-float single-float)
(frob %double-float double-float)
#!+long-float
;;; desired number of fraction bits, then do round-to-nearest.
(defun float-ratio (x format)
(let* ((signed-num (numerator x))
- (plusp (plusp signed-num))
- (num (if plusp signed-num (- signed-num)))
- (den (denominator x))
- (digits (float-format-digits format))
- (scale 0))
+ (plusp (plusp signed-num))
+ (num (if plusp signed-num (- signed-num)))
+ (den (denominator x))
+ (digits (float-format-digits format))
+ (scale 0))
(declare (fixnum digits scale))
;; Strip any trailing zeros from the denominator and move it into the scale
;; factor (to minimize the size of the operands.)
;; Guess how much we need to scale by from the magnitudes of the numerator
;; and denominator. We want one extra bit for a guard bit.
(let* ((num-len (integer-length num))
- (den-len (integer-length den))
- (delta (- den-len num-len))
- (shift (1+ (the fixnum (+ delta digits))))
- (shifted-num (ash num shift)))
+ (den-len (integer-length den))
+ (delta (- den-len num-len))
+ (shift (1+ (the fixnum (+ delta digits))))
+ (shifted-num (ash num shift)))
(declare (fixnum delta shift))
(decf scale delta)
(labels ((float-and-scale (bits)
- (let* ((bits (ash bits -1))
- (len (integer-length bits)))
- (cond ((> len digits)
- (aver (= len (the fixnum (1+ digits))))
- (scale-float (floatit (ash bits -1)) (1+ scale)))
- (t
- (scale-float (floatit bits) scale)))))
- (floatit (bits)
- (let ((sign (if plusp 0 1)))
- (case format
- (single-float
- (single-from-bits sign sb!vm:single-float-bias bits))
- (double-float
- (double-from-bits sign sb!vm:double-float-bias bits))
- #!+long-float
- (long-float
- (long-from-bits sign sb!vm:long-float-bias bits))))))
- (loop
- (multiple-value-bind (fraction-and-guard rem)
- (truncate shifted-num den)
- (let ((extra (- (integer-length fraction-and-guard) digits)))
- (declare (fixnum extra))
- (cond ((/= extra 1)
- (aver (> extra 1)))
- ((oddp fraction-and-guard)
- (return
- (if (zerop rem)
- (float-and-scale
- (if (zerop (logand fraction-and-guard 2))
- fraction-and-guard
- (1+ fraction-and-guard)))
- (float-and-scale (1+ fraction-and-guard)))))
- (t
- (return (float-and-scale fraction-and-guard)))))
- (setq shifted-num (ash shifted-num -1))
- (incf scale)))))))
+ (let* ((bits (ash bits -1))
+ (len (integer-length bits)))
+ (cond ((> len digits)
+ (aver (= len (the fixnum (1+ digits))))
+ (scale-float (floatit (ash bits -1)) (1+ scale)))
+ (t
+ (scale-float (floatit bits) scale)))))
+ (floatit (bits)
+ (let ((sign (if plusp 0 1)))
+ (case format
+ (single-float
+ (single-from-bits sign sb!vm:single-float-bias bits))
+ (double-float
+ (double-from-bits sign sb!vm:double-float-bias bits))
+ #!+long-float
+ (long-float
+ (long-from-bits sign sb!vm:long-float-bias bits))))))
+ (loop
+ (multiple-value-bind (fraction-and-guard rem)
+ (truncate shifted-num den)
+ (let ((extra (- (integer-length fraction-and-guard) digits)))
+ (declare (fixnum extra))
+ (cond ((/= extra 1)
+ (aver (> extra 1)))
+ ((oddp fraction-and-guard)
+ (return
+ (if (zerop rem)
+ (float-and-scale
+ (if (zerop (logand fraction-and-guard 2))
+ fraction-and-guard
+ (1+ fraction-and-guard)))
+ (float-and-scale (1+ fraction-and-guard)))))
+ (t
+ (return (float-and-scale fraction-and-guard)))))
+ (setq shifted-num (ash shifted-num -1))
+ (incf scale)))))))
#|
These might be useful if we ever have a machine without float/integer
(declare (single-float x) (values fixnum))
(locally (declare (optimize (speed 3) (safety 0)))
(let* ((bits (single-float-bits x))
- (exp (ldb sb!vm:single-float-exponent-byte bits))
- (frac (logior (ldb sb!vm:single-float-significand-byte bits)
- sb!vm:single-float-hidden-bit))
- (shift (- exp sb!vm:single-float-digits sb!vm:single-float-bias)))
+ (exp (ldb sb!vm:single-float-exponent-byte bits))
+ (frac (logior (ldb sb!vm:single-float-significand-byte bits)
+ sb!vm:single-float-hidden-bit))
+ (shift (- exp sb!vm:single-float-digits sb!vm:single-float-bias)))
(when (> exp sb!vm:single-float-normal-exponent-max)
- (error 'floating-point-invalid-operation :operator 'truncate
- :operands (list x)))
+ (error 'floating-point-invalid-operation :operator 'truncate
+ :operands (list x)))
(if (<= shift (- sb!vm:single-float-digits))
- 0
- (let ((res (ash frac shift)))
- (declare (type (unsigned-byte 31) res))
- (if (minusp bits)
- (- res)
- res))))))
+ 0
+ (let ((res (ash frac shift)))
+ (declare (type (unsigned-byte 31) res))
+ (if (minusp bits)
+ (- res)
+ res))))))
;;; Double-float version of this operation (see above single op).
(defun %unary-truncate-double-float/fixnum (x)
(declare (double-float x) (values fixnum))
(locally (declare (optimize (speed 3) (safety 0)))
(let* ((hi-bits (double-float-high-bits x))
- (exp (ldb sb!vm:double-float-exponent-byte hi-bits))
- (frac (logior (ldb sb!vm:double-float-significand-byte hi-bits)
- sb!vm:double-float-hidden-bit))
- (shift (- exp (- sb!vm:double-float-digits sb!vm:n-word-bits)
- sb!vm:double-float-bias)))
+ (exp (ldb sb!vm:double-float-exponent-byte hi-bits))
+ (frac (logior (ldb sb!vm:double-float-significand-byte hi-bits)
+ sb!vm:double-float-hidden-bit))
+ (shift (- exp (- sb!vm:double-float-digits sb!vm:n-word-bits)
+ sb!vm:double-float-bias)))
(when (> exp sb!vm:double-float-normal-exponent-max)
- (error 'floating-point-invalid-operation :operator 'truncate
- :operands (list x)))
+ (error 'floating-point-invalid-operation :operator 'truncate
+ :operands (list x)))
(if (<= shift (- sb!vm:n-word-bits sb!vm:double-float-digits))
- 0
- (let* ((res-hi (ash frac shift))
- (res (if (plusp shift)
- (logior res-hi
- (the fixnum
- (ash (double-float-low-bits x)
- (- shift sb!vm:n-word-bits))))
- res-hi)))
- (declare (type (unsigned-byte 31) res-hi res))
- (if (minusp hi-bits)
- (- res)
- res))))))
+ 0
+ (let* ((res-hi (ash frac shift))
+ (res (if (plusp shift)
+ (logior res-hi
+ (the fixnum
+ (ash (double-float-low-bits x)
+ (- shift sb!vm:n-word-bits))))
+ res-hi)))
+ (declare (type (unsigned-byte 31) res-hi res))
+ (if (minusp hi-bits)
+ (- res)
+ res))))))
|#
;;; This function is called when we are doing a truncate without any funky
((ratio) (values (truncate (numerator number) (denominator number))))
(((foreach single-float double-float #!+long-float long-float))
(if (< (float most-negative-fixnum number)
- number
- (float most-positive-fixnum number))
- (truly-the fixnum (%unary-truncate number))
- (multiple-value-bind (bits exp) (integer-decode-float number)
- (let ((res (ash bits exp)))
- (if (minusp number)
- (- res)
- res)))))))
+ number
+ (float most-positive-fixnum number))
+ (truly-the fixnum (%unary-truncate number))
+ (multiple-value-bind (bits exp) (integer-decode-float number)
+ (let ((res (ash bits exp)))
+ (if (minusp number)
+ (- res)
+ res)))))))
;;; Similar to %UNARY-TRUNCATE, but rounds to the nearest integer. If we
;;; can't use the round primitive, then we do our own round-to-nearest on the
((ratio) (values (round (numerator number) (denominator number))))
(((foreach single-float double-float #!+long-float long-float))
(if (< (float most-negative-fixnum number)
- number
- (float most-positive-fixnum number))
- (truly-the fixnum (%unary-round number))
- (multiple-value-bind (bits exp) (integer-decode-float number)
- (let* ((shifted (ash bits exp))
- (rounded (if (and (minusp exp)
- (oddp shifted)
- (eql (logand bits
- (lognot (ash -1 (- exp))))
- (ash 1 (- -1 exp))))
- (1+ shifted)
- shifted)))
- (if (minusp number)
- (- rounded)
- rounded)))))))
+ number
+ (float most-positive-fixnum number))
+ (truly-the fixnum (%unary-round number))
+ (multiple-value-bind (bits exp) (integer-decode-float number)
+ (let* ((shifted (ash bits exp))
+ (rounded (if (and (minusp exp)
+ (oddp shifted)
+ (eql (logand bits
+ (lognot (ash -1 (- exp))))
+ (ash 1 (- -1 exp))))
+ (1+ shifted)
+ shifted)))
+ (if (minusp number)
+ (- rounded)
+ rounded)))))))
+
+(defun %unary-ftruncate (number)
+ (number-dispatch ((number real))
+ ((integer) (float number))
+ ((ratio) (float (truncate (numerator number) (denominator number))))
+ (((foreach single-float double-float #!+long-float long-float))
+ (%unary-ftruncate number))))
(defun rational (x)
#!+sb-doc
(((foreach single-float double-float #!+long-float long-float))
(multiple-value-bind (bits exp) (integer-decode-float x)
(if (eql bits 0)
- 0
- (let* ((int (if (minusp x) (- bits) bits))
- (digits (float-digits x))
- (ex (+ exp digits)))
- (if (minusp ex)
- (integer-/-integer int (ash 1 (+ digits (- ex))))
- (integer-/-integer (ash int ex) (ash 1 digits)))))))
+ 0
+ (let* ((int (if (minusp x) (- bits) bits))
+ (digits (float-digits x))
+ (ex (+ exp digits)))
+ (if (minusp ex)
+ (integer-/-integer int (ash 1 (+ digits (- ex))))
+ (integer-/-integer (ash int ex) (ash 1 digits)))))))
((rational) x)))
+;;; This algorithm for RATIONALIZE, due to Bruno Haible, is included
+;;; with permission.
+;;;
+;;; Algorithm (recursively presented):
+;;; If x is a rational number, return x.
+;;; If x = 0.0, return 0.
+;;; If x < 0.0, return (- (rationalize (- x))).
+;;; If x > 0.0:
+;;; Call (integer-decode-float x). It returns a m,e,s=1 (mantissa,
+;;; exponent, sign).
+;;; If m = 0 or e >= 0: return x = m*2^e.
+;;; Search a rational number between a = (m-1/2)*2^e and b = (m+1/2)*2^e
+;;; with smallest possible numerator and denominator.
+;;; Note 1: If m is a power of 2, we ought to take a = (m-1/4)*2^e.
+;;; But in this case the result will be x itself anyway, regardless of
+;;; the choice of a. Therefore we can simply ignore this case.
+;;; Note 2: At first, we need to consider the closed interval [a,b].
+;;; but since a and b have the denominator 2^(|e|+1) whereas x itself
+;;; has a denominator <= 2^|e|, we can restrict the seach to the open
+;;; interval (a,b).
+;;; So, for given a and b (0 < a < b) we are searching a rational number
+;;; y with a <= y <= b.
+;;; Recursive algorithm fraction_between(a,b):
+;;; c := (ceiling a)
+;;; if c < b
+;;; then return c ; because a <= c < b, c integer
+;;; else
+;;; ; a is not integer (otherwise we would have had c = a < b)
+;;; k := c-1 ; k = floor(a), k < a < b <= k+1
+;;; return y = k + 1/fraction_between(1/(b-k), 1/(a-k))
+;;; ; note 1 <= 1/(b-k) < 1/(a-k)
+;;;
+;;; You can see that we are actually computing a continued fraction expansion.
+;;;
+;;; Algorithm (iterative):
+;;; If x is rational, return x.
+;;; Call (integer-decode-float x). It returns a m,e,s (mantissa,
+;;; exponent, sign).
+;;; If m = 0 or e >= 0, return m*2^e*s. (This includes the case x = 0.0.)
+;;; Create rational numbers a := (2*m-1)*2^(e-1) and b := (2*m+1)*2^(e-1)
+;;; (positive and already in lowest terms because the denominator is a
+;;; power of two and the numerator is odd).
+;;; Start a continued fraction expansion
+;;; p[-1] := 0, p[0] := 1, q[-1] := 1, q[0] := 0, i := 0.
+;;; Loop
+;;; c := (ceiling a)
+;;; if c >= b
+;;; then k := c-1, partial_quotient(k), (a,b) := (1/(b-k),1/(a-k)),
+;;; goto Loop
+;;; finally partial_quotient(c).
+;;; Here partial_quotient(c) denotes the iteration
+;;; i := i+1, p[i] := c*p[i-1]+p[i-2], q[i] := c*q[i-1]+q[i-2].
+;;; At the end, return s * (p[i]/q[i]).
+;;; This rational number is already in lowest terms because
+;;; p[i]*q[i-1]-p[i-1]*q[i] = (-1)^i.
+;;;
+;;; See also
+;;; Hardy, Wright: An introduction to number theory
+;;; and/or
+;;; <http://modular.fas.harvard.edu/edu/Fall2001/124/lectures/lecture17/lecture17/>
+;;; <http://modular.fas.harvard.edu/edu/Fall2001/124/lectures/lecture17/lecture18/>
+
(defun rationalize (x)
- #!+sb-doc
- "Converts any REAL to a RATIONAL. Floats are converted to a simple rational
+ "Converts any REAL to a RATIONAL. Floats are converted to a simple rational
representation exploiting the assumption that floats are only accurate to
- their precision. RATIONALIZE (and also RATIONAL) preserve the invariant:
+ their precision. RATIONALIZE (and also RATIONAL) preserve the invariant:
(= x (float (rationalize x) x))"
(number-dispatch ((x real))
(((foreach single-float double-float #!+long-float long-float))
- ;; Thanks to Kim Fateman, who stole this function rationalize-float from
- ;; macsyma's rational. Macsyma'a rationalize was written by the legendary
- ;; Gosper (rwg). Guy Steele said about Gosper, "He has been called the
- ;; only living 17th century mathematician and is also the best pdp-10
- ;; hacker I know." So, if you can understand or debug this code you win
- ;; big.
- (cond ((minusp x) (- (rationalize (- x))))
- ((zerop x) 0)
- (t
- (let ((eps (etypecase x
- (single-float single-float-epsilon)
- (double-float double-float-epsilon)
- #!+long-float
- (long-float long-float-epsilon)))
- (y ())
- (a ()))
- (do ((xx x (setq y (/ (float 1.0 x) (- xx (float a x)))))
- (num (setq a (truncate x))
- (+ (* (setq a (truncate y)) num) onum))
- (den 1 (+ (* a den) oden))
- (onum 1 num)
- (oden 0 den))
- ((and (not (zerop den))
- (not (> (abs (/ (- x (/ (float num x)
- (float den x)))
- x))
- eps)))
- (integer-/-integer num den))
- (declare ((dispatch-type x) xx)))))))
+ ;; This is a fairly straigtforward implementation of the
+ ;; iterative algorithm above.
+ (multiple-value-bind (frac expo sign)
+ (integer-decode-float x)
+ (cond ((or (zerop frac) (>= expo 0))
+ (if (minusp sign)
+ (- (ash frac expo))
+ (ash frac expo)))
+ (t
+ ;; expo < 0 and (2*m-1) and (2*m+1) are coprime to 2^(1-e),
+ ;; so build the fraction up immediately, without having to do
+ ;; a gcd.
+ (let ((a (build-ratio (- (* 2 frac) 1) (ash 1 (- 1 expo))))
+ (b (build-ratio (+ (* 2 frac) 1) (ash 1 (- 1 expo))))
+ (p0 0)
+ (q0 1)
+ (p1 1)
+ (q1 0))
+ (do ((c (ceiling a) (ceiling a)))
+ ((< c b)
+ (let ((top (+ (* c p1) p0))
+ (bot (+ (* c q1) q0)))
+ (build-ratio (if (minusp sign)
+ (- top)
+ top)
+ bot)))
+ (let* ((k (- c 1))
+ (p2 (+ (* k p1) p0))
+ (q2 (+ (* k q1) q0)))
+ (psetf a (/ (- b k))
+ b (/ (- a k)))
+ (setf p0 p1
+ q0 q1
+ p1 p2
+ q1 q2))))))))
((rational) x)))
projects / sbcl.git / blobdiff