X-Git-Url: http://repo.macrolet.net/gitweb/?a=blobdiff_plain;f=src%2Fcode%2Fnumbers.lisp;h=d525b8a38dcd1f6be93f10afc0225e044c566ed4;hb=568214ddf4c8ecc881caec98e20848d017974ec0;hp=e6ae2979c42237d0cc36df3d7613ec4de3f27a25;hpb=6e73f7320651975ce7cd8e72e2334041b7e80df1;p=sbcl.git diff --git a/src/code/numbers.lisp b/src/code/numbers.lisp index e6ae297..d525b8a 100644 --- a/src/code/numbers.lisp +++ b/src/code/numbers.lisp @@ -211,24 +211,6 @@ ;;;; COMPLEXes -(defun upgraded-complex-part-type (spec) - #!+sb-doc - "Return the element type of the most specialized COMPLEX number type that - can hold parts of type SPEC." - (cond ((unknown-type-p (specifier-type spec)) - (error "undefined type: ~S" spec)) - ((subtypep spec 'single-float) - 'single-float) - ((subtypep spec 'double-float) - 'double-float) - #!+long-float - ((subtypep spec 'long-float) - 'long-float) - ((subtypep spec 'rational) - 'rational) - (t - 'real))) - (defun complex (realpart &optional (imagpart 0)) #!+sb-doc "Return a complex number with the specified real and imaginary components." @@ -283,7 +265,7 @@ ((complex rational) (sb!kernel:%imagpart number)) (float - (float 0 number)) + (* 0 number)) (t 0))) @@ -406,7 +388,7 @@ (cond ((eql t1 0) 0) ((eql g2 1) (%make-ratio t1 (* t2 dy))) - (T (let* ((nn (truncate t1 g2)) + (t (let* ((nn (truncate t1 g2)) (t3 (truncate dy g2)) (nd (if (eql t2 1) t3 (* t2 t3)))) (if (eql nd 1) nn (%make-ratio nn nd)))))))))))) @@ -577,7 +559,7 @@ (numerator divisor)))) (values q (- number (* q divisor))))) ((fixnum bignum) - (values 0 number)) + (bignum-truncate (make-small-bignum number) divisor)) ((ratio (or float rational)) (let ((q (truncate (numerator number) (* (denominator number) divisor)))) @@ -653,19 +635,21 @@ (if (eql divisor 1) (round number) (multiple-value-bind (tru rem) (truncate number divisor) - (let ((thresh (/ (abs divisor) 2))) - (cond ((or (> rem thresh) - (and (= rem thresh) (oddp tru))) - (if (minusp divisor) - (values (- tru 1) (+ rem divisor)) - (values (+ tru 1) (- rem divisor)))) - ((let ((-thresh (- thresh))) - (or (< rem -thresh) - (and (= rem -thresh) (oddp tru)))) - (if (minusp divisor) - (values (+ tru 1) (- rem divisor)) - (values (- tru 1) (+ rem divisor)))) - (t (values tru rem))))))) + (if (zerop rem) + (values tru rem) + (let ((thresh (/ (abs divisor) 2))) + (cond ((or (> rem thresh) + (and (= rem thresh) (oddp tru))) + (if (minusp divisor) + (values (- tru 1) (+ rem divisor)) + (values (+ tru 1) (- rem divisor)))) + ((let ((-thresh (- thresh))) + (or (< rem -thresh) + (and (= rem -thresh) (oddp tru)))) + (if (minusp divisor) + (values (+ tru 1) (- rem divisor)) + (values (- tru 1) (+ rem divisor)))) + (t (values tru rem)))))))) (defun rem (number divisor) #!+sb-doc @@ -685,39 +669,94 @@ (+ rem divisor) rem))) -(macrolet ((def (name op doc) - `(defun ,name (number &optional (divisor 1)) - ,doc - (multiple-value-bind (res rem) (,op number divisor) - (values (float res (if (floatp rem) rem 1.0)) rem))))) - (def ffloor floor - "Same as FLOOR, but returns first value as a float.") - (def fceiling ceiling - "Same as CEILING, but returns first value as a float." ) - (def ftruncate truncate - "Same as TRUNCATE, but returns first value as a float.") - (def fround round - "Same as ROUND, but returns first value as a float.")) +(defmacro !define-float-rounding-function (name op doc) + `(defun ,name (number &optional (divisor 1)) + ,doc + (multiple-value-bind (res rem) (,op number divisor) + (values (float res (if (floatp rem) rem 1.0)) rem)))) + +(defun ftruncate (number &optional (divisor 1)) + #!+sb-doc + "Same as TRUNCATE, but returns first value as a float." + (macrolet ((ftruncate-float (rtype) + `(let* ((float-div (coerce divisor ',rtype)) + (res (%unary-ftruncate (/ number float-div)))) + (values res + (- number + (* (coerce res ',rtype) float-div)))))) + (number-dispatch ((number real) (divisor real)) + (((foreach fixnum bignum ratio) (or fixnum bignum ratio)) + (multiple-value-bind (q r) + (truncate number divisor) + (values (float q) r))) + (((foreach single-float double-float #!+long-float long-float) + (or rational single-float)) + (if (eql divisor 1) + (let ((res (%unary-ftruncate number))) + (values res (- number (coerce res '(dispatch-type number))))) + (ftruncate-float (dispatch-type number)))) + #!+long-float + ((long-float (or single-float double-float long-float)) + (ftruncate-float long-float)) + #!+long-float + (((foreach double-float single-float) long-float) + (ftruncate-float long-float)) + ((double-float (or single-float double-float)) + (ftruncate-float double-float)) + ((single-float double-float) + (ftruncate-float double-float)) + (((foreach fixnum bignum ratio) + (foreach single-float double-float #!+long-float long-float)) + (ftruncate-float (dispatch-type divisor)))))) + +(defun ffloor (number &optional (divisor 1)) + "Same as FLOOR, but returns first value as a float." + (multiple-value-bind (tru rem) (ftruncate number divisor) + (if (and (not (zerop rem)) + (if (minusp divisor) + (plusp number) + (minusp number))) + (values (1- tru) (+ rem divisor)) + (values tru rem)))) + +(defun fceiling (number &optional (divisor 1)) + "Same as CEILING, but returns first value as a float." + (multiple-value-bind (tru rem) (ftruncate number divisor) + (if (and (not (zerop rem)) + (if (minusp divisor) + (minusp number) + (plusp number))) + (values (+ tru 1) (- rem divisor)) + (values tru rem)))) + +;;; FIXME: this probably needs treatment similar to the use of +;;; %UNARY-FTRUNCATE for FTRUNCATE. +(defun fround (number &optional (divisor 1)) + "Same as ROUND, but returns first value as a float." + (multiple-value-bind (res rem) + (round number divisor) + (values (float res (if (floatp rem) rem 1.0)) rem))) ;;;; comparisons (defun = (number &rest more-numbers) #!+sb-doc "Return T if all of its arguments are numerically equal, NIL otherwise." + (the number number) (do ((nlist more-numbers (cdr nlist))) - ((atom nlist) T) + ((atom nlist) t) (declare (list nlist)) (if (not (= (car nlist) number)) (return nil)))) (defun /= (number &rest more-numbers) #!+sb-doc "Return T if no two of its arguments are numerically equal, NIL otherwise." - (do* ((head number (car nlist)) + (do* ((head (the number number) (car nlist)) (nlist more-numbers (cdr nlist))) ((atom nlist) t) (declare (list nlist)) (unless (do* ((nl nlist (cdr nl))) - ((atom nl) T) + ((atom nl) t) (declare (list nl)) (if (= head (car nl)) (return nil))) (return nil)))) @@ -725,7 +764,7 @@ (defun < (number &rest more-numbers) #!+sb-doc "Return T if its arguments are in strictly increasing order, NIL otherwise." - (do* ((n number (car nlist)) + (do* ((n (the number number) (car nlist)) (nlist more-numbers (cdr nlist))) ((atom nlist) t) (declare (list nlist)) @@ -734,7 +773,7 @@ (defun > (number &rest more-numbers) #!+sb-doc "Return T if its arguments are in strictly decreasing order, NIL otherwise." - (do* ((n number (car nlist)) + (do* ((n (the number number) (car nlist)) (nlist more-numbers (cdr nlist))) ((atom nlist) t) (declare (list nlist)) @@ -743,7 +782,7 @@ (defun <= (number &rest more-numbers) #!+sb-doc "Return T if arguments are in strictly non-decreasing order, NIL otherwise." - (do* ((n number (car nlist)) + (do* ((n (the number number) (car nlist)) (nlist more-numbers (cdr nlist))) ((atom nlist) t) (declare (list nlist)) @@ -752,7 +791,7 @@ (defun >= (number &rest more-numbers) #!+sb-doc "Return T if arguments are in strictly non-increasing order, NIL otherwise." - (do* ((n number (car nlist)) + (do* ((n (the number number) (car nlist)) (nlist more-numbers (cdr nlist))) ((atom nlist) t) (declare (list nlist)) @@ -760,7 +799,8 @@ (defun max (number &rest more-numbers) #!+sb-doc - "Return the greatest of its arguments." + "Return the greatest of its arguments; among EQUALP greatest, return +the first." (do ((nlist more-numbers (cdr nlist)) (result number)) ((null nlist) (return result)) @@ -770,7 +810,8 @@ (defun min (number &rest more-numbers) #!+sb-doc - "Return the least of its arguments." + "Return the least of its arguments; among EQUALP least, return +the first." (do ((nlist more-numbers (cdr nlist)) (result number)) ((null nlist) (return result)) @@ -778,6 +819,15 @@ (declare (type real number result)) (if (< (car nlist) result) (setq result (car nlist))))) +(defconstant most-positive-exactly-single-float-fixnum + (min #xffffff most-positive-fixnum)) +(defconstant most-negative-exactly-single-float-fixnum + (max #x-ffffff most-negative-fixnum)) +(defconstant most-positive-exactly-double-float-fixnum + (min #x1fffffffffffff most-positive-fixnum)) +(defconstant most-negative-exactly-double-float-fixnum + (max #x-1fffffffffffff most-negative-fixnum)) + (eval-when (:compile-toplevel :execute) ;;; The INFINITE-X-FINITE-Y and INFINITE-Y-FINITE-X args tell us how @@ -797,6 +847,40 @@ #!+long-float ((long-float (foreach single-float double-float)) (,op x (coerce y 'long-float))) + ((fixnum (foreach single-float double-float)) + (if (float-infinity-p y) + ,infinite-y-finite-x + ;; If the fixnum has an exact float representation, do a + ;; float comparison. Otherwise do the slow float -> ratio + ;; conversion. + (multiple-value-bind (lo hi) + (case '(dispatch-type y) + ('single-float + (values most-negative-exactly-single-float-fixnum + most-positive-exactly-single-float-fixnum)) + ('double-float + (values most-negative-exactly-double-float-fixnum + most-positive-exactly-double-float-fixnum))) + (if (<= lo y hi) + (,op (coerce x '(dispatch-type y)) y) + (,op x (rational y)))))) + (((foreach single-float double-float) fixnum) + (if (eql y 0) + (,op x (coerce 0 '(dispatch-type x))) + (if (float-infinity-p x) + ,infinite-x-finite-y + ;; Likewise + (multiple-value-bind (lo hi) + (case '(dispatch-type x) + ('single-float + (values most-negative-exactly-single-float-fixnum + most-positive-exactly-single-float-fixnum)) + ('double-float + (values most-negative-exactly-double-float-fixnum + most-positive-exactly-double-float-fixnum))) + (if (<= lo y hi) + (,op x (coerce y '(dispatch-type x))) + (,op (rational x) y)))))) (((foreach single-float double-float) double-float) (,op (coerce x 'double-float) y)) ((double-float single-float) @@ -953,36 +1037,6 @@ (declare (integer result))) -1)) -(defun lognand (integer1 integer2) - #!+sb-doc - "Return the complement of the logical AND of integer1 and integer2." - (lognand integer1 integer2)) - -(defun lognor (integer1 integer2) - #!+sb-doc - "Return the complement of the logical OR of integer1 and integer2." - (lognor integer1 integer2)) - -(defun logandc1 (integer1 integer2) - #!+sb-doc - "Return the logical AND of (LOGNOT integer1) and integer2." - (logandc1 integer1 integer2)) - -(defun logandc2 (integer1 integer2) - #!+sb-doc - "Return the logical AND of integer1 and (LOGNOT integer2)." - (logandc2 integer1 integer2)) - -(defun logorc1 (integer1 integer2) - #!+sb-doc - "Return the logical OR of (LOGNOT integer1) and integer2." - (logorc1 integer1 integer2)) - -(defun logorc2 (integer1 integer2) - #!+sb-doc - "Return the logical OR of integer1 and (LOGNOT integer2)." - (logorc2 integer1 integer2)) - (defun lognot (number) #!+sb-doc "Return the bit-wise logical not of integer." @@ -990,13 +1044,39 @@ (fixnum (lognot (truly-the fixnum number))) (bignum (bignum-logical-not number)))) -(macrolet ((def (name op big-op) - `(defun ,name (x y) - (number-dispatch ((x integer) (y integer)) - (bignum-cross-fixnum ,op ,big-op))))) +(macrolet ((def (name op big-op &optional doc) + `(defun ,name (integer1 integer2) + ,@(when doc + (list doc)) + (let ((x integer1) + (y integer2)) + (number-dispatch ((x integer) (y integer)) + (bignum-cross-fixnum ,op ,big-op)))))) (def two-arg-and logand bignum-logical-and) (def two-arg-ior logior bignum-logical-ior) - (def two-arg-xor logxor bignum-logical-xor)) + (def two-arg-xor logxor bignum-logical-xor) + ;; BIGNUM-LOGICAL-{AND,IOR,XOR} need not return a bignum, so must + ;; call the generic LOGNOT... + (def two-arg-eqv logeqv (lambda (x y) (lognot (bignum-logical-xor x y)))) + (def lognand lognand + (lambda (x y) (lognot (bignum-logical-and x y))) + #!+sb-doc "Complement the logical AND of INTEGER1 and INTEGER2.") + (def lognor lognor + (lambda (x y) (lognot (bignum-logical-ior x y))) + #!+sb-doc "Complement the logical AND of INTEGER1 and INTEGER2.") + ;; ... but BIGNUM-LOGICAL-NOT on a bignum will always return a bignum + (def logandc1 logandc1 + (lambda (x y) (bignum-logical-and (bignum-logical-not x) y)) + #!+sb-doc "Bitwise AND (LOGNOT INTEGER1) with INTEGER2.") + (def logandc2 logandc2 + (lambda (x y) (bignum-logical-and x (bignum-logical-not y))) + #!+sb-doc "Bitwise AND INTEGER1 with (LOGNOT INTEGER2).") + (def logorc1 logorc1 + (lambda (x y) (bignum-logical-ior (bignum-logical-not x) y)) + #!+sb-doc "Bitwise OR (LOGNOT INTEGER1) with INTEGER2.") + (def logorc2 logorc2 + (lambda (x y) (bignum-logical-ior x (bignum-logical-not y))) + #!+sb-doc "Bitwise OR INTEGER1 with (LOGNOT INTEGER2).")) (defun logcount (integer) #!+sb-doc @@ -1004,8 +1084,9 @@ if INTEGER is negative." (etypecase integer (fixnum - (logcount (truly-the (integer 0 #.(max most-positive-fixnum - (lognot most-negative-fixnum))) + (logcount (truly-the (integer 0 + #.(max sb!xc:most-positive-fixnum + (lognot sb!xc:most-negative-fixnum))) (if (minusp (truly-the fixnum integer)) (lognot (truly-the fixnum integer)) integer)))) @@ -1020,7 +1101,12 @@ (defun logbitp (index integer) #!+sb-doc "Predicate returns T if bit index of integer is a 1." - (logbitp index integer)) + (number-dispatch ((index integer) (integer integer)) + ((fixnum fixnum) (if (> index #.(- sb!vm:n-word-bits sb!vm:n-lowtag-bits)) + (minusp integer) + (not (zerop (logand integer (ash 1 index)))))) + ((fixnum bignum) (bignum-logbitp index integer)) + ((bignum (foreach fixnum bignum)) (minusp integer)))) (defun ash (integer count) #!+sb-doc @@ -1052,7 +1138,8 @@ (defun integer-length (integer) #!+sb-doc - "Return the number of significant bits in the absolute value of integer." + "Return the number of non-sign bits in the twos-complement representation + of INTEGER." (etypecase integer (fixnum (integer-length (truly-the fixnum integer))) @@ -1118,6 +1205,18 @@ (let ((mask (ash (ldb (byte size 0) -1) posn))) (logior (logand newbyte mask) (logand integer (lognot mask))))) + +(defun sb!c::mask-signed-field (size integer) + #!+sb-doc + "Extract SIZE lower bits from INTEGER, considering them as a +2-complement SIZE-bits representation of a signed integer." + (cond ((zerop size) + 0) + ((logbitp (1- size) integer) + (dpb integer (byte size 0) -1)) + (t + (ldb (byte size 0) integer)))) + ;;;; BOOLE @@ -1193,22 +1292,22 @@ (defun boole (op integer1 integer2) #!+sb-doc "Bit-wise boolean function on two integers. Function chosen by OP: - 0 BOOLE-CLR - 1 BOOLE-SET - 2 BOOLE-1 - 3 BOOLE-2 - 4 BOOLE-C1 - 5 BOOLE-C2 - 6 BOOLE-AND - 7 BOOLE-IOR - 8 BOOLE-XOR - 9 BOOLE-EQV - 10 BOOLE-NAND - 11 BOOLE-NOR - 12 BOOLE-ANDC1 - 13 BOOLE-ANDC2 - 14 BOOLE-ORC1 - 15 BOOLE-ORC2" + 0 BOOLE-CLR + 1 BOOLE-SET + 2 BOOLE-1 + 3 BOOLE-2 + 4 BOOLE-C1 + 5 BOOLE-C2 + 6 BOOLE-AND + 7 BOOLE-IOR + 8 BOOLE-XOR + 9 BOOLE-EQV + 10 BOOLE-NAND + 11 BOOLE-NOR + 12 BOOLE-ANDC1 + 13 BOOLE-ANDC2 + 14 BOOLE-ORC1 + 15 BOOLE-ORC2" (case op (0 (boole 0 integer1 integer2)) (1 (boole 1 integer1 integer2)) @@ -1259,7 +1358,20 @@ (defun two-arg-lcm (n m) (declare (integer n m)) - (* (truncate (max n m) (gcd n m)) (min n m))) + (if (or (zerop n) (zerop m)) + 0 + ;; KLUDGE: I'm going to assume that it was written this way + ;; originally for a reason. However, this is a somewhat + ;; complicated way of writing the algorithm in the CLHS page for + ;; LCM, and I don't know why. To be investigated. -- CSR, + ;; 2003-09-11 + (let ((m (abs m)) + (n (abs n))) + (multiple-value-bind (max min) + (if (> m n) + (values m n) + (values n m)) + (* (truncate max (gcd n m)) min))))) ;;; Do the GCD of two integer arguments. With fixnum arguments, we use the ;;; binary GCD algorithm from Knuth's seminumerical algorithms (slightly @@ -1267,8 +1379,8 @@ ;;; of 0 before the dispatch so that the bignum code doesn't have to worry ;;; about "small bignum" zeros. (defun two-arg-gcd (u v) - (cond ((eql u 0) v) - ((eql v 0) u) + (cond ((eql u 0) (abs v)) + ((eql v 0) (abs u)) (t (number-dispatch ((u integer) (v integer)) ((fixnum fixnum) @@ -1334,3 +1446,79 @@ (def minusp "Is this real number strictly negative?") (def oddp "Is this integer odd?") (def evenp "Is this integer even?")) + +;;;; modular functions +#. +(collect ((forms)) + (flet ((definition (name lambda-list width pattern) + `(defun ,name ,lambda-list + (flet ((prepare-argument (x) + (declare (integer x)) + (etypecase x + ((unsigned-byte ,width) x) + (fixnum (logand x ,pattern)) + (bignum (logand x ,pattern))))) + (,name ,@(loop for arg in lambda-list + collect `(prepare-argument ,arg))))))) + (loop for infos being each hash-value of (sb!c::modular-class-funs sb!c::*unsigned-modular-class*) + ;; FIXME: We need to process only "toplevel" functions + when (listp infos) + do (loop for info in infos + for name = (sb!c::modular-fun-info-name info) + and width = (sb!c::modular-fun-info-width info) + and lambda-list = (sb!c::modular-fun-info-lambda-list info) + for pattern = (1- (ash 1 width)) + do (forms (definition name lambda-list width pattern))))) + `(progn ,@(forms))) + +#. +(collect ((forms)) + (flet ((definition (name lambda-list width) + `(defun ,name ,lambda-list + (flet ((prepare-argument (x) + (declare (integer x)) + (etypecase x + ((signed-byte ,width) x) + (fixnum (sb!c::mask-signed-field ,width x)) + (bignum (sb!c::mask-signed-field ,width x))))) + (,name ,@(loop for arg in lambda-list + collect `(prepare-argument ,arg))))))) + (loop for infos being each hash-value of (sb!c::modular-class-funs sb!c::*signed-modular-class*) + ;; FIXME: We need to process only "toplevel" functions + when (listp infos) + do (loop for info in infos + for name = (sb!c::modular-fun-info-name info) + and width = (sb!c::modular-fun-info-width info) + and lambda-list = (sb!c::modular-fun-info-lambda-list info) + do (forms (definition name lambda-list width))))) + `(progn ,@(forms))) + +;;; KLUDGE: these out-of-line definitions can't use the modular +;;; arithmetic, as that is only (currently) defined for constant +;;; shifts. See also the comment in (LOGAND OPTIMIZER) for more +;;; discussion of this hack. -- CSR, 2003-10-09 +#!+#.(cl:if (cl:= sb!vm:n-machine-word-bits 32) '(and) '(or)) +(defun sb!vm::ash-left-mod32 (integer amount) + (etypecase integer + ((unsigned-byte 32) (ldb (byte 32 0) (ash integer amount))) + (fixnum (ldb (byte 32 0) (ash (logand integer #xffffffff) amount))) + (bignum (ldb (byte 32 0) (ash (logand integer #xffffffff) amount))))) +#!+#.(cl:if (cl:= sb!vm:n-machine-word-bits 64) '(and) '(or)) +(defun sb!vm::ash-left-mod64 (integer amount) + (etypecase integer + ((unsigned-byte 64) (ldb (byte 64 0) (ash integer amount))) + (fixnum (ldb (byte 64 0) (ash (logand integer #xffffffffffffffff) amount))) + (bignum (ldb (byte 64 0) + (ash (logand integer #xffffffffffffffff) amount))))) + +#!+x86 +(defun sb!vm::ash-left-smod30 (integer amount) + (etypecase integer + ((signed-byte 30) (sb!c::mask-signed-field 30 (ash integer amount))) + (integer (sb!c::mask-signed-field 30 (ash (sb!c::mask-signed-field 30 integer) amount))))) + +#!+x86-64 +(defun sb!vm::ash-left-smod61 (integer amount) + (etypecase integer + ((signed-byte 61) (sb!c::mask-signed-field 61 (ash integer amount))) + (integer (sb!c::mask-signed-field 61 (ash (sb!c::mask-signed-field 61 integer) amount)))))