X-Git-Url: http://repo.macrolet.net/gitweb/?a=blobdiff_plain;f=src%2Fcode%2Ffloat.lisp;h=a3a0114a7f752f74f4a94239572b150d64baef9a;hb=54da325f13fb41669869aea688ae195426c0e231;hp=c0e0419c5e788851ab6e8eb222f4878ea5cbeaa3;hpb=43980afbf2f02ff68b3cfb62be9051fabe164de0;p=sbcl.git diff --git a/src/code/float.lisp b/src/code/float.lisp index c0e0419..a3a0114 100644 --- a/src/code/float.lisp +++ b/src/code/float.lisp @@ -19,7 +19,7 @@ #!-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 @@ -27,15 +27,15 @@ (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)))))) + (not (zerop x)))))) (defmacro !define-float-dispatching-function (name doc single double #!+(and long-float x86) long) @@ -44,25 +44,25 @@ (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))) + (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))) + (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)))))) + (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 -)." @@ -75,22 +75,37 @@ (!define-float-dispatching-function float-nan-p "Return true if the float X is a NaN (Not a Number)." + #!-(or mips hppa) (not (zerop (ldb sb!vm:single-float-significand-byte bits))) + #!+(or mips hppa) + (zerop (logand (ldb sb!vm:single-float-significand-byte bits) + sb!vm:single-float-trapping-nan-bit)) + #!-(or mips hppa) (or (not (zerop (ldb sb!vm:double-float-significand-byte hi))) (not (zerop lo))) + #!+(or mips hppa) + (zerop (logand (ldb sb!vm:double-float-significand-byte hi) + sb!vm:double-float-trapping-nan-bit)) #!+(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)." + #!-(or mips hppa) (zerop (logand (ldb sb!vm:single-float-significand-byte bits) - sb!vm:single-float-trapping-nan-bit)) + sb!vm:single-float-trapping-nan-bit)) + #!+(or mips hppa) + (not (zerop (ldb sb!vm:single-float-significand-byte bits))) + #!-(or mips hppa) (zerop (logand (ldb sb!vm:double-float-significand-byte hi) - sb!vm:double-float-trapping-nan-bit)) + sb!vm:double-float-trapping-nan-bit)) + #!+(or mips hppa) + (or (not (zerop (ldb sb!vm:double-float-significand-byte hi))) + (not (zerop lo))) #!+(and long-float x86) (zerop (logand (ldb sb!vm:long-float-significand-byte hi) - sb!vm:long-float-trapping-nan-bit))) + 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 @@ -101,25 +116,25 @@ "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 @@ -128,12 +143,12 @@ 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) @@ -155,160 +170,160 @@ (defun float-radix (x) #!+sb-doc "Return (as an integer) the radix b of its floating-point argument." - (declare (ignore x)) + (declare (ignore x) (type float x)) 2) ;;;; 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 (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))))) + (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) @@ -337,103 +352,103 @@ (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))))) + (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)))) + (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) @@ -461,32 +476,32 @@ (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, @@ -499,66 +514,74 @@ 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 - (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))))))) + (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. @@ -584,40 +607,40 @@ 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 (frob %long-float long-float)) ;;; Convert a ratio to a float. We avoid any rounding error by doing an -;;; integer division. Accuracy is important to preserve read/print +;;; integer division. Accuracy is important to preserve print-read ;;; consistency, since this is ultimately how the reader reads a float. We ;;; scale the numerator by a power of two until the division results in the ;;; 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.) @@ -628,128 +651,147 @@ ;; 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))))))) - -#| -These might be useful if we ever have a machine without float/integer -conversion hardware. For now, we'll use special ops that -uninterruptibly frob the rounding modes & do ieee round-to-integer. - -;;; The compiler compiles a call to this when we are doing %UNARY-TRUNCATE -;;; and the result is known to be a fixnum. We can avoid some generic -;;; arithmetic in this case. -(defun %unary-truncate-single-float/fixnum (x) - (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))) - (when (> exp sb!vm:single-float-normal-exponent-max) - (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)))))) - -;;; 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))) - (when (> exp sb!vm:double-float-normal-exponent-max) - (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)))))) -|# + (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 +;;; conversion hardware. For now, we'll use special ops that +;;; uninterruptibly frob the rounding modes & do ieee round-to-integer. +#+nil +(progn + ;; The compiler compiles a call to this when we are doing %UNARY-TRUNCATE + ;; and the result is known to be a fixnum. We can avoid some generic + ;; arithmetic in this case. + (defun %unary-truncate-single-float/fixnum (x) + (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))) + (when (> exp sb!vm:single-float-normal-exponent-max) + (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)))))) + ;; 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))) + (when (> exp sb!vm:double-float-normal-exponent-max) + (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))))))) ;;; This function is called when we are doing a truncate without any funky ;;; divisor, i.e. converting a float or ratio to an integer. Note that we do ;;; *not* return the second value of truncate, so it must be computed by the ;;; caller if needed. ;;; -;;; In the float case, we pick off small arguments so that compiler can use -;;; special-case operations. We use an exclusive test, since (due to round-off -;;; error), (float most-positive-fixnum) may be greater than -;;; most-positive-fixnum. +;;; In the float case, we pick off small arguments so that compiler +;;; can use special-case operations. We use an exclusive test, since +;;; (due to round-off error), (float most-positive-fixnum) is likely +;;; to be equal to (1+ most-positive-fixnum). An exclusive test is +;;; good enough, because most-positive-fixnum will be one less than a +;;; power of two, and that power of two will be exactly representable +;;; as a float (at least until we get 128-bit fixnums). (defun %unary-truncate (number) (number-dispatch ((number real)) ((integer) number) ((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))))))) + +;;; Specialized versions for floats. +(macrolet ((def (type name) + `(defun ,name (number) + (if (< ,(coerce sb!xc:most-negative-fixnum type) + number + ,(coerce sb!xc:most-positive-fixnum type)) + (truly-the fixnum (,name number)) + ;; General -- slow -- case. + (multiple-value-bind (bits exp) (integer-decode-float number) + (let ((res (ash bits exp))) + (if (minusp number) + (- res) + res))))))) + (def single-float %unary-truncate/single-float) + (def double-float %unary-truncate/double-float) + #!+long-float + (def double-float %unary-truncate/long-float)) ;;; 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 @@ -763,21 +805,22 @@ uninterruptibly frob the rounding modes & do ieee round-to-integer. ((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 (minusp exp) + (let ((fractional-bits (logand bits (lognot (ash -1 (- exp))))) + (0.5bits (ash 1 (- -1 exp)))) + (cond + ((> fractional-bits 0.5bits) (1+ shifted)) + ((< fractional-bits 0.5bits) shifted) + (t (if (oddp shifted) (1+ shifted) shifted)))) + shifted))) + (if (minusp number) + (- rounded) + rounded))))))) (defun %unary-ftruncate (number) (number-dispatch ((number real)) @@ -795,13 +838,13 @@ uninterruptibly frob the rounding modes & do ieee round-to-integer. (((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 @@ -876,36 +919,36 @@ uninterruptibly frob the rounding modes & do ieee round-to-integer. ;; This is a fairly straigtforward implementation of the ;; iterative algorithm above. (multiple-value-bind (frac expo sign) - (integer-decode-float x) + (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)))))))) + (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)))