1 ;;;; This file contains floating-point-specific transforms, and may be
2 ;;;; somewhat implementation-dependent in its assumptions of what the
5 ;;;; This software is part of the SBCL system. See the README file for
8 ;;;; This software is derived from the CMU CL system, which was
9 ;;;; written at Carnegie Mellon University and released into the
10 ;;;; public domain. The software is in the public domain and is
11 ;;;; provided with absolutely no warranty. See the COPYING and CREDITS
12 ;;;; files for more information.
18 (defknown %single-float (real) single-float (movable foldable))
19 (defknown %double-float (real) double-float (movable foldable))
21 (deftransform float ((n f) (* single-float) *)
24 (deftransform float ((n f) (* double-float) *)
27 (deftransform float ((n) *)
32 (deftransform %single-float ((n) (single-float) *)
35 (deftransform %double-float ((n) (double-float) *)
39 (macrolet ((frob (fun type)
40 `(deftransform random ((num &optional state)
41 (,type &optional *) *)
42 "Use inline float operations."
43 '(,fun num (or state *random-state*)))))
44 (frob %random-single-float single-float)
45 (frob %random-double-float double-float))
47 ;;; Mersenne Twister RNG
49 ;;; FIXME: It's unpleasant to have RANDOM functionality scattered
50 ;;; through the code this way. It would be nice to move this into the
51 ;;; same file as the other RANDOM definitions.
52 (deftransform random ((num &optional state)
53 ((integer 1 #.(expt 2 sb!vm::n-word-bits)) &optional *))
54 ;; FIXME: I almost conditionalized this as #!+sb-doc. Find some way
55 ;; of automatically finding #!+sb-doc in proximity to DEFTRANSFORM
56 ;; to let me scan for places that I made this mistake and didn't
58 "use inline (UNSIGNED-BYTE 32) operations"
59 (let ((type (lvar-type num))
60 (limit (expt 2 sb!vm::n-word-bits))
61 (random-chunk (ecase sb!vm::n-word-bits
63 (64 'sb!kernel::big-random-chunk))))
64 (if (numeric-type-p type)
65 (let ((num-high (numeric-type-high (lvar-type num))))
67 (cond ((constant-lvar-p num)
68 ;; Check the worst case sum absolute error for the
69 ;; random number expectations.
70 (let ((rem (rem limit num-high)))
71 (unless (< (/ (* 2 rem (- num-high rem))
73 (expt 2 (- sb!kernel::random-integer-extra-bits)))
74 (give-up-ir1-transform
75 "The random number expectations are inaccurate."))
76 (if (= num-high limit)
77 `(,random-chunk (or state *random-state*))
79 `(rem (,random-chunk (or state *random-state*)) num)
81 ;; Use multiplication, which is faster.
82 `(values (sb!bignum::%multiply
83 (,random-chunk (or state *random-state*))
85 ((> num-high random-fixnum-max)
86 (give-up-ir1-transform
87 "The range is too large to ensure an accurate result."))
90 `(values (sb!bignum::%multiply
91 (,random-chunk (or state *random-state*))
94 `(rem (,random-chunk (or state *random-state*)) num))))
95 ;; KLUDGE: a relatively conservative treatment, but better
96 ;; than a bug (reported by PFD sbcl-devel towards the end of
98 '(rem (random-chunk (or state *random-state*)) num))))
102 (defknown make-single-float ((signed-byte 32)) single-float
103 (movable foldable flushable))
105 (defknown make-double-float ((signed-byte 32) (unsigned-byte 32)) double-float
106 (movable foldable flushable))
108 (defknown single-float-bits (single-float) (signed-byte 32)
109 (movable foldable flushable))
111 (defknown double-float-high-bits (double-float) (signed-byte 32)
112 (movable foldable flushable))
114 (defknown double-float-low-bits (double-float) (unsigned-byte 32)
115 (movable foldable flushable))
117 (deftransform float-sign ((float &optional float2)
118 (single-float &optional single-float) *)
120 (let ((temp (gensym)))
121 `(let ((,temp (abs float2)))
122 (if (minusp (single-float-bits float)) (- ,temp) ,temp)))
123 '(if (minusp (single-float-bits float)) -1f0 1f0)))
125 (deftransform float-sign ((float &optional float2)
126 (double-float &optional double-float) *)
128 (let ((temp (gensym)))
129 `(let ((,temp (abs float2)))
130 (if (minusp (double-float-high-bits float)) (- ,temp) ,temp)))
131 '(if (minusp (double-float-high-bits float)) -1d0 1d0)))
133 ;;;; DECODE-FLOAT, INTEGER-DECODE-FLOAT, and SCALE-FLOAT
135 (defknown decode-single-float (single-float)
136 (values single-float single-float-exponent (single-float -1f0 1f0))
137 (movable foldable flushable))
139 (defknown decode-double-float (double-float)
140 (values double-float double-float-exponent (double-float -1d0 1d0))
141 (movable foldable flushable))
143 (defknown integer-decode-single-float (single-float)
144 (values single-float-significand single-float-int-exponent (integer -1 1))
145 (movable foldable flushable))
147 (defknown integer-decode-double-float (double-float)
148 (values double-float-significand double-float-int-exponent (integer -1 1))
149 (movable foldable flushable))
151 (defknown scale-single-float (single-float integer) single-float
152 (movable foldable flushable))
154 (defknown scale-double-float (double-float integer) double-float
155 (movable foldable flushable))
157 (deftransform decode-float ((x) (single-float) *)
158 '(decode-single-float x))
160 (deftransform decode-float ((x) (double-float) *)
161 '(decode-double-float x))
163 (deftransform integer-decode-float ((x) (single-float) *)
164 '(integer-decode-single-float x))
166 (deftransform integer-decode-float ((x) (double-float) *)
167 '(integer-decode-double-float x))
169 (deftransform scale-float ((f ex) (single-float *) *)
170 (if (and #!+x86 t #!-x86 nil
171 (csubtypep (lvar-type ex)
172 (specifier-type '(signed-byte 32))))
173 '(coerce (%scalbn (coerce f 'double-float) ex) 'single-float)
174 '(scale-single-float f ex)))
176 (deftransform scale-float ((f ex) (double-float *) *)
177 (if (and #!+x86 t #!-x86 nil
178 (csubtypep (lvar-type ex)
179 (specifier-type '(signed-byte 32))))
181 '(scale-double-float f ex)))
183 ;;; What is the CROSS-FLOAT-INFINITY-KLUDGE?
185 ;;; SBCL's own implementation of floating point supports floating
186 ;;; point infinities. Some of the old CMU CL :PROPAGATE-FLOAT-TYPE and
187 ;;; :PROPAGATE-FUN-TYPE code, like the DEFOPTIMIZERs below, uses this
188 ;;; floating point support. Thus, we have to avoid running it on the
189 ;;; cross-compilation host, since we're not guaranteed that the
190 ;;; cross-compilation host will support floating point infinities.
192 ;;; If we wanted to live dangerously, we could conditionalize the code
193 ;;; with #+(OR SBCL SB-XC) instead. That way, if the cross-compilation
194 ;;; host happened to be SBCL, we'd be able to run the infinity-using
196 ;;; * SBCL itself gets built with more complete optimization.
198 ;;; * You get a different SBCL depending on what your cross-compilation
200 ;;; So far the pros and cons seem seem to be mostly academic, since
201 ;;; AFAIK (WHN 2001-08-28) the propagate-foo-type optimizations aren't
202 ;;; actually important in compiling SBCL itself. If this changes, then
203 ;;; we have to decide:
204 ;;; * Go for simplicity, leaving things as they are.
205 ;;; * Go for performance at the expense of conceptual clarity,
206 ;;; using #+(OR SBCL SB-XC) and otherwise leaving the build
208 ;;; * Go for performance at the expense of build time, using
209 ;;; #+(OR SBCL SB-XC) and also making SBCL do not just
210 ;;; make-host-1.sh and make-host-2.sh, but a third step
211 ;;; make-host-3.sh where it builds itself under itself. (Such a
212 ;;; 3-step build process could also help with other things, e.g.
213 ;;; using specialized arrays to represent debug information.)
214 ;;; * Rewrite the code so that it doesn't depend on unportable
215 ;;; floating point infinities.
217 ;;; optimizers for SCALE-FLOAT. If the float has bounds, new bounds
218 ;;; are computed for the result, if possible.
219 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
222 (defun scale-float-derive-type-aux (f ex same-arg)
223 (declare (ignore same-arg))
224 (flet ((scale-bound (x n)
225 ;; We need to be a bit careful here and catch any overflows
226 ;; that might occur. We can ignore underflows which become
230 (scale-float (type-bound-number x) n)
231 (floating-point-overflow ()
234 (when (and (numeric-type-p f) (numeric-type-p ex))
235 (let ((f-lo (numeric-type-low f))
236 (f-hi (numeric-type-high f))
237 (ex-lo (numeric-type-low ex))
238 (ex-hi (numeric-type-high ex))
242 (if (< (float-sign (type-bound-number f-hi)) 0.0)
244 (setf new-hi (scale-bound f-hi ex-lo)))
246 (setf new-hi (scale-bound f-hi ex-hi)))))
248 (if (< (float-sign (type-bound-number f-lo)) 0.0)
250 (setf new-lo (scale-bound f-lo ex-hi)))
252 (setf new-lo (scale-bound f-lo ex-lo)))))
253 (make-numeric-type :class (numeric-type-class f)
254 :format (numeric-type-format f)
258 (defoptimizer (scale-single-float derive-type) ((f ex))
259 (two-arg-derive-type f ex #'scale-float-derive-type-aux
260 #'scale-single-float t))
261 (defoptimizer (scale-double-float derive-type) ((f ex))
262 (two-arg-derive-type f ex #'scale-float-derive-type-aux
263 #'scale-double-float t))
265 ;;; DEFOPTIMIZERs for %SINGLE-FLOAT and %DOUBLE-FLOAT. This makes the
266 ;;; FLOAT function return the correct ranges if the input has some
267 ;;; defined range. Quite useful if we want to convert some type of
268 ;;; bounded integer into a float.
270 ((frob (fun type most-negative most-positive)
271 (let ((aux-name (symbolicate fun "-DERIVE-TYPE-AUX")))
273 (defun ,aux-name (num)
274 ;; When converting a number to a float, the limits are
276 (let* ((lo (bound-func (lambda (x)
277 (if (< x ,most-negative)
280 (numeric-type-low num)))
281 (hi (bound-func (lambda (x)
282 (if (< ,most-positive x )
285 (numeric-type-high num))))
286 (specifier-type `(,',type ,(or lo '*) ,(or hi '*)))))
288 (defoptimizer (,fun derive-type) ((num))
290 (one-arg-derive-type num #',aux-name #',fun)
293 (frob %single-float single-float
294 most-negative-single-float most-positive-single-float)
295 (frob %double-float double-float
296 most-negative-double-float most-positive-double-float))
301 (defun safe-ctype-for-single-coercion-p (x)
302 ;; See comment in SAFE-SINGLE-COERCION-P -- this deals with the same
303 ;; problem, but in the context of evaluated and compiled (+ <int> <single>)
304 ;; giving different result if we fail to check for this.
305 (or (not (csubtypep x (specifier-type 'integer)))
306 (csubtypep x (specifier-type `(integer ,most-negative-exactly-single-float-fixnum
307 ,most-positive-exactly-single-float-fixnum)))))
309 ;;; Do some stuff to recognize when the loser is doing mixed float and
310 ;;; rational arithmetic, or different float types, and fix it up. If
311 ;;; we don't, he won't even get so much as an efficiency note.
312 (deftransform float-contagion-arg1 ((x y) * * :defun-only t :node node)
313 (if (or (not (types-equal-or-intersect (lvar-type y) (specifier-type 'single-float)))
314 (safe-ctype-for-single-coercion-p (lvar-type x)))
315 `(,(lvar-fun-name (basic-combination-fun node))
317 (give-up-ir1-transform)))
318 (deftransform float-contagion-arg2 ((x y) * * :defun-only t :node node)
319 (if (or (not (types-equal-or-intersect (lvar-type x) (specifier-type 'single-float)))
320 (safe-ctype-for-single-coercion-p (lvar-type y)))
321 `(,(lvar-fun-name (basic-combination-fun node))
323 (give-up-ir1-transform)))
325 (dolist (x '(+ * / -))
326 (%deftransform x '(function (rational float) *) #'float-contagion-arg1)
327 (%deftransform x '(function (float rational) *) #'float-contagion-arg2))
329 (dolist (x '(= < > + * / -))
330 (%deftransform x '(function (single-float double-float) *)
331 #'float-contagion-arg1)
332 (%deftransform x '(function (double-float single-float) *)
333 #'float-contagion-arg2))
335 (macrolet ((def (type &rest args)
336 `(deftransform * ((x y) (,type (constant-arg (member ,@args))) *
338 :policy (zerop float-accuracy))
339 "optimize multiplication by one"
340 (let ((y (lvar-value y)))
344 (def * single-float 1.0 -1.0)
345 (def * double-float 1.0d0 -1.0d0))
347 ;;; Return the reciprocal of X if it can be represented exactly, NIL otherwise.
348 (defun maybe-exact-reciprocal (x)
350 (multiple-value-bind (significand exponent sign)
351 ;; Signals an error for NaNs and infinities.
352 (handler-case (integer-decode-float x)
353 (error () (return-from maybe-exact-reciprocal nil)))
354 (let ((expected (/ sign significand (expt 2 exponent))))
355 (let ((reciprocal (/ 1 x)))
356 (multiple-value-bind (significand exponent sign) (integer-decode-float reciprocal)
357 (when (eql expected (* sign significand (expt 2 exponent)))
360 ;;; Replace constant division by multiplication with exact reciprocal,
362 (macrolet ((def (type)
363 `(deftransform / ((x y) (,type (constant-arg ,type)) *
365 "convert to multiplication by reciprocal"
366 (let ((n (lvar-value y)))
367 (if (policy node (zerop float-accuracy))
369 (let ((r (maybe-exact-reciprocal n)))
372 (give-up-ir1-transform
373 "~S does not have an exact reciprocal"
378 ;;; Optimize addition and subsctraction of zero
379 (macrolet ((def (op type &rest args)
380 `(deftransform ,op ((x y) (,type (constant-arg (member ,@args))) *
382 :policy (zerop float-accuracy))
384 ;; No signed zeros, thanks.
385 (def + single-float 0 0.0)
386 (def - single-float 0 0.0)
387 (def + double-float 0 0.0 0.0d0)
388 (def - double-float 0 0.0 0.0d0))
390 ;;; On most platforms (+ x x) is faster than (* x 2)
391 (macrolet ((def (type &rest args)
392 `(deftransform * ((x y) (,type (constant-arg (member ,@args))))
394 (def single-float 2 2.0)
395 (def double-float 2 2.0 2.0d0))
397 ;;; Prevent ZEROP, PLUSP, and MINUSP from losing horribly. We can't in
398 ;;; general float rational args to comparison, since Common Lisp
399 ;;; semantics says we are supposed to compare as rationals, but we can
400 ;;; do it for any rational that has a precise representation as a
401 ;;; float (such as 0).
402 (macrolet ((frob (op)
403 `(deftransform ,op ((x y) (float rational) *)
404 "open-code FLOAT to RATIONAL comparison"
405 (unless (constant-lvar-p y)
406 (give-up-ir1-transform
407 "The RATIONAL value isn't known at compile time."))
408 (let ((val (lvar-value y)))
409 (unless (eql (rational (float val)) val)
410 (give-up-ir1-transform
411 "~S doesn't have a precise float representation."
413 `(,',op x (float y x)))))
418 ;;;; irrational derive-type methods
420 ;;; Derive the result to be float for argument types in the
421 ;;; appropriate domain.
422 #+sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
423 (dolist (stuff '((asin (real -1.0 1.0))
424 (acos (real -1.0 1.0))
426 (atanh (real -1.0 1.0))
428 (destructuring-bind (name type) stuff
429 (let ((type (specifier-type type)))
430 (setf (fun-info-derive-type (fun-info-or-lose name))
432 (declare (type combination call))
433 (when (csubtypep (lvar-type
434 (first (combination-args call)))
436 (specifier-type 'float)))))))
438 #+sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
439 (defoptimizer (log derive-type) ((x &optional y))
440 (when (and (csubtypep (lvar-type x)
441 (specifier-type '(real 0.0)))
443 (csubtypep (lvar-type y)
444 (specifier-type '(real 0.0)))))
445 (specifier-type 'float)))
447 ;;;; irrational transforms
449 (defknown (%tan %sinh %asinh %atanh %log %logb %log10 %tan-quick)
450 (double-float) double-float
451 (movable foldable flushable))
453 (defknown (%sin %cos %tanh %sin-quick %cos-quick)
454 (double-float) (double-float -1.0d0 1.0d0)
455 (movable foldable flushable))
457 (defknown (%asin %atan)
459 (double-float #.(coerce (- (/ pi 2)) 'double-float)
460 #.(coerce (/ pi 2) 'double-float))
461 (movable foldable flushable))
464 (double-float) (double-float 0.0d0 #.(coerce pi 'double-float))
465 (movable foldable flushable))
468 (double-float) (double-float 1.0d0)
469 (movable foldable flushable))
471 (defknown (%acosh %exp %sqrt)
472 (double-float) (double-float 0.0d0)
473 (movable foldable flushable))
476 (double-float) (double-float -1d0)
477 (movable foldable flushable))
480 (double-float double-float) (double-float 0d0)
481 (movable foldable flushable))
484 (double-float double-float) double-float
485 (movable foldable flushable))
488 (double-float double-float)
489 (double-float #.(coerce (- pi) 'double-float)
490 #.(coerce pi 'double-float))
491 (movable foldable flushable))
494 (double-float double-float) double-float
495 (movable foldable flushable))
498 (double-float (signed-byte 32)) double-float
499 (movable foldable flushable))
502 (double-float) double-float
503 (movable foldable flushable))
505 (macrolet ((def (name prim rtype)
507 (deftransform ,name ((x) (single-float) ,rtype)
508 `(coerce (,',prim (coerce x 'double-float)) 'single-float))
509 (deftransform ,name ((x) (double-float) ,rtype)
513 (def sqrt %sqrt float)
514 (def asin %asin float)
515 (def acos %acos float)
521 (def acosh %acosh float)
522 (def atanh %atanh float))
524 ;;; The argument range is limited on the x86 FP trig. functions. A
525 ;;; post-test can detect a failure (and load a suitable result), but
526 ;;; this test is avoided if possible.
527 (macrolet ((def (name prim prim-quick)
528 (declare (ignorable prim-quick))
530 (deftransform ,name ((x) (single-float) *)
531 #!+x86 (cond ((csubtypep (lvar-type x)
532 (specifier-type '(single-float
533 (#.(- (expt 2f0 64)))
535 `(coerce (,',prim-quick (coerce x 'double-float))
539 "unable to avoid inline argument range check~@
540 because the argument range (~S) was not within 2^64"
541 (type-specifier (lvar-type x)))
542 `(coerce (,',prim (coerce x 'double-float)) 'single-float)))
543 #!-x86 `(coerce (,',prim (coerce x 'double-float)) 'single-float))
544 (deftransform ,name ((x) (double-float) *)
545 #!+x86 (cond ((csubtypep (lvar-type x)
546 (specifier-type '(double-float
547 (#.(- (expt 2d0 64)))
552 "unable to avoid inline argument range check~@
553 because the argument range (~S) was not within 2^64"
554 (type-specifier (lvar-type x)))
556 #!-x86 `(,',prim x)))))
557 (def sin %sin %sin-quick)
558 (def cos %cos %cos-quick)
559 (def tan %tan %tan-quick))
561 (deftransform atan ((x y) (single-float single-float) *)
562 `(coerce (%atan2 (coerce x 'double-float) (coerce y 'double-float))
564 (deftransform atan ((x y) (double-float double-float) *)
567 (deftransform expt ((x y) ((single-float 0f0) single-float) *)
568 `(coerce (%pow (coerce x 'double-float) (coerce y 'double-float))
570 (deftransform expt ((x y) ((double-float 0d0) double-float) *)
572 (deftransform expt ((x y) ((single-float 0f0) (signed-byte 32)) *)
573 `(coerce (%pow (coerce x 'double-float) (coerce y 'double-float))
575 (deftransform expt ((x y) ((double-float 0d0) (signed-byte 32)) *)
576 `(%pow x (coerce y 'double-float)))
578 ;;; ANSI says log with base zero returns zero.
579 (deftransform log ((x y) (float float) float)
580 '(if (zerop y) y (/ (log x) (log y))))
582 ;;; Handle some simple transformations.
584 (deftransform abs ((x) ((complex double-float)) double-float)
585 '(%hypot (realpart x) (imagpart x)))
587 (deftransform abs ((x) ((complex single-float)) single-float)
588 '(coerce (%hypot (coerce (realpart x) 'double-float)
589 (coerce (imagpart x) 'double-float))
592 (deftransform phase ((x) ((complex double-float)) double-float)
593 '(%atan2 (imagpart x) (realpart x)))
595 (deftransform phase ((x) ((complex single-float)) single-float)
596 '(coerce (%atan2 (coerce (imagpart x) 'double-float)
597 (coerce (realpart x) 'double-float))
600 (deftransform phase ((x) ((float)) float)
601 '(if (minusp (float-sign x))
605 ;;; The number is of type REAL.
606 (defun numeric-type-real-p (type)
607 (and (numeric-type-p type)
608 (eq (numeric-type-complexp type) :real)))
610 ;;; Coerce a numeric type bound to the given type while handling
611 ;;; exclusive bounds.
612 (defun coerce-numeric-bound (bound type)
615 (list (coerce (car bound) type))
616 (coerce bound type))))
618 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
621 ;;;; optimizers for elementary functions
623 ;;;; These optimizers compute the output range of the elementary
624 ;;;; function, based on the domain of the input.
626 ;;; Generate a specifier for a complex type specialized to the same
627 ;;; type as the argument.
628 (defun complex-float-type (arg)
629 (declare (type numeric-type arg))
630 (let* ((format (case (numeric-type-class arg)
631 ((integer rational) 'single-float)
632 (t (numeric-type-format arg))))
633 (float-type (or format 'float)))
634 (specifier-type `(complex ,float-type))))
636 ;;; Compute a specifier like '(OR FLOAT (COMPLEX FLOAT)), except float
637 ;;; should be the right kind of float. Allow bounds for the float
639 (defun float-or-complex-float-type (arg &optional lo hi)
640 (declare (type numeric-type arg))
641 (let* ((format (case (numeric-type-class arg)
642 ((integer rational) 'single-float)
643 (t (numeric-type-format arg))))
644 (float-type (or format 'float))
645 (lo (coerce-numeric-bound lo float-type))
646 (hi (coerce-numeric-bound hi float-type)))
647 (specifier-type `(or (,float-type ,(or lo '*) ,(or hi '*))
648 (complex ,float-type)))))
652 (eval-when (:compile-toplevel :execute)
653 ;; So the problem with this hack is that it's actually broken. If
654 ;; the host does not have long floats, then setting *R-D-F-F* to
655 ;; LONG-FLOAT doesn't actually buy us anything. FIXME.
656 (setf *read-default-float-format*
657 #!+long-float 'long-float #!-long-float 'double-float))
658 ;;; Test whether the numeric-type ARG is within in domain specified by
659 ;;; DOMAIN-LOW and DOMAIN-HIGH, consider negative and positive zero to
661 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
662 (defun domain-subtypep (arg domain-low domain-high)
663 (declare (type numeric-type arg)
664 (type (or real null) domain-low domain-high))
665 (let* ((arg-lo (numeric-type-low arg))
666 (arg-lo-val (type-bound-number arg-lo))
667 (arg-hi (numeric-type-high arg))
668 (arg-hi-val (type-bound-number arg-hi)))
669 ;; Check that the ARG bounds are correctly canonicalized.
670 (when (and arg-lo (floatp arg-lo-val) (zerop arg-lo-val) (consp arg-lo)
671 (minusp (float-sign arg-lo-val)))
672 (compiler-notify "float zero bound ~S not correctly canonicalized?" arg-lo)
673 (setq arg-lo 0e0 arg-lo-val arg-lo))
674 (when (and arg-hi (zerop arg-hi-val) (floatp arg-hi-val) (consp arg-hi)
675 (plusp (float-sign arg-hi-val)))
676 (compiler-notify "float zero bound ~S not correctly canonicalized?" arg-hi)
677 (setq arg-hi (ecase *read-default-float-format*
678 (double-float (load-time-value (make-unportable-float :double-float-negative-zero)))
680 (long-float (load-time-value (make-unportable-float :long-float-negative-zero))))
682 (flet ((fp-neg-zero-p (f) ; Is F -0.0?
683 (and (floatp f) (zerop f) (minusp (float-sign f))))
684 (fp-pos-zero-p (f) ; Is F +0.0?
685 (and (floatp f) (zerop f) (plusp (float-sign f)))))
686 (and (or (null domain-low)
687 (and arg-lo (>= arg-lo-val domain-low)
688 (not (and (fp-pos-zero-p domain-low)
689 (fp-neg-zero-p arg-lo)))))
690 (or (null domain-high)
691 (and arg-hi (<= arg-hi-val domain-high)
692 (not (and (fp-neg-zero-p domain-high)
693 (fp-pos-zero-p arg-hi)))))))))
694 (eval-when (:compile-toplevel :execute)
695 (setf *read-default-float-format* 'single-float))
697 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
700 ;;; Handle monotonic functions of a single variable whose domain is
701 ;;; possibly part of the real line. ARG is the variable, FUN is the
702 ;;; function, and DOMAIN is a specifier that gives the (real) domain
703 ;;; of the function. If ARG is a subset of the DOMAIN, we compute the
704 ;;; bounds directly. Otherwise, we compute the bounds for the
705 ;;; intersection between ARG and DOMAIN, and then append a complex
706 ;;; result, which occurs for the parts of ARG not in the DOMAIN.
708 ;;; Negative and positive zero are considered distinct within
709 ;;; DOMAIN-LOW and DOMAIN-HIGH.
711 ;;; DEFAULT-LOW and DEFAULT-HIGH are the lower and upper bounds if we
712 ;;; can't compute the bounds using FUN.
713 (defun elfun-derive-type-simple (arg fun domain-low domain-high
714 default-low default-high
715 &optional (increasingp t))
716 (declare (type (or null real) domain-low domain-high))
719 (cond ((eq (numeric-type-complexp arg) :complex)
720 (complex-float-type arg))
721 ((numeric-type-real-p arg)
722 ;; The argument is real, so let's find the intersection
723 ;; between the argument and the domain of the function.
724 ;; We compute the bounds on the intersection, and for
725 ;; everything else, we return a complex number of the
727 (multiple-value-bind (intersection difference)
728 (interval-intersection/difference (numeric-type->interval arg)
734 ;; Process the intersection.
735 (let* ((low (interval-low intersection))
736 (high (interval-high intersection))
737 (res-lo (or (bound-func fun (if increasingp low high))
739 (res-hi (or (bound-func fun (if increasingp high low))
741 (format (case (numeric-type-class arg)
742 ((integer rational) 'single-float)
743 (t (numeric-type-format arg))))
744 (bound-type (or format 'float))
749 :low (coerce-numeric-bound res-lo bound-type)
750 :high (coerce-numeric-bound res-hi bound-type))))
751 ;; If the ARG is a subset of the domain, we don't
752 ;; have to worry about the difference, because that
754 (if (or (null difference)
755 ;; Check whether the arg is within the domain.
756 (domain-subtypep arg domain-low domain-high))
759 (specifier-type `(complex ,bound-type))))))
761 ;; No intersection so the result must be purely complex.
762 (complex-float-type arg)))))
764 (float-or-complex-float-type arg default-low default-high))))))
767 ((frob (name domain-low domain-high def-low-bnd def-high-bnd
768 &key (increasingp t))
769 (let ((num (gensym)))
770 `(defoptimizer (,name derive-type) ((,num))
774 (elfun-derive-type-simple arg #',name
775 ,domain-low ,domain-high
776 ,def-low-bnd ,def-high-bnd
779 ;; These functions are easy because they are defined for the whole
781 (frob exp nil nil 0 nil)
782 (frob sinh nil nil nil nil)
783 (frob tanh nil nil -1 1)
784 (frob asinh nil nil nil nil)
786 ;; These functions are only defined for part of the real line. The
787 ;; condition selects the desired part of the line.
788 (frob asin -1d0 1d0 (- (/ pi 2)) (/ pi 2))
789 ;; Acos is monotonic decreasing, so we need to swap the function
790 ;; values at the lower and upper bounds of the input domain.
791 (frob acos -1d0 1d0 0 pi :increasingp nil)
792 (frob acosh 1d0 nil nil nil)
793 (frob atanh -1d0 1d0 -1 1)
794 ;; Kahan says that (sqrt -0.0) is -0.0, so use a specifier that
796 (frob sqrt (load-time-value (make-unportable-float :double-float-negative-zero)) nil 0 nil))
798 ;;; Compute bounds for (expt x y). This should be easy since (expt x
799 ;;; y) = (exp (* y (log x))). However, computations done this way
800 ;;; have too much roundoff. Thus we have to do it the hard way.
801 (defun safe-expt (x y)
803 (when (< (abs y) 10000)
808 ;;; Handle the case when x >= 1.
809 (defun interval-expt-> (x y)
810 (case (sb!c::interval-range-info y 0d0)
812 ;; Y is positive and log X >= 0. The range of exp(y * log(x)) is
813 ;; obviously non-negative. We just have to be careful for
814 ;; infinite bounds (given by nil).
815 (let ((lo (safe-expt (type-bound-number (sb!c::interval-low x))
816 (type-bound-number (sb!c::interval-low y))))
817 (hi (safe-expt (type-bound-number (sb!c::interval-high x))
818 (type-bound-number (sb!c::interval-high y)))))
819 (list (sb!c::make-interval :low (or lo 1) :high hi))))
821 ;; Y is negative and log x >= 0. The range of exp(y * log(x)) is
822 ;; obviously [0, 1]. However, underflow (nil) means 0 is the
824 (let ((lo (safe-expt (type-bound-number (sb!c::interval-high x))
825 (type-bound-number (sb!c::interval-low y))))
826 (hi (safe-expt (type-bound-number (sb!c::interval-low x))
827 (type-bound-number (sb!c::interval-high y)))))
828 (list (sb!c::make-interval :low (or lo 0) :high (or hi 1)))))
830 ;; Split the interval in half.
831 (destructuring-bind (y- y+)
832 (sb!c::interval-split 0 y t)
833 (list (interval-expt-> x y-)
834 (interval-expt-> x y+))))))
836 ;;; Handle the case when x <= 1
837 (defun interval-expt-< (x y)
838 (case (sb!c::interval-range-info x 0d0)
840 ;; The case of 0 <= x <= 1 is easy
841 (case (sb!c::interval-range-info y)
843 ;; Y is positive and log X <= 0. The range of exp(y * log(x)) is
844 ;; obviously [0, 1]. We just have to be careful for infinite bounds
846 (let ((lo (safe-expt (type-bound-number (sb!c::interval-low x))
847 (type-bound-number (sb!c::interval-high y))))
848 (hi (safe-expt (type-bound-number (sb!c::interval-high x))
849 (type-bound-number (sb!c::interval-low y)))))
850 (list (sb!c::make-interval :low (or lo 0) :high (or hi 1)))))
852 ;; Y is negative and log x <= 0. The range of exp(y * log(x)) is
853 ;; obviously [1, inf].
854 (let ((hi (safe-expt (type-bound-number (sb!c::interval-low x))
855 (type-bound-number (sb!c::interval-low y))))
856 (lo (safe-expt (type-bound-number (sb!c::interval-high x))
857 (type-bound-number (sb!c::interval-high y)))))
858 (list (sb!c::make-interval :low (or lo 1) :high hi))))
860 ;; Split the interval in half
861 (destructuring-bind (y- y+)
862 (sb!c::interval-split 0 y t)
863 (list (interval-expt-< x y-)
864 (interval-expt-< x y+))))))
866 ;; The case where x <= 0. Y MUST be an INTEGER for this to work!
867 ;; The calling function must insure this! For now we'll just
868 ;; return the appropriate unbounded float type.
869 (list (sb!c::make-interval :low nil :high nil)))
871 (destructuring-bind (neg pos)
872 (interval-split 0 x t t)
873 (list (interval-expt-< neg y)
874 (interval-expt-< pos y))))))
876 ;;; Compute bounds for (expt x y).
877 (defun interval-expt (x y)
878 (case (interval-range-info x 1)
881 (interval-expt-> x y))
884 (interval-expt-< x y))
886 (destructuring-bind (left right)
887 (interval-split 1 x t t)
888 (list (interval-expt left y)
889 (interval-expt right y))))))
891 (defun fixup-interval-expt (bnd x-int y-int x-type y-type)
892 (declare (ignore x-int))
893 ;; Figure out what the return type should be, given the argument
894 ;; types and bounds and the result type and bounds.
895 (cond ((csubtypep x-type (specifier-type 'integer))
896 ;; an integer to some power
897 (case (numeric-type-class y-type)
899 ;; Positive integer to an integer power is either an
900 ;; integer or a rational.
901 (let ((lo (or (interval-low bnd) '*))
902 (hi (or (interval-high bnd) '*)))
903 (if (and (interval-low y-int)
904 (>= (type-bound-number (interval-low y-int)) 0))
905 (specifier-type `(integer ,lo ,hi))
906 (specifier-type `(rational ,lo ,hi)))))
908 ;; Positive integer to rational power is either a rational
909 ;; or a single-float.
910 (let* ((lo (interval-low bnd))
911 (hi (interval-high bnd))
913 (floor (type-bound-number lo))
916 (ceiling (type-bound-number hi))
919 (bound-func #'float lo)
922 (bound-func #'float hi)
924 (specifier-type `(or (rational ,int-lo ,int-hi)
925 (single-float ,f-lo, f-hi)))))
927 ;; A positive integer to a float power is a float.
928 (modified-numeric-type y-type
929 :low (interval-low bnd)
930 :high (interval-high bnd)))
932 ;; A positive integer to a number is a number (for now).
933 (specifier-type 'number))))
934 ((csubtypep x-type (specifier-type 'rational))
935 ;; a rational to some power
936 (case (numeric-type-class y-type)
938 ;; A positive rational to an integer power is always a rational.
939 (specifier-type `(rational ,(or (interval-low bnd) '*)
940 ,(or (interval-high bnd) '*))))
942 ;; A positive rational to rational power is either a rational
943 ;; or a single-float.
944 (let* ((lo (interval-low bnd))
945 (hi (interval-high bnd))
947 (floor (type-bound-number lo))
950 (ceiling (type-bound-number hi))
953 (bound-func #'float lo)
956 (bound-func #'float hi)
958 (specifier-type `(or (rational ,int-lo ,int-hi)
959 (single-float ,f-lo, f-hi)))))
961 ;; A positive rational to a float power is a float.
962 (modified-numeric-type y-type
963 :low (interval-low bnd)
964 :high (interval-high bnd)))
966 ;; A positive rational to a number is a number (for now).
967 (specifier-type 'number))))
968 ((csubtypep x-type (specifier-type 'float))
969 ;; a float to some power
970 (case (numeric-type-class y-type)
971 ((or integer rational)
972 ;; A positive float to an integer or rational power is
976 :format (numeric-type-format x-type)
977 :low (interval-low bnd)
978 :high (interval-high bnd)))
980 ;; A positive float to a float power is a float of the
984 :format (float-format-max (numeric-type-format x-type)
985 (numeric-type-format y-type))
986 :low (interval-low bnd)
987 :high (interval-high bnd)))
989 ;; A positive float to a number is a number (for now)
990 (specifier-type 'number))))
992 ;; A number to some power is a number.
993 (specifier-type 'number))))
995 (defun merged-interval-expt (x y)
996 (let* ((x-int (numeric-type->interval x))
997 (y-int (numeric-type->interval y)))
998 (mapcar (lambda (type)
999 (fixup-interval-expt type x-int y-int x y))
1000 (flatten-list (interval-expt x-int y-int)))))
1002 (defun expt-derive-type-aux (x y same-arg)
1003 (declare (ignore same-arg))
1004 (cond ((or (not (numeric-type-real-p x))
1005 (not (numeric-type-real-p y)))
1006 ;; Use numeric contagion if either is not real.
1007 (numeric-contagion x y))
1008 ((csubtypep y (specifier-type 'integer))
1009 ;; A real raised to an integer power is well-defined.
1010 (merged-interval-expt x y))
1011 ;; A real raised to a non-integral power can be a float or a
1013 ((or (csubtypep x (specifier-type '(rational 0)))
1014 (csubtypep x (specifier-type '(float (0d0)))))
1015 ;; But a positive real to any power is well-defined.
1016 (merged-interval-expt x y))
1017 ((and (csubtypep x (specifier-type 'rational))
1018 (csubtypep x (specifier-type 'rational)))
1019 ;; A rational to the power of a rational could be a rational
1020 ;; or a possibly-complex single float
1021 (specifier-type '(or rational single-float (complex single-float))))
1023 ;; a real to some power. The result could be a real or a
1025 (float-or-complex-float-type (numeric-contagion x y)))))
1027 (defoptimizer (expt derive-type) ((x y))
1028 (two-arg-derive-type x y #'expt-derive-type-aux #'expt))
1030 ;;; Note we must assume that a type including 0.0 may also include
1031 ;;; -0.0 and thus the result may be complex -infinity + i*pi.
1032 (defun log-derive-type-aux-1 (x)
1033 (elfun-derive-type-simple x #'log 0d0 nil nil nil))
1035 (defun log-derive-type-aux-2 (x y same-arg)
1036 (let ((log-x (log-derive-type-aux-1 x))
1037 (log-y (log-derive-type-aux-1 y))
1038 (accumulated-list nil))
1039 ;; LOG-X or LOG-Y might be union types. We need to run through
1040 ;; the union types ourselves because /-DERIVE-TYPE-AUX doesn't.
1041 (dolist (x-type (prepare-arg-for-derive-type log-x))
1042 (dolist (y-type (prepare-arg-for-derive-type log-y))
1043 (push (/-derive-type-aux x-type y-type same-arg) accumulated-list)))
1044 (apply #'type-union (flatten-list accumulated-list))))
1046 (defoptimizer (log derive-type) ((x &optional y))
1048 (two-arg-derive-type x y #'log-derive-type-aux-2 #'log)
1049 (one-arg-derive-type x #'log-derive-type-aux-1 #'log)))
1051 (defun atan-derive-type-aux-1 (y)
1052 (elfun-derive-type-simple y #'atan nil nil (- (/ pi 2)) (/ pi 2)))
1054 (defun atan-derive-type-aux-2 (y x same-arg)
1055 (declare (ignore same-arg))
1056 ;; The hard case with two args. We just return the max bounds.
1057 (let ((result-type (numeric-contagion y x)))
1058 (cond ((and (numeric-type-real-p x)
1059 (numeric-type-real-p y))
1060 (let* (;; FIXME: This expression for FORMAT seems to
1061 ;; appear multiple times, and should be factored out.
1062 (format (case (numeric-type-class result-type)
1063 ((integer rational) 'single-float)
1064 (t (numeric-type-format result-type))))
1065 (bound-format (or format 'float)))
1066 (make-numeric-type :class 'float
1069 :low (coerce (- pi) bound-format)
1070 :high (coerce pi bound-format))))
1072 ;; The result is a float or a complex number
1073 (float-or-complex-float-type result-type)))))
1075 (defoptimizer (atan derive-type) ((y &optional x))
1077 (two-arg-derive-type y x #'atan-derive-type-aux-2 #'atan)
1078 (one-arg-derive-type y #'atan-derive-type-aux-1 #'atan)))
1080 (defun cosh-derive-type-aux (x)
1081 ;; We note that cosh x = cosh |x| for all real x.
1082 (elfun-derive-type-simple
1083 (if (numeric-type-real-p x)
1084 (abs-derive-type-aux x)
1086 #'cosh nil nil 0 nil))
1088 (defoptimizer (cosh derive-type) ((num))
1089 (one-arg-derive-type num #'cosh-derive-type-aux #'cosh))
1091 (defun phase-derive-type-aux (arg)
1092 (let* ((format (case (numeric-type-class arg)
1093 ((integer rational) 'single-float)
1094 (t (numeric-type-format arg))))
1095 (bound-type (or format 'float)))
1096 (cond ((numeric-type-real-p arg)
1097 (case (interval-range-info (numeric-type->interval arg) 0.0)
1099 ;; The number is positive, so the phase is 0.
1100 (make-numeric-type :class 'float
1103 :low (coerce 0 bound-type)
1104 :high (coerce 0 bound-type)))
1106 ;; The number is always negative, so the phase is pi.
1107 (make-numeric-type :class 'float
1110 :low (coerce pi bound-type)
1111 :high (coerce pi bound-type)))
1113 ;; We can't tell. The result is 0 or pi. Use a union
1116 (make-numeric-type :class 'float
1119 :low (coerce 0 bound-type)
1120 :high (coerce 0 bound-type))
1121 (make-numeric-type :class 'float
1124 :low (coerce pi bound-type)
1125 :high (coerce pi bound-type))))))
1127 ;; We have a complex number. The answer is the range -pi
1128 ;; to pi. (-pi is included because we have -0.)
1129 (make-numeric-type :class 'float
1132 :low (coerce (- pi) bound-type)
1133 :high (coerce pi bound-type))))))
1135 (defoptimizer (phase derive-type) ((num))
1136 (one-arg-derive-type num #'phase-derive-type-aux #'phase))
1140 (deftransform realpart ((x) ((complex rational)) *)
1141 '(sb!kernel:%realpart x))
1142 (deftransform imagpart ((x) ((complex rational)) *)
1143 '(sb!kernel:%imagpart x))
1145 ;;; Make REALPART and IMAGPART return the appropriate types. This
1146 ;;; should help a lot in optimized code.
1147 (defun realpart-derive-type-aux (type)
1148 (let ((class (numeric-type-class type))
1149 (format (numeric-type-format type)))
1150 (cond ((numeric-type-real-p type)
1151 ;; The realpart of a real has the same type and range as
1153 (make-numeric-type :class class
1156 :low (numeric-type-low type)
1157 :high (numeric-type-high type)))
1159 ;; We have a complex number. The result has the same type
1160 ;; as the real part, except that it's real, not complex,
1162 (make-numeric-type :class class
1165 :low (numeric-type-low type)
1166 :high (numeric-type-high type))))))
1167 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1168 (defoptimizer (realpart derive-type) ((num))
1169 (one-arg-derive-type num #'realpart-derive-type-aux #'realpart))
1170 (defun imagpart-derive-type-aux (type)
1171 (let ((class (numeric-type-class type))
1172 (format (numeric-type-format type)))
1173 (cond ((numeric-type-real-p type)
1174 ;; The imagpart of a real has the same type as the input,
1175 ;; except that it's zero.
1176 (let ((bound-format (or format class 'real)))
1177 (make-numeric-type :class class
1180 :low (coerce 0 bound-format)
1181 :high (coerce 0 bound-format))))
1183 ;; We have a complex number. The result has the same type as
1184 ;; the imaginary part, except that it's real, not complex,
1186 (make-numeric-type :class class
1189 :low (numeric-type-low type)
1190 :high (numeric-type-high type))))))
1191 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1192 (defoptimizer (imagpart derive-type) ((num))
1193 (one-arg-derive-type num #'imagpart-derive-type-aux #'imagpart))
1195 (defun complex-derive-type-aux-1 (re-type)
1196 (if (numeric-type-p re-type)
1197 (make-numeric-type :class (numeric-type-class re-type)
1198 :format (numeric-type-format re-type)
1199 :complexp (if (csubtypep re-type
1200 (specifier-type 'rational))
1203 :low (numeric-type-low re-type)
1204 :high (numeric-type-high re-type))
1205 (specifier-type 'complex)))
1207 (defun complex-derive-type-aux-2 (re-type im-type same-arg)
1208 (declare (ignore same-arg))
1209 (if (and (numeric-type-p re-type)
1210 (numeric-type-p im-type))
1211 ;; Need to check to make sure numeric-contagion returns the
1212 ;; right type for what we want here.
1214 ;; Also, what about rational canonicalization, like (complex 5 0)
1215 ;; is 5? So, if the result must be complex, we make it so.
1216 ;; If the result might be complex, which happens only if the
1217 ;; arguments are rational, we make it a union type of (or
1218 ;; rational (complex rational)).
1219 (let* ((element-type (numeric-contagion re-type im-type))
1220 (rat-result-p (csubtypep element-type
1221 (specifier-type 'rational))))
1223 (type-union element-type
1225 `(complex ,(numeric-type-class element-type))))
1226 (make-numeric-type :class (numeric-type-class element-type)
1227 :format (numeric-type-format element-type)
1228 :complexp (if rat-result-p
1231 (specifier-type 'complex)))
1233 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1234 (defoptimizer (complex derive-type) ((re &optional im))
1236 (two-arg-derive-type re im #'complex-derive-type-aux-2 #'complex)
1237 (one-arg-derive-type re #'complex-derive-type-aux-1 #'complex)))
1239 ;;; Define some transforms for complex operations. We do this in lieu
1240 ;;; of complex operation VOPs.
1241 (macrolet ((frob (type)
1243 (deftransform complex ((r) (,type))
1244 '(complex r ,(coerce 0 type)))
1245 (deftransform complex ((r i) (,type (and real (not ,type))))
1246 '(complex r (truly-the ,type (coerce i ',type))))
1247 (deftransform complex ((r i) ((and real (not ,type)) ,type))
1248 '(complex (truly-the ,type (coerce r ',type)) i))
1250 #!-complex-float-vops
1251 (deftransform %negate ((z) ((complex ,type)) *)
1252 '(complex (%negate (realpart z)) (%negate (imagpart z))))
1253 ;; complex addition and subtraction
1254 #!-complex-float-vops
1255 (deftransform + ((w z) ((complex ,type) (complex ,type)) *)
1256 '(complex (+ (realpart w) (realpart z))
1257 (+ (imagpart w) (imagpart z))))
1258 #!-complex-float-vops
1259 (deftransform - ((w z) ((complex ,type) (complex ,type)) *)
1260 '(complex (- (realpart w) (realpart z))
1261 (- (imagpart w) (imagpart z))))
1262 ;; Add and subtract a complex and a real.
1263 #!-complex-float-vops
1264 (deftransform + ((w z) ((complex ,type) real) *)
1265 `(complex (+ (realpart w) z)
1266 (+ (imagpart w) ,(coerce 0 ',type))))
1267 #!-complex-float-vops
1268 (deftransform + ((z w) (real (complex ,type)) *)
1269 `(complex (+ (realpart w) z)
1270 (+ (imagpart w) ,(coerce 0 ',type))))
1271 ;; Add and subtract a real and a complex number.
1272 #!-complex-float-vops
1273 (deftransform - ((w z) ((complex ,type) real) *)
1274 `(complex (- (realpart w) z)
1275 (- (imagpart w) ,(coerce 0 ',type))))
1276 #!-complex-float-vops
1277 (deftransform - ((z w) (real (complex ,type)) *)
1278 `(complex (- z (realpart w))
1279 (- ,(coerce 0 ',type) (imagpart w))))
1280 ;; Multiply and divide two complex numbers.
1281 #!-complex-float-vops
1282 (deftransform * ((x y) ((complex ,type) (complex ,type)) *)
1283 '(let* ((rx (realpart x))
1287 (complex (- (* rx ry) (* ix iy))
1288 (+ (* rx iy) (* ix ry)))))
1289 (deftransform / ((x y) ((complex ,type) (complex ,type)) *)
1290 #!-complex-float-vops
1291 '(let* ((rx (realpart x))
1295 (if (> (abs ry) (abs iy))
1296 (let* ((r (/ iy ry))
1297 (dn (+ ry (* r iy))))
1298 (complex (/ (+ rx (* ix r)) dn)
1299 (/ (- ix (* rx r)) dn)))
1300 (let* ((r (/ ry iy))
1301 (dn (+ iy (* r ry))))
1302 (complex (/ (+ (* rx r) ix) dn)
1303 (/ (- (* ix r) rx) dn)))))
1304 #!+complex-float-vops
1305 `(let* ((cs (conjugate (sb!vm::swap-complex x)))
1308 (if (> (abs ry) (abs iy))
1309 (let* ((r (/ iy ry))
1310 (dn (+ ry (* r iy))))
1311 (/ (+ x (* cs r)) dn))
1312 (let* ((r (/ ry iy))
1313 (dn (+ iy (* r ry))))
1314 (/ (+ (* x r) cs) dn)))))
1315 ;; Multiply a complex by a real or vice versa.
1316 #!-complex-float-vops
1317 (deftransform * ((w z) ((complex ,type) real) *)
1318 '(complex (* (realpart w) z) (* (imagpart w) z)))
1319 #!-complex-float-vops
1320 (deftransform * ((z w) (real (complex ,type)) *)
1321 '(complex (* (realpart w) z) (* (imagpart w) z)))
1322 ;; Divide a complex by a real or vice versa.
1323 #!-complex-float-vops
1324 (deftransform / ((w z) ((complex ,type) real) *)
1325 '(complex (/ (realpart w) z) (/ (imagpart w) z)))
1326 (deftransform / ((x y) (,type (complex ,type)) *)
1327 #!-complex-float-vops
1328 '(let* ((ry (realpart y))
1330 (if (> (abs ry) (abs iy))
1331 (let* ((r (/ iy ry))
1332 (dn (+ ry (* r iy))))
1334 (/ (- (* x r)) dn)))
1335 (let* ((r (/ ry iy))
1336 (dn (+ iy (* r ry))))
1337 (complex (/ (* x r) dn)
1339 #!+complex-float-vops
1340 '(let* ((ry (realpart y))
1342 (if (> (abs ry) (abs iy))
1343 (let* ((r (/ iy ry))
1344 (dn (+ ry (* r iy))))
1345 (/ (complex x (- (* x r))) dn))
1346 (let* ((r (/ ry iy))
1347 (dn (+ iy (* r ry))))
1348 (/ (complex (* x r) (- x)) dn)))))
1349 ;; conjugate of complex number
1350 #!-complex-float-vops
1351 (deftransform conjugate ((z) ((complex ,type)) *)
1352 '(complex (realpart z) (- (imagpart z))))
1354 (deftransform cis ((z) ((,type)) *)
1355 '(complex (cos z) (sin z)))
1357 #!-complex-float-vops
1358 (deftransform = ((w z) ((complex ,type) (complex ,type)) *)
1359 '(and (= (realpart w) (realpart z))
1360 (= (imagpart w) (imagpart z))))
1361 #!-complex-float-vops
1362 (deftransform = ((w z) ((complex ,type) real) *)
1363 '(and (= (realpart w) z) (zerop (imagpart w))))
1364 #!-complex-float-vops
1365 (deftransform = ((w z) (real (complex ,type)) *)
1366 '(and (= (realpart z) w) (zerop (imagpart z)))))))
1369 (frob double-float))
1371 ;;; Here are simple optimizers for SIN, COS, and TAN. They do not
1372 ;;; produce a minimal range for the result; the result is the widest
1373 ;;; possible answer. This gets around the problem of doing range
1374 ;;; reduction correctly but still provides useful results when the
1375 ;;; inputs are union types.
1376 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1378 (defun trig-derive-type-aux (arg domain fun
1379 &optional def-lo def-hi (increasingp t))
1382 (cond ((eq (numeric-type-complexp arg) :complex)
1383 (make-numeric-type :class (numeric-type-class arg)
1384 :format (numeric-type-format arg)
1385 :complexp :complex))
1386 ((numeric-type-real-p arg)
1387 (let* ((format (case (numeric-type-class arg)
1388 ((integer rational) 'single-float)
1389 (t (numeric-type-format arg))))
1390 (bound-type (or format 'float)))
1391 ;; If the argument is a subset of the "principal" domain
1392 ;; of the function, we can compute the bounds because
1393 ;; the function is monotonic. We can't do this in
1394 ;; general for these periodic functions because we can't
1395 ;; (and don't want to) do the argument reduction in
1396 ;; exactly the same way as the functions themselves do
1398 (if (csubtypep arg domain)
1399 (let ((res-lo (bound-func fun (numeric-type-low arg)))
1400 (res-hi (bound-func fun (numeric-type-high arg))))
1402 (rotatef res-lo res-hi))
1406 :low (coerce-numeric-bound res-lo bound-type)
1407 :high (coerce-numeric-bound res-hi bound-type)))
1411 :low (and def-lo (coerce def-lo bound-type))
1412 :high (and def-hi (coerce def-hi bound-type))))))
1414 (float-or-complex-float-type arg def-lo def-hi))))))
1416 (defoptimizer (sin derive-type) ((num))
1417 (one-arg-derive-type
1420 ;; Derive the bounds if the arg is in [-pi/2, pi/2].
1421 (trig-derive-type-aux
1423 (specifier-type `(float ,(- (/ pi 2)) ,(/ pi 2)))
1428 (defoptimizer (cos derive-type) ((num))
1429 (one-arg-derive-type
1432 ;; Derive the bounds if the arg is in [0, pi].
1433 (trig-derive-type-aux arg
1434 (specifier-type `(float 0d0 ,pi))
1440 (defoptimizer (tan derive-type) ((num))
1441 (one-arg-derive-type
1444 ;; Derive the bounds if the arg is in [-pi/2, pi/2].
1445 (trig-derive-type-aux arg
1446 (specifier-type `(float ,(- (/ pi 2)) ,(/ pi 2)))
1451 (defoptimizer (conjugate derive-type) ((num))
1452 (one-arg-derive-type num
1454 (flet ((most-negative-bound (l h)
1456 (if (< (type-bound-number l) (- (type-bound-number h)))
1458 (set-bound (- (type-bound-number h)) (consp h)))))
1459 (most-positive-bound (l h)
1461 (if (> (type-bound-number h) (- (type-bound-number l)))
1463 (set-bound (- (type-bound-number l)) (consp l))))))
1464 (if (numeric-type-real-p arg)
1466 (let ((low (numeric-type-low arg))
1467 (high (numeric-type-high arg)))
1468 (let ((new-low (most-negative-bound low high))
1469 (new-high (most-positive-bound low high)))
1470 (modified-numeric-type arg :low new-low :high new-high))))))
1473 (defoptimizer (cis derive-type) ((num))
1474 (one-arg-derive-type num
1476 (sb!c::specifier-type
1477 `(complex ,(or (numeric-type-format arg) 'float))))
1482 ;;;; TRUNCATE, FLOOR, CEILING, and ROUND
1484 (macrolet ((define-frobs (fun ufun)
1486 (defknown ,ufun (real) integer (movable foldable flushable))
1487 (deftransform ,fun ((x &optional by)
1489 (constant-arg (member 1))))
1490 '(let ((res (,ufun x)))
1491 (values res (- x res)))))))
1492 (define-frobs truncate %unary-truncate)
1493 (define-frobs round %unary-round))
1495 ;;; Convert (TRUNCATE x y) to the obvious implementation. We only want
1496 ;;; this when under certain conditions and let the generic TRUNCATE
1497 ;;; handle the rest. (Note: if Y = 1, the divide and multiply by Y
1498 ;;; should be removed by other DEFTRANSFORMs.)
1499 (deftransform truncate ((x &optional y)
1500 (float &optional (or float integer)))
1501 (let ((defaulted-y (if y 'y 1)))
1502 `(let ((res (%unary-truncate (/ x ,defaulted-y))))
1503 (values res (- x (* ,defaulted-y res))))))
1505 (deftransform floor ((number &optional divisor)
1506 (float &optional (or integer float)))
1507 (let ((defaulted-divisor (if divisor 'divisor 1)))
1508 `(multiple-value-bind (tru rem) (truncate number ,defaulted-divisor)
1509 (if (and (not (zerop rem))
1510 (if (minusp ,defaulted-divisor)
1513 (values (1- tru) (+ rem ,defaulted-divisor))
1514 (values tru rem)))))
1516 (deftransform ceiling ((number &optional divisor)
1517 (float &optional (or integer float)))
1518 (let ((defaulted-divisor (if divisor 'divisor 1)))
1519 `(multiple-value-bind (tru rem) (truncate number ,defaulted-divisor)
1520 (if (and (not (zerop rem))
1521 (if (minusp ,defaulted-divisor)
1524 (values (1+ tru) (- rem ,defaulted-divisor))
1525 (values tru rem)))))
1527 (defknown %unary-ftruncate (real) float (movable foldable flushable))
1528 (defknown %unary-ftruncate/single (single-float) single-float
1529 (movable foldable flushable))
1530 (defknown %unary-ftruncate/double (double-float) double-float
1531 (movable foldable flushable))
1533 (defun %unary-ftruncate/single (x)
1534 (declare (type single-float x))
1535 (declare (optimize speed (safety 0)))
1536 (let* ((bits (single-float-bits x))
1537 (exp (ldb sb!vm:single-float-exponent-byte bits))
1538 (biased (the single-float-exponent
1539 (- exp sb!vm:single-float-bias))))
1540 (declare (type (signed-byte 32) bits))
1542 ((= exp sb!vm:single-float-normal-exponent-max) x)
1543 ((<= biased 0) (* x 0f0))
1544 ((>= biased (float-digits x)) x)
1546 (let ((frac-bits (- (float-digits x) biased)))
1547 (setf bits (logandc2 bits (- (ash 1 frac-bits) 1)))
1548 (make-single-float bits))))))
1550 (defun %unary-ftruncate/double (x)
1551 (declare (type double-float x))
1552 (declare (optimize speed (safety 0)))
1553 (let* ((high (double-float-high-bits x))
1554 (low (double-float-low-bits x))
1555 (exp (ldb sb!vm:double-float-exponent-byte high))
1556 (biased (the double-float-exponent
1557 (- exp sb!vm:double-float-bias))))
1558 (declare (type (signed-byte 32) high)
1559 (type (unsigned-byte 32) low))
1561 ((= exp sb!vm:double-float-normal-exponent-max) x)
1562 ((<= biased 0) (* x 0d0))
1563 ((>= biased (float-digits x)) x)
1565 (let ((frac-bits (- (float-digits x) biased)))
1566 (cond ((< frac-bits 32)
1567 (setf low (logandc2 low (- (ash 1 frac-bits) 1))))
1570 (setf high (logandc2 high (- (ash 1 (- frac-bits 32)) 1)))))
1571 (make-double-float high low))))))
1574 ((def (float-type fun)
1575 `(deftransform %unary-ftruncate ((x) (,float-type))
1577 (def single-float %unary-ftruncate/single)
1578 (def double-float %unary-ftruncate/double))