1 ;;;; portable implementations or stubs for nonportable floating point
2 ;;;; things, useful for building Python as a cross-compiler when
3 ;;;; running under an ordinary ANSI Common Lisp implementation
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.
14 (in-package "SB!IMPL")
16 ;;; There seems to be no portable way to mask float traps, but we shouldn't
17 ;;; encounter any float traps when cross-compiling SBCL itself, anyway, so we
18 ;;; just make this a no-op.
19 (defmacro sb!vm::with-float-traps-masked (traps &body body)
20 (declare (ignore traps))
21 ;; FIXME: should become STYLE-WARNING?
22 (format *error-output*
23 "~&(can't portably mask float traps, proceeding anyway)~%")
26 ;;; a helper function for DOUBLE-FLOAT-FOO-BITS functions
28 ;;; Return the low N bits of X as a signed N-bit value.
29 (defun mask-and-sign-extend (x n)
31 (let* ((high-bit (ash 1 (1- n)))
32 (mask (1- (ash high-bit 1)))
33 (uresult (logand mask x)))
34 (if (zerop (logand uresult high-bit))
37 (logand -1 (lognot mask))))))
39 ;;; portable implementations of SINGLE-FLOAT-BITS, DOUBLE-FLOAT-LOW-BITS, and
40 ;;; DOUBLE-FLOAT-HIGH-BITS
42 ;;; KLUDGE: These will fail if the target's floating point isn't IEEE, and so
43 ;;; I'd be more comfortable if there were an assertion "target's floating point
44 ;;; is IEEE" in the code, but I can't see how to express that.
46 ;;; KLUDGE: It's sort of weird that these functions return signed 32-bit values
47 ;;; instead of unsigned 32-bit values. This is the way that the CMU CL
48 ;;; machine-dependent functions behaved, and I've copied that behavior, but it
49 ;;; seems to me that it'd be more idiomatic to return unsigned 32-bit values.
50 ;;; Maybe someday the machine-dependent functions could be tweaked to return
51 ;;; unsigned 32-bit values?
52 (defun single-float-bits (x)
53 (declare (type single-float x))
54 (assert (= (float-radix x) 2))
56 0 ; known property of IEEE floating point: 0.0 is represented as 0.
57 (multiple-value-bind (lisp-significand lisp-exponent lisp-sign)
58 (integer-decode-float x)
59 (assert (plusp lisp-significand))
60 ;; Calculate IEEE-style fields from Common-Lisp-style fields.
62 ;; KLUDGE: This code was written from my foggy memory of what IEEE
63 ;; format looks like, augmented by some experiments with
64 ;; the existing implementation of SINGLE-FLOAT-BITS, and what
65 ;; I found floating around on the net at
66 ;; <http://www.scri.fsu.edu/~jac/MAD3401/Backgrnd/ieee.html>,
67 ;; <http://rodin.cs.uh.edu/~johnson2/ieee.html>,
69 ;; <http://www.ttu.ee/sidu/cas/IEEE_Floating.htm>.
70 ;; And beyond the probable sheer flakiness of the code, all the bare
71 ;; numbers floating around here are sort of ugly, too. -- WHN 19990711
72 (let* ((significand lisp-significand)
73 (exponent (+ lisp-exponent 23 127))
75 (if (plusp exponent) ; if not obviously denormalized
78 (cond (;; ordinary termination case
79 (>= significand (expt 2 23))
80 (assert (< 0 significand (expt 2 24)))
81 ;; Exponent 0 is reserved for denormalized numbers,
82 ;; and 255 is reserved for specials like NaN.
83 (assert (< 0 exponent 255))
84 (return (logior (ash exponent 23)
87 (;; special termination case, denormalized float number
89 ;; Denormalized numbers have exponent one greater than
90 ;; the exponent field.
91 (return (ash significand -1)))
93 ;; Shift as necessary to set bit 24 of significand.
94 (setf significand (ash significand 1)
95 exponent (1- exponent)))))
98 ;; Denormalized numbers have exponent one greater than the
100 (ash significand -1))
101 (unless (zerop (logand significand 1))
102 (warn "denormalized SINGLE-FLOAT-BITS ~S losing bits" x))
103 (setf significand (ash significand -1)
104 exponent (1+ exponent))))))
107 (-1 (logior unsigned-result (- (expt 2 31)))))))))
108 (defun double-float-bits (x)
109 (declare (type double-float x))
110 (assert (= (float-radix x) 2))
112 0 ; known property of IEEE floating point: 0.0d0 is represented as 0.
113 ;; KLUDGE: As per comments in SINGLE-FLOAT-BITS, above.
114 (multiple-value-bind (lisp-significand lisp-exponent lisp-sign)
115 (integer-decode-float x)
116 (assert (plusp lisp-significand))
117 (let* ((significand lisp-significand)
118 (exponent (+ lisp-exponent 52 1023))
120 (if (plusp exponent) ; if not obviously denormalized
123 (cond (;; ordinary termination case
124 (>= significand (expt 2 52))
125 (assert (< 0 significand (expt 2 53)))
126 ;; Exponent 0 is reserved for denormalized numbers,
127 ;; and 2047 is reserved for specials like NaN.
128 (assert (< 0 exponent 2047))
129 (return (logior (ash exponent 52)
132 (;; special termination case, denormalized float number
134 ;; Denormalized numbers have exponent one greater than
135 ;; the exponent field.
136 (return (ash significand -1)))
138 ;; Shift as necessary to set bit 53 of significand.
139 (setf significand (ash significand 1)
140 exponent (1- exponent)))))
143 ;; Denormalized numbers have exponent one greater than the
145 (ash significand -1))
146 (unless (zerop (logand significand 1))
147 (warn "denormalized SINGLE-FLOAT-BITS ~S losing bits" x))
148 (setf significand (ash significand -1)
149 exponent (1+ exponent))))))
152 (-1 (logior unsigned-result (- (expt 2 63)))))))))
153 (defun double-float-low-bits (x)
154 (declare (type double-float x))
157 ;; Unlike DOUBLE-FLOAT-HIGH-BITS or SINGLE-FLOAT-BITS, the CMU CL
158 ;; DOUBLE-FLOAT-LOW-BITS seems to return a unsigned value, not a signed
160 (logand #xffffffff (double-float-bits x))))
161 (defun double-float-high-bits (x)
162 (declare (type double-float x))
165 (mask-and-sign-extend (ash (double-float-bits x) -32) 32)))
167 ;;; KLUDGE: These functions will blow up on any cross-compilation
168 ;;; host Lisp which has less floating point precision than the target
169 ;;; Lisp. In practice, this may not be a major problem: IEEE
170 ;;; floating point arithmetic is so common these days that most
171 ;;; cross-compilation host Lisps are likely to have exactly the same
172 ;;; floating point precision as the target Lisp. If it turns out to be
173 ;;; a problem, there are possible workarounds involving portable
174 ;;; representations for target floating point numbers, like
175 ;;; (DEFSTRUCT TARGET-SINGLE-FLOAT
176 ;;; (SIGN (REQUIRED-ARGUMENT) :TYPE BIT)
177 ;;; (EXPONENT (REQUIRED-ARGUMENT) :TYPE UNSIGNED-BYTE)
178 ;;; (MANTISSA (REQUIRED-ARGUMENT) :TYPE UNSIGNED-BYTE))
179 ;;; with some sort of MAKE-LOAD-FORM-ish magic to cause them to be
180 ;;; written out in the appropriate target format. (And yes, those
181 ;;; workarounds *do* look messy to me, which is why I just went
182 ;;; with this quick kludge instead.) -- WHN 19990711
183 (defun make-single-float (bits)
184 (if (zerop bits) ; IEEE float special case
186 (let ((sign (ecase (ldb (byte 1 31) bits)
189 (expt (- (ldb (byte 8 23) bits) 127))
190 (mant (* (logior (ldb (byte 23 0) bits)
193 (* sign (expt 2.0 expt) mant))))
194 (defun make-double-float (hi lo)
195 (if (and (zerop hi) (zerop lo)) ; IEEE float special case
197 (let* ((bits (logior (ash hi 32) lo))
198 (sign (ecase (ldb (byte 1 63) bits)
201 (expt (- (ldb (byte 11 52) bits) 1023))
202 (mant (* (logior (ldb (byte 52 0) bits)
205 (* sign (expt 2.0d0 expt) mant))))