) ; EVAL-WHEN
\f
+#!+x86 ;; for constant folding
+(macrolet ((def (name ll)
+ `(defun ,name ,ll (,name ,@ll))))
+ (def %atan2 (x y))
+ (def %atan (x))
+ (def %tan-quick (x))
+ (def %cos-quick (x))
+ (def %sin-quick (x))
+ (def %sqrt (x))
+ (def %log (x))
+ (def %exp (x)))
+
;;;; stubs for the Unix math library
;;;;
;;;; Many of these are unnecessary on the X86 because they're built
;;; INTEXP -- Handle the rational base, integer power case.
-;;; FIXME: As long as the system dies on stack overflow or memory
-;;; exhaustion, it seems reasonable to have this, but its default
-;;; should be NIL, and when it's NIL, anything should be accepted.
-(defparameter *intexp-maximum-exponent* 10000)
+(declaim (type (or integer null) *intexp-maximum-exponent*))
+(defparameter *intexp-maximum-exponent* nil)
;;; This function precisely calculates base raised to an integral
;;; power. It separates the cases by the sign of power, for efficiency
;;; a positive integer. Values of power are calculated as positive
;;; integers, and inverted if negative.
(defun intexp (base power)
- (when (> (abs power) *intexp-maximum-exponent*)
- ;; FIXME: should be ordinary error, not CERROR. (Once we set the
- ;; default for the variable to NIL, the un-continuable error will
- ;; be less obnoxious.)
- (cerror "Continue with calculation."
- "The absolute value of ~S exceeds ~S."
- power '*intexp-maximum-exponent* base power))
+ (when (and *intexp-maximum-exponent*
+ (> (abs power) *intexp-maximum-exponent*))
+ (error "The absolute value of ~S exceeds ~S."
+ power '*intexp-maximum-exponent*))
(cond ((minusp power)
(/ (intexp base (- power))))
((eql base 2)
#!+sb-doc
"Return BASE raised to the POWER."
(if (zerop power)
- (1+ (* base power))
+ (let ((result (1+ (* base power))))
+ (if (and (floatp result) (float-nan-p result))
+ (float 1 result)
+ result))
(labels (;; determine if the double float is an integer.
;; 0 - not an integer
;; 1 - an odd int
(coerce (%sqrt (coerce number 'double-float)) 'single-float)))
(((foreach single-float double-float))
(if (minusp number)
- (complex-sqrt number)
+ (complex-sqrt (complex number))
(coerce (%sqrt (coerce number 'double-float))
'(dispatch-type number))))
((complex)
(((foreach single-float double-float))
(if (or (> number (coerce 1 '(dispatch-type number)))
(< number (coerce -1 '(dispatch-type number))))
- (complex-asin number)
+ (complex-asin (complex number))
(coerce (%asin (coerce number 'double-float))
'(dispatch-type number))))
((complex)
(((foreach single-float double-float))
(if (or (> number (coerce 1 '(dispatch-type number)))
(< number (coerce -1 '(dispatch-type number))))
- (complex-acos number)
+ (complex-acos (complex number))
(coerce (%acos (coerce number 'double-float))
'(dispatch-type number))))
((complex)
(coerce (%acosh (coerce number 'double-float)) 'single-float)))
(((foreach single-float double-float))
(if (< number (coerce 1 '(dispatch-type number)))
- (complex-acosh number)
+ (complex-acosh (complex number))
(coerce (%acosh (coerce number 'double-float))
'(dispatch-type number))))
((complex)
(((foreach single-float double-float))
(if (or (> number (coerce 1 '(dispatch-type number)))
(< number (coerce -1 '(dispatch-type number))))
- (complex-atanh number)
+ (complex-atanh (complex number))
(coerce (%atanh (coerce number 'double-float))
'(dispatch-type number))))
((complex)
;;; they're effectively implemented as special variable references,
;;; and the code below which uses them might be unnecessarily
;;; inefficient. Perhaps some sort of MAKE-LOAD-TIME-VALUE hackery
-;;; should be used instead?
+;;; should be used instead? (KLUDGED 2004-03-08 CSR, by replacing the
+;;; special variable references with (probably equally slow)
+;;; constructors)
+;;;
+;;; FIXME: As of 2004-05, when PFD noted that IMAGPART and COMPLEX
+;;; differ in their interpretations of the real line, IMAGPART was
+;;; patch, which without a certain amount of effort would have altered
+;;; all the branch cut treatment. Clients of these COMPLEX- routines
+;;; were patched to use explicit COMPLEX, rather than implicitly
+;;; passing in real numbers for treatment with IMAGPART, and these
+;;; COMPLEX- functions altered to require arguments of type COMPLEX;
+;;; however, someone needs to go back to Kahan for the definitive
+;;; answer for treatment of negative real floating point numbers and
+;;; branch cuts. If adjustment is needed, it is probably the removal
+;;; of explicit calls to COMPLEX in the clients of irrational
+;;; functions. -- a slightly bitter CSR, 2004-05-16
(declaim (inline square))
(defun square (x)
(cond ((float-nan-p x)
x)
((float-infinity-p x)
- sb!ext:double-float-positive-infinity)
+ ;; DOUBLE-FLOAT-POSITIVE-INFINITY
+ (double-from-bits 0 (1+ sb!vm:double-float-normal-exponent-max) 0))
((zerop x)
;; The answer is negative infinity, but we are supposed to
;; signal divide-by-zero, so do the actual division
(defun coerce-to-complex-type (x y z)
(declare (double-float x y)
(number z))
- (if (subtypep (type-of (realpart z)) 'double-float)
+ (if (typep (realpart z) 'double-float)
(complex x y)
- ;; Convert anything that's not a DOUBLE-FLOAT to a SINGLE-FLOAT.
+ ;; Convert anything that's not already a DOUBLE-FLOAT (because
+ ;; the initial argument was a (COMPLEX DOUBLE-FLOAT) and we
+ ;; haven't done anything to lose precision) to a SINGLE-FLOAT.
(complex (float x 1f0)
(float y 1f0))))
(float-infinity-p rho))
(or (float-infinity-p (abs x))
(float-infinity-p (abs y))))
- (values sb!ext:double-float-positive-infinity 0))
+ ;; DOUBLE-FLOAT-POSITIVE-INFINITY
+ (values
+ (double-from-bits 0 (1+ sb!vm:double-float-normal-exponent-max) 0)
+ 0))
((let ((threshold #.(/ least-positive-double-float
double-float-epsilon))
(traps (ldb sb!vm::float-sticky-bits
;;; principal square root of Z
;;;
-;;; Z may be any NUMBER, but the result is always a COMPLEX.
+;;; Z may be RATIONAL or COMPLEX; the result is always a COMPLEX.
(defun complex-sqrt (z)
- (declare (number z))
+ ;; KLUDGE: Here and below, we can't just declare Z to be of type
+ ;; COMPLEX, because one-arg COMPLEX on rationals returns a rational.
+ ;; Since there isn't a rational negative zero, this is OK from the
+ ;; point of view of getting the right answer in the face of branch
+ ;; cuts, but declarations of the form (OR RATIONAL COMPLEX) are
+ ;; still ugly. -- CSR, 2004-05-16
+ (declare (type (or complex rational) z))
(multiple-value-bind (rho k)
(cssqs z)
(declare (type (or (member 0d0) (double-float 0d0)) rho)
;;;
;;; This is for use with J /= 0 only when |z| is huge.
(defun complex-log-scaled (z j)
- (declare (number z)
+ (declare (type (or rational complex) z)
(fixnum j))
;; The constants t0, t1, t2 should be evaluated to machine
;; precision. In addition, Kahan says the accuracy of log1p
;;;
;;; Z may be any number, but the result is always a complex.
(defun complex-log (z)
- (declare (number z))
+ (declare (type (or rational complex) z))
(complex-log-scaled z 0))
;;; KLUDGE: Let us note the following "strange" behavior. atanh 1.0d0
;;; i*y is never 0 since we have positive and negative zeroes. -- rtoy
;;; Compute atanh z = (log(1+z) - log(1-z))/2.
(defun complex-atanh (z)
- (declare (number z))
+ (declare (type (or rational complex) z))
(let* (;; constants
(theta (/ (sqrt most-positive-double-float) 4.0d0))
(rho (/ 4.0d0 (sqrt most-positive-double-float)))
(declare (optimize (speed 3)))
(cond ((or (> x theta)
(> (abs y) theta))
- ;; To avoid overflow...
- (setf eta (float-sign y half-pi))
- ;; nu is real part of 1/(x + iy). This is x/(x^2+y^2),
+ ;; To avoid overflow...
+ (setf nu (float-sign y half-pi))
+ ;; ETA is real part of 1/(x + iy). This is x/(x^2+y^2),
;; which can cause overflow. Arrange this computation so
;; that it won't overflow.
- (setf nu (let* ((x-bigger (> x (abs y)))
- (r (if x-bigger (/ y x) (/ x y)))
- (d (+ 1.0d0 (* r r))))
- (if x-bigger
- (/ (/ x) d)
- (/ (/ r y) d)))))
+ (setf eta (let* ((x-bigger (> x (abs y)))
+ (r (if x-bigger (/ y x) (/ x y)))
+ (d (+ 1.0d0 (* r r))))
+ (if x-bigger
+ (/ (/ x) d)
+ (/ (/ r y) d)))))
((= x 1.0d0)
;; Should this be changed so that if y is zero, eta is set
;; to +infinity instead of approx 176? In any case
;; tanh(176) is 1.0d0 within working precision.
(let ((t1 (+ 4d0 (square y)))
(t2 (+ (abs y) rho)))
- (setf eta (log (/ (sqrt (sqrt t1)))
- (sqrt t2)))
+ (setf eta (log (/ (sqrt (sqrt t1))
+ (sqrt t2))))
(setf nu (* 0.5d0
(float-sign y
(+ half-pi (atan (* 0.5d0 t2))))))))
;;; Compute tanh z = sinh z / cosh z.
(defun complex-tanh (z)
- (declare (number z))
+ (declare (type (or rational complex) z))
(let ((x (float (realpart z) 1.0d0))
(y (float (imagpart z) 1.0d0)))
(locally
;;
;; and these two expressions are equal if and only if arg conj z =
;; -arg z, which is clearly true for all z.
- (declare (number z))
+ (declare (type (or rational complex) z))
(let ((sqrt-1+z (complex-sqrt (+ 1 z)))
(sqrt-1-z (complex-sqrt (- 1 z))))
(with-float-traps-masked (:divide-by-zero)
;;;
;;; Z may be any NUMBER, but the result is always a COMPLEX.
(defun complex-acosh (z)
- (declare (number z))
+ (declare (type (or rational complex) z))
(let ((sqrt-z-1 (complex-sqrt (- z 1)))
(sqrt-z+1 (complex-sqrt (+ z 1))))
(with-float-traps-masked (:divide-by-zero)
;;;
;;; Z may be any NUMBER, but the result is always a COMPLEX.
(defun complex-asin (z)
- (declare (number z))
+ (declare (type (or rational complex) z))
(let ((sqrt-1-z (complex-sqrt (- 1 z)))
(sqrt-1+z (complex-sqrt (+ 1 z))))
(with-float-traps-masked (:divide-by-zero)
;;;
;;; Z may be any number, but the result is always a complex.
(defun complex-asinh (z)
- (declare (number z))
+ (declare (type (or rational complex) z))
;; asinh z = -i * asin (i*z)
(let* ((iz (complex (- (imagpart z)) (realpart z)))
(result (complex-asin iz)))
;;;
;;; Z may be any number, but the result is always a complex.
(defun complex-atan (z)
- (declare (number z))
+ (declare (type (or rational complex) z))
;; atan z = -i * atanh (i*z)
(let* ((iz (complex (- (imagpart z)) (realpart z)))
(result (complex-atanh iz)))
;;;
;;; Z may be any number, but the result is always a complex.
(defun complex-tan (z)
- (declare (number z))
+ (declare (type (or rational complex) z))
;; tan z = -i * tanh(i*z)
(let* ((iz (complex (- (imagpart z)) (realpart z)))
(result (complex-tanh iz)))
projects / sbcl.git / blobdiff