(defun cis (theta)
#!+sb-doc
- "Return cos(Theta) + i sin(Theta), AKA exp(i Theta)."
+ "Return cos(Theta) + i sin(Theta), i.e. exp(i Theta)."
(declare (type real theta))
(complex (cos theta) (sin theta)))
;; error. These bad definitions also mean that sin and cos for
;; complex numbers can also lose big.
-#+nil
-(defun sinh (number)
- #!+sb-doc
- "Return the hyperbolic sine of NUMBER."
- (/ (- (exp number) (exp (- number))) 2))
-
(defun sinh (number)
#!+sb-doc
"Return the hyperbolic sine of NUMBER."
(complex (* (sinh x) (cos y))
(* (cosh x) (sin y)))))))
-#+nil
-(defun cosh (number)
- #!+sb-doc
- "Return the hyperbolic cosine of NUMBER."
- (/ (+ (exp number) (exp (- number))) 2))
-
(defun cosh (number)
#!+sb-doc
"Return the hyperbolic cosine of NUMBER."
((complex)
(complex-atanh number))))
-;;; HP-UX does not supply a C version of log1p, so
-;;; use the definition.
+;;; HP-UX does not supply a C version of log1p, so use the definition.
+;;;
+;;; FIXME: This is really not a good definition. As per Raymond Toy
+;;; working on CMU CL, "The definition really loses big-time in
+;;; roundoff as x gets small."
#!+hpux
#!-sb-fluid (declaim (inline %log1p))
#!+hpux
(optimize (speed 3) (safety 0)))
(the double-float (log (the (double-float 0d0) (+ number 1d0)))))
\f
-;;;; OLD-SPECFUN stuff
+;;;; not-OLD-SPECFUN stuff
;;;;
;;;; (This was conditional on #-OLD-SPECFUN in the CMU CL sources,
;;;; but OLD-SPECFUN was mentioned nowhere else, so it seems to be
;;; should be used instead?
(declaim (inline square))
-(declaim (ftype (function (double-float) (double-float 0d0)) square))
(defun square (x)
- (declare (double-float x)
- (values (double-float 0d0)))
+ (declare (double-float x))
(* x x))
;;; original CMU CL comment, apparently re. SCALB and LOGB and
(type double-float-exponent n))
(scale-float x n))
+;;; This is like LOGB, but X is not infinity and non-zero and not a
+;;; NaN, so we can always return an integer.
+(declaim (inline logb-finite))
+(defun logb-finite (x)
+ (declare (type double-float x))
+ (multiple-value-bind (signif exponent sign)
+ (decode-float x)
+ (declare (ignore signif sign))
+ ;; DECODE-FLOAT is almost right, except that the exponent is off
+ ;; by one.
+ (1- exponent)))
+
;;; Compute an integer N such that 1 <= |2^N * x| < 2.
;;; For the special cases, the following values are used:
;;; x logb
sb!ext:double-float-positive-infinity)
((zerop x)
;; The answer is negative infinity, but we are supposed to
- ;; signal divide-by-zero.
- ;; (error 'division-by-zero :operation 'logb :operands (list x))
+ ;; signal divide-by-zero, so do the actual division
(/ -1.0d0 x)
)
(t
- (multiple-value-bind (signif expon sign)
- (decode-float x)
- (declare (ignore signif sign))
- ;; DECODE-FLOAT is almost right, except that the exponent
- ;; is off by one.
- (1- expon)))))
+ (logb-finite x))))
;;; This function is used to create a complex number of the
;;; appropriate type:
(if (subtypep (type-of (realpart z)) 'double-float)
(complex x y)
;; Convert anything that's not a DOUBLE-FLOAT to a SINGLE-FLOAT.
- (complex (float x 1.0)
- (float y 1.0))))
+ (complex (float x 1f0)
+ (float y 1f0))))
;;; Compute |(x+i*y)/2^k|^2 scaled to avoid over/underflow. The
;;; result is r + i*k, where k is an integer.
#!+long-float (eval-when (:compile-toplevel :load-toplevel :execute)
(error "needs work for long float support"))
(defun cssqs (z)
- ;; Save all FP flags
(let ((x (float (realpart z) 1d0))
- (y (float (imagpart z) 1d0))
- (k 0)
- (rho 0d0))
- (declare (double-float x y)
- (type (double-float 0d0) rho)
- (fixnum k))
+ (y (float (imagpart z) 1d0)))
;; Would this be better handled using an exception handler to
;; catch the overflow or underflow signal? For now, we turn all
;; traps off and look at the accrued exceptions to see if any
;; signal would have been raised.
(with-float-traps-masked (:underflow :overflow)
- (setf rho (+ (square x) (square y)))
+ (let ((rho (+ (square x) (square y))))
+ (declare (optimize (speed 3) (space 0)))
(cond ((and (or (float-nan-p rho)
(float-infinity-p rho))
(or (float-infinity-p (abs x))
(float-infinity-p (abs y))))
- (setf rho sb!ext:double-float-positive-infinity))
+ (values sb!ext:double-float-positive-infinity 0))
((let ((threshold #.(/ least-positive-double-float
double-float-epsilon))
(traps (ldb sb!vm::float-sticky-bits
(sb!vm:floating-point-modes))))
- ;; overflow raised or (underflow raised and rho < lambda/eps)
+ ;; Overflow raised or (underflow raised and rho <
+ ;; lambda/eps)
(or (not (zerop (logand sb!vm:float-overflow-trap-bit traps)))
(and (not (zerop (logand sb!vm:float-underflow-trap-bit
traps)))
(< rho threshold))))
- (setf k (logb (max (abs x) (abs y))))
- (setf rho (+ (square (scalb x (- k)))
- (square (scalb y (- k))))))))
- (values rho k)))
+ ;; If we're here, neither x nor y are infinity and at
+ ;; least one is non-zero.. Thus logb returns a nice
+ ;; integer.
+ (let ((k (- (logb-finite (max (abs x) (abs y))))))
+ (values (+ (square (scalb x k))
+ (square (scalb y k)))
+ (- k))))
+ (t
+ (values rho 0)))))))
;;; principal square root of Z
;;;
(declare (number z))
(multiple-value-bind (rho k)
(cssqs z)
- (declare (type (double-float 0d0) rho)
- (fixnum k))
+ (declare (type (or (member 0d0) (double-float 0d0)) rho)
+ (type fixnum k))
(let ((x (float (realpart z) 1.0d0))
(y (float (imagpart z) 1.0d0))
(eta 0d0)
(nu 0d0))
(declare (double-float x y eta nu))
+ (locally
+ ;; space 0 to get maybe-inline functions inlined.
+ (declare (optimize (speed 3) (space 0)))
+
(if (not (float-nan-p x))
(setf rho (+ (scalb (abs x) (- k)) (sqrt rho))))
(when (< x 0d0)
(setf eta (abs nu))
(setf nu (float-sign y rho))))
- (coerce-to-complex-type eta nu z))))
+ (coerce-to-complex-type eta nu z)))))
;;; Compute log(2^j*z).
;;;
(y (float (imagpart z) 1.0d0)))
(multiple-value-bind (rho k)
(cssqs z)
- (declare (type (double-float 0d0) rho)
- (fixnum k))
+ (declare (optimize (speed 3)))
(let ((beta (max (abs x) (abs y)))
(theta (min (abs x) (abs y))))
- (declare (type (double-float 0d0) beta theta))
- (if (and (zerop k)
+ (coerce-to-complex-type (if (and (zerop k)
(< t0 beta)
(or (<= beta t1)
(< rho t2)))
- (setf rho (/ (%log1p (+ (* (- beta 1.0d0)
+ (/ (%log1p (+ (* (- beta 1.0d0)
(+ beta 1.0d0))
(* theta theta)))
- 2d0))
- (setf rho (+ (/ (log rho) 2d0)
- (* (+ k j) ln2))))
- (setf theta (atan y x))
- (coerce-to-complex-type rho theta z)))))
+ 2d0)
+ (+ (/ (log rho) 2d0)
+ (* (+ k j) ln2)))
+ (atan y x)
+ z)))))
;;; log of Z = log |Z| + i * arg Z
;;;
(defun complex-atanh (z)
(declare (number z))
(let* (;; constants
- (theta #.(/ (sqrt most-positive-double-float) 4.0d0))
- (rho #.(/ 4.0d0 (sqrt most-positive-double-float)))
- (half-pi #.(/ pi 2.0d0))
+ (theta (/ (sqrt most-positive-double-float) 4.0d0))
+ (rho (/ 4.0d0 (sqrt most-positive-double-float)))
+ (half-pi (/ pi 2.0d0))
(rp (float (realpart z) 1.0d0))
(beta (float-sign rp 1.0d0))
(x (* beta rp))
(y (* beta (- (float (imagpart z) 1.0d0))))
(eta 0.0d0)
(nu 0.0d0))
- (declare (double-float theta rho half-pi rp beta y eta nu)
- (type (double-float 0d0) x))
+ ;; Shouldn't need this declare.
+ (declare (double-float x y))
+ (locally
+ (declare (optimize (speed 3)))
(cond ((or (> x theta)
(> (abs y) theta))
- ;; to avoid overflow...
+ ;; 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),
;; which can cause overflow. Arrange this computation so
(setf nu (let* ((x-bigger (> x (abs y)))
(r (if x-bigger (/ y x) (/ x y)))
(d (+ 1.0d0 (* r r))))
- (declare (double-float r d))
(if x-bigger
(/ (/ x) d)
(/ (/ r y) d)))))
;; tanh(176) is 1.0d0 within working precision.
(let ((t1 (+ 4d0 (square y)))
(t2 (+ (abs y) rho)))
- (declare (type (double-float 0d0) t1 t2))
- #+nil
(setf eta (log (/ (sqrt (sqrt t1)))
(sqrt t2)))
- (setf eta (* 0.5d0 (log (the (double-float 0.0d0)
- (/ (sqrt t1) t2)))))
(setf nu (* 0.5d0
(float-sign y
(+ half-pi (atan (* 0.5d0 t2))))))))
(t
(let ((t1 (+ (abs y) rho)))
- (declare (double-float t1))
- ;; normal case using log1p(x) = log(1 + x)
+ ;; Normal case using log1p(x) = log(1 + x)
(setf eta (* 0.25d0
(%log1p (/ (* 4.0d0 x)
(+ (square (- 1.0d0 x))
(square t1))))))))
(coerce-to-complex-type (* beta eta)
(- (* beta nu))
- z)))
+ z))))
;;; Compute tanh z = sinh z / cosh z.
(defun complex-tanh (z)
(declare (number z))
(let ((x (float (realpart z) 1.0d0))
(y (float (imagpart z) 1.0d0)))
- (declare (double-float x y))
+ (locally
+ ;; space 0 to get maybe-inline functions inlined
+ (declare (optimize (speed 3) (space 0)))
(cond ((> (abs x)
#-(or linux hpux) #.(/ (asinh most-positive-double-float) 4d0)
;; This is more accurate under linux.
#+(or linux hpux) #.(/ (+ (log 2.0d0)
- (log most-positive-double-float))
- 4d0))
- (complex (float-sign x)
- (float-sign y 0.0d0)))
+ (log most-positive-double-float)) 4d0))
+ (coerce-to-complex-type (float-sign x)
+ (float-sign y) z))
(t
(let* ((tv (%tan y))
(beta (+ 1.0d0 (* tv tv)))
(s (sinh x))
(rho (sqrt (+ 1.0d0 (* s s)))))
- (declare (double-float tv s)
- (type (double-float 0.0d0) beta rho))
(if (float-infinity-p (abs tv))
(coerce-to-complex-type (/ rho s)
(/ tv)
(coerce-to-complex-type (/ (* beta rho s)
den)
(/ tv den)
- z))))))))
+ z)))))))))
;;; Compute acos z = pi/2 - asin z.
;;;
projects / sbcl.git / blobdiff