\f
;;;; miscellaneous constants, utility functions, and macros
-(defconstant pi 3.14159265358979323846264338327950288419716939937511L0)
-;(defconstant e 2.71828182845904523536028747135266249775724709369996L0)
+(defconstant pi
+ #!+long-float 3.14159265358979323846264338327950288419716939937511l0
+ #!-long-float 3.14159265358979323846264338327950288419716939937511d0)
;;; Make these INLINE, since the call to C is at least as compact as a
;;; Lisp call, and saves number consing to boot.
(sb!xc:defmacro def-math-rtn (name num-args)
(let ((function (symbolicate "%" (string-upcase name))))
`(progn
- (proclaim '(inline ,function))
+ (declaim (inline ,function))
(sb!alien:define-alien-routine (,name ,function) double-float
,@(let ((results nil))
(dotimes (i num-args (nreverse results))
(* base power)
(exp (* power (log base)))))))))
+;;; FIXME: Maybe rename this so that it's clearer that it only works
+;;; on integers?
+(defun log2 (x)
+ (declare (type integer x))
+ ;; CMUCL comment:
+ ;;
+ ;; Write x = 2^n*f where 1/2 < f <= 1. Then log2(x) = n +
+ ;; log2(f). So we grab the top few bits of x and scale that
+ ;; appropriately, take the log of it and add it to n.
+ ;;
+ ;; Motivated by an attempt to get LOG to work better on bignums.
+ (let ((n (integer-length x)))
+ (if (< n sb!vm:double-float-digits)
+ (log (coerce x 'double-float) 2.0d0)
+ (let ((f (ldb (byte sb!vm:double-float-digits
+ (- n sb!vm:double-float-digits))
+ x)))
+ (+ n (log (scale-float (coerce f 'double-float)
+ (- sb!vm:double-float-digits))
+ 2.0d0))))))
+
(defun log (number &optional (base nil base-p))
#!+sb-doc
"Return the logarithm of NUMBER in the base BASE, which defaults to e."
(if base-p
- (if (zerop base)
- base ; ANSI spec
- (/ (log number) (log base)))
+ (cond
+ ((zerop base) 0f0) ; FIXME: type
+ ((and (typep number '(integer (0) *))
+ (typep base '(integer (0) *)))
+ (coerce (/ (log2 number) (log2 base)) 'single-float))
+ (t (/ (log number) (log base))))
(number-dispatch ((number number))
- (((foreach fixnum bignum ratio))
+ (((foreach fixnum bignum))
+ (if (minusp number)
+ (complex (log (- number)) (coerce pi 'single-float))
+ (coerce (/ (log2 number) (log (exp 1.0d0) 2.0d0)) 'single-float)))
+ ((ratio)
(if (minusp number)
(complex (log (- number)) (coerce pi 'single-float))
- (coerce (%log (coerce number 'double-float)) 'single-float)))
+ (let ((numerator (numerator number))
+ (denominator (denominator number)))
+ (if (= (integer-length numerator)
+ (integer-length denominator))
+ (coerce (%log1p (coerce (- number 1) 'double-float))
+ 'single-float)
+ (coerce (/ (- (log2 numerator) (log2 denominator))
+ (log (exp 1.0d0) 2.0d0))
+ 'single-float)))))
(((foreach single-float double-float))
;; Is (log -0) -infinity (libm.a) or -infinity + i*pi (Kahan)?
;; Since this doesn't seem to be an implementation issue
(float-sign y pi))
(float-sign y (/ pi 2)))
(%atan2 y x))))
- (number-dispatch ((y number) (x number))
+ (number-dispatch ((y real) (x real))
((double-float
(foreach double-float single-float fixnum bignum ratio))
(atan2 y (coerce x 'double-float)))
((complex)
(complex-atan y)))))
-;; It seems that everyone has a C version of sinh, cosh, and
-;; tanh. Let's use these for reals because the original
-;; implementations based on the definitions lose big in round-off
-;; error. These bad definitions also mean that sin and cos for
-;; complex numbers can also lose big.
+;;; It seems that every target system has a C version of sinh, cosh,
+;;; and tanh. Let's use these for reals because the original
+;;; implementations based on the definitions lose big in round-off
+;;; error. These bad definitions also mean that sin and cos for
+;;; complex numbers can also lose big.
(defun sinh (number)
#!+sb-doc
;; 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))
- (coerce-to-complex-type (float-sign x)
- (float-sign y) z))
+ ;; FIXME: this form is hideously broken wrt
+ ;; cross-compilation portability. Much else in this
+ ;; file is too, of course, sometimes hidden by
+ ;; constant-folding, but this one in particular clearly
+ ;; depends on host and target
+ ;; MOST-POSITIVE-DOUBLE-FLOATs being equal. -- CSR,
+ ;; 2003-04-20
+ #.(/ (+ (log 2.0d0)
+ (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)))