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;; Copyright (C) 1994 M. Hagiya, W. Schelter, T. Yuasa
;; Copyright (C) 2024 Camm Maguire
;; This file is part of GNU Common Lisp, herein referred to as GCL
;;
;; GCL is free software; you can redistribute it and/or modify it under
;; the terms of the GNU LIBRARY GENERAL PUBLIC LICENSE as published by
;; the Free Software Foundation; either version 2, or (at your option)
;; any later version.
;;
;; GCL is distributed in the hope that it will be useful, but WITHOUT
;; ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
;; FITNESS FOR A PARTICULAR PURPOSE. See the GNU Library General Public
;; License for more details.
;;
;; You should have received a copy of the GNU Library General Public License
;; along with GCL; see the file COPYING. If not, write to the Free Software
;; Foundation, 675 Mass Ave, Cambridge, MA 02139, USA.
;;;; numlib.lsp
;;;;
;;;; number routines
(in-package :system)
(defun powm (a b c)
(declare (optimize (safety 1)))
(check-type a integer)
(check-type b (integer 0))
(check-type c (integer 0))
(if (typep b 'fixnum)
(gmp:mpz_powm_ui a b c)
(gmp:mpz_powm a b c)))
(declaim (inline powm))
(defconstant imag-one #C(0.0d0 1.0d0))
(defun isqrt (i)
(declare (optimize (safety 1)))
(check-type i (integer 0))
(typecase
i
(fixnum (do* ((y 0 (floor i x))
(x (ash 1 (ceiling (integer-length i) 2)) (+ (ash x -1) (ash y -1) (logand x y 1))))
((<= x y) x)))
(otherwise (mpz_sqrt i))))
(deftype bytespec nil `(cons (integer 0) (integer 0)))
(defun byte (size position)
(declare (optimize (safety 1)))
(check-type size (integer 0))
(check-type position (integer 0))
(cons size position))
(defun byte-position (bytespec)
(declare (optimize (safety 1)))
(check-type bytespec cons)
(cdr bytespec))
(defun byte-size (bytespec)
(declare (optimize (safety 1)))
(check-type bytespec cons)
(car bytespec))
(defun ldb (bytespec integer)
(declare (optimize (safety 1)))
(check-type bytespec bytespec)
(check-type integer integer)
(logand (ash integer (- (byte-position bytespec)))
(1- (ash 1 (byte-size bytespec)))))
(defun ldb-test (bytespec integer)
(declare (optimize (safety 1)))
(check-type bytespec bytespec)
(check-type integer integer)
(not (zerop (ldb bytespec integer))))
(defun dpb (newbyte bytespec integer &aux (z (1- (ash 1 (byte-size bytespec)))))
(declare (optimize (safety 1)))
(check-type newbyte integer)
(check-type bytespec bytespec)
(check-type integer integer)
(logior (logandc2 integer (ash z (byte-position bytespec)))
(ash (logand newbyte z) (byte-position bytespec))))
(defun deposit-field (newbyte bytespec integer &aux (z (ash (1- (ash 1 (byte-size bytespec))) (byte-position bytespec))))
(declare (optimize (safety 1)))
(check-type newbyte integer)
(check-type bytespec bytespec)
(check-type integer integer)
(logior (logandc2 integer z) (logand newbyte z)))
(defun mask-field (bytespec integer)
(declare (optimize (safety 1)))
(check-type bytespec bytespec)
(check-type integer integer)
(logand integer (ash (1- (ash 1 (byte-size bytespec))) (byte-position bytespec))))
(defun phase (x)
(declare (optimize (safety 1)))
(check-type x number)
(if (= 0 x) 0.0
(atan (imagpart x) (realpart x))))
(defun signum (x)
(declare (optimize (safety 1)))
(check-type x number)
(if (zerop x) x
(typecase x
(rational (if (minusp x) -1 1))
(short-float (if (minusp x) -1.0s0 1.0s0))
(long-float (if (minusp x) -1.0 1.0))
(fcomplex (/ x (abs x)))
(dcomplex (/ x (abs x)))
(complex (let* ((y (max (abs (realpart x)) (abs (imagpart x))))
(z (complex (/ (realpart x) y) (/ (imagpart x) y))))
(/ z (abs z)))))))
(defun cis (x)
(declare (optimize (safety 1)))
(check-type x real)
(exp (* #c(0 1) (float x))))
(defun ffloor (x &optional (y 1.0s0))
(declare (optimize (safety 1)))
(check-type x real)
(check-type y real)
(multiple-value-bind (i r) (floor x y)
(values (float i (if (floatp x) x 1.0)) r)))
(defun fceiling (x &optional (y 1.0s0))
(declare (optimize (safety 1)))
(check-type x real)
(check-type y real)
(multiple-value-bind (i r) (ceiling x y)
(values (float i (if (floatp x) x 1.0)) r)))
(defun ftruncate (x &optional (y 1.0s0))
(declare (optimize (safety 1)))
(check-type x real)
(check-type y real)
(multiple-value-bind (i r) (truncate x y)
(values (float i (if (floatp x) x 1.0)) r)))
(defun fround (x &optional (y 1.0s0))
(declare (optimize (safety 1)))
(check-type x real)
(check-type y real)
(multiple-value-bind (i r) (round x y)
(values (float i (if (floatp x) x 1.0)) r)))
(defun logtest (x y)
(declare (optimize (safety 1)))
(check-type x integer)
(check-type y integer)
(not (zerop (logand x y))))
(defconstant +make-complex-alist+
`((complex-integer #tinteger #tinteger)
(complex-integer-ratio #tinteger #tratio)
(complex-ratio-integer #tratio #tinteger)
(complex-ratio #tratio #tratio)
(complex-short-float #tshort-float #tshort-float)
(complex-long-float #tlong-float #tlong-float)))
(eval-when (compile eval) (defmacro complex-tt (s) (or (position s +make-complex-alist+ :key 'car) (baboon))))
(defun complex (rp &optional (ip (typecase rp (rational 0)(short-float 0.0s0)(long-float 0.0))))
(declare (optimize (safety 1)))
(check-type rp real)
(check-type ip real)
(typecase rp
(integer
(typecase ip
((integer 0 0) rp)
(integer (make-complex #.(complex-tt complex-integer) rp ip))
(ratio (make-complex #.(complex-tt complex-integer-ratio) rp ip))
(short-float (make-complex #.(complex-tt complex-short-float) (float rp ip) ip))
(long-float (make-complex #.(complex-tt complex-long-float) (float rp ip) ip))))
(ratio
(typecase ip
((integer 0 0) rp)
(integer (make-complex #.(complex-tt complex-ratio-integer) rp ip))
(ratio (make-complex #.(complex-tt complex-ratio) rp ip))
(short-float (make-complex #.(complex-tt complex-short-float) (float rp ip) ip))
(long-float (make-complex #.(complex-tt complex-long-float) (float rp ip) ip))))
(short-float
(typecase ip
(rational (make-complex #.(complex-tt complex-short-float) rp (float ip rp)))
(short-float (make-complex #.(complex-tt complex-short-float) rp ip))
(long-float (make-complex #.(complex-tt complex-long-float) (float rp ip) ip))))
(long-float (make-complex #.(complex-tt complex-long-float) rp (float ip rp)))))
(defun make-complex-propagator (f t1 t2 t3 &aux (i -1))
(declare (ignore f))
(reduce 'tp-or
(mapcan (lambda (x)
(when (tp-and t1 (object-tp (incf i)))
(list (cmp-norm-tp `(complex* ,(cmp-unnorm-tp (tp-and t2 (cadr x))) ,(cmp-unnorm-tp (tp-and t3 (caddr x))))))))
+make-complex-alist+)
:initial-value nil))
(setf (get 'make-complex 'type-propagator) 'make-complex-propagator)
(defun float-digits (x)
(declare (optimize (safety 1)))
(check-type x float);FIXME etypecase
(typecase x
(short-float 24)
(t 53)))
(defun float-precision (x)
(declare (optimize (safety 1)))
(check-type x float);FIXME etypecase
(typecase x
((member 0.0 0.0s0) 0)
(short-float 24)
(t 53)))
(defun float-sign (x &optional (y 1.0))
(declare (optimize (safety 1)))
(check-type x float)
(check-type y float)
(let ((y (float (abs y) x)))
(if (minusp x) (- y) y)))
(defun float-radix (x)
(declare (optimize (safety 1)))
(check-type x float);FIXME etypecase
2)
(defun atomic-tp-propagator (f &rest r); tp &aux (atp (atomic-tp tp)))
(declare (dynamic-extent r))
(unless (member-if-not 'atomic-tp r)
(let ((l (multiple-value-list (apply f (mapcar (lambda (x) (car (atomic-tp x))) r)))))
(if (cdr l)
`(returns-exactly ,@(mapcar 'object-tp l))
(object-tp (car l))))))
(dolist (l '(integer-decode-float decode-float scale-float));float-radix float-digits float-precision float-sign
(setf (get l 'type-propagator) 'atomic-tp-propagator (get l 'compiler::c1no-side-effects) t))
(declaim (inline fryi))
(defun fryi (x a)
(labels ((fryn (x a) (abs (- (* x (denominator a)) (numerator a))))
(fryk (x a b &aux (c (fryn x a))(d (fryn x b))
(kf 0.8);heuristic guard against overshoot
(cf (* c kf))(df (* d kf)))
(cond ((> cf d 0) (values (truncate (/ cf d))))
((> df c 0) (values (truncate (/ df c))))
(1)))
(med (a b k)
(/ (+ (numerator a) (* k (numerator b)))
(+ (denominator a) (* k (denominator b)))))
(fry (x a b)
(cond ((= (float a x) x) a)
((= (float b x) x) b)
((< (med a b 1) x) (fry x (med a b (fryk x a b)) b))
((fry x a (med b a (fryk x a b)))))))
(fry x a (1+ a))))
(defun rationalize (x)
(declare (optimize (safety 1)))
(check-type x real)
(typecase x
(rational x)
(float
(if (isnan x)
(rational x)
(multiple-value-bind
(f r) (truncate x)
(cond ((minusp r) (fryi x (1- f)))
((zerop r) f)
((fryi x f))))))))
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