#| -*-Scheme-*-

Copyright (C) 1986, 1987, 1988, 1989, 1990, 1991, 1992, 1993, 1994,
    1995, 1996, 1997, 1998, 1999, 2000, 2001, 2002, 2003, 2004, 2005,
    2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014, 2015, 2016,
    2017, 2018, 2019, 2020 Massachusetts Institute of Technology

This file is part of MIT/GNU Scheme.

MIT/GNU Scheme is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2 of the License, or (at
your option) any later version.

MIT/GNU Scheme 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
General Public License for more details.

You should have received a copy of the GNU General Public License
along with MIT/GNU Scheme; if not, write to the Free Software
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301,
USA.

|#

;;;; Scheme Arithmetic for 6.001
;;; package: (student number)

(declare (usual-integrations))

(define-integrable (int:->flonum n)
  ((ucode-primitive integer->flonum 2) n #b10))

(define-integrable (flonum? object)
  (object-type? (ucode-type big-flonum) object))

(declare (integrate flo:integer?))
(define (flo:integer? x)
  (flo:= x (flo:round x)))

(define (flo:->integer x)
  (if (not (flo:integer? x))
      (error:wrong-type-argument x "integer" 'FLONUM->INTEGER))
  (flo:truncate->exact x))

(define-syntax define-standard-unary
  (sc-macro-transformer
   (lambda (form environment)
     `(DEFINE (,(list-ref form 1) X)
	(IF (FLONUM? X)
	    (,(close-syntax (list-ref form 2) environment) X)
	    (,(close-syntax (list-ref form 3) environment) X))))))

(define-standard-unary rational? (lambda (x) x true) int:integer?)
(define-standard-unary integer? flo:integer? int:integer?)
(define-standard-unary exact? (lambda (x) x false)
  (lambda (x)
    (guarantee int:integer? x 'EXACT?)
    true))
(define-standard-unary zero? flo:zero? int:zero?)
(define-standard-unary negative? flo:negative? int:negative?)
(define-standard-unary positive? flo:positive? int:positive?)
(define-standard-unary abs flo:abs int:abs)
(define-standard-unary floor flo:floor (lambda (x) x))
(define-standard-unary ceiling flo:ceiling (lambda (x) x))
(define-standard-unary truncate flo:truncate (lambda (x) x))
(define-standard-unary round flo:round (lambda (x) x))
(define-standard-unary exact->inexact (lambda (x) x) int:->flonum)
(define-standard-unary inexact->exact
  (lambda (x)
    (if (not (flo:integer? x))
	(error:bad-range-argument x 'INEXACT->EXACT))
    (flo:truncate->exact x))
  (lambda (x)
    (guarantee int:integer? x 'INEXACT->EXACT)
    x))

(define-syntax define-standard-binary
  (sc-macro-transformer
   (lambda (form environment)
     (let ((flo:op (close-syntax (list-ref form 2) environment))
	   (int:op (close-syntax (list-ref form 3) environment)))
       `(DEFINE (,(list-ref form 1) X Y)
	  (IF (FLONUM? X)
	      (IF (FLONUM? Y)
		  (,flo:op X Y)
		  (,flo:op X (INT:->FLONUM Y)))
	      (IF (FLONUM? Y)
		  (,flo:op (INT:->FLONUM X) Y)
		  (,int:op X Y))))))))

(define-standard-binary real:+ flo:+ int:+)
(define-standard-binary real:- flo:- int:-)
(define-standard-binary rationalize
  flo:rationalize
  int:rationalize)

(define (int:rationalize q e)
  (int:simplest-rational (int:- q e) (int:+ q e)))

(define (int:simplest-rational x y)
  (let ((x<y
	 (lambda (x y)
	   (cond ((int:positive? x) x)
		 ((int:negative? y) y)
		 (else 0)))))
    (cond ((int:< x y) (x<y x y))
	  ((int:< y x) (x<y y x))
	  (else x))))

(define (real:* x y)
  (cond ((flonum? x)
	 (cond ((flonum? y) (flo:* x y))
	       ((int:zero? y) y)
	       (else (flo:* x (int:->flonum y)))))
	((int:zero? x) x)
	((flonum? y) (flo:* (int:->flonum x) y))
	(else (int:* x y))))

(define (real:/ x y)
  (cond ((flonum? x) (flo:/ x (if (flonum? y) y (int:->flonum y))))
	((flonum? y) (if (int:zero? x) x (flo:/ (int:->flonum x) y)))
	((int:= (int:remainder x y) 0) (int:quotient x y))
	(else (flo:/ (int:->flonum x) (int:->flonum y)))))

(define (real:invert x)
  (cond ((flonum? x) (flo:/ 1. x))
	((int:= 1 x) x)
	(else (flo:/ 1. (int:->flonum x)))))

(define (real:= x y)
  (if (flonum? x)
      (if (flonum? y)
	  (flo:= x y)
	  (begin
	    (guarantee int:integer? y '=)
	    (and (flo:= x (flo:truncate x))
		 (int:= (flo:truncate->exact x) y))))
      (if (flonum? y)
	  (begin
	    (guarantee int:integer? x '=)
	    (and (flo:= y (flo:truncate y))
		 (int:= x (flo:truncate->exact y))))
	  (int:= x y))))

(define (real:< x y)
  (if (flonum? x)
      (if (flonum? y)
	  (flo:< x y)
	  (flo/int:< x y))
      (if (flonum? y)
	  (int/flo:< x y)
	  (int:< x y))))

(define (real:max x y)
  (if (flonum? x)
      (if (flonum? y)
	  (if (flo:< x y) y x)
	  (if (flo/int:< x y) (int:->flonum y) x))
      (if (flonum? y)
	  (if (int/flo:< x y) y (int:->flonum x))
	  (if (int:< x y) y x))))

(define (real:min x y)
  (if (flonum? x)
      (if (flonum? y)
	  (if (flo:< x y) x y)
	  (if (flo/int:< x y) x (int:->flonum y)))
      (if (flonum? y)
	  (if (int/flo:< x y) (int:->flonum x) y)
	  (if (int:< x y) x y))))

(define-integrable (flo/int:< x y)
  (let ((ix (flo:truncate->exact x)))
    (cond ((int:< ix y) true)
	  ((int:< y ix) false)
	  (else (flo:< x (flo:truncate x))))))

(define-integrable (int/flo:< x y)
  (let ((iy (flo:truncate->exact y)))
    (cond ((int:< x iy) true)
	  ((int:< iy x) false)
	  (else (flo:< (flo:truncate y) y)))))

(define (even? n)
  (int:even? (if (flonum? n) (flo:->integer n) n)))

(define-syntax define-integer-binary
  (sc-macro-transformer
   (lambda (form environment)
     (let ((operator (close-syntax (list-ref form 3) environment))
	   (flo->int
	    (lambda (n)
	      `(IF (FLO:INTEGER? ,n)
		   (FLO:->INTEGER ,n)
		   (ERROR:WRONG-TYPE-ARGUMENT ,n "integer"
					      ',(list-ref form 2))))))
       `(DEFINE (,(list-ref form 1) N M)
	  (IF (FLONUM? N)
	      (INT:->FLONUM
	       (,operator ,(flo->int 'N)
			  (IF (FLONUM? M) (FLO:->INTEGER M) M)))
	      (IF (FLONUM? M)
		  (INT:->FLONUM (,operator N ,(flo->int 'M)))
		  (,operator N M))))))))

(define-integer-binary quotient quotient int:quotient)
(define-integer-binary remainder remainder int:remainder)
(define-integer-binary modulo modulo int:modulo)
(define-integer-binary real:gcd gcd int:gcd)
(define-integer-binary real:lcm lcm int:lcm)

(define (numerator q)
  (if (flonum? q)
      (int:->flonum (rat:numerator (flo:->rational q)))
      (begin
	(guarantee int:integer? q 'NUMERATOR)
	q)))

(define (denominator q)
  (if (flonum? q)
      (int:->flonum (rat:denominator (flo:->rational q)))
      (begin
	(guarantee int:integer? q 'DENOMINATOR)
	1)))

(define-syntax define-transcendental-unary
  (sc-macro-transformer
   (lambda (form environment)
     `(DEFINE (,(list-ref form 1) X)
	(IF (,(close-syntax (list-ref form 2) environment) X)
	    ,(close-syntax (list-ref form 3) environment)
	    (,(close-syntax (list-ref form 4) environment)
	     (REAL:->FLONUM X)))))))

(define-transcendental-unary exp real:exact0= 1 flo:exp)
(define-transcendental-unary log real:exact1= 0 flo:log)
(define-transcendental-unary sin real:exact0= 0 flo:sin)
(define-transcendental-unary cos real:exact0= 1 flo:cos)
(define-transcendental-unary tan real:exact0= 0 flo:tan)
(define-transcendental-unary asin real:exact0= 0 flo:asin)
(define-transcendental-unary acos real:exact1= 0 flo:acos)
(define-transcendental-unary real:atan real:exact0= 0 flo:atan)

(define (real:atan2 y x)
  (if (and (real:exact0= y) (exact? x))
      0
      (flo:atan2 (real:->flonum y) (real:->flonum x))))

(define-integrable (real:exact0= x)
  (if (flonum? x) false (int:zero? x)))

(define-integrable (real:exact1= x)
  (if (flonum? x) false (int:= 1 x)))

(define (real:->flonum x)
  (if (flonum? x)
      x
      (int:->flonum x)))

(define (sqrt x)
  (if (flonum? x)
      (begin
	(if (flo:negative? x)
	    (error:bad-range-argument x 'SQRT))
	(flo:sqrt x))
      (int:sqrt x)))

(define (int:sqrt x)
  (if (int:negative? x)
      (error:bad-range-argument x 'SQRT))
  (let ((guess (flo:sqrt (int:->flonum x))))
    (let ((n (flo:round->exact guess)))
      (if (int:= x (int:* n n))
	  n
	  guess))))

(define (expt x y)
  (let ((general-case
	 (lambda (x y)
	   (cond ((flo:zero? y) 1.)
		 ((flo:zero? x)
		  (if (not (flo:positive? y))
		      (error:divide-by-zero 'EXPT (list x y)))
		  x)
		 (else
		  (if (and (flo:negative? x)
			   (not (flo:integer? y)))
		      (error:bad-range-argument x 'EXPT))
		  (flo:expt x y))))))
    (if (flonum? x)
	(if (flonum? y)
	    (general-case x y)
	    (let ((exact-method
		   (lambda (y)
		     (if (int:= 1 y)
			 x
			 (let loop ((x x) (y y) (answer 1.))
			   (let ((qr (int:divide y 2)))
			     (let ((x (flo:* x x))
				   (y (integer-divide-quotient qr))
				   (answer
				    (if (int:zero?
					 (integer-divide-remainder qr))
					answer
					(flo:* answer x))))
			       (if (int:= 1 y)
				   (flo:* answer x)
				   (loop x y answer)))))))))
	      (cond ((int:positive? y) (exact-method y))
		    ((int:negative? y)
		     (flo:/ 1. (exact-method (int:negate y))))
		    (else 1.))))
	(if (flonum? y)
	    (general-case (int:->flonum x) y)
	    (if (int:negative? y)
		(real:invert (int:expt x (int:negate y)))
		(int:expt x y))))))

(define number? rational?)
(define complex? rational?)
(define real? rational?)

(define (inexact? z)
  (not (exact? z)))

(define (odd? n)
  (not (even? n)))

(define (inc z)
  (+ z 1))

(define (dec z)
  (- z 1))

(define (= . zs)
  (reduce-comparator real:= zs '=))

(define (< . xs)
  (reduce-comparator real:< xs '<))

(define (> . xs)
  (reduce-comparator (lambda (x y) (real:< y x)) xs '>))

(define (<= . xs)
  (reduce-comparator (lambda (x y) (not (real:< y x))) xs '<=))

(define (>= . xs)
  (reduce-comparator (lambda (x y) (not (real:< x y))) xs '>=))

(define (max x . xs)
  (reduce-max/min real:max x xs 'MAX))

(define (min x . xs)
  (reduce-max/min real:min x xs 'MIN))

(define (+ . zs)
  (cond ((null? zs)
	 0)
	((null? (cdr zs))
	 (if (not (number? (car zs)))
	     (error:wrong-type-argument (car zs) false '+))
	 (car zs))
	((null? (cddr zs))
	 (real:+ (car zs) (cadr zs)))
	(else
	 (real:+ (car zs)
		 (real:+ (cadr zs)
			 (reduce real:+ 0 (cddr zs)))))))

(define (* . zs)
  (cond ((null? zs)
	 1)
	((null? (cdr zs))
	 (if (not (number? (car zs)))
	     (error:wrong-type-argument (car zs) false '*))
	 (car zs))
	((null? (cddr zs))
	 (real:* (car zs) (cadr zs)))
	(else
	 (real:* (car zs)
		 (real:* (cadr zs)
			 (reduce real:* 1 (cddr zs)))))))

(define (- z1 . zs)
  (cond ((null? zs)
	 (if (flonum? z1) (flo:negate z1) (int:negate z1)))
	((null? (cdr zs))
	 (real:- z1 (car zs)))
	(else
	 (real:- z1
		 (real:+ (car zs)
			 (real:+ (cadr zs)
				 (reduce real:+ 0 (cddr zs))))))))

(define (/ z1 . zs)
  (cond ((null? zs)
	 (real:invert z1))
	((null? (cdr zs))
	 (real:/ z1 (car zs)))
	(else
	 (real:/ z1
		 (real:* (car zs)
			 (real:* (cadr zs)
				 (reduce real:* 1 (cddr zs))))))))

(define (gcd . integers)
  (reduce real:gcd 0 integers))

(define (lcm . integers)
  (reduce real:lcm 1 integers))

(define (atan z #!optional x)
  (if (default-object? x) (real:atan z) (real:atan2 z x)))