From 302e3218b7d487539ec305bf23881a6ee7d5be99 Mon Sep 17 00:00:00 2001
From: Bryan Newbold <bnewbold@robocracy.org>
Date: Mon, 20 Feb 2017 00:05:29 -0800
Subject: Import Upstream version 5e1

---
 Transcen.scm | 136 +++++++++++++++++++++++++++++++++++++++++++++++++++++------
 1 file changed, 124 insertions(+), 12 deletions(-)

(limited to 'Transcen.scm')

diff --git a/Transcen.scm b/Transcen.scm
index b0d1a2b..dd869a7 100644
--- a/Transcen.scm
+++ b/Transcen.scm
@@ -1,4 +1,4 @@
-;; Copyright (C) 1992, 1993, 1995, 1997 Free Software Foundation, Inc.
+;; Copyright (C) 1992, 1993, 1995, 1997, 2005 Free Software Foundation, Inc.
 ;;
 ;; This program is free software; you can redistribute it and/or modify
 ;; it under the terms of the GNU General Public License as published by
@@ -40,6 +40,8 @@
 
 ;;;; "Transcen.scm", Complex trancendental functions for SCM.
 ;;; Author: Jerry D. Hedden.
+;;;; 2005-05 SRFI-70 extensions.
+;;; Author: Aubrey Jaffer
 
 (define compile-allnumbers #t)		;for HOBBIT compiler
 
@@ -63,17 +65,6 @@
 	  ($sqrt z))
       (make-polar ($sqrt (magnitude z)) (/ (angle z) 2))))
 
-(define expt
-  (let ((integer-expt integer-expt))
-    (lambda (z1 z2)
-      (cond ((zero? z1) (if (zero? z2) 1 0))
-	    ((exact? z2)
-	     (integer-expt z1 z2))
-	    ((and (real? z2) (real? z1) (>= z1 0))
-	     ($expt z1 z2))
-	    (else
-	     (exp (* z2 (log z1))))))))
-
 (define (sinh z)
   (if (real? z) ($sinh z)
       (let ((x (real-part z)) (y (imag-part z)))
@@ -137,3 +128,124 @@
       (if (real? z) ($atan z)
 	  (/ (log (/ (- +i z) (+ +i z))) +2i))
       ($atan2 z (car y))))
+
+;;;; SRFI-70
+(define expt
+  (let ((integer-expt integer-expt))
+    (lambda (z1 z2)
+      (cond ((and (exact? z2) (not (and (zero? z1) (not (positive? z2)))))
+	     (integer-expt z1 z2))
+	    ((and (real? z2) (real? z1) (positive? z1))
+	     ($expt z1 z2))
+	    (else
+	     (exp (* (if (zero? z1) (real-part z2) z2) (log z1))))))))
+
+(set! quotient
+      (let ((integer-quotient quotient))
+	(lambda (x1 x2)
+	  (if (and (exact? x1) (exact? x2))
+	      (integer-quotient x1 x2)
+	      (truncate (/ x1 x2))))))
+
+(set! remainder
+      (let ((integer-remainder remainder))
+	(lambda (x1 x2)
+	  (if (and (exact? x1) (exact? x2))
+	      (integer-remainder x1 x2)
+	      (- x1 (* x2 (quotient x1 x2)))))))
+
+(set! modulo
+      (let ((integer-modulo modulo))
+	(lambda (x1 x2)
+	  (if (and (exact? x1) (exact? x2))
+	      (integer-modulo x1 x2)
+	      (- x1 (* x2 (floor (/ x1 x2))))))))
+
+(define (infinite? z) (and (= z (* 2 z)) (not (zero? z))))
+(define (finite? z) (not (infinite? z)))
+
+(define (invintp f1 f2 f3)
+  (define f1^2 (* f1 f1))
+  (define f2^2 (* f2 f2))
+  (define f3^2 (expt f3 2))
+  (let ((c (+ (* -3 f1^2 f2)
+	      (* 3 f1 f2^2)
+	      (* (- (* 2 f1^2) f2^2) f3)
+	      (* (- f2 (* 2 f1)) f3^2)))
+	(b (+ (- f1^2 (* 2 f2^2)) f3^2))
+	(a (- (* 2 f2) f1 f3)))
+    (define disc (- (* b b) (* 4 a c)))
+    (if (negative? (real-part disc))
+	(/ b -2 a)
+	(let ((sqrt-disc (sqrt disc)))
+	  (define root+ (/ (- sqrt-disc b) 2 a))
+	  (define root- (/ (+ sqrt-disc b) -2 a))
+	  (if (< (magnitude (- root+ f1)) (magnitude (- root- f1)))
+	      root+
+	      root-)))))
+
+(define (extrapolate-0 fs)
+  (define n (length fs))
+  (define (choose n k)
+    (do ((kdx 1 (+ 1 kdx))
+	 (prd 1 (/ (* (- n kdx -1) prd) kdx)))
+	((> kdx k) prd)))
+  (do ((k 1 (+ 1 k))
+       (lst fs (cdr lst))
+       (L 0 (+ (* -1 (expt -1 k) (choose n k) (car lst)) L)))
+      ((null? lst) L)))
+
+(define (sequence->limit proc sequence)
+  (define lval (proc (car sequence)))
+  (if (finite? lval)
+      (let ((val (proc (cadr sequence))))
+	(define h_n*nsamps (* (length sequence) (magnitude (- val lval))))
+	(if (finite? val)
+	    (let loop ((sequence (cddr sequence))
+		       (fxs (list val lval))
+		       (trend #f)
+		       (ldelta (- val lval))
+		       (jdx (+ -1 (length sequence))))
+	      (cond ((null? sequence)
+		     (case trend
+		       ((diverging) (and (real? val) (* ldelta 1/0)))
+		       ((bounded) (invintp val lval (caddr fxs)))
+		       (else (cond ((zero? ldelta) val)
+				   ((not (real? val)) #f)
+				   (else (extrapolate-0 fxs))))))
+		    (else
+		     (set! lval val)
+		     (set! val (proc (car sequence)))
+		     (if (finite? val)
+			 (let ((delta (- val lval)))
+			   (define h_j (/ h_n*nsamps jdx))
+			   (cond ((case trend
+				    ((converging) (<= (magnitude delta) h_j))
+				    ((bounded)    (<= (magnitude ldelta) (magnitude delta)))
+				    ((diverging)  (>= (magnitude delta) h_j))
+				    (else #f))
+				  (loop (cdr sequence) (cons val fxs) trend delta (+ -1 jdx)))
+				 (trend #f)
+				 (else
+				  (loop (cdr sequence) (cons val fxs)
+					(cond ((> (magnitude delta) h_j) 'diverging)
+					      ((< (magnitude ldelta) (magnitude delta)) 'bounded)
+					      (else 'converging))
+					delta (+ -1 jdx)))))
+			 (and (eq? trend 'diverging) val)))))
+	    (and (real? val) val)))
+      (and (real? lval) lval)))
+
+(define (limit proc x1 x2 . k)
+  (set! k (if (null? k) 8 (car k)))
+  (cond ((not (finite? x2)) (slib:error 'limit 'infinite 'x2 x2))
+	((not (finite? x1))
+	 (or (positive? (* x1 x2)) (slib:error 'limit 'start 'mismatch x1 x2))
+	 (limit (lambda (x) (proc (/ x))) 0.0 (/ x2) k))
+	((= x1 (+ x1 x2)) (slib:error 'limit 'null 'range x1 (+ x1 x2)))
+	(else (let ((dec (/ x2 k)))
+		(do ((x (+ x1 x2 0.0) (- x dec))
+		     (cnt (+ -1 k) (+ -1 cnt))
+		     (lst '() (cons x lst)))
+		    ((negative? cnt)
+		     (sequence->limit proc (reverse lst))))))))
-- 
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