Refactor elisp/grains

elisp/grains/grains.el

@@ -5,7 +5,7 @@
 ;;; simpler: simply shift an unsigned long long to get the number of
 ;;; grains at square n.
 ;;;
-;;; In Emacs, that approach doesn't seem to work. Only 30 bits are used
+;;; In Emacs, that approach doesn't seem to work. Only 61 bits are used
 ;;; for integers, resulting in overflows above square 60.
 ;;;
 ;;; The solution, if one wants to calculate it, seems to be to rely on
@@ -15,15 +15,14 @@
 ;;; However, it also occurred to me that the values here are known,
 ;;; limited, and not likely to change anytime soon. By using contants,
 ;;; we can get constant time determination of the number of grains for
-;;; a square. The functions used by the tests, square and total, simply
+;;; a square. The functions used by the tests, square and total, return
-;;; return constant values, with the number of grains for a square
+;;; these constant values.
-;;; relying on a vector that matches the n-th index to the corresponding
-;;; grains.
 ;;;
 ;;; Emacs itself was useful in effectuating this solution. I used a
 ;;; macro to evaluate calculate-square for n, and then insert the
 ;;; results in this buffer. There's probably a more elegant way to do
-;;; this in Emacs, but this approach was adequate for the task.
+;;; this, but the approach was adequate for this task.
+;;;
 ;;; Sometimes, making the programmer's life easier can lead to more
 ;;; efficient code.
 
@@ -31,82 +30,18 @@
 
 (require 'calc)
 
-(defun calculate-square(n)
+(defvar grains
-  "Return the number of grains at square N. Use left shifts when n is equal to or below 60, and calc for numbers up to 65."
+  [0 1 2 4 8 16 32 64 128 256 512 1024 2048 4096 8192 16384 32768 65536 131072
-  (cond ((< n 0) 0)
+     262144 524288 1048576 2097152 4194304 8388608 16777216 33554432 67108864
-	((> n 65) 0)
+     134217728 268435456 536870912 1073741824 2147483648 4294967296 8589934592
-	((<= n 60) (lsh 1 (- n 1)))
+     17179869184 34359738368 68719476736 137438953472 274877906944 549755813888
-	(t (string-to-number (calc-eval (format "2^%d" (1- n)))))))
+     1099511627776 2199023255552 4398046511104 8796093022208 17592186044416
-
+     35184372088832 70368744177664 140737488355328 281474976710656
-(defun calculate-total()
+     562949953421312 1125899906842624 2251799813685248 4503599627370496
-  "Return the total number of grains on a chessboard with 64 squares."
+     9007199254740992  18014398509481984 36028797018963968 72057594037927936
-  (1- (square 65)))
+     144115188075855872 288230376151711744 576460752303423488
-
+     1152921504606846976 2305843009213693952 4611686018427387904
-(defvar grains [0
+     9223372036854775808]
-		1
-		2
-		4
-		8
-		16
-		32
-		64
-		128
-		256
-		512
-		1024
-		2048
-		4096
-		8192
-		16384
-		32768
-		65536
-		131072
-		262144
-		524288
-		1048576
-		2097152
-		4194304
-		8388608
-		16777216
-		33554432
-		67108864
-		134217728
-		268435456
-		536870912
-		1073741824
-		2147483648
-		4294967296
-		8589934592
-		17179869184
-		34359738368
-		68719476736
-		137438953472
-		274877906944
-		549755813888
-		1099511627776
-		2199023255552
-		4398046511104
-		8796093022208
-		17592186044416
-		35184372088832
-		70368744177664
-		140737488355328
-		281474976710656
-		562949953421312
-		1125899906842624
-		2251799813685248
-		4503599627370496
-		9007199254740992
-		18014398509481984
-		36028797018963968
-		72057594037927936
-		144115188075855872
-		288230376151711744
-		576460752303423488
-		1152921504606846976
-		2305843009213693952
-		4611686018427387904
-		9223372036854775808]
   "Vector containing the number of grains for a square with the corresponding index.")
 
 (defun square(n)
@@ -119,5 +54,16 @@
   "Return the total number of grains on a chessboard with 64 squares."
   18446744073709551616)
 
+(defun calculate-square(n) ;; Not used, for reference only.
+  "Return the number of grains at square N. Use left shifts when n is equal to or below 60, and calc for numbers up to 65."
+  (cond ((< n 0) 0)
+	((> n 65) 0)
+	((<= n 60) (lsh 1 (- n 1)))
+	(t (string-to-number (calc-eval (format "2^%d" (1- n)))))))
+
+(defun calculate-total() ;; Not used, for reference only.
+  "Return the total number of grains on a chessboard with 64 squares."
+  (1- (square 65)))
+
 (provide 'grains)
 ;;; grains.el ends here