File: calc-units.el

package info (click to toggle)
calc 2.02f-11
  • links: PTS
  • area: main
  • in suites: woody
  • size: 3,212 kB
  • ctags: 2,321
  • sloc: lisp: 44,231; makefile: 133; sh: 48
file content (1352 lines) | stat: -rw-r--r-- 42,760 bytes parent folder | download | duplicates (5)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
1001
1002
1003
1004
1005
1006
1007
1008
1009
1010
1011
1012
1013
1014
1015
1016
1017
1018
1019
1020
1021
1022
1023
1024
1025
1026
1027
1028
1029
1030
1031
1032
1033
1034
1035
1036
1037
1038
1039
1040
1041
1042
1043
1044
1045
1046
1047
1048
1049
1050
1051
1052
1053
1054
1055
1056
1057
1058
1059
1060
1061
1062
1063
1064
1065
1066
1067
1068
1069
1070
1071
1072
1073
1074
1075
1076
1077
1078
1079
1080
1081
1082
1083
1084
1085
1086
1087
1088
1089
1090
1091
1092
1093
1094
1095
1096
1097
1098
1099
1100
1101
1102
1103
1104
1105
1106
1107
1108
1109
1110
1111
1112
1113
1114
1115
1116
1117
1118
1119
1120
1121
1122
1123
1124
1125
1126
1127
1128
1129
1130
1131
1132
1133
1134
1135
1136
1137
1138
1139
1140
1141
1142
1143
1144
1145
1146
1147
1148
1149
1150
1151
1152
1153
1154
1155
1156
1157
1158
1159
1160
1161
1162
1163
1164
1165
1166
1167
1168
1169
1170
1171
1172
1173
1174
1175
1176
1177
1178
1179
1180
1181
1182
1183
1184
1185
1186
1187
1188
1189
1190
1191
1192
1193
1194
1195
1196
1197
1198
1199
1200
1201
1202
1203
1204
1205
1206
1207
1208
1209
1210
1211
1212
1213
1214
1215
1216
1217
1218
1219
1220
1221
1222
1223
1224
1225
1226
1227
1228
1229
1230
1231
1232
1233
1234
1235
1236
1237
1238
1239
1240
1241
1242
1243
1244
1245
1246
1247
1248
1249
1250
1251
1252
1253
1254
1255
1256
1257
1258
1259
1260
1261
1262
1263
1264
1265
1266
1267
1268
1269
1270
1271
1272
1273
1274
1275
1276
1277
1278
1279
1280
1281
1282
1283
1284
1285
1286
1287
1288
1289
1290
1291
1292
1293
1294
1295
1296
1297
1298
1299
1300
1301
1302
1303
1304
1305
1306
1307
1308
1309
1310
1311
1312
1313
1314
1315
1316
1317
1318
1319
1320
1321
1322
1323
1324
1325
1326
1327
1328
1329
1330
1331
1332
1333
1334
1335
1336
1337
1338
1339
1340
1341
1342
1343
1344
1345
1346
1347
1348
1349
1350
1351
1352
;; Calculator for GNU Emacs, part II [calc-units.el]
;; Copyright (C) 1990, 1991, 1992, 1993 Free Software Foundation, Inc.
;; Written by Dave Gillespie, daveg@synaptics.com.

;; This file is part of GNU Emacs.

;; GNU Emacs is distributed in the hope that it will be useful,
;; but WITHOUT ANY WARRANTY.  No author or distributor
;; accepts responsibility to anyone for the consequences of using it
;; or for whether it serves any particular purpose or works at all,
;; unless he says so in writing.  Refer to the GNU Emacs General Public
;; License for full details.

;; Everyone is granted permission to copy, modify and redistribute
;; GNU Emacs, but only under the conditions described in the
;; GNU Emacs General Public License.   A copy of this license is
;; supposed to have been given to you along with GNU Emacs so you
;; can know your rights and responsibilities.  It should be in a
;; file named COPYING.  Among other things, the copyright notice
;; and this notice must be preserved on all copies.



;; This file is autoloaded from calc-ext.el.
(require 'calc-ext)

(require 'calc-macs)

(defun calc-Need-calc-units () nil)


;;; Units commands.

(defun calc-base-units ()
  (interactive)
  (calc-slow-wrapper
   (let ((calc-autorange-units nil))
     (calc-enter-result 1 "bsun" (math-simplify-units
				  (math-to-standard-units (calc-top-n 1)
							  nil)))))
)

(defun calc-quick-units ()
  (interactive)
  (calc-slow-wrapper
   (let* ((num (- last-command-char ?0))
	  (pos (if (= num 0) 10 num))
	  (units (calc-var-value 'var-Units))
	  (expr (calc-top-n 1)))
     (or (and (>= num 0) (<= num 9))
	 (error "Bad unit number"))
     (or (math-vectorp units)
	 (error "No \"quick units\" are defined"))
     (or (< pos (length units))
	 (error "Unit number %d not defined" pos))
     (if (math-units-in-expr-p expr nil)
	 (calc-enter-result 1 (format "cun%d" num)
			    (math-convert-units expr (nth pos units)))
       (calc-enter-result 1 (format "*un%d" num)
			  (math-simplify-units
			   (math-mul expr (nth pos units)))))))
)

(defun calc-convert-units (&optional old-units new-units)
  (interactive)
  (calc-slow-wrapper
   (let ((expr (calc-top-n 1))
	 (uoldname nil)
	 unew)
     (or (math-units-in-expr-p expr t)
	 (let ((uold (or old-units
			 (progn
			   (setq uoldname (read-string "Old units: "))
			   (if (equal uoldname "")
			       (progn
				 (setq uoldname "1")
				 1)
			     (if (string-match "\\` */" uoldname)
				 (setq uoldname (concat "1" uoldname)))
			     (math-read-expr uoldname))))))
	   (if (eq (car-safe uold) 'error)
	       (error "Bad format in units expression: %s" (nth 1 uold)))
	   (setq expr (math-mul expr uold))))
     (or new-units
	 (setq new-units (read-string (if uoldname
					  (concat "Old units: "
						  uoldname
						  ", new units: ")
					"New units: "))))
     (if (string-match "\\` */" new-units)
	 (setq new-units (concat "1" new-units)))
     (setq units (math-read-expr new-units))
     (if (eq (car-safe units) 'error)
	 (error "Bad format in units expression: %s" (nth 2 units)))
     (let ((unew (math-units-in-expr-p units t))
	   (std (and (eq (car-safe units) 'var)
		     (assq (nth 1 units) math-standard-units-systems))))
       (if std
	   (calc-enter-result 1 "cvun" (math-simplify-units
					(math-to-standard-units expr
								(nth 1 std))))
	 (or unew
	     (error "No units specified"))
	 (calc-enter-result 1 "cvun"
			    (math-convert-units
			     expr units
			     (and uoldname (not (equal uoldname "1")))))))))
)

(defun calc-autorange-units (arg)
  (interactive "P")
  (calc-wrapper
   (calc-change-mode 'calc-autorange-units arg nil t)
   (message (if calc-autorange-units
		"Adjusting target unit prefix automatically."
	      "Using target units exactly.")))
)

(defun calc-convert-temperature (&optional old-units new-units)
  (interactive)
  (calc-slow-wrapper
   (let ((expr (calc-top-n 1))
	 (uold nil)
	 (uoldname nil)
	 unew)
     (setq uold (or old-units
		    (let ((units (math-single-units-in-expr-p expr)))
		      (if units
			  (if (consp units)
			      (list 'var (car units)
				    (intern (concat "var-"
						    (symbol-name
						     (car units)))))
			    (error "Not a pure temperature expression"))
			(math-read-expr
			 (setq uoldname (read-string
					 "Old temperature units: ")))))))
     (if (eq (car-safe uold) 'error)
	 (error "Bad format in units expression: %s" (nth 2 uold)))
     (or (math-units-in-expr-p expr nil)
	 (setq expr (math-mul expr uold)))
     (setq unew (or new-units
		    (math-read-expr
		     (read-string (if uoldname
				      (concat "Old temperature units: "
					      uoldname
					      ", new units: ")
				    "New temperature units: ")))))
     (if (eq (car-safe unew) 'error)
	 (error "Bad format in units expression: %s" (nth 2 unew)))
     (calc-enter-result 1 "cvtm" (math-simplify-units
				  (math-convert-temperature expr uold unew
							    uoldname)))))
)

(defun calc-remove-units ()
  (interactive)
  (calc-slow-wrapper
   (calc-enter-result 1 "rmun" (math-simplify-units
				(math-remove-units (calc-top-n 1)))))
)

(defun calc-extract-units ()
  (interactive)
  (calc-slow-wrapper
   (calc-enter-result 1 "rmun" (math-simplify-units
				(math-extract-units (calc-top-n 1)))))
)

(defun calc-explain-units ()
  (interactive)
  (calc-wrapper
   (let ((num-units nil)
	 (den-units nil))
     (calc-explain-units-rec (calc-top-n 1) 1)
     (and den-units (string-match "^[^(].* .*[^)]$" den-units)
	  (setq den-units (concat "(" den-units ")")))
     (if num-units
	 (if den-units
	     (message "%s per %s" num-units den-units)
	   (message "%s" num-units))
       (if den-units
	   (message "1 per %s" den-units)
	 (message "No units in expression")))))
)

(defun calc-explain-units-rec (expr pow)
  (let ((u (math-check-unit-name expr))
	pos)
    (if (and u (not (math-zerop pow)))
	(let ((name (or (nth 2 u) (symbol-name (car u)))))
	  (if (eq (aref name 0) ?\*)
	      (setq name (substring name 1)))
	  (if (string-match "[^a-zA-Z0-9']" name)
	      (if (string-match "^[a-zA-Z0-9' ()]*$" name)
		  (while (setq pos (string-match "[ ()]" name))
		    (setq name (concat (substring name 0 pos)
				       (if (eq (aref name pos) 32) "-" "")
				       (substring name (1+ pos)))))
		(setq name (concat "(" name ")"))))
	  (or (eq (nth 1 expr) (car u))
	      (setq name (concat (nth 2 (assq (aref (symbol-name
						     (nth 1 expr)) 0)
					      math-unit-prefixes))
				 (if (and (string-match "[^a-zA-Z0-9']" name)
					  (not (memq (car u) '(mHg gf))))
				     (concat "-" name)
				   (downcase name)))))
	  (cond ((or (math-equal-int pow 1)
		     (math-equal-int pow -1)))
		((or (math-equal-int pow 2)
		     (math-equal-int pow -2))
		 (if (equal (nth 4 u) '((m . 1)))
		     (setq name (concat "Square-" name))
		   (setq name (concat name "-squared"))))
		((or (math-equal-int pow 3)
		     (math-equal-int pow -3))
		 (if (equal (nth 4 u) '((m . 1)))
		     (setq name (concat "Cubic-" name))
		   (setq name (concat name "-cubed"))))
		(t
		 (setq name (concat name "^"
				    (math-format-number (math-abs pow))))))
	  (if (math-posp pow)
	      (setq num-units (if num-units
				  (concat num-units " " name)
				name))
	    (setq den-units (if den-units
				(concat den-units " " name)
			      name))))
      (cond ((eq (car-safe expr) '*)
	     (calc-explain-units-rec (nth 1 expr) pow)
	     (calc-explain-units-rec (nth 2 expr) pow))
	    ((eq (car-safe expr) '/)
	     (calc-explain-units-rec (nth 1 expr) pow)
	     (calc-explain-units-rec (nth 2 expr) (- pow)))
	    ((memq (car-safe expr) '(neg + -))
	     (calc-explain-units-rec (nth 1 expr) pow))
	    ((and (eq (car-safe expr) '^)
		  (math-realp (nth 2 expr)))
	     (calc-explain-units-rec (nth 1 expr)
				     (math-mul pow (nth 2 expr)))))))
)

(defun calc-simplify-units ()
  (interactive)
  (calc-slow-wrapper
   (calc-with-default-simplification
    (calc-enter-result 1 "smun" (math-simplify-units (calc-top-n 1)))))
)

(defun calc-view-units-table (n)
  (interactive "P")
  (and n (setq math-units-table-buffer-valid nil))
  (let ((win (get-buffer-window "*Units Table*")))
    (if (and win
	     math-units-table
	     math-units-table-buffer-valid)
	(progn
	  (bury-buffer (window-buffer win))
	  (let ((curwin (selected-window)))
	    (select-window win)
	    (switch-to-buffer nil)
	    (select-window curwin)))
      (math-build-units-table-buffer nil)))
)

(defun calc-enter-units-table (n)
  (interactive "P")
  (and n (setq math-units-table-buffer-valid nil))
  (math-build-units-table-buffer t)
  (message (substitute-command-keys "Type \\[calc] to return to the Calculator."))
)

(defun calc-define-unit (uname desc)
  (interactive "SDefine unit name: \nsDescription: ")
  (calc-wrapper
   (let ((form (calc-top-n 1))
	 (unit (assq uname math-additional-units)))
     (or unit
	 (setq math-additional-units
	       (cons (setq unit (list uname nil nil))
		     math-additional-units)
	       math-units-table nil))
     (setcar (cdr unit) (and (not (and (eq (car-safe form) 'var)
				       (eq (nth 1 form) uname)))
			     (not (math-equal-int form 1))
			     (math-format-flat-expr form 0)))
     (setcar (cdr (cdr unit)) (and (not (equal desc ""))
				   desc))))
  (calc-invalidate-units-table)
)

(defun calc-undefine-unit (uname)
  (interactive "SUndefine unit name: ")
  (calc-wrapper
   (let ((unit (assq uname math-additional-units)))
     (or unit
	 (if (assq uname math-standard-units)
	     (error "\"%s\" is a predefined unit name" uname)
	   (error "Unit name \"%s\" not found" uname)))
     (setq math-additional-units (delq unit math-additional-units)
	   math-units-table nil)))
  (calc-invalidate-units-table)
)

(defun calc-invalidate-units-table ()
  (setq math-units-table nil)
  (let ((buf (get-buffer "*Units Table*")))
    (and buf
	 (save-excursion
	   (set-buffer buf)
	   (save-excursion
	     (goto-char (point-min))
	     (if (looking-at "Calculator Units Table")
		 (let ((buffer-read-only nil))
		   (insert "(Obsolete) ")))))))
)

(defun calc-get-unit-definition (uname)
  (interactive "SGet definition for unit: ")
  (calc-wrapper
   (math-build-units-table)
   (let ((unit (assq uname math-units-table)))
     (or unit
	 (error "Unit name \"%s\" not found" uname))
     (let ((msg (nth 2 unit)))
       (if (stringp msg)
	   (if (string-match "^\\*" msg)
	       (setq msg (substring msg 1)))
	 (setq msg (symbol-name uname)))
       (if (nth 1 unit)
	   (progn
	     (calc-enter-result 0 "ugdf" (nth 1 unit))
	     (message "Derived unit: %s" msg))
	 (calc-enter-result 0 "ugdf" (list 'var uname
					   (intern
					    (concat "var-"
						    (symbol-name uname)))))
	 (message "Base unit: %s" msg)))))
)

(defun calc-permanent-units ()
  (interactive)
  (calc-wrapper
   (let (pos)
     (set-buffer (find-file-noselect (substitute-in-file-name
				      calc-settings-file)))
     (goto-char (point-min))
     (if (and (search-forward ";;; Custom units stored by Calc" nil t)
	      (progn
		(beginning-of-line)
		(setq pos (point))
		(search-forward "\n;;; End of custom units" nil t)))
	 (progn
	   (beginning-of-line)
	   (forward-line 1)
	   (delete-region pos (point)))
       (goto-char (point-max))
       (insert "\n\n")
       (forward-char -1))
     (insert ";;; Custom units stored by Calc on " (current-time-string) "\n")
     (if math-additional-units
	 (progn
	   (insert "(setq math-additional-units '(\n")
	   (let ((list math-additional-units))
	     (while list
	       (insert "  (" (symbol-name (car (car list))) " "
		       (if (nth 1 (car list))
			   (if (stringp (nth 1 (car list)))
			       (prin1-to-string (nth 1 (car list)))
			     (prin1-to-string (math-format-flat-expr
					       (nth 1 (car list)) 0)))
			 "nil")
		       " "
		       (prin1-to-string (nth 2 (car list)))
		       ")\n")
	       (setq list (cdr list))))
	   (insert "))\n"))
       (insert ";;; (no custom units defined)\n"))
     (insert ";;; End of custom units\n")
     (save-buffer)))
)





;;; Units operations.

;;; Units table last updated 9-Jan-91 by Ulrich Mueller (ulm@vsnhd1.cern.ch)
;;; with some additions by Przemek Klosowski (przemek@rrdstrad.nist.gov)

(defvar math-standard-units
  '( ;; Length
     ( m       nil		     "*Meter" )
     ( in      "2.54 cm"             "Inch" )
     ( ft      "12 in"		     "Foot" )
     ( yd      "3 ft"		     "Yard" )
     ( mi      "5280 ft"	     "Mile" )
     ( au      "1.495979e11 m"       "Astronomical Unit" )
     ( lyr     "9460536207068016 m"  "Light Year" )
     ( pc      "206264.80625 au"     "Parsec" )
     ( nmi     "1852 m"		     "Nautical Mile" )
     ( fath    "6 ft"		     "Fathom" )
     ( u       "1 um"		     "Micron" )
     ( mil     "in/1000"	     "Mil" )
     ( point   "in/72"		     "Point (1/72 inch)" )
     ( tpt     "in/72.27"	     "Point (TeX conventions)" )
     ( Ang     "1e-10 m"	     "Angstrom" )
     ( mfi     "mi+ft+in"	     "Miles + feet + inches" )
     
     ;; Area
     ( hect    "10000 m^2"	     "*Hectare" )
     ( acre    "mi^2 / 640"	     "Acre" )
     ( b       "1e-28 m^2"	     "Barn" )
     
     ;; Volume
     ( l       "1e-3 m^3"	     "*Liter" )
     ( L       "1e-3 m^3"	     "Liter" )
     ( gal     "4 qt"		     "US Gallon" )
     ( qt      "2 pt"		     "Quart" )
     ( pt      "2 cup"		     "Pint" )
     ( cup     "8 ozfl"		     "Cup" )
     ( ozfl    "2 tbsp"		     "Fluid Ounce" )
     ( floz    "2 tbsp"		     "Fluid Ounce" )
     ( tbsp    "3 tsp"		     "Tablespoon" )
     ( tsp     "4.92892159375 ml"    "Teaspoon" )
     ( vol     "tsp+tbsp+ozfl+cup+pt+qt+gal" "Gallons + ... + teaspoons" )
     ( galC    "4.54609 l"	     "Canadian Gallon" )
     ( galUK   "4.546092 l"	     "UK Gallon" )
     
     ;; Time
     ( s       nil		     "*Second" )
     ( sec     "s"		     "Second" )
     ( min     "60 s"		     "Minute" )
     ( hr      "60 min"		     "Hour" )
     ( day     "24 hr"		     "Day" )
     ( wk      "7 day"		     "Week" )
     ( hms     "wk+day+hr+min+s"     "Hours, minutes, seconds" )
     ( yr      "365.25 day"	     "Year" )
     ( Hz      "1/s"		     "Hertz" )

     ;; Speed
     ( mph     "mi/hr"		     "*Miles per hour" )
     ( kph     "km/hr"		     "Kilometers per hour" )
     ( knot    "nmi/hr"		     "Knot" )
     ( c       "2.99792458e8 m/s"    "Speed of light" )     
     
     ;; Acceleration
     ( ga      "9.80665 m/s^2"	     "*\"g\" acceleration" )

     ;; Mass
     ( g       nil                   "*Gram" )
     ( lb      "16 oz"		     "Pound (mass)" )
     ( oz      "28.349523125 g"	     "Ounce (mass)" )
     ( ton     "2000 lb"	     "Ton" )
     ( tpo     "ton+lb+oz"	     "Tons + pounds + ounces (mass)" )
     ( t       "1000 kg"	     "Metric ton" )
     ( tonUK   "1016.0469088 kg"     "UK ton" )
     ( lbt     "12 ozt"		     "Troy pound" )
     ( ozt     "31.103475 g"	     "Troy ounce" )
     ( ct      ".2 g"		     "Carat" )
     ( amu     "1.6605402e-24 g"     "Unified atomic mass" )

     ;; Force
     ( N       "m kg/s^2"	     "*Newton" )
     ( dyn     "1e-5 N"		     "Dyne" )
     ( gf      "ga g"		     "Gram (force)" )
     ( lbf     "4.44822161526 N"     "Pound (force)" )
     ( kip     "1000 lbf"	     "Kilopound (force)" )
     ( pdl     "0.138255 N"	     "Poundal" )

     ;; Energy
     ( J       "N m"		     "*Joule" )
     ( erg     "1e-7 J"		     "Erg" )
     ( cal     "4.1868 J"	     "International Table Calorie" )
     ( Btu     "1055.05585262 J"     "International Table Btu" )
     ( eV      "ech V"               "Electron volt" )
     ( ev      "eV"                  "Electron volt" )
     ( therm   "105506000 J"	     "EEC therm" )
     ( invcm   "h c/cm"	  	     "Energy in inverse centimeters" )
     ( Kayser  "invcm"		     "Kayser (inverse centimeter energy)" )
     ( men     "100/invcm"	     "Inverse energy in meters" )
     ( Hzen    "h Hz"		     "Energy in Hertz")
     ( Ken     "k K"		     "Energy in Kelvins")
     ;; ( invcm   "eV / 8065.47835185"    "Energy in inverse centimeters" )
     ;; ( Hzen    "eV / 2.41796958004e14" "Energy in Hertz")
     ;; ( Ken     "eV / 11604.7967327"    "Energy in Kelvins")

     ;; Power
     ( W       "J/s"		     "*Watt" )
     ( hp      "745.7 W"	     "Horsepower" )

     ;; Temperature
     ( K       nil                   "*Degree Kelvin"     K )
     ( dK      "K"		     "Degree Kelvin"	  K )
     ( degK    "K"		     "Degree Kelvin"	  K )
     ( dC      "K"		     "Degree Celsius"	  C )
     ( degC    "K"      	     "Degree Celsius"	  C )
     ( dF      "(5/9) K"	     "Degree Fahrenheit"  F )
     ( degF    "(5/9) K"	     "Degree Fahrenheit"  F )

     ;; Pressure
     ( Pa      "N/m^2"		     "*Pascal" )
     ( bar     "1e5 Pa"		     "Bar" )
     ( atm     "101325 Pa"	     "Standard atmosphere" )
     ( torr    "atm/760"	     "Torr" )
     ( mHg     "1000 torr"	     "Meter of mercury" )
     ( inHg    "25.4 mmHg"	     "Inch of mercury" )
     ( inH2O   "248.84 Pa"	     "Inch of water" )
     ( psi     "6894.75729317 Pa"    "Pound per square inch" )

     ;; Viscosity
     ( P       "0.1 Pa s"	     "*Poise" )
     ( St      "1e-4 m^2/s"	     "Stokes" )

     ;; Electromagnetism
     ( A       nil                   "*Ampere" )
     ( C       "A s"		     "Coulomb" )
     ( Fdy     "ech Nav"  	     "Faraday" )
     ( e       "1.60217733e-19 C"    "Elementary charge" )
     ( ech     "1.60217733e-19 C"    "Elementary charge" )
     ( V       "W/A"		     "Volt" )
     ( ohm     "V/A"		     "Ohm" )
     ( mho     "A/V"		     "Mho" )
     ( S       "A/V"		     "Siemens" )
     ( F       "C/V"		     "Farad" )
     ( H       "Wb/A"		     "Henry" )
     ( T       "Wb/m^2"		     "Tesla" )
     ( G       "1e-4 T"		     "Gauss" )
     ( Wb      "V s"		     "Weber" )

     ;; Luminous intensity
     ( cd      nil                   "*Candela" )
     ( sb      "1e4 cd/m^2"	     "Stilb" )
     ( lm      "cd sr"		     "Lumen" )
     ( lx      "lm/m^2"		     "Lux" )
     ( ph      "1e4 lx"		     "Phot" )
     ( fc      "10.76 lx"	     "Footcandle" )
     ( lam     "1e4 lm/m^2"	     "Lambert" )
     ( flam    "1.07639104e-3 lam"   "Footlambert" )

     ;; Radioactivity
     ( Bq      "1/s"  		     "*Becquerel" )
     ( Ci      "3.7e10 Bq"	     "Curie" )
     ( Gy      "J/kg"		     "Gray" )
     ( Sv      "Gy"		     "Sievert" )
     ( R       "2.58e-4 C/kg"	     "Roentgen" )
     ( rd      ".01 Gy"		     "Rad" )
     ( rem     "rd"		     "Rem" )

     ;; Amount of substance
     ( mol     nil                   "*Mole" )

     ;; Plane angle
     ( rad     nil                   "*Radian" )
     ( circ    "2 pi rad"	     "Full circle" )
     ( rev     "circ"		     "Full revolution" )
     ( deg     "circ/360"            "Degree" )
     ( arcmin  "deg/60"		     "Arc minute" )
     ( arcsec  "arcmin/60"	     "Arc second" )
     ( grad    "circ/400"            "Grade" )
     ( rpm     "rev/min"	     "Revolutions per minute" )

     ;; Solid angle
     ( sr      nil		     "*Steradian" )

     ;; Other physical quantities (Physics Letters B239, 1 (1990))
     ( h       "6.6260755e-34 J s"   "*Planck's constant" )
     ( hbar    "h / 2 pi"	     "Planck's constant" )
     ( mu0     "4 pi 1e-7 H/m"       "Permeability of vacuum" )
     ( Grav    "6.67259e-11 N m^2/kg^2"  "Gravitational constant" )
     ( Nav     "6.0221367e23 / mol"  "Avagadro's constant" )
     ( me      "0.51099906 MeV/c^2"  "Electron rest mass" )
     ( mp      "1.007276470 amu"     "Proton rest mass" )
     ( mn      "1.008664904 amu"     "Neutron rest mass" )
     ( mu      "0.113428913 amu"     "Muon rest mass" )
     ( Ryd     "1.0973731571e5 invcm" "Rydberg's constant" )
     ( k       "1.3806513e-23 J/K"   "Boltzmann's constant" )
     ( fsc     "1 / 137.0359895"     "Fine structure constant" )
     ( muB     "5.78838263e-11 MeV/T"  "Bohr magneton" )
     ( muN     "3.15245166e-14 MeV/T"  "Nuclear magneton" )
     ( mue     "1.001159652193 muB"  "Electron magnetic moment" )
     ( mup     "2.792847386 muN"     "Proton magnetic moment" )
     ( R0      "Nav k"               "Molar gas constant" )
     ( V0      "22.413992 L/mol"     "Standard volume of ideal gas" )
))


(defvar math-additional-units nil
  "*Additional units table for user-defined units.
Must be formatted like math-standard-units.
If this is changed, be sure to set math-units-table to nil to ensure
that the combined units table will be rebuilt.")

(defvar math-unit-prefixes
  '( ( ?E  (float 1 18)  "Exa"    )
     ( ?P  (float 1 15)  "Peta"   )
     ( ?T  (float 1 12)  "Tera"	  )
     ( ?G  (float 1 9)   "Giga"	  )
     ( ?M  (float 1 6)   "Mega"	  )
     ( ?k  (float 1 3)   "Kilo"	  )
     ( ?K  (float 1 3)   "Kilo"	  )
     ( ?h  (float 1 2)   "Hecto"  )
     ( ?H  (float 1 2)   "Hecto"  )
     ( ?D  (float 1 1)   "Deka"	  )
     ( 0   (float 1 0)   nil      )
     ( ?d  (float 1 -1)  "Deci"	  )
     ( ?c  (float 1 -2)  "Centi"  )
     ( ?m  (float 1 -3)  "Milli"  )
     ( ?u  (float 1 -6)  "Micro"  )
     ( ?n  (float 1 -9)  "Nano"	  )
     ( ?p  (float 1 -12) "Pico"	  )
     ( ?f  (float 1 -15) "Femto"  )
     ( ?a  (float 1 -18) "Atto"   )
))

(defvar math-standard-units-systems
  '( ( base  nil )
     ( si    ( ( g   '(* (var kg var-kg) (float 1 -3)) ) ) )
     ( mks   ( ( g   '(* (var kg var-kg) (float 1 -3)) ) ) )
     ( cgs   ( ( m   '(* (var cm var-cm) 100         ) ) ) )
))

(defvar math-units-table nil
  "Internal units table derived from math-defined-units.
Entries are (SYMBOL EXPR DOC-STRING TEMP-TYPE BASE-UNITS).")

(defvar math-units-table-buffer-valid nil)


(defun math-build-units-table ()
  (or math-units-table
      (let* ((combined-units (append math-additional-units
				     math-standard-units))
	     (unit-list (mapcar 'car combined-units))
	     tab)
	(message "Building units table...")
	(setq math-units-table-buffer-valid nil)
	(setq tab (mapcar (function
			   (lambda (x)
			     (list (car x)
				   (and (nth 1 x)
					(if (stringp (nth 1 x))
					    (let ((exp (math-read-plain-expr
							(nth 1 x))))
					      (if (eq (car-safe exp) 'error)
						  (error "Format error in definition of %s in units table: %s"
							 (car x) (nth 2 exp))
						exp))
					  (nth 1 x)))
				   (nth 2 x)
				   (nth 3 x)
				   (and (not (nth 1 x))
					(list (cons (car x) 1))))))
			  combined-units))
	(let ((math-units-table tab))
	  (mapcar 'math-find-base-units tab))
	(message "Building units table...done")
	(setq math-units-table tab)))
)

(defun math-find-base-units (entry)
  (if (eq (nth 4 entry) 'boom)
      (error "Circular definition involving unit %s" (car entry)))
  (or (nth 4 entry)
      (let (base)
	(setcar (nthcdr 4 entry) 'boom)
	(math-find-base-units-rec (nth 1 entry) 1)
	'(or base
	    (error "Dimensionless definition for unit %s" (car entry)))
	(while (eq (cdr (car base)) 0)
	  (setq base (cdr base)))
	(let ((b base))
	  (while (cdr b)
	    (if (eq (cdr (car (cdr b))) 0)
		(setcdr b (cdr (cdr b)))
	      (setq b (cdr b)))))
	(setq base (sort base 'math-compare-unit-names))
	(setcar (nthcdr 4 entry) base)
	base))
)

(defun math-compare-unit-names (a b)
  (memq (car b) (cdr (memq (car a) unit-list)))
)

(defun math-find-base-units-rec (expr pow)
  (let ((u (math-check-unit-name expr)))
    (cond (u
	   (let ((ulist (math-find-base-units u)))
	     (while ulist
	       (let ((p (* (cdr (car ulist)) pow))
		     (old (assq (car (car ulist)) base)))
		 (if old
		     (setcdr old (+ (cdr old) p))
		   (setq base (cons (cons (car (car ulist)) p) base))))
	       (setq ulist (cdr ulist)))))
	  ((math-scalarp expr))
	  ((and (eq (car expr) '^)
		(integerp (nth 2 expr)))
	   (math-find-base-units-rec (nth 1 expr) (* pow (nth 2 expr))))
	  ((eq (car expr) '*)
	   (math-find-base-units-rec (nth 1 expr) pow)
	   (math-find-base-units-rec (nth 2 expr) pow))
	  ((eq (car expr) '/)
	   (math-find-base-units-rec (nth 1 expr) pow)
	   (math-find-base-units-rec (nth 2 expr) (- pow)))
	  ((eq (car expr) 'neg)
	   (math-find-base-units-rec (nth 1 expr) pow))
	  ((eq (car expr) '+)
	   (math-find-base-units-rec (nth 1 expr) pow))
	  ((eq (car expr) 'var)
	   (or (eq (nth 1 expr) 'pi)
	       (error "Unknown name %s in defining expression for unit %s"
		      (nth 1 expr) (car entry))))
	  (t (error "Malformed defining expression for unit %s" (car entry)))))
)


(defun math-units-in-expr-p (expr sub-exprs)
  (and (consp expr)
       (if (eq (car expr) 'var)
	   (math-check-unit-name expr)
	 (and (or sub-exprs
		  (memq (car expr) '(* / ^)))
	      (or (math-units-in-expr-p (nth 1 expr) sub-exprs)
		  (math-units-in-expr-p (nth 2 expr) sub-exprs)))))
)

(defun math-only-units-in-expr-p (expr)
  (and (consp expr)
       (if (eq (car expr) 'var)
	   (math-check-unit-name expr)
	 (if (memq (car expr) '(* /))
	     (and (math-only-units-in-expr-p (nth 1 expr))
		  (math-only-units-in-expr-p (nth 2 expr)))
	   (and (eq (car expr) '^)
		(and (math-only-units-in-expr-p (nth 1 expr))
		     (math-realp (nth 2 expr)))))))
)

(defun math-single-units-in-expr-p (expr)
  (cond ((math-scalarp expr) nil)
	((eq (car expr) 'var)
	 (math-check-unit-name expr))
	((eq (car expr) '*)
	 (let ((u1 (math-single-units-in-expr-p (nth 1 expr)))
	       (u2 (math-single-units-in-expr-p (nth 2 expr))))
	   (or (and u1 u2 'wrong)
	       u1
	       u2)))
	((eq (car expr) '/)
	 (if (math-units-in-expr-p (nth 2 expr) nil)
	     'wrong
	   (math-single-units-in-expr-p (nth 1 expr))))
	(t 'wrong))
)

(defun math-check-unit-name (v)
  (and (eq (car-safe v) 'var)
       (or (assq (nth 1 v) (or math-units-table (math-build-units-table)))
	   (let ((name (symbol-name (nth 1 v))))
	     (and (> (length name) 1)
		  (assq (aref name 0) math-unit-prefixes)
		  (or (assq (intern (substring name 1)) math-units-table)
		      (and (eq (aref name 0) ?M)
			   (> (length name) 3)
			   (eq (aref name 1) ?e)
			   (eq (aref name 2) ?g)
			   (assq (intern (substring name 3))
				 math-units-table)))))))
)


(defun math-to-standard-units (expr which-standard)
  (math-to-standard-rec expr)
)

(defun math-to-standard-rec (expr)
  (if (eq (car-safe expr) 'var)
      (let ((u (math-check-unit-name expr))
	    (base (nth 1 expr)))
	(if u
	    (progn
	      (if (nth 1 u)
		  (setq expr (math-to-standard-rec (nth 1 u)))
		(let ((st (assq (car u) which-standard)))
		  (if st
		      (setq expr (nth 1 st))
		    (setq expr (list 'var (car u)
				     (intern (concat "var-"
						     (symbol-name
						      (car u)))))))))
	      (or (null u)
		  (eq base (car u))
		  (setq expr (list '*
				   (nth 1 (assq (aref (symbol-name base) 0)
						math-unit-prefixes))
				   expr)))
	      expr)
	  (if (eq base 'pi)
	      (math-pi)
	    expr)))
    (if (Math-primp expr)
	expr
      (cons (car expr)
	    (mapcar 'math-to-standard-rec (cdr expr)))))
)

(defun math-apply-units (expr units ulist &optional pure)
  (if ulist
      (let ((new 0)
	    value)
	(setq expr (math-simplify-units expr))
	(or (math-numberp expr)
	    (error "Incompatible units"))
	(while (cdr ulist)
	  (setq value (math-div expr (nth 1 (car ulist)))
		value (math-floor (let ((calc-internal-prec
					 (1- calc-internal-prec)))
				    (math-normalize value)))
		new (math-add new (math-mul value (car (car ulist))))
		expr (math-sub expr (math-mul value (nth 1 (car ulist))))
		ulist (cdr ulist)))
	(math-add new (math-mul (math-div expr (nth 1 (car ulist)))
				(car (car ulist)))))
    (math-simplify-units (if pure
			     expr
			   (list '* expr units))))
)

(defun math-decompose-units (units)
  (let ((u (math-check-unit-name units)))
    (and u (eq (car-safe (nth 1 u)) '+)
	 (setq units (nth 1 u))))
  (setq units (calcFunc-expand units))
  (and (eq (car-safe units) '+)
       (let ((entry (list units calc-internal-prec calc-prefer-frac)))
	 (or (equal entry (car math-decompose-units-cache))
	     (let ((ulist nil)
		   (utemp units)
		   qty unit)
	       (while (eq (car-safe utemp) '+)
		 (setq ulist (cons (math-decompose-unit-part (nth 2 utemp))
				   ulist)
		       utemp (nth 1 utemp)))
	       (setq ulist (cons (math-decompose-unit-part utemp) ulist)
		     utemp ulist)
	       (while (setq utemp (cdr utemp))
		 (or (equal (nth 2 (car utemp)) (nth 2 (car ulist)))
		     (error "Inconsistent units in sum")))
	       (setq math-decompose-units-cache
		     (cons entry
			   (sort ulist
				 (function
				  (lambda (x y)
				    (not (Math-lessp (nth 1 x)
						     (nth 1 y))))))))))
	 (cdr math-decompose-units-cache)))
)
(setq math-decompose-units-cache nil)

(defun math-decompose-unit-part (unit)
  (cons unit
	(math-is-multiple (math-simplify-units (math-to-standard-units
						unit nil))
			  t))
)

(defun math-find-compatible-unit (expr unit)
  (let ((u (math-check-unit-name unit)))
    (if u
	(math-find-compatible-unit-rec expr 1)))
)

(defun math-find-compatible-unit-rec (expr pow)
  (cond ((eq (car-safe expr) '*)
	 (or (math-find-compatible-unit-rec (nth 1 expr) pow)
	     (math-find-compatible-unit-rec (nth 2 expr) pow)))
	((eq (car-safe expr) '/)
	 (or (math-find-compatible-unit-rec (nth 1 expr) pow)
	     (math-find-compatible-unit-rec (nth 2 expr) (- pow))))
	((and (eq (car-safe expr) '^)
	      (integerp (nth 2 expr)))
	 (math-find-compatible-unit-rec (nth 1 expr) (* pow (nth 2 expr))))
	(t
	 (let ((u2 (math-check-unit-name expr)))
	   (if (equal (nth 4 u) (nth 4 u2))
	       (cons expr pow)))))
)

(defun math-convert-units (expr new-units &optional pure)
  (math-with-extra-prec 2
    (let ((compat (and (not pure) (math-find-compatible-unit expr new-units)))
	  (unit-list nil)
	  (math-combining-units nil))
      (if compat
	  (math-simplify-units
	   (math-mul (math-mul (math-simplify-units
				(math-div expr (math-pow (car compat)
							 (cdr compat))))
			       (math-pow new-units (cdr compat)))
		     (math-simplify-units
		      (math-to-standard-units
		       (math-pow (math-div (car compat) new-units)
				 (cdr compat))
		       nil))))
	(if (setq unit-list (math-decompose-units new-units))
	    (setq new-units (nth 2 (car unit-list))))
	(if (eq (car-safe expr) '+)
	    (setq expr (math-simplify-units expr)))
	(if (math-units-in-expr-p expr t)
	    (math-convert-units-rec expr)
	  (math-apply-units (math-to-standard-units
			     (list '/ expr new-units) nil)
			    new-units unit-list pure)))))
)

(defun math-convert-units-rec (expr)
  (if (math-units-in-expr-p expr nil)
      (math-apply-units (math-to-standard-units (list '/ expr new-units) nil)
			new-units unit-list pure)
    (if (Math-primp expr)
	expr
      (cons (car expr)
	    (mapcar 'math-convert-units-rec (cdr expr)))))
)

(defun math-convert-temperature (expr old new &optional pure)
  (let* ((units (math-single-units-in-expr-p expr))
	 (uold (if old
		   (if (or (null units)
			   (equal (nth 1 old) (car units)))
		       (math-check-unit-name old)
		     (error "Inconsistent temperature units"))
		 units))
	 (unew (math-check-unit-name new)))
    (or (and (consp unew) (nth 3 unew))
	(error "Not a valid temperature unit"))
    (or (and (consp uold) (nth 3 uold))
	(error "Not a pure temperature expression"))
    (let ((v (car uold)))
      (setq expr (list '/ expr (list 'var v
				     (intern (concat "var-"
						     (symbol-name v)))))))
    (or (eq (nth 3 uold) (nth 3 unew))
	(cond ((eq (nth 3 uold) 'K)
	       (setq expr (list '- expr '(float 27315 -2)))
	       (if (eq (nth 3 unew) 'F)
		   (setq expr (list '+ (list '* expr '(frac 9 5)) 32))))
	      ((eq (nth 3 uold) 'C)
	       (if (eq (nth 3 unew) 'F)
		   (setq expr (list '+ (list '* expr '(frac 9 5)) 32))
		 (setq expr (list '+ expr '(float 27315 -2)))))
	      (t
	       (setq expr (list '* (list '- expr 32) '(frac 5 9)))
	       (if (eq (nth 3 unew) 'K)
		   (setq expr (list '+ expr '(float 27315 -2)))))))
    (if pure
	expr
      (list '* expr new)))
)



(defun math-simplify-units (a)
  (let ((math-simplifying-units t)
	(calc-matrix-mode 'scalar))
    (math-simplify a))
)
(fset 'calcFunc-usimplify (symbol-function 'math-simplify-units))

(math-defsimplify (+ -)
  (and math-simplifying-units
       (math-units-in-expr-p (nth 1 expr) nil)
       (let* ((units (math-extract-units (nth 1 expr)))
	      (ratio (math-simplify (math-to-standard-units
				     (list '/ (nth 2 expr) units) nil))))
	 (if (math-units-in-expr-p ratio nil)
	     (progn
	       (calc-record-why "*Inconsistent units" expr)
	       expr)
	   (list '* (math-add (math-remove-units (nth 1 expr))
			      (if (eq (car expr) '-) (math-neg ratio) ratio))
		 units))))
)

(math-defsimplify *
  (math-simplify-units-prod)
)

(defun math-simplify-units-prod ()
  (and math-simplifying-units
       calc-autorange-units
       (Math-realp (nth 1 expr))
       (let* ((num (math-float (nth 1 expr)))
	      (xpon (calcFunc-xpon num))
	      (unitp (cdr (cdr expr)))
	      (unit (car unitp))
	      (pow (if (eq (car expr) '*) 1 -1))
	      u)
	 (and (eq (car-safe unit) '*)
	      (setq unitp (cdr unit)
		    unit (car unitp)))
	 (and (eq (car-safe unit) '^)
	      (integerp (nth 2 unit))
	      (setq pow (* pow (nth 2 unit))
		    unitp (cdr unit)
		    unit (car unitp)))
	 (and (setq u (math-check-unit-name unit))
	      (integerp xpon)
	      (or (< xpon 0)
		  (>= xpon (if (eq (car u) 'm) 1 3)))
	      (let* ((uxpon 0)
		     (pref (if (< pow 0)
			       (reverse math-unit-prefixes)
			     math-unit-prefixes))
		     (p pref)
		     pxpon pname)
		(or (eq (car u) (nth 1 unit))
		    (setq uxpon (* pow
				   (nth 2 (nth 1 (assq
						  (aref (symbol-name
							 (nth 1 unit)) 0)
						  math-unit-prefixes))))))
		(setq xpon (+ xpon uxpon))
		(while (and p
			    (or (memq (car (car p)) '(?d ?D ?h ?H))
				(and (eq (car (car p)) ?c)
				     (not (eq (car u) 'm)))
				(< xpon (setq pxpon (* (nth 2 (nth 1 (car p)))
						       pow)))
				(progn
				  (setq pname (math-build-var-name
					       (if (eq (car (car p)) 0)
						   (car u)
						 (concat (char-to-string
							  (car (car p)))
							 (symbol-name
							  (car u))))))
				  (and (/= (car (car p)) 0)
				       (assq (nth 1 pname)
					     math-units-table)))))
		  (setq p (cdr p)))
		(and p
		     (/= pxpon uxpon)
		     (or (not (eq p pref))
			 (< xpon (+ pxpon (* (math-abs pow) 3))))
		     (progn
		       (setcar (cdr expr)
			       (let ((calc-prefer-frac nil))
				 (calcFunc-scf (nth 1 expr)
					       (- uxpon pxpon))))
		       (setcar unitp pname)
		       expr))))))
)

(math-defsimplify /
  (and math-simplifying-units
       (let ((np (cdr expr))
	     (try-cancel-units 0)
	     n nn)
	 (setq n (if (eq (car-safe (nth 2 expr)) '*)
		     (cdr (nth 2 expr))
		   (nthcdr 2 expr)))
	 (if (math-realp (car n))
	     (progn
	       (setcar (cdr expr) (math-mul (nth 1 expr)
					    (let ((calc-prefer-frac nil))
					      (math-div 1 (car n)))))
	       (setcar n 1)))
	 (while (eq (car-safe (setq n (car np))) '*)
	   (math-simplify-units-divisor (cdr n) (cdr (cdr expr)))
	   (setq np (cdr (cdr n))))
	 (math-simplify-units-divisor np (cdr (cdr expr)))
	 (if (eq try-cancel-units 0)
	     (let* ((math-simplifying-units nil)
		    (base (math-simplify (math-to-standard-units expr nil))))
	       (if (Math-numberp base)
		   (setq expr base))))
	 (if (eq (car-safe expr) '/)
	     (math-simplify-units-prod))
	 expr))
)

(defun math-simplify-units-divisor (np dp)
  (let ((n (car np))
	d dd temp)
    (while (eq (car-safe (setq d (car dp))) '*)
      (if (setq temp (math-simplify-units-quotient n (nth 1 d)))
	  (progn
	    (setcar np (setq n temp))
	    (setcar (cdr d) 1)))
      (setq dp (cdr (cdr d))))
    (if (setq temp (math-simplify-units-quotient n d))
	(progn
	  (setcar np (setq n temp))
	  (setcar dp 1))))
)

;; Simplify, e.g., "in / cm" to "2.54" in a units expression.
(defun math-simplify-units-quotient (n d)
  (let ((pow1 1)
	(pow2 1))
    (and (eq (car-safe n) '^)
	 (integerp (nth 2 n))
	 (setq pow1 (nth 2 n) n (nth 1 n)))
    (and (eq (car-safe d) '^)
	 (integerp (nth 2 d))
	 (setq pow2 (nth 2 d) d (nth 1 d)))
    (let ((un (math-check-unit-name n))
	  (ud (math-check-unit-name d)))
      (and un ud
	   (if (and (equal (nth 4 un) (nth 4 ud))
		    (eq pow1 pow2))
	       (math-to-standard-units (list '/ n d) nil)
	     (let (ud1)
	       (setq un (nth 4 un)
		     ud (nth 4 ud))
	       (while un
		 (setq ud1 ud)
		 (while ud1
		   (and (eq (car (car un)) (car (car ud1)))
			(setq try-cancel-units
			      (+ try-cancel-units
				 (- (* (cdr (car un)) pow1)
				    (* (cdr (car ud)) pow2)))))
		   (setq ud1 (cdr ud1)))
		 (setq un (cdr un)))
	       nil)))))
)

(math-defsimplify ^
  (and math-simplifying-units
       (math-realp (nth 2 expr))
       (if (memq (car-safe (nth 1 expr)) '(* /))
	   (list (car (nth 1 expr))
		 (list '^ (nth 1 (nth 1 expr)) (nth 2 expr))
		 (list '^ (nth 2 (nth 1 expr)) (nth 2 expr)))
	 (math-simplify-units-pow (nth 1 expr) (nth 2 expr))))
)

(math-defsimplify calcFunc-sqrt
  (and math-simplifying-units
       (if (memq (car-safe (nth 1 expr)) '(* /))
	   (list (car (nth 1 expr))
		 (list 'calcFunc-sqrt (nth 1 (nth 1 expr)))
		 (list 'calcFunc-sqrt (nth 2 (nth 1 expr))))
	 (math-simplify-units-pow (nth 1 expr) '(frac 1 2))))
)

(math-defsimplify (calcFunc-floor
		   calcFunc-ceil
		   calcFunc-round
		   calcFunc-rounde
		   calcFunc-roundu
		   calcFunc-trunc
		   calcFunc-float
		   calcFunc-frac
		   calcFunc-abs
		   calcFunc-clean)
  (and math-simplifying-units
       (= (length expr) 2)
       (if (math-only-units-in-expr-p (nth 1 expr))
	   (nth 1 expr)
	 (if (and (memq (car-safe (nth 1 expr)) '(* /))
		  (or (math-only-units-in-expr-p
		       (nth 1 (nth 1 expr)))
		      (math-only-units-in-expr-p
		       (nth 2 (nth 1 expr)))))
	     (list (car (nth 1 expr))
		   (cons (car expr)
			 (cons (nth 1 (nth 1 expr))
			       (cdr (cdr expr))))
		   (cons (car expr)
			 (cons (nth 2 (nth 1 expr))
			       (cdr (cdr expr)))))))))

(defun math-simplify-units-pow (a pow)
  (if (and (eq (car-safe a) '^)
	   (math-check-unit-name (nth 1 a))
	   (math-realp (nth 2 a)))
      (list '^ (nth 1 a) (math-mul pow (nth 2 a)))
    (let* ((u (math-check-unit-name a))
	   (pf (math-to-simple-fraction pow))
	   (d (and (eq (car-safe pf) 'frac) (nth 2 pf))))
      (and u d
	   (math-units-are-multiple u d)
	   (list '^ (math-to-standard-units a nil) pow))))
)


(defun math-units-are-multiple (u n)
  (setq u (nth 4 u))
  (while (and u (= (% (cdr (car u)) n) 0))
    (setq u (cdr u)))
  (null u)
)

(math-defsimplify calcFunc-sin
  (and math-simplifying-units
       (math-units-in-expr-p (nth 1 expr) nil)
       (let ((rad (math-simplify-units
		   (math-evaluate-expr
		    (math-to-standard-units (nth 1 expr) nil))))
	     (calc-angle-mode 'rad))
	 (and (eq (car-safe rad) '*)
	      (math-realp (nth 1 rad))
	      (eq (car-safe (nth 2 rad)) 'var)
	      (eq (nth 1 (nth 2 rad)) 'rad)
	      (list 'calcFunc-sin (nth 1 rad)))))
)

(math-defsimplify calcFunc-cos
  (and math-simplifying-units
       (math-units-in-expr-p (nth 1 expr) nil)
       (let ((rad (math-simplify-units
		   (math-evaluate-expr
		    (math-to-standard-units (nth 1 expr) nil))))
	     (calc-angle-mode 'rad))
	 (and (eq (car-safe rad) '*)
	      (math-realp (nth 1 rad))
	      (eq (car-safe (nth 2 rad)) 'var)
	      (eq (nth 1 (nth 2 rad)) 'rad)
	      (list 'calcFunc-cos (nth 1 rad)))))
)

(math-defsimplify calcFunc-tan
  (and math-simplifying-units
       (math-units-in-expr-p (nth 1 expr) nil)
       (let ((rad (math-simplify-units
		   (math-evaluate-expr
		    (math-to-standard-units (nth 1 expr) nil))))
	     (calc-angle-mode 'rad))
	 (and (eq (car-safe rad) '*)
	      (math-realp (nth 1 rad))
	      (eq (car-safe (nth 2 rad)) 'var)
	      (eq (nth 1 (nth 2 rad)) 'rad)
	      (list 'calcFunc-tan (nth 1 rad)))))
)


(defun math-remove-units (expr)
  (if (math-check-unit-name expr)
      1
    (if (Math-primp expr)
	expr
      (cons (car expr)
	    (mapcar 'math-remove-units (cdr expr)))))
)

(defun math-extract-units (expr)
  (if (memq (car-safe expr) '(* /))
      (cons (car expr)
	    (mapcar 'math-extract-units (cdr expr)))
    (if (math-check-unit-name expr) expr 1))
)

(defun math-build-units-table-buffer (enter-buffer)
  (if (not (and math-units-table math-units-table-buffer-valid
		(get-buffer "*Units Table*")))
      (let ((buf (get-buffer-create "*Units Table*"))
	    (uptr (math-build-units-table))
	    (calc-language (if (eq calc-language 'big) nil calc-language))
	    (calc-float-format '(float 0))
	    (calc-group-digits nil)
	    (calc-number-radix 10)
	    (calc-point-char ".")
	    (std nil)
	    u name shadowed)
	(save-excursion
	  (message "Formatting units table...")
	  (set-buffer buf)
	  (setq buffer-read-only nil)
	  (erase-buffer)
	  (insert "Calculator Units Table:\n\n")
	  (insert "Unit    Type  Definition                  Description\n\n")
	  (while uptr
	    (setq u (car uptr)
		  name (nth 2 u))
	    (if (eq (car u) 'm)
		(setq std t))
	    (setq shadowed (and std (assq (car u) math-additional-units)))
	    (if (and name
		     (> (length name) 1)
		     (eq (aref name 0) ?\*))
		(progn
		  (or (eq uptr math-units-table)
		      (insert "\n"))
		  (setq name (substring name 1))))
	    (insert " ")
	    (and shadowed (insert "("))
	    (insert (symbol-name (car u)))
	    (and shadowed (insert ")"))
	    (if (nth 3 u)
		(progn
		  (indent-to 10)
		  (insert (symbol-name (nth 3 u))))
	      (or std
		  (progn
		    (indent-to 10)
		    (insert "U"))))
	    (indent-to 14)
	    (and shadowed (insert "("))
	    (if (nth 1 u)
		(insert (math-format-value (nth 1 u) 80))
	      (insert (symbol-name (car u))))
	    (and shadowed (insert ")"))
	    (indent-to 41)
	    (insert " ")
	    (if name
		(insert name))
	    (if shadowed
		(insert " (redefined above)")
	      (or (nth 1 u)
		  (insert " (base unit)")))
	    (insert "\n")
	    (setq uptr (cdr uptr)))
	  (insert "\n\nUnit Prefix Table:\n\n")
	  (setq uptr math-unit-prefixes)
	  (while uptr
	    (setq u (car uptr))
	    (insert " " (char-to-string (car u)))
	    (if (equal (nth 1 u) (nth 1 (nth 1 uptr)))
		(insert " " (char-to-string (car (car (setq uptr (cdr uptr)))))
			"   ")
	      (insert "     "))
	    (insert "10^" (int-to-string (nth 2 (nth 1 u))))
	    (indent-to 15)
	    (insert "   " (nth 2 u) "\n")
	    (while (eq (car (car (setq uptr (cdr uptr)))) 0)))
	  (insert "\n")
	  (setq buffer-read-only t)
	  (message "Formatting units table...done"))
	(setq math-units-table-buffer-valid t)
	(let ((oldbuf (current-buffer)))
	  (set-buffer buf)
	  (goto-char (point-min))
	  (set-buffer oldbuf))
	(if enter-buffer
	    (pop-to-buffer buf)
	  (display-buffer buf)))
    (if enter-buffer
	(pop-to-buffer (get-buffer "*Units Table*"))
      (display-buffer (get-buffer "*Units Table*"))))
)