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Remark on remarks on algorithm 48: of a complex number

Remark on remarks on algorithm 48: of a complex number ADDITIONAL BIBLIOGRAPHY Date Title (or Subject) Proposed American Standard for Bit Sequencing of ASCII in Serial-byBit Data Transmission Letter Ballot on Publication of Proposed Standard for Bit Order Sequencing of ASCII Statement of Position (UNIVAC) Analysis of the Report of the Select Committee on ASCII Bit Order of Data Transmission ASCII Letter to E. H. Clamons re. Clamon's memorandum to X3, March 19, 1964 Reply to ASA letter of April 2, 1964 Letter to C. A. Phillips re. Letter Ballot on Publication of Proposed Standard for Bit Order Sequencing of ASCII Prepared By Date 4/10/64 Title (or Subject) Letter to C. A. Phillips re. Letter Ballot on Publication of Proposed Standard for Bit Order Sequencing of ASCII Letter to C. A. Phillips re. Letter Ballot on Publication of Proposed Standard for Bit Order Sequencing of ASCII Explanation for Negative Vote on Acceptability for Publication of Proposed Standard for Bit Sequencing of ASCII Results of Ballot on Acceptability for Publication of Proposed Standard on Bit Sequencing of ASCII and Approval of Publication Period Prepared By 3/9/64 3/10/64 X3.3/4 4/10/64 C. A. Phillips E. H. Clamons IF W. Claussen L. ¢ C. White S. N. Alexander V. G. Grey E. H. Clamons (undated) R. W. Ferguson 3/19/64 3/20/64 L. Wolff 3/26/64 4/2/64 4/9/64 (undated) L. W. Claussen 4/14/64 C A. Phillips G. L. Bowlby Editor's Note Publication of the following proposed American Standards, developed by a Subcommittee of ASA Sectional Committee X3, has been authorized by the American Standards Association for the purpose of obtaining comment, criticism and general public reaction, with the understanding that such proposed American Standards have not been finally accepted by ASA as standards and, therefore, are subject to change, modificatwn or withdrawal in whole or in part. Comments should be addressed to the Secretary, Business Equipment Manufacturers Association, 235 East ~2 Street, New York 17, N.Y.--E.L. ALGORITHMS--Cont'd from page 482 standard ElliotL ALGOL compiler. The expression 2 X Gauss (x) - 1 was evaluated for x = 0(.01)6 and the answers checked with those given in Tables of Probability Functions, vol. II, U.S. National Bureau of Standards, Washington, D.C., 1942, where they are given to 15 decimal places ¢ There was a maximum error of 1 in the 8th decimal place. PROPOSED AMERICAN STANDARDS REMARK ON REMARKS ON ALGORITHM 48 [B3] LOGARITHM OF A COMPLEX NUMBER [John R. H e r n d o n , Comm. A C M ~ ( A p r . 1961), 179; 5 ( J u n . 62), 347; 5 (Jul. 62), 391] DAVID S. COLLENS ( R e c d . 24 J a n . 1964 a n d 1 J u n . 1964) Computer L a b o r a t o r y , T h e U n i v e r s i t y , L i v e r p o o l 3, England This procedure was designed to compute logo(a+bi), namely c+di, and although some very necessary precautions about its use have already been stated, some points seem to have escaped notice ¢ In particular, A. P. Relph [Comm. ACM, June 1962, 347] remarked that if a = 0, then c becomes '--infinity', but this is only the case if b = 0 also. Margaret L. Johnson and Ward Sangren [Comm. ACM, July 1962, 391] conceded that a = b = 0 was a special case, but wrongly gave zero as the result. The only reasonable way of dealing with this case is to exit to some nonlocal label and to let the user decide whether to terminate his program or to assign particular values to c and d. The obvious values to use here are, for c, a negative number, larger than the largest which would be given by the procedure, and possibly zero for d. (In an implementation where 2-'59 is the smallest representable nonzero number, the largest negative value of c possible is -89.416.) Finally, in the Johnson-Sangren version of the procedure, the last conditional statement should read ira = 0A d := the omission typographical b < 0then begin c := Interchangeable Perforated Tape Variable Block Formats for Positioning and Straight Cut (RS-273) and Contouring and Contouring/Positioning (RS-274) Numerically Controlled Machine Tools T h e s e s t a n d a r d s a r e i n t e n d e d t o s e r v e a s g u i d e s in t h e c o o r d i n a t i o n of s y s t e m design, t o m i n i m i z e t h e v a r i e t y of p r o g r a m m a n u s c r i p t s r e q u i r e d a n d t h e n u m b e r of w o r d a n d b l o c k f o r m a t s y s t e m s used, t o p r o m o t e u n i f o r m i t y of p r o g r a m m i n g t e c h n i q u e s , a n d t o f o s t e r i n t e r c h a n g e a b i l i t y of i n p u t t a p e s b e t w e e n n u m e r i c a l l y c o n t r o l l e d m a c h i n e t o o l s of t h e s a m e c l a s s i f i c a t i o n b y t y p e , p r o c e s s f u n c t i o n , size a n d a c c u r a c y . I t is i n t e n d e d t h a t s i m p l e n u m e r i c a l l y c o n t r o l l e d m a c h i n e t o o l s be p r o g r a m m e d u s i n g a s i m p l e f o r m a t w h i c h is s y s t e m a t i c a l l y e x t e n s i b l e f o r m o r e c o m p l e x m a c h i n e tools. T h e s e s t a n d a r d s a p p l y w h e r e v e r a v a r i a b l e b l o c k f o r m a t is u s e d o n perforated tape to control positioning and straight cut and contouring or c o n t o u r i n g / p o s i t i o n i n g n u m e r i c a l l y c o n t r o l l e d m a c h i n e tools. T h e s e f o r m a t s will u s u a l l y b e u s e d w i t h t a p e r e a d r o w - b y - r o w . P e r f o r a t e d t a p e w i t h v a r i a b l e b l o c k f o r m a t as d e s c r i b e d s h a l l be u s a b l e interchangeably among numerically controlled machine tools which conf o r m t o t h e s a m e f o r m a t classification as d e s c r i b e d in t h e s t a n d a r d s . ( N o t e : T h e d e g r e e of i n t e r c h a n g e a b i l i t y will d e p e n d u p o n t h e c o n f o r m i t y of t h e m a c h i n e s w i t h r e s p e c t t o f u n c t i o n , c a p a c i t y , r a n g e , h o r s e p o w e r , g e o m e t r i c r e l a t i o n s h i p of axes, p r e p a r a t o r y , m i s c e l l a n e o u s , a n d t o o l i n g f u n c t i o n s , a n d use of a b s o l u t e or i n c r e m e n t a l d i m e n s i o n s . ) T h e i n t e r c h a n g e a b l e t a p e d e s c r i b e d in t h e s e s t a n d a r d s is a c o m b i n a t i o n of w o r d a d d r e s s a n d t a b s e q u e n t i a l f o r m a t , a n d i n c l u d e s b o t h t a b a n d address characters. These standards cover interchangeable perforated tape variable block f o r m a t o n l y , a n d a r e n o t i n t e n d e d t o s p e c i f y m a c h i n e t o o l design. I n c e r t a i n c a s e s p r o v i s i o n s m u s t be i n c l u d e d b y t h e c o n t r o l s y s t e m b u i l d e r a n d m a c h i n e t o o l b u i l d e r , in o r d e r t o g a i n full u s e of i n t e r c h a n g e a b l e perforated tape. [Full t e x t s of t h e s e t w o s t a n d a r d s a r e a v a i l a b l e f r o m E l e c t r o n i c I n d u s t r i e s A s s o c i a t i o n , E n g i n e e r i n g D e p a r t m e n t , 11 W e s t 42 S t r e e t , N e w Y o r k 36, N. Y.: 1~S-273, $1.10; R S - 2 7 4 , $1.30.] In(abs(b)); end; being probably --1.570963; go to RETURN sign in the of the minus in origin. original V o l u m e 7 / N u m b e r 8 / A u g u s t , 1964 Communications of the ACM http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Communications of the ACM Association for Computing Machinery

Remark on remarks on algorithm 48: of a complex number

Communications of the ACM , Volume 7 (8) – Aug 1, 1964

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Publisher
Association for Computing Machinery
Copyright
Copyright © 1964 by ACM Inc.
ISSN
0001-0782
DOI
10.1145/355586.364810
Publisher site
See Article on Publisher Site

Abstract

ADDITIONAL BIBLIOGRAPHY Date Title (or Subject) Proposed American Standard for Bit Sequencing of ASCII in Serial-byBit Data Transmission Letter Ballot on Publication of Proposed Standard for Bit Order Sequencing of ASCII Statement of Position (UNIVAC) Analysis of the Report of the Select Committee on ASCII Bit Order of Data Transmission ASCII Letter to E. H. Clamons re. Clamon's memorandum to X3, March 19, 1964 Reply to ASA letter of April 2, 1964 Letter to C. A. Phillips re. Letter Ballot on Publication of Proposed Standard for Bit Order Sequencing of ASCII Prepared By Date 4/10/64 Title (or Subject) Letter to C. A. Phillips re. Letter Ballot on Publication of Proposed Standard for Bit Order Sequencing of ASCII Letter to C. A. Phillips re. Letter Ballot on Publication of Proposed Standard for Bit Order Sequencing of ASCII Explanation for Negative Vote on Acceptability for Publication of Proposed Standard for Bit Sequencing of ASCII Results of Ballot on Acceptability for Publication of Proposed Standard on Bit Sequencing of ASCII and Approval of Publication Period Prepared By 3/9/64 3/10/64 X3.3/4 4/10/64 C. A. Phillips E. H. Clamons IF W. Claussen L. ¢ C. White S. N. Alexander V. G. Grey E. H. Clamons (undated) R. W. Ferguson 3/19/64 3/20/64 L. Wolff 3/26/64 4/2/64 4/9/64 (undated) L. W. Claussen 4/14/64 C A. Phillips G. L. Bowlby Editor's Note Publication of the following proposed American Standards, developed by a Subcommittee of ASA Sectional Committee X3, has been authorized by the American Standards Association for the purpose of obtaining comment, criticism and general public reaction, with the understanding that such proposed American Standards have not been finally accepted by ASA as standards and, therefore, are subject to change, modificatwn or withdrawal in whole or in part. Comments should be addressed to the Secretary, Business Equipment Manufacturers Association, 235 East ~2 Street, New York 17, N.Y.--E.L. ALGORITHMS--Cont'd from page 482 standard ElliotL ALGOL compiler. The expression 2 X Gauss (x) - 1 was evaluated for x = 0(.01)6 and the answers checked with those given in Tables of Probability Functions, vol. II, U.S. National Bureau of Standards, Washington, D.C., 1942, where they are given to 15 decimal places ¢ There was a maximum error of 1 in the 8th decimal place. PROPOSED AMERICAN STANDARDS REMARK ON REMARKS ON ALGORITHM 48 [B3] LOGARITHM OF A COMPLEX NUMBER [John R. H e r n d o n , Comm. A C M ~ ( A p r . 1961), 179; 5 ( J u n . 62), 347; 5 (Jul. 62), 391] DAVID S. COLLENS ( R e c d . 24 J a n . 1964 a n d 1 J u n . 1964) Computer L a b o r a t o r y , T h e U n i v e r s i t y , L i v e r p o o l 3, England This procedure was designed to compute logo(a+bi), namely c+di, and although some very necessary precautions about its use have already been stated, some points seem to have escaped notice ¢ In particular, A. P. Relph [Comm. ACM, June 1962, 347] remarked that if a = 0, then c becomes '--infinity', but this is only the case if b = 0 also. Margaret L. Johnson and Ward Sangren [Comm. ACM, July 1962, 391] conceded that a = b = 0 was a special case, but wrongly gave zero as the result. The only reasonable way of dealing with this case is to exit to some nonlocal label and to let the user decide whether to terminate his program or to assign particular values to c and d. The obvious values to use here are, for c, a negative number, larger than the largest which would be given by the procedure, and possibly zero for d. (In an implementation where 2-'59 is the smallest representable nonzero number, the largest negative value of c possible is -89.416.) Finally, in the Johnson-Sangren version of the procedure, the last conditional statement should read ira = 0A d := the omission typographical b < 0then begin c := Interchangeable Perforated Tape Variable Block Formats for Positioning and Straight Cut (RS-273) and Contouring and Contouring/Positioning (RS-274) Numerically Controlled Machine Tools T h e s e s t a n d a r d s a r e i n t e n d e d t o s e r v e a s g u i d e s in t h e c o o r d i n a t i o n of s y s t e m design, t o m i n i m i z e t h e v a r i e t y of p r o g r a m m a n u s c r i p t s r e q u i r e d a n d t h e n u m b e r of w o r d a n d b l o c k f o r m a t s y s t e m s used, t o p r o m o t e u n i f o r m i t y of p r o g r a m m i n g t e c h n i q u e s , a n d t o f o s t e r i n t e r c h a n g e a b i l i t y of i n p u t t a p e s b e t w e e n n u m e r i c a l l y c o n t r o l l e d m a c h i n e t o o l s of t h e s a m e c l a s s i f i c a t i o n b y t y p e , p r o c e s s f u n c t i o n , size a n d a c c u r a c y . I t is i n t e n d e d t h a t s i m p l e n u m e r i c a l l y c o n t r o l l e d m a c h i n e t o o l s be p r o g r a m m e d u s i n g a s i m p l e f o r m a t w h i c h is s y s t e m a t i c a l l y e x t e n s i b l e f o r m o r e c o m p l e x m a c h i n e tools. T h e s e s t a n d a r d s a p p l y w h e r e v e r a v a r i a b l e b l o c k f o r m a t is u s e d o n perforated tape to control positioning and straight cut and contouring or c o n t o u r i n g / p o s i t i o n i n g n u m e r i c a l l y c o n t r o l l e d m a c h i n e tools. T h e s e f o r m a t s will u s u a l l y b e u s e d w i t h t a p e r e a d r o w - b y - r o w . P e r f o r a t e d t a p e w i t h v a r i a b l e b l o c k f o r m a t as d e s c r i b e d s h a l l be u s a b l e interchangeably among numerically controlled machine tools which conf o r m t o t h e s a m e f o r m a t classification as d e s c r i b e d in t h e s t a n d a r d s . ( N o t e : T h e d e g r e e of i n t e r c h a n g e a b i l i t y will d e p e n d u p o n t h e c o n f o r m i t y of t h e m a c h i n e s w i t h r e s p e c t t o f u n c t i o n , c a p a c i t y , r a n g e , h o r s e p o w e r , g e o m e t r i c r e l a t i o n s h i p of axes, p r e p a r a t o r y , m i s c e l l a n e o u s , a n d t o o l i n g f u n c t i o n s , a n d use of a b s o l u t e or i n c r e m e n t a l d i m e n s i o n s . ) T h e i n t e r c h a n g e a b l e t a p e d e s c r i b e d in t h e s e s t a n d a r d s is a c o m b i n a t i o n of w o r d a d d r e s s a n d t a b s e q u e n t i a l f o r m a t , a n d i n c l u d e s b o t h t a b a n d address characters. These standards cover interchangeable perforated tape variable block f o r m a t o n l y , a n d a r e n o t i n t e n d e d t o s p e c i f y m a c h i n e t o o l design. I n c e r t a i n c a s e s p r o v i s i o n s m u s t be i n c l u d e d b y t h e c o n t r o l s y s t e m b u i l d e r a n d m a c h i n e t o o l b u i l d e r , in o r d e r t o g a i n full u s e of i n t e r c h a n g e a b l e perforated tape. [Full t e x t s of t h e s e t w o s t a n d a r d s a r e a v a i l a b l e f r o m E l e c t r o n i c I n d u s t r i e s A s s o c i a t i o n , E n g i n e e r i n g D e p a r t m e n t , 11 W e s t 42 S t r e e t , N e w Y o r k 36, N. Y.: 1~S-273, $1.10; R S - 2 7 4 , $1.30.] In(abs(b)); end; being probably --1.570963; go to RETURN sign in the of the minus in origin. original V o l u m e 7 / N u m b e r 8 / A u g u s t , 1964 Communications of the ACM

Journal

Communications of the ACMAssociation for Computing Machinery

Published: Aug 1, 1964

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