COMPILATION LISTING OF SEGMENT erf_ Compiled by: Multics PL/I Compiler, Release 28d, of September 14, 1983 Compiled at: Honeywell LCPD Phoenix, System M Compiled on: 10/03/83 1402.7 mst Mon Options: optimize map 1 /* ****************************************************** 2* * * 3* * * 4* * Copyright (c) 1972 by Massachusetts Institute of * 5* * Technology and Honeywell Information Systems, Inc. * 6* * * 7* * * 8* ****************************************************** */ 9 10 /* calls to round_ removed 07/16/73 by A. Downing */ 11 erf_: procedure (number) returns (float binary (27)); 12 13 /* compute the error (or complementary error) function of a single-precision floating-point number */ 14 declare (number, s) float binary (27), 15 (f, n, p, q, r) float binary (63), 16 exerfc_ entry (float binary (27)) returns (float binary (27)), 17 (abs, exp, round) builtin; 18 r = 0.0e0; 19 erfs: n = number; 20 f = abs (n); 21 if f < 0.5e0 then small: do; 22 q = 1.128379167095512574e0 * n; 23 if f < 5.e-5 then go to comp; 24 p = f*f; 25 q = ((((((( - 0.1322751322751322751e-4 *p + 0.1068376068376068376e-3)*p - 0.7575757575757575758e-3)*p 26 + 0.4629629629629629630e-2)*p - 0.2380952380952380952e-1)*p + 0.1e0)*p 27 - 0.3333333333333333333e0)*p + 1.e0)*q; 28 comp: if r ^= 0.0e0 then q = 1.e0 - q; 29 go to finis; 30 end small; 31 if f >= 2.5e0 then large: do; 32 s = f; 33 if f >= 9.30630096e0 then q = 0.0e0; 34 else q = exp (-f*f) * exerfc_ (s); 35 end large; else middle: do; 36 if f < 1.5e0 then lower: do; 37 p = f - 1.e0; 38 q = (((((((( 0.4854967260442840621e-5 *p - 0.2100986406780402429e-4)*p - 0.1658718964594168655e-4)*p 39 + 0.1772942579639506779e-3)*p - 0.7579366392581423493e-4)*p - 0.1086769072243678816e-2)*p 40 + 0.1670704693150730120e-2)*p + 0.4233533251576121955e-2)*p - 0.1343051928086217999e-1)*p; 41 q = ((((((( q - 0.4087549346349359129e-2)*p + 0.6131324019524038693e-1)*p - 0.6131324019524038693e-1)*p 42 - 0.1226264803904807739e0)*p + 0.3678794411714423216e0)*p - 0.3678794411714423216e0)*p 43 + 0.1394027926403309882e0) * 1.128379167095512574e0; 44 end lower; else upper: do; 45 p = f - 2.e0; 46 q = (((((((( 0.6206354808105919169e-6 *p - 0.8484562971386512658e-6)*p - 0.3501612055936534974e-5)*p 47 + 0.1439484990506010484e-4)*p - 0.4634950036778170257e-5)*p - 0.9195995379200109923e-4)*p 48 + 0.2329025685851383420e-3)*p + 0.4441623187303262417e-4)*p - 0.1410013470005726578e-2)*p; 49 q = ((((((((q + 0.2994461596094635826e-2)*p - 0.4070141975274262287e-3)*p - 0.1159990462953164752e-1)*p 50 + 0.3052606481455696716e-1)*p - 0.4273649074037975402e-1)*p + 0.3663127777746836059e-1)*p 51 - 0.1831563888873418029e-1)*p + 0.4145534690336333682e-2) * 1.128379167095512574e0; 52 end upper; end middle; 53 if r = 0.0e0 then q = 1.e0 - q; 54 if n < 0.0e0 then q = r - q; 55 finis: s = round (q, 28); 56 return (s); 57 erfc_: entry (number) returns (float binary (27)); 58 r = 2.e0; 59 go to erfs; 60 end erf_; SOURCE FILES USED IN THIS COMPILATION. LINE NUMBER DATE MODIFIED NAME PATHNAME 0 10/03/83 1005.0 erf_.pl1 >spec>on>pl128d>erf_.pl1 NAMES DECLARED IN THIS COMPILATION. IDENTIFIER OFFSET LOC STORAGE CLASS DATA TYPE ATTRIBUTES AND REFERENCES (* indicates a set context) NAMES DECLARED BY DECLARE STATEMENT. abs builtin function dcl 14 ref 20 exerfc_ 000010 constant entry external dcl 14 ref 34 exp builtin function dcl 14 ref 34 f 000102 automatic float bin(63) dcl 14 set ref 20* 21 23 24 24 31 32 33 34 34 36 37 45 n 000104 automatic float bin(63) dcl 14 set ref 19* 20 22 54 number parameter float bin(27) dcl 14 ref 11 19 57 p 000106 automatic float bin(63) dcl 14 set ref 24* 25 25 25 25 25 25 25 37* 38 38 38 38 38 38 38 38 38 41 41 41 41 41 41 45* 46 46 46 46 46 46 46 46 46 49 49 49 49 49 49 49 q 000110 automatic float bin(63) dcl 14 set ref 22* 25* 25 28* 28 33* 34* 38* 41* 41 46* 49* 49 53* 53 54* 54 55 r 000112 automatic float bin(63) dcl 14 set ref 18* 28 53 54 58* round builtin function dcl 14 ref 55 s 000100 automatic float bin(27) dcl 14 set ref 32* 34* 55* 56 NAMES DECLARED BY EXPLICIT CONTEXT. comp 000203 constant label dcl 28 ref 23 erf_ 000132 constant entry external dcl 11 erfc_ 000405 constant entry external dcl 57 erfs 000141 constant label dcl 19 ref 59 finis 000374 constant label dcl 55 ref 29 large 000214 constant label dcl 31 lower 000247 constant label dcl 36 middle 000244 constant label dcl 35 small 000152 constant label dcl 21 upper 000314 constant label dcl 44 THERE WERE NO NAMES DECLARED BY CONTEXT OR IMPLICATION. STORAGE REQUIREMENTS FOR THIS PROGRAM. Object Text Link Symbol Defs Static Start 0 0 452 464 415 462 Length 624 415 12 123 35 0 BLOCK NAME STACK SIZE TYPE WHY NONQUICK/WHO SHARES STACK FRAME erf_ 116 external procedure is an external procedure. STORAGE FOR AUTOMATIC VARIABLES. STACK FRAME LOC IDENTIFIER BLOCK NAME erf_ 000100 s erf_ 000102 f erf_ 000104 n erf_ 000106 p erf_ 000110 q erf_ 000112 r erf_ THE FOLLOWING EXTERNAL OPERATORS ARE USED BY THIS PROGRAM. call_ext_out return ext_entry round_fl dexp THE FOLLOWING EXTERNAL ENTRIES ARE CALLED BY THIS PROGRAM. exerfc_ NO EXTERNAL VARIABLES ARE USED BY THIS PROGRAM. LINE LOC LINE LOC LINE LOC LINE LOC LINE LOC LINE LOC LINE LOC 11 000126 18 000137 19 000141 20 000144 21 000147 22 000152 23 000155 24 000160 25 000163 28 000203 29 000210 31 000211 32 000214 33 000216 34 000223 35 000243 36 000244 37 000247 38 000252 41 000274 44 000313 45 000314 46 000317 49 000341 53 000362 54 000367 55 000374 56 000400 57 000403 58 000412 59 000414 ----------------------------------------------------------- Historical Background This edition of the Multics software materials and documentation is provided and donated to Massachusetts Institute of Technology by Group BULL including BULL HN Information Systems Inc. as a contribution to computer science knowledge. This donation is made also to give evidence of the common contributions of Massachusetts Institute of Technology, Bell Laboratories, General Electric, Honeywell Information Systems Inc., Honeywell BULL Inc., Groupe BULL and BULL HN Information Systems Inc. to the development of this operating system. Multics development was initiated by Massachusetts Institute of Technology Project MAC (1963-1970), renamed the MIT Laboratory for Computer Science and Artificial Intelligence in the mid 1970s, under the leadership of Professor Fernando Jose Corbato. Users consider that Multics provided the best software architecture for managing computer hardware properly and for executing programs. Many subsequent operating systems incorporated Multics principles. Multics was distributed in 1975 to 2000 by Group Bull in Europe , and in the U.S. by Bull HN Information Systems Inc., as successor in interest by change in name only to Honeywell Bull Inc. and Honeywell Information Systems Inc. . ----------------------------------------------------------- Permission to use, copy, modify, and distribute these programs and their documentation for any purpose and without fee is hereby granted,provided that the below copyright notice and historical background appear in all copies and that both the copyright notice and historical background and this permission notice appear in supporting documentation, and that the names of MIT, HIS, BULL or BULL HN not be used in advertising or publicity pertaining to distribution of the programs without specific prior written permission. Copyright 1972 by Massachusetts Institute of Technology and Honeywell Information Systems Inc. Copyright 2006 by BULL HN Information Systems Inc. Copyright 2006 by Bull SAS All Rights Reserved