ASSEMBLY LISTING OF SEGMENT >spec>install>1110>exponential_.alm ASSEMBLED ON: 11/11/89 0944.9 mst Sat OPTIONS USED: -target l68 list symbols ASSEMBLED BY: ALM Version 8.14 March 1989 ASSEMBLER CREATED: 06/09/89 1002.3 mst Fri 1 " ****************************************** 2 " * * 3 " * Copyright, (C) Honeywell Limited, 1985 * 4 " * * 5 " ****************************************** 000000 6 name exponential_ 7 " Modification history: 8 " Written by H. Hoover, M. Mabey, and B. Wong, April 1985, 9 " based on GCOS routine '7naz'. 10 " 11 " Function: Calculates the exponential function 'e**x' to single precision 12 " accuracy in either BFP or HFP mode. 13 " 14 " Entry: through the appropriately named entry point with: 15 " EAQ = the argument x. 16 " PR2 = the address of a 4 word, even-word aligned scratch area. 17 " PR3 = the return address. 18 " 19 " Exit: EAQ = the desired exponential 20 " 21 " Uses: X0 22 " X0 = index to the table "scale" 23 24 000000 25 segref math_constants_,almost_one,hfp_almost_one,log_2_of_e,max_value 26 000000 27 equ iy,0 000002 28 equ z,2 29 001400 30 bool M0.5H,001400 " yields HFP -0.5 under 'du' modification 002040 31 bool P1.0H,002040 " yields HFP +1.0 under 'du' modification 002100 32 bool P2.0H,002100 " yields HFP +2.0 under 'du' modification 33 000043 34 segdef exponential_,hfp_exponential_ 35 36 000000 37 exponential_: 000000 0a 000202 5150 00 38 fcmp lb " if x <= -89.415987: 000001 aa 000003 6054 04 39 tpnz 3,ic 000002 aa 400000 4310 03 40 fld =0.0,du " result = 0 000003 aa 3 00000 7101 00 41 tra pr3|0 " return 000004 0a 000200 5150 00 42 fcmp ub " if x >= 88.0296926 goto overflow_error 000005 0a 000124 6050 00 43 tpl overflow_error 000006 4a 4 00010 4631 20 44 dfmp log_2_of_e " y = x*log_2_of_e 000007 aa 002400 4750 03 45 fad =1.0,du " EAQ := y + 1 46 000010 aa 016000 4350 03 47 ufa =7b25,du " AQ := 8/floor(y+1),64/fraction part of y 000011 aa 2 00000 7551 00 48 sta pr2|iy 000012 aa 776000 2750 03 49 ora =o776000,du " AQ := 8/-1,64/fraction part of y 000013 aa 016000 4110 03 50 lde =7b25,du " EAQ := ry = unnormalized y - floor(y+1) 000014 aa 400000 4750 03 51 fad =0.0,du " EAQ := ry = normalized y - floor(y+1) 52 " result = part_exp2 (ry) 53 54 " The function part_exp2 calculates 2**z, given z in the range [-1, 0) 55 " in the EAQ. 56 000015 57 part_exp2: 000015 0a 000130 4250 00 58 fcmg eps 000016 aa 000003 6050 04 59 tpl 3,ic " if abs (z) < 1.56417309e-19: 000017 aa 002400 4310 03 60 fld =1.0,du " result = 1.0 000020 aa 3 00000 7101 00 61 tra pr3|0 " return 62 000021 aa 000000 4710 00 63 frd 0 000022 aa 2 00002 4551 00 64 fst pr2|z 65 000023 0a 000174 4610 00 66 fmp p7 " result = p(z) 000024 0a 000170 4770 00 67 dfad p6 000025 aa 2 00002 4611 00 68 fmp pr2|z 000026 0a 000164 4770 00 69 dfad p5 000027 aa 2 00002 4611 00 70 fmp pr2|z 000030 0a 000160 4770 00 71 dfad p4 000031 aa 2 00002 4611 00 72 fmp pr2|z 000032 0a 000154 4770 00 73 dfad p3 000033 aa 2 00002 4611 00 74 fmp pr2|z 000034 0a 000150 4770 00 75 dfad p2 000035 aa 2 00002 4611 00 76 fmp pr2|z 000036 0a 000144 4770 00 77 dfad p1 000037 aa 2 00002 4611 00 78 fmp pr2|z 000040 0a 000140 4770 00 79 dfad p0 80 000041 aa 2 00000 4151 00 81 ade pr2|iy " addr (result) -> expon = addr (result) -> expon + iy 000042 aa 3 00000 7101 00 82 tra pr3|0 " return result in EAQ 83 84 85 000043 86 hfp_exponential_: 000043 0a 000206 5150 00 87 fcmp hfp_lb " if x <= -357.6639451: 000044 aa 000003 6054 04 88 tpnz 3,ic 000045 aa 400000 4310 03 89 fld =0.0,du " result = 0 000046 aa 3 00000 7101 00 90 tra pr3|0 " return 000047 0a 000204 5150 00 91 fcmp hfp_ub " if x >= 352.1187677 goto overflow_error 000050 0a 000124 6050 00 92 tpl overflow_error 000051 0a 000132 4250 00 93 fcmg hfp_eps " if abs (x) < 1.0842021e-19: 000052 aa 000003 6050 04 94 tpl 3,ic 000053 aa 002040 4310 03 95 fld P1.0H,du " result = 1.0 000054 aa 3 00000 7101 00 96 tra pr3|0 " return 000055 0a 000136 4630 00 97 dfmp hfp_log_16_of_e " y = x*log_16_of_e 000056 aa 002040 4750 03 98 fad P1.0H,du " EAQ := y + 1 99 000057 aa 002100 4610 03 100 fmp P2.0H,du 000060 aa 004000 4350 03 101 ufa =2b25,du " AQ := 8/floor(y+1),64/fraction part of y 000061 aa 2 00000 7551 00 102 sta pr2|iy 000062 aa 776000 2750 03 103 ora =o776000,du " AQ := 8/-1,64/fraction part of y 000063 aa 004000 4110 03 104 lde =2b25,du " EAQ := unnormalized 2*(y - floor(y+1)) 000064 aa 400000 4750 03 105 fad =0.0,du " EAQ := 2*(y - floor(y+1)) 000065 aa 002100 4610 03 106 fmp P2.0H,du " EAQ := ry = 4*(y - floor(y+1)) 107 000066 aa 000000 6200 00 108 eax0 0 " scale = 1.0 109 000067 aa 000000 0110 03 110 even 000070 111 do_while_ry_less_than_neg_one: 000070 0a 000216 5170 00 112 dfcmp =-1.0d0 " do while ry < -1.0: 000071 0a 000075 6050 00 113 tpl hfp_part_exp2 000072 aa 000001 0600 03 114 adx0 =1,du " scale = 0.5*scale 000073 aa 002040 4750 03 115 fad P1.0H,du " ry = ry + 1 000074 0a 000070 7100 00 116 tra do_while_ry_less_than_neg_one 117 118 " result = part_exp2 (ry) 119 120 " The function hfp_part_exp2 calculates 2**z, given z in the range [-1, 0) 121 " in the EAQ. 122 000075 123 hfp_part_exp2: 000075 0a 000134 4250 00 124 fcmg hfp_eps1 000076 aa 000003 6050 04 125 tpl 3,ic " if abs (z) < 1.56417309e-19: 000077 aa 002040 4310 03 126 fld P1.0H,du " result = 1.0 000100 aa 3 00000 7101 00 127 tra pr3|0 " return 128 000101 aa 000000 4710 00 129 frd 0 000102 aa 2 00002 4551 00 130 fst pr2|z 131 000103 0a 000176 4610 00 132 fmp hfp_p7 " result = p(z) 000104 0a 000172 4770 00 133 dfad hfp_p6 000105 aa 2 00002 4611 00 134 fmp pr2|z 000106 0a 000166 4770 00 135 dfad hfp_p5 000107 aa 2 00002 4611 00 136 fmp pr2|z 000110 0a 000162 4770 00 137 dfad hfp_p4 000111 aa 2 00002 4611 00 138 fmp pr2|z 000112 0a 000156 4770 00 139 dfad hfp_p3 000113 aa 2 00002 4611 00 140 fmp pr2|z 000114 0a 000152 4770 00 141 dfad hfp_p2 000115 aa 2 00002 4611 00 142 fmp pr2|z 000116 0a 000146 4770 00 143 dfad hfp_p1 000117 aa 2 00002 4611 00 144 fmp pr2|z 000120 0a 000142 4770 00 145 dfad hfp_p0 146 000121 0a 000210 4610 10 147 fmp scale,x0 " result = scale * part_exp2 (ry) 000122 aa 2 00000 4151 00 148 ade pr2|iy " addr (result) -> expon = addr (result) -> expon + iy 000123 aa 3 00000 7101 00 149 tra pr3|0 " return result in EAQ 150 151 000124 152 overflow_error: 000124 4a 4 00012 4311 20 153 fld max_value 000125 4a 4 00012 4751 20 154 fad max_value " cause an overflow 000126 4a 4 00012 4311 20 155 fld max_value 000127 aa 3 00000 7101 00 156 tra pr3|0 " return to caller 157 158 even 159 000130 aa 604561 250730 160 eps: dec 1.56417309d-19 000131 aa 645767 466564 000132 aa 742100 000427 161 hfp_eps: oct 742100000427,000000000000 " 1.08422022d-19 000133 aa 000000 000000 000134 162 hfp_eps1: 000134 aa 742134 252166 163 oct 742134252166,000000000000 " 1.56417309d-19 000135 aa 000000 000000 000136 164 hfp_log_16_of_e: 000136 aa 000270 524354 165 oct 000270524354,512701376057 " log_16_of_e = 0.36067376022224085183998d0 000137 aa 512701 376057 166 000140 aa 000777 777777 167 p0: dec 0.999999999959788989221d00 000141 aa 775171 146650 000142 aa 000777 777777 168 hfp_p0: oct 000777777777,775171146650 000143 aa 775171 146650 000144 aa 000542 710277 169 p1: dec 0.693147175773076184335d00 000145 aa 064122 746306 000146 aa 000542 710277 170 hfp_p1: oct 000542710277,064122746306 000147 aa 064122 746306 000150 aa 774753 767514 171 p2: dec 0.240226411617528907564d00 000151 aa 542060 151212 000152 aa 000172 775723 172 hfp_p2: oct 000172775723,130414032243 000153 aa 130414 032243 000154 aa 770706 536015 173 p3: dec 0.555033746338694398430d-01 000155 aa 336576 334575 000156 aa 776706 536015 174 hfp_p3: oct 776706536015,336576334575 000157 aa 336576 334575 000160 aa 764473 046222 175 p4: dec 0.961531912935043645900d-02 000161 aa 315773 407052 000162 aa 776116 611444 176 hfp_p4: oct 776116611444,463376701613 000163 aa 463376 701613 000164 aa 756533 765571 177 p5: dec 0.132743818109838796600d-02 000165 aa 150540 215300 000166 aa 774255 772674 178 hfp_p5: oct 774255772674,464260106540 000167 aa 464260 106540 000170 aa 750464 227646 179 p6: dec 0.147007243118869978000d-03 000171 aa 455135 010071 000172 aa 772464 227646 180 hfp_p6: oct 772464227646,455135010071 000173 aa 455135 010071 000174 aa 740550 540762 181 p7: dec 0.107493818486964670000d-04 000175 aa 530201 244720 000176 aa 770550 540762 182 hfp_p7: oct 770550540762,530201244720 000177 aa 530201 244720 183 000200 aa 016540 074637 184 ub: dec 8.802969265d01 " 2**127 - 2**100 = e**88.0296926 000201 aa 000053 475651 000202 aa 017232 254036 185 lb: dec -8.9415987d01 " 2**(-129) = e**-89.415987 000203 aa 007734 054130 000204 aa 006054 007464 186 hfp_ub: oct 006054007464,000000000000 " 16**127 - 16**100 = e**352.1187677 000205 aa 000000 000000 000206 aa 007723 225403 187 hfp_lb: oct 007723225403,000000000000 " 16**(-129) = e**-357.6639541 000207 aa 000000 000000 188 000210 aa 002040 000000 189 scale: oct 002040000000 " 1 000211 aa 000400 000000 190 oct 000400000000 " 0.5 000212 aa 000200 000000 191 oct 000200000000 " 0.25 000213 aa 000100 000000 192 oct 000100000000 " 0.125 000214 aa 000040 000000 193 oct 000040000000 " 0.0625 194 195 end LITERALS 000216 aa 001000 000000 000217 aa 000000 000000 NAME DEFINITIONS FOR ENTRY POINTS AND SEGDEFS 000220 5a 000003 000000 000221 5a 000040 600000 000222 aa 000000 000000 000223 55 000012 000002 000224 5a 000002 400003 000225 55 000006 000012 000226 aa 014 145 170 160 000227 aa 157 156 145 156 000230 aa 164 151 141 154 000231 aa 137 000 000 000 000232 55 000022 000003 000233 0a 000043 400000 000234 55 000015 000003 000235 aa 020 150 146 160 hfp_exponential_ 000236 aa 137 145 170 160 000237 aa 157 156 145 156 000240 aa 164 151 141 154 000241 aa 137 000 000 000 000242 55 000031 000012 000243 0a 000000 400000 000244 55 000025 000003 000245 aa 014 145 170 160 exponential_ 000246 aa 157 156 145 156 000247 aa 164 151 141 154 000250 aa 137 000 000 000 000251 55 000002 000022 000252 6a 000000 400002 000253 55 000034 000003 000254 aa 014 163 171 155 symbol_table 000255 aa 142 157 154 137 000256 aa 164 141 142 154 000257 aa 145 000 000 000 DEFINITIONS HASH TABLE 000260 aa 000000 000015 000261 aa 000000 000000 000262 aa 000000 000000 000263 aa 000000 000000 000264 aa 000000 000000 000265 aa 000000 000000 000266 5a 000022 000000 000267 5a 000031 000000 000270 aa 000000 000000 000271 aa 000000 000000 000272 5a 000012 000000 000273 aa 000000 000000 000274 aa 000000 000000 000275 aa 000000 000000 EXTERNAL NAMES 000276 aa 011 155 141 170 max_value 000277 aa 137 166 141 154 000300 aa 165 145 000 000 000301 aa 012 154 157 147 log_2_of_e 000302 aa 137 062 137 157 000303 aa 146 137 145 000 000304 aa 016 150 146 160 hfp_almost_one 000305 aa 137 141 154 155 000306 aa 157 163 164 137 000307 aa 157 156 145 000 000310 aa 012 141 154 155 almost_one 000311 aa 157 163 164 137 000312 aa 157 156 145 000 000313 aa 017 155 141 164 math_constants_ 000314 aa 150 137 143 157 000315 aa 156 163 164 141 000316 aa 156 164 163 137 NO TRAP POINTER WORDS TYPE PAIR BLOCKS 000317 aa 000004 000000 000320 55 000073 000056 000321 aa 000004 000000 000322 55 000073 000061 000323 aa 000004 000000 000324 55 000073 000064 000325 aa 000004 000000 000326 55 000073 000070 000327 aa 000001 000000 000330 aa 000000 000000 INTERNAL EXPRESSION WORDS 000331 5a 000077 000000 000332 5a 000101 000000 000333 aa 000000 000000 LINKAGE INFORMATION 000000 aa 000000 000000 000001 0a 000220 000000 000002 aa 000000 000000 000003 aa 000000 000000 000004 aa 000000 000000 000005 aa 000000 000000 000006 22 000010 000014 000007 a2 000000 000000 000010 9a 777770 0000 46 math_constants_|log_2_of_e 000011 5a 000112 0000 00 000012 9a 777766 0000 46 math_constants_|max_value 000013 5a 000111 0000 00 SYMBOL INFORMATION SYMBOL TABLE HEADER 000000 aa 000000 000001 000001 aa 163171 155142 000002 aa 164162 145145 000003 aa 000000 000010 000004 aa 000000 117244 000005 aa 361023 525721 000006 aa 000000 117547 000007 aa 253350 366537 000010 aa 141154 155040 000011 aa 040040 040040 000012 aa 000024 000040 000013 aa 000034 000040 000014 aa 000044 000100 000015 aa 000002 000002 000016 aa 000064 000000 000017 aa 000000 000146 000020 aa 000000 000103 000021 aa 000125 000121 000022 aa 000140 000103 000023 aa 000064 000000 000024 aa 101114 115040 000025 aa 126145 162163 000026 aa 151157 156040 000027 aa 070056 061064 000030 aa 040115 141162 000031 aa 143150 040061 000032 aa 071070 071040 000033 aa 040040 040040 000034 aa 110151 162156 000035 aa 145151 163145 000036 aa 156056 123171 000037 aa 163115 141151 000040 aa 156164 056141 000041 aa 040040 040040 000042 aa 040040 040040 000043 aa 040040 040040 000044 aa 055164 141162 000045 aa 147145 164040 000046 aa 154066 070040 000047 aa 040040 040040 000050 aa 040040 040040 000051 aa 040040 040040 000052 aa 040040 040040 000053 aa 040040 040040 000054 aa 040040 040040 000055 aa 040040 040040 000056 aa 040154 151163 000057 aa 164040 163171 000060 aa 155142 157154 000061 aa 163040 040040 000062 aa 040040 040040 000063 aa 040040 040040 000064 aa 000000 000001 000065 aa 000000 000001 000066 aa 000072 000043 000067 aa 175453 020000 000070 aa 000000 117547 000071 aa 176767 600000 000072 aa 076163 160145 >spec>install>1110>exponential_.alm 000073 aa 143076 151156 000074 aa 163164 141154 000075 aa 154076 061061 000076 aa 061060 076145 000077 aa 170160 157156 000100 aa 145156 164151 000101 aa 141154 137056 000102 aa 141154 155040 MULTICS ASSEMBLY CROSS REFERENCE LISTING Value Symbol Source file Line number almost_one exponential_: 25. 70 do_while_ry_less_than_neg_one exponential_: 111, 116. 130 eps exponential_: 58, 160. 0 exponential_ exponential_: 34, 37. hfp_almost_one exponential_: 25. 132 hfp_eps exponential_: 93, 161. 134 hfp_eps1 exponential_: 124, 162. 43 hfp_exponential_ exponential_: 34, 86. 206 hfp_lb exponential_: 87, 187. 136 hfp_log_16_of_e exponential_: 97, 164. 142 hfp_p0 exponential_: 145, 168. 146 hfp_p1 exponential_: 143, 170. 152 hfp_p2 exponential_: 141, 172. 156 hfp_p3 exponential_: 139, 174. 162 hfp_p4 exponential_: 137, 176. 166 hfp_p5 exponential_: 135, 178. 172 hfp_p6 exponential_: 133, 180. 176 hfp_p7 exponential_: 132, 182. 75 hfp_part_exp2 exponential_: 113, 123. 204 hfp_ub exponential_: 91, 186. 0 iy exponential_: 27, 48, 81, 102, 148. 202 lb exponential_: 38, 185. log_2_of_e exponential_: 25, 44. 1400 M0.5H exponential_: 30. math_constants_ exponential_: 25. max_value exponential_: 25, 153, 154, 155. 124 overflow_error exponential_: 43, 92, 152. 140 p0 exponential_: 79, 167. 144 p1 exponential_: 77, 169. 2040 P1.0H exponential_: 31, 95, 98, 115, 126. 150 p2 exponential_: 75, 171. 2100 P2.0H exponential_: 32, 100, 106. 154 p3 exponential_: 73, 173. 160 p4 exponential_: 71, 175. 164 p5 exponential_: 69, 177. 170 p6 exponential_: 67, 179. 174 p7 exponential_: 66, 181. 15 part_exp2 exponential_: 57. 210 scale exponential_: 147, 189. 200 ub exponential_: 42, 184. 2 z exponential_: 28, 64, 68, 70, 72, 74, 76, 78, 130, 134, 136, 138, 140, 142, 144. NO FATAL ERRORS ----------------------------------------------------------- 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