ASSEMBLY LISTING OF SEGMENT >spec>install>1110>double_principal_angle_.alm ASSEMBLED ON: 11/11/89 0945.5 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 Bull Inc., 1987 * 4 " * * 5 " * Copyright, (C) Honeywell Information Systems Inc., 1985 * 6 " * * 7 " *********************************************************** 000000 8 name double_principal_angle_ 9 " Modification history: 10 " Written by H. Hoover, M. Mabey and B. Wong, April 1985. 11 " 12 " Function: Scale an angle into the range -pi/4 to pi/4. 13 " 14 " Entry: through the appropriately named entry point with: 15 " EAQ = input angle to be scaled. 16 " X0 = the return address. 17 " X2 = a two word offset for HFP constants - this register is used 18 " by all of the floting point math_routines for the same thing. 19 " PR2 = points to an even word aligned, 14 word long, scratch area. 20 " 21 " Exit: EAQ = the scaled angle. 22 " X1 = mod ((input EAQ)/HALF_PI + 0.5), 4) 23 " 24 " Uses: X1 25 " X1 = used to return mod ((input EAQ)/HALF_PI + 0.5), 4) 26 000043 27 segdef double_principal_degrees_,double_principal_radians_ 28 000000 29 segref math_constants_,pi,half_pi,almost_one 30 002100 31 bool P2.0H,002100 " yields HFP +2.0 under 'du' modification 004132 32 bool P45.0H,004132 " yields HFP +45.0 under 'du' modification 33 000000 34 equ angle,0 000000 35 equ temp,angle 000002 36 equ n1,2 000003 37 equ n2,3 000004 38 equ t1,4 000006 39 equ t2,6 000010 40 equ t3,8 000012 41 equ t4,10 000014 42 equ t5,12 000002 43 equ HFP,2 44 45 000000 46 double_principal_degrees_: 000000 aa 000002 1020 03 47 cmpx2 HFP,du 000001 0a 000022 6000 00 48 tze hfp_principal_degrees 49 000002 50 bfp_principal_degrees: 000002 aa 000000 4730 00 51 dfrd 0 000003 0a 000256 4270 00 52 dfcmg two_pwr_54 " is the EAQ too large 000004 0a 000230 6054 00 53 tpnz angle_too_big " Yup. 54 000005 aa 2 00000 4571 00 55 dfst pr2|angle 000006 0a 000240 5670 00 56 dfdv ninety " EAQ = EAQ/90 000007 aa 000400 4750 03 57 fad =0.5,du " EAQ = EAQ/90 + 0.5 000010 4a 4 00010 4371 20 58 dufa almost_one 000011 4a 4 00010 5371 20 59 dufs almost_one 000012 aa 216000 4350 03 60 ufa =71b25,du " AQ = EAQ/90 + 0.5 in integer form 61 000013 aa 000000 6210 06 62 eax1 0,ql 000014 aa 000003 3610 03 63 anx1 =3,du " X1 = mod(AQ,4) 64 000015 aa 400000 4750 03 65 fad =0.0,du " EAQ = floor(EAQ/90 + 0.5) in floating point form 000016 aa 016550 4610 03 66 fmp =90.0,du " EAQ = floor(EAQ/90 + 0.5)*90 000017 aa 000000 5130 00 67 fneg 0 " EAQ = -floor(EAQ/90 + 0.5)*90 000020 aa 2 00000 4771 00 68 dfad pr2|angle " EAQ = angle-floor(EAQ/90 + 0.5)*180 000021 aa 000000 7100 10 69 tra 0,x0 " return to caller 70 000022 71 hfp_principal_degrees: 000022 aa 000000 4730 00 72 dfrd 0 000023 0a 000254 4270 00 73 dfcmg hfp_two_pwr_48 " is the EAQ too large 000024 0a 000230 6054 00 74 tpnz angle_too_big " Yup. 75 000025 aa 2 00000 4571 00 76 dfst pr2|angle 000026 0a 000240 5670 12 77 dfdv ninety,x2 " EAQ = EAQ/90 000027 aa 000400 4750 03 78 fad =0.5,du " EAQ = EAQ/90 + 0.5 000030 4a 4 00010 4371 20 79 dufa almost_one 000031 4a 4 00010 5371 20 80 dufs almost_one 000032 aa 002100 4210 03 81 ufm P2.0H,du 000033 aa 044000 4350 03 82 ufa =18b25,du " AQ = EAQ/90 + 0.5 83 000034 aa 000000 6210 06 84 eax1 0,ql 000035 aa 000003 3610 03 85 anx1 =3,du " X1 = mod(AQ,4) 86 000036 aa 400000 4750 03 87 fad =0.0,du " EAQ = floor(EAQ/90 + 0.5)*2 000037 aa 004132 4610 03 88 fmp P45.0H,du " EAQ = floor(EAQ/90 + 0.5)*90 in floating point form 000040 aa 000000 5130 00 89 fneg 0 " EAQ = -floor(EAQ/90 + 0.5)*90 000041 aa 2 00000 4771 00 90 dfad pr2|angle " EAQ = angle-floor(EAQ/90 + 0.5)*90 000042 aa 000000 7100 10 91 tra 0,x0 " return to caller 92 93 000043 94 double_principal_radians_: 000043 aa 000002 1020 03 95 cmpx2 HFP,du 000044 0a 000063 6000 00 96 tze hfp_principal_radians 97 000045 98 bfp_principal_radians: 000045 aa 000000 4730 00 99 dfrd 0 000046 aa 2 00000 4571 00 100 dfst pr2|angle 000047 0a 000252 4270 00 101 dfcmg two_pwr_27 " is the EAQ too large 000050 0a 000145 6054 00 102 tpnz bfp_big_angle " Yup. 103 000051 0a 000244 4630 00 104 dfmp one_over_half_pi " EAQ = EAQ/half_pi 000052 aa 000400 4750 03 105 fad =0.5,du " EAQ = EAQ/half_pi + 0.5 000053 4a 4 00010 4371 20 106 dufa almost_one 000054 4a 4 00010 5371 20 107 dufs almost_one 000055 aa 216000 4350 03 108 ufa =71b25,du " AQ = EAQ/half_pi + 0.5 in integer form 109 000056 aa 000000 6210 06 110 eax1 0,ql 000057 aa 000003 3610 03 111 anx1 =3,du " X1 = mod(AQ,4) 112 000060 aa 400000 4750 03 113 fad =0.0,du " EAQ = floor(EAQ/half_pi + 0.5) in floating point form 000061 aa 2 00002 4551 00 114 fst pr2|n1 " n1 = EAQ 000062 0a 000102 7100 00 115 tra small_angle_join " goto common code for HFP and BFP 116 117 000063 118 hfp_principal_radians: 000063 aa 000000 4730 00 119 dfrd 0 000064 aa 2 00000 4571 00 120 dfst pr2|angle 000065 0a 000250 4270 00 121 dfcmg hfp_two_pwr_24 " is the EAQ too large 000066 0a 000127 6054 00 122 tpnz hfp_big_angle " Yup. 123 000067 0a 000244 4630 12 124 dfmp one_over_half_pi,x2 " EAQ = EAQ/half_pi 000070 aa 000400 4750 03 125 fad =0.5,du " EAQ = EAQ/half_pi + 0.5 000071 4a 4 00010 4371 20 126 dufa almost_one 000072 4a 4 00010 5371 20 127 dufs almost_one 000073 aa 002100 4210 03 128 ufm P2.0H,du 000074 aa 044000 4350 03 129 ufa =18b25,du " AQ = EAQ/half_pi + 0.5 in integer form 130 000075 aa 000000 6210 06 131 eax1 0,ql 000076 aa 000003 3610 03 132 anx1 =3,du " X1 = mod(AQ,4) 133 000077 aa 400000 4750 03 134 fad =0.0,du " EAQ = floor(EAQ/half_pi + 0.5)*2 000100 aa 000400 4610 03 135 fmp =0.5,du " EAQ = floor(EAQ/half_pi + 0.5) in floating point form 000101 aa 2 00002 4551 00 136 fst pr2|n1 " n1 = EAQ 137 000102 138 small_angle_join: 000102 0a 000262 4610 12 139 fmp half_pi1,x2 000103 aa 2 00004 4571 00 140 dfst pr2|t1 " t1 = n1*half_pi1 141 000104 aa 2 00002 4311 00 142 fld pr2|n1 000105 0a 000266 4610 12 143 fmp half_pi2,x2 000106 aa 2 00006 4571 00 144 dfst pr2|t2 " t2 = n1*half_pi2 145 000107 aa 2 00002 4311 00 146 fld pr2|n1 000110 0a 000272 4610 12 147 fmp half_pi3,x2 000111 aa 2 00010 4571 00 148 dfst pr2|t3 " t3 = n1*half_pi3 149 000112 aa 2 00002 4311 00 150 fld pr2|n1 000113 0a 000276 4610 12 151 fmp half_pi4,x2 000114 aa 2 00012 4571 00 152 dfst pr2|t4 " t4 = n1*half_pi4 153 000115 aa 2 00002 4311 00 154 fld pr2|n1 000116 0a 000302 4630 12 155 dfmp half_pi5,x2 000117 aa 2 00014 4571 00 156 dfst pr2|t5 " t5 = n1*half_pi5 157 000120 aa 2 00000 4331 00 158 dfld pr2|angle " answer = angle - t1 - t2 - t3 - t4 - t5 000121 aa 2 00004 5771 00 159 dfsb pr2|t1 000122 aa 2 00006 5771 00 160 dfsb pr2|t2 000123 aa 2 00010 5771 00 161 dfsb pr2|t3 000124 aa 2 00012 5771 00 162 dfsb pr2|t4 000125 aa 2 00014 5771 00 163 dfsb pr2|t5 000126 aa 000000 7100 10 164 tra 0,x0 165 000127 166 hfp_big_angle: 000127 0a 000254 4270 00 167 dfcmg hfp_two_pwr_48 " is the EAQ too large? 000130 0a 000230 6054 00 168 tpnz angle_too_big " Yup. 169 000131 0a 000244 4630 12 170 dfmp one_over_half_pi,x2 " EAQ = EAQ/half_pi 000132 aa 000400 4750 03 171 fad =0.5,du " EAQ = EAQ/half_pi + 0.5 000133 4a 4 00010 4371 20 172 dufa almost_one 000134 4a 4 00010 5371 20 173 dufs almost_one 000135 aa 002100 4210 03 174 ufm P2.0H,du 000136 aa 044000 4350 03 175 ufa =18b25,du " AQ = EAQ/half_pi + 0.5 in integer form 176 000137 aa 000000 6210 06 177 eax1 0,ql 000140 aa 000003 3610 03 178 anx1 =3,du " X1 = mod(AQ,4) 179 000141 aa 400000 4750 03 180 fad =0.0,du " EAQ = floor(EAQ/half_pi + 0.5)*2 000142 aa 000400 4610 03 181 fmp =0.5,du " EAQ = floor(EAQ/half_pi + 0.5) in floating point form 000143 aa 2 00002 4551 00 182 fst pr2|n1 " n1 = EAQ 000144 0a 000160 7100 00 183 tra big_angle_join 184 000145 185 bfp_big_angle: 000145 0a 000256 4270 00 186 dfcmg two_pwr_54 " is the EAQ too large? 000146 0a 000230 6054 00 187 tpnz angle_too_big " Yup. 188 000147 0a 000244 4630 00 189 dfmp one_over_half_pi " EAQ = EAQ/half_pi 000150 aa 000400 4750 03 190 fad =0.5,du " EAQ = EAQ/half_pi + 0.5 000151 4a 4 00010 4371 20 191 dufa almost_one 000152 4a 4 00010 5371 20 192 dufs almost_one 000153 aa 216000 4350 03 193 ufa =71b25,du " AQ = EAQ/half_pi + 0.5 in integer form 194 000154 aa 000000 6210 06 195 eax1 0,ql 000155 aa 000003 3610 03 196 anx1 =3,du " X1 = mod(AQ,4) 197 000156 aa 400000 4750 03 198 fad =0.0,du " EAQ = floor(EAQ/half_pi + 0.5) in floating point form 000157 aa 2 00002 4551 00 199 fst pr2|n1 " n1 = EAQ 200 000160 201 big_angle_join: 000160 aa 2 00002 5751 00 202 fsb pr2|n1 000161 aa 2 00003 4551 00 203 fst pr2|n2 " n2 = n - n1 204 000162 aa 2 00002 4311 00 205 fld pr2|n1 000163 0a 000262 4610 12 206 fmp half_pi1,x2 000164 aa 2 00004 4571 00 207 dfst pr2|t1 " t1 = n1*half_pi1 208 000165 aa 2 00002 4311 00 209 fld pr2|n1 " calculate n1*half_pi2 + n2*half_pi1 000166 0a 000266 4610 12 210 fmp half_pi2,x2 000167 aa 2 00006 4571 00 211 dfst pr2|t2 000170 aa 2 00003 4311 00 212 fld pr2|n2 000171 0a 000262 4610 12 213 fmp half_pi1,x2 000172 aa 2 00006 4771 00 214 dfad pr2|t2 000173 aa 2 00006 4571 00 215 dfst pr2|t2 " t2 = (n1*half_pi2 + n2*half_pi1) 216 000174 aa 2 00002 4311 00 217 fld pr2|n1 " calculate n1*half_pi3 + n2*half_pi2 000175 0a 000272 4610 12 218 fmp half_pi3,x2 000176 aa 2 00010 4571 00 219 dfst pr2|t3 000177 aa 2 00003 4311 00 220 fld pr2|n2 000200 0a 000266 4610 12 221 fmp half_pi2,x2 000201 aa 2 00010 4771 00 222 dfad pr2|t3 000202 aa 2 00010 4571 00 223 dfst pr2|t3 " t3 = (n1*half_pi3 + n2*half_pi2) 224 000203 aa 2 00002 4311 00 225 fld pr2|n1 " calculate n1*half_pi4 + n2*half_pi3 000204 0a 000276 4610 12 226 fmp half_pi4,x2 000205 aa 2 00012 4571 00 227 dfst pr2|t4 000206 aa 2 00003 4311 00 228 fld pr2|n2 000207 0a 000272 4610 12 229 fmp half_pi3,x2 000210 aa 2 00012 4771 00 230 dfad pr2|t4 000211 aa 2 00012 4571 00 231 dfst pr2|t4 " t4 = (n1*half_pi4 + n2*half_pi3) 232 000212 aa 2 00002 4311 00 233 fld pr2|n1 " calculate n1*half_pi5 + n2*half_pi4 000213 0a 000302 4630 12 234 dfmp half_pi5,x2 000214 aa 2 00014 4571 00 235 dfst pr2|t5 000215 aa 2 00003 4311 00 236 fld pr2|n2 000216 0a 000276 4610 12 237 fmp half_pi4,x2 000217 aa 2 00014 4771 00 238 dfad pr2|t5 000220 aa 2 00014 4571 00 239 dfst pr2|t5 " t5 = (n1*half_pi5 + n2*half_pi4) 240 000221 aa 2 00000 4331 00 241 dfld pr2|angle " answer = angle - t1 - t2 - t3 - t4 - t5 000222 aa 2 00004 5771 00 242 dfsb pr2|t1 000223 aa 2 00006 5771 00 243 dfsb pr2|t2 000224 aa 2 00010 5771 00 244 dfsb pr2|t3 000225 aa 2 00012 5771 00 245 dfsb pr2|t4 000226 aa 2 00014 5771 00 246 dfsb pr2|t5 247 000227 aa 000000 7100 10 248 tra 0,x0 " return to caller. The indicators are set. 249 000230 250 angle_too_big: 000230 0a 000306 2360 12 251 ldq code,x2 " load the error code 000231 aa 2 00000 7401 00 252 stx0 pr2|temp " save X0 000232 4a 4 00012 7001 20 253 tsx0 |[call_math_error_] 000233 aa 2 00000 2201 00 254 ldx0 pr2|temp " restore X0 255 000234 aa 000000 6210 00 256 eax1 0 " X1 = 0 000235 aa 400000 4310 03 257 fld =0.0,du " EAQ = 0, set indicators 000236 aa 000000 7100 10 258 tra 0,x0 " return to caller 259 260 261 " Constants: 262 000237 aa 000000 0110 03 263 even 000240 aa 016550 000000 264 ninety: dec 90.0d0 000241 aa 000000 000000 000242 aa 004264 000000 265 oct 004264000000,000000000000 000243 aa 000000 000000 000244 266 one_over_half_pi: 000244 aa 000505 746033 267 dec 6.3661977236758134307553d-1 000245 aa 344710 405225 000246 aa 000505 746033 268 oct 000505746033,344710405225 000247 aa 344710 405225 000250 269 hfp_two_pwr_24: 000250 aa 016040 000000 270 oct 016040000000,000000000000 000251 aa 000000 000000 000252 271 two_pwr_27: 000252 aa 070400 000000 272 oct 070400000000,000000000000 000253 aa 000000 000000 000254 273 hfp_two_pwr_48: 000254 aa 032040 000000 274 oct 032040000000,000000000000 000255 aa 000000 000000 000256 275 two_pwr_54: 000256 aa 156400 000000 276 oct 156400000000,000000000000 000257 aa 000000 000000 000260 aa 034200 000000 277 oct 034200000000,000000000000 000261 aa 000000 000000 000262 aa 002622 077325 278 half_pi1: oct 002622077325,000000000000 000263 aa 000000 000000 000264 aa 002062 207732 279 oct 002062207732,000000000000 000265 aa 000000 000000 000266 aa 706420 550604 280 half_pi2: oct 706420550604,000000000000 000267 aa 000000 000000 000270 aa 766050 420550 281 oct 766050420550,000000000000 000271 aa 000000 000000 000272 aa 616646 114314 282 half_pi3: oct 616646114314,000000000000 000273 aa 000000 000000 000274 aa 752060 432304 283 oct 752060432304,000000000000 000275 aa 000000 000000 000276 aa 526505 600670 284 half_pi4: oct 526505600670,000000000000 000277 aa 000000 000000 000300 aa 736061 461213 285 oct 736061461213,000000000000 000301 aa 000000 000000 000302 aa 434715 045101 286 half_pi5: oct 434715045101,000000000000 000303 aa 000000 000000 000304 aa 722040 156034 287 oct 722040156034,642244022341 000305 aa 642244 022341 000306 aa 000000 000110 288 code: dec 72,0,73 000307 aa 000000 000000 000310 aa 000000 000111 289 290 end NO LITERALS NAME DEFINITIONS FOR ENTRY POINTS AND SEGDEFS 000312 5a 000003 000000 000313 5a 000047 600000 000314 aa 000000 000000 000315 55 000014 000002 000316 5a 000002 400003 000317 55 000006 000014 000320 aa 027 144 157 165 000321 aa 142 154 145 137 000322 aa 160 162 151 156 000323 aa 143 151 160 141 000324 aa 154 137 141 156 000325 aa 147 154 145 137 000326 55 000026 000003 000327 0a 000043 400000 000330 55 000017 000003 000331 aa 031 144 157 165 double_principal_radians_ 000332 aa 142 154 145 137 000333 aa 160 162 151 156 000334 aa 143 151 160 141 000335 aa 154 137 162 141 000336 aa 144 151 141 156 000337 aa 163 137 000 000 000340 55 000040 000014 000341 0a 000000 400000 000342 55 000031 000003 000343 aa 031 144 157 165 double_principal_degrees_ 000344 aa 142 154 145 137 000345 aa 160 162 151 156 000346 aa 143 151 160 141 000347 aa 154 137 144 145 000350 aa 147 162 145 145 000351 aa 163 137 000 000 000352 55 000002 000026 000353 6a 000000 400002 000354 55 000043 000003 000355 aa 014 163 171 155 symbol_table 000356 aa 142 157 154 137 000357 aa 164 141 142 154 000360 aa 145 000 000 000 DEFINITIONS HASH TABLE 000361 aa 000000 000015 000362 aa 000000 000000 000363 aa 000000 000000 000364 aa 000000 000000 000365 aa 000000 000000 000366 aa 000000 000000 000367 5a 000014 000000 000370 5a 000026 000000 000371 5a 000040 000000 000372 aa 000000 000000 000373 aa 000000 000000 000374 aa 000000 000000 000375 aa 000000 000000 000376 aa 000000 000000 EXTERNAL NAMES 000377 aa 020 143 141 154 call_math_error_ 000400 aa 154 137 155 141 000401 aa 164 150 137 145 000402 aa 162 162 157 162 000403 aa 137 000 000 000 000404 aa 012 141 154 155 almost_one 000405 aa 157 163 164 137 000406 aa 157 156 145 000 000407 aa 007 150 141 154 half_pi 000410 aa 146 137 160 151 000411 aa 002 160 151 000 pi 000412 aa 017 155 141 164 math_constants_ 000413 aa 150 137 143 157 000414 aa 156 163 164 141 000415 aa 156 164 163 137 NO TRAP POINTER WORDS TYPE PAIR BLOCKS 000416 aa 000004 000000 000417 55 000065 000065 000420 aa 000004 000000 000421 55 000100 000072 000422 aa 000004 000000 000423 55 000100 000075 000424 aa 000004 000000 000425 55 000100 000077 000426 aa 000001 000000 000427 aa 000000 000000 INTERNAL EXPRESSION WORDS 000430 5a 000104 000000 000431 5a 000106 000000 LINKAGE INFORMATION 000000 aa 000000 000000 000001 0a 000312 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_|almost_one 000011 5a 000117 0000 00 000012 9a 777766 0000 46 call_math_error_|call_math_error_ 000013 5a 000116 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 253561 540744 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 000156 000020 aa 000000 000106 000021 aa 000135 000131 000022 aa 000150 000106 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 000056 000067 aa 175453 017766 000070 aa 000000 117547 000071 aa 176723 600000 000072 aa 076163 160145 >spec>install>1110>double_principal_angle_.alm 000073 aa 143076 151156 000074 aa 163164 141154 000075 aa 154076 061061 000076 aa 061060 076144 000077 aa 157165 142154 000100 aa 145137 160162 000101 aa 151156 143151 000102 aa 160141 154137 000103 aa 141156 147154 000104 aa 145137 056141 000105 aa 154155 040040 MULTICS ASSEMBLY CROSS REFERENCE LISTING Value Symbol Source file Line number almost_one double_principal_angle_: 29, 58, 59, 79, 80, 106, 107, 126, 127, 172, 173, 191, 192. 0 angle double_principal_angle_: 34, 35, 55, 68, 76, 90, 100, 120, 158, 241. 230 angle_too_big double_principal_angle_: 53, 74, 168, 187, 250. 145 bfp_big_angle double_principal_angle_: 102, 185. 2 bfp_principal_degrees double_principal_angle_: 50. 45 bfp_principal_radians double_principal_angle_: 98. 160 big_angle_join double_principal_angle_: 183, 201. call_math_error_ double_principal_angle_: 253. 306 code double_principal_angle_: 251, 288. 0 double_principal_degrees_ double_principal_angle_: 27, 46. 43 double_principal_radians_ double_principal_angle_: 27, 94. half_pi double_principal_angle_: 29. 262 half_pi1 double_principal_angle_: 139, 206, 213, 278. 266 half_pi2 double_principal_angle_: 143, 210, 221, 280. 272 half_pi3 double_principal_angle_: 147, 218, 229, 282. 276 half_pi4 double_principal_angle_: 151, 226, 237, 284. 302 half_pi5 double_principal_angle_: 155, 234, 286. 2 HFP double_principal_angle_: 43, 47, 95. 127 hfp_big_angle double_principal_angle_: 122, 166. 22 hfp_principal_degrees double_principal_angle_: 48, 71. 63 hfp_principal_radians double_principal_angle_: 96, 118. 250 hfp_two_pwr_24 double_principal_angle_: 121, 269. 254 hfp_two_pwr_48 double_principal_angle_: 73, 167, 273. math_constants_ double_principal_angle_: 29. 2 n1 double_principal_angle_: 36, 114, 136, 142, 146, 150, 154, 182, 199, 202, 205, 209, 217, 225, 233. 3 n2 double_principal_angle_: 37, 203, 212, 220, 228, 236. 240 ninety double_principal_angle_: 56, 77, 264. 244 one_over_half_pi double_principal_angle_: 104, 124, 170, 189, 266. 2100 P2.0H double_principal_angle_: 31, 81, 128, 174. 4132 P45.0H double_principal_angle_: 32, 88. pi double_principal_angle_: 29. 102 small_angle_join double_principal_angle_: 115, 138. 4 t1 double_principal_angle_: 38, 140, 159, 207, 242. 6 t2 double_principal_angle_: 39, 144, 160, 211, 214, 215, 243. 10 t3 double_principal_angle_: 40, 148, 161, 219, 222, 223, 244. 12 t4 double_principal_angle_: 41, 152, 162, 227, 230, 231, 245. 14 t5 double_principal_angle_: 42, 156, 163, 235, 238, 239, 246. 0 temp double_principal_angle_: 35, 252, 254. 252 two_pwr_27 double_principal_angle_: 101, 271. 256 two_pwr_54 double_principal_angle_: 52, 186, 275. 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