ASSEMBLY LISTING OF SEGMENT >spec>install>1110>double_sine_.alm ASSEMBLED ON: 11/11/89 0945.4 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 double_sine_ 7 " Modification history: 8 " Written by H. Hoover, M. Mabey, and B. Wong, April 1985, 9 " based on the GCOS routine '7nat'. 10 " 11 " Function: Approximate to double precision the sine or cosine of an 12 " angle given in degrees or radians. 13 " 14 " Entry: through the appropriately named entry point with: 15 " EAQ = the angle whose sine or cosine is desired. 16 " PR2 = the address of a 14 word, even-word aligned scratch area. 17 " 4 words are used in this program and 14 are used by the 18 " routine "double_principal_angle_". The storage for 19 " double_sine_ and double_principal_angle_ overlap. 20 " PR3 = the return address. 21 " 22 " Exit: EAQ = the desired sine or cosine. 23 " 24 " Uses: X0, X1, X2. 25 " X0 = saves a return address from double_principal_angle_ routines 26 " X1 = shift (returned by double_principal_angle_ routines) 27 " X2 = indicates BFP or HFP mode - all of the floating point math 28 " math routines use this register for the same thing. 29 " The double_principal_angle_ routines use registers X1 and X2. 30 31 000000 32 segref math_constants_,half_pi,one_degree,pi 000000 33 segref double_principal_angle_,double_principal_radians_,double_principal_degrees_ 34 000000 35 equ BFP,0 000002 36 equ HFP,2 000000 37 equ x,0 000002 38 equ xx,2 39 000000 40 segdef double_cosine_degrees_,hfp_double_cosine_degrees_ 000010 41 segdef double_cosine_radians_,hfp_double_cosine_radians_ 000020 42 segdef double_sine_degrees_,hfp_double_sine_degrees_ 000030 43 segdef double_sine_radians_,hfp_double_sine_radians_ 44 45 000000 46 hfp_double_cosine_degrees_: 000000 aa 000002 6220 00 47 eax2 HFP " 2 word offset for HFP constants 000001 0a 000003 7100 00 48 tra double_cosine_degrees 49 000002 50 double_cosine_degrees_: 000002 aa 000000 6220 00 51 eax2 BFP " no offset for BFP constants 52 000003 53 double_cosine_degrees: 000003 aa 400000 4750 03 54 fad =0.0,du " normalize input 000004 0a 000172 4270 12 55 dfcmg one_eighty,x2 " if abs_angle <= 180: 000005 0a 000070 6040 00 56 tmi case1_degrees " then no angle reduction is necessary 000006 4a 4 00010 7001 20 57 tsx0 double_principal_degrees_ 000007 0a 000064 7100 11 58 tra case_degrees+1,x1 " select appropriate case 59 60 000010 61 hfp_double_cosine_radians_: 000010 aa 000002 6220 00 62 eax2 HFP " 2 word offset for HFP constants 000011 0a 000013 7100 00 63 tra double_cosine_radians 64 000012 65 double_cosine_radians_: 000012 aa 000000 6220 00 66 eax2 BFP " no offset for BFP constants 67 000013 68 double_cosine_radians: 000013 aa 400000 4750 03 69 fad =0.0,du " normalize input and set indicators 000014 4a 4 00012 4271 20 70 dfcmg pi,x2 " if abs (angle) <= pi 000015 0a 000045 6040 00 71 tmi case1_radians " then no angle reduction is necessary 000016 4a 4 00014 7001 20 72 tsx0 double_principal_radians_ 000017 0a 000041 7100 11 73 tra case_radians+1,x1 " select appropriate case 74 75 000020 76 hfp_double_sine_degrees_: 000020 aa 000002 6220 00 77 eax2 HFP " 2 word offset for HFP constants 000021 0a 000023 7100 00 78 tra double_sine_degrees 79 000022 80 double_sine_degrees_: 000022 aa 000000 6220 00 81 eax2 BFP " no offset for BFP constants 82 000023 83 double_sine_degrees: 000023 aa 400000 4750 03 84 fad =0.0,du " normalize input 000024 0a 000166 4270 12 85 dfcmg ninety,x2 " if abs (angle) < pi/2 000025 0a 000103 6040 00 86 tmi case0_degrees " then no angle reduction is necessary 000026 4a 4 00010 7001 20 87 tsx0 double_principal_degrees_ 000027 0a 000063 7100 11 88 tra case_degrees,x1 " select appropriate case 89 90 000030 91 hfp_double_sine_radians_: 000030 aa 000002 6220 00 92 eax2 HFP " 2 word offset for HFP constants 000031 0a 000033 7100 00 93 tra double_sine_radians 94 000032 95 double_sine_radians_: 000032 aa 000000 6220 00 96 eax2 BFP " no offset for BFP constants 97 000033 98 double_sine_radians: 000033 aa 400000 4750 03 99 fad =0.0,du " normalize input 000034 4a 4 00016 4271 20 100 dfcmg half_pi,x2 " if abs (angle) <= pi/2 000035 0a 000107 6044 00 101 tmoz case0_radians " then no angle reduction is necessary 000036 4a 4 00014 7001 20 102 tsx0 double_principal_radians_ 000037 0a 000040 7100 11 103 tra case_radians,x1 " Case select appropriate case_radians 104 000040 105 case_radians: 000040 0a 000107 7100 00 106 tra case0_radians 000041 0a 000045 7100 00 107 tra case1_radians 000042 0a 000053 7100 00 108 tra case2_radians 000043 0a 000055 7100 00 109 tra case3_radians 000044 0a 000107 7100 00 110 tra case0_radians 111 000045 112 case1_radians: 000045 aa 400000 4750 03 113 fad =0.0,du " set indicators 000046 aa 000002 6040 04 114 tmi 2,ic " EAQ = - abs (EAQ) 000047 aa 000000 5330 00 115 negl 0 " fneg underflows at o400400000000 116 000050 0a 000156 4770 12 117 dfad half_pi1,x2 000051 0a 000162 4770 12 118 dfad half_pi2,x2 000052 0a 000107 7100 00 119 tra part_sine_radians 120 000053 121 case2_radians: 000053 aa 000000 5130 00 122 fneg 0 000054 0a 000107 7100 00 123 tra part_sine_radians 124 000055 125 case3_radians: 000055 aa 400000 4750 03 126 fad =0.0,du " set indicators 000056 aa 000002 6050 04 127 tpl 2,ic " EAQ = abs (EAQ) 000057 aa 000000 5130 00 128 fneg 0 129 000060 0a 000156 5770 12 130 dfsb half_pi1,x2 000061 0a 000162 5770 12 131 dfsb half_pi2,x2 000062 0a 000107 7100 00 132 tra part_sine_radians 133 000063 134 case_degrees: 000063 0a 000103 7100 00 135 tra case0_degrees 000064 0a 000070 7100 00 136 tra case1_degrees 000065 0a 000075 7100 00 137 tra case2_degrees 000066 0a 000077 7100 00 138 tra case3_degrees 000067 0a 000103 7100 00 139 tra case0_degrees 140 000070 141 case1_degrees: 000070 aa 400000 4750 03 142 fad =0.0,du " set indicators 000071 aa 000002 6040 04 143 tmi 2,ic " EAQ = - abs (EAQ) 000072 aa 000000 5330 00 144 negl 0 " fneg underflows at o400400000000 145 000073 0a 000166 4750 12 146 fad ninety,x2 000074 0a 000103 7100 00 147 tra part_sine_degrees 148 000075 149 case2_degrees: 000075 aa 000000 5130 00 150 fneg 0 000076 0a 000103 7100 00 151 tra part_sine_degrees 152 000077 153 case3_degrees: 000077 aa 400000 4750 03 154 fad =0.0,du " set indicators 000100 aa 000002 6050 04 155 tpl 2,ic " EAQ = abs (EAQ) 000101 aa 000000 5130 00 156 fneg 157 000102 0a 000166 5750 12 158 fsb ninety,x2 159 " tra part_sine_degrees 160 000103 161 case0_degrees: " case0_degrees is just part_sine_degrees 162 000103 163 part_sine_degrees: 000103 0a 000146 4270 12 164 dfcmg eps2,x2 " if conversion to radians underflows 000104 aa 000002 6050 04 165 tpl 2,ic 000105 aa 400000 4310 03 166 fld =0.0,du " then use zero 000106 4a 4 00020 4631 20 167 dfmp one_degree,x2 " convert to radians. 168 " tra part_sine_radians 169 000107 170 case0_radians: " case0_radians is just part_sine_radians 171 172 173 " Procedure part_sine (x) calculates 'sin(x)' for 'x' in the range 174 " [-pi/2, pi/2] given 'x' in the EAQ. 175 000107 176 part_sine_radians: 000107 aa 000000 4730 00 177 dfrd 0 000110 0a 000152 4270 12 178 dfcmg eps3,x2 "if abs (x) < 5e-10: 000111 aa 3 00000 6041 00 179 tmi pr3|0 " sine is x for small x 000112 aa 2 00000 4571 00 180 dfst pr2|x 000113 aa 2 00000 4631 00 181 dfmp pr2|x " calculate xx = x*x 000114 aa 2 00002 4721 00 182 dfstr pr2|xx 000115 0a 000242 4630 12 183 dfmp p9,x2 " calculate p(xx) 000116 0a 000236 4770 12 184 dfad p8,x2 000117 aa 2 00002 4631 00 185 dfmp pr2|xx 000120 0a 000232 4770 12 186 dfad p7,x2 000121 aa 2 00002 4631 00 187 dfmp pr2|xx 000122 0a 000226 4770 12 188 dfad p6,x2 000123 aa 2 00002 4631 00 189 dfmp pr2|xx 000124 0a 000222 4770 12 190 dfad p5,x2 000125 aa 2 00002 4631 00 191 dfmp pr2|xx 000126 0a 000216 4770 12 192 dfad p4,x2 000127 aa 2 00002 4631 00 193 dfmp pr2|xx 000130 0a 000212 4770 12 194 dfad p3,x2 000131 aa 2 00002 4631 00 195 dfmp pr2|xx 000132 0a 000206 4770 12 196 dfad p2,x2 000133 aa 2 00002 4631 00 197 dfmp pr2|xx 000134 0a 000202 4770 12 198 dfad p1,x2 000135 aa 2 00002 4631 00 199 dfmp pr2|xx 000136 0a 000176 4750 12 200 fad p0,x2 000137 aa 2 00000 4631 00 201 dfmp pr2|x " return x*p(xx) 000140 aa 000000 4730 00 202 dfrd 0 000141 aa 3 00000 7101 00 203 tra pr3|0 204 205 206 " Constants: 207 208 even 000142 aa 716504 072231 209 eps1: dec 1.886591d-8 000143 aa 175750 642262 000144 aa 764242 035115 210 oct 764242035115,000000000000 000145 aa 000000 000000 000146 aa 412712 273406 211 eps2: dec 8.418858142948452884d-38 000147 aa 461701 757347 000150 aa 402162 456701 212 oct 402162456701,514360373670 " 2.670821537926801391d-154 000151 aa 514360 373670 000152 aa 704422 701372 213 eps3: dec 5.0d-10 000153 aa 023326 451314 000154 aa 762104 560276 214 oct 762104560276,404665512263 000155 aa 404665 512263 000156 aa 002622 077325 215 half_pi1: oct 002622077325,042055060432 " 1.570796326794896619d0 000157 aa 042055 060432 000160 aa 002062 207732 216 oct 002062207732,504205506043 " 1.570796326794896619d0 000161 aa 504205 506043 000162 aa 602611 431424 217 half_pi2: oct 602611431424,270033407150 " 8.333742918520878328d-20 000163 aa 270033 407150 000164 aa 742461 143142 218 oct 742461143142,427003340714 " 5.170182981794105568d-19 000165 aa 427003 340714 000166 aa 016550 000000 219 ninety: dec 90.0d0 000167 aa 000000 000000 000170 aa 004264 000000 220 oct 004264000000,000000000000 000171 aa 000000 000000 000172 221 one_eighty: 000172 aa 020550 000000 222 dec 180.0d0 000173 aa 000000 000000 000174 aa 004550 000000 223 oct 004550000000,000000000000 000175 aa 000000 000000 000176 aa 002400 000000 224 p0: dec 9.9999999999999999998d-1 " this rounds to 1.0d0 000177 aa 000000 000000 000200 aa 002040 000000 225 oct 002040000000,000000000000 000201 aa 000000 000000 000202 aa 775252 525252 226 p1: dec -1.6666666666666666664d-1 000203 aa 525252 525254 000204 aa 001652 525252 227 oct 001652525252,525252525253 000205 aa 525252 525253 000206 aa 764421 042104 228 p2: dec 8.333333333333332952d-3 000207 aa 210421 041543 000210 aa 776104 210421 229 oct 776104210421,042104210331 000211 aa 042104 210331 000212 aa 751137 713771 230 p3: dec -1.9841269841269648946d-4 000213 aa 377140 131713 000214 aa 773137 713771 231 oct 773137713771,377140131713 000215 aa 377140 131713 000216 aa 734561 674351 232 p4: dec 2.7557319223936401884d-6 000217 aa 253231 434555 000220 aa 770134 357072 233 oct 770134357072,252646307133 000221 aa 252646 307133 000222 aa 717121 467246 234 p5: dec -2.5052108378101760587d-8 000223 aa 026224 465270 000224 aa 765450 633523 235 oct 765450633523,013112232534 000225 aa 013112 232534 000226 aa 700541 110601 236 p6: dec 1.60590431721336921d-10 000227 aa 052315 030325 000230 aa 760541 110601 237 oct 760541110601,052315030325 000231 aa 052315 030325 000232 aa 661121 402455 238 p7: dec -7.647126379076958d-13 000233 aa 333370 604367 000234 aa 755121 402455 239 oct 755121402455,333370604367 000235 aa 333370 604367 000236 aa 640624 773046 240 p8: dec 2.8101852815318d-15 000237 aa 213725 310300 000240 aa 750624 773046 241 oct 750624773046,213725310300 000241 aa 213725 310300 000242 aa 621331 460002 242 p9: dec -7.9798971356d-18 000243 aa 411662 206514 000244 aa 745331 460002 243 oct 745331460002,411662206514 000245 aa 411662 206514 244 245 end NO LITERALS NAME DEFINITIONS FOR ENTRY POINTS AND SEGDEFS 000246 5a 000003 000000 000247 5a 000135 600000 000250 aa 000000 000000 000251 55 000012 000002 000252 5a 000002 400003 000253 55 000006 000012 000254 aa 014 144 157 165 000255 aa 142 154 145 137 000256 aa 163 151 156 145 000257 aa 137 000 000 000 000260 55 000024 000003 000261 0a 000030 400000 000262 55 000015 000003 000263 aa 030 150 146 160 hfp_double_sine_radians_ 000264 aa 137 144 157 165 000265 aa 142 154 145 137 000266 aa 163 151 156 145 000267 aa 137 162 141 144 000270 aa 151 141 156 163 000271 aa 137 000 000 000 000272 55 000035 000012 000273 0a 000032 400000 000274 55 000027 000003 000275 aa 024 144 157 165 double_sine_radians_ 000276 aa 142 154 145 137 000277 aa 163 151 156 145 000300 aa 137 162 141 144 000301 aa 151 141 156 163 000302 aa 137 000 000 000 000303 55 000047 000024 000304 0a 000020 400000 000305 55 000040 000003 000306 aa 030 150 146 160 hfp_double_sine_degrees_ 000307 aa 137 144 157 165 000310 aa 142 154 145 137 000311 aa 163 151 156 145 000312 aa 137 144 145 147 000313 aa 162 145 145 163 000314 aa 137 000 000 000 000315 55 000060 000035 000316 0a 000022 400000 000317 55 000052 000003 000320 aa 024 144 157 165 double_sine_degrees_ 000321 aa 142 154 145 137 000322 aa 163 151 156 145 000323 aa 137 144 145 147 000324 aa 162 145 145 163 000325 aa 137 000 000 000 000326 55 000072 000047 000327 0a 000010 400000 000330 55 000063 000003 000331 aa 032 150 146 160 hfp_double_cosine_radians_ 000332 aa 137 144 157 165 000333 aa 142 154 145 137 000334 aa 143 157 163 151 000335 aa 156 145 137 162 000336 aa 141 144 151 141 000337 aa 156 163 137 000 000340 55 000103 000060 000341 0a 000012 400000 000342 55 000075 000003 000343 aa 026 144 157 165 double_cosine_radians_ 000344 aa 142 154 145 137 000345 aa 143 157 163 151 000346 aa 156 145 137 162 000347 aa 141 144 151 141 000350 aa 156 163 137 000 000351 55 000115 000072 000352 0a 000000 400000 000353 55 000106 000003 000354 aa 032 150 146 160 hfp_double_cosine_degrees_ 000355 aa 137 144 157 165 000356 aa 142 154 145 137 000357 aa 143 157 163 151 000360 aa 156 145 137 144 000361 aa 145 147 162 145 000362 aa 145 163 137 000 000363 55 000126 000103 000364 0a 000002 400000 000365 55 000120 000003 000366 aa 026 144 157 165 double_cosine_degrees_ 000367 aa 142 154 145 137 000370 aa 143 157 163 151 000371 aa 156 145 137 144 000372 aa 145 147 162 145 000373 aa 145 163 137 000 000374 55 000002 000115 000375 6a 000000 400002 000376 55 000131 000003 000377 aa 014 163 171 155 symbol_table 000400 aa 142 157 154 137 000401 aa 164 141 142 154 000402 aa 145 000 000 000 DEFINITIONS HASH TABLE 000403 aa 000000 000015 000404 aa 000000 000000 000405 aa 000000 000000 000406 aa 000000 000000 000407 aa 000000 000000 000410 5a 000024 000000 000411 5a 000047 000000 000412 5a 000126 000000 000413 5a 000072 000000 000414 5a 000012 000000 000415 5a 000035 000000 000416 5a 000115 000000 000417 5a 000060 000000 000420 5a 000103 000000 EXTERNAL NAMES 000421 aa 031 144 157 165 double_principal_degrees_ 000422 aa 142 154 145 137 000423 aa 160 162 151 156 000424 aa 143 151 160 141 000425 aa 154 137 144 145 000426 aa 147 162 145 145 000427 aa 163 137 000 000 000430 aa 031 144 157 165 double_principal_radians_ 000431 aa 142 154 145 137 000432 aa 160 162 151 156 000433 aa 143 151 160 141 000434 aa 154 137 162 141 000435 aa 144 151 141 156 000436 aa 163 137 000 000 000437 aa 027 144 157 165 double_principal_angle_ 000440 aa 142 154 145 137 000441 aa 160 162 151 156 000442 aa 143 151 160 141 000443 aa 154 137 141 156 000444 aa 147 154 145 137 000445 aa 002 160 151 000 pi 000446 aa 012 157 156 145 one_degree 000447 aa 137 144 145 147 000450 aa 162 145 145 000 000451 aa 007 150 141 154 half_pi 000452 aa 146 137 160 151 000453 aa 017 155 141 164 math_constants_ 000454 aa 150 137 143 157 000455 aa 156 163 164 141 000456 aa 156 164 163 137 NO TRAP POINTER WORDS TYPE PAIR BLOCKS 000457 aa 000004 000000 000460 55 000171 000153 000461 aa 000004 000000 000462 55 000171 000162 000463 aa 000004 000000 000464 55 000205 000177 000465 aa 000004 000000 000466 55 000205 000200 000467 aa 000004 000000 000470 55 000205 000203 000471 aa 000001 000000 000472 aa 000000 000000 INTERNAL EXPRESSION WORDS 000473 5a 000217 000000 000474 5a 000221 000000 000475 5a 000213 000000 000476 5a 000215 000000 000477 5a 000211 000000 LINKAGE INFORMATION 000000 aa 000000 000000 000001 0a 000246 000000 000002 aa 000000 000000 000003 aa 000000 000000 000004 aa 000000 000000 000005 aa 000000 000000 000006 22 000010 000022 000007 a2 000000 000000 000010 9a 777770 0000 46 double_principal_angle_|double_principal_degrees_ 000011 5a 000231 0000 00 000012 9a 777766 0000 46 math_constants_|pi 000013 5a 000230 0000 12 000014 9a 777764 0000 46 double_principal_angle_|double_principal_radians_ 000015 5a 000227 0000 00 000016 9a 777762 0000 46 math_constants_|half_pi 000017 5a 000226 0000 12 000020 9a 777760 0000 46 math_constants_|one_degree 000021 5a 000225 0000 12 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 253520 477746 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 000163 000020 aa 000000 000103 000021 aa 000132 000125 000022 aa 000155 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 020014 000070 aa 000000 117547 000071 aa 176724 200000 000072 aa 076163 160145 >spec>install>1110>double_sine_.alm 000073 aa 143076 151156 000074 aa 163164 141154 000075 aa 154076 061061 000076 aa 061060 076144 000077 aa 157165 142154 000100 aa 145137 163151 000101 aa 156145 137056 000102 aa 141154 155040 MULTICS ASSEMBLY CROSS REFERENCE LISTING Value Symbol Source file Line number 0 BFP double_sine_: 35, 51, 66, 81, 96. 103 case0_degrees double_sine_: 86, 135, 139, 161. 107 case0_radians double_sine_: 101, 106, 110, 170. 70 case1_degrees double_sine_: 56, 136, 141. 45 case1_radians double_sine_: 71, 107, 112. 75 case2_degrees double_sine_: 137, 149. 53 case2_radians double_sine_: 108, 121. 77 case3_degrees double_sine_: 138, 153. 55 case3_radians double_sine_: 109, 125. 63 case_degrees double_sine_: 58, 88, 134. 40 case_radians double_sine_: 73, 103, 105. 3 double_cosine_degrees double_sine_: 48, 53. 2 double_cosine_degrees_ double_sine_: 40, 50. 13 double_cosine_radians double_sine_: 63, 68. 12 double_cosine_radians_ double_sine_: 41, 65. double_principal_angle_ double_sine_: 33. double_principal_degrees_ double_sine_: 33, 57, 87. double_principal_radians_ double_sine_: 33, 72, 102. 23 double_sine_degrees double_sine_: 78, 83. 22 double_sine_degrees_ double_sine_: 42, 80. 33 double_sine_radians double_sine_: 93, 98. 32 double_sine_radians_ double_sine_: 43, 95. 142 eps1 double_sine_: 209. 146 eps2 double_sine_: 164, 211. 152 eps3 double_sine_: 178, 213. half_pi double_sine_: 32, 100. 156 half_pi1 double_sine_: 117, 130, 215. 162 half_pi2 double_sine_: 118, 131, 217. 2 HFP double_sine_: 36, 47, 62, 77, 92. 0 hfp_double_cosine_degrees_ double_sine_: 40, 46. 10 hfp_double_cosine_radians_ double_sine_: 41, 61. 20 hfp_double_sine_degrees_ double_sine_: 42, 76. 30 hfp_double_sine_radians_ double_sine_: 43, 91. math_constants_ double_sine_: 32. 166 ninety double_sine_: 85, 146, 158, 219. one_degree double_sine_: 32, 167. 172 one_eighty double_sine_: 55, 221. 176 p0 double_sine_: 200, 224. 202 p1 double_sine_: 198, 226. 206 p2 double_sine_: 196, 228. 212 p3 double_sine_: 194, 230. 216 p4 double_sine_: 192, 232. 222 p5 double_sine_: 190, 234. 226 p6 double_sine_: 188, 236. 232 p7 double_sine_: 186, 238. 236 p8 double_sine_: 184, 240. 242 p9 double_sine_: 183, 242. 103 part_sine_degrees double_sine_: 147, 151, 163. 107 part_sine_radians double_sine_: 119, 123, 132, 176. pi double_sine_: 32, 70. 0 x double_sine_: 37, 180, 181, 201. 2 xx double_sine_: 38, 182, 185, 187, 189, 191, 193, 195, 197, 199. 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