#
# trig_calc.txt, 29 May 11

# Numbers originally from
# Cody and Waite, "Software Manual For The Elementary Functions".

!fuzz 0.00000001

!title trig function calculation

!msgpostfix Extended precision argument reduction (pi/4) for 24-bit significand\n

!need all
0.78515625
2.4187564849853515625e-4
3.77489497744594108e-8

!msgpostfix arcsin/arccos from Cody & Waite (fixed-point mantissa <= 24 bits)\n

!need all
 0.08333 31098
-0.04500 65898

# 0.50000 00000
-0.49507 79396
 0.08922 78749


!msgpostfix Calculate arcsin/arccos from Cody & Waite (fixed-point 25 to 36 bit mantissa)\n

!need all
 0.08333 33331 91669
-0.08800 38762 68233
 0.01800 43563 66662

 0.50000 00000 00000
-0.75302 33061 60715
 0.31295 90818 27048
-0.03028 47984 82806


!msgpostfix Calculate arcsin/arccos from Cody & Waite (fixed-point 37 to 48 bit mantissa)\n

!need all
 0.04166 66666 66628 83
-0.06554 00387 86926 70
 0.02912 89116 60093 97
-0.00319 21054 85259 50

 0.25000 00000 00000 00
-0.50574 02327 43102 17
 0.33539 22897 63774 92
-0.08018 59602 95834 55
 0.00488 05915 81071 13


!msgpostfix Calculate arcsin/arccos from Cody & Waite (mantissa <= 24 bits)\n

!need all

 0.93393 5835 e+0
-0.50440 0557 e+0

 0.56036 3004 e+1
-0.55484 6723 e+1
# 0.10000 0000 e+1


!msgpostfix Calculate arcsin/arccos from Cody & Waite (25 to 36 bit mantissa)\n

!need all
-0.27516 55529 0596 e+1
 0.29058 76237 4859 e+1
-0.59450 14419 3246 e+0

-0.16509 93320 2424 e+2
 0.24864 72896 9164 e+2
-0.10333 86707 2113 e+2
# 0.10000 00000 0000 e+1


!msgpostfix Calculate arcsin/arccos from Cody & Waite (37 to 48 bit mantissa)\n

!need all
 0.85372 16436 67719 50 e+1
-0.13428 70791 34253 12 e+2
 0.59683 15761 77515 34 e+1
-0.65404 06899 93350 09 e+0

 0.51223 29862 01096 91 e+2
-0.10362 27318 64014 80 e+3
 0.68719 59765 38088 06 e+2
-0.16429 55755 74951 70 e+2
# 0.10000 00000 00000 00 e+1


!msgpostfix Calculate arcsin/arccos from Cody & Waite (49 to 60 bit mantissa)\n

!need all
-0.27368 49452 41642 55994 e+2
 0.57208 22787 78917 31407 e+2
-0.39688 86299 75048 77339 e+2
 0.10152 52223 38064 63645 e+2
-0.69674 57344 73506 46411 e+0

-0.16421 09671 44985 60795 e+3
 0.41714 43024 82604 12556 e+3
-0.38186 30336 17501 49284 e+3
 0.15095 27084 10306 04719 e+3
-0.23823 85915 36702 38830 e+2
# 0.10000 00000 00000 00000 e+1


!msgpostfix Calculate arctan from Cody & Waite (fixed-point mantissa <= 24 bits)\n

!need all
-0.47083 25141
 0.05090 95825

 0.70625 03702
# 0.50000 00000


!msgpostfix Calculate arctan from Cody & Waite (fixed-point 25 to 32 bit mantissa)\n

!need all
-0.36002 08621 86
-0.18000 67122 25

 0.54003 12986 49
 0.59402 82307 49
# 0.12500 00000 00


!msgpostfix Calculate arctan from Cody & Waite (fixed-point 33 to 50 bit mantissa)\n

!need all
-0.26714 54200 16400 69
-0.26715 31158 54956 46
-0.04964 94559 63021 02

 0.40071 81300 24749 50
 0.64116 05517 63182 67
 0.28743 41765 10949 94
 0.03125 00000 00000 00


!msgpostfix Calculate arctan from Cody & Waite (mantissa <= 24 bits)\n

!need all
-0.47083 25141 e+0
-0.50909 58253 e-1

 0.14125 00740 e+1
 0.10000 00000 e+1


!msgpostfix Calculate arctan from Cody & Waite (25 to 32 bit mantissa)\n

!need all
-0.14400 83448 74 e+1
-0.7002 68488 98 e+0

 0.43202 50389 19 e+1
 0.47522 25845 99 e+1
# 0.10000 00000 00 e+1


!msgpostfix Calculate arctan from Cody & Waite (33 to 50 bit mantissa)\n

!need all
-0.42743 26720 26241 096 e+1
-0.42744 49853 67930 329 e+1
-0.79439 12954 08336 251 e+0

 0.12822 98016 07919 841 e+2
 0.20517 13765 64218 456 e+2
 0.91978 93648 35039 806 e+1
# 0.10000 00000 00000 000 e+1


!msgpostfix Calculate arctan from Cody & Waite (51 to 60 bit mantissa)\n

!need all
-0.13688 76889 41919 26929 e+2
-0.20505 85519 58616 51981 e+2
-0.84946 24035 13206 83534 e+1
-0.83758 29936 81500 59274 e+0

 0.41066 30668 25757 81263 e+2
 0.86157 34959 71302 42515 e+2
 0.59578 43614 25973 44465 e+2
 0.15024 00116 00285 76121 e+2
# 0.10000 00000 00000 00000 e+1

!msgpostfix cos function single-precision evaluation, Cephes math library\n

!need all
 2.443315711809948e-5
-1.388731625493765e-3
 4.166664568298827e-2


!msgpostfix sine function single-precision evaluation, Cephes math library\n

!need all
-1.9515295891E-4
 8.3321608736E-3
-1.6666654611E-1

!msgpostfix Calculate sin/cos from Cody & Waite (fixed-point mantissa <= 24 bits)\n

!need all
-0.66666 62674
 0.13332 84022
-0.01267 67480
 0.00066 60872


!msgpostfix Calculate sin/cos from Cody & Waite (fixed-point 25 to 32 bit mantissa)\n

!need all
-0.66666 66643 530
 0.13333 32915 289
-0.01269 81330 068
 0.00070 46136 593
-0.00002 44411 867


!msgpostfix Calculate sin/cos from Cody & Waite (fixed-point 33 to 50 bit mantissa)\n

!need all
-0.66666 66666 66638 613
 0.13333 33333 32414 742
-0.01269 84126 86862 404
 0.00070 54673 00385 092
-0.00002 06531 15784 674
 0.00000 00120 76093 891


!msgpostfix Calculate sin/cos from Cody & Waite (fixed-point 51 to 60 bit mantissa)\n

!need all
-0.66666 66666 66666 60209
 0.13333 33333 33330 64050
-0.01269 84126 98369 17789
 0.00070 54673 71779 91056
-0.00002 56533 57361 43317
 0.00000 06577 74038 64562
-0.00000 00125 22156 53481
 0.00000 00001 78289 31802


!msgpostfix Calculate sin/cos from Cody & Waite (mantissa <= 24 bits)\n

!need all
-0.16666 65668 e+0
 0.83330 25139 e-2
-0.19807 41872 e-3
 0.26019 03036 e-5


!msgpostfix Calculate sin/cos from Cody & Waite (25 to 32 bit mantissa)\n

!need all
-0.16666 66660 883 e+0
 0.83333 30720 556 e-2
-0.19840 83282 313 e-3
 0.27523 97106 775 e-5
-0.23868 34640 601 e-7


!msgpostfix Calculate sin/cos from Cody & Waite (33 to 50 bit mantissa)\n

!need all
-0.16666 66666 66659 653 e+0
 0.83333 33333 27592 139 e-2
-0.19841 26982 32225 068 e-3
 0.27557 31642 12926 457 e-5
-0.25051 87088 34705 760 e-7
 0.16047 84463 23816 900 e-9
-0.73706 62775 07114 174 e-12


!msgpostfix Calculate sin/cos from Cody & Waite (51 to 60 bit mantissa)\n

# 3.1416015625
# -8.908910206761537356617e-6

!need all
-0.16666 66666 66666 65052 e+0
 0.83333 33333 33316 50314 e-2
-0.19841 26984 12018 40457 e-3
 0.27557 31921 01527 56119 e-5
-0.25052 10679 82745 84544 e-7
 0.16058 93649 03715 89114 e-9
-0.76429 17806 89104 67734 e-12
 0.27204 79095 78888 46175 e-14


!msgpostfix Calculate tan/cotan from Cody & Waite (fixed-point mantissa <= 22 bits)\n

!need all
 0.16666 75142
-0.00083 48534

# 0.50000 00000
-0.20248 56694


!msgpostfix Calculate tan/cotan from Cody & Waite (fixed-point 23 to 32 bit mantissa)\n

!need all
 0.16666 66658 406
-0.00744 91186 974

# 0.50000 00000 000
-0.22234 73860 140
 0.00798 66960 665


!msgpostfix Calculate tan/cotan from Cody & Waite (fixed-point 33 to 52 bit mantissa)\n

!need all
 0.16666 66666 66665 2540
-0.01026 94672 90449 3698
 0.00010 04822 04626 8875

# 0.50000 00000 00000 0000
-0.23080 84018 71452 4420
 0.01167 24264 11034 3640
-0.00010 42240 22110 1935


!msgpostfix Calculate tan/cotan from Cody & Waite (mantissa <= 24 bits)\n

!need all
# 0.10000 0000 e+1
-0.95801 7723 e-1

# 0.10000 0000 e+1
-0.42913 5777 e+0
 0.97168 5835 e-2


!msgpostfix Calculate tan/cotan from Cody & Waite (25 to 32 bit mantissa)\n

!need all
# 0.10000 00000 000 e+1
-0.11136 14403 566 e+0
 0.10751 54738 488 e-2

# 0.10000 00000 000 e+1
-0.44469 47720 281 e+0
 0.15973 39213 300 e-1


!msgpostfix Calculate tan/cotan from Cody & Waite (33 to 53 bit mantissa)\n

!need all
# 0.10000 00000 00000 0000 e+1
-0.12828 34704 09574 3847 e+0
 0.28059 18241 16998 8906 e-2
-0.74836 34966 61206 5149 e-5

# 0.10000 00000 00000 0000 e+1
-0.46161 68037 42904 8840 e+0
 0.23344 85282 20687 2802 e-1
-0.20844 80442 20387 0948 e-3


!msgpostfix Calculate tan/cotan from Cody & Waite (53 to 60 bit mantissa)\n

# 3217.0 / 2048.0
# -4.454455103380768678308e-6

!need all
# 0.10000 00000 00000 00000 e+1
-0.13338 35000 64219 60681 e+0
 0.34248 87823 58905 89960 e-2
-0.17861 70734 22544 26711 e-4

#  0.1000 00000 00000 000000 e+1
-0.46671 68333 97552 94240 e+0
 0.25663 83228 94401 12864 e-1
-0.31181 53190 70100 27307 e-3
 0.49819 43399 37865 12270 e-6


!msgpostfix Calculate sinh/cosh from Cody & Waite (fixed-point mantissa <= 24 bits)\n

!need all
 0.16666 7338 e+0
 0.83299 1192 e-2
 0.20393 9897 e-3


!msgpostfix Calculate sinh/cosh from Cody & Waite (fixed-point 25 to 32 bit mantissa)\n

!need all
 0.16666 66643 02 e+0
 0.83333 52592 90 e-2
 0.19835 81244 79 e-3
 0.28185 23941 73 e-5


!msgpostfix Calculate sinh/cosh from Cody & Waite (fixed-point 33 to 40 bit mantissa)\n

!need all
 0.16666 66666 7209 e+0
 0.83333 33269 0119 e-2
 0.19841 29762 2826 e-3
 0.27551 91453 3845 e-5
 0.25535 00764 7784 e-7


!msgpostfix Calculate sinh/cosh from Cody & Waite (fixed-point 41 to 50 bit mantissa)\n

!need all
 0.16666 66666 66657 93 e+0
 0.83333 33333 47538 58 e-2
 0.19841 26975 50150 70 e-3
 0.27557 34409 51771 46 e-5
 0.25048 43562 94822 61 e-7
 0.16327 26568 62665 98 e-9


!msgpostfix Calculate sinh/cosh from Cody & Waite (mantissa <= 24 bits)\n

!need all
-0.71379 3159 e+1
-0.19033 3399 e+0

-0.42827 7109 e+2
# 0.10000 0000 e+1


!msgpostfix Calculate sinh/cosh from Cody & Waite (25 to 40 bit mantissa)\n

!need all
 0.10622 28883 7151 e+4
 0.31359 75645 6058 e+2
 0.34364 14035 8506 e+0

 0.63733 73302 1822 e+4
-0.13051 01250 9199 e+3
# 0.10000 00000 0000 e+1


!msgpostfix Calculate sinh/cosh from Cody & Waite (41 to 50 bit mantissa)\n

!need all
 0.23941 43592 30500 69 e+4
 0.85943 28483 85490 10 e+2
 0.13286 42866 92242 29 e+1
 0.77239 39820 29419 23 e-2

 0.14364 86155 38302 92 e+5
-0.20258 33686 64278 69 e+3
# 0.10000 00000 00000 00 e+1


!msgpostfix Calculate sinh/cosh from Cody & Waite (51 to 60 bit mantissa)\n

# 0.69316101074218750000e+0
# 0.24999308500451499336e+0
# 0.13830277879601902638e-4

!need all
-0.35181 28343 01771 17881 e+6
-0.11563 52119 68517 68270 e+5
-0.16375 79820 26307 51372 e+3
-0.78966 12741 73570 99479 e+0

-0.21108 77005 81062 71242 e+7
 0.36162 72310 94218 36460 e+5
-0.27773 52311 96507 01667 e+3
# 0.10000 00000 00000 00000 e+1


!msgpostfix Calculate tanh from Cody & Waite (fixed-point mantissa <= 24 bits)\n

!need all
-0.20594 32032
-0.00095 77527

 0.61782 89136
# 0.25000 00000


!msgpostfix Calculate exp from Cody & Waite (fixed-point 25 to 36 bit mantissa)\n

!need all
-0.16456 21718 76916
-0.00729 40215 35344

 0.49368 65157 46738
 0.21935 66677 38052
 0.00781 25000 00000


!msgpostfix Calculate exp from Cody & Waite (fixed-point 37 to 48 bit mantissa)\n

!need all
-0.14890 25189 60799 158
-0.00721 23976 13392 670
-0.00000 28314 39213 644

 0.44670 75568 82545 442
 0.20032 02155 87335 741
 0.00781 25000 00000 000


!msgpostfix Calculate tanh from Cody & Waite (mantissa <= 24 bits)\n

!need all
-0.82377 28127 e+0
-0.38310 10665 e-2

 0.24713 19654 e+1
# 0.10000 00000 e+1


!msgpostfix Calculate tanh from Cody & Waite (25 to 36 bit mantissa)\n

!need all
-0.21063 95800 0245 e+2
-0.93363 47565 2401 e+0

 0.63191 87401 5582 e+2
 0.28077 65347 0471 e+2
# 0.10000 00000 0000 e+1


!msgpostfix Calculate tanh from Cody & Waite (37 to 48 bit mantissa)\n

!need all
-0.19059 52242 69822 92 e+2
-0.92318 68945 14261 77 e+0
-0.36242 42193 46421 73 e-3

 0.57178 56728 09658 17 e+2
 0.25640 98759 51789 75 e+2
# 0.10000 00000 00000 00 e+1


!msgpostfix Calculate tanh from Cody & Waite (49 to 60 bit mantissa)\n

!need all
-0.16134 11902 39962 28053e+4
-0.99225 92967 22360 83313e+2
-0.96437 49277 72254 69787e+0

 0.48402 35707 19886 88686e+4
 0.22337 72071 89623 12926e+4
 0.11274 47438 05349 49335e+3
# 0.10000 00000 00000 00000e+1


!msgpostfix Calculate exp from Cody & Waite (fixed-point mantissa <= 29 bits)\n

!need all
0.24999 99995 0
0.00416 02886 3

# 0.50000 00000 0
0.04998 71787 8


!msgpostfix Calculate exp from Cody & Waite (fixed-point 30 to 42 bit mantissa)\n

!need all
0.24999 99999 9992
0.00595 04254 9776

0.50000 00000 0000
0.05356 75176 4522
0.00029 72936 3682


!msgpostfix Calculate exp from Cody & Waite (fixed-point 43 to 56 bit mantissa)\n

!need all
0.24999 99999 99999 993
0.00694 36000 15117 929
0.00001 65203 30026 828

0.50000 00000 00000 000
0.05555 38666 96900 119
0.00049 58628 84905 441


!msgpostfix Calculate exp from Cody & Waite (mantissa <= 29 bits)\n

!need all
0.24999 99995 0 e+0
0.41602 88626 8 e-2

# 0.50000 00000 0 e+0
0.49987 17877 8 e-1


!msgpostfix Calculate exp from Cody & Waite (30 to 42 bit mantissa)\n

!need all
0.24999 99999 9992 e+0
0.59504 25497 7591 e-2

0.50000 00000 0000 e+0
0.53567 51764 5222 e-1
0.29729 36368 2238 e-3


!msgpostfix Calculate exp from Cody & Waite (43 to 56 bit mantissa)\n

!need all
0.24999 99999 99999 993 e+0
0.69436 00015 11792 852 e-2
0.16520 33002 68279 130 e-4

0.50000 00000 00000 000 e+0
0.55553 86669 69001 188 e-1
0.49586 28849 05441 294 e-3


!msgpostfix Calculate exp from Cody & Waite (57 to 65 bit mantissa)\n

# 355.0/512.0
# -2.1219444005469058277e-4

!need all
# 0.25000 00000 00000 00000 e+0
 0.75753 18015 94227 76666 e-2
 0.31555 19276 56846 46356 e-4

# 0.50000 00000 00000 00000 e+0
 0.56817 30269 85512 21787 e-1
 0.63121 89437 43985 03557 e-3
 0.75104 02839 98700 46114 e-6


!msgpostfix Calculate ln/log from Cody & Waite (fixed-point mantissa <= 24 bits)\n

!need all
 0.06908 84357

 0.82908 97767
-0.12500 00000

!msgpostfix Calculate ln/log from Cody & Waite (fixed-point 25 to 32 bit mantissa)\n

!need all
 0.01360 09546 862

 0.04862 85276 587

 0.69735 92187 803
-0.12500 00000 000

!msgpostfix Calculate ln/log from Cody & Waite (fixed-point 33 to 48 bit mantissa)\n

!need all
 0.00444 45515 10980 33

 0.05523 07791 33055 91
-0.00889 05729 08757 20

 0.70010 94180 58381 82
-0.22363 05368 10708 18
 0.01562 50000 00000 00

!msgpostfix Calculate ln/log from Cody & Waite (25 to 32 bit mantissa)\n

!need all
-0.46490 62303 464 e+0
 0.13600 95468 621 e-1

-0.55788 73750 242 e+1
# 0.10000 00000 000 e+1

!msgpostfix Calculate ln/log from Cody & Waite (33 to 48 bit mantissa)\n

!need all
 0.37339 16896 31608 66 e+1
-0.63260 86623 38596 65 e+0
 0.44445 51510 98033 23 e-2

 0.44807 00275 57364 36 e+2
-0.14312 34535 58853 24 e+2
# 0.10000 00000 00000 00 e+1

!msgpostfix Calculate ln/log from Cody & Waite (49 to 60 bit mantissa)\n

# 355.0/512.0
# -2.121944400546905827679e-4

!need all
-0.64124 94342 37455 81147 e+2
 0.16383 94356 30215 34222 e+2
-0.78956 11288 74912 57267 e+0

-0.76949 93210 84948 79777 e+3
 0.31203 22209 19245 32844 e+3
-0.35667 97773 90346 46171 e+2
# 0.10000 00000 00000 00000 e+1


#!msgpostfix Calculate pow from Cody & Waite (fixed-point 25 to 36 bit mantissa)\n
#
#!need all
#0.00130 20832 59758
#0.00000 30533 41066
#
#
#!msgpostfix Calculate pow from Cody & Waite (fixed-point 37 to 50 bit mantissa)\n
#
#!need all
#0.00130 20833 33345 65
#0.00000 30517 57315 68
#0.00000 00085 21363 65


!msgpostfix Calculate pow from Cody & Waite (fixed-point mantissa <= 24 bits)\n

!need all
0.69314 675
0.24018 510
0.5436 038


!msgpostfix Calculate pow from Cody & Waite (fixed-point 25 to 45 bit mantissa)\n

!need all
0.69314 71805 56341
0.24022 65061 44710
0.05550 40488 13077
0.00961 62065 95838
0.00130 52551 59428


!msgpostfix Calculate pow from Cody & Waite (fixed-point 46 to 52 bit mantissa)\n

!need all
0.69314 71805 59937 815
0.24022 65069 56777 522
0.05550 41084 24756 866
0.00961 81176 91387 241
0.00133 30810 11340 821
0.00015 07740 61788 142

!msgpostfix Calculate pow from Cody & Waite (25 to 36 bit mantissa)\n

!need all
0.83333 32861 45 e-1
0.12506 48500 52 e-1

!msgpostfix Calculate pow from Cody & Waite (25 to 45 bit mantissa)\n

!need all
0.69314 71805 56341 e+0
0.24022 65061 44710 e+0
0.55504 04881 30765 e-1
0.96161 06595 83789 e-2
0.13052 55159 42810 e-2


!msgpostfix Calculate pow from Cody & Waite (37 to 50 bit mantissa)\n

!need all
0.83333 33333 41213 6 e-1
0.12499 99796 50060 8 e-1
0.22338 24352 81541 8 e-2

!msgpostfix Calculate pow from Cody & Waite (46 to 52 bit mantissa)\n

!need all
0.69314 71805 59937 815 e+0
0.24022 65069 56777 522 e+0
0.55504 10842 47568 661 e-1
0.96181 17691 38724 104 e-2
0.13330 81011 34082 075 e-2
0.15077 40617 88142 382 e-3

!msgpostfix Calculate pow from Cody & Waite (51 to 64 bit mantissa)\n

# 0.44269504088896340736e+0

!need all
0.83333 33333 33332 11405 e-1
0.12500 00000 05037 99174 e-1
0.22321 42128 59242 58967 e-2
0.43445 77567 21631 19635 e-3

!msgpostfix Calculate pow from Cody & Waite (53 to 64 bit mantissa)\n

!need all
0.69314 71805 59945 29629 e+0
0.24022 65069 59095 37056 e+0
0.55504 10866 40855 95326 e-1
0.96181 29059 51724 16964 e-2
0.13333 54131 35857 84703 e-2
0.15400 29044 09897 64601 e-3
0.14928 85268 05956 08186 e-4

# 0.10000000000000000e+1
#0.95760328069857365
#0.91700404320467114
#0.87812608018664963
#0.84089641525371447
#0.80524516597462714
#0.77110541270397030
#0.73841307296974960
#0.70710678118654755
#0.67712777346844630
#0.64841977732550475
#0.62092890603674195
#0.59460355750136049
#0.56939431737834578
#0.54525386633262877
#0.52213689121370681
# 0.50000000000000000

 
!msgpostfix e^x calculated using Taylors series (multiply)\n

!need all
#0.5000000000000000000000000000000000000000
0.1666666666666666666666666666666666666666
0.0416666666666666666666666666666666666666
0.0083333333333333333333333333333333333333
0.0013888888888888888888888888888888888888
0.0001984126984126984126984126984126984126
0.0000248015873015873015873015873015873015
0.0000027557319223985890652557319223985890
0.0000000001605904383682161459939237717015
0.0000000000114707455977297247138516979786


# The following are used to divide rather than multiple
# the appropriate power of x
!msgpostfix e^x calculated using Taylors series (divide)\n

!need all
6.0
24.0
120.0
720.0
5040.0
40320.0
362880.0
3628800.0
39916800.0
479001600.0
6227020800.0


!msgpostfix cos calculated using Taylors series\n

!need all
-0.5000000000000000000000000000000000000000
 0.0416666666666666666666666666666666666666
-0.0013888888888888888888888888888888888888
 0.0000248015873015873015873015873015873015
-0.0000002755731922398589065255731922398589
 0.0000000020876756987868098979210090321201
#-0.0000000000114707455977297247138516979786 | 1/14!


# The following are used to divide rather than multiple
# the appropriate power of x
!msgpostfix cos calculated using Taylors series\n

!need all
 24.0
-720.0
 40320.0
-3628800.0
 479001600.0

!msgpostfix sin calculated using Taylors series\n

!need all
-0.1666666666666666666666666666666666666666
 0.0083333333333333333333333333333333333333
-0.0001984126984126984126984126984126984126
 0.0000027557319223985890652557319223985890
-0.0000000250521083854417187750521083854417
#-0.0000000001605904383682161459939237717015 | 1/13!

# The following are used to divide rather than multiple
# the appropriate power of x
!msgpostfix sin calculated using Taylors series\n

!need all
-6.0
 120.0
-5040.0
 362880.0
-39916800.0
 6227020800.0

!msgpostfix cosh calculated using Taylors series\n

!need all
#0.5000000000000000000000000000000000000000
0.0416666666666666666666666666666666666666
0.0013888888888888888888888888888888888888
0.0000248015873015873015873015873015873015
0.0000002755731922398589065255731922398589
0.0000000020876756987868098979210090321201
#0.0000000000114707455977297247138516979786 | 1/14!


# The following are used to divide rather than multiple
# the appropriate power of x
!msgpostfix cosh calculated using Taylors series\n

!need all
24.0
720.0
40320.0
3628800.0
479001600.0

!msgpostfix sinh calculated using Taylors series\n

!need all
0.1666666666666666666666666666666666666666
0.0083333333333333333333333333333333333333
0.0001984126984126984126984126984126984126
0.0000027557319223985890652557319223985890
0.0000000250521083854417187750521083854417
#0.0000000001605904383682161459939237717015 | 1/13!


# The following are used to divide rather than multiple
# the appropriate power of x
!msgpostfix sinh calculated using Taylors series\n

!need all
6.0
120.0
5040.0
362880.0
39916800.0
6227020800.0
1307674368000.0
355687428096000.0


!fuzz 0.00000001


# Pade' coefficients for exp(x) - 1
# [A similar the approach used to calculate  e^x-1]
#  Theoretical peak relative error = 2.2e-37,
#  relative peak error spread = 9.2e-38
# 128-bit accuracy
# Cephes Math Library Release 2.2:  December, 1990

!msgpostfix Calculate exp(x), Cephes math library\n
 
!need all
 3.279723985560247033712687707263393506266E-10
 6.141506007208645008909088812338454698548E-7
 2.708775201978218837374512615596512792224E-4
 3.508710990737834361215404761139478627390E-2
 9.999999999999999999999999999999999998502E-1

 2.980756652081995192255342779918052538681E-12
 1.771372078166251484503904874657985291164E-8
 1.504792651814944826817779302637284053660E-5
 3.611828913847589925056132680618007270344E-3
 2.368408864814233538909747618894558968880E-1
 2.000000000000000000000000000000000000150E0

# Range reduction is accomplished by separating the argument
# into an integer k and fraction f such that 
# 
#  x    k  f
# e  = 2  e.
# 
# An expansion x + .5 x^2 + x^3 R(x) approximates exp(f) - 1
# in the basic range [-0.5 ln 2, 0.5 ln 2].
# 128-bit accuracy
# Cephes Math Library Release 2.9:  April, 2001

!msgpostfix Calculate exp(x)-1, Cephes math library\n
 
!need all
 2.943520915569954073888921213330863757240E8
-5.722847283900608941516165725053359168840E7
 8.944630806357575461578107295909719817253E6
-7.212432713558031519943281748462837065308E5
 4.578962475841642634225390068461943438441E4
-1.716772506388927649032068540558788106762E3
 4.401308817383362136048032038528753151144E1
-4.888737542888633647784737721812546636240E-1

 1.766112549341972444333352727998584753865E9
-7.848989743695296475743081255027098295771E8
 1.615869009634292424463780387327037251069E8
-2.019684072836541751428967854947019415698E7
 1.682912729190313538934190635536631941751E6
-9.615511549171441430850103489315371768998E4
 3.697714952261803935521187272204485251835E3
-8.802340681794263968892934703309274564037E1
# Q8 = 1.000000000000000000000000000000000000000E0 */

# C1 + C2 = ln 2 */
 6.93145751953125E-1
 1.428606820309417232121458176568075500134E-6
# ln 2^-114 */
-7.9018778583833765273564461846232128760607E1


# 128-bit accuracy
# Cephes Math Library Release 2.2:  January, 1991
# If |x| < 0.5, the function is approximated by a rational
# form  x + x**3 P(x)/Q(x).  Otherwise,
# 
# asinh(x) = log( x + sqrt(1 + x*x) ).
 
# arcsinh(x) = x + x^3 R(x^2)
# Theoretical peak relative error = 8.4e-36
# relative peak error spread = 1.4e-7

!msgpostfix Calculate asinh(x), Cephes math library\n
 
!need all
-8.104404283317298189545629468767571317688E-1
-4.954206127425209147110732546633675599008E1
-8.438175619831548439550086251740438689853E2
-6.269710069245210459536983820505214648057E3
-2.418935474493501382372711518024193326434E4
-5.208121780431312783866941311277024486498E4
-6.302755086521614763280617114866439227971E4
-4.003566436224198252093684987323233921339E4
-1.037690841528359305134494613113086980551E4

# 1.000000000000000000000000000000000000000E0 */
 8.175806439951395194771977809279448392548E1
 1.822215299975696008284027212745010251320E3
 1.772040003462901790853111853838978236828E4
 9.077625379864046240143413577745818879353E4
 2.675554475070211205153169988669677418808E5
 4.689758557916492969463473819426544383586E5
 4.821923684550711724710891114802924039911E5
 2.682316388947175963642524537892687560973E5
 6.226145049170155830806967678679167550122E4

# acoshl domain |x| < 1
# 128-bit accuracy
# Cephes Math Library Release 2.2:  January, 1991

!msgpostfix Calculate acosh(x), Cephes math library\n
 
!need all
 1.895467874386341763387398084072833727168E-1
 6.443902084393244878979969557171256604767E1
 3.914593556594721458616408528941154205393E3
 9.164040999602964494412169748897754668733E4
 1.065909694792026382660307834723001543839E6
 6.899169896709615182428217047370629406305E6
 2.599781868717579447900896150777162652518E7
 5.663733059389964024656501196827345337766E7
 6.606302846870644033621560858582696134512E7
 3.190482951215438078279772140481195200593E7

# 1.000000000000000000000000000000000000000E0 */
 1.635418024331924674147953764918262009321E2
 7.290983678312632723073455563799692165828E3
 1.418207894088607063257675159183397062114E5
 1.453154285419072886840913424715826321357E6
 8.566841438576725234955968880501739464425E6
 3.003448667795089562511136059766833630017E7
 6.176592872899557661256383958395266919654E7
 6.872176426138597206811541870289420510034E7
 3.190482951215438078279772140481195226621E7


# 128-bit accuracy
# Cephes Math Library Release 2.2:  January, 1991
# atanh(x) = x + x^3 R(x^2)
# Theoretical peak relative error = 7.0e-37
# relative peak error spread = 2.7e-6

!msgpostfix Calculate atanh(x), Cephes math library\n
 
!need all
-9.217569843805850417698565442251656375681E-1
 5.321929116410615470118183794063211260728E1
-9.139522976807685333981548145417830690552E2
 7.204314536952949779101646454146682033772E3
-3.097809640165146436529075324081668598891E4
 7.865376554210973897486215630898496100534E4
-1.211716814094785128366087489224821937203E5
 1.112669508789123834670923967462068457013E5
-5.600242872292477863751728708249167956542E4
 1.188901082233997739779618679364295772810E4

# 1.000000000000000000000000000000000000000E0 */
-6.807348436010016270202879229504392062418E1
 1.386763299649315831625106608182196351693E3
-1.310805752656879543134785263832907269320E4
 6.872174720355764193772953852564737816928E4
-2.181008360536226513009076189881617939380E5
 4.362736119602298592874941767284979857248E5
-5.535251007539393347687001489396152923502E5
 4.321594849688346708841188057241308805551E5
-1.894075056489862952285849974761239845873E5
 3.566703246701993219338856038092901974725E4


# sinhl domain |x| < 1
# 128-bit accuracy
# Cephes Math Library Release 2.2:  January, 1991

!msgpostfix Calculate sinh(x), Cephes math library\n
 
!need all
 1.622194395724068297909052717437740288268E3
 1.124862584587770079742188354390171794549E6
 3.047548980769660162696832999871894196102E8
 3.966215348072348368191433063260384329745E10
 2.375869584584371194838551715348965605295E12
 6.482835792103233269752264509192030816323E13

# 1.000000000000000000000000000000000000000E0 */
-9.101683853129357776079049616394849086007E2
 4.486400519836461218634448973793765123186E5
-1.492531313030440305095318968983514314656E8
 3.457771488856930054902696708717192082887E10
-5.193289868803472640225483235513427062460E12
 3.889701475261939961851358705515223019890E14


# 128-bit accuracy
# Cephes Math Library Release 2.1:  February, 1989
# A rational function is used for |x| < 0.625.  The form
# x + x**3 P(x)/Q(x) of Cody _& Waite is employed.
# Otherwise,   
# tanh(x) = sinh(x)/cosh(x) = 1  -  2/(exp(2x) + 1).

# tanh(x) = x + x^3 R(x^2)
# 0 <= x <= 0.625
# Theoretical peak relative error = 7.7e-37,
# relative peak error spread = 3.9e-11
!msgpostfix Calculate tanh(x), Cephes math library\n
 
!need all
-6.505693197948351084912624750702492767503E-6
-9.804083860188429726356968570322356183383E-1
-5.055287638900473250703725789725376004355E2
-7.307477148073823966594990496301416814519E4
-3.531606586182691280701462523692471322688E6
-4.551377146142783468144190926206842300707E7

# 1.000000000000000000000000000000000000000E0 */
 5.334865598460027935735737253027154828002E2
 8.058475607422391042912151298751537172870E4
 4.197073523796142343374222405869721575491E6
 6.521134551226147545983467868553677881771E7
 1.365413143842835040443257277862054198329E8


# 128-bit accuracy
# Cephes Math Library Release 2.2:  January, 1991

# sin(x) = x + x^3 P(x^2)
# Theoretical peak relative error = 5.6e-39
# relative peak error spread = 1.7e-9

!msgpostfix Calculate sin(x), Cephes math library\n
 
!need all
 6.410290407010279602425714995528976754871E-26
-3.868105354403065333804959405965295962871E-23
 1.957294039628045847156851410307133941611E-20
-8.220635246181818130416407184286068307901E-18
 2.811457254345322887443598804951004537784E-15
-7.647163731819815869711749952353081768709E-13
 1.605904383682161459812515654720205050216E-10
-2.505210838544171877505034150892770940116E-8
 2.755731922398589065255731765498970284004E-6
-1.984126984126984126984126984045294307281E-4
 8.333333333333333333333333333333119885283E-3
-1.666666666666666666666666666666666647199E-1

7.853981633974483067550664827649598009884357452392578125E-1
2.8605943630549158983813312792950660807511260829685741796657E-18
2.1679525325309452561992610065108379921905808E-35

# cos(x) = 1 - .5 x^2 + x^2 (x^2 P(x^2))
# Theoretical peak relative error = 2.1e-37,
# relative peak error spread = 1.4e-8

!msgpostfix Calculate cos(x), Cephes math library\n
 
!need all
 1.601961934248327059668321782499768648351E-24
-8.896621117922334603659240022184527001401E-22
 4.110317451243694098169570731967589555498E-19
-1.561920696747074515985647487260202922160E-16
 4.779477332386900932514186378501779328195E-14
-1.147074559772972328629102981460088437917E-11
 2.087675698786809897637922200570559726116E-9
-2.755731922398589065255365968070684102298E-7
 2.480158730158730158730158440896461945271E-5
-1.388888888888888888888888888765724370132E-3
 4.166666666666666666666666666666459301466E-2

7.853981633974483067550664827649598009884357452392578125E-1
2.8605943630549158983813312792950660807511260829685741796657E-18
2.1679525325309452561992610065108379921905808E-35

# 128-bit accuracy
# Cephes Math Library Release 2.2:  December, 1990
# tan(x) = x + x^3 P(x^2)
# 0 <= |x| <= pi/4
# Theoretical peak relative error = 4.3e-38
# relative peak error spread = 6.1e-11

!msgpostfix Calculate tan(x), Cephes math library\n
 
!need all
-9.889929415807650724957118893791829849557E-1
 1.272297782199996882828849455156962260810E3
-4.249691853501233575668486667664718192660E5
 5.160188250214037865511600561074819366815E7
-2.307030822693734879744223131873392503321E9
 2.883414728874239697964612246732416606301E10

# 1.000000000000000000000000000000000000000E0 */
-1.317243702830553658702531997959756728291E3
 4.529422062441341616231663543669583527923E5
-5.733709132766856723608447733926138506824E7
 2.758476078803232151774723646710890525496E9
-4.152206921457208101480801635640958361612E10
 8.650244186622719093893836740197250197602E10

7.853981633974483067550664827649598009884357452392578125E-1
2.8605943630549158983813312792950660807511260829685741796657E-18
2.1679525325309452561992610065108379921905808E-35


# 128-bit accuracy
# Cephes Math Library Release 2.2:  December, 1990
# A rational function of the form x + x**3 P(x**2)/Q(x**2)
# is used for |x| in the interval [0, 0.5].  If |x| > 0.5 it is
# transformed by the identity
# 
# asin(x) = pi/2 - 2 asin( sqrt( (1-x)/2 ) ).
# arcsin(x) = x + x^3 R(x^2)
# Theoretical peak relative error = 3.1e-37
# relative peak error spread = 9.4e-6
#
# Analytically, acos(x) = pi/2 - asin(x).  However if |x| is
# near 1, there is cancellation error in subtracting asin(x)
# from pi/2.  Hence if x < -0.5,
# 
# acos(x) =  pi - 2.0 * asin( sqrt((1+x)/2) );
# 
# or if x > +0.5,
# 
# acos(x) =  2.0 * asin(  sqrt((1-x)/2) ).

!msgpostfix Calculate asin/acos(x), Cephes math library\n
 
!need all
-8.067112765482705313585175280952515549833E-1
 4.845649797786849136525020822000172350977E1
-8.510195404865297879959793548843395926847E2
 6.815196841370292688574521445731895826485E3
-2.967135182120339728996157454994675519735E4
 7.612250656518818109652985996692466409670E4
-1.183360579752620455689557157684221905030E5
 1.095432262510413338755837156377401348063E5
-5.554124580991113991999636773382495788705E4
 1.187132626694762543537732514905488896985E4

#  1.000000000000000000000000000000000000000E0 */
-8.005471061732009595694099899234272342478E1
 1.817324228942812880965069608562483918025E3
-1.867017317425756524289537002141956583706E4
 1.048196619402464497478959760337779705622E5
-3.527040897897253459022458866536165564103E5
 7.426302422018858001691440351763370029242E5
-9.863068411558756277454631976667880674474E5
 8.025654653926121907774766642393757364326E5
-3.653000557802254281954969843055623398839E5
 7.122795760168575261226395089432959614179E4


# 128-bit accuracy
# Cephes Math Library Release 2.2:  January, 1991
# Returns radian angle between -pi/2 and +pi/2 whose tangent
# is x.
# 
# Range reduction is from four intervals into the interval
# from zero to  tan( pi/8 ).  The approximant uses a rational
# function of degree 3/4 of the form x + x**3 P(x)/Q(x).

# atanh(x) = x + x^3 R(x^2)
# Theoretical peak relative error = 7.0e-37
# relative peak error spread = 2.7e-6

# arctan(x) = x + x^3 P(x^2)
# Theoretical peak relative error = 3.0e-36
# relative peak error spread = 6.6e-8

!msgpostfix Calculate atan(x), Cephes math library\n
 
!need all
-6.635810778635296712545011270011752799963E-4
-8.768423468036849091777415076702113400070E-1
-2.548067867495502632615671450650071218995E1
-2.497759878476618348858065206895055957104E2
-1.148164399808514330375280133523543970854E3
-2.792272753241044941703278827346430350236E3
-3.696264445691821235400930243493001671932E3
-2.514829758941713674909996882101723647996E3
-6.880597774405940432145577545328795037141E2

# 1.000000000000000000000000000000000000000E0 */
 3.566239794444800849656497338030115886153E1
 4.308348370818927353321556740027020068897E2
 2.494680540950601626662048893678584497900E3
 7.928572347062145288093560392463784743935E3
 1.458510242529987155225086911411015961174E4
 1.547394317752562611786521896296215170819E4
 8.782996876218210302516194604424986107121E3
 2.064179332321782129643673263598686441900E3
 
# tan( 3*pi/8 ) */
2.414213562373095048801688724209698078569672
# tan( pi/8 ) */
0.414213562373095048801688724209698078569672


# 128-bit accuracy
# Cephes Math Library Release 2.2:  January, 1991
# for log(x) = z + z^3 P(z^2)/Q(z^2),
# where z = 2(x-1)/(x+1)
# 1/sqrt(2) <= x < sqrt(2)
# Theoretical peak relative error = 1.1e-35,
# relative peak error spread 1.1e-9 

!msgpostfix Calculate log(x), Cephes math library\n
 
!need all
-8.828896441624934385266096344596648080902E-1
 8.057002716646055371965756206836056074715E1
-2.024301798136027039250415126250455056397E3
 2.048819892795278657810231591630928516206E4
-8.977257995689735303686582344659576526998E4
 1.418134209872192732479751274970992665513E5

# 1.000000000000000000000000000000000000000E0 */
-1.186359407982897997337150403816839480438E2
 3.998526750980007367835804959888064681098E3
-5.748542087379434595104154610899551484314E4
 4.001557694070773974936904547424676279307E5
-1.332535117259762928288745111081235577029E6
 1.701761051846631278975701529965589676574E6

6.93145751953125E-1
1.428606820309417232121458176568075500134E-6
0.7071067811865475244008443621048490392848


# 128-bit accuracy
# Cephes Math Library Release 2.2:  January, 1991
# Also uses tables for log(x) and log(x+1)
# which are not listed below

!msgpostfix Calculate base-10 log(x), Cephes math library\n
 
!need all
# log10(2) */
 0.3125
-1.14700043360188047862611052755069732318101185E-2
# log10(e) */
 0.5
-6.570551809674817234887108108339491770560299E-2
 0.7071067811865475244008443621048490392848359


# 128-bit accuracy
# Cephes Math Library Release 2.2:  December, 1990
# Coefficients for log(1+x) = x - x**2/2 + x**3 P(x)/Q(x)
# 1/sqrt(2) <= 1+x < sqrt(2)
# Theoretical peak relative error = 5.3e-37,
# relative peak error spread = 2.3e-14

!msgpostfix Calculate log(x+1), Cephes math library\n
 
!need all
 1.538612243596254322971797716843006400388E-6
 4.998469661968096229986658302195402690910E-1
 2.321125933898420063925789532045674660756E1
 4.114517881637811823002128927449878962058E2
 3.824952356185897735160588078446136783779E3
 2.128857716871515081352991964243375186031E4
 7.594356839258970405033155585486712125861E4
 1.797628303815655343403735250238293741397E5
 2.854829159639697837788887080758954924001E5
 3.007007295140399532324943111654767187848E5
 2.014652742082537582487669938141683759923E5
 7.771154681358524243729929227226708890930E4
 1.313572404063446165910279910527789794488E4

# 1.000000000000000000000000000000000000000E0 */
 4.839208193348159620282142911143429644326E1
 9.104928120962988414618126155557301584078E2
 9.147150349299596453976674231612674085381E3
 5.605842085972455027590989944010492125825E4
 2.248234257620569139969141618556349415120E5
 6.132189329546557743179177159925690841200E5
 1.158019977462989115839826904108208787040E6
 1.514882452993549494932585972882995548426E6
 1.347518538384329112529391120390701166528E6
 7.777690340007566932935753241556479363645E5
 2.626900195321832660448791748036714883242E5
 3.940717212190338497730839731583397586124E4


!msgpostfix log-10(x), 10^(-1/2) <= x <= 10^(1/2), error <= 1e-7, from Abramowitz and Stegun 4.1.42\n

!need all
0.868591718
0.289335524
0.177522071
0.094376476
0.191337714


!msgpostfix log-10(x), error < 1 ulp, from SunPro 1995\n

!need all
6.666666666666735130e-01
3.999999999940941908e-01
2.857142874366239149e-01
2.222219843214978396e-01
1.818357216161805012e-01
1.531383769920937332e-01
1.479819860511658591e-01


# 128-bit accuracy
# Cephes Math Library Release 2.2:  January, 1991
# Range reduction is accomplished by expressing the argument
# as 10**x = 2**n 10**f, with |f| < 0.5 log10(2).
# The Pade' form
# 
# 1 + 2x P(x**2)/( Q(x**2) - P(x**2) )

!msgpostfix Calculate 10^x, Cephes math library\n
 
!need all
 6.781965388610215141646963666801877147888E1
 4.930988843306627886355612005613845141123E4
 9.112966716416345527154611203937593471620E6
 5.880306836049276068401249115246879608067E8
 1.294143447497151402129871056524193102276E10
 6.737236378815985929063482575381049393067E10

# 1.000000000000000000000000000000000000000E0 */
 2.269602544366008200564158516293459788943E3
 7.712352920905011963059413773034169405418E5
 8.312829542416079818945631366865677745737E7
 3.192530874297321568824835872165913128965E9
 3.709588725051672862074295071447979432510E10
 5.851889165195258152098281616369230806944E10

3.321928094887362347870319429489390175864831
3.01025390625e-1
4.6050389811952137388947244930267681898814621E-6
4.932075448958667902381898051166093750570023E3


!msgpostfix 10^x, 0 <= x <= 1, error <= 5e-8, from Abramowitz and Stegun 4.2.47\n

!need all
1.15129277603
0.66273088429
0.25439357484
0.07295173666
0.01742111988
0.00255491796
0.00093264267


# 128-bit accuracy
# Cephes Math Library Release 2.2:  December, 1990

!msgpostfix Calculate square root, Cephes math library\n
 
!need all
-0.20440583154734771959904
 0.89019407351052789754347
 0.31356706742295303132394

1.4142135623730950488017E0


# 128-bit accuracy
# Cephes Math Library Release 2.2:  January, 1991
# Computes x raised to the yth power.  Analytically,
# 
# x**y  =  exp( y log(x) ). 
# 
# Following Cody and Waite, this program uses a lookup table
# of 2**-i/32 and pseudo extended precision arithmetic to
# obtain several extra bits of accuracy in both the logarithm
# and the exponential.

!msgpostfix Calculate x^y, Cephes math library\n
 
!need all
 8.3319510773868690346226E-4
 4.9000050881978028599627E-1
 1.7500123722550302671919E0
 1.4000100839971580279335E0

# 1.0000000000000000000000E0*/
 5.2500282295834889175431E0
 8.4000598057587009834666E0
 4.2000302519914740834728E0

# A[i] = 2^(-i/32), rounded to IEEE long double precision.
# If i is even, A[i] + B[i/2] gives additional accuracy.
# 1.0000000000000000000000E0
 9.7857206208770013448287E-1
 9.5760328069857364691013E-1
 9.3708381705514995065011E-1
 9.1700404320467123175367E-1
 8.9735453750155359320742E-1
 8.7812608018664974155474E-1
 8.5930964906123895780165E-1
 8.4089641525371454301892E-1
 8.2287773907698242225554E-1
 8.0524516597462715409607E-1
 7.8799042255394324325455E-1
 7.7110541270397041179298E-1
 7.5458221379671136985669E-1
 7.3841307296974965571198E-1
 7.2259040348852331001267E-1
 7.0710678118654752438189E-1
 6.9195494098191597746178E-1
 6.7712777346844636413344E-1
 6.6261832157987064729696E-1
 6.4841977732550483296079E-1
 6.3452547859586661129850E-1
 6.2092890603674202431705E-1
 6.0762367999023443907803E-1
 5.9460355750136053334378E-1
 5.8186242938878875689693E-1
 5.6939431737834582684856E-1
 5.5719337129794626814472E-1
 5.4525386633262882960438E-1
 5.3357020033841180906486E-1
 5.2213689121370692017331E-1
 5.1094857432705833910408E-1
 5.0000000000000000000000E-1

# 0.0000000000000000000000E0
 2.6176170809902549338711E-20
-1.0126791927256478897086E-20
 1.3438228172316276937655E-21
 1.2207982955417546912101E-20
-6.3084814358060867200133E-21
 1.3164426894366316434230E-20
-1.8527916071632873716786E-20
 1.8950325588932570796551E-20
 1.5564775779538780478155E-20
 6.0859793637556860974380E-21
-2.0208749253662532228949E-20
 1.4966292219224761844552E-20
 3.3540909728056476875639E-21
-8.6987564101742849540743E-22
-1.2327176863327626135542E-20
# 0.0000000000000000000000E0

# 2^x = 1 + x P(x),
# on the interval -1/32 <= x <= 0
 1.5089970579127659901157E-5
 1.5402715328927013076125E-4
 1.3333556028915671091390E-3
 9.6181291046036762031786E-3
 5.5504108664798463044015E-2
 2.4022650695910062854352E-1
 6.9314718055994530931447E-1


!msgpostfix x^y, nearly rounded, from SunPro 1995\n

!need all
5.99999999999994648725e-01
4.28571428578550184252e-01
3.33333329818377432918e-01
2.72728123808534006489e-01
2.30660745775561754067e-01
2.06975017800338417784e-01

 1.66666666666666019037e-01
-2.77777777770155933842e-03
 6.61375632143793436117e-05
-1.65339022054652515390e-06
 4.13813679705723846039e-08

8.0085662595372944372e-017
9.61796693925975554329e-01


# 128-bit accuracy
# Cephes Math Library Release 2.2:  January, 1991
# The argument is separated into its exponent and fractional
# parts.  If the exponent is between -1 and +1, the (natural)
# logarithm of the fraction is approximated by
# 
# log(1+x) = x - 0.5 x**2 + x**3 P(x)/Q(x).
# 
# Otherwise, setting  z = 2(x-1)/x+1),
# 
# log(x) = z + z**3 P(z)/Q(z).

# 1/sqrt(2) <= x < sqrt(2)
# Theoretical peak relative error = 5.3e-37,
# relative peak error spread = 2.3e-14

!msgpostfix Calculate base-2 log(x), Cephes math library\n
 
!need all
 1.538612243596254322971797716843006400388E-6
 4.998469661968096229986658302195402690910E-1
 2.321125933898420063925789532045674660756E1
 4.114517881637811823002128927449878962058E2
 3.824952356185897735160588078446136783779E3
 2.128857716871515081352991964243375186031E4
 7.594356839258970405033155585486712125861E4
 1.797628303815655343403735250238293741397E5
 2.854829159639697837788887080758954924001E5
 3.007007295140399532324943111654767187848E5
 2.014652742082537582487669938141683759923E5
 7.771154681358524243729929227226708890930E4
 1.313572404063446165910279910527789794488E4

# 1.000000000000000000000000000000000000000E0 */
 4.839208193348159620282142911143429644326E1
 9.104928120962988414618126155557301584078E2
 9.147150349299596453976674231612674085381E3
 5.605842085972455027590989944010492125825E4
 2.248234257620569139969141618556349415120E5
 6.132189329546557743179177159925690841200E5
 1.158019977462989115839826904108208787040E6
 1.514882452993549494932585972882995548426E6
 1.347518538384329112529391120390701166528E6
 7.777690340007566932935753241556479363645E5
 2.626900195321832660448791748036714883242E5
 3.940717212190338497730839731583397586124E4

4.4269504088896340735992468100189213742664595E-1
7.071067811865475244008443621048490392848359E-1


# Coefficients for log(x) = z + z^3 P(z^2)/Q(z^2),
# where z = 2(x-1)/(x+1)
# 1/sqrt(2) <= x < sqrt(2)
# Theoretical peak relative error = 1.1e-35,
# relative peak error spread 1.1e-9
-8.828896441624934385266096344596648080902E-1
 8.057002716646055371965756206836056074715E1
-2.024301798136027039250415126250455056397E3
 2.048819892795278657810231591630928516206E4
-8.977257995689735303686582344659576526998E4
 1.418134209872192732479751274970992665513E5

# 1.000000000000000000000000000000000000000E0 */
-1.186359407982897997337150403816839480438E2
 3.998526750980007367835804959888064681098E3
-5.748542087379434595104154610899551484314E4
 4.001557694070773974936904547424676279307E5
-1.332535117259762928288745111081235577029E6
 1.701761051846631278975701529965589676574E6


# 128-bit accuracy
# Cephes Math Library Release 2.2:  January, 1991
# Range reduction is accomplished by separating the argument
# into an integer k and fraction f such that
#  x    k  f
# 2  = 2  2.
# 
# A Pade' form
# 
# 1 + 2x P(x**2) / (Q(x**2) - x P(x**2) )
# 
# approximates 2**x in the basic range [-0.5, 0.5].

!msgpostfix Calculate 2^x, Cephes math library\n
 
!need all
# Pade' coefficients for 2^x - 1
# Theoretical peak relative error = 1.4e-40,
# relative peak error spread = 6.8e-14
 1.587171580015525194694938306936721666031E2
 6.185032670011643762127954396427045467506E5
 5.677513871931844661829755443994214173883E8
 1.530625323728429161131811299626419117557E11
 9.079594442980146270952372234833529694788E12

# 1.000000000000000000000000000000000000000E0 */
 1.236602014442099053716561665053645270207E4
 2.186249607051644894762167991800811827835E7
 1.092141473886177435056423606755843616331E10
 1.490560994263653042761789432690793026977E12
 2.619817175234089411411070339065679229869E13


!fuzz 0.000000000001
!msgpostfix Argument reduction to within range +/-pi/4\n

!need all
3.14159265160560607910E0
1.98418714791870343106E-9
1.14423774522196636802E-17

!msgpostfix Minimax 5th-degree polynomial fit of 2^x in range [0, 1[\n

!need all
0.999999999690134838155
0.583974334321735217258
0.164553105719676828492
0.0292811063701710962255
0.00354944426657875141846
0.000296253726543423377365

!msgpostfix Minimax 5th-degree polynomial single-precision fit of 2^x in range [-0.5, 0.5[\n

!need all
9.9999994e-1
6.9315308e-1
2.4015361e-1
5.5826318e-2
8.9893397e-3
1.8775767e-3

!msgpostfix sin/cos evaluation, Intel approximate maths library\n

!need all
 0.15707963267948963959e1
-0.64596409750621907082e0
 0.7969262624561800806e-1
-0.468175413106023168e-2

!msgpostfix tan evaluation, Intel approximate maths library\n

!need all
-1.79565251976484877988e7
 1.15351664838587416140e6
-1.30936939181383777646e4

-5.38695755929454629881e7
 2.50083801823357915839e7
-1.32089234440210967447e6
 1.36812963470692954678e4

 3.68935e19

!msgpostfix atan evaluation, Intel approximate maths library\n

!need all
-0.91646118527267623468e-1
-0.13956945682312098640e1
-0.94393926122725531747e2
 0.12888383034157279340e2

0.12797564625607904396e1
0.21972168858277355914e1
0.68193064729268275701e1
0.28205206687035841409e2


!msgpostfix exp evaluation, Intel approximate maths library\n

!need all
 88.3762626647949
-88.3762626647949

1.4426950408889634073599

1.26177193074810590878e-4
3.02994407707441961300e-2

3.00198505138664455042e-6
2.52448340349684104192e-3
2.27265548208155028766e-1
2.00000000000000000009e0

6.93145751953125e-1
1.42860682030941723212e-6

!msgpostfix exp base-2 evaluation, Intel approximate maths library\n

!need all
 127.4999961853
-127.4999961853

2.30933477057345225087e-2
2.02020656693165307700e1
1.51390680115615096133e3

2.33184211722314911771e2
4.36821166879210612817e3

!msgpostfix log evaluation, Intel approximate maths library\n

!need all
-7.89580278884799154124e-1
 1.63866645699558079767e1
-6.41409952958715622951e1

-3.56722798256324312549e1
 3.12093766372244180303e2
-7.69691943550460008604e2

0.693147180559945

