Bioequivalence and Bioavailability Forum • ... full precision is the question

... full precision is the question [🇷 for BE/BA]

posted by Helmut – Vienna, Austria, 2011-01-17 19:06 (5228 d 11:27 ago) – Posting: # 6434
Views: 32,253

Dear D. Labes,

THX for supporting an ol’ fart.

❝ BTW: R

❝ > options(digits=30)

❝ Error in options(digits = 30) :

❝ invalid 'digits' parameter, allowed 1...22

❝ > options(digits=22)

❝ > pi

❝ [1] 3.141592653589793

❝ # only 16 digits!

Right. Interesting, that signif doesn’t throw an error for values > 22.
options(signif=32)
However

pi

[1] 3.141592653589793

Doesn’t really surprise me; that’s the numeric resolution of my 32 bit XP; I guess you have one of these fancy 64 bit operating systems?
There’s a package for R being able to handle floating point operations in arbitrary precision – essentially by converting all numbers to character strings. :-D

❝ I have learned in my early days during learning draftsman in agrar melioration engineering that 22/7=3.142857 is an good estimate. Very near to your 3.14! Maybe there were not so much circles involved, but more triangles and rectangles :-D .

Yes, I’ve learned that one also. Another one is Archimedes’: 3+10/71 < π < 3+10/70 (the upper limit is your’s; the mean is just 0.008% off). Not so bad for 250 BCE!
Maniacs might click here or there.

Fascinating that calc.exe comes up with:
Pi 3.1415926535897932384626433832795
Maybe it’s stored somewhere? Let’s try a true calculation:
[o] Rad 1 [x] Inv tan
0.78539816339744830961566084581988
* 4 =
3.1415926535897932384626433832795
Amazing. According to the online help calculations are performed in 32 digit precision.
- Pi =
-1.393267707463821448075635979701e-37
Gotcha!

If you have Java onboard, a true overkill for nerds (calling a Java implementation of Python ‘Jython’, library sympy for symbolic mathematics from R):

require(rSymPy)

sympy("pi.evalf(1000)")

[1]  "3.141 592 653 589 793 238 462 643 383 279 502 884 197 169 399 375 105 820 974 944 592 307 816 406 286 208 998 628 034 825 342 117 067 982 148 086 513 282 306 647 093 844 609 550 582 231 725 359 408 128 481 117 450 284 102 701 938 521 105 559 644 622 948 954 930 381 964 428 810 975 665 933 446 128 475 648 233 786 783 165 271 201 909 145 648 566 923 460 348 610 454 326 648 213 393 607 260 249 141 273 724 587 006 606 315 588 174 881 520 920 962 829 254 091 715 364 367 892 590 360 011 330 530 548 820 466 521 384 146 951 941 511 609 433 057 270 365 759 591 953 092 186 117 381 932 611 793 105 118 548 074 462 379 962 749 567 351 885 752 724 891 227 938 183 011 949 129 833 673 362 440 656 643 086 021 394 946 395 224 737 190 702 179 860 943 702 770 539 217 176 293 176 752 384 674 818 467 669 405 132 000 568 127 145 263 560 827 785 771 342 757 789 609 173 637 178 721 468 440 901 224 953 430 146 549 585 371 050 792 279 689 258 923 542 019 956 112 129 021 960 864 034 418 159 813 629 774 771 309 960 518 707 211 349 999 998 372 978 049 951 059 731 732 816 096 318 595 024 459 455 346 908 302 642 522 308 253 344 685 035 261 931 188 171 010 003 137 838 752 886 587 533 208 381 420 617 177 669 147 303 598 253 490 428 755 468 731 159 562 863 882 353 787 593 751 957 781 857 780 532 171 226 806 613 001 927 876 611 195 909 216 420 198"

Wow!

Remember that one?

factorial(170)

[1] 7.25741561530888e+306

factorial(171)

[1] Inf

Warning:

In factorial(171) : Value out of range in 'gammafn'

But:

sympy("factorial(170)")

[1]  "7 257 415 615 307 998 967 396 728 211 129 263 114 716 991 681 296 451 376 543 577 798 900 561 843 401 706 157 852 350 749 242 617 459 511 490 991 237 838 520 776 666 022 565 442 753 025 328 900 773 207 510 902 400 430 280 058 295 603 966 612 599 658 257 104 398 558 294 257 568 966 313 439 612 262 571 094 946 806 711 205 568 880 457 193 340 212 661 452 800 000 000 000 000 000 000 000 000 000 000 000 000 000"

sympy("factorial(171)")

[1]  "1 241 018 070 217 667 823 424 840 524 103 103 992 616 605 577 501 693 185 388 951 803 611 996 075 221 691 752 992 751 978 120 487 585 576 464 959 501 670 387 052 809 889 858 690 710 767 331 242 032 218 484 364 310 473 577 889 968 548 278 290 754 541 561 964 852 153 468 318 044 293 239 598 173 696 899 657 235 903 947 616 152 278 558 180 061 176 365 108 428 800 000 000 000 000 000 000 000 000 000 000 000 000 000"

(stopped testing at 100 000! – lots of digits)

—
Dif-tor heh smusma 🖖🏼 Довге життя Україна!
Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. 🚮
Science Quotes

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