Programowanie w systemie UNIX/ARB
Arb [1]
właściwości[edytuj]
Arb is a C library
- automatic error bound tracking to get an output that is guaranteed to be accurate, no error analysis needs to be done by the user
- interval arithemtic : midpoint-radius arithmetic = ball arithmetic
- a midpoint-radius (ball) representation of real numbers
- arbitrary precision arithmetic
Instalacja[edytuj]
Wymagania[edytuj]
- gmp
- mpfr
- flint
- python
- sphinx-build (dla dokumentacji)
- git (do instalacji)
- make (do budowania)
- gcc (do kompilacji)
pakiety[edytuj]
- flint-arb
sudo apt-get install libflint-arb-dev
git[edytuj]
instalacja[edytuj]
git clone https://github.com/fredrik-johansson/arb/ cd arb ./configure make make check sudo make install
Przykładowe programy:
make examples
Dokumentacja[edytuj]
cd doc make man
Pliki będą w
build/man.
więc
man ~/arb/doc/build/man/arb.1
Plik pdf:
make latexpdf
uaktualnienie[edytuj]
git pull
sprawdzanie[edytuj]
sudo find / -name "libarb.so"
kompilacja[edytuj]
gcc a.c -larb -lflint -lgmp -L/usr/local/lib/ -lmpfr -Wall gcc a.c -larb -lflint -lgmp -lmpfr -Wall
problemy[edytuj]
linkowanie[edytuj]
error while loading shared libraries: libarb.so: cannot open shared object file: No such file or directory
Problem: biblioteka libarb.so nie jest w katalogu wyszukiwania( ang. library path)[5]. Sprawdź zmienną LD_LIBRARY_PATH.
Rozwiązanie:[6]
- check library is present, use below command
- compile your program with -L option, example below
- export Library path before running if required
sudo find / -name "libarb.so" # gcc program.c -L <path to library> -larb export LD_LIBRARY_PATH=$LD_LIBRARY_PATH:<path to library>
Ewentualnie użyj:
fmpcb.h[edytuj]
Błąd :[7]
fatal error: fmpcb.h: No such file or directory
typy[edytuj]
- arf_t - arbitrary-precision floats[8]
- mag_t - unsigned floats with 30-bit precision
- arb_t = typ dla liczb rzeczywistych ( real numbers, plik arb.h): [mid ± rad]
- acb_t = typ dla liczb zespolonych ( acb.h ): [a ± r] + [b ± s]i
- typy całkowite [9]
- slong
- ulong
- mp_limb_t
- mp_ptr = Pointer to a writable array of limbs.
- mp_srcptr = Pointer to a read-only array of limbs.
- mp_size_t = A limb count (always nonnegative).
- mp_bitcnt_t = A bit offset within an array of limbs (always nonnegative).Arb uses the following FLINT types for exact (integral and rational) arbitrary-size values. For details, refer to the FLINT documentation.
- fmpz_t The FLINT multi-precision integer type uses an inline representation for small integers, specifically when the absolute value is at most 262−1262−1 (on 64-bit machines) or 230−1230−1 (on 32-bit machines). It switches automatically to a GMP integer for larger values. The fmpz_t type is functionally identical to the GMP mpz_t type, but faster for small values.
- fmpq_t = FLINT multi-precision rational number.
- fmpz_poly_t
- fmpq_poly_t
- fmpz_mat_t
- fmpq_mat_t
- arb_poly_t, acb_poly_t - real and complex polynomials
- arb_mat_t, acb_mat_t - real and complex matrices
Przykłady[edytuj]
arb_sub[edytuj]
// http://arblib.org/arb-2.14.0.pdf
# include "arb.h"
int main() {
arb_t x, y;
// init
arb_init(x);
arb_init(y);
// set
arb_set_ui(x, 3); /* x = 3 */
arb_const_pi(y, 128); /* y = pi, to 128 bits */
// compute
arb_sub(y, y, x, 53); /* y = y - x, to 53 bits */
// clear
arb_clear(x);
arb_clear(y);
}
arb_sqrt[edytuj]
void arb_sqrt(arb_t z, const arb_t x, slong prec) // z = sqrt(x)
gdzie :
- z = wynik ( output, result)
- x = wejście ( input)
- prec = precyzja w bitach z jaką jest zaokrąglany wynik
/*
original file :
This file is public domain. Author: Fredrik Johansson.
https://raw.githubusercontent.com/fredrik-johansson/arb/master/examples/logistic.c
export LD_LIBRARY_PATH=$LD_LIBRARY_PATH:/usr/local/lib/
gcc s.c -larb -lflint -lgmp -lmpfr -lpthread -Wall
./a.out
./a.out
-----------------
relative determinate error in the square root of Q is one half the relative determinate error in Q
IEEE-754 standard guarantees me that the result will be as close to the 'real result' as possible, i.e. error will be less than or equal to 1/2 unit-in-the-last-place. In particular,
http://stackoverflow.com/questions/22259537/guaranteed-precision-of-sqrt-function-in-c-c
=====================
decimal digits required = ceil(-log10(sqrt(x+1)-sqrt(x)))
http://stackoverflow.com/questions/30029410/sqrt-and-decimals
============
https://groups.google.com/forum/#!topic/flint-devel/yrOCnfi6DuI
I thought that the number will be decreasing but will be greater then 1.0 ( not equal to 1.0)
Correct.
and I will display such number ( all digits )
Note that the ball radius in most of your results is larger than the first nonzero digit after the 1.
For example, if I have the number 1.000123456.... with a ball radius of 1e-2, I will only see 1.00+/-1e-2. If I have a ball radius of 1e-5, I'll see 1.00012+/-1e-5.
In your calculation, you kept the precision at 64 bits for too long. Then you started doubling the precision unnecessarily. Try increasing the precision by 1 bit on every iteration, right from the start, instead of doubling it after the digits of interest are already gone.
Bill Hart
*/
#include "arb.h"
int main()
{
slong prec;
slong dec_digits;
slong bits; // the number of bits needed to represent the absolute value of the mantissa of the midpoint of x, i.e. the minimum precision sufficient to represent x exactly.
arb_t z; // arbitrary-precision floating-point numbers with ball arithmethic
slong i =0;
double z0 = 2.0;
arb_init(z);
prec = 64;
dec_digits = (prec-3)/3.3219280948873623;
arb_set_d(z, z0); // z = 2.0
bits = arb_bits(z);
while (1)
{
flint_printf("i = %3wd; prec = %10wd; bits = %10wd; dec_digits = %10wd; z = ", i, prec, bits, dec_digits);
arb_printn(z, dec_digits, 0);
flint_printf("\n");
//
arb_sqrt(z,z,prec); // z = sqrt(z)
bits = arb_bits(z); // Returns the number of bits needed to represent the absolute value of the mantissa of the midpoint of x, i.e. the minimum precision sufficient to represent x exactly.
//
prec += 1;
if (i>500) break;
dec_digits = (prec-3)/3.3219280948873623;
//
i+=1;
}
flint_printf("Computed with: \narb-%s\n Flint-%s\n MPFR-%s \n GMP-%s \n", arb_version, FLINT_VERSION ,mpfr_version, gmp_version ); //
arb_clear(z);
flint_cleanup();
return 0;
}
Wynik :
i = 0; prec = 64; bits = 1; dec_digits = 18; z = 2.00000000000000000 i = 1; prec = 65; bits = 62; dec_digits = 18; z = [1.41421356237309505 +/- 1.35e-18] i = 2; prec = 66; bits = 64; dec_digits = 18; z = [1.18920711500272107 +/- 3.42e-18] i = 3; prec = 67; bits = 66; dec_digits = 19; z = [1.090507732665257659 +/- 2.55e-19] i = 4; prec = 68; bits = 67; dec_digits = 19; z = [1.044273782427413840 +/- 3.55e-19] i = 5; prec = 69; bits = 67; dec_digits = 19; z = [1.021897148654116678 +/- 2.53e-19] i = 6; prec = 70; bits = 69; dec_digits = 20; z = [1.0108892860517004600 +/- 3.05e-20] i = 7; prec = 71; bits = 69; dec_digits = 20; z = [1.0054299011128028213 +/- 5.67e-20] i = 8; prec = 72; bits = 71; dec_digits = 20; z = [1.0027112750502024854 +/- 3.42e-20] i = 9; prec = 73; bits = 70; dec_digits = 21; z = [1.00135471989210820588 +/- 4.18e-21] i = 10; prec = 74; bits = 73; dec_digits = 21; z = [1.00067713069306635668 +/- 4.70e-21] i = 11; prec = 75; bits = 74; dec_digits = 21; z = [1.00033850805268231295 +/- 3.94e-21] i = 12; prec = 76; bits = 75; dec_digits = 21; z = [1.00016923970530223108 +/- 4.01e-21] i = 13; prec = 77; bits = 71; dec_digits = 22; z = [1.000084616272694313202 +/- 8.19e-22] i = 14; prec = 78; bits = 75; dec_digits = 22; z = [1.000042307241395819339 +/- 3.56e-22] i = 15; prec = 79; bits = 78; dec_digits = 22; z = [1.000021153396964808094 +/- 3.08e-22] i = 16; prec = 80; bits = 72; dec_digits = 23; z = [1.0000105766425497202348 +/- 7.91e-23] i = 17; prec = 81; bits = 76; dec_digits = 23; z = [1.0000052883072917631114 +/- 7.15e-23] i = 18; prec = 82; bits = 81; dec_digits = 23; z = [1.0000026441501501165475 +/- 1.73e-23] i = 19; prec = 83; bits = 82; dec_digits = 24; z = [1.0000013220742011181771 +/- 2.50e-23] i = 20; prec = 84; bits = 83; dec_digits = 24; z = [1.00000066103688207420883 +/- 6.59e-24] i = 21; prec = 85; bits = 84; dec_digits = 24; z = [1.00000033051838641590253 +/- 6.33e-24] i = 22; prec = 86; bits = 85; dec_digits = 24; z = [1.00000016525917955265305 +/- 5.00e-24] i = 23; prec = 87; bits = 86; dec_digits = 25; z = [1.000000082629586362502256 +/- 8.71e-25] i = 24; prec = 88; bits = 87; dec_digits = 25; z = [1.000000041314792327795095 +/- 6.06e-25] i = 25; prec = 89; bits = 87; dec_digits = 25; z = [1.000000020657395950533544 +/- 2.37e-25] i = 26; prec = 90; bits = 89; dec_digits = 26; z = [1.000000010328697921925772 +/- 5.03e-25] i = 27; prec = 91; bits = 87; dec_digits = 26; z = [1.0000000051643489476276358 +/- 7.99e-26] i = 28; prec = 92; bits = 91; dec_digits = 26; z = [1.0000000025821744704800054 +/- 3.90e-26] i = 29; prec = 93; bits = 87; dec_digits = 27; z = [1.0000000012910872344065496 +/- 4.35e-26] i = 30; prec = 94; bits = 88; dec_digits = 27; z = [1.00000000064554361699491150 +/- 9.18e-27] i = 31; prec = 95; bits = 89; dec_digits = 27; z = [1.00000000032277180844536493 +/- 4.50e-27] i = 32; prec = 96; bits = 90; dec_digits = 27; z = [1.00000000016138590420965976 +/- 2.25e-27] i = 33; prec = 97; bits = 91; dec_digits = 28; z = [1.000000000080692952101574204 +/- 8.87e-28] i = 34; prec = 98; bits = 92; dec_digits = 28; z = [1.000000000040346476049973183 +/- 4.53e-28] i = 35; prec = 99; bits = 92; dec_digits = 28; z = [1.000000000020173238024783112 +/- 4.99e-28] i = 36; prec = 100; bits = 95; dec_digits = 29; z = [1.000000000010086619012340686 +/- 1.95e-28] i = 37; prec = 101; bits = 97; dec_digits = 29; z = [1.0000000000050433095061576255 +/- 8.41e-29] i = 38; prec = 102; bits = 99; dec_digits = 29; z = [1.0000000000025216547530756334 +/- 6.42e-29] i = 39; prec = 103; bits = 101; dec_digits = 30; z = [1.0000000000012608273765370218 +/- 5.50e-29] i = 40; prec = 104; bits = 103; dec_digits = 30; z = [1.00000000000063041368826831221 +/- 8.57e-30] i = 41; prec = 105; bits = 104; dec_digits = 30; z = [1.00000000000031520684413410643 +/- 7.11e-30] i = 42; prec = 106; bits = 105; dec_digits = 31; z = [1.00000000000015760342206704079 +/- 6.05e-30] i = 43; prec = 107; bits = 106; dec_digits = 31; z = [1.00000000000007880171103351729 +/- 3.19e-30] i = 44; prec = 108; bits = 107; dec_digits = 31; z = [1.000000000000039400855516757870 +/- 6.77e-31] i = 45; prec = 109; bits = 107; dec_digits = 31; z = [1.000000000000019700427758378741 +/- 3.99e-31] i = 46; prec = 110; bits = 108; dec_digits = 32; z = [1.000000000000009850213879189322 +/- 2.18e-31] i = 47; prec = 111; bits = 109; dec_digits = 32; z = [1.000000000000004925106939594649 +/- 2.39e-31] i = 48; prec = 112; bits = 110; dec_digits = 32; z = [1.0000000000000024625534697973214 +/- 5.24e-32] i = 49; prec = 113; bits = 111; dec_digits = 33; z = [1.0000000000000012312767348986599 +/- 5.27e-32] i = 50; prec = 114; bits = 112; dec_digits = 33; z = [1.0000000000000006156383674493298 +/- 3.21e-32] i = 51; prec = 115; bits = 113; dec_digits = 33; z = [1.00000000000000030781918372466484 +/- 6.23e-33] i = 52; prec = 116; bits = 113; dec_digits = 34; z = [1.00000000000000015390959186233241 +/- 3.64e-33] i = 53; prec = 117; bits = 116; dec_digits = 34; z = [1.00000000000000007695479593116620 +/- 2.73e-33] i = 54; prec = 118; bits = 117; dec_digits = 34; z = [1.000000000000000038477397965583100 +/- 6.60e-34] i = 55; prec = 119; bits = 116; dec_digits = 34; z = [1.000000000000000019238698982791550 +/- 5.23e-34] i = 56; prec = 120; bits = 117; dec_digits = 35; z = [1.000000000000000009619349491395775 +/- 3.13e-34] i = 57; prec = 121; bits = 118; dec_digits = 35; z = [1.000000000000000004809674745697887 +/- 5.01e-34] i = 58; prec = 122; bits = 116; dec_digits = 35; z = [1.0000000000000000024048373728489437 +/- 4.78e-35] i = 59; prec = 123; bits = 121; dec_digits = 36; z = [1.0000000000000000012024186864244719 +/- 7.05e-35] i = 60; prec = 124; bits = 123; dec_digits = 36; z = [1.0000000000000000006012093432122359 +/- 3.68e-35] i = 61; prec = 125; bits = 122; dec_digits = 36; z = [1.00000000000000000030060467160611796 +/- 8.38e-36] i = 62; prec = 126; bits = 125; dec_digits = 37; z = [1.00000000000000000015030233580305898 +/- 4.19e-36] i = 63; prec = 127; bits = 125; dec_digits = 37; z = [1.00000000000000000007515116790152949 +/- 2.10e-36] i = 64; prec = 128; bits = 127; dec_digits = 37; z = [1.00000000000000000003757558395076475 +/- 5.45e-36] i = 65; prec = 129; bits = 125; dec_digits = 37; z = [1.000000000000000000018787791975382373 +/- 7.34e-37] i = 66; prec = 130; bits = 129; dec_digits = 38; z = [1.000000000000000000009393895987691186 +/- 5.12e-37] i = 67; prec = 131; bits = 129; dec_digits = 38; z = [1.000000000000000000004696947993845593 +/- 2.56e-37] i = 68; prec = 132; bits = 131; dec_digits = 38; z = [1.0000000000000000000023484739969227966 +/- 7.12e-38] i = 69; prec = 133; bits = 130; dec_digits = 39; z = [1.0000000000000000000011742369984613983 +/- 3.63e-38] i = 70; prec = 134; bits = 133; dec_digits = 39; z = [1.0000000000000000000005871184992306991 +/- 5.70e-38] i = 71; prec = 135; bits = 133; dec_digits = 39; z = [1.00000000000000000000029355924961534957 +/- 8.50e-39] i = 72; prec = 136; bits = 135; dec_digits = 40; z = [1.00000000000000000000014677962480767479 +/- 7.32e-39] i = 73; prec = 137; bits = 132; dec_digits = 40; z = [1.00000000000000000000007338981240383739 +/- 4.63e-39] i = 74; prec = 138; bits = 137; dec_digits = 40; z = [1.00000000000000000000003669490620191870 +/- 4.38e-39] i = 75; prec = 139; bits = 137; dec_digits = 40; z = [1.000000000000000000000018347453100959348 +/- 6.56e-40] i = 76; prec = 140; bits = 139; dec_digits = 41; z = [1.000000000000000000000009173726550479674 +/- 3.28e-40] i = 77; prec = 141; bits = 138; dec_digits = 41; z = [1.000000000000000000000004586863275239837 +/- 1.64e-40] i = 78; prec = 142; bits = 141; dec_digits = 41; z = [1.0000000000000000000000022934316376199185 +/- 8.20e-41] i = 79; prec = 143; bits = 141; dec_digits = 42; z = [1.0000000000000000000000011467158188099593 +/- 6.53e-41] i = 80; prec = 144; bits = 143; dec_digits = 42; z = [1.0000000000000000000000005733579094049796 +/- 4.55e-41] i = 81; prec = 145; bits = 141; dec_digits = 42; z = [1.0000000000000000000000002866789547024898 +/- 2.28e-41] i = 82; prec = 146; bits = 145; dec_digits = 43; z = [1.00000000000000000000000014333947735124491 +/- 5.93e-42] i = 83; prec = 147; bits = 145; dec_digits = 43; z = [1.00000000000000000000000007166973867562245 +/- 5.69e-42] i = 84; prec = 148; bits = 147; dec_digits = 43; z = [1.00000000000000000000000003583486933781123 +/- 4.03e-42] i = 85; prec = 149; bits = 146; dec_digits = 43; z = [1.000000000000000000000000017917434668905613 +/- 9.22e-43] i = 86; prec = 150; bits = 149; dec_digits = 44; z = [1.000000000000000000000000008958717334452807 +/- 5.18e-43] i = 87; prec = 151; bits = 149; dec_digits = 44; z = [1.000000000000000000000000004479358667226403 +/- 4.81e-43] i = 88; prec = 152; bits = 151; dec_digits = 44; z = [1.0000000000000000000000000022396793336132017 +/- 8.23e-44] i = 89; prec = 153; bits = 146; dec_digits = 45; z = [1.0000000000000000000000000011198396668066008 +/- 7.02e-44] i = 90; prec = 154; bits = 153; dec_digits = 45; z = [1.0000000000000000000000000005599198334033004 +/- 3.51e-44] i = 91; prec = 155; bits = 153; dec_digits = 45; z = [1.00000000000000000000000000027995991670165021 +/- 8.32e-45] i = 92; prec = 156; bits = 155; dec_digits = 46; z = [1.00000000000000000000000000013997995835082510 +/- 8.77e-45] i = 93; prec = 157; bits = 154; dec_digits = 46; z = [1.00000000000000000000000000006998997917541255 +/- 4.39e-45] i = 94; prec = 158; bits = 157; dec_digits = 46; z = [1.00000000000000000000000000003499498958770628 +/- 4.86e-45] i = 95; prec = 159; bits = 157; dec_digits = 46; z = [1.000000000000000000000000000017497494793853138 +/- 5.96e-46] i = 96; prec = 160; bits = 159; dec_digits = 47; z = [1.000000000000000000000000000008748747396926569 +/- 2.98e-46] i = 97; prec = 161; bits = 157; dec_digits = 47; z = [1.000000000000000000000000000004374373698463285 +/- 6.16e-46] i = 98; prec = 162; bits = 161; dec_digits = 47; z = [1.000000000000000000000000000002187186849231642 +/- 3.25e-46] i = 99; prec = 163; bits = 161; dec_digits = 48; z = [1.0000000000000000000000000000010935934246158211 +/- 6.23e-47] i = 100; prec = 164; bits = 163; dec_digits = 48; z = [1.0000000000000000000000000000005467967123079106 +/- 5.30e-47] Computed with: arb-2.10.0 Flint-2.5.2 MPFR-3.1.5 GMP-6.1.1
Porównaj z:
acb_sqrt[edytuj]
void acb_sqrt(acb_t r, const acb_t z, slong prec) // r = sqrt( z)
/*
export LD_LIBRARY_PATH=$LD_LIBRARY_PATH:/usr/local/lib/
gcc a.c -larb -lflint -lgmp -lmpfr -lpthread -Wall
./a.out
*/
#include "arb.h"
#include <acb.h> // acb_t
int main()
{
acb_t z;
acb_init(z);
acb_t r;
acb_init(r);
acb_set_d_d(z, 1.0, 1.0);
acb_sqrt(r,z, 10); // r=sqrt(z) with precision
flint_printf("sqrt(z) = ");
acb_print(r);
flint_printf("\n");
flint_printf("Computed with: \narb-%s\n Flint-%s\n MPFR-%s \n GMP-%s \n", arb_version, FLINT_VERSION ,mpfr_version, gmp_version ); //
acb_clear(z);
acb_clear(r);
}
Wynik:
./a.out
sqrt(z) = ((281 * 2^-8) +/- (593337151 * 2^-38), (233 * 2^-9) +/- (630453476 * 2^-40))
Computed with:
arb-2.10.0
Flint-2.5.2
MPFR-3.1.5
GMP-6.1.1
pi[edytuj]
/*
export LD_LIBRARY_PATH=$LD_LIBRARY_PATH:/usr/local/lib/
gcc a.c -larb -lflint -lgmp -lmpfr -lpthread -Wall
./a.out
*/
#include "arb.h"
int main()
{
arb_t x;
arb_init(x);
arb_const_pi(x, 50 * 3.33);
arb_printn(x, 50, 0); flint_printf("\n");
flint_printf("Computed with: \narb-%s\n Flint-%s\n MPFR-%s \n GMP-%s \n", arb_version, FLINT_VERSION ,mpfr_version, gmp_version ); //
arb_clear(x);
}
Kompilacja:
export LD_LIBRARY_PATH=$LD_LIBRARY_PATH:/usr/local/lib/ gcc a.c -larb -lflint -lgmp -lmpfr -lpthread -Wall
Użycie:
./a.out
wynik:
[3.1415926535897932384626433832795028841971693993751 +/- 6.27e-50] Computed with: arb-2.9.0-git Flint-2.5.2 MPFR-3.1.5 GMP-6.1.1
liczby zespolone[edytuj]
/*
export LD_LIBRARY_PATH=$LD_LIBRARY_PATH:/usr/local/lib/
gcc a.c -larb -lflint -lgmp -lmpfr -lpthread -Wall
./a.out
*/
#include "arb.h"
#include <acb.h> // acb_t
int main()
{
acb_t z;
acb_init(z);
acb_t r;
acb_init(r);
acb_set_d_d(z, 1.0, 1.0);
acb_sqrt(r,z, 10); // r=sqrt(z) with precision
flint_printf("sqrt(z) = ");
acb_print(r);
flint_printf("\n");
flint_printf("Computed with: \narb-%s\n Flint-%s\n MPFR-%s \n GMP-%s \n", arb_version, FLINT_VERSION ,mpfr_version, gmp_version ); //
acb_clear(z);
acb_clear(r);
}
Kompiluj:
export LD_LIBRARY_PATH=$LD_LIBRARY_PATH:/usr/local/lib/ gcc a.c -larb -lflint -lgmp -lmpfr -lpthread -Wall
uruchom:
./a.out
wynik:
sqrt(z) = ((281 * 2^-8) +/- (593337151 * 2^-38), (233 * 2^-9) +/- (630453476 * 2^-40)) Computed with: arb-2.10.0 Flint-2.5.2 MPFR-3.1.5 GMP-6.1.1
complex_plot[edytuj]
Kompilacja:
export LD_LIBRARY_PATH=$LD_LIBRARY_PATH:/usr/local/lib/
gcc complex_plot.c -larb -lflint -lgmp -lmpfr -lpthread -lm -Wall -o complex_plot
Użycie:
complex_plot [-range xa xb ya yb] [-size xn yn] [-color n] <func>
Domyślne parametry:
[-10,10] + [-10,10]i xn = yn = 512
Gotowe funkcje:[10]
- gamma - Gamma function
- digamma - Digamma function
- lgamma - Logarithmic gamma function
- zeta - Riemann zeta function
- erf - Error function
- ai - Airy function Ai[11]
- bi - Airy function Bi
- besselj - Bessel function J_0
- bessely - Bessel function Y_0
- besseli - Bessel function I_0
- besselk - Bessel function K_0
- modj - Modular j-function[12][13]
- modeta - Dedekind eta function
- barnesg - Barnes G-function
- agm - Arithmetic geometric mean
Przykład użycia:
./complex_plot gamma
Tekstowy wynik:
row 480 row 448 row 416 row 384 row 352 row 320 row 288 row 256 row 224 row 192 row 160 row 128 row 96 row 64 row 32 row 0 cpu/wall(s): 2.069 2.076
oraz plik arbplot.ppm
logistic[edytuj]
Oblicza n-tą iterację odwzorowania logistycznego[14]
export LD_LIBRARY_PATH=$LD_LIBRARY_PATH:/usr/local/lib/ ./logistic 0 0.5 3.75 10 ./logistic: error while loading shared libraries: libarb.so.2: cannot open shared object file: No such file or directory a@zelman:~/arb/build/examples$ export LD_LIBRARY_PATH=$LD_LIBRARY_PATH:/usr/local/lib/ ~/arb/build/examples$ ./logistic 0 0.5 3.75 10Trying prec=64 bits...success! cpu/wall(s): 0 0 x_0 = 0.5000000000 ~/arb/build/examples$ ./logistic 1 0.5 3.75 10 Trying prec=64 bits...success! cpu/wall(s): 0 0.001 x_1 = 0.9375000000 ~/arb/build/examples$ ./logistic 100 0.5 3.75 10 Trying prec=64 bits...ran out of accuracy at step 18 Trying prec=128 bits...ran out of accuracy at step 53 Trying prec=256 bits...success! cpu/wall(s): 0 0 x_100 = [0.8882939923 +/- 1.60e-11] ~/arb/build/examples$ ./logistic 1000 0.5 3.75 100 Trying prec=64 bits...ran out of accuracy at step 4 Trying prec=128 bits...ran out of accuracy at step 5 Trying prec=256 bits...ran out of accuracy at step 6 Trying prec=512 bits...ran out of accuracy at step 99 Trying prec=1024 bits...ran out of accuracy at step 369 Trying prec=2048 bits...ran out of accuracy at step 906 Trying prec=4096 bits...success! cpu/wall(s): 0.003 0.003 x_1000 = [0.7917467409224436376869853580586396204499342746098639418369939567972864824346152847471492894632044257 +/- 4.39e-101]
Zobacz również[edytuj]
- OwenMaresh: acb_hypgeom_bessel_k
- gd(sin(z))^z, [-20,20]x[-20,20] in arb
- OwenMaresh: iterated K-Bessel function, made with arb
Źródła[edytuj]
- ↑ Arb by Fredrik Johansson
- ↑ stackexchange questions : how-can-i-link-my-c-program-against-the-arb-library
- ↑ Modular forms in arb
- ↑ askubuntu questions : libarb-so-libflint-so-13-cannot-open-shared-object-file-no-such-file-or-dire
- ↑ askubuntu question libarb-so-libflint-so-13-cannot-open-shared-object-file-no-such-file-or-dire
- ↑ stackoverflow question : libarb-so-cannot-open-shared-object-file-no-such-file-or-directory
- ↑ unix SE question: how-can-i-link-my-c-program-against-the-arb-library
- ↑ Fundamental algorithms in Arb
- ↑ arb : Integer types
- ↑ fredrikj phaseful-plots
- ↑ fredrik j airy-in-the-library
- ↑ fredrik j modular-forms-in-arb/
- ↑ The j-invariant magnified 100 orders of magnitude (10x zoom per second) by Fredrik Johansson
- ↑ wikipedia : Odwzorowanie logistyczne