Oscar Veliz | exp(x) explained @OscarVeliz | Uploaded 1 year ago | Updated 3 hours ago
The algorithms behind the exponential function in the computer revealed. Lesson also includes discussion of the pow(x,y) function, historical digital computing of the exponential function, modern versions of the algorithm, and a high-precision approach to finding any number of digits for e.
Example code hosted on GitHub github.com/osveliz/numerical-veliz
Chapters:
0:00 MATLAB
0:16 Euler's Number
0:38 Computing e^x
0:52 Computing pow(x,y)
1:19 pow(x,y) source code
1:56 Computing e^x continued
3:21 exp(x) source code
4:03 Long Story Short
4:29 High-precison e
4:54 e-spigot
5:58 Why does e-spigot work?
6:22 Mathemaniac
6:52 Oscar's Notes
7:28 Outro
Recommended Viewing:
@mathemaniac 's exp video youtu.be/u1taDXNzFto
Computing π: Machin-like formula youtu.be/M_fTdDx8IlY
Reference links:
math.h github.com/openbsd/src/blob/master/include/math.h
exp(x) source code netlib.org/fdlibm/e_exp.c
pow(x,y) source code netlib.org/fdlibm/e_pow.c
"Algorithms for Digital Computers" by Hastings et. al. https://press.princeton.edu/books/paperback/9780691626949/approximations-for-digital-computers
"The Mathematical-Function Computation Handbook" by Beebe link.springer.com/book/10.1007/978-3-319-64110-2
"A Spigot Algorithm for the Digits of π" by Rabinowitz & Wagon tandfonline.com/doi/abs/10.1080/00029890.1995.11990560?journalCode=uamm20
Background music "Drifting at 432 Hz" by @UnicornHeads
#NumericalAnalysis #SoME3 #exp
The algorithms behind the exponential function in the computer revealed. Lesson also includes discussion of the pow(x,y) function, historical digital computing of the exponential function, modern versions of the algorithm, and a high-precision approach to finding any number of digits for e.
Example code hosted on GitHub github.com/osveliz/numerical-veliz
Chapters:
0:00 MATLAB
0:16 Euler's Number
0:38 Computing e^x
0:52 Computing pow(x,y)
1:19 pow(x,y) source code
1:56 Computing e^x continued
3:21 exp(x) source code
4:03 Long Story Short
4:29 High-precison e
4:54 e-spigot
5:58 Why does e-spigot work?
6:22 Mathemaniac
6:52 Oscar's Notes
7:28 Outro
Recommended Viewing:
@mathemaniac 's exp video youtu.be/u1taDXNzFto
Computing π: Machin-like formula youtu.be/M_fTdDx8IlY
Reference links:
math.h github.com/openbsd/src/blob/master/include/math.h
exp(x) source code netlib.org/fdlibm/e_exp.c
pow(x,y) source code netlib.org/fdlibm/e_pow.c
"Algorithms for Digital Computers" by Hastings et. al. https://press.princeton.edu/books/paperback/9780691626949/approximations-for-digital-computers
"The Mathematical-Function Computation Handbook" by Beebe link.springer.com/book/10.1007/978-3-319-64110-2
"A Spigot Algorithm for the Digits of π" by Rabinowitz & Wagon tandfonline.com/doi/abs/10.1080/00029890.1995.11990560?journalCode=uamm20
Background music "Drifting at 432 Hz" by @UnicornHeads
#NumericalAnalysis #SoME3 #exp
