#fixedpoint — Public Fediverse posts

**Fixed-Point Iteration:** An iterative method to find `x` such that `x = g(x)`.
Ex: For `f(x)=0`, rewrite as `x=g(x)`. Start `x_0`, then `x_n+1 = g(x_n)`.
Pro-Tip: Convergence depends on `|g'(x)| < 1` near the fixed point. Check this!
#FixedPoint #NumericalMethods #STEM #StudyNotes

Числа с фиксированной запятой для NES/DENDY

Консоль Dendy в первую очередь ассоциируется с относительно простыми играми (Super Mario Bros, Duck Hunt, Battle City и т. д.), которые обычно не требуют сложных расчётов и обходятся целочисленной математикой. Но как только нужно сделать трёхмерную графику или сложную физику, сразу появляется потребность в точных вычислениях и дробных числах. Самым простым и быстрым способом программного представления дробей являются числа с фиксированной запятой (Fixed‑point числа). О реализации такой арифметики для NES/Dendy мы и поговорим.

https://habr.com/ru/companies/sberbank/articles/850348/

#c #assembler #python #разработка_игр #nes #dendy #gamedev #ретроконсоли #математика #fixedpoint

Числа с фиксированной запятой для NES/DENDY

Консоль Dendy в первую очередь ассоциируется с относительно простыми играми (Super Mario Bros, Duck Hunt, Battle City и т. д.), которые обычно не требуют сложных расчётов и обходятся целочисленной математикой. Но как только нужно сделать трёхмерную графику или сложную физику, сразу появляется потребность в точных вычислениях и дробных числах. Самым простым и быстрым способом программного представления дробей являются числа с фиксированной запятой (Fixed‑point числа). О реализации такой арифметики для NES/Dendy мы и поговорим.

https://habr.com/ru/companies/sberbank/articles/850348/

#c #assembler #python #разработка_игр #nes #dendy #gamedev #ретроконсоли #математика #fixedpoint

Числа с фиксированной запятой для NES/DENDY

Консоль Dendy в первую очередь ассоциируется с относительно простыми играми (Super Mario Bros, Duck Hunt, Battle City и т. д.), которые обычно не требуют сложных расчётов и обходятся целочисленной математикой. Но как только нужно сделать трёхмерную графику или сложную физику, сразу появляется потребность в точных вычислениях и дробных числах. Самым простым и быстрым способом программного представления дробей являются числа с фиксированной запятой (Fixed‑point числа). О реализации такой арифметики для NES/Dendy мы и поговорим.

https://habr.com/ru/companies/sberbank/articles/850348/

#c #assembler #python #разработка_игр #nes #dendy #gamedev #ретроконсоли #математика #fixedpoint

Имплементация чисел с фиксированной точкой (часть 2)

Итак, в прошлый раз я представил базовую идею как можно реализовать Fixed-point arithmetic , а так же набросок кода на C++, в котором в комментариях нашли довольно много проблем (а я сам нашёл ещё больше). В этот раз хочется представить улучшенную реализацию, разбор тонких моментов в коде и провести более детальный анализ получаемых результатов.

https://habr.com/ru/articles/832258/

#fixedpoint_arithmetic #fixedpoint #fixed_point

Имплементация чисел с фиксированной точкой (часть 2)

Итак, в прошлый раз я представил базовую идею как можно реализовать Fixed-point arithmetic , а так же набросок кода на C++, в котором в комментариях нашли довольно много проблем (а я сам нашёл ещё больше). В этот раз хочется представить улучшенную реализацию, разбор тонких моментов в коде и провести более детальный анализ получаемых результатов.

https://habr.com/ru/articles/832258/

#fixedpoint_arithmetic #fixedpoint #fixed_point

Имплементация чисел с фиксированной точкой (часть 2)

Итак, в прошлый раз я представил базовую идею как можно реализовать Fixed-point arithmetic , а так же набросок кода на C++, в котором в комментариях нашли довольно много проблем (а я сам нашёл ещё больше). В этот раз хочется представить улучшенную реализацию, разбор тонких моментов в коде и провести более детальный анализ получаемых результатов.

https://habr.com/ru/articles/832258/

#fixedpoint_arithmetic #fixedpoint #fixed_point

Fixed Point Math Exposed https://hackaday.com/2024/06/23/fixed-point-math-exposed/ #SoftwareDevelopment #Microcontrollers #floatingpoint #fixedpoint

Fixed Point Math Exposed https://hackaday.com/2024/06/23/fixed-point-math-exposed/ #SoftwareDevelopment #Microcontrollers #floatingpoint #fixedpoint

Fixed Point Math Exposed https://hackaday.com/2024/06/23/fixed-point-math-exposed/ #SoftwareDevelopment #Microcontrollers #floatingpoint #fixedpoint

Fixed Point Math Exposed https://hackaday.com/2024/06/23/fixed-point-math-exposed/ #SoftwareDevelopment #Microcontrollers #floatingpoint #fixedpoint

Fixed Point Math Exposed - If you are used to writing software for modern machines, you probably don’t think ... - https://hackaday.com/2024/06/23/fixed-point-math-exposed/ #softwaredevelopment #microcontrollers #floatingpoint #fixedpoint

Fixed Point Math Exposed - If you are used to writing software for modern machines, you probably don’t think ... - https://hackaday.com/2024/06/23/fixed-point-math-exposed/ #softwaredevelopment #microcontrollers #floatingpoint #fixedpoint

Fixed Point Math Exposed - If you are used to writing software for modern machines, you probably don’t think ... - https://hackaday.com/2024/06/23/fixed-point-math-exposed/ #softwaredevelopment #microcontrollers #floatingpoint #fixedpoint

Fixed Point Math Exposed - If you are used to writing software for modern machines, you probably don’t think ... - https://hackaday.com/2024/06/23/fixed-point-math-exposed/ #softwaredevelopment #microcontrollers #floatingpoint #fixedpoint

Fixed Point Math Exposed - If you are used to writing software for modern machines, you probably don’t think ... - https://hackaday.com/2024/06/23/fixed-point-math-exposed/ #softwaredevelopment #microcontrollers #floatingpoint #fixedpoint

#Journal, Day 1452
Sunday, 10 March 2024
Ukraine War: Day 747
Hamas-Israel War: Day 155
Mass shootings in the USA in 2024: 73

#OscarSunday #Timechange #rescuebird #budgie #birthdays #familyandfriends #fixedpoint

#Journal, Day 1452
Sunday, 10 March 2024
Ukraine War: Day 747
Hamas-Israel War: Day 155
Mass shootings in the USA in 2024: 73

#OscarSunday #Timechange #rescuebird #budgie #birthdays #familyandfriends #fixedpoint

#Journal, Day 1452
Sunday, 10 March 2024
Ukraine War: Day 747
Hamas-Israel War: Day 155
Mass shootings in the USA in 2024: 73

#OscarSunday #Timechange #rescuebird #budgie #birthdays #familyandfriends #fixedpoint

#Journal, Day 1452
Sunday, 10 March 2024
Ukraine War: Day 747
Hamas-Israel War: Day 155
Mass shootings in the USA in 2024: 73

#OscarSunday #Timechange #rescuebird #budgie #birthdays #familyandfriends #fixedpoint

#Journal, Day 1452
Sunday, 10 March 2024
Ukraine War: Day 747
Hamas-Israel War: Day 155
Mass shootings in the USA in 2024: 73

#OscarSunday #Timechange #rescuebird #budgie #birthdays #familyandfriends #fixedpoint

#FICS23 (International Workshop on Fixed Points in Computer Science), which runs alongside #CSL2023 , "is to bring together people from different fields such as algebra/coalgebra, verification, logic, around the thematic of fixed points". No proceedings, but "Depending on the nature of the contributions, a special issue of #FundamentaInformaticae might be published with selected contributions". #FixedPoint I couldn't find a website but here is a web link to the call: https://sympa.inria.fr/sympa/arc/coq-club/2022-11/msg00032.html

#FICS23 (International Workshop on Fixed Points in Computer Science), which runs alongside #CSL2023 , "is to bring together people from different fields such as algebra/coalgebra, verification, logic, around the thematic of fixed points". No proceedings, but "Depending on the nature of the contributions, a special issue of #FundamentaInformaticae might be published with selected contributions". #FixedPoint I couldn't find a website but here is a web link to the call: https://sympa.inria.fr/sympa/arc/coq-club/2022-11/msg00032.html

#FICS23 (International Workshop on Fixed Points in Computer Science), which runs alongside #CSL2023 , "is to bring together people from different fields such as algebra/coalgebra, verification, logic, around the thematic of fixed points". No proceedings, but "Depending on the nature of the contributions, a special issue of #FundamentaInformaticae might be published with selected contributions". #FixedPoint I couldn't find a website but here is a web link to the call: https://sympa.inria.fr/sympa/arc/coq-club/2022-11/msg00032.html

#FICS23 (International Workshop on Fixed Points in Computer Science), which runs alongside #CSL2023 , "is to bring together people from different fields such as algebra/coalgebra, verification, logic, around the thematic of fixed points". No proceedings, but "Depending on the nature of the contributions, a special issue of #FundamentaInformaticae might be published with selected contributions". #FixedPoint I couldn't find a website but here is a web link to the call: https://sympa.inria.fr/sympa/arc/coq-club/2022-11/msg00032.html

#FICS23 (International Workshop on Fixed Points in Computer Science), which runs alongside #CSL2023 , "is to bring together people from different fields such as algebra/coalgebra, verification, logic, around the thematic of fixed points". No proceedings, but "Depending on the nature of the contributions, a special issue of #FundamentaInformaticae might be published with selected contributions". #FixedPoint I couldn't find a website but here is a web link to the call: https://sympa.inria.fr/sympa/arc/coq-club/2022-11/msg00032.html

Now, rise-over-run, that's a #FloatingPoint operation.
But *of course* you can't do that. You're running on a single-threaded #CPU (no #GPU) with no lookahead; everything blocks, and floating point ops block for a LONG time. So instead you're going to have integers mimick floating point (#FixedPoint)

Okay, so you check to see when they're going over a certain remainder value and you should move up or down one row of #pixels? OF COURSE you don't have time for that.

Now, rise-over-run, that's a #FloatingPoint operation.
But *of course* you can't do that. You're running on a single-threaded #CPU (no #GPU) with no lookahead; everything blocks, and floating point ops block for a LONG time. So instead you're going to have integers mimick floating point (#FixedPoint)

Okay, so you check to see when they're going over a certain remainder value and you should move up or down one row of #pixels? OF COURSE you don't have time for that.

Now, rise-over-run, that's a #FloatingPoint operation.
But *of course* you can't do that. You're running on a single-threaded #CPU (no #GPU) with no lookahead; everything blocks, and floating point ops block for a LONG time. So instead you're going to have integers mimick floating point (#FixedPoint)

Okay, so you check to see when they're going over a certain remainder value and you should move up or down one row of #pixels? OF COURSE you don't have time for that.

Now, rise-over-run, that's a #FloatingPoint operation.
But *of course* you can't do that. You're running on a single-threaded #CPU (no #GPU) with no lookahead; everything blocks, and floating point ops block for a LONG time. So instead you're going to have integers mimick floating point (#FixedPoint)

Okay, so you check to see when they're going over a certain remainder value and you should move up or down one row of #pixels? OF COURSE you don't have time for that.

Now, rise-over-run, that's a #FloatingPoint operation.
But *of course* you can't do that. You're running on a single-threaded #CPU (no #GPU) with no lookahead; everything blocks, and floating point ops block for a LONG time. So instead you're going to have integers mimick floating point (#FixedPoint)

Okay, so you check to see when they're going over a certain remainder value and you should move up or down one row of #pixels? OF COURSE you don't have time for that.

Hello! My brief introduction: I'm a professor of #economics and a public policy scholar at Rice U. I use #math modeling to inform science-based policy. I work on the economics of emerging infectious diseases, climate and the energy transition, and using #gametheory to study symbiotic relationships in #ecology. In #math I am interested in #topology and have studied #fixedpoint theorems for locally contractive set-valued maps. I enjoy travel, kayaking, reading, and dreaming of classic cars.

Hello! My brief introduction: I'm a professor of #economics and a public policy scholar at Rice U. I use #math modeling to inform science-based policy. I work on the economics of emerging infectious diseases, climate and the energy transition, and using #gametheory to study symbiotic relationships in #ecology. In #math I am interested in #topology and have studied #fixedpoint theorems for locally contractive set-valued maps. I enjoy travel, kayaking, reading, and dreaming of classic cars.

Hello! My brief #introduction: I'm a professor of #economics and a #publicpolicy scholar at Rice U. I use #math modeling to inform science-based policy. I work on the economics of emerging infectious diseases, climate and the energy transition, and using #gametheory to study symbiotic relationships in #ecology. In #math I am interested in #topology and have studied #fixedpoint theorems for locally contractive set-valued maps. I enjoy travel, kayaking, reading, and dreaming of classic cars.

Hello! My brief introduction: I'm a professor of #economics and a public policy scholar at Rice U. I use #math modeling to inform science-based policy. I work on the economics of emerging infectious diseases, climate and the energy transition, and using #gametheory to study symbiotic relationships in #ecology. In #math I am interested in #topology and have studied #fixedpoint theorems for locally contractive set-valued maps. I enjoy travel, kayaking, reading, and dreaming of classic cars.

Hello! My brief #introduction: I'm a professor of #economics and a #publicpolicy scholar at Rice U. I use #math modeling to inform science-based policy. I work on the economics of emerging infectious diseases, climate and the energy transition, and using #gametheory to study symbiotic relationships in #ecology. In #math I am interested in #topology and have studied #fixedpoint theorems for locally contractive set-valued maps. I enjoy travel, kayaking, reading, and dreaming of classic cars.

@JordiGH

Aha! I finished searching and found a fixed-point triplet that isn't associative under multiplication like the floating point one you gave for addition! :D

If the fixed-denominator is 16

(8/16 * 11/16) * 9/16 =? 8/16 * (11/16 * 9/16)

Left-hand side:
(8/16 * 11/16) * 9/16
(88/16)/16) * 9/16
5/16 * 9/16
(45/16)/16
2/16

Right-hand side:
8/16 * (11/16 * 9/16)
8/16 * (99/16)/16
8/16 * 6/16
(48/16)/16
3/16

(a * b) * c ≠ a * (b * c)
:O

:D

#FixedPoint #Maths #Programming

@JordiGH

Aha! I finished searching and found a fixed-point triplet that isn't associative under multiplication like the floating point one you gave for addition! :D

If the fixed-denominator is 16

(8/16 * 11/16) * 9/16 =? 8/16 * (11/16 * 9/16)

Left-hand side:
(8/16 * 11/16) * 9/16
(88/16)/16) * 9/16
5/16 * 9/16
(45/16)/16
2/16

Right-hand side:
8/16 * (11/16 * 9/16)
8/16 * (99/16)/16
8/16 * 6/16
(48/16)/16
3/16

(a * b) * c ≠ a * (b * c)
:O

:D

#FixedPoint #Maths #Programming