Large integer modulo division is not very convincing
0
Look at these:
>>>from mpmath import mp
>>> 20988936657440586486151264256610222593863921 % 2623617082180073274358906876623916797788160
291280009243618888211558641
>>> 20988936657440586486151264256610222593863921 % 5247234164360146548717813753247833595576320
291280009243618888211558641 <<<HOW CAN THIS BE THE SAME ANSWER AS ABOVE?
>>> mp.fdiv(20988936657440586486151264256610222593863921, 5247234164360146548717813753247833595576320)
mpf('4.00000000000000005551115123125782779)
>>> mp.fdiv(20988936657440586486151264256610222593863921, 2623617082180073274358906876623916797788160)
mpf('8.00000000000000011102230246251565558)
I am trying to write a program that returns true if a large number is prime.
As you probably already know, python has its limits. Not just with floating point numbers but also with large numbers above a decillion. If my Python 3.7 (64-bit) can support large integers up to:
import sys
int(sys.float_info.max)
179769313486231570814527423731704356798070567525844996598917476803157260780028538760589558632766878171540458953514382464234321326889464182768467546703537516986049910576551282076245490090389328944075868508455133942304583236903222948165808559332123348274797826204144723168738177180919299881250404026184124858368
...then why can I not do a simple modulo on the numbers above and not get inconsistencies? Can anyone refer me to some other tool to help me or is there something I'm just missing?
python integer modulo
edited Nov 15 '18 at 5:49
Gunasekar
5221518
asked Nov 15 '18 at 3:15
Infinity LoopInfinity Loop
3019
|
show 5 more comments
0
Look at these:
>>>from mpmath import mp
>>> 20988936657440586486151264256610222593863921 % 2623617082180073274358906876623916797788160
291280009243618888211558641
>>> 20988936657440586486151264256610222593863921 % 5247234164360146548717813753247833595576320
291280009243618888211558641 <<<HOW CAN THIS BE THE SAME ANSWER AS ABOVE?
>>> mp.fdiv(20988936657440586486151264256610222593863921, 5247234164360146548717813753247833595576320)
mpf('4.00000000000000005551115123125782779)
>>> mp.fdiv(20988936657440586486151264256610222593863921, 2623617082180073274358906876623916797788160)
mpf('8.00000000000000011102230246251565558)
I am trying to write a program that returns true if a large number is prime.
As you probably already know, python has its limits. Not just with floating point numbers but also with large numbers above a decillion. If my Python 3.7 (64-bit) can support large integers up to:
import sys
int(sys.float_info.max)
179769313486231570814527423731704356798070567525844996598917476803157260780028538760589558632766878171540458953514382464234321326889464182768467546703537516986049910576551282076245490090389328944075868508455133942304583236903222948165808559332123348274797826204144723168738177180919299881250404026184124858368
...then why can I not do a simple modulo on the numbers above and not get inconsistencies? Can anyone refer me to some other tool to help me or is there something I'm just missing?
python integer modulo
edited Nov 15 '18 at 5:49
Gunasekar
5221518
asked Nov 15 '18 at 3:15
Infinity LoopInfinity Loop
3019
1
I'm getting the exact same results in Clojure using BigIntegers. I'm too tired to consider the maths, but the results you're getting seem legitimate. The first two do in fact result in the same answer.
– Carcigenicate
Nov 15 '18 at 3:22
right...but look at the mpmath divisions.... They are 4.00000000000000then5551115123125782779 I guess it rounds it to a 4 or what? If it does, then the modulo actually gives a wrong answer.
– Infinity Loop
Nov 15 '18 at 3:25
Python appears to be correct here. What makes you think it isn't?
– jwodder
Nov 15 '18 at 3:32
The two mp.fdiv() show different floating point answers. Since the floating point decimal answers are different, the remainder of the modulo on the two shouldn't be the same. I'm guessing Python is rounding it because the zeros go above 15-16 places from the decimal point.
– Infinity Loop
Nov 15 '18 at 3:33
Again, I'm way too tired to consider math in any depth right now, but I can replicate your results exactly in my Clojure REPL. If there is something wrong here, it's also wrong in the JVM/Clojure number module.
– Carcigenicate
Nov 15 '18 at 3:38
|
show 5 more comments
0
0
0
Look at these:
>>>from mpmath import mp
>>> 20988936657440586486151264256610222593863921 % 2623617082180073274358906876623916797788160
291280009243618888211558641
>>> 20988936657440586486151264256610222593863921 % 5247234164360146548717813753247833595576320
291280009243618888211558641 <<<HOW CAN THIS BE THE SAME ANSWER AS ABOVE?
>>> mp.fdiv(20988936657440586486151264256610222593863921, 5247234164360146548717813753247833595576320)
mpf('4.00000000000000005551115123125782779)
>>> mp.fdiv(20988936657440586486151264256610222593863921, 2623617082180073274358906876623916797788160)
mpf('8.00000000000000011102230246251565558)
I am trying to write a program that returns true if a large number is prime.
As you probably already know, python has its limits. Not just with floating point numbers but also with large numbers above a decillion. If my Python 3.7 (64-bit) can support large integers up to:
import sys
int(sys.float_info.max)
179769313486231570814527423731704356798070567525844996598917476803157260780028538760589558632766878171540458953514382464234321326889464182768467546703537516986049910576551282076245490090389328944075868508455133942304583236903222948165808559332123348274797826204144723168738177180919299881250404026184124858368
...then why can I not do a simple modulo on the numbers above and not get inconsistencies? Can anyone refer me to some other tool to help me or is there something I'm just missing?
python integer modulo
edited Nov 15 '18 at 5:49
Gunasekar
5221518
asked Nov 15 '18 at 3:15
Infinity LoopInfinity Loop
3019
Look at these:
>>>from mpmath import mp
>>> 20988936657440586486151264256610222593863921 % 2623617082180073274358906876623916797788160
291280009243618888211558641
>>> 20988936657440586486151264256610222593863921 % 5247234164360146548717813753247833595576320
291280009243618888211558641 <<<HOW CAN THIS BE THE SAME ANSWER AS ABOVE?
>>> mp.fdiv(20988936657440586486151264256610222593863921, 5247234164360146548717813753247833595576320)
mpf('4.00000000000000005551115123125782779)
>>> mp.fdiv(20988936657440586486151264256610222593863921, 2623617082180073274358906876623916797788160)
mpf('8.00000000000000011102230246251565558)
I am trying to write a program that returns true if a large number is prime.
As you probably already know, python has its limits. Not just with floating point numbers but also with large numbers above a decillion. If my Python 3.7 (64-bit) can support large integers up to:
import sys
int(sys.float_info.max)
179769313486231570814527423731704356798070567525844996598917476803157260780028538760589558632766878171540458953514382464234321326889464182768467546703537516986049910576551282076245490090389328944075868508455133942304583236903222948165808559332123348274797826204144723168738177180919299881250404026184124858368
...then why can I not do a simple modulo on the numbers above and not get inconsistencies? Can anyone refer me to some other tool to help me or is there something I'm just missing?
python integer modulo
python integer modulo
edited Nov 15 '18 at 5:49
Gunasekar
5221518
asked Nov 15 '18 at 3:15
Infinity LoopInfinity Loop
3019
edited Nov 15 '18 at 5:49
Gunasekar
5221518
asked Nov 15 '18 at 3:15
Infinity LoopInfinity Loop
3019
edited Nov 15 '18 at 5:49
Gunasekar
5221518
edited Nov 15 '18 at 5:49
Gunasekar
5221518
edited Nov 15 '18 at 5:49
Gunasekar
5221518
5221518
asked Nov 15 '18 at 3:15
Infinity LoopInfinity Loop
3019
asked Nov 15 '18 at 3:15
Infinity LoopInfinity Loop
3019
asked Nov 15 '18 at 3:15
Infinity LoopInfinity Loop
3019
3019
1
I'm getting the exact same results in Clojure using BigIntegers. I'm too tired to consider the maths, but the results you're getting seem legitimate. The first two do in fact result in the same answer.
– Carcigenicate
Nov 15 '18 at 3:22
right...but look at the mpmath divisions.... They are 4.00000000000000then5551115123125782779 I guess it rounds it to a 4 or what? If it does, then the modulo actually gives a wrong answer.
– Infinity Loop
Nov 15 '18 at 3:25
Python appears to be correct here. What makes you think it isn't?
– jwodder
Nov 15 '18 at 3:32
The two mp.fdiv() show different floating point answers. Since the floating point decimal answers are different, the remainder of the modulo on the two shouldn't be the same. I'm guessing Python is rounding it because the zeros go above 15-16 places from the decimal point.
– Infinity Loop
Nov 15 '18 at 3:33
Again, I'm way too tired to consider math in any depth right now, but I can replicate your results exactly in my Clojure REPL. If there is something wrong here, it's also wrong in the JVM/Clojure number module.
– Carcigenicate
Nov 15 '18 at 3:38
|
show 5 more comments
1
I'm getting the exact same results in Clojure using BigIntegers. I'm too tired to consider the maths, but the results you're getting seem legitimate. The first two do in fact result in the same answer.
– Carcigenicate
Nov 15 '18 at 3:22
right...but look at the mpmath divisions.... They are 4.00000000000000then5551115123125782779 I guess it rounds it to a 4 or what? If it does, then the modulo actually gives a wrong answer.
– Infinity Loop
Nov 15 '18 at 3:25
Python appears to be correct here. What makes you think it isn't?
– jwodder
Nov 15 '18 at 3:32
The two mp.fdiv() show different floating point answers. Since the floating point decimal answers are different, the remainder of the modulo on the two shouldn't be the same. I'm guessing Python is rounding it because the zeros go above 15-16 places from the decimal point.
– Infinity Loop
Nov 15 '18 at 3:33
Again, I'm way too tired to consider math in any depth right now, but I can replicate your results exactly in my Clojure REPL. If there is something wrong here, it's also wrong in the JVM/Clojure number module.
– Carcigenicate
Nov 15 '18 at 3:38
1
1
I'm getting the exact same results in Clojure using BigIntegers. I'm too tired to consider the maths, but the results you're getting seem legitimate. The first two do in fact result in the same answer.
– Carcigenicate
Nov 15 '18 at 3:22
I'm getting the exact same results in Clojure using BigIntegers. I'm too tired to consider the maths, but the results you're getting seem legitimate. The first two do in fact result in the same answer.
– Carcigenicate
Nov 15 '18 at 3:22
right...but look at the mpmath divisions.... They are 4.00000000000000then5551115123125782779 I guess it rounds it to a 4 or what? If it does, then the modulo actually gives a wrong answer.
– Infinity Loop
Nov 15 '18 at 3:25
right...but look at the mpmath divisions.... They are 4.00000000000000then5551115123125782779 I guess it rounds it to a 4 or what? If it does, then the modulo actually gives a wrong answer.
– Infinity Loop
Nov 15 '18 at 3:25
Python appears to be correct here. What makes you think it isn't?
– jwodder
Nov 15 '18 at 3:32
Python appears to be correct here. What makes you think it isn't?
– jwodder
Nov 15 '18 at 3:32
The two mp.fdiv() show different floating point answers. Since the floating point decimal answers are different, the remainder of the modulo on the two shouldn't be the same. I'm guessing Python is rounding it because the zeros go above 15-16 places from the decimal point.
– Infinity Loop
Nov 15 '18 at 3:33
The two mp.fdiv() show different floating point answers. Since the floating point decimal answers are different, the remainder of the modulo on the two shouldn't be the same. I'm guessing Python is rounding it because the zeros go above 15-16 places from the decimal point.
– Infinity Loop
Nov 15 '18 at 3:33
Again, I'm way too tired to consider math in any depth right now, but I can replicate your results exactly in my Clojure REPL. If there is something wrong here, it's also wrong in the JVM/Clojure number module.
– Carcigenicate
Nov 15 '18 at 3:38
Again, I'm way too tired to consider math in any depth right now, but I can replicate your results exactly in my Clojure REPL. If there is something wrong here, it's also wrong in the JVM/Clojure number module.
– Carcigenicate
Nov 15 '18 at 3:38
|
show 5 more comments
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1
I'm getting the exact same results in Clojure using BigIntegers. I'm too tired to consider the maths, but the results you're getting seem legitimate. The first two do in fact result in the same answer.
– Carcigenicate
Nov 15 '18 at 3:22
right...but look at the mpmath divisions.... They are 4.00000000000000then5551115123125782779 I guess it rounds it to a 4 or what? If it does, then the modulo actually gives a wrong answer.
– Infinity Loop
Nov 15 '18 at 3:25
Python appears to be correct here. What makes you think it isn't?
– jwodder
Nov 15 '18 at 3:32
The two mp.fdiv() show different floating point answers. Since the floating point decimal answers are different, the remainder of the modulo on the two shouldn't be the same. I'm guessing Python is rounding it because the zeros go above 15-16 places from the decimal point.
– Infinity Loop
Nov 15 '18 at 3:33
Again, I'm way too tired to consider math in any depth right now, but I can replicate your results exactly in my Clojure REPL. If there is something wrong here, it's also wrong in the JVM/Clojure number module.
– Carcigenicate
Nov 15 '18 at 3:38