What is JavaScript s highest integer value that a number can go to without losing precision

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Is this defined by the language  Is there a defined maximum  Is it different in different browsers

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Jimmy s answer correctly represents the continuous JavaScript integer spectrum as -9007199254740992 to 9007199254740992 inclusive  sorry 9007199254740993  you might think you are 9007199254740993  but you are wrong   Demonstration below or in jsfiddle      x000D   x000D  console log 9007199254740993   x000D   x000D   x000D    However  there is no answer that finds proves this programatically  other than the one CoolAJ86 alluded to in his answer that would finish in 28 56 years     so here s a slightly more efficient way to do that  to be precise  it s more efficient by about 28 559999999968312 years     along with a test fiddle    x000D   x000D      x000D     Checks if adding subtracting one to from a number yields the correct result  x000D     x000D      param number The number to test x000D      return true if you can add subtract 1  false otherwise  x000D      x000D  var canAddSubtractOneFromNumber   function number    x000D      var numMinusOne   number - 1  x000D      var numPlusOne   number   1  x000D       x000D      return   number - numMinusOne      1   amp  amp    number - numPlusOne      -1   x000D    x000D   x000D    Find the highest number x000D  var highestNumber   3    Start with an integer 1 or higher x000D   x000D    Get a number higher than the valid integer range x000D  while  canAddSubtractOneFromNumber highestNumber     x000D      highestNumber    2  x000D    x000D   x000D    Find the lowest number you can t add subtract 1 from x000D  var numToSubtract   highestNumber   4  x000D  while  numToSubtract  gt   1    x000D      while   canAddSubtractOneFromNumber highestNumber - numToSubtract     x000D          highestNumber   highestNumber - numToSubtract  x000D        x000D       x000D      numToSubtract    2  x000D            x000D   x000D    And there was much rejoicing   Yay      x000D  console log  HighestNumber       highestNumber   x000D   x000D   x000D

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Let s get to the sources Description  The MAX SAFE INTEGER constant has a value of 9007199254740991  9 007 199 254 740 991 or  9 quadrillion   The reasoning behind that number is that JavaScript uses double-precision floating-point format numbers as specified in IEEE 754 and can only safely represent numbers between - 2 53 - 1  and 2 53 - 1  Safe in this context refers to the ability to represent integers exactly and to correctly compare them  For example  Number MAX SAFE INTEGER   1     Number MAX SAFE INTEGER   2 will evaluate to true  which is mathematically incorrect  See Number isSafeInteger   for more information  Because MAX SAFE INTEGER is a static property of Number  you always use it as Number MAX SAFE INTEGER  rather than as a property of a Number object you created   Browser compatibility

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Many earlier answers have shown that 9007199254740992     9007199254740992   1     true to verify that 9 007 199 254 740 991 is the maximum and safe integer  But what if we keep doing accumulation  input  9007199254740992   1   output  9007199254740992      expected  9007199254740993 input  9007199254740992   2   output  9007199254740994      expected  9007199254740994 input  9007199254740992   3   output  9007199254740996      expected  9007199254740995 input  9007199254740992   4   output  9007199254740996      expected  9007199254740996  We can find out that among numbers greater than 9 007 199 254 740 992  only even numbers are representable  It s an entrance to explaining how the 64-bit double-precision format works  Let s see how 9 007 199 254 740 992 is represented using this binary format  First  here is 4 503 599 627 370 496    1   0000 ----- 0000     2 52               gt   1 0000 ----- 0000          - 52 bits -        exponent part           - 52 bits -     On the left side of the arrow  we have bit value 1  an adjacent radix point and a fraction part consisting of 52 bits  This number multiplied with 2 52  which moves the radix point 52 steps to the right  The radix point ends up at the end  and we get 4503599627370496 in binary  Now let s keep incrementing the fraction part with 1 until all the bits are set to 1  which equals 9 007 199 254 740 991    1   0000 ----- 0000     2 52    gt   1 0000 ----- 0000   like above           1     1   0000 ----- 0001     2 52    gt   1 0000 ----- 0001           1     1   0000 ----- 0010     2 52    gt   1 0000 ----- 0010                              1   1111 ----- 1111     2 52    gt   1 1111 ----- 1111   Because the 64-bit double-precision format strictly allots 52 bits for the fraction part  no more bits are available to carry another 1  so what we can do is to set all bits back to 0  and manipulate the exponent part  which can technically go as high as 2 1023          This bit is implicit and persistent        1   1111 ----- 1111     2 52        gt   1 1111 ----- 1111           1   radix point won t have anywhere to go     1   0000 ----- 0000     2 52   2    gt   1 0000 ----- 0000    2      gt     1   0000 ----- 0000     2 53  exponent has increased   Now  we ve reached our limit of 9 007 199 254 740 992  Since the exponent has increased to be 2 to the power of 53  and our fraction part is only 52 bits long  the format can only handle increments of 2  for every increment of 1 on the fraction part  the resulting decimal number is 2 greater                            Consume 2 52 to move radix point to                           the end again  you end up with     1   0000 ----- 0000     2 53    gt   1 0000 ----- 0000      2   lt --- we re left with a multiplication of 2 here         - 52 bits -                     - 52 bits -     This is why the 64-bit double-precision format cannot hold odd numbers when the number is greater than 9 007 199 254 740 992 and why people like to point out that 9007199254740992     9007199254740992   1     true  Following this pattern  when the number gets greater than 9 007 199 254 740 992   2   18 014 398 509 481 984 only 4 times the fraction can be held  input  18014398509481984   1   output  18014398509481984    expected  18014398509481985 input  18014398509481984   2   output  18014398509481984    expected  18014398509481986 input  18014398509481984   3   output  18014398509481984    expected  18014398509481987 input  18014398509481984   4   output  18014398509481988    expected  18014398509481988   How about numbers 2 251 799 813 685 248 through 4 503 599 627 370 495  We ve seen that we can technically go beyond what we like to treat as the biggest possible number  it s rather the biggest safe number  it s called MAX SAFE NUMBER for a reason   but that we re then limited to increments of 2  later 4  then 8  etc  Below those numbers  though  there are other limits  Again  following the same pattern   1   0000 ----- 0001     2 51    gt   1 0000 ----- 000   1        - 52 bits -                     - 52 bits    -    The value 0 1 in binary is is exactly 2 -1   1 2    0 5   So when the number is in the aforementioned range  the least significant bit represents 1 2  input  4503599627370495 5      output  4503599627370495 5 input  4503599627370495 7      output  4503599627370495 5  A higher precision isn t possible  Less than 2 251 799 813 685 248  2 51   input  2251799813685246 3      output  2251799813685246 25 input  2251799813685246 5      output  2251799813685246 5 input  2251799813685246 75     output  2251799813685246 75     Please note that if you try this yourself and  say  log these numbers to the console     they will get rounded  JavaScript rounds if the number of digits exceed 17  The value    is internally held correctly   input  2251799813685246 25 toString 2  output   quot 111111111111111111111111111111111111111111111111110 01 quot  input  2251799813685246 75 toString 2  output   quot 111111111111111111111111111111111111111111111111110 11 quot  input  2251799813685246 78 toString 2  output   quot 111111111111111111111111111111111111111111111111110 11 quot   The exponent part has 11 bits allotted for it by the format  From Wikipedia  for more details  go there     So to make the exponent part be 2 52  we exactly need to set e   1075

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Anything you want to use for bitwise operations must be between 0x80000000  -2147483648 or -2 31  and 0x7fffffff  2147483647 or 2 31 - 1    The console will tell you that 0x80000000 equals  2147483648  but 0x80000000  amp  0x80000000 equals -2147483648

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Jimmy s answer correctly represents the continuous JavaScript integer spectrum as -9007199254740992 to 9007199254740992 inclusive  sorry 9007199254740993  you might think you are 9007199254740993  but you are wrong   Demonstration below or in jsfiddle      x000D   x000D  console log 9007199254740993   x000D   x000D   x000D    However  there is no answer that finds proves this programatically  other than the one CoolAJ86 alluded to in his answer that would finish in 28 56 years     so here s a slightly more efficient way to do that  to be precise  it s more efficient by about 28 559999999968312 years     along with a test fiddle    x000D   x000D      x000D     Checks if adding subtracting one to from a number yields the correct result  x000D     x000D      param number The number to test x000D      return true if you can add subtract 1  false otherwise  x000D      x000D  var canAddSubtractOneFromNumber   function number    x000D      var numMinusOne   number - 1  x000D      var numPlusOne   number   1  x000D       x000D      return   number - numMinusOne      1   amp  amp    number - numPlusOne      -1   x000D    x000D   x000D    Find the highest number x000D  var highestNumber   3    Start with an integer 1 or higher x000D   x000D    Get a number higher than the valid integer range x000D  while  canAddSubtractOneFromNumber highestNumber     x000D      highestNumber    2  x000D    x000D   x000D    Find the lowest number you can t add subtract 1 from x000D  var numToSubtract   highestNumber   4  x000D  while  numToSubtract  gt   1    x000D      while   canAddSubtractOneFromNumber highestNumber - numToSubtract     x000D          highestNumber   highestNumber - numToSubtract  x000D        x000D       x000D      numToSubtract    2  x000D            x000D   x000D    And there was much rejoicing   Yay      x000D  console log  HighestNumber       highestNumber   x000D   x000D   x000D

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ECMAScript 6   Number MAX SAFE INTEGER   Math pow 2  53 -1  Number MIN SAFE INTEGER   -Number MAX SAFE INTEGER

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Let s get to the sources Description  The MAX SAFE INTEGER constant has a value of 9007199254740991  9 007 199 254 740 991 or  9 quadrillion   The reasoning behind that number is that JavaScript uses double-precision floating-point format numbers as specified in IEEE 754 and can only safely represent numbers between - 2 53 - 1  and 2 53 - 1  Safe in this context refers to the ability to represent integers exactly and to correctly compare them  For example  Number MAX SAFE INTEGER   1     Number MAX SAFE INTEGER   2 will evaluate to true  which is mathematically incorrect  See Number isSafeInteger   for more information  Because MAX SAFE INTEGER is a static property of Number  you always use it as Number MAX SAFE INTEGER  rather than as a property of a Number object you created   Browser compatibility

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Firefox 3 doesn t seem to have a problem with huge numbers    1e 200   1e 100 will calculate fine to 1e 300   Safari seem to have no problem with it as well   For the record  this is on a Mac if anyone else decides to test this    Unless I lost my brain at this time of day  this is way bigger than a 64-bit integer

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gt   ES6  Number MIN SAFE INTEGER  Number MAX SAFE INTEGER    lt   ES5 From the reference  Number MAX VALUE  Number MIN VALUE    x000D   x000D  console log  MIN VALUE   Number MIN VALUE   console log  MAX VALUE   Number MAX VALUE    console log  MIN SAFE INTEGER   Number MIN SAFE INTEGER     ES6 console log  MAX SAFE INTEGER   Number MAX SAFE INTEGER     ES6 x000D   x000D   x000D

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In JavaScript  there is a number called Infinity   Examples    Infinity gt 100    gt  true     Also worth noting Infinity - 1    Infinity   gt  true  Math pow 2 1024      Infinity   gt  true   This may be sufficient for some questions regarding this topic

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ECMAScript 6   Number MAX SAFE INTEGER   Math pow 2  53 -1  Number MIN SAFE INTEGER   -Number MAX SAFE INTEGER

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In JavaScript the representation of numbers is 2 53 - 1   However  Bitwise operation are calculated on 32 bits   4 bytes    meaning if you exceed 32bits shifts you will start loosing bits

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gt   ES6  Number MIN SAFE INTEGER  Number MAX SAFE INTEGER    lt   ES5 From the reference  Number MAX VALUE  Number MIN VALUE    x000D   x000D  console log  MIN VALUE   Number MIN VALUE   console log  MAX VALUE   Number MAX VALUE    console log  MIN SAFE INTEGER   Number MIN SAFE INTEGER     ES6 console log  MAX SAFE INTEGER   Number MAX SAFE INTEGER     ES6 x000D   x000D   x000D

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Try   maxInt   -1  gt  gt  gt  1   In Firefox 3 6 it s 2 31 - 1

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Other may have already given the generic answer  but I thought it would be a good idea to give a fast way of determining it    for  var x   2  x   1     x  x    2   console log x     Which gives me 9007199254740992 within less than a millisecond in Chrome 30   It will test powers of 2 to find which one  when  added  1  equals himself

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Scato wrotes      anything you want to use for bitwise operations must be between   0x80000000  -2147483648 or -2 31  and 0x7fffffff  2147483647 or 2 31 -   1        the console will tell you that 0x80000000 equals  2147483648  but   0x80000000  amp  0x80000000 equals -2147483648   Hex-Decimals are unsigned positive values  so 0x80000000   2147483648 - thats mathematically correct  If you want to make it a signed value you have to right shift  0x80000000    0   -2147483648  You can write 1  lt  lt  31 instead  too

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JavaScript has two number types  Number and BigInt    The most frequently-used number type  Number  is a 64-bit floating point IEEE 754 number    The largest exact integral value of this type is Number MAX SAFE INTEGER  which is    253-1  or    - 9 007 199 254 740 991  or nine quadrillion seven trillion one hundred ninety-nine billion two hundred fifty-four million seven hundred forty thousand nine hundred ninety-one    To put this in perspective  one quadrillion bytes is a petabyte  or one thousand terabytes     Safe  in this context refers to the ability to represent integers exactly and to correctly compare them   From the spec      Note that all the positive and negative integers whose magnitude is no   greater than 253 are representable in the Number type  indeed  the   integer 0 has two representations   0 and -0     To safely use integers larger than this  you need to use BigInt  which has no upper bound    Note that the bitwise operators and shift operators operate on 32-bit integers  so in that case  the max safe integer is 231-1  or 2 147 483 647      x000D   x000D  const log   console log x000D  var x   9007199254740992 x000D  var y   -x x000D  log x    x   1     true   x000D  log y    y - 1     also true   x000D   x000D     Arithmetic operators work  but bitwise shifts only operate on int32  x000D  log x   2          4503599627370496 x000D  log x  gt  gt  1         0 x000D  log x   1          1 x000D   x000D   x000D      Technical note on the subject of the number 9 007 199 254 740 992  There is an exact IEEE-754 representation of this value  and you can assign and read this value from a variable  so for very carefully chosen applications in the domain of integers less than or equal to this value  you could treat this as a maximum value   In the general case  you must treat this IEEE-754 value as inexact  because it is ambiguous whether it is encoding the logical value 9 007 199 254 740 992 or  9 007 199 254 740 993

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Scato wrotes      anything you want to use for bitwise operations must be between   0x80000000  -2147483648 or -2 31  and 0x7fffffff  2147483647 or 2 31 -   1        the console will tell you that 0x80000000 equals  2147483648  but   0x80000000  amp  0x80000000 equals -2147483648   Hex-Decimals are unsigned positive values  so 0x80000000   2147483648 - thats mathematically correct  If you want to make it a signed value you have to right shift  0x80000000    0   -2147483648  You can write 1  lt  lt  31 instead  too

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I did a simple test with a formula  X- X 1  -1  and the largest value of X I can get to work on Safari  Opera and Firefox  tested on OS nbsp X  is 9e15  Here is the code I used for testing   javascript  alert 9e15- 9e15 1

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In JavaScript  there is a number called Infinity   Examples    Infinity gt 100    gt  true     Also worth noting Infinity - 1    Infinity   gt  true  Math pow 2 1024      Infinity   gt  true   This may be sufficient for some questions regarding this topic

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gt   ES6  Number MIN SAFE INTEGER  Number MAX SAFE INTEGER    lt   ES5 From the reference  Number MAX VALUE  Number MIN VALUE    x000D   x000D  console log  MIN VALUE   Number MIN VALUE   console log  MAX VALUE   Number MAX VALUE    console log  MIN SAFE INTEGER   Number MIN SAFE INTEGER     ES6 console log  MAX SAFE INTEGER   Number MAX SAFE INTEGER     ES6 x000D   x000D   x000D

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At the moment of writing  JavaScript is receiving a new data type  BigInt  It is a TC39 proposal at stage 4 to be included in EcmaScript 2020  BigInt is available in Chrome 67   FireFox 68   Opera 54 and Node 10 4 0  It is underway in Safari  et al    It introduces numerical literals having an  n  suffix and allows for arbitrary precision   var a   123456789012345678901012345678901n    Precision will still be lost  of course  when such a number is  maybe unintentionally  coerced to a number data type    And  obviously  there will always be precision limitations due to finite memory  and a cost in terms of time in order to allocate the necessary memory and to perform arithmetic on such large numbers    For instance  the generation of a number with a hundred thousand decimal digits  will take a noticeable delay before completion   console log BigInt  1  padEnd 100000  0      1n       but it works

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I did a simple test with a formula  X- X 1  -1  and the largest value of X I can get to work on Safari  Opera and Firefox  tested on OS nbsp X  is 9e15  Here is the code I used for testing   javascript  alert 9e15- 9e15 1

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Node js and Google Chrome seem to both be using 1024 bit floating point values so   Number MAX VALUE   1 7976931348623157e 308

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Try   maxInt   -1  gt  gt  gt  1   In Firefox 3 6 it s 2 31 - 1

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At the moment of writing  JavaScript is receiving a new data type  BigInt  It is a TC39 proposal at stage 4 to be included in EcmaScript 2020  BigInt is available in Chrome 67   FireFox 68   Opera 54 and Node 10 4 0  It is underway in Safari  et al    It introduces numerical literals having an  n  suffix and allows for arbitrary precision   var a   123456789012345678901012345678901n    Precision will still be lost  of course  when such a number is  maybe unintentionally  coerced to a number data type    And  obviously  there will always be precision limitations due to finite memory  and a cost in terms of time in order to allocate the necessary memory and to perform arithmetic on such large numbers    For instance  the generation of a number with a hundred thousand decimal digits  will take a noticeable delay before completion   console log BigInt  1  padEnd 100000  0      1n       but it works

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JavaScript has two number types  Number and BigInt    The most frequently-used number type  Number  is a 64-bit floating point IEEE 754 number    The largest exact integral value of this type is Number MAX SAFE INTEGER  which is    253-1  or    - 9 007 199 254 740 991  or nine quadrillion seven trillion one hundred ninety-nine billion two hundred fifty-four million seven hundred forty thousand nine hundred ninety-one    To put this in perspective  one quadrillion bytes is a petabyte  or one thousand terabytes     Safe  in this context refers to the ability to represent integers exactly and to correctly compare them   From the spec      Note that all the positive and negative integers whose magnitude is no   greater than 253 are representable in the Number type  indeed  the   integer 0 has two representations   0 and -0     To safely use integers larger than this  you need to use BigInt  which has no upper bound    Note that the bitwise operators and shift operators operate on 32-bit integers  so in that case  the max safe integer is 231-1  or 2 147 483 647      x000D   x000D  const log   console log x000D  var x   9007199254740992 x000D  var y   -x x000D  log x    x   1     true   x000D  log y    y - 1     also true   x000D   x000D     Arithmetic operators work  but bitwise shifts only operate on int32  x000D  log x   2          4503599627370496 x000D  log x  gt  gt  1         0 x000D  log x   1          1 x000D   x000D   x000D      Technical note on the subject of the number 9 007 199 254 740 992  There is an exact IEEE-754 representation of this value  and you can assign and read this value from a variable  so for very carefully chosen applications in the domain of integers less than or equal to this value  you could treat this as a maximum value   In the general case  you must treat this IEEE-754 value as inexact  because it is ambiguous whether it is encoding the logical value 9 007 199 254 740 992 or  9 007 199 254 740 993

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It is 253    9 007 199 254 740 992  This is because Numbers are stored as floating-point in a 52-bit mantissa   The min value is -253   This makes some fun things happening  Math pow 2  53     Math pow 2  53    1  gt  gt  true   And can also be dangerous     var MAX INT   Math pow 2  53      9 007 199 254 740 992 for  var i   MAX INT  i  lt  MAX INT   2    i           infinite loop     Further reading  http   blog vjeux com 2010 javascript javascript-max int-number-limits html

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The short answer is    it depends      If you   re using bitwise operators anywhere  or if you   re referring to the length of an Array   the ranges are   Unsigned  0    -1 gt  gt  gt 0   Signed   - -1 gt  gt  gt 1 -1     -1 gt  gt  gt 1    It so happens that the bitwise operators and the maximum length of an array are restricted to 32-bit integers    If you   re not using bitwise operators or working with array lengths   Signed   -Math pow 2 53       Math pow 2 53    These limitations are imposed by the internal representation of the    Number    type  which generally corresponds to IEEE 754 double-precision floating-point representation   Note that unlike typical signed integers  the magnitude of the negative limit is the same as the magnitude of the positive limit  due to characteristics of the internal representation  which actually includes a negative 0

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Many earlier answers have shown that 9007199254740992     9007199254740992   1     true to verify that 9 007 199 254 740 991 is the maximum and safe integer  But what if we keep doing accumulation  input  9007199254740992   1   output  9007199254740992      expected  9007199254740993 input  9007199254740992   2   output  9007199254740994      expected  9007199254740994 input  9007199254740992   3   output  9007199254740996      expected  9007199254740995 input  9007199254740992   4   output  9007199254740996      expected  9007199254740996  We can find out that among numbers greater than 9 007 199 254 740 992  only even numbers are representable  It s an entrance to explaining how the 64-bit double-precision format works  Let s see how 9 007 199 254 740 992 is represented using this binary format  First  here is 4 503 599 627 370 496    1   0000 ----- 0000     2 52               gt   1 0000 ----- 0000          - 52 bits -        exponent part           - 52 bits -     On the left side of the arrow  we have bit value 1  an adjacent radix point and a fraction part consisting of 52 bits  This number multiplied with 2 52  which moves the radix point 52 steps to the right  The radix point ends up at the end  and we get 4503599627370496 in binary  Now let s keep incrementing the fraction part with 1 until all the bits are set to 1  which equals 9 007 199 254 740 991    1   0000 ----- 0000     2 52    gt   1 0000 ----- 0000   like above           1     1   0000 ----- 0001     2 52    gt   1 0000 ----- 0001           1     1   0000 ----- 0010     2 52    gt   1 0000 ----- 0010                              1   1111 ----- 1111     2 52    gt   1 1111 ----- 1111   Because the 64-bit double-precision format strictly allots 52 bits for the fraction part  no more bits are available to carry another 1  so what we can do is to set all bits back to 0  and manipulate the exponent part  which can technically go as high as 2 1023          This bit is implicit and persistent        1   1111 ----- 1111     2 52        gt   1 1111 ----- 1111           1   radix point won t have anywhere to go     1   0000 ----- 0000     2 52   2    gt   1 0000 ----- 0000    2      gt     1   0000 ----- 0000     2 53  exponent has increased   Now  we ve reached our limit of 9 007 199 254 740 992  Since the exponent has increased to be 2 to the power of 53  and our fraction part is only 52 bits long  the format can only handle increments of 2  for every increment of 1 on the fraction part  the resulting decimal number is 2 greater                            Consume 2 52 to move radix point to                           the end again  you end up with     1   0000 ----- 0000     2 53    gt   1 0000 ----- 0000      2   lt --- we re left with a multiplication of 2 here         - 52 bits -                     - 52 bits -     This is why the 64-bit double-precision format cannot hold odd numbers when the number is greater than 9 007 199 254 740 992 and why people like to point out that 9007199254740992     9007199254740992   1     true  Following this pattern  when the number gets greater than 9 007 199 254 740 992   2   18 014 398 509 481 984 only 4 times the fraction can be held  input  18014398509481984   1   output  18014398509481984    expected  18014398509481985 input  18014398509481984   2   output  18014398509481984    expected  18014398509481986 input  18014398509481984   3   output  18014398509481984    expected  18014398509481987 input  18014398509481984   4   output  18014398509481988    expected  18014398509481988   How about numbers 2 251 799 813 685 248 through 4 503 599 627 370 495  We ve seen that we can technically go beyond what we like to treat as the biggest possible number  it s rather the biggest safe number  it s called MAX SAFE NUMBER for a reason   but that we re then limited to increments of 2  later 4  then 8  etc  Below those numbers  though  there are other limits  Again  following the same pattern   1   0000 ----- 0001     2 51    gt   1 0000 ----- 000   1        - 52 bits -                     - 52 bits    -    The value 0 1 in binary is is exactly 2 -1   1 2    0 5   So when the number is in the aforementioned range  the least significant bit represents 1 2  input  4503599627370495 5      output  4503599627370495 5 input  4503599627370495 7      output  4503599627370495 5  A higher precision isn t possible  Less than 2 251 799 813 685 248  2 51   input  2251799813685246 3      output  2251799813685246 25 input  2251799813685246 5      output  2251799813685246 5 input  2251799813685246 75     output  2251799813685246 75     Please note that if you try this yourself and  say  log these numbers to the console     they will get rounded  JavaScript rounds if the number of digits exceed 17  The value    is internally held correctly   input  2251799813685246 25 toString 2  output   quot 111111111111111111111111111111111111111111111111110 01 quot  input  2251799813685246 75 toString 2  output   quot 111111111111111111111111111111111111111111111111110 11 quot  input  2251799813685246 78 toString 2  output   quot 111111111111111111111111111111111111111111111111110 11 quot   The exponent part has 11 bits allotted for it by the format  From Wikipedia  for more details  go there     So to make the exponent part be 2 52  we exactly need to set e   1075

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To be safe  var MAX INT   4294967295    Reasoning  I thought I d be clever and find the value at which x   1     x with a more pragmatic approach   My machine can only count 10 million per second or so    so I ll post back with the definitive answer in 28 56 years   If you can t wait that long  I m willing to bet that   Most of your loops don t run for 28 56 years 9007199254740992     Math pow 2  53    1 is proof enough You should stick to 4294967295 which is Math pow 2 32  - 1 as to avoid expected issues with bit-shifting   Finding x   1     x    function         use strict      var x   0       start   new Date   valueOf            while  x   1    x        if    x   10000000           console log x              x    1        console log x  new Date   valueOf   - start

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I did a simple test with a formula  X- X 1  -1  and the largest value of X I can get to work on Safari  Opera and Firefox  tested on OS nbsp X  is 9e15  Here is the code I used for testing   javascript  alert 9e15- 9e15 1

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JavaScript has two number types  Number and BigInt    The most frequently-used number type  Number  is a 64-bit floating point IEEE 754 number    The largest exact integral value of this type is Number MAX SAFE INTEGER  which is    253-1  or    - 9 007 199 254 740 991  or nine quadrillion seven trillion one hundred ninety-nine billion two hundred fifty-four million seven hundred forty thousand nine hundred ninety-one    To put this in perspective  one quadrillion bytes is a petabyte  or one thousand terabytes     Safe  in this context refers to the ability to represent integers exactly and to correctly compare them   From the spec      Note that all the positive and negative integers whose magnitude is no   greater than 253 are representable in the Number type  indeed  the   integer 0 has two representations   0 and -0     To safely use integers larger than this  you need to use BigInt  which has no upper bound    Note that the bitwise operators and shift operators operate on 32-bit integers  so in that case  the max safe integer is 231-1  or 2 147 483 647      x000D   x000D  const log   console log x000D  var x   9007199254740992 x000D  var y   -x x000D  log x    x   1     true   x000D  log y    y - 1     also true   x000D   x000D     Arithmetic operators work  but bitwise shifts only operate on int32  x000D  log x   2          4503599627370496 x000D  log x  gt  gt  1         0 x000D  log x   1          1 x000D   x000D   x000D      Technical note on the subject of the number 9 007 199 254 740 992  There is an exact IEEE-754 representation of this value  and you can assign and read this value from a variable  so for very carefully chosen applications in the domain of integers less than or equal to this value  you could treat this as a maximum value   In the general case  you must treat this IEEE-754 value as inexact  because it is ambiguous whether it is encoding the logical value 9 007 199 254 740 992 or  9 007 199 254 740 993

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In the Google Chrome built-in javascript  you can go to approximately 2 1024 before the number is called infinity

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It is 253    9 007 199 254 740 992  This is because Numbers are stored as floating-point in a 52-bit mantissa   The min value is -253   This makes some fun things happening  Math pow 2  53     Math pow 2  53    1  gt  gt  true   And can also be dangerous     var MAX INT   Math pow 2  53      9 007 199 254 740 992 for  var i   MAX INT  i  lt  MAX INT   2    i           infinite loop     Further reading  http   blog vjeux com 2010 javascript javascript-max int-number-limits html

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In JavaScript the representation of numbers is 2 53 - 1   However  Bitwise operation are calculated on 32 bits   4 bytes    meaning if you exceed 32bits shifts you will start loosing bits

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Firefox 3 doesn t seem to have a problem with huge numbers    1e 200   1e 100 will calculate fine to 1e 300   Safari seem to have no problem with it as well   For the record  this is on a Mac if anyone else decides to test this    Unless I lost my brain at this time of day  this is way bigger than a 64-bit integer

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Other may have already given the generic answer  but I thought it would be a good idea to give a fast way of determining it    for  var x   2  x   1     x  x    2   console log x     Which gives me 9007199254740992 within less than a millisecond in Chrome 30   It will test powers of 2 to find which one  when  added  1  equals himself

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Node js and Google Chrome seem to both be using 1024 bit floating point values so   Number MAX VALUE   1 7976931348623157e 308

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JavaScript has two number types  Number and BigInt    The most frequently-used number type  Number  is a 64-bit floating point IEEE 754 number    The largest exact integral value of this type is Number MAX SAFE INTEGER  which is    253-1  or    - 9 007 199 254 740 991  or nine quadrillion seven trillion one hundred ninety-nine billion two hundred fifty-four million seven hundred forty thousand nine hundred ninety-one    To put this in perspective  one quadrillion bytes is a petabyte  or one thousand terabytes     Safe  in this context refers to the ability to represent integers exactly and to correctly compare them   From the spec      Note that all the positive and negative integers whose magnitude is no   greater than 253 are representable in the Number type  indeed  the   integer 0 has two representations   0 and -0     To safely use integers larger than this  you need to use BigInt  which has no upper bound    Note that the bitwise operators and shift operators operate on 32-bit integers  so in that case  the max safe integer is 231-1  or 2 147 483 647      x000D   x000D  const log   console log x000D  var x   9007199254740992 x000D  var y   -x x000D  log x    x   1     true   x000D  log y    y - 1     also true   x000D   x000D     Arithmetic operators work  but bitwise shifts only operate on int32  x000D  log x   2          4503599627370496 x000D  log x  gt  gt  1         0 x000D  log x   1          1 x000D   x000D   x000D      Technical note on the subject of the number 9 007 199 254 740 992  There is an exact IEEE-754 representation of this value  and you can assign and read this value from a variable  so for very carefully chosen applications in the domain of integers less than or equal to this value  you could treat this as a maximum value   In the general case  you must treat this IEEE-754 value as inexact  because it is ambiguous whether it is encoding the logical value 9 007 199 254 740 992 or  9 007 199 254 740 993

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Firefox 3 doesn t seem to have a problem with huge numbers    1e 200   1e 100 will calculate fine to 1e 300   Safari seem to have no problem with it as well   For the record  this is on a Mac if anyone else decides to test this    Unless I lost my brain at this time of day  this is way bigger than a 64-bit integer

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Anything you want to use for bitwise operations must be between 0x80000000  -2147483648 or -2 31  and 0x7fffffff  2147483647 or 2 31 - 1    The console will tell you that 0x80000000 equals  2147483648  but 0x80000000  amp  0x80000000 equals -2147483648

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gt   ES6  Number MIN SAFE INTEGER  Number MAX SAFE INTEGER    lt   ES5 From the reference  Number MAX VALUE  Number MIN VALUE    x000D   x000D  console log  MIN VALUE   Number MIN VALUE   console log  MAX VALUE   Number MAX VALUE    console log  MIN SAFE INTEGER   Number MIN SAFE INTEGER     ES6 console log  MAX SAFE INTEGER   Number MAX SAFE INTEGER     ES6 x000D   x000D   x000D

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I write it like this   var max int   0x20000000000000  var min int   -0x20000000000000   max int   1      0x20000000000000     true  max int - 1   lt  0x20000000000000       true   Same for int32  var max int32    0x80000000  var min int32   -0x80000000

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I write it like this   var max int   0x20000000000000  var min int   -0x20000000000000   max int   1      0x20000000000000     true  max int - 1   lt  0x20000000000000       true   Same for int32  var max int32    0x80000000  var min int32   -0x80000000

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In the Google Chrome built-in javascript  you can go to approximately 2 1024 before the number is called infinity

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I did a simple test with a formula  X- X 1  -1  and the largest value of X I can get to work on Safari  Opera and Firefox  tested on OS nbsp X  is 9e15  Here is the code I used for testing   javascript  alert 9e15- 9e15 1

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Firefox 3 doesn t seem to have a problem with huge numbers    1e 200   1e 100 will calculate fine to 1e 300   Safari seem to have no problem with it as well   For the record  this is on a Mac if anyone else decides to test this    Unless I lost my brain at this time of day  this is way bigger than a 64-bit integer

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The short answer is    it depends      If you   re using bitwise operators anywhere  or if you   re referring to the length of an Array   the ranges are   Unsigned  0    -1 gt  gt  gt 0   Signed   - -1 gt  gt  gt 1 -1     -1 gt  gt  gt 1    It so happens that the bitwise operators and the maximum length of an array are restricted to 32-bit integers    If you   re not using bitwise operators or working with array lengths   Signed   -Math pow 2 53       Math pow 2 53    These limitations are imposed by the internal representation of the    Number    type  which generally corresponds to IEEE 754 double-precision floating-point representation   Note that unlike typical signed integers  the magnitude of the negative limit is the same as the magnitude of the positive limit  due to characteristics of the internal representation  which actually includes a negative 0

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To be safe  var MAX INT   4294967295    Reasoning  I thought I d be clever and find the value at which x   1     x with a more pragmatic approach   My machine can only count 10 million per second or so    so I ll post back with the definitive answer in 28 56 years   If you can t wait that long  I m willing to bet that   Most of your loops don t run for 28 56 years 9007199254740992     Math pow 2  53    1 is proof enough You should stick to 4294967295 which is Math pow 2 32  - 1 as to avoid expected issues with bit-shifting   Finding x   1     x    function         use strict      var x   0       start   new Date   valueOf            while  x   1    x        if    x   10000000           console log x              x    1        console log x  new Date   valueOf   - start

[javascript] What is JavaScript's highest integer value that a number can go to without losing precision?

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