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All numbers in Javascript are 64bit (8 bytes) floating point numbers but why the effective range of JavaScript is 5e-324 (negative) to 1.7976931348623157e+308 (positive)?
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Description. The MAX_SAFE_INTEGER constant has a value of 9007199254740991 (9,007,199,254,740,991, or ~9 quadrillion). Double precision floating point format only has 52 bits to represent the mantissa, so it can only safely represent integers between -(253 – 1) and 253 – 1.
To check if a number is between two numbers: Use the && (and) operator to chain two conditions. In the first condition check that the number is greater than the lower range and in the second, that the number is lower than the higher range. If both conditions are met, the number is in the range.
JavaScript Range is a function that is supported by JavaScript in order to return all the integer and its value from starting to the ending while traversing from start index to the end index.
If x is in range, then it must be greater than or equal to low, i.e., (x-low) >= 0. And must be smaller than or equal to high i.e., (high – x) <= 0. So if result of the multiplication is less than or equal to 0, then x is in range.
Because that is what is defined by the IEEE 754 spec.
0x 0000 0000 0000 0001 = 2⁻¹⁰²²⁻⁵² ≈ 4.9406564584124654 x 10⁻³²⁴ (Min subnormal positive double)
0x 000f ffff ffff ffff = 2⁻¹⁰²² - 2⁻¹⁰²²⁻⁵² ≈ 2.2250738585072009 x 10⁻³⁰⁸ (Max subnormal positive double)
0x 0010 0000 0000 0000 = 2⁻¹⁰²² ≈ 2.2250738585072014 x 10⁻³⁰⁸ (Min normal positive double)
0x 7fef ffff ffff ffff = (1 + (1 - 2⁻⁵²)) x 2¹⁰²³ ≈ 1.7976931348623157 x 10³⁰⁸ (Max Double)
Because of denormal values; see e.g. http://en.wikipedia.org/wiki/Denormal_number. These extend the range of floating-point values to allow values closer to zero than would otherwise be possible.
You would be well advised to treat these as an implementation detail whose purpose is to make calculations with very small intermediate results not behave too pathologically; when you use these very small values some precision is lost.
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