Javascript - 科学记数法受限制的最大数量是多少？

Question

In JavaScript, I was curious to find out what was the maximum possible number representable in scientific notation without getting "Infinity" as a result, so I wrote a little program and found out it's this one:

17976931348623158079372897140530341507993413271003782693617377898044496829276475094664901797758720709633028641669288791094655554785194040263065748867150582068190890200070838367627385484581771153176447573027006985557136695962284291481986083493647529271907416844436551070434271155969950809304288017790417449779

which can be abbreviated to 1.7976931348623157e+308.

My question is, what makes this specific number the maximum possible in JavaScript? Is it hardware-dependent (maybe maximum one on 64 bit?) or language-specific? Why exactly is 308 the maximum usable power of 10?

And also, how different is it in other languages?

Answer 1

Short answer:
Double precision float. Due to how the double data-type is defined.

Long answer:

All floating point numbers (double is a double-precision float) are written as a product of two values, the mantissa and the exponent. In principle, this works similar to how numbers are written in scientific notation: for the number 1.34 * 10^24, the mantissa is 1.34 and the exponent is 24.

https://en.wikipedia.org/wiki/Double-precision_floating-point_format

Number.MAX_VALUE

The value of Number.MAX_VALUE is the largest positive finite value of the Number type, which is approximately 1.7976931348623157e+308.

This property has the attributes { [[Writable]]: false, [[Enumerable]]: fafalselse, [[Configurable]]: false } .

http://ecma262-5.com/ELS5_HTML.htm#Section_8.5

What differs for floats (and doubles) is that you split the total bytes that hold the number into two parts, one for the mantissa and one for the exponent.

That gives you an exponent of 10 bits, and one sign bit for the exponent, so that would give you a number from -1023 to +1024.

However, the base of the exponent is not 10, but 2. The way the floating point number exponent is stored uses 8 bits (for floats) or 11 bits (for doubles), meaning you get exponent values of -127 to +128 (float) or -1023 to +1024 (double).

And 2^1024 gives us a value of 1.797693134862315907729305190789 * 10^308, which is the largest exponent of a double precision float.