Floating Point Integer format, for zkSNARK circuits

[HarryR]

It has been suggested that floating point numbers offer a larger dynamic range than integers, which is useful when dealing with cryptocurrencies that may have many zeros and arbitrary units.

Implement a floating point integer format in-circuit with matching Python implementation.

References:

• https://en.wikipedia.org/wiki/Half-precision_floating-point_format
• https://github.com/xennygrimmato/z3-floating-point-proofs
• https://github.com/fredrik-johansson/mpmath
• https://github.com/qlootens/FloatingPointConverter
• http://www.toves.org/books/float/
• https://en.wikipedia.org/wiki/Single-precision_floating-point_format
• https://www.eetimes.com/author.asp?section_id=36&doc_id=1287491
• https://blog.penjee.com/binary-numbers-floating-point-conversion/
• https://www.eetimes.com/author.asp?section_id=36&doc_id=1287491

Operations required:

• Validate
• Convert to Unsigned Integer
• Convert from Unsigned Integer

There is no need for addition, multiplication or division operations, it is only necessary to use it as a mechanism for compressing payment amounts.

The precision required by the exponent/mantissa format should be enough to make transfers of up to 1 million units of an ERC-20 token with 18 decimal places. This is different from 'floating point', it is more like a 'high dynamic range integer' where a smaller number of bits control the exponentiation of the integer while a smaller number represent its entropy.

10**18 * 1000000 = 1000000000000000000000000

The dynamic range for integers in Wei should be 0 to 1000000000000000000000000, with as much precision as possible to allow for payments which as closely match what the user desired.

[HarryR]

There is an implementation by Matter Inc - https://github.com/matterinc/sapling-crypto/blob/master/src/circuit/float_point.rs