Incorrect results for Float80 exact powers of two

[tbkka]

I've been comparing ryu_generic128 output against other implementations and believe it generates incorrect output for certain exact powers of two. One example:

• Input float80: 0x1p-16367
• Expected output: 1.10169395793497080013e-4927
• Ryu_generic128 result: 1.1016939579349708001E-4927

The "expected output" here agrees with both gdtoa and Swift's standard library, so I'm reasonably certain it's correct. Similar discrepancies occur for about 4000 other exact powers of two.

This issue seems to be limited to float80. I've not seen any similar failures for float128, double, float, or float16.

[ulfjack]

Thanks for the report. The reported powers of two are all cases where the next lower floating-point number is closer than the next higher floating-point number. The code detects that case by comparing the mantissa against 0, which is correct only if the format has an implicit leading one, but incorrect for an explicit leading one, as is the case for the Float80 format. I have a fix.