[worst cases for decimal32]

The decimal64 format from IEEE 754R has a 16-digit significand, and an exponent emin ≤ e ≤ emax, with emin = -383, emax = +384, the significand being between 1.000000000000000 and 9.999999999999999 for normal numbers, and between 0.000000000000001 and 0.999999999999999 for subnormal numbers.

The smallest positive normal number is thus 1.0E-383, the smallest positive subnormal is 1.0E-398, and the largest number is 9.999999999999999E+384.

### The exponential function

With Vincent Lefèvre and Damien Stehlé, we have computed the worst cases of the exponential function in the IEEE 754r decimal64 format. The worst case for all rounding modes and |x| ≥ 3E-11 is
exp(9.407822313572878E-2) = 1.09864568206633850000000000000000278...
The complete list of bad-cases with a distance less than 10-15 ulp to a breakpoint (either for rounding to nearest or directed rounding) are (excluding values of x very near from 0 that give exp(x) = 1 for rounding to nearest): x > 0 and x < 0 (in those files, e is the exponent, m the mantissa, such that x = m*10e-16, and d is twice the absolute value of the distance in ulp to the nearest breakpoint).