B5 Coverage Issue

[Lamarr3314]

1. Remove sign cross from test 9: "One number for every exponent in the range [MinNorm.exp, MinNorm.exp + 5]" There are no restrictions on the sign in this description:
   BF16
   F16
   F32
   F64
   F128
2. Correct the sign cross for each precision and each test. Every precision uses F32_sign:
   BF16
   F16
   F64
   F128
3. Correct the check for minSubNorm+-3ulp. Our updated definition for +-3ulp is that the last bit is the sticky bit, an or of the remaining bits.
   BF16
   F16
   F32
   F64
   F128
4. Correct the supported operations. The support operations are: Multiplication, Division, FMA, and High to Low Precision Converts, addition and subtraction.
   Operations Coverpoint
5. For Division, remove cross for MinNorm+-3ulp. It is difficult to reliably hit these values using division and considering that we need exact precision, we cannot use guess and check with softfloat to hit these values.
6. For addition and subtraction, restrict crosses to the possible results. The smallest result of an addition or subtraction is minSubNorm. Anything below should be excluded. Any values above this limit must be a multiple of minSN to be included in the tests.
7. Correct the check for minNorm +-3ulp. This should use our new definition where the last bit is an or of the remaining bits.
   MinNorm+-3ulp examples BF_16:
   MinNorm - 3 ulp:
   0.1111_111|01 <- last bit represents an or of the remaining bits
   MinNorm - 2 ulp:
   0.1111_111|10
   MinNorm - 1 ulp:
   0.1111_111|11
   MinNorm + 0 ulp:
   1.0000_000|00
   MinNorm + 1 ulp:
   1.0000_000|01
   MinNorm + 2 ulp:
   1.0000_000|10
   MinNorm + 3 ulp:
   1.0000_000|11
   BF_16 MinSubNorm +- 3 ulp examples:
   MinSubNorm - 3 ulp:
   0.0000_000|01 <- last bit represents an or of the remaining bits
   MinSubNorm - 2 ulp:
   0.0000_000|10
   MinSubNorm - 1 ulp:
   0.0000_000|11
   MinSubNorm - 0 ulp:
   0.0000_001|00
   MinSubNorm + 1 ulp:
   0.0000_001|01
   MinSubNorm + 2 ulp:
   0.0000_001|10
   MinSubNorm + 3 ulp:
   0.0000_001|11

[coreyqh]

@Lamarr3314 A few clarifications as I wrap this up.

Points 4 and 6 seem to contradict each other. Is add/sub supported?

Point 5: is this also applicable for minsubnorm +- 3ulp or just minNorm?

[coreyqh]

#103 (WIP) will address these issues.

[Lamarr3314]

Regarding your question on add/sub.
Add and Sub are supported even though they can't trigger underflow. The goal of including them is just to have consistency between our tests and the IBM test suite. We just need to limit the coverage to the select add/sub operations that can satisfy some of the values in the IBM paper. For example:
Tests 1 and 2) "A random positive/negative SubNorm". We can hit a random subNorm with add/sub.
Tests 3 and 4) "All values in the range positive/negative MinSubNorm +-3ulp". The only value in this range we can hit with add/sub is minSubNorm.
Tests 5 and 6) "All values in the range positive/negative MinNorm +- 3ulp". The only value in this range we can hit with add/sub is MinNorm.
Tests 7 and 8) "A random number in the range positive/negative in the range (0, MinSubNorm)". We cannot hit any value within this range.
Test 9) "One number for every exponent in the range [MinNorm.exp, MinNorm.exp + 5]" We can hit every value in this range with add/sub.
Regarding your question on point 5
We can reliably hit MinSubNorm +-3ulp with division. Point 5 only applies to MinNorm +-3ulp.

[coreyqh]

I see limited value in including add/sub. Really, the only purpose for having them is to ensure that they do not erroneously raise the UF flag when near underflow boundaries.

I say we exclude them for now.