`Real.realMod` and `Real.split` produce incorrect result for values close to zero

Version

110.99.3 (Latest)

Operating System

[x] Any
[ ] Linux
[ ] macOS
[ ] Windows
[ ] Other Unix

OS Version

No response

Processor

[ ] Any
[ ] Arm (using Rosetta)
[ ] PowerPC
[ ] Sparc
[ ] x86 (32-bit)
[X] x86-64 (64-bit)
[ ] Other

System Component

Basis Library

Severity

Minor

Description

For x : real where 0.0 < Real.abs x and Real.abs x <= 1E~16, both Real.realMod x #frac (Real.split x) return 0.0 but should instead return x.

Transcript

- Standard ML of New Jersey (64-bit) v110.99.3 [built: Thu Sep 22 14:05:58 2022]
- val x = 1E~16;
val x = 1E~16 : real
- Real.realMod x;
[autoloading]
[library $SMLNJ-BASIS/basis.cm is stable]
[library $SMLNJ-BASIS/(basis.cm):basis-common.cm is stable]
[autoloading done]
val it = 0.0 : real
- Real.class it;
val it = ZERO : IEEEReal.float_class
- #frac (Real.split x);
val it = 0.0 : real
- Real.class it;
val it = ZERO : IEEEReal.float_class
- val x = ~1E~16;
val x = ~1E~16 : real
- Real.realMod x;
val it = 0.0 : real
- Real.class it;
val it = ZERO : IEEEReal.float_class
- #frac (Real.split x);
val it = 0.0 : real
- Real.class it;
val it = ZERO : IEEEReal.float_class

Expected Behavior

See description.

Steps to Reproduce

val x = 1E~16;
Real.realMod x;        (* should not be 0.0 *)
Real.class it;         (* should not be ZERO *)
#frac (Real.split x);  (* should not be 0.0 *)
Real.class it;         (* should not be ZERO *)

Additional Information