Decimal Ulp At Explicit Exponent Tool

Description

Return decimal spacing at a supplied base-ten order and significant-digit count, not binary IEEE spacing.

Decimal rounding and scale alignment depend on retained places, discarded digits, tie rules, and the number of rounding stages. A decimal spacing is different from the binary floating-point spacing of a runtime number. Text-based digit operations can preserve widths that disappear when a value is parsed numerically.

Return decimal spacing at a supplied base-ten order and significant-digit count, not binary IEEE spacing.

When to use this tool

Use Decimal Ulp At Explicit Exponent when you need this specific decimal tie, scale, digit-carry, spacing, or staged-rounding check.

How to use the tool and how it works

Enter exponent, digits. Use the units and conventions below.
Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
Read ulp. Use the output convention below.

For decimal exponent in -300..300 and significant digits in 1..16 return ulp=10^(exponent-digits+1).^[1]

Input field	Meaning and units	Accepted input
exponent	Exponent	Required. Safe integer; minimum -300; maximum 300.
digits	Digits	Required. Safe integer; minimum 1; maximum 16.

Output field	Interpretation	Returned shape
ulp	Decimal spacing at the supplied exponent, not runtime binary ULP.	Required. Finite number.

json

{
  "input": {
    "exponent": 3,
    "digits": 4
  },
  "output": {
    "ulp": 1
  }
}

Limitations and assumptions

This is spacing for an explicitly supplied decimal exponent/precision convention, not the binary floating-point ULP of an input value. No value is inspected and very small results use the runtime's finite floating-point approximation.
Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.

Alternative or Complementary methods

Use an exact decimal representation when binary floating-point rounding is inadequate. Apply a complete rounding rule rather than treating a tie-only flag or digit-count term as the whole decision.

References

Calculation and input contract: number/decimal-ulp-at-explicit-exponent — tool.io

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