Introduction / Context:
Rounding functions in the C/C++ standard math library have distinct behaviors: some always round up, some always round down, and others round to the nearest integer with ties following specific rules. This question focuses on rounding 1.66 upward to 2.0 using the correct function.
Given Data / Assumptions:
- The value is 1.66 (double by default).
- We want the result 2.0, i.e., the smallest integer not less than the argument.
- Standard functions are declared in / .
Concept / Approach:
- 'ceil(x)' returns the least integer value not less than x (rounds toward +infinity).
- 'floor(x)' returns the greatest integer value not greater than x (rounds toward -infinity).
- 'rint/nearbyint/round' round to the nearest integer under specified tie-breaking; 1.66 still rounds to 2 in common modes but the explicit 'round up' operation is 'ceil'.
- Names like 'roundup' and 'roundto' are not standard C functions.
Step-by-Step Solution:
Identify desired behavior → always round upward.Choose 'ceil(1.66)' → returns 2.0.Confirm alternatives: 'floor(1.66)' gives 1.0; 'round' gives nearest (2); but the canonical 'always up' function is 'ceil'.
Verification / Alternative check:
Test values: ceil(2.0) = 2.0, ceil(-1.2) = -1.0; behavior matches 'toward +infinity' definition.
Why Other Options Are Wrong:
- floor(1.66): Moves downward to 1.0.
- roundup/roundto: Not standard C library functions.
- rint: Rounds to nearest according to current rounding mode; not explicitly 'always up'.
Common Pitfalls:
- Assuming 'round' and 'ceil' are interchangeable; only 'ceil' guarantees upward rounding regardless of fractional part.
- Forgetting to include / and link the math library where required.
Final Answer:
ceil(1.66)
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