One decimal literal, three types
In C, `0.2F`, `0.2`, and `0.2L` have types `float`, `double`, and `long double`, respectively. Their displayed hexadecimal values differ: choosing a type also chooses a precision for representing the value. section 5.3
Floating-point types approximate real numbers; C also has complex floating-point types. A value has a restricted magnitude and a finite number of digits. Unlike integer arithmetic without overflow, floating-point computations generally produce approximations cut off after a certain number of binary digits. section 5.2 section 5.8
A simplified binary model builds a value from a sign `s`, an exponent `e`, and `p` bits `f₁ … fₚ`: `s × 2ᵉ × Σ(fₖ × 2⁻ᵏ)`. The exponent ranges from `e_min` to `e_max`; `p` is the precision. The cutoff position changes with the number’s magnitude—that is the “floating” part. section 5.7.8
Evaluating the bits
For `s = −1`, `e = −2`, and bits `1, 0, 1`, the model gives `−1 × 2⁻² × (2⁻¹ + 2⁻³) = −5/32`. The bits determine a value through the exponent; they are not decimal digits. section 5.7.8
TAKEAWAY — Check the type and representation before expecting an exact result.
- `<float.h>` supplies type-dependent limits and precision information. For `double`, examples include `DBL_MAX`, `DBL_MANT_DIG`, `DBL_MIN_EXP`, and `DBL_MAX_EXP`. Precision names the number of mantissa bits, not the accuracy of a computation. section 5.7.8 section 5.8
- Decimal notation such as `1.7E-13` uses a power of ten. Hexadecimal floating-point notation such as `0x1.7aP-13` uses a hexadecimal fraction and a power of two, making exactly representable values easier to specify. section 5.3
- For ordinary decimal output, use `printf`’s `%g`; `%a` selects hexadecimal floating-point output. Match format specifiers and modifiers to arguments: a mismatch can cause undefined behavior. section 8.4.4
float |
double |
long double |
|
| Literal | 0.2F |
0.2 |
0.2L |
| Value | 0x1.9999’9AP-3F |
0x1.9999’9999’9999AP-3 |
0xC.CCCC’ CCCC’ CCCC’ CCDP-6L |
Compare the hexadecimal values shown for `0.2F`, `0.2`, and `0.2L` to see how the literal’s type affects its represented value. section 5.3
Rounding can also depend on floating-point environment state, and expression contraction can be controlled. Consequently, a function using floating-point arithmetic is generally not pure enough for C23’s `[[unsequenced]]` attribute. Explicit rounding and contraction pragmas can help establish a stable environment for a carefully justified function. section 16.3
