math/big: rounding to denormal float32/64 still incorrect #14651
Description
This is a follow-up to issue #14553. In the special case of a math.Float number that is smaller than the smallest denormal, but that should be rounded up to the smallest denormal, rounding up doesn't happen for values x with 0.5 * 2**-149 (0.1000p-149) < x < 0.75 * 2**-149 (0.1100p-149) for float32 (analogously for float64).
Since the compiler is using this code, for these numbers we get the wrong bit patterns when converting/rounding at compile-time (constant evaluation):
package main
import (
"fmt"
"math"
)
const p149 = 1.0 / (1 << 149) // 1p-149
const (
m0000 = 0x0 / 16.0 * p149 // = 0.0000p-149
m1000 = 0x8 / 16.0 * p149 // = 0.1000p-149
m1001 = 0x9 / 16.0 * p149 // = 0.1001p-149
m1011 = 0xb / 16.0 * p149 // = 0.1011p-149
m1100 = 0xc / 16.0 * p149 // = 0.1100p-149
)
func main() {
print(float32(m0000), f32(m0000))
print(float32(m1000), f32(m1000))
print(float32(m1001), f32(m1001))
print(float32(m1011), f32(m1011))
print(float32(m1100), f32(m1100))
}
func f32(x float64) float32 {
return float32(x)
}
func print(a, b float32) {
fmt.Printf("%016x %016x\n", math.Float32bits(a), math.Float32bits(b))
}
produces
0000000000000000 0000000000000000
0000000000000000 0000000000000000
0000000000000000 0000000000000001
0000000000000000 0000000000000001
0000000000000001 0000000000000001
(the left column is incorrect).
The problem in this case seems to be with rounding per se, and not so much the Float32/64 conversions.