Add: PI upper/lower bound f16 constants to ScalarValue

[xonx4l]

Which issue does this PR close?

• Closes Support scalarvalue APIs for f16 regarding Pi values #19465.

Rationale for this change

To add Support scalarvalue APIs for f16 regarding Pi values

What changes are included in this PR?

Added half::f16 support to ScalarValue mathematical APIs.

Are these changes tested?

Yes

Are there any user-facing changes?

Yes

[Jefffrey]

How/where are these constants sourced from?

[xonx4l]

These are the IEEE 754 binary16 half-precision bit representations closest to pi.

[xonx4l]

I converted std::f64::consts::PI to f16 which results in 0x4248 (approx 3.1406). Since this value is slightly lower than the actual Pi. I used the next representable bit pattern (0x4249) to ensure a strict upper bound.

[Jefffrey]

Did some quick sanity checks on Rust playground with following code:

use half::f16;

fn main() {
    println!("f16 PI + next_up");
    println!("0x{:X}", (f16::PI).to_bits());
    println!("0x{:X}\n", next_up(f16::PI).to_bits());

    println!("f16 -PI + next_down");
    println!("0x{:X}", (-f16::PI).to_bits());
    println!("0x{:X}\n", next_down(-f16::PI).to_bits());
    
    println!("f16 FRAC_PI_2 + next_up");
    println!("0x{:X}", (f16::FRAC_PI_2).to_bits());
    println!("0x{:X}\n", next_up(f16::FRAC_PI_2).to_bits());

    println!("f16 -FRAC_PI_2 + next_down");
    println!("0x{:X}", (-f16::FRAC_PI_2).to_bits());
    println!("0x{:X}\n", next_down(-f16::FRAC_PI_2).to_bits());
}

pub fn next_up(v: f16) -> f16 {
    let bits = v.to_bits();
    
    let sign_mask = 0x8000u16;

    let abs = bits & !sign_mask;
    let next_bits = if abs == 0 {
        let tiny_bits = 0x1u16;
        tiny_bits
    } else if bits == abs {
        bits + 1
    } else {
        bits - 1
    };
    f16::from_bits(next_bits)
}

pub fn next_down(v: f16) -> f16 {
    let bits = v.to_bits();
    
    let sign_mask = 0x8000u16;

    let abs = bits & !sign_mask;
    let next_bits = if abs == 0 {
        let tiny_bits = 0x1u16 | sign_mask;
        tiny_bits
    } else if bits == abs {
        bits - 1
    } else {
        bits + 1
    };
    f16::from_bits(next_bits)
}

Adapted next_up and next_down from f32/f64 to f16, see references:

• https://docs.rs/half/latest/src/half/binary16.rs.html#764
• https://doc.rust-lang.org/src/core/num/f32.rs.html#754

Constants look correct

[xonx4l]

Thanks for taking the time to write this . Looks great!

[Jefffrey]

Thanks @xonx4l