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std: added tests for expo2f #24688

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std: added tests for expo2f #24688

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30 changes: 28 additions & 2 deletions lib/std/math/expo2.zig
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Original file line number Diff line number Diff line change
Expand Up @@ -5,7 +5,8 @@
// https://git.musl-libc.org/cgit/musl/tree/src/math/__expo2.c

const math = @import("../math.zig");

const std = @import("../std.zig");
const expectApproxEqAbs = std.testing.expectApproxEqAbs;
/// Returns exp(x) / 2 for x >= log(maxFloat(T)).
pub fn expo2(x: anytype) @TypeOf(x) {
const T = @TypeOf(x);
Expand All @@ -15,7 +16,15 @@ pub fn expo2(x: anytype) @TypeOf(x) {
else => @compileError("expo2 not implemented for " ++ @typeName(T)),
};
}

/// Fast approximation of `2^x` for 32-bit floats.
///
/// This uses a scaling trick to approximate `2^x` as:
/// `exp(x - kln2) * scale^2`
/// where `kln2` ≈ k * ln(2), and `scale` is constructed using bit manipulation
/// to approximate `2^(k/2)`.
///
/// This avoids expensive floating-point operations and is optimized
/// for performance over precision.
fn expo2f(x: f32) f32 {
const k: u32 = 235;
const kln2 = 0x1.45C778p+7;
Expand All @@ -25,6 +34,7 @@ fn expo2f(x: f32) f32 {
return @exp(x - kln2) * scale * scale;
}

// This function is similar to `expo2f`, but for 64-bit floats.
fn expo2d(x: f64) f64 {
const k: u32 = 2043;
const kln2 = 0x1.62066151ADD8BP+10;
Expand All @@ -33,3 +43,19 @@ fn expo2d(x: f64) f64 {
const scale = @as(f64, @bitCast(@as(u64, u) << 32));
return @exp(x - kln2) * scale * scale;
}

test "expo2f approximates 2^x" {
try expectApproxEqAbs(expo2f(7.3), math.pow(f32, 2.0, 7.3), 1e-6);
try expectApproxEqAbs(expo2f(-1.0), math.pow(f32, 2.0, -1.0), 1e-6);
try expectApproxEqAbs(expo2f(0.0), 1.0, 1e-6);
try expectApproxEqAbs(expo2f(10.0), math.pow(f32, 2.0, 10.0), 1e-6);
try expectApproxEqAbs(expo2f(3.5), math.pow(f32, 2.0, 3.5), 1e-6);
}

test "expo2d approximates 2^x" {
try expectApproxEqAbs(expo2d(7.3), math.pow(f64, 2.0, 7.3), 1e-12);
try expectApproxEqAbs(expo2d(-1.0), math.pow(f64, 2.0, -1.0), 1e-12);
try expectApproxEqAbs(expo2d(0.0), 1.0, 1e-12);
try expectApproxEqAbs(expo2d(10.0), math.pow(f64, 2.0, 10.0), 1e-12);
try expectApproxEqAbs(expo2d(3.5), math.pow(f64, 2.0, 3.5), 1e-12);
}
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