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Fix bug in exp2() #9999

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Merged
merged 4 commits into from
Oct 26, 2021
Merged

Fix bug in exp2() #9999

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297d278
Fix bug in exp2_64 to handle negative values (bad translation from C)
LewisGaul Oct 21, 2021
a28f093
Apply fix to exp2_32() as well, and modify comment on musl behaviour
LewisGaul Oct 22, 2021
1ff1bb9
Use +%= instead of @addWithOverflow()
LewisGaul Oct 22, 2021
e5b0ad8
Merge remote-tracking branch 'upstream/master' into LG-exp2_64-bug
LewisGaul Oct 23, 2021
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32 changes: 21 additions & 11 deletions lib/std/math/exp2.zig
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Original file line number Diff line number Diff line change
Expand Up @@ -78,13 +78,15 @@ fn exp2_32(x: f32) f32 {
return 1.0 + x;
}

// NOTE: musl relies on unsafe behaviours which are replicated below
// (addition/bit-shift overflow). Appears that this produces the
// intended result but should confirm how GCC/Clang handle this to ensure.

var uf = x + redux;
var i_0 = @bitCast(u32, uf);
i_0 += tblsiz / 2;
i_0 +%= tblsiz / 2;

const k = i_0 / tblsiz;
// NOTE: musl relies on undefined overflow shift behaviour. Appears that this produces the
// intended result but should confirm how GCC/Clang handle this to ensure.
const uk = @bitCast(f64, @as(u64, 0x3FF + k) << 52);
i_0 &= tblsiz - 1;
uf -= redux;
Expand Down Expand Up @@ -357,7 +359,7 @@ const exp2dt = [_]f64{
};

fn exp2_64(x: f64) f64 {
const tblsiz = @intCast(u32, exp2dt.len / 2);
const tblsiz: u32 = @intCast(u32, exp2dt.len / 2);
const redux: f64 = 0x1.8p52 / @intToFloat(f64, tblsiz);
const P1: f64 = 0x1.62e42fefa39efp-1;
const P2: f64 = 0x1.ebfbdff82c575p-3;
Expand Down Expand Up @@ -400,22 +402,27 @@ fn exp2_64(x: f64) f64 {
return 1.0 + x;
}

// NOTE: musl relies on unsafe behaviours which are replicated below
// (addition overflow, division truncation, casting). Appears that this
// produces the intended result but should confirm how GCC/Clang handle this
// to ensure.

// reduce x
var uf = x + redux;
var uf: f64 = x + redux;
// NOTE: musl performs an implicit 64-bit to 32-bit u32 truncation here
var i_0 = @truncate(u32, @bitCast(u64, uf));
i_0 += tblsiz / 2;
var i_0: u32 = @truncate(u32, @bitCast(u64, uf));
i_0 +%= tblsiz / 2;

const k: u32 = i_0 / tblsiz * tblsiz;
const ik = @bitCast(i32, k / tblsiz);
const ik: i32 = @divTrunc(@bitCast(i32, k), tblsiz);
i_0 %= tblsiz;
uf -= redux;

// r = exp2(y) = exp2t[i_0] * p(z - eps[i])
var z = x - uf;
const t = exp2dt[@intCast(usize, 2 * i_0)];
var z: f64 = x - uf;
const t: f64 = exp2dt[@intCast(usize, 2 * i_0)];
z -= exp2dt[@intCast(usize, 2 * i_0 + 1)];
const r = t + t * z * (P1 + z * (P2 + z * (P3 + z * (P4 + z * P5))));
const r: f64 = t + t * z * (P1 + z * (P2 + z * (P3 + z * (P4 + z * P5))));

return math.scalbn(r, ik);
}
Expand All @@ -433,6 +440,7 @@ test "math.exp2_32" {
try expect(math.approxEqAbs(f32, exp2_32(0.8923), 1.856133, epsilon));
try expect(math.approxEqAbs(f32, exp2_32(1.5), 2.828427, epsilon));
try expect(math.approxEqAbs(f32, exp2_32(37.45), 187747237888, epsilon));
try expect(math.approxEqAbs(f32, exp2_32(-1), 0.5, epsilon));
}

test "math.exp2_64" {
Expand All @@ -442,6 +450,8 @@ test "math.exp2_64" {
try expect(math.approxEqAbs(f64, exp2_64(0.2), 1.148698, epsilon));
try expect(math.approxEqAbs(f64, exp2_64(0.8923), 1.856133, epsilon));
try expect(math.approxEqAbs(f64, exp2_64(1.5), 2.828427, epsilon));
try expect(math.approxEqAbs(f64, exp2_64(-1), 0.5, epsilon));
try expect(math.approxEqAbs(f64, exp2_64(-0x1.a05cc754481d1p-2), 0x1.824056efc687cp-1, epsilon));
}

test "math.exp2_32.special" {
Expand Down