fn log1p_32(x: f32) f32x: f3230
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101fn log1p_32(x: f32) f32 {
const ln2_hi = 6.9313812256e-01;
const ln2_lo = 9.0580006145e-06;
const Lg1: f32 = 0xaaaaaa.0p-24;
const Lg2: f32 = 0xccce13.0p-25;
const Lg3: f32 = 0x91e9ee.0p-25;
const Lg4: f32 = 0xf89e26.0p-26;
const u: u32 = @bitCast(x);
const ix = u;
var k: i32 = 1;
var f: f32 = undefined;
var c: f32 = undefined;
// 1 + x < sqrt(2)+
if (ix < 0x3ED413D0 or ix >> 31 != 0) {
// x = -1.0
if (ix == 0xBF800000)
// log1p(-1) = -inf
return x / 0.0;
// x < -1.0
if (ix > 0xBF800000)
// log1p(x < -1) = nan
return (x - x) / 0.0;
// |x| < 2^(-24)
if ((ix << 1) < (0x33800000 << 1)) {
// underflow if subnormal
if (ix & 0x7F800000 == 0) {
mem.doNotOptimizeAway(x * x);
}
return x;
}
// sqrt(2) / 2- <= 1 + x < sqrt(2)+
if (ix <= 0xBE95F619) {
k = 0;
c = 0;
f = x;
}
} else if (ix >= 0x7F800000) {
return x;
}
if (k != 0) {
const uf = 1 + x;
var iu = @as(u32, @bitCast(uf));
iu += 0x3F800000 - 0x3F3504F3;
k = @as(i32, @intCast(iu >> 23)) - 0x7F;
// correction to avoid underflow in c / u
if (k < 25) {
c = if (k >= 2) 1 - (uf - x) else x - (uf - 1);
c /= uf;
} else {
c = 0;
}
// u into [sqrt(2)/2, sqrt(2)]
iu = (iu & 0x007FFFFF) + 0x3F3504F3;
f = @as(f32, @bitCast(iu)) - 1;
}
const s = f / (2.0 + f);
const z = s * s;
const w = z * z;
const t1 = w * (Lg2 + w * Lg4);
const t2 = z * (Lg1 + w * Lg3);
const R = t2 + t1;
const hfsq = 0.5 * f * f;
const dk = @as(f32, @floatFromInt(k));
return s * (hfsq + R) + (dk * ln2_lo + c) - hfsq + f + dk * ln2_hi;
}