exp_reduced_() [2/2]

float fl::detail::exp_reduced_ ( float x )

inline

Definition at line 125 of file math.cpp.hpp.

                                                {
    FloatBits xb;
    xb.f = x;
    const u32 ax = xb.u & 0x7fffffffu;
    if (ax >= 0x42b17218u) {           // |x| >= 88.7228, or NaN
        if (ax > 0x7f800000u) return x;  // NaN
        if ((xb.u >> 31) == 0u) {        // overflow -> +inf
            FloatBits inf;
            inf.u = 0x7f800000u;
            return inf.f;
        }
        if (ax >= 0x42cff1b5u) return 0.0f;  // x <= -103.972: underflow
    }
    // k = round(x / ln2) via the 1.5 * 2^23 magic constant: adding it puts
    // the integer in the low mantissa bits, so no float<->int conversions.
    const float kMagic = 12582912.0f;
    FloatBits t;
    t.f = x * 1.44269504088896341f + kMagic;
    const int k = t.i - 0x4b400000;
    const float kf = t.f - kMagic;
    const float r = (x - kf * 6.9314575195e-01f) - kf * 1.4286067653e-06f;
    // e^r = 1 + r + r^2 * P(r), P minimax on |r| <= ln2/2: worst case 1 ulp.
    float p = 1.393364297e-03f;
    p = p * r + 8.363175565e-03f;
    p = p * r + 4.166646498e-02f;
    p = p * r + 1.666657700e-01f;
    p = p * r + 5.000000013e-01f;
    p = (p * r * r) + r + 1.0f;
    return scale_pow2_(p, k);
}

References fl::detail::FloatBits::f, fl::FL_NO_EXCEPT, scale_pow2_(), fl::t, fl::detail::FloatBits::u, and fl::x.

Referenced by fl::exp_impl_double(), fl::exp_impl_float(), and exp_reduced_().

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