Function Cosh

tensorflow/compiler/xla/client/lib/math.cc:1262–1267

Cosh(x) = (e^x + e^-x) / 2 = e^(x + log(1/2)) + e^(-x + log(1/2)). The second formulation avoids overflowing when e^x = inf but (e^x)/2 is not inf. This incorrectly overflows to inf for two f32 input values, namely +/-89.4159851, due to rounding error when computing x +/- log(1/2). The correct answer of 3.40281961e+38 (0x7f7fffec) is very close to max-float, so we deem this acceptable.

// correct answer of 3.40281961e+38 (0x7f7fffec) is very close to max-float, so
// we deem this acceptable.
XlaOp Cosh(XlaOp x) {
  return DoWithUpcastToF32(x, {BF16, F16}, [](XlaOp x) {
    auto log_one_half = Log(ScalarLike(x, 0.5));
    return Exp(x + log_one_half) + Exp(-x + log_one_half);
  });
}

// Sinh(x) = (e^x - e^-x) / 2
//         = e^(x + log(1/2)) - e^(-x + log(1/2)).