By exploiting large antenna arrays, massive MIMO (multiple input multiple output) systems can greatly increase spectral and energy efficiency over traditional MIMO systems. However, increasing the number of antennas at the base station (BS) makes the uplink joint channel estimation and data detection (JED) challenging in massive MIMO systems. In this paper, we consider the JED problem for massive SIMO (single input multiple output) wireless systems, which is a special case of wireless systems with large antenna arrays. We propose exact Generalized Likelihood Ratio Test (GLRT) optimal JED algorithms with low expected complexity, for both constantmodulus and nonconstant-modulus constellations. We show that, despite the large number of unknown channel coefficients, the expected computational complexity of these algorithms is polynomial in channel coherence time (T ) and the number of receive antennas (N), even when the number of receive antennas grows polynomially in the channel coherence time (N = O(T 11) suffices to guarantee an expected computational complexity cubic in T and linear in N). Simulation results show that the GLRT-optimal JED algorithms achieve significant performance gains (up to 5 dB improvement in energy efficiency) with low computational complexity.