Analog optical and electronic hardware has emerged as a promising alternative to digital electronics to improve the efficiency of deep neural networks (DNNs). However, previous work has been limited in scalability (input vector length K ≈ 100 elements) or has required nonstandard DNN models and retraining, hindering widespread adoption. Here, we present an analog, CMOS-compatible DNN processor that uses free-space optics to reconfigurably distribute an input vector and optoelectronics for static, updatable weighting and the nonlinearity-with K ≈ 1000 and beyond. We demonstrate single-shot-per-layer classification of the MNIST, Fashion-MNIST, and QuickDraw datasets with standard fully connected DNNs, achieving respective accuracies of 95.6, 83.3, and 79.0% without preprocessing or retraining. We also experimentally determine the fundamental upper bound on throughput (∼0.9 exaMAC/s), set by the maximum optical bandwidth before substantial increase in error. Our combination of wide spectral and spatial bandwidths enables highly efficient computing for next-generation DNNs.