Hardware simulation of channel codes offers the potential of improving code evaluation speed by orders of magnitude over workstation- or PC-based simulation. We describe a hardware-based Gaussian noise generator used as a key component in a hardware simulation system, for exploring channel code behavior at very low bit error rates (BERs) in the range of 10^-9 to 10^-10. The main novelty is the design and use of non-uniform piecewise linear approximations in computing trigonometric and logarithmic functions. The parameters of the approximation are chosen carefully to enable rapid computation of coefficients from the inputs, while still retaining extremely high fidelity to the modelled functions. The output of the noise generator accurately models a true Gaussian PDF even at very high \sigma values. Its properties are explored using: (a) several different statistical tests, including the chi-square test and the Kolmogorov-Smirnov test, and (b) an application for decoding of low density parity check (LDPC) codes. An implementation at 133MHz on a Xilinx Virtex-II XC2V4000-6 FPGA produces 133 million samples per second, which is 40 times faster than a 2.13GHz PC; another implementation on a Xilinx Spartan-IIE XC2S300E-7 FPGA at 62MHz is capable of a 20 times speedup. The performance can be improved by exploiting parallelism: an XC2V4000-6 FPGA with three parallel instances of the noise generator at 126MHz can run 100 times faster than a 2.13GHz PC. We illustrate the deterioration of clock speed with the increase in the number of instances.