Round the exponent up to the nearest multiple of 8 and shift the mantissa to the left with zeros to keep the value identical (making it up to 8 bits wider). Compress the sign bit, exponent, and mantissa separately using standard lossless integer-sampled image compression, e.g., JPEG 2000 Lossless. The mantissa probably needs to get sliced bitwise into several 8-bit planes.
Motivation was to compress intermediate computations of the Mandelbrot set with real (continuous) escape times.
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