The Shape of Code

Many people believe that with a few historical exceptions the IEEE 754 standard has won the floating-point value bit-representation battle.  What these people have forgotten is that money rules; customers are willing to ditch standards if it increases profit. FPGA devices can be configured to perform float-point operations faster and more cheaply than commodity cpus.

Making optimal use of a FPGA may require using a radix of 4 and for the time being automatically convert back and forth between an external 754 radix-2 representation.  In those cases where multiplication/division operations are more common than addition/subtraction use of a logarithmic number system has performance benefits.  For specialist scientific calculations (where cpu time is measured in days) purpose built FPGA devices are the path to significant performance improvements.  In many mass market applications the full power of a 32-bit representation is not needed and a representation using fewer bits does an acceptable job using less powerful (ie, cheaper) hardware.

Customer demand for higher performance and lower cost will push vendors to deliver purpose designed products.  IEEE 754 may be the floating-point representation that people without spending power use because it was once  designed into cpus and vendors are forced to continue to support it for backwards compatibility.