We identify a timing channel in the floating point instructions of modern x86 processors: the running time of floating point addition and multiplication instructions can vary by two orders of magnitude depending on their operands. We develop a benchmark measuring the timing variability of floating point operations and report on its results. We use floating point data timing variability to demonstrate practical attacks on the security of the Firefox browser (versions 23 through 27) and the Fuzz differentially private database. Finally, we initiate the study of mitigations to floating-point data timing channels with libfixedtimefixedpoint, a new fixed-point, constant-time math library. Modern floating point standards and implementations are sophisticated, complex, and subtle, a fact that has not been sufficiently recognized by the security community. More work is needed to assess the implications of the use of floating-point instructions in security-relevant software. Our attacks show that data timing channels are not a hypothetical threat but a real and pervasive danger to software security. More work is needed to search for, identify, and mitigate data timing channels in popular CPUs and in emerging computing platforms like GPGPUs.