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Date: Tue, 4 Mar 2014 18:24:00 -0000
Subject: Re: [PHC] wider integer multiply on 32-bit x86

> There seems to be no FPU emulation trick like we had on x86 machines,
> but I could be wrong about that.

In fact there is such a trick, but modern OS don't do it.

It is a matter of "calling convention". In the old one (called "ATPCS"),
computations on FP types are supposed to use FP registers and opcodes, and
it is up to the OS, when the hardware does not actually have an FPU, to
trap on the unsupported opcodes and emulate the FPU (just like the "FPU
emulation trick" on x86). This works, but it means that FP computations on
FPU-less systems incur the overhead of emulation AND the overhead of
trapping on FPU opcodes, the latter being quite expensive in itself. Since
in the embedded world, ARM-with-FPU are a rarity, this was felt to be
quite suboptimal.

A new calling convention was needed anyway, to enable proper support for
Thumb and Thumb-2, to prepare the path for 64-bit ARM, and to fix some
alignment issues. So a new convention dubbed "AAPCS" was defined, and in
that new convention, all FP operations are emulated explicitly; no FP
opcode or register appears in the binary produced by the compiler. The
compiler uses library-provided functions and inline code which do all the
computations on the integer registers. On all the ARM without FPU, this
gives a very substantial performance boost to FP computations (like twice
faster). However, this means that the few ARM who have a FPU will not
benefit from that hardware FPU when running such code.

A side-effect is that modern OS which follow the AAPCS don't actually
bother maintaining a trap-based FPU emulator (although they technically
could), since it is not mandated by AAPCS.

The underlying market force at work here is that general-purpose computers
(including smartphones and servers) have, usually, little need for 64-bit
IEEE 754 floating-point types -- at least, very little or no
_performance-critical_ need. What user machines need, for 3D rendering and
audio/video processing, is to be able to do a lot of single-precision
floating-point computations (single-precision values have a 24-bit
mantissa, not 53-bit, and they fit on 32 bits). Which is why newer ARM
processors have a NEON engine, which implements a SIMD instruction set
that can compute four single-precision multiplies in parallel, but is
completely incapable of doing any double-precision operation. NEON and VFP
(the FPU for ARM) are supposed to share their registers (similarly to MMX
vs i387 in the x86 world), but there are ARM CPU with NEON but without

In a similar vein, OpenGL ES, aka "OpenGL for embedded systems", is mostly
a subset of OpenGL with all double-precision functions removed; with
OpenGL ES you use 'float', not 'double'.

It shall also be noted that a number of such implementations of 32-bit FP
operations are known not to be IEEE-754 compliant, meaning that you can
encounter occasional rounding issues. An incorrect least significant bit
rarely matters for 3D rendering or video decoding, but it can be deadly
for a cryptographic algorithm where exact reproducibility of computations
is necessary. Using the FPU or a NEON-like engine for cryptography with
floating-point types is thus rather risky. Personally, I'd recommend
against it.

        --Thomas Pornin

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