Metal QD: QD extended precision library for Metal

Metal QD is (preliminary work on) a port of the QD extended precision library to Apple's Metal GPU compute language.

QD is a library for Quad-Double arithmetic in which extended precision numbers are represented by the unevaluated sum of four double precision machine numbers. QD comes from http://crd-legacy.lbl.gov/~dhbailey/mpdist/

Metal QD adapts QD to the Metal environment primarily by using single precision floats instead of doubles. This allows calculations with 96-bits of precision. This port also disables references to features unavailable on the GPU, such as iostream, string, limits, cmath.

Metal QD is based off of qd-2.3.17

What is supported?

• Constructors
• Arithmetic operators: +, -, *, =, +=, -=
• Comparison operators: <, >, ==, !=
• Special Functions: sqr(), mul_pwr2()

What hasn't been ported?

• Anything not implemented in the inline library.
• Division
• Trig and other transendental functions
• The DD (Double-Double) type
• I/O

Usage

• Copy these files to project: metal_qd.h, qd_real.h, qd_config.h, qd_inline.h, inline.h

• In Metal or Objective-C++ source file: #include "metal_qd.h"

• Disable Metal's unsafe floating-point optimizations. Add -fno-fast-math to Build Phases -> Compile Sources -> Compiler Flags for any Metal files using metal_qd.h

• Read the README_QD section C. Programming techniques

Example Code Snipet

qd_real q;
q=1.;            // native 1.0 converted to qd_real q
q+=exp2(-95.);   // native 2^-95 added to qd_real q
// q now represents 1.000000000000000000000000000025
// This has more precision than can be represented in a native double

// Conversion to/from float4 usefull for passing values between CPU and GPU
simd::float4 vq;
vq=to_float4(q); // Convert qd_real to float4

qd_real qvq;     // Convert and float4 back to qd_real
qvq=vq;

Find the above in tests/metal_qd_test.cpp

Future Work

• Port non-inline and DD portions of library
• Create proper Metal framework
• Create demo app using Metal QD on GPU (in addition to CPU)
• Test having both QD and Metal_QD in same CPU source
• Update documentation to reflect Metal_QD