Banded emulated double precision

Banded emulated double precision#

Compute 1/3 with aether::banded::BandedReal and compare it to the native double result.

Time: ~2 min · Runs on: CPU · You need: Banded/emulated real arithmetic

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%run ../_shared/setup.py

running on: cpu

aether::banded::BandedReal emulates double precision using float maths – see Banded/emulated real arithmetic for how. Useful on a GPU with slow or missing FP64 hardware:

print(run_cpp(r"""
    using aether::banded::BandedReal;

    BandedReal a = BandedReal::fromDouble(1.0);
    BandedReal b = BandedReal::fromDouble(3.0);
    BandedReal q = a / b;
    double banded_result = q.toDouble();

    double native_result = 1.0 / 3.0;
    std::printf("banded 1/3 = %.17g\n", banded_result);
    std::printf("native 1/3 = %.17g\n", native_result);
    std::printf("difference = %.3e\n", banded_result - native_result);
""", includes=("<aether/banded/banded.h>",)))

banded 1/3 = 0.33333333333333331
native 1/3 = 0.33333333333333331
difference = 0.000e+00

BandedReal never implicitly converts to double – fromDouble/toDouble are the only crossing points, by design.