Since the original 8087 from Intel and the closely related IEEE standard for floating point arithmetic, we've had available the choice of floats, doubles, and long doubles. In many cases, these are 32, 64 and 80 bit floating point representations, supported directly by the hardware.
But since the rise of ARM and the fall of most other architectures, and especially since Apple's introduction of the M1 product line, we're in a position that not all common laptops and computers offer the 80 bit long double. It's just not there in the hardware.
William Kahan, who had a lot to do with the original 8087 and the closely related IEEE standard, apparently said in 2002:
So, perhaps we should say the 80 bit format is a great idea but not the final story. It turns out there's already a standard for quad precision, a 128 bit format, which might in the future be the one to look for. Whether it will be offered in commodity machines is another question - I'm guessing not in low-end machines. It seems the market is satisfied with 64 bit floats, and has forgotten or discounted the arguments which led to the 80bit compromise.For now the 10-byte Extended format is a tolerable compromise between the value of extra-precise arithmetic and the price of implementing it to run fast; very soon two more bytes of precision will become tolerable, and ultimately a 16-byte format ... That kind of gradual evolution towards wider precision was already in view when IEEE Standard 754 for Floating-Point Arithmetic was framed.
It turns out that ARM64 procedure call standard defines long double as quad precision, which is not to say that quad precision is natively available. And there's a library for GCC which offers quad precision. See
Wikipedia's Quadruple-precision floating-point format.
See also Paul Zimmermann's slide deck "How Slow is Quadruple Precision?"
Possibly, if we're unlikely to get 128bit float support in hardware, we're better off with double-double floats, which are not an IEEE standard but are (presumably? hopefully?) higher performance than quad precision. This presentation suggests no worse than a 10x slowdown.Quadruple precision is indeed slow, but we can do much better!
We saved a factor of 10 with little effort, probably we can save another factor of 2 with more effort.