Red Hat engineer Siddhesh Pyarekar takes a look at the mathematical functions in GLibC and makes some improvements.
Mathematical function implementations usually have to trade off between speed of computation and the accuracy of the result. This is especially true for transcendentals (i.e. the exponential and trigonometric functions), where results often have to be computed to a fairly large precision to get last bit accuracy in a result that is to be stored in an IEEE-754 double variable.
Transcendental functions in glibc are implemented as multiple phases. The first phases of computation use a lookup table of pre-computed values and a polynomial approximation, a combination of which gives an accurate result for a majority of inputs. If it is found that the lookup table may not give an accurate result the next, slower phase is employed. This phase uses a multiple precision representation to compute results to precisions of up to 768 bits before rounding the result to double. As expected, this kills performance; the slowest path for pow for example is a few thousand times slower than the table lookup phase.
I looked into this problem not very long ago and tried to improve performance of the multiple precision phase so that it is not as bad as it currently is. The result of that was an improvement of about 8 times in the performance of the slowest path of the pow function. Other transcendentals got similar improvements since the fixes were mostly in the generic multiple precision code. These improvements went into glibc-2.18 upstream. We’ll take a look at what these changes were but first, a quick look at the multiple precision number for context on the changes.
We are angry, frustrated, and in pain because of the violence and murder of Black people by the police because of racism. We are in the fight AGAINST RACISM. George Floyd was murdered, his life stolen. The Adafruit teams have specific actions we’ve done, are doing, and will do together as a company and culture. We are asking the Adafruit community to get involved and share what you are doing. The Adafruit teams will not settle for a hash tag, a Tweet, or an icon change. We will work on real change, and that requires real action and real work together. That is what we will do each day, each month, each year – we will hold ourselves accountable and publish our collective efforts, partnerships, activism, donations, openly and publicly. Our blog and social media platforms will be utilized in actionable ways. Join us and the anti-racist efforts working to end police brutality, reform the criminal justice system, and dismantle the many other forms of systemic racism at work in this country, read more @ adafruit.com/blacklivesmatter
Stop breadboarding and soldering – start making immediately! Adafruit’s Circuit Playground is jam-packed with LEDs, sensors, buttons, alligator clip pads and more. Build projects with Circuit Playground in a few minutes with the drag-and-drop MakeCode programming site, learn computer science using the CS Discoveries class on code.org, jump into CircuitPython to learn Python and hardware together, TinyGO, or even use the Arduino IDE. Circuit Playground Express is the newest and best Circuit Playground board, with support for CircuitPython, MakeCode, and Arduino. It has a powerful processor, 10 NeoPixels, mini speaker, InfraRed receive and transmit, two buttons, a switch, 14 alligator clip pads, and lots of sensors: capacitive touch, IR proximity, temperature, light, motion and sound. A whole wide world of electronics and coding is waiting for you, and it fits in the palm of your hand.