> The C standard for math.h requires these functions to be present as specified. They are specified to round correctly, the C standard specifies them to be present as specified, therefore the C standard specifies them as present and correctly rounded. I literally quoted the relevant sections, there are no conforming C specification which give different results.
Forgive me, but I cannot see that in the document sections you point out. The closest I can see is F.10-3, on page 517, but my reading of that is that it only applies to the Special cases (i.e values in Section 9.2.1), not the full domain.
In fact, my reading of F.10-10 (page 518) suggests that a conforming implementation does not even have to honor the rounding mode.
That section is recommended but not required for a conforming implementation:
> 9. Recommended operations
> Clause 5 completely specifies the operations required for all supported arithmetic formats. This clause specifies additional operations, recommended for all supported arithmetic formats.
Since this is using fetch/XHR under the hood, I guess requests from the browser are restricted only to same-origin URLs or servers responding with permissive CORS headers?
I love my lava lamp. I use it as the light for my bedside table.
I’m too young to have seen the craze the first time around, but for me they are the ultimate nostalgia object. You see, lava lamps take me back to being a young child visiting The Gadget Shop with my father. He knew I liked the place, so every time we travelled into the city centre together we’d visit. The place was small, but packed full with the sounds and flashing colours of the gadgets within.
The central island would always have a sales assistant behind it demonstrating this or that. A miniature blimp, effortlessly floating above us. A skilled performance with light-up juggling balls or advanced yo-yo tricks. A remote control car, driven and flipped onto its back to return the way it came. I vividly remember the tickling feeling brushing my hand over the tips of a fibre optic lamp on display, with its twinkling light at the end of each fibre.
All around the outside of the shop were wall to ceiling shelves, full of trinkets protected with panes of glass. Plasma globes flickering and buzzing with mysterious electrical power. A row of chrome perpetual motion toys each moving slowly and gracefully, dancing its own dance. Glow in the dark decorations illuminating with their curious green-white light. The rhythmic click-clack-click sound of a Newtons Cradle ticking away the seconds on a shelf somewhere.
And, of course, the rows and rows of lava lamps on display. A multitude of different colours of bulb, liquid and lava. Some had glitter inside, rather than wax, but to me they just weren’t the same. I could have sat and watched the spheres of lava split and recombine together for hours. But alas, it was time to go home.
I still live in the same city. I would love to share the same memory with my own children one day, but The Gadget Shop is unfortunately no more. It seemed to dissapear around the late 90s. What I loved about the place was how analogue and tactile everything was. Any item could be removed from the shelf and interacted with. In my memory, there were no digital gadgets there at all. Though, I could have simply forgotten about them.
There are similar shops around now, but they don’t spark that same joy in my soul. Sure, they have the odd remote control car or mini toy drone on display… but the torrent of lights, colours and sound is gone. Replaced by rows of boxed collectible plastic figurines or, what feels to me, like branded tat.
Sometimes I wonder if perhaps it’s not the gadgets that have changed, but instead I have just grown up. Whenever this happens, I stop and watch my lava lamp for a little while. Without fail, it always invokes the same sense of wonder I felt as a child in The Gadget Shop, and takes me back to my fond memories of the time spent there with my father.
It can happen, the Pólya conjecture is the usual example which holds until n = 906150257.
Another fun one I just found is the statement “n^17 + 9 and (n + 1)^17 + 9 are relatively prime”. The first counterexample is at n=8424432925592889329288197322308900672459420460792433.
Do you like your initial value to be at index 1? Cool. Prefer to index arrays from 0 instead? Sure, go ahead.
How about an array with indexing symmetric around zero?
Beautiful!