Adam Hyland Protonk

Two mechanical errata in Mike Day, Generalising the Fast Reciprocal Square Root Algorithm (arXiv:2307.15600v1, 28 Jul 2023), surfaced while reproducing the paper's numbers. Verified by 2 robots and 1 human.

Eq (57): ε last-digit error

The paper prints

kind	display_name	q	p_num	q_den	layer_dependent	min_depth	max_depth	tol	dyadic_bits	n_digits	split_counts	sequence	runs_at_max_depth	elapsed
uniform_x	uniform	3	1	2	False	3	7	1e-10	20	4	[0, 2, 4, 4]	1.0244	9	0.012370109558105469
geometric_x	geometric	3	1	2	False	3	7	1e-10	20	4	[1, 1, 2, 0]	1.1120	2	0.0012631416320800781
harmonic_x	harmonic	3	1	2	False	3	7	1e-10	20	4	[2, 1, 1, 0]	1.2110	2	0.0012788772583007812
mirror_harmonic_x	mirror-harmonic	3	1	2	False	3	7	1e-10	20	4	[2, 2, 1, 5]	1.2215	11	0.0025589466094970703
ruler_x	ruler	3	1	2	False	3	7	1e-10	20	4	[0, 2, 5, 4]	1.0254	7	0.0023572444915771484
sinusoidal_x	sinusoidal	3	1	2	False	3	7	1e-10	20	4	[1, 3, 2, 1]	1.1321	3	0.0012438297271728516
chebyshev_x	chebyshev	3	1	2	False	3	7	1e-10	20	4	[1, 0, 0, 0]	1.1000	2	0.0012700557708740234
thuemorse_x	thue-morse	3	1	2	False	3	7	1e-10	20	4	[0, 2, 2, 3]	1.0223	7	0.0016057491302490234
bitrev_geometric_x	bitrev-geometric	3	1	2	False	3	7	1e-10	20	4	[1, 2, 1, 3]	1.1213	7	0.0028460025787353516

macOS Seatbelt/Sandbox Trace Script

macOS sandbox profiles used to be able to include a trace command that would write all the denied operations to a sandbox profile, allowing a profile to be iterativley built up. Apple removed that functionality for reasons explained below.

trace.sh examines the kernel log for the denied operations and creates the relevant allow rules in a sandbox profile, just like the sandbox profile trace command used to.

shrink.sh tries to reduce a sandbox profile to the minimum lines necessary.

It's very rough and ready at the moment (check the sed regex'es in the script to see what I mean) and needs more testing with a wider set of use cases.

	% Compact "happy path" for the classic FRSR exponent x^(-1/2),
	% from "Generalising the Fast Reciprocal Square Root Algorithm"
	% (arXiv:2307.15600).

	% 1. Pseudolog and inverse.
	% The IEEE-754 float bit-pattern of x approximately encodes log2(x).
	% Day's pseudolog makes that precise:
	% L(x) = floor(log2 x) + x * 2^{-floor(log2 x)} - 1.
	% It is piecewise linear on each octave [2^e, 2^(e+1)), agrees with log2
	% at powers of two, and has an explicit inverse on each affine segment.

	## there are simpler ways to do this in R. See
	## for example https://github.com/itchyny/fastinvsqrt/blob/main/src/r/fastinvsqrt.r
	## contains a reasonable way to do this unreasonable thing.
	## What follows is an unreasonable way to do an unreasonable thing.

	doubleTofloatBits <- function(x) {
	# Convert double to character in scientific notation
	x_char <- format(x, scientific = TRUE)

	# Parse the character representation

	### Compare original and adjusted values
	library(dplyr)
	library(ggplot2)
	library(latex2exp)


	## blends from standard form to original Kadlec constants
	## A = 0.70395 & B = 2.38924
	original_kadlec_blend <- read.csv(text = "
	input,output,error,diff,iters,alpha

	kadlec <- read.csv(text = "
	reference,kadlec,iters,error,input
	1.189297,1.189539,1,0.000242,0.707000
	1.189297,1.162983,2,0.026314,0.707000
	1.189297,1.173180,3,0.016117,0.707000
	1.189297,1.169557,4,0.019740,0.707000
	1.189297,1.170886,5,0.018411,0.707000
	1.189297,1.170404,6,0.018893,0.707000
	")

	// accepts a double and splits it, like KahanNg
	// See https://inbetweennames.net/blog/2021-05-06-i76rsqrt/
	// for more details and the original recovered code (in C++)
	// It is different from KahanNg as it splits the double into
	// exponent and mantissa, whereas KahanNg splits it into
	// high 32 and low 32 bits
	double i76ISR(double x, int NR) {
	// Interstate76's lookup table generator
	// uint8_t LUT[256];
	// void generateLUT(){

	;SMBDIS.ASM - A COMPREHENSIVE SUPER MARIO BROS. DISASSEMBLY
	;by doppelganger (doppelheathen@gmail.com)

	;This file is provided for your own use as-is. It will require the character rom data
	;and an iNES file header to get it to work.

	;There are so many people I have to thank for this, that taking all the credit for
	;myself would be an unforgivable act of arrogance. Without their help this would
	;probably not be possible. So I thank all the peeps in the nesdev scene whose insight into
	;the 6502 and the NES helped me learn how it works (you guys know who you are, there's no

	// c++ -O3 -o nanof2a nanof2a.cpp && ./nanof2a
	#include <cstdint>
	#include <cstring>

	namespace { // anonymous namespace to encourage inlining

	struct f2a {
	char str[16];

	f2a(float f) { // example usage: printf("%s", f2a(f).str)