Interval arithmetic with mpfi

Interval arithmetic is a mature field in computer science that was conceived in the 50s or 60s. Mostly it was used to ensure the precision of floating point numbers, i.e. a floating point number's possible max and min value fall into certain precision. E.g. 3.13< pi< 3.15

Problem: having an f(x), we want to find the max and min of f(x) for x between x1 and x2.

I'm trying to solve this problem with mpfi library:

• libmpfi-dev - multiple precision floating-point interval computation library
• libmpfi0 - multiple precision floating-point interval computation library

Here is the code for f(x)=x^3 with x1=-4 and x2=3:

 
#include "stdio.h"
#include "mpfi.h"
#include "mpfi_io.h"

int main(int argc, char** argv) {
  mpfi_t x, fx;

  mpfi_init(x);
  mpfi_init(fx);
  mpfi_interv_si(x, -4, 3);

  //fx = x*x*x
  mpfi_mul(fx, x, x); //fx = x*x
  mpfi_mul(fx, fx, x); //fx = fx*x
  mpfi_out_str(stdout, 10, 2, fx); printf("\n");
  mpfi_clear(x);
  mpfi_clear(fx);
  return 0;
}

Compilation:

 $ gcc -lmpfi test.c
$ ./a.out
[-6.4e1,4.8e1]

The result is min f(x)= -64 and max f(x)= 48 for x1=-4 and x2=3

Cheap Class D audio amplifier experiments

I have a nice vintage micro sound system. It can easily accept any audio signal from my gadgets, but it consumes around 60W of power. So lets try to make a smaller carbon footage :D. I tried class D amps to drive the speakers. I did two experiments:

1. 12 Volt amp
The setup was very simple. Audio outputs from a gadget went to amp line-in. But put a variable resistor as the volume control, between the gadget audio-out and the amp's line-in. It should be a stereo one. I tried with 12V unused power supply from old networking equipment, it worked. It also worked with a 9V power supply that usually comes with todays network router.
It worked fine with phone, but there was severe hums and buzz with laptop headphone port. I suspected the problem was the connector. I used a 4-ports audio connector that usually comes with a smart phone; 2 ports for L/R channel, 1 port for microphone and the last port for the ground.
Apparently the audio port on computer didn't connect the ground correctly. The ground connector might be connected into the microphone port, thus leaved the ground unconnected. Therefore it sounded terrible,
the audio signal was very small compared to the noise. The solution was simple, just shorted the microphone port to the ground port.
However before I tried the solution, the amp was already damaged. So then I tried with the second experiment.

2. 5 Volt amp
Still same setup as the previous one, but the power supply is given from USB. Nice, no need a dedicated power supply and USB is ubquitous. I use my laptop USB to power the amp.

Observations:
It sounds rather vintage, closer to crispy sound of tube lamp amp, than deep sub wooferish sound of modern audio system. So? There is a simple rule for a good audio system, it should reproduce sound as closer as the original, a sub woofer definitely distort the original sound, thus I guess I can consider my D class amp setup sounds good.