This is z80 assembly code that converts a string like
6.62607015e-34
into a 64 bit double-precision floating-point format according to the IEEE754 standard:
0x 39 0B 86 0B DE 02 31 11
Also supported is the representation into a power of 2 with the mantisse between 1 and 2:
1.7202261612138196*2^-111
In an MSX emulator the output will look like this:
There are no real limitations on the input string as long as it represents a valid floating point string that can be stored in a double precision number (so between DBL_MIN (2.23e–308) and DBL_MAX (1.80e+308)). There is however (although only theoretically) a limitation: to calculate the double value an intermediate array of digits is used which has a fixed size of 800 (I copied this value from the wuffs library). For 'normal' values between 1e-100 and 1e+100 a max of 300 would also suffice. The number of digits needed to calculate numbers close to DBL_MIN (e.g. 2.2299999999e-308) is 341, and close to DBL_MAX (e.g. 1.79999999999e+308) is 725. This maximum of 800 can be found in .digits in Double/Double.asm. There is no check if the program writes beyond this size so this could theoretically break.
There is some validation on the input so in case of invalid input it will result in Parse error.
Valid examples include:
29979245800299792458.00002.99792458e8+2.99792458e+80000.0000299792458000e+0013-6.62607015e-34-0.00e+10
The algorithm I've used is a slightly more efficient version of the so called Simple Decimal Conversion which is explained in this great article written by Nigel Tao.
The code is (deliberately) incomplete. The following features are missing:
- use of NaN and infinity
- use of the smarter Eisel-Lemire ParseNumberF64 Algorithm
This code is written as a 16K ROM (the code itself is just under 2.5K) to easily load it into an emulator. To run it in an emulator I've used these tools:
- to compile: z80asm (version 1.8) written by Bas Wijnen (also RUG alumni 💪)
- to emulate: WebMSX (version 6.0.3) written by Paulo Augusto Peccin
Just download, unpack and configure z80asm the usual way. It can be installed anywhere but the makefile in this repo expects the z80asm-1.8 directory to be in the same directory as this repo.
Then compile the code with make and you should now have a fresh data.rom.
Clone WebMSX anywhere you want. WebMSX works out of the box if you load file://<install path of WebMSX>/release/stable/6.0/standalone/index.html in your favorite browser.
To load the ROM I append the following url parameters to this url:
- MACHINE=MSX2E (I still own a machine like this)
- FAST_BOOT=1 (because I like fast)
- WEB_EXTENSIONS_PROXY_SERVER= (this is to avoid using a proxy server)
- ROM=http://localhost/data.rom (the actual rom)
As you can see in the last line I use a webserver (in my case apache) and localhost to load the data.rom binary (but of course you can serve it from any place). To make this happen I created /etc/apache2/other/webmsx.conf (I use a mac, you might find your apache configuration files elsewhere). You may also need to uncomment or add this line into your httpd.conf:
Include /etc/apache2/other/*.conf
or wherever you have the configuration.
The content of webmsx.conf is (you may need to enable modules in httpd.conf to make this work):
DocumentRoot [your install path to the StringToDouble repo]
<Directory [your install path to the StringToDouble repo]>
Header set Access-Control-Allow-Origin "*"
FileETag None
Header unset ETag
Header set Cache-Control "max-age=0, no-cache, no-store, must-revalidate"
Header set Expires "Wed, 12 Jan 1980 05:00:00 GMT"
Header set Pragma "no-cache"
Require all granted
</Directory>
These directives will disable the cache since we want to (down)load the binary every time we update the rom.
Restart your apache with:
sudo apachectl restart
So the complete url looks like this:
file://<install path of WebMSX>/release/stable/6.0/standalone/index.html?MACHINE=MSX2E&FAST_BOOT=1&WEB_EXTENSIONS_PROXY_SERVER=&ROM=http://localhost/data.rom
That's it.