• January 28, 2022, 11:50:57 AM

### Author Topic:  Fixed Arbitrary Precision and multiplication  (Read 153 times)

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#### superheal

• Fractal Feline
• Posts: 176
##### Fixed Arbitrary Precision and multiplication
« on: January 13, 2022, 04:38:06 PM »
I was reading through this: http://www.hpdz.net/TechInfo/Bignum.htm#General and I was also exploring MandelMachine's BigNum_Arb class, which is basically a fixed precision lib. I wanted to find some way to do the multiplication but I am kinda struggling. MM is probably doing the multiplication part on c or asm. It also has some other BigNum hardcoded precision obsolete classes that have multiplication implemented, but their data storing format seems different (If I stored the same number created in the arb class, on the fixed digits, the printed double value is wrong).

The format is an array of 64 bit longs , but only the 60 bits are used (4 bits are there for overflow).
[60bits] .decimal_point. [60bits][60bits][60bits]...
I have tried to make a small example with only 2 decimals in order to try the multiplication as described in http://www.hpdz.net/TechInfo/Bignum.htm#General
but I probably mess up the sub-products because the need twice as much bits to be calculated.

Does anyone have any experience on this?

#### marcm200

• 3e
• Posts: 1111
##### Re: Fixed Arbitrary Precision and multiplication
« Reply #1 on: January 13, 2022, 07:08:17 PM »
The multiplication in the link is standard school math multiplication in base-10.

I implemented my own fixed precision number type, where I use digits to base 1 billion (which fit in 32 bit) and then multiplying two such numbers is performed after casting each digit to int64_t by multiplying one number with each of the digits of the 2nd one, shifting the sub-result an appropriate amount of digit positions (performed by tailing zeros after shifting as the fractional part is left-aligned and the integer part right-aligned), then adding with a fixed-number addition routine to the ongoing overall result respecting carry-over. That way I can reuse all tested and working routines.

I suspect you're doing the same. or are you using the presumed speed-up described in the article where some of the sub-products are not computed in the first place (when truncation is used as rounding mode) ?
(I'm not using any of those as my number type is intended for interval arithmetics and I perform outward rounding according to sign left or right interval end).
« Last Edit: January 13, 2022, 08:21:45 PM by marcm200, Reason: interval rounding description »

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