# Multiplying 8 by 16 bits...

I thought this would be an easy operation…
I have a byte value that I want to make little larger by multiplying with a little higher than 1.
This is in a tight loop, so I’d like to avoid floating point math.
Let’s say I want to multiply by 1.5. I could store 256*1.5 as an integer value in a word. Multiplying by that instead gives a value that is 256 times too large, so I’ll just shift result down 8 steps. This is what’s normally called “fixed point”.

``````byte b = whatever;
word w = 0x180;   // 1.5 in fixed point notation

result = (b * w) >> 8;
``````

The above fails. Apparently, the 24 bit result of b*w is truncated to a 16 bit int before shifting.

I tried to multiply b with the highbyte and lowbyte of w separately and then adding the results up, keeping only the upper 16 bits:

``````result = b * highByte(w) + highByte(b * lowByte(w));
``````

That at least gives me the correct result, but I looked at the assembler… the expression above does 2 multiplications of bytes, which should map directly to the cpu’s mul instruction. But the actual code generated has no less than 6 mul instructions in it.

Is there a way, short of writing inline assembler, to express a 8*16 bit multiplication that generates sane code?

b is a byte and w is 2 bytes, so I think when the compiler encounters b * w it tries to store the intermediate result in a variable that is large as the largest operand, i.e. 2 bytes. I think if you want to have an intermediate variable of 3 bytes you should cast b or w to long.

you should cast b or w to long

if I do that, it will call the compiler's builtin 32x32 bit __mulsi3 function, which contains 10 mul instructions. I still don't want more than 2...

Anything wrong with:

``````result = (b*3)/2;
``````

to multiply by 1.5?

http://www.ruggedcircuits.com

`result = (b*3)/2;`

it is more like "some user-changeable value between 1.00 and 4.00"

I only see 2 multiplications in this test code:

``````#include <avr/io.h>

#define lowByte(w) ((uint8_t) ((w) & 0xff))
#define highByte(w) ((uint8_t) ((w) >> 8))

uint8_t func(uint8_t b, uint16_t w)
{
return b*highByte(w) + highByte(b*lowByte(w));
}
/*
Compiled with avr-gcc -mmcu=atmega328p -O3 -S test.c

.text
.global      func
.type      func, @function
func:
mul r24,r22
movw r18,r0
clr r1
mov r18,r19
lsl r19
sbc r19,r19
mul r24,r23
mov r24,r0
clr r1
ret
*/
``````
``````result = (b*3)/2;
``````

… but you’re on to something there. I don’t need that many different values to multiply with. As long as the number to divide by can be a power of 2 it might work.

I only see 2 multiplications in this test code:

The result of the (fixed point) multiplication can be greater than 255 so the return type needs to be unit16_t, which results in more muls.

Well, I got it down to 2 multiplications through this annoying code:

``````#include <avr/io.h>

#define lowByte(w) ((uint8_t) ((w) & 0xff))
#define highByte(w) ((uint8_t) ((w) >> 8))

uint16_t hi(uint8_t b, uint16_t w)
{
return b*highByte(w);
}

uint8_t lo(uint8_t b, uint16_t w)
{
return highByte(b*lowByte(w));
}

uint16_t func(uint8_t b, uint16_t w)
{
return hi(b,w) + lo(b,w);
}
/*
Compiled with avr-gcc -mmcu=atmega328p -O3 -S -fno-inline test.c
*/
``````

I agree that it shouldn’t expand out to 6 multiplications. If you take the -fno-inline flag out it goes back to 6 muls.

Perhaps in-line assembly is the solution here.

``````{ 1, 149, 87, 203, 237, 69, 161, 47, 219, 4};
{ 0,   7,  6,   7,   7,  5,   6,  4,   6, 0};
``````

The solution. Above is my list of 10 values, geometrically spread from 1.00 to 4.00. I multiply the byte with a value in the first row, and then shift down the resulting word by the corresponding value in the second row.

Thanks to RuggedCircuits for the hint.