I'm implementing a relative branching function in my simple VM.
Basically, I'm given an 8-bit relative value. I then shift this left by 1 bit to make it a 9-bit value. So, for instance, if you were to say "branch +127" this would really mean, 127 instructions, and thus would add 256 to the IP.
My current code looks like this:
uint8_t argument = 0xFF; //-1 or whatever
int16_t difference = argument << 1;
*ip += difference; //ip is a uint16_t
I don't believe difference will ever be detected as a less than 0 with this however. I'm rusty on how signed to unsigned works. Beyond that, I'm not sure the difference would be correctly be subtracted from IP in the case argument is say -1 or -2 or something.
Basically, I'm wanting something that would satisfy these "tests"
//case 1
argument = -5
difference -> -10
ip = 20 -> 10 //ip starts at 20, but becomes 10 after applying difference
//case 2
argument = 127 (must fit in a byte)
difference -> 254
ip = 20 -> 274
Hopefully that makes it a bit more clear.
Anyway, how would I do this cheaply? I saw one "solution" to a similar problem, but it involved division. I'm working with slow embedded processors (assumed to be without efficient ways to multiply and divide), so that's a pretty big thing I'd like to avoid.
To clarify: you worry that left shifting a negative 8 bit number will make it appear like a positive nine bit number? Just pad the top 9 bits with the sign bit of the initial number before left shift:
diff = 0xFF;
int16 diff16=(diff + (diff & 0x80)*0x01FE) << 1;
Now your diff16 is signed 2*diff
As was pointed out by Richard J Ross III, you can avoid the multiplication (if that's expensive on your platform) with a conditional branch:
int16 diff16 = (diff + ((diff & 0x80)?0xFF00:0))<<1;
If you are worried about things staying in range and such ("undefined behavior"), you can do
int16 diff16 = diff;
diff16 = (diff16 | ((diff16 & 0x80)?0x7F00:0))<<1;
At no point does this produce numbers that are going out of range.
The cleanest solution, though, seems to be "cast and shift":
diff16 = (signed char)diff; // recognizes and preserves the sign of diff
diff16 = (short int)((unsigned short)diff16)<<1; // left shift, preserving sign
This produces the expected result, because the compiler automatically takes care of the sign bit (so no need for the mask) in the first line; and in the second line, it does a left shift on an unsigned int (for which overflow is well defined per the standard); the final cast back to short int ensures that the number is correctly interpreted as negative. I believe that in this form the construct is never "undefined".
All of my quotes come from the C standard, section 6.3.1.3. Unsigned to signed is well defined when the value is within range of the signed type:
1 When a value with integer type is converted to another integer type
other than _Bool, if the value can be represented by the new type, it
is unchanged.
Signed to unsigned is well defined:
2 Otherwise, if the new type is unsigned, the value is converted by
repeatedly adding or subtracting one more than the maximum value that
can be represented in the new type until the value is in the range of
the new type.
Unsigned to signed, when the value lies out of range isn't too well defined:
3 Otherwise, the new type is signed and the value cannot be
represented in it; either the result is implementation-defined or an
implementation-defined signal is raised.
Unfortunately, your question lies in the realm of point 3. C doesn't guarantee any implicit mechanism to convert out-of-range values, so you'll need to explicitly provide one. The first step is to decide which representation you intend to use: Ones' complement, two's complement or sign and magnitude
The representation you use will affect the translation algorithm you use. In the example below, I'll use two's complement: If the sign bit is 1 and the value bits are all 0, this corresponds to your lowest value. Your lowest value is another choice you must make: In the case of two's complement, it'd make sense to use either of INT16_MIN (-32768) or INT8_MIN (-128). In the case of the other two, it'd make sense to use INT16_MIN - 1 or INT8_MIN - 1 due to the presense of negative zeros, which should probably be translated to be indistinguishable from regular zeros. In this example, I'll use INT8_MIN, since it makes sense that (uint8_t) -1 should translate to -1 as an int16_t.
Separate the sign bit from the value bits. The value should be the absolute value, except in the case of a two's complement minimum value when sign will be 1 and the value will be 0. Of course, the sign bit can be where-ever you like it to be, though it's conventional for it to rest at the far left hand side. Hence, shifting right 7 places obtains the conventional "sign" bit:
uint8_t sign = input >> 7;
uint8_t value = input & (UINT8_MAX >> 1);
int16_t result;
If the sign bit is 1, we'll call this a negative number and add to INT8_MIN to construct the sign so we don't end up in the same conundrum we started with, or worse: undefined behaviour (which is the fate of one of the other answers).
if (sign == 1) {
result = INT8_MIN + value;
}
else {
result = value;
}
This can be shortened to:
int16_t result = (input >> 7) ? INT8_MIN + (input & (UINT8_MAX >> 1)) : input;
... or, better yet:
int16_t result = input <= INT8_MAX ? input
: INT8_MIN + (int8_t)(input % (uint8_t) INT8_MIN);
The sign test now involves checking if it's in the positive range. If it is, the value remains unchanged. Otherwise, we use addition and modulo to produce the correct negative value. This is fairly consistent with the C standard's language above. It works well for two's complement, because int16_t and int8_t are guaranteed to use a two's complement representation internally. However, types like int aren't required to use a two's complement representation internally. When converting unsigned int to int for example, there needs to be another check, so that we're treating values less than or equal to INT_MAX as positive, and values greater than or equal to (unsigned int) INT_MIN as negative. Any other values need to be handled as errors; In this case I treat them as zeros.
/* Generate some random input */
srand(time(NULL));
unsigned int input = rand();
for (unsigned int x = UINT_MAX / ((unsigned int) RAND_MAX + 1); x > 1; x--) {
input *= (unsigned int) RAND_MAX + 1;
input += rand();
}
int result = /* Handle positives: */ input <= INT_MAX ? input
: /* Handle negatives: */ input >= (unsigned int) INT_MIN ? INT_MIN + (int)(input % (unsigned int) INT_MIN)
: /* Handle errors: */ 0;
If the offset is in the 2's complement representation, then
convert this
uint8_t argument = 0xFF; //-1
int16_t difference = argument << 1;
*ip += difference;
into this:
uint8_t argument = 0xFF; //-1
int8_t signed_argument;
signed_argument = argument; // this relies on implementation-defined
// conversion of unsigned to signed, usually it's
// just a bit-wise copy on 2's complement systems
// OR
// memcpy(&signed_argument, &argument, sizeof argument);
*ip += signed_argument + signed_argument;
Related
I would like to create a mask for the MSB only, however the width of the int on the operating system is suppose to be unknown, so you cannot assume 32 bits.
see the following
// THE FOLLOWING FAILS BECAUSE OF SYSTEM IMPLEMENTING A LOGICAL
// RIGHT SHIFT
// Idea is
// 1. 0 inverted = all 1's
// 2. Arithmetic shift right
// 3. Then invert again to preseve MSB '1'
const int unsigned mask = ~(~0>>1); // FAIL, because of logic shift
Assuming 16 bit system
~0 give FFFF
~0>>1 give 7FFF
~(~0 >> 1) give 8000
You should add an u suffix to make what is shifted unsigned so that logical right shift is performed instead of arithmetic one.
const int unsigned mask = ~(~0u>>1);
You can just left shift the (unsigned) value 1 by the number of bits in the type minus 1 (i.e. for a 32-bit type, the MSB will be 1 << 31). To get the number of bits, use a combination of the sizeof operator and the CHAR_BIT constant (defined in <limits.h>):
const unsigned int MSB = 1u << (sizeof(unsigned int) * CHAR_BIT - 1);
INT_MAX is the int bit pattern of 0111...1111 (of some width)* for all implementations.
To form 1000...0000, invert those bits.
~INT_MAX
The above treads on undefined beahvior (UB).
Better to looks to unsigned or wider types.
unsigned mask = ~(unsigned) INT_MAX;
On rare machines, INT_MAX == UINT_MAX, so on those, look to wider types:
long long = ~(long long) INT_MAX;
On rarer machines (unheard of), INT_MAX == LONG_MAX is also true, then we are out of luck.
Pedantic: Rare machines use padding on int/unsigned, so best to drive code with (U)INT_MAX than sizeof.
* Maybe some padding bits too - very rare.
I was curious why the following only works when defining an unsigned char:
#define BITS 8
unsigned char d = 0b00001011; // will fail if doing `char d`
d = ~d;
char buffer[BITS+1] = "00000000";
for(int ix=0; d!=0; d>>=1, ix++) {
buffer[BITS-1-ix] = d&1 ? '1' : '0';
}
printf("%s\n", buffer);
Otherwise I get a SegFault, which I'm guessing is due to the d>>=1 on the signed type. Why does that occur exactly though? Wouldn't it have the same bit pattern and doing >>1 would just push the bits to the right once?
Shifting a negative signed number rightward has implementation-defined behaviour; exactly what it does will depend on your compiler.
Likely your compiler is using two's complement and arithmetic shifts right, i.e. the sign bit is filled with a copy of the bit that left it upon every shift.
This is often a better choice because e.g. it means that -4 >> 1 is -2 rather than, in an 8-bit quantity, being 126.
Slightly off topic, but the simplest fix for your code is just to switch the exit condition to d != 0 && ix < 8.
I am doing some work in embedded C with an accelerometer that returns data as a 14 bit 2's complement number. I am storing this result directly into a uint16_t. Later in my code I am trying to convert this "raw" form of the data into a signed integer to represent / work with in the rest of my code.
I am having trouble getting the compiler to understand what I am trying to do. In the following code I'm checking if the 14th bit is set (meaning the number is negative) and then I want to invert the bits and add 1 to get the magnitude of the number.
int16_t fxls8471qr1_convert_raw_accel_to_mag(uint16_t raw, enum fxls8471qr1_fs_range range) {
int16_t raw_signed;
if(raw & _14BIT_SIGN_MASK) {
// Convert 14 bit 2's complement to 16 bit 2's complement
raw |= (1 << 15) | (1 << 14); // 2's complement extension
raw_signed = -(~raw + 1);
}
else {
raw_signed = raw;
}
uint16_t divisor;
if(range == FXLS8471QR1_FS_RANGE_2G) {
divisor = FS_DIV_2G;
}
else if(range == FXLS8471QR1_FS_RANGE_4G) {
divisor = FS_DIV_4G;
}
else {
divisor = FS_DIV_8G;
}
return ((int32_t)raw_signed * RAW_SCALE_FACTOR) / divisor;
}
This code unfortunately doesn't work. The disassembly shows me that for some reason the compiler is optimizing out my statement raw_signed = -(~raw + 1); How do I acheive the result I desire?
The math works out on paper, but I feel like for some reason the compiler is fighting with me :(.
Converting the 14 bit 2's complement value to 16 bit signed, while maintaining the value is simply a metter of:
int16_t accel = (int16_t)(raw << 2) / 4 ;
The left-shift pushes the sign bit into the 16 bit sign bit position, the divide by four restores the magnitude but maintains its sign. The divide avoids the implementation defined behaviour of an right-shift, but will normally result in a single arithmetic-shift-right on instruction sets that allow. The cast is necessary because raw << 2 is an int expression, and unless int is 16 bit, the divide will simply restore the original value.
It would be simpler however to just shift the accelerometer data left by two bits and treat it as if the sensor was 16 bit in the first place. Normalising everything to 16 bit has the benefit that the code needs no change if you use a sensor with any number of bits up-to 16. The magnitude will simply be four times greater, and the least significant two bits will be zero - no information is gained or lost, and the scaling is arbitrary in any case.
int16_t accel = raw << 2 ;
In both cases, if you want the unsigned magnitude then that is simply:
int32_t mag = (int32_t)labs( (int)accel ) ;
I would do simple arithmetic instead. The result is 14-bit signed, which is represented as a number from 0 to 2^14 - 1. Test if the number is 2^13 or above (signifying a negative) and then subtract 2^14.
int16_t fxls8471qr1_convert_raw_accel_to_mag(uint16_t raw, enum fxls8471qr1_fs_range range)
{
int16_t raw_signed = raw;
if(raw_signed >= 1 << 13) {
raw_signed -= 1 << 14;
}
uint16_t divisor;
if(range == FXLS8471QR1_FS_RANGE_2G) {
divisor = FS_DIV_2G;
}
else if(range == FXLS8471QR1_FS_RANGE_4G) {
divisor = FS_DIV_4G;
}
else {
divisor = FS_DIV_8G;
}
return ((int32_t)raw_signed * RAW_SCALE_FACTOR) / divisor;
}
Please check my arithmetic. (Do I have 13 and 14 correct?)
Supposing that int in your particular C implementation is 16 bits wide, the expression (1 << 15), which you use in mangling raw, produces undefined behavior. In that case, the compiler is free to generate code to do pretty much anything -- or nothing -- if the branch of the conditional is taken wherein that expression is evaluated.
Also if int is 16 bits wide, then the expression -(~raw + 1) and all intermediate values will have type unsigned int == uint16_t. This is a result of "the usual arithmetic conversions", given that (16-bit) int cannot represent all values of type uint16_t. The result will have the high bit set and therefore be outside the range representable by type int, so assigning it to an lvalue of type int produces implementation-defined behavior. You'd have to consult your documentation to determine whether the behavior it defines is what you expected and wanted.
If you instead perform a 14-bit sign conversion, forcing the higher-order bits off ((~raw + 1) & 0x3fff) then the result -- the inverse of the desired negative value -- is representable by a 16-bit signed int, so an explicit conversion to int16_t is well-defined and preserves the (positive) value. The result you want is the inverse of that, which you can obtain simply by negating it. Overall:
raw_signed = -(int16_t)((~raw + 1) & 0x3fff);
Of course, if int were wider than 16 bits in your environment then I see no reason why your original code would not work as expected. That would not invalidate the expression above, however, which produces consistently-defined behavior regardless of the size of default int.
Assuming when code reaches return ((int32_t)raw_signed ..., it has a value in the [-8192 ... +8191] range:
If RAW_SCALE_FACTOR is a multiple of 4 then a little savings can be had.
So rather than
int16_t raw_signed = raw << 2;
raw_signed >>= 2;
instead
int16_t fxls8471qr1_convert_raw_accel_to_mag(uint16_t raw,enum fxls8471qr1_fs_range range){
int16_t raw_signed = raw << 2;
uint16_t divisor;
...
// return ((int32_t)raw_signed * RAW_SCALE_FACTOR) / divisor;
return ((int32_t)raw_signed * (RAW_SCALE_FACTOR/4)) / divisor;
}
To convert the 14-bit two's-complement into a signed value, you can flip the sign bit and subtract the offset:
int16_t raw_signed = (raw ^ 1 << 13) - (1 << 13);
I am attempting exercise 2.1 of K&R. The exercise reads:
Write a program to determine the ranges of char, short, int, and long variables, both signed and unsigned, by printing appropriate values from standard headers and by direct computation. Harder if you compute them: determine the ranges of the various floating-point types.
Printing the values of constants in the standards headers is easy, just like this (only integer shown for example):
printf("Integral Ranges (from constants)\n");
printf("int max: %d\n", INT_MAX);
printf("int min: %d\n", INT_MIN);
printf("unsigned int max: %u\n", UINT_MAX);
However, I want to determine the limits programmatically.
I tried this code which seems like it should work but it actually goes into an infinite loop and gets stuck there:
printf("Integral Ranges (determined programmatically)\n");
int i_max = 0;
while ((i_max + 1) > i_max) {
++i_max;
}
printf("int max: %d\n", i_max);
Why is this getting stuck in a loop? It would seem that when an integer overflows it jumps from 2147483647 to -2147483648. The incremented value is obviously smaller than the previous value so the loop should end, but it doesn't.
Ok, I was about to write a comment but it got too long...
Are you allowed to use sizeof?
If true, then there is an easy way to find the max value for any type:
For example, I'll find the maximum value for an integer:
Definition: INT_MAX = (1 << 31) - 1 for 32-bit integer (2^31 - 1)
The previous definition overflows if we use integers to compute int max, so, it has to be adapted properly:
INT_MAX = (1 << 31) - 1
= ((1 << 30) * 2) - 1
= ((1 << 30) - 1) * 2 + 2) - 1
= ((1 << 30) - 1) * 2) + 1
And using sizeof:
INT_MAX = ((1 << (sizeof(int)*8 - 2) - 1) * 2) + 1
You can do the same for any signed/unsigned type by just reading the rules for each type.
So it actually wasn't getting stuck in an infinite loop. C code is usually so fast that I assume it's broken if it doesn't complete immediately.
It did eventually return the correct answer after I let it run for about 10 seconds. Turns out that 2,147,483,647 increments takes quite a few cycles to complete.
I should also note that I compiled with cc -O0 to disable optimizations, so this wasn't the problem.
A faster solution might look something like this:
int i_max = 0;
int step_size = 256;
while ((i_max + step_size) > i_max) {
i_max += step_size;
}
while ((i_max + 1) > i_max) {
++i_max;
}
printf("int max: %d\n", i_max);
However, as signed overflow is undefined behavior, probably it is a terrible idea to ever try to programmatically guess this in practice. Better to use INT_MAX.
The simplest I could come up with is:
signed int max_signed_int = ~(1 << ((sizeof(int) * 8) -1));
signed int min_signed_int = (1 << ((sizeof(int) * 8) -1));
unsigned int max_unsigned_int = ~0U;
unsigned int min_unsigned_int = 0U;
In my system:
// max_signed_int = 2147483647
// min_signed_int = -2147483648
// max_unsigned_int = 4294967295
// min_unsigned_int = 0
Assuming a two's complement processor, use unsigned math:
unsigned ... smax, smin;
smax = ((unsigned ...)0 - (unsigned ...)1) / (unsigned ...) 2;
smin = ~smax;
As it has been pointed here in other solutions, trying to overflow an integer in C is undefined behaviour, but, at least in this case, I think you can get an valid answer, even from the U.B. thing:
The case is tha if you increment a value and compare the new value with the last, you always get a greater value, except on an overflow (in this case you'll get a value lesser or equal ---you don't have more values greater, that's the case in an overflow) So you can try at least:
int i_old = 0, i = 0;
while (++i > i_old)
i_old = i;
printf("MAX_INT guess: %d\n", i_old);
After this loop, you will have got the expected overflow, and old_i will store the last valid number. Of course, in case you go down, you'll have to use this snippet of code:
int i_old = 0, i = 0;
while (--i < i_old)
i_old = i;
printf("MIN_INT guess: %d\n", i_old);
Of course, U.B. can even mean program stopping run (in this case, you'll have to put traces, to get at least the last value printed)
By the way, in the ancient times of K&R, integers used to be 16bit wide, a value easily accessible by counting up (easier than now, try 64bit integers overflow from 0 up)
I would use the properties of two's complement to compute the values.
unsigned int uint_max = ~0U;
signed int int_max = uint_max >> 1;
signed int int_min1 = (-int_max - 1);
signed int int_min2 = ~int_max;
2^3 is 1000. 2^3 - 1 is 0111. 2^4 - 1 is 1111.
w is the length in bits of your data type.
uint_max is 2^w - 1, or 111...111. This effect is achieved by using ~0U.
int_max is 2^(w-1) - 1, or 0111...111. This effect can be achieved by bitshifting uint_max 1 bit to the right. Since uint_max is an unsigned value, the logical shift is applied by the >> operator, means it adds in leading zeroes instead of extending the sign bit.
int_min is -2^(w-1), or 100...000. In two's complement, the most significant bit has a negative weight!
This is how to visualize the first expression for computing int_min1:
...
011...111 int_max +2^(w-1) - 1
100...000 (-int_max - 1) -2^(w-1) == -2^(w-1) + 1 - 1
100...001 -int_max -2^(w-1) + 1 == -(+2^(w-1) - 1)
...
Adding 1 would be moving down, and subtracting 1 would be moving up. First we negate int_max in order to generate a valid int value, then we subtract 1 to get int_min. We can't just negate (int_max + 1) because that would exceed int_max itself, the biggest int value.
Depending on which version of C or C++ you are using, the expression -(int_max + 1) would either become a signed 64-bit integer, keeping the signedness but sacrificing the original bit width, or it would become an unsigned 32-bit integer, keeping the original bit width but sacrificing the signedness. We need to declare int_min programatically in this roundabout way to keep it a valid int value.
If that's a bit (or byte) too complicated for you, you can just do ~int_max, observing that int_max is 011...111 and int_min is 100...000.
Keep in mind that these techniques I've mentioned here can be used for any bit width w of an integer data type. They can be used for char, short, int, long, and also long long. Keep in mind that integer literals are almost always 32-bits by default, so you may have to cast the 0U to the data type with the appropriate bit width before bitwise NOTing it. But other than that, these techniques are based on the fundamental mathematical principles of two's complement integer representation. That said, they won't work if your computer uses a different way of representing integers, for example ones' complement or most-significant sign-bit.
The assignment says that "printing appropriate values from standard headers" is allowed, and in the real world, that is what you would do. As your prof wrote, direct computation is harder, and why make things harder for its own sake when you're working on another interesting problem and you just want the result? Look up the constants in <limits.h>, for example, INT_MIN and INT_MAX.
Since this is homework and you want to solve it yourself, here are some hints.
The language standard technically allows any of three different representations for signed numbers: two's-complement, one's-complement and sign-and-magnitude. Sure, every computer made in the last fifty years has used two's-complement (with the partial exception of legacy code for certain Unisys mainframes), but if you really want to language-lawyer, you could compute the smallest number for each of the three possible representations and find the minimum by comparing them.
Attempting to find the answer by overflowing or underflowing a signed value does not work! This is undefined behavior! You may in theory, but not in practice, increment an unsigned value of the same width, convert to the corresponding signed type, and compare to the result of casting the previous or next unsigned value. For 32-bit long, this might just be tolerable; it will not scale to a machine where long is 64 bits wide.
You want to use the bitwise operators, particularly ~ and <<, to calculate the largest and smallest value for every type. Note: CHAR_BITS * sizeof(x) gives you the number of bits in x, and left-shifting 0x01UL by one fewer than that, then casting to the desired type, sets the highest bit.
For floating-point values, the only portable way is to use the constants in <math.h>; floating-point values might or might not be able to represent positive and negative infinity, are not constrained to use any particular format. That said, if your compiler supports the optional Annex G of the C11 standard, which specifies IEC 60559 complex arithmetic, then dividing a nonzero floating-point number by zero will be defined as producing infinity, which does allow you to "compute" infinity and negative infinity. If so, the implementation will #define __STDC_IEC_559_COMPLEX__ as 1.
If you detect that infinity is not supported on your implementation, for instance by checking whether INFINITY and -INFINITY are infinities, you would want to use HUGE_VAL and -HUGE_VAL instead.
#include <stdio.h>
int main() {
int n = 1;
while(n>0) {
n=n<<1;
}
int int_min = n;
int int_max = -(n+1);
printf("int_min is: %d\n",int_min);
printf("int_max is: %d\n", int_max);
return 0;
}
unsigned long LMAX=(unsigned long)-1L;
long SLMAX=LMAX/2;
long SLMIN=-SLMAX-1;
If you don't have yhe L suffix just use a variable or cast to signed before castong to unsigned.
For long long:
unsigned long long LLMAX=(unsigned long long)-1LL;
I'm working with some embedded hardware, a Rabbit SBC, which uses Dynamic C 9.
I'm using the microcontroller to read information from a digital compass sensor using one of its serial ports.
The sensor sends values to the microcontroller using a single signed byte. (-85 to 85)
When I receive this data, I am putting it into a char variable
This works fine for positive values, but when the sensor starts to send negative values, the reading jumps to 255, then works its way back down to 0. I presume this is because the last bit is being used to determine the negative/positive, and is skewing the real values.
My inital thought was to change my data type to a signed char.
However, the problem I have is that the version of Dynamic C on the Microcontroller I am using does not natively support signed char values, only unsigned.
I am wondering if there is a way to manually cast the data I receive into a signed value?
You just need to pull out your reference book and read how negative numbers are represented by your controller. The rest is just typing.
For example, two's complement is represented by taking the value mod 256, so you just need to adjust by the modulus.
int signed_from_unsignedchar(unsigned char c)
{
int result = c;
if (result >= 128) result -= 256;
return result;
}
One's complement is much simpler: You just flip the bits.
int signed_from_unsignedchar(unsigned char c)
{
int result = c;
if (result >= 128) result = -(int)(unsigned char)~c;
return result;
}
Sign-magnitude represents negative numbers by setting the high bit, so you just need to clear the bit and negate:
int signed_from_unsignedchar(unsigned char c)
{
int result = c;
if (result >= 128) result = -(result & 0x7F);
return result;
}
I think this is what you're after (assumes a 32-bit int and an 8-bit char):
unsigned char c = 255;
int i = ((int)(((unsigned int)c) << 24)) >> 24;
of course I'm assuming here that your platform does support signed integers, which may not be the case.
Signed and unsigned values are all just a bunch of bits, it is YOUR interpretation that makes them signed or unsigned. For example, if your hardware produces 2's complement, if you read 0xff, you can either interpret it as -1 or 255 but they are really the same number.
Now if you have only unsigned char at your disposal, you have to emulate the behavior of negative values with it.
For example:
c < 0
changes to
c > 127
Luckily, addition doesn't need change. Also subtraction is the same (check this I'm not 100% sure).
For multiplication for example, you need to check it yourself. First, in 2's complement, here's how you get the positive value of the number:
pos_c = ~neg_c+1
which is mathematically speaking 256-neg_c which congruent modulo 256 is simply -neg_c
Now let's say you want to multiply two numbers that are unsigned, but you want to interpret them as signed.
unsigned char abs_a = a, abs_b = b;
char final_sign = 0; // 0 for positive, 1 for negative
if (a > 128)
{
abs_a = ~a+1
final_sign = 1-final_sign;
}
if (b > 128)
{
abs_b = ~b+1
final_sign = 1-final_sign;
}
result = abs_a*abs_b;
if (sign == 1)
result = ~result+1;
You get the idea!
If your platform supports signed ints, check out some of the other answers.
If not, and the value is definitely between -85 and +85, and it is two's complement, add 85 to the input value and work out your program logic to interpret values between 0 and 170 so you don't have to mess with signed integers anymore.
If it's one's complement, try this:
if (x >= 128) {
x = 85 - (x ^ 0xff);
} else {
x = x + 85;
}
That will leave you with a value between 0 and 170 as well.
EDIT: Yes, there is also sign-magnitude. Then use the same code here but change the second line to x = 85 - (x & 0x7f).