# Change Arithmetic Right Shift to Logical Right Shift

The following code is a solution to a textbook (Bryant&O’Hallaron: Computer Systems A programmer’s Perspective 2nd Ed) problem in bit-level data manipulation (attempted for the challenge, not a class). The function srl is not written necessarily in a practical manner, but within the constraints required by the problem.

## Questions

Is there is a clearer, more straight-forward way to write this within the required constraints of the problem (perhaps with fewer ~ operations)?

There is a need to avoid undefined behavior of the left shift, when k = 0. In this case int_bits – k = int_bits, which causes the shift to work unpredictably. Is there a better way to handle the undefined behavior of the shift operations, when the shift is larger than the number of bits in the interger?

It seems to work correctly, but I lack an answer, so any feedback on the solution would be appreciated.

## Requirements

• No additional right shifts or type casts may be used beyond the given expression

``  /*Perform shift arithmetically*/    unsigned xsra = (int) x >> k; ``
• Only addition or subtraction may be used, no multiplication, division, or modulus

• No comparison operators and no conditionals

• Only bit-wise operations (except further right shifts) and logical operators may be used

## Code

``unsigned srl(unsigned x, int k) {     /*Perform shift arithmetically*/     unsigned xsra = (int) x >> k;      unsigned int_bits = sizeof(int) << 3;//calculates the number of bits in int (assumes 8-bit byte)      unsigned zero_or_all_bits = ~0 + !k;//for k = 0, corrects for the undefined behavior in                                         //the left shift produced from int_bits - k = int_bits                                         //if k != 0, !k == 0, and zero_or_all_bits == ~0                                         //if k == 0, zero_or_all_bits == 0      unsigned high_bit_mask = ~(zero_or_all_bits << (zero_or_all_bits & (int_bits - k)));     /******************************************/     //creates a mask of either all bits set in an unsigned int (UINT_MAX)     //or a mask with k high bits cleared.     //if k == 0, then high_bit_mask = ~(0 << 0) = ~0.     //if k != 0, then high_bit_mask = ~(~0 << (~0 & (int_bits - k)))     //ex. k == 3, high_bit_mask == 0x1FFFFFFF     //ex. k == 0, high_bit_mask == 0xFFFFFFFF     //ex. k == 31, high_bit_mask == 0xFFFFFFFE     /******************************************/      return xsra & high_bit_mask; ``

}

## Test Code

``printf("Test srl:\n"); printf("srl(-1, 1): 0x%.8x\n", srl(-1, 1)); printf("srl(-1, 4): 0x%.8x\n", srl(-1, 4)); printf("srl(-1, 5): 0x%.8x\n", srl(-1, 5)); printf("srl(-1, 31): 0x%.8x\n", srl(-1, 31)); printf("srl(-1, 0): 0x%.8x\n", srl(-1, 0));  printf("srl(0x7FFFFFFF, 1): 0x%.8x\n", srl(0x7FFFFFFF, 1)); printf("srl(0x7FFFFFFF, 4): 0x%.8x\n", srl(0x7FFFFFFF, 4)); printf("srl(0x7FFFFFFF, 5): 0x%.8x\n", srl(0x7FFFFFFF, 5)); printf("srl(0x7FFFFFFF, 31): 0x%.8x\n", srl(0x7FFFFFFF, 31)); printf("srl(0x7FFFFFFF, 0): 0x%.8x\n", srl(0x7FFFFFFF, 0));  printf("srl(0x80000000, 1): 0x%.8x\n", srl(0x80000000, 1)); printf("srl(0x80000000, 4): 0x%.8x\n", srl(0x80000000, 4)); printf("srl(0x80000000, 5): 0x%.8x\n", srl(0x80000000, 5)); printf("srl(0x80000000, 31): 0x%.8x\n", srl(0x80000000, 31)); printf("srl(0x80000000, 0): 0x%.8x\n", srl(0x80000000, 0));  printf("srl(0, 1): 0x%.8x\n", srl(0, 1)); printf("srl(0, 4): 0x%.8x\n", srl(0, 4)); printf("srl(0, 5): 0x%.8x\n", srl(0, 5)); printf("srl(0, 31): 0x%.8x\n", srl(0, 31)); printf("srl(0, 0): 0x%.8x\n", srl(0, 0));  printf("srl(1, 1): 0x%.8x\n", srl(1, 1)); printf("srl(1, 4): 0x%.8x\n", srl(1, 4)); printf("srl(1, 5): 0x%.8x\n", srl(1, 5)); printf("srl(1, 31): 0x%.8x\n", srl(1, 31)); printf("srl(1, 0): 0x%.8x\n", srl(1, 0)); ``

## Output

Test srl:
srl(-1, 1): 0x7fffffff
srl(-1, 4): 0x0fffffff
srl(-1, 5): 0x07ffffff
srl(-1, 31): 0x00000001
srl(-1, 0): 0xffffffff
srl(0x7FFFFFFF, 1): 0x3fffffff
srl(0x7FFFFFFF, 4): 0x07ffffff
srl(0x7FFFFFFF, 5): 0x03ffffff
srl(0x7FFFFFFF, 31): 0x00000000
srl(0x7FFFFFFF, 0): 0x7fffffff
srl(0x80000000, 1): 0x40000000
srl(0x80000000, 4): 0x08000000
srl(0x80000000, 5): 0x04000000
srl(0x80000000, 31): 0x00000001
srl(0x80000000, 0): 0x80000000
srl(0, 1): 0x00000000
srl(0, 4): 0x00000000
srl(0, 5): 0x00000000
srl(0, 31): 0x00000000
srl(0, 0): 0x00000000
srl(1, 1): 0x00000000
srl(1, 4): 0x00000000
srl(1, 5): 0x00000000
srl(1, 31): 0x00000000
srl(1, 0): 0x00000001