#include <stdio.h>
#include <math.h>
#include "lfsr.h"
#include "../compiler/compiler.h"
/*
* LFSR taps retrieved from:
* http://home1.gte.net/res0658s/electronics/LFSRtaps.html
*
* The memory overhead of the following tap table should be relatively small,
* no more than 400 bytes.
*/
static uint8_t lfsr_taps[64][FIO_MAX_TAPS] =
{
{0}, {0}, {0}, //LFSRs with less that 3-bits cannot exist
{3, 2}, //Tap position for 3-bit LFSR
{4, 3}, //Tap position for 4-bit LFSR
{5, 3}, //Tap position for 5-bit LFSR
{6, 5}, //Tap position for 6-bit LFSR
{7, 6}, //Tap position for 7-bit LFSR
{8, 6, 5 ,4}, //Tap position for 8-bit LFSR
{9, 5}, //Tap position for 9-bit LFSR
{10, 7}, //Tap position for 10-bit LFSR
{11, 9}, //Tap position for 11-bit LFSR
{12, 6, 4, 1}, //Tap position for 12-bit LFSR
{13, 4, 3, 1}, //Tap position for 13-bit LFSR
{14, 5, 3, 1}, //Tap position for 14-bit LFSR
{15, 14}, //Tap position for 15-bit LFSR
{16, 15, 13, 4}, //Tap position for 16-bit LFSR
{17, 14}, //Tap position for 17-bit LFSR
{18, 11}, //Tap position for 18-bit LFSR
{19, 6, 2, 1}, //Tap position for 19-bit LFSR
{20, 17}, //Tap position for 20-bit LFSR
{21, 19}, //Tap position for 21-bit LFSR
{22, 21}, //Tap position for 22-bit LFSR
{23, 18}, //Tap position for 23-bit LFSR
{24, 23, 22, 17}, //Tap position for 24-bit LFSR
{25, 22}, //Tap position for 25-bit LFSR
{26, 6, 2, 1}, //Tap position for 26-bit LFSR
{27, 5, 2, 1}, //Tap position for 27-bit LFSR
{28, 25}, //Tap position for 28-bit LFSR
{29, 27}, //Tap position for 29-bit LFSR
{30, 6, 4, 1}, //Tap position for 30-bit LFSR
{31, 28}, //Tap position for 31-bit LFSR
{32, 31, 29, 1}, //Tap position for 32-bit LFSR
{33, 20}, //Tap position for 33-bit LFSR
{34, 27, 2, 1}, //Tap position for 34-bit LFSR
{35, 33}, //Tap position for 35-bit LFSR
{36, 25}, //Tap position for 36-bit LFSR
{37, 5, 4, 3, 2, 1}, //Tap position for 37-bit LFSR
{38, 6, 5, 1}, //Tap position for 38-bit LFSR
{39, 35}, //Tap position for 39-bit LFSR
{40, 38, 21, 19}, //Tap position for 40-bit LFSR
{41, 38}, //Tap position for 41-bit LFSR
{42, 41, 20, 19}, //Tap position for 42-bit LFSR
{43, 42, 38, 37}, //Tap position for 43-bit LFSR
{44, 43, 18, 17}, //Tap position for 44-bit LFSR
{45, 44, 42, 41}, //Tap position for 45-bit LFSR
{46, 45, 26, 25}, //Tap position for 46-bit LFSR
{47, 42}, //Tap position for 47-bit LFSR
{48, 47, 21, 20}, //Tap position for 48-bit LFSR
{49, 40}, //Tap position for 49-bit LFSR
{50, 49, 24, 23}, //Tap position for 50-bit LFSR
{51, 50, 36, 35}, //Tap position for 51-bit LFSR
{52, 49}, //Tap position for 52-bit LFSR
{53, 52, 38, 37}, //Tap position for 53-bit LFSR
{54, 53, 18, 17}, //Tap position for 54-bit LFSR
{55, 31}, //Tap position for 55-bit LFSR
{56, 55, 35, 34}, //Tap position for 56-bit LFSR
{57, 50}, //Tap position for 57-bit LFSR
{58, 39}, //Tap position for 58-bit LFSR
{59, 58, 38, 37}, //Tap position for 59-bit LFSR
{60, 59}, //Tap position for 60-bit LFSR
{61, 60, 46, 45}, //Tap position for 61-bit LFSR
{62, 61, 6, 5}, //Tap position for 62-bit LFSR
{63, 62}, //Tap position for 63-bit LFSR
};
#define __LFSR_NEXT(__fl, __v) \
__v = ((__v >> 1) | __fl->cached_bit) ^ \
(((__v & 1UL) - 1UL) & __fl->xormask);
static inline void __lfsr_next(struct fio_lfsr *fl, unsigned int spin)
{
/*
* This should be O(1) since most compilers will create a jump table for
* this switch.
*/
switch (spin) {
case 15: __LFSR_NEXT(fl, fl->last_val);
case 14: __LFSR_NEXT(fl, fl->last_val);
case 13: __LFSR_NEXT(fl, fl->last_val);
case 12: __LFSR_NEXT(fl, fl->last_val);
case 11: __LFSR_NEXT(fl, fl->last_val);
case 10: __LFSR_NEXT(fl, fl->last_val);
case 9: __LFSR_NEXT(fl, fl->last_val);
case 8: __LFSR_NEXT(fl, fl->last_val);
case 7: __LFSR_NEXT(fl, fl->last_val);
case 6: __LFSR_NEXT(fl, fl->last_val);
case 5: __LFSR_NEXT(fl, fl->last_val);
case 4: __LFSR_NEXT(fl, fl->last_val);
case 3: __LFSR_NEXT(fl, fl->last_val);
case 2: __LFSR_NEXT(fl, fl->last_val);
case 1: __LFSR_NEXT(fl, fl->last_val);
case 0: __LFSR_NEXT(fl, fl->last_val);
default: break;
}
}
/*
* lfsr_next does the following:
*
* a. Return if the number of max values has been exceeded.
* b. Check if we have a spin value that produces a repeating subsequence.
* This is previously calculated in `prepare_spin` and cycle_length should
* be > 0. If we do have such a spin:
*
* i. Decrement the calculated cycle.
* ii. If it reaches zero, add "+1" to the spin and reset the cycle_length
* (we have it cached in the struct fio_lfsr)
*
* In either case, continue with the calculation of the next value.
* c. Check if the calculated value exceeds the desirable range. In this case,
* go back to b, else return.
*/
int lfsr_next(struct fio_lfsr *fl, uint64_t *off)
{
if (fl->num_vals++ > fl->max_val)
return 1;
do {
if (fl->cycle_length && !--fl->cycle_length) {
__lfsr_next(fl, fl->spin + 1);
fl->cycle_length = fl->cached_cycle_length;
} else
__lfsr_next(fl, fl->spin);
} while (fio_unlikely(fl->last_val > fl->max_val));
*off = fl->last_val;
return 0;
}
static uint64_t lfsr_create_xormask(uint8_t *taps)
{
int i;
uint64_t xormask = 0;
for(i = 0; i < FIO_MAX_TAPS && taps[i] != 0; i++)
xormask |= 1UL << (taps[i] - 1);
return xormask;
}
static uint8_t *find_lfsr(uint64_t size)
{
int i;
/*
* For an LFSR, there is always a prohibited state (all ones).
* Thus, if we need to find the proper LFSR for our size, we must
* take that into account.
*/
for (i = 3; i < 64; i++)
if ((1UL << i) > size)
return lfsr_taps[i];
return NULL;
}
/*
* It is well-known that all maximal n-bit LFSRs will start repeating
* themselves after their 2^n iteration. The introduction of spins however, is
* possible to create a repetition of a sub-sequence before we hit that mark.
* This happens if:
*
* [1]: ((2^n - 1) * i) % (spin + 1) == 0,
* where "n" is LFSR's bits and "i" any number within the range [1,spin]
*
* It is important to know beforehand if a spin can cause a repetition of a
* sub-sequence (cycle) and its length. However, calculating (2^n - 1) * i may
* produce a buffer overflow for "n" close to 64, so we expand the above to:
*
* [2]: (2^n - 1) -> (x * (spin + 1) + y), where x >= 0 and 0 <= y <= spin
*
* Thus, [1] is equivalent to (y * i) % (spin + 1) == 0;
* Also, the cycle's length will be (x * i) + (y * i) / (spin + 1)
*/
static int prepare_spin(struct fio_lfsr *fl, unsigned int spin)
{
uint64_t max = (fl->cached_bit << 1) - 1;
uint64_t x, y;
int i;
if (spin > 15)
return 1;
x = max / (spin + 1);
y = max % (spin + 1);
fl->cycle_length = 0; /* No cycle occurs, other than the expected */
fl->spin = spin;
for (i = 1; i <= spin; i++) {
if ((y * i) % (spin + 1) == 0) {
fl->cycle_length = (x * i) + (y * i) / (spin + 1);
break;
}
}
fl->cached_cycle_length = fl->cycle_length;
/*
* Increment cycle length for the first time only since the stored value
* will not be printed otherwise.
*/
fl->cycle_length++;
return 0;
}
int lfsr_reset(struct fio_lfsr *fl, unsigned long seed)
{
uint64_t bitmask = (fl->cached_bit << 1) - 1;
fl->num_vals = 0;
fl->last_val = seed & bitmask;
/* All-ones state is illegal for XNOR LFSRs */
if (fl->last_val == bitmask)
return 1;
return 0;
}
int lfsr_init(struct fio_lfsr *fl, uint64_t nums, unsigned long seed,
unsigned int spin)
{
uint8_t *taps;
taps = find_lfsr(nums);
if (!taps)
return 1;
fl->max_val = nums - 1;
fl->xormask = lfsr_create_xormask(taps);
fl->cached_bit = 1UL << (taps[0] - 1);
if (prepare_spin(fl, spin))
return 1;
if (lfsr_reset(fl, seed))
return 1;
return 0;
}