#include <stdio.h>
-#include <math.h>
#include "lfsr.h"
+#include "../compiler/compiler.h"
/*
* LFSR taps retrieved from:
* The memory overhead of the following tap table should be relatively small,
* no more than 400 bytes.
*/
-static uint8_t taps[64][FIO_MAX_TAPS] =
+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
+ {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) \
* this switch.
*/
switch (spin) {
- case 16: __LFSR_NEXT(fl, fl->last_val);
case 15: __LFSR_NEXT(fl, fl->last_val);
case 14: __LFSR_NEXT(fl, fl->last_val);
case 13: __LFSR_NEXT(fl, fl->last_val);
}
}
-int lfsr_next(struct fio_lfsr *fl, uint64_t *off, uint64_t last)
+/*
+ * 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)
{
- int repeat;
- unsigned int spin;
-
- repeat = fl->num_vals % fl->cycle_length;
- if (repeat == 0)
- spin = fl->spin + 1;
- else
- spin = fl->spin;
-
- if (fl->num_vals > fl->max_val)
+ if (fl->num_vals++ > fl->max_val)
return 1;
- fl->num_vals++;
-
do {
- __lfsr_next(fl, spin);
- } while (fl->last_val > fl->max_val);
+ 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;
{
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) /* TODO: Explain why. */
- return taps[i];
+ if ((1UL << i) > size)
+ return lfsr_taps[i];
return NULL;
}
* Thus, [1] is equivalent to (y * i) % (spin + 1) == 0;
* Also, the cycle's length will be (x * i) + (y * i) / (spin + 1)
*/
-int prepare_spin(struct fio_lfsr *fl, unsigned int spin)
+static int prepare_spin(struct fio_lfsr *fl, unsigned int spin)
{
uint64_t max = (fl->cached_bit << 1) - 1;
uint64_t x, y;
x = max / (spin + 1);
y = max % (spin + 1);
- fl->cycle_length = max; /* This is the expected cycle */
+ fl->cycle_length = 0; /* No cycle occurs, other than the expected */
fl->spin = spin;
for (i = 1; i <= spin; i++) {
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_init(struct fio_lfsr *fl, uint64_t nums, unsigned long seed,
unsigned int spin)
{
- uint8_t *lfsr_taps;
+ uint8_t *taps;
- lfsr_taps = find_lfsr(nums);
- if (!lfsr_taps)
+ taps = find_lfsr(nums);
+ if (!taps)
return 1;
fl->max_val = nums - 1;
- fl->xormask = lfsr_create_xormask(lfsr_taps);
- fl->cached_bit = 1UL << (lfsr_taps[0] - 1);
+ fl->xormask = lfsr_create_xormask(taps);
+ fl->cached_bit = 1UL << (taps[0] - 1);
if (prepare_spin(fl, spin))
return 1;
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