107 lines
3.9 KiB
C
107 lines
3.9 KiB
C
/*
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Fixed point arithmetic.
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https://github.com/howerj/q/blob/master/q.c
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*/
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#include "fix.h"
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#include "def.h"
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#include "std.h"
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#include "time.h"
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#include <stdbool.h>
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#include <stdint.h>
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// 4-bit LUT (16 entries) for the normalized range [0.5, 2.0)
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// It stores the initial guess scaled to Q16.16.
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static const uint32_t com_fix_sqrt_lut[16] = {
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46340, 49547, 52521, 55314, 57954, 60464, 62862, 65161,
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67373, 69508, 71572, 73572, 75514, 77402, 79240, 81033};
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/* TODO: Test performance of uint_fast16_t here. */
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/* Used for other quadrants as well as cosine eval, all from the same table. */
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/* Only fractional part is present, reducing the cache footprint. */
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const uint16_t com_fix_sin_lut[128] = {
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0, 804, 1608, 2412, 3215, 4018, 4821, 5622, 6423, 7223, 8022,
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8819, 9616, 10410, 11204, 11995, 12785, 13573, 14359, 15142, 15923, 16702,
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17479, 18253, 19024, 19792, 20557, 21319, 22078, 22833, 23586, 24334, 25079,
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25820, 26557, 27291, 28020, 28745, 29465, 30181, 30893, 31600, 32302, 32999,
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33692, 34379, 35061, 35738, 36409, 37075, 37736, 38390, 39039, 39682, 40319,
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40950, 41575, 42194, 42806, 43412, 44011, 44603, 45189, 45768, 46340, 46906,
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47464, 48015, 48558, 49095, 49624, 50146, 50660, 51166, 51665, 52155, 52639,
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53114, 53581, 54040, 54491, 54933, 55368, 55794, 56212, 56621, 57022, 57414,
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57797, 58172, 58538, 58895, 59243, 59583, 59913, 60235, 60547, 60850, 61144,
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61429, 61705, 61971, 62228, 62475, 62714, 62942, 63162, 63371, 63571, 63762,
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63943, 64115, 64276, 64428, 64571, 64703, 64826, 64939, 65043, 65136, 65220,
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65294, 65358, 65412, 65457, 65491, 65516, 65531};
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com_fix_t com_fix_sqrt(com_fix_t a) {
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// 1. Handle sign and edge cases
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com_std_assert(a >= 0);
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if (a == 0)
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return 0;
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// 2. Normalize input to the range [0.5, 2.0) to maximize LUT precision
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// clz = count leading zeros. On modern hardware, use __builtin_clz
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uint32_t leading_zeros = __builtin_clz(a);
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// Calculate how much we need to shift to place the highest bit properly
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// We want the value to land squarely within an optimal window
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int32_t shift = (31 - leading_zeros) - COM_FIX_FRACBITS;
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// Normalize shift to always be even so we can cleanly pull out 2^(shift/2)
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if (shift & 1)
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shift -= 1;
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uint32_t normalized_a = shift > 0 ? a >> shift : a << (-shift);
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// 3. LUT Lookup using 4 MSBs of the normalized value
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// Extracted index corresponds to the interval [0.5, 2.0)
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uint32_t lut_index = (normalized_a >> (COM_FIX_FRACBITS - 3)) & 0xF;
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uint64_t x = com_fix_sqrt_lut[lut_index];
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// 4. Newton-Raphson Iterations: x = 0.5 * (x + normalized_a / x)
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// We upscale to 64-bit to prevent intermediate overflow during division
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x = (x + ((uint64_t)normalized_a << COM_FIX_FRACBITS) / x) >>
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1; // Iteration 1
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x = (x + ((uint64_t)normalized_a << COM_FIX_FRACBITS) / x) >>
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1; // Iteration 2
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// 5. Denormalize back to the target scale: result = x * 2^(shift / 2)
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int32_t final_shift = shift / 2;
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return final_shift > 0 ? (int32_t)(x << final_shift)
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: (int32_t)(x >> (-final_shift));
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}
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void com_fix_run_bench(void) {
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uint64_t start = com_timer_count_ns();
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for (int i = 5000000; i--;) {
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com_fix_t sqrt = com_fix_sqrt(i);
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com_def_profile_sink(sqrt);
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}
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com_timer_profile(start, "fixed: sqrt");
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start = com_timer_count_ns();
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for (int i = 50000000; i--;) {
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com_fix_t sin = com_fix_sin(i);
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com_def_profile_sink(sin);
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}
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com_timer_profile(start, "fixed: sin");
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start = com_timer_count_ns();
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for (int i = 50000000; i--;) {
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com_fix_t cos = com_fix_cos(i);
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com_def_profile_sink(cos);
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}
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com_timer_profile(start, "fixed: cos");
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start = com_timer_count_ns();
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for (int i = 50000000; i--;) {
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com_fix_t sin, cos;
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com_fix_sincos(i, &sin, &cos);
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com_fix_t sinv = sin;
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com_fix_t cosv = cos;
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com_def_profile_sink(sinv);
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com_def_profile_sink(cosv);
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}
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com_timer_profile(start, "fixed: sincos");
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}
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