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/* SPDX-License-Identifier: GPL-2.0 */
#ifndef MEAN_AND_VARIANCE_H_
#define MEAN_AND_VARIANCE_H_
#include <linux/types.h>
#include <linux/limits.h>
#include <linux/math64.h>
#include <linux/printbuf.h>
#define SQRT_U64_MAX 4294967295ULL
#if defined(CONFIG_ARCH_SUPPORTS_INT128) && defined(__SIZEOF_INT128__)
typedef unsigned __int128 u128;
static inline u128 u64_to_u128(u64 a)
{
return (u128)a;
}
static inline u64 u128_to_u64(u128 a)
{
return (u64)a;
}
static inline u64 u128_shr64_to_u64(u128 a)
{
return (u64)(a >> 64);
}
static inline u128 u128_add(u128 a, u128 b)
{
return a + b;
}
static inline u128 u128_sub(u128 a, u128 b)
{
return a - b;
}
static inline u128 u128_shl(u128 i, s8 shift)
{
return i << shift;
}
static inline u128 u128_shl64_add(u64 a, u64 b)
{
return ((u128)a << 64) + b;
}
static inline u128 u128_square(u64 i)
{
return i*i;
}
#else
typedef struct {
u64 hi, lo;
} u128;
static inline u128 u64_to_u128(u64 a)
{
return (u128){ .lo = a };
}
static inline u64 u128_to_u64(u128 a)
{
return a.lo;
}
static inline u64 u128_shr64_to_u64(u128 a)
{
return a.hi;
}
static inline u128 u128_add(u128 a, u128 b)
{
u128 c;
c.lo = a.lo + b.lo;
c.hi = a.hi + b.hi + (c.lo < a.lo);
return c;
}
static inline u128 u128_sub(u128 a, u128 b)
{
u128 c;
c.lo = a.lo - b.lo;
c.hi = a.hi - b.hi - (c.lo > a.lo);
return c;
}
static inline u128 u128_shl(u128 i, s8 shift)
{
u128 r;
r.lo = i.lo << shift;
if (shift < 64)
r.hi = (i.hi << shift) | (i.lo >> (64 - shift));
else {
r.hi = i.lo << (shift - 64);
r.lo = 0;
}
return r;
}
static inline u128 u128_shl64_add(u64 a, u64 b)
{
return u128_add(u128_shl(u64_to_u128(a), 64), u64_to_u128(b));
}
static inline u128 u128_square(u64 i)
{
u128 r;
u64 h = i >> 32, l = i & (u64)U32_MAX;
r = u128_shl(u64_to_u128(h*h), 64);
r = u128_add(r, u128_shl(u64_to_u128(h*l), 32));
r = u128_add(r, u128_shl(u64_to_u128(l*h), 32));
r = u128_add(r, u64_to_u128(l*l));
return r;
}
#endif
static inline u128 u128_div(u128 n, u64 d)
{
u128 r;
u64 rem;
u64 hi = u128_shr64_to_u64(n);
u64 lo = u128_to_u64(n);
u64 h = hi & ((u64)U32_MAX << 32);
u64 l = (hi & (u64)U32_MAX) << 32;
r = u128_shl(u64_to_u128(div64_u64_rem(h, d, &rem)), 64);
r = u128_add(r, u128_shl(u64_to_u128(div64_u64_rem(l + (rem << 32), d, &rem)), 32));
r = u128_add(r, u64_to_u128(div64_u64_rem(lo + (rem << 32), d, &rem)));
return r;
}
struct mean_and_variance {
s64 n;
s64 sum;
u128 sum_squares;
};
/* expontentially weighted variant */
struct mean_and_variance_weighted {
bool init;
u8 w;
s64 mean;
u64 variance;
};
s64 fast_divpow2(s64 n, u8 d);
static inline struct mean_and_variance
mean_and_variance_update_inlined(struct mean_and_variance s1, s64 v1)
{
struct mean_and_variance s2;
u64 v2 = abs(v1);
s2.n = s1.n + 1;
s2.sum = s1.sum + v1;
s2.sum_squares = u128_add(s1.sum_squares, u128_square(v2));
return s2;
}
static inline struct mean_and_variance_weighted
mean_and_variance_weighted_update_inlined(struct mean_and_variance_weighted s1, s64 x)
{
struct mean_and_variance_weighted s2;
// previous weighted variance.
u64 var_w0 = s1.variance;
u8 w = s2.w = s1.w;
// new value weighted.
s64 x_w = x << w;
s64 diff_w = x_w - s1.mean;
s64 diff = fast_divpow2(diff_w, w);
// new mean weighted.
s64 u_w1 = s1.mean + diff;
BUG_ON(w % 2 != 0);
if (!s1.init) {
s2.mean = x_w;
s2.variance = 0;
} else {
s2.mean = u_w1;
s2.variance = ((var_w0 << w) - var_w0 + ((diff_w * (x_w - u_w1)) >> w)) >> w;
}
s2.init = true;
return s2;
}
struct mean_and_variance mean_and_variance_update(struct mean_and_variance s1, s64 v1);
s64 mean_and_variance_get_mean(struct mean_and_variance s);
u64 mean_and_variance_get_variance(struct mean_and_variance s1);
u32 mean_and_variance_get_stddev(struct mean_and_variance s);
struct mean_and_variance_weighted mean_and_variance_weighted_update(struct mean_and_variance_weighted s1, s64 v1);
s64 mean_and_variance_weighted_get_mean(struct mean_and_variance_weighted s);
u64 mean_and_variance_weighted_get_variance(struct mean_and_variance_weighted s);
u32 mean_and_variance_weighted_get_stddev(struct mean_and_variance_weighted s);
#endif // MEAN_AND_VAIRANCE_H_
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