6064bc6c06
The autoconf changes were adapted from: https://github.com/glennrp/libpng/blob/libpng16/configure.ac
530 lines
39 KiB
C
530 lines
39 KiB
C
#ifndef VECTOR_MATH_H
|
|
#define VECTOR_MATH_H
|
|
|
|
#include <stdlib.h>
|
|
#include <stdint.h>
|
|
#include <math.h>
|
|
#include "vector.h"
|
|
|
|
#define ks_lt_index(a, b) ((a).value < (b).value)
|
|
|
|
#if defined(INTEL_SSE)
|
|
#include <emmintrin.h>
|
|
#elif defined(ARM_NEON)
|
|
#include "sse2neon.h"
|
|
#endif
|
|
|
|
/*
|
|
Useful macro definitions for memory alignment:
|
|
http://homepage1.nifty.com/herumi/prog/gcc-and-vc.html#MIE_ALIGN
|
|
*/
|
|
|
|
#ifdef _MSC_VER
|
|
#define MIE_ALIGN(x) __declspec(align(x))
|
|
#else
|
|
#define MIE_ALIGN(x) __attribute__((aligned(x)))
|
|
#endif
|
|
|
|
#define CONST_128D(var, val) \
|
|
MIE_ALIGN(16) static const double var[2] = {(val), (val)}
|
|
|
|
|
|
#define VECTOR_INIT_NUMERIC(name, type, unsigned_type, type_abs) \
|
|
__VECTOR_BASE(name, type) \
|
|
__VECTOR_DESTROY(name, type) \
|
|
\
|
|
static inline void name##_zero(type *array, size_t n) { \
|
|
memset(array, 0, n * sizeof(type)); \
|
|
} \
|
|
\
|
|
static inline void name##_raw_copy(type *dst, const type *src, size_t n) { \
|
|
memcpy(dst, src, n * sizeof(type)); \
|
|
} \
|
|
\
|
|
static inline void name##_set(type *array, type value, size_t n) { \
|
|
for (size_t i = 0; i < n; i++) { \
|
|
array[i] = value; \
|
|
} \
|
|
} \
|
|
\
|
|
static inline name *name##_new_value(size_t n, type value) { \
|
|
name *vector = name##_new_size(n); \
|
|
if (vector == NULL) return NULL; \
|
|
name##_set(vector->a, n, (type)value); \
|
|
vector->n = n; \
|
|
return vector; \
|
|
} \
|
|
\
|
|
static inline name *name##_new_ones(size_t n) { \
|
|
return name##_new_value(n, (type)1); \
|
|
} \
|
|
\
|
|
static inline name *name##_new_zeros(size_t n) { \
|
|
name *vector = name##_new_size(n); \
|
|
if (vector == NULL) return NULL; \
|
|
name##_zero(vector->a, n); \
|
|
vector->n = n; \
|
|
return vector; \
|
|
} \
|
|
\
|
|
static inline bool name##_resize_fill_zeros(name *self, size_t n) { \
|
|
size_t old_n = self->n; \
|
|
bool ret = name##_resize(self, n); \
|
|
if (ret && n > old_n) { \
|
|
memset(self->a + old_n, 0, (n - old_n) * sizeof(type)); \
|
|
} \
|
|
return ret; \
|
|
} \
|
|
\
|
|
static inline bool name##_resize_aligned_fill_zeros(name *self, size_t n, size_t alignment) { \
|
|
size_t old_n = self->n; \
|
|
bool ret = name##_resize_aligned(self, n, alignment); \
|
|
if (ret && n > old_n) { \
|
|
memset(self->a + old_n, 0, (n - old_n) * sizeof(type)); \
|
|
} \
|
|
return ret; \
|
|
} \
|
|
\
|
|
static inline type name##_max(type *array, size_t n) { \
|
|
if (n < 1) return (type) 0; \
|
|
type val = array[0]; \
|
|
type max_val = val; \
|
|
for (size_t i = 1; i < n; i++) { \
|
|
val = array[i]; \
|
|
if (val > max_val) max_val = val; \
|
|
} \
|
|
return max_val; \
|
|
} \
|
|
\
|
|
static inline type name##_min(type *array, size_t n) { \
|
|
if (n < 1) return (type) 0; \
|
|
type val = array[0]; \
|
|
type min_val = val; \
|
|
for (size_t i = 1; i < n; i++) { \
|
|
val = array[i]; \
|
|
if (val < min_val) min_val = val; \
|
|
} \
|
|
return min_val; \
|
|
} \
|
|
\
|
|
static inline int64_t name##_argmax(type *array, size_t n) { \
|
|
if (n < 1) return -1; \
|
|
type val = array[0]; \
|
|
type max_val = val; \
|
|
int64_t argmax = 0; \
|
|
for (size_t i = 0; i < n; i++) { \
|
|
val = array[i]; \
|
|
if (val > max_val) { \
|
|
max_val = val; \
|
|
argmax = i; \
|
|
} \
|
|
} \
|
|
return argmax; \
|
|
} \
|
|
\
|
|
static inline int64_t name##_argmin(type *array, size_t n) { \
|
|
if (n < 1) return (type) -1; \
|
|
type val = array[0]; \
|
|
type min_val = val; \
|
|
int64_t argmin = 0; \
|
|
for (size_t i = 1; i < n; i++) { \
|
|
val = array[i]; \
|
|
if (val < min_val) { \
|
|
min_val = val; \
|
|
argmin = i; \
|
|
} \
|
|
} \
|
|
return argmin; \
|
|
} \
|
|
\
|
|
typedef struct type##_index { \
|
|
size_t index; \
|
|
type value; \
|
|
} type##_index_t; \
|
|
\
|
|
KSORT_INIT_GENERIC(type) \
|
|
KSORT_INIT(type##_indices, type##_index_t, ks_lt_index) \
|
|
\
|
|
static inline void name##_sort(type *array, size_t n) { \
|
|
ks_introsort(type, n, array); \
|
|
} \
|
|
\
|
|
static inline size_t *name##_argsort(type *array, size_t n) { \
|
|
type##_index_t *type_indices = malloc(sizeof(type##_index_t) * n); \
|
|
size_t i; \
|
|
for (i = 0; i < n; i++) { \
|
|
type_indices[i] = (type##_index_t){i, array[i]}; \
|
|
} \
|
|
ks_introsort(type##_indices, n, type_indices); \
|
|
size_t *indices = malloc(sizeof(size_t) * n); \
|
|
for (i = 0; i < n; i++) { \
|
|
indices[i] = type_indices[i].index; \
|
|
} \
|
|
free(type_indices); \
|
|
return indices; \
|
|
} \
|
|
\
|
|
static inline void name##_add(type *array, type c, size_t n) { \
|
|
for (size_t i = 0; i < n; i++) { \
|
|
array[i] += c; \
|
|
} \
|
|
} \
|
|
\
|
|
static inline void name##_sub(type *array, type c, size_t n) { \
|
|
for (size_t i = 0; i < n; i++) { \
|
|
array[i] -= c; \
|
|
} \
|
|
} \
|
|
\
|
|
static inline void name##_mul(type *array, type c, size_t n) { \
|
|
for (size_t i = 0; i < n; i++) { \
|
|
array[i] *= c; \
|
|
} \
|
|
} \
|
|
\
|
|
static inline void name##_div(type *array, type c, size_t n) { \
|
|
for (size_t i = 0; i < n; i++) { \
|
|
array[i] /= c; \
|
|
} \
|
|
} \
|
|
\
|
|
static inline type name##_sum(type *array, size_t n) { \
|
|
type result = 0; \
|
|
for (size_t i = 0; i < n; i++) { \
|
|
result += array[i]; \
|
|
} \
|
|
return result; \
|
|
} \
|
|
\
|
|
static inline unsigned_type name##_l1_norm(type *array, size_t n) { \
|
|
unsigned_type result = 0; \
|
|
for (size_t i = 0; i < n; i++) { \
|
|
result += type_abs(array[i]); \
|
|
} \
|
|
return result; \
|
|
} \
|
|
\
|
|
static inline double name##_l2_norm(type *array, size_t n) { \
|
|
unsigned_type result = 0; \
|
|
for (size_t i = 0; i < n; i++) { \
|
|
result += array[i] * array[i]; \
|
|
} \
|
|
return sqrt((double)result); \
|
|
} \
|
|
\
|
|
static inline unsigned_type name##_sum_sq(type *array, size_t n) { \
|
|
unsigned_type result = 0; \
|
|
for (size_t i = 0; i < n; i++) { \
|
|
result += array[i] * array[i]; \
|
|
} \
|
|
return result; \
|
|
} \
|
|
\
|
|
static inline double name##_mean(type *array, size_t n) { \
|
|
unsigned_type sum = name##_sum(array, n); \
|
|
return (double)sum / n; \
|
|
} \
|
|
\
|
|
static inline double name##_var(type *array, size_t n) { \
|
|
double mu = name##_mean(array, n); \
|
|
double sigma2 = 0.0; \
|
|
for (size_t i = 0; i < n; i++) { \
|
|
double dev = (double)array[i] - mu; \
|
|
sigma2 += dev * dev; \
|
|
} \
|
|
return sigma2 / n; \
|
|
} \
|
|
\
|
|
static inline double name##_std(type *array, size_t n) { \
|
|
double sigma2 = name##_var(array, n); \
|
|
return sqrt(sigma2); \
|
|
} \
|
|
\
|
|
static inline type name##_product(type *array, size_t n) { \
|
|
type result = 0; \
|
|
for (size_t i = 0; i < n; i++) { \
|
|
result *= array[i]; \
|
|
} \
|
|
return result; \
|
|
} \
|
|
\
|
|
static inline void name##_add_array(type *a1, const type *a2, size_t n) { \
|
|
for (size_t i = 0; i < n; i++) { \
|
|
a1[i] += a2[i]; \
|
|
} \
|
|
} \
|
|
\
|
|
static inline void name##_add_array_times_scalar(type *a1, const type *a2, double v, size_t n) { \
|
|
for (size_t i = 0; i < n; i++) { \
|
|
a1[i] += a2[i] * v; \
|
|
} \
|
|
} \
|
|
\
|
|
static inline void name##_sub_array(type *a1, const type *a2, size_t n) { \
|
|
for (size_t i = 0; i < n; i++) { \
|
|
a1[i] -= a2[i]; \
|
|
} \
|
|
} \
|
|
\
|
|
\
|
|
static inline void name##_sub_array_times_scalar(type *a1, const type *a2, double v, size_t n) { \
|
|
for (size_t i = 0; i < n; i++) { \
|
|
a1[i] -= a2[i] * v; \
|
|
} \
|
|
} \
|
|
\
|
|
static inline void name##_mul_array(type *a1, const type *a2, size_t n) { \
|
|
for (size_t i = 0; i < n; i++) { \
|
|
a1[i] *= a2[i]; \
|
|
} \
|
|
} \
|
|
\
|
|
static inline void name##_mul_array_times_scalar(type *a1, const type *a2, double v, size_t n) { \
|
|
for (size_t i = 0; i < n; i++) { \
|
|
a1[i] *= a2[i] * v; \
|
|
} \
|
|
} \
|
|
\
|
|
static inline void name##_div_array(type *a1, const type *a2, size_t n) { \
|
|
for (size_t i = 0; i < n; i++) { \
|
|
a1[i] /= a2[i]; \
|
|
} \
|
|
} \
|
|
\
|
|
static inline void name##_div_array_times_scalar(type *a1, const type *a2, double v, size_t n) { \
|
|
for (size_t i = 0; i < n; i++) { \
|
|
a1[i] /= a2[i] * v; \
|
|
} \
|
|
} \
|
|
\
|
|
static inline type name##_dot(const type *a1, const type *a2, size_t n) { \
|
|
type result = 0; \
|
|
for (size_t i = 0; i < n; i++) { \
|
|
result += a1[i] * a2[i]; \
|
|
} \
|
|
return result; \
|
|
}
|
|
|
|
|
|
#define VECTOR_INIT_NUMERIC_FLOAT(name, type, type_abs) \
|
|
VECTOR_INIT_NUMERIC(name, type, type, type_abs) \
|
|
\
|
|
static inline void name##_log(type *array, size_t n) { \
|
|
for (size_t i = 0; i < n; i++) { \
|
|
array[i] = log(array[i]); \
|
|
} \
|
|
} \
|
|
\
|
|
static inline void name##_exp(type *array, size_t n) { \
|
|
for (size_t i = 0; i < n; i++) { \
|
|
array[i] = exp(array[i]); \
|
|
} \
|
|
} \
|
|
\
|
|
static inline type name##_sum_log(type *array, size_t n) { \
|
|
type result = 0; \
|
|
for (size_t i = 0; i < n; i++) { \
|
|
result += log(array[i]); \
|
|
} \
|
|
return result; \
|
|
} \
|
|
\
|
|
static inline type name##_log_sum_exp(type *array, size_t n) { \
|
|
type max = name##_max(array, n); \
|
|
type result = 0; \
|
|
for (size_t i = 0; i < n; i++) { \
|
|
result += exp(array[i] - max); \
|
|
} \
|
|
return max + log(result); \
|
|
}
|
|
|
|
|
|
|
|
#if defined(INTEL_SSE) || defined(ARM_NEON)
|
|
/*
|
|
From https://github.com/herumi/fmath/blob/master/fastexp.cpp
|
|
|
|
The best performing C routine appears to be this version of the Remez algorithm:
|
|
Remez 9th [0,log2] SSE
|
|
*/
|
|
static inline void remez9_0_log2_sse(double *values, size_t num)
|
|
{
|
|
size_t i;
|
|
CONST_128D(one, 1.);
|
|
CONST_128D(log2e, 1.4426950408889634073599);
|
|
CONST_128D(maxlog, 7.09782712893383996843e2); // log(2**1024)
|
|
CONST_128D(minlog, -7.08396418532264106224e2); // log(2**-1022)
|
|
CONST_128D(c1, 6.93145751953125E-1);
|
|
CONST_128D(c2, 1.42860682030941723212E-6);
|
|
CONST_128D(w9, 3.9099787920346160288874633639268318097077213911751e-6);
|
|
CONST_128D(w8, 2.299608440919942766555719515783308016700833740918e-5);
|
|
CONST_128D(w7, 1.99930498409474044486498978862963995247838069436646e-4);
|
|
CONST_128D(w6, 1.38812674551586429265054343505879910146775323730237e-3);
|
|
CONST_128D(w5, 8.3335688409829575034112982839739473866857586300664e-3);
|
|
CONST_128D(w4, 4.1666622504201078708502686068113075402683415962893e-2);
|
|
CONST_128D(w3, 0.166666671414320541875332123507829990378055646330574);
|
|
CONST_128D(w2, 0.49999999974109940909767965915362308135415179642286);
|
|
CONST_128D(w1, 1.0000000000054730504284163017295863259125942049362);
|
|
CONST_128D(w0, 0.99999999999998091336479463057053516986466888462081);
|
|
const __m128i offset = _mm_setr_epi32(1023, 1023, 0, 0);
|
|
|
|
for (i = 0;i < num;i += 4) {
|
|
__m128i k1, k2;
|
|
__m128d p1, p2;
|
|
__m128d a1, a2;
|
|
__m128d xmm0, xmm1;
|
|
__m128d x1, x2;
|
|
|
|
/* Load four double values. */
|
|
xmm0 = _mm_load_pd(maxlog);
|
|
xmm1 = _mm_load_pd(minlog);
|
|
x1 = _mm_load_pd(values+i);
|
|
x2 = _mm_load_pd(values+i+2);
|
|
x1 = _mm_min_pd(x1, xmm0);
|
|
x2 = _mm_min_pd(x2, xmm0);
|
|
x1 = _mm_max_pd(x1, xmm1);
|
|
x2 = _mm_max_pd(x2, xmm1);
|
|
|
|
/* a = x / log2; */
|
|
xmm0 = _mm_load_pd(log2e);
|
|
xmm1 = _mm_setzero_pd();
|
|
a1 = _mm_mul_pd(x1, xmm0);
|
|
a2 = _mm_mul_pd(x2, xmm0);
|
|
|
|
/* k = (int)floor(a); p = (float)k; */
|
|
p1 = _mm_cmplt_pd(a1, xmm1);
|
|
p2 = _mm_cmplt_pd(a2, xmm1);
|
|
xmm0 = _mm_load_pd(one);
|
|
p1 = _mm_and_pd(p1, xmm0);
|
|
p2 = _mm_and_pd(p2, xmm0);
|
|
a1 = _mm_sub_pd(a1, p1);
|
|
a2 = _mm_sub_pd(a2, p2);
|
|
k1 = _mm_cvttpd_epi32(a1);
|
|
k2 = _mm_cvttpd_epi32(a2);
|
|
p1 = _mm_cvtepi32_pd(k1);
|
|
p2 = _mm_cvtepi32_pd(k2);
|
|
|
|
/* x -= p * log2; */
|
|
xmm0 = _mm_load_pd(c1);
|
|
xmm1 = _mm_load_pd(c2);
|
|
a1 = _mm_mul_pd(p1, xmm0);
|
|
a2 = _mm_mul_pd(p2, xmm0);
|
|
x1 = _mm_sub_pd(x1, a1);
|
|
x2 = _mm_sub_pd(x2, a2);
|
|
a1 = _mm_mul_pd(p1, xmm1);
|
|
a2 = _mm_mul_pd(p2, xmm1);
|
|
x1 = _mm_sub_pd(x1, a1);
|
|
x2 = _mm_sub_pd(x2, a2);
|
|
|
|
/* Compute e^x using a polynomial approximation. */
|
|
xmm0 = _mm_load_pd(w9);
|
|
xmm1 = _mm_load_pd(w8);
|
|
a1 = _mm_mul_pd(x1, xmm0);
|
|
a2 = _mm_mul_pd(x2, xmm0);
|
|
a1 = _mm_add_pd(a1, xmm1);
|
|
a2 = _mm_add_pd(a2, xmm1);
|
|
|
|
xmm0 = _mm_load_pd(w7);
|
|
xmm1 = _mm_load_pd(w6);
|
|
a1 = _mm_mul_pd(a1, x1);
|
|
a2 = _mm_mul_pd(a2, x2);
|
|
a1 = _mm_add_pd(a1, xmm0);
|
|
a2 = _mm_add_pd(a2, xmm0);
|
|
a1 = _mm_mul_pd(a1, x1);
|
|
a2 = _mm_mul_pd(a2, x2);
|
|
a1 = _mm_add_pd(a1, xmm1);
|
|
a2 = _mm_add_pd(a2, xmm1);
|
|
|
|
xmm0 = _mm_load_pd(w5);
|
|
xmm1 = _mm_load_pd(w4);
|
|
a1 = _mm_mul_pd(a1, x1);
|
|
a2 = _mm_mul_pd(a2, x2);
|
|
a1 = _mm_add_pd(a1, xmm0);
|
|
a2 = _mm_add_pd(a2, xmm0);
|
|
a1 = _mm_mul_pd(a1, x1);
|
|
a2 = _mm_mul_pd(a2, x2);
|
|
a1 = _mm_add_pd(a1, xmm1);
|
|
a2 = _mm_add_pd(a2, xmm1);
|
|
|
|
xmm0 = _mm_load_pd(w3);
|
|
xmm1 = _mm_load_pd(w2);
|
|
a1 = _mm_mul_pd(a1, x1);
|
|
a2 = _mm_mul_pd(a2, x2);
|
|
a1 = _mm_add_pd(a1, xmm0);
|
|
a2 = _mm_add_pd(a2, xmm0);
|
|
a1 = _mm_mul_pd(a1, x1);
|
|
a2 = _mm_mul_pd(a2, x2);
|
|
a1 = _mm_add_pd(a1, xmm1);
|
|
a2 = _mm_add_pd(a2, xmm1);
|
|
|
|
xmm0 = _mm_load_pd(w1);
|
|
xmm1 = _mm_load_pd(w0);
|
|
a1 = _mm_mul_pd(a1, x1);
|
|
a2 = _mm_mul_pd(a2, x2);
|
|
a1 = _mm_add_pd(a1, xmm0);
|
|
a2 = _mm_add_pd(a2, xmm0);
|
|
a1 = _mm_mul_pd(a1, x1);
|
|
a2 = _mm_mul_pd(a2, x2);
|
|
a1 = _mm_add_pd(a1, xmm1);
|
|
a2 = _mm_add_pd(a2, xmm1);
|
|
|
|
/* p = 2^k; */
|
|
k1 = _mm_add_epi32(k1, offset);
|
|
k2 = _mm_add_epi32(k2, offset);
|
|
k1 = _mm_slli_epi32(k1, 20);
|
|
k2 = _mm_slli_epi32(k2, 20);
|
|
k1 = _mm_shuffle_epi32(k1, _MM_SHUFFLE(1,3,0,2));
|
|
k2 = _mm_shuffle_epi32(k2, _MM_SHUFFLE(1,3,0,2));
|
|
p1 = _mm_castsi128_pd(k1);
|
|
p2 = _mm_castsi128_pd(k2);
|
|
|
|
/* a *= 2^k. */
|
|
a1 = _mm_mul_pd(a1, p1);
|
|
a2 = _mm_mul_pd(a2, p2);
|
|
|
|
/* Store the results. */
|
|
_mm_store_pd(values+i, a1);
|
|
_mm_store_pd(values+i+2, a2);
|
|
}
|
|
}
|
|
|
|
|
|
// TODO: look into SIMD log function
|
|
#define VECTOR_INIT_NUMERIC_DOUBLE(name, type, type_abs) \
|
|
VECTOR_INIT_NUMERIC(name, type, type, type_abs) \
|
|
\
|
|
static inline void name##_log(type *array, size_t n) { \
|
|
for (size_t i = 0; i < n; i++) { \
|
|
array[i] = log(array[i]); \
|
|
} \
|
|
} \
|
|
\
|
|
static inline void name##_exp(type *array, size_t n) { \
|
|
remez9_0_log2_sse(array, n); \
|
|
} \
|
|
\
|
|
static inline type name##_sum_log(type *array, size_t n) { \
|
|
type result = 0; \
|
|
for (size_t i = 0; i < n; i++) { \
|
|
result += log(array[i]); \
|
|
} \
|
|
return result; \
|
|
} \
|
|
\
|
|
static inline type name##_log_sum_exp(type *array, size_t n) { \
|
|
type max = name##_max(array, n); \
|
|
type result = 0; \
|
|
for (size_t i = 0; i < n; i++) { \
|
|
result += exp(array[i] - max); \
|
|
} \
|
|
return max + log(result); \
|
|
}
|
|
|
|
#else
|
|
#define VECTOR_INIT_NUMERIC_DOUBLE VECTOR_INIT_NUMERIC_FLOAT
|
|
#endif
|
|
|
|
|
|
|
|
#endif
|