#ifndef VECTOR_MATH_H #define VECTOR_MATH_H #include #include #include #include "vector.h" #define ks_lt_index(a, b) ((a).value < (b).value) #ifdef USE_SSE #include #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 unsigned_type 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 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); \ } #ifdef USE_SSE /* 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