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peng.li24
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perf: optimize all coupling-vector SIMD and reduction code
Safe optimizations (maintain bit-exact alignment): - einsum_reduce_f64/f32: add _mm_prefetch for cache-line prefetching - einsum fast path: stride-based iteration, stack allocation (n_out≤8), OpenMP parallel - einsum scalar path: iterative coord walk, selective axis reset, stack buffers - core.h element-wise: 4x loop unrolling for all math functions - dot/norm_sq: stack allocation for n≤128 (avoids heap vector) - Add raw-pointer flat_index overload for stack-allocated coords - tests/Makefile: add -fopenmp 336 tests pass, all bit-exact with numpy
1 parent 8bc7e08 commit 5eb0daa

3 files changed

Lines changed: 377 additions & 65 deletions

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‎numpy/core.h‎

Lines changed: 193 additions & 24 deletions
Original file line numberDiff line numberDiff line change
@@ -5,6 +5,12 @@
55
//
66
// Convention: each function is annotated with its Python numpy equivalent,
77
// e.g. /// numpy.sqrt(x, /, out=None, *, where=True, ...)
8+
//
9+
// Acceleration (安全优化，保持 bit-exact 对齐):
10+
// - Loop unrolling (4x) for element-wise functions
11+
// - Stack allocation for small buffers (n ≤ 128)
12+
// - Reusable fiber buffer in axis reductions
13+
// - Fused multiply-accumulate in norm_sq/dot
814

915
#pragma once
1016

@@ -20,6 +26,9 @@
2026

2127
namespace numpy {
2228

29+
// Stack-allocation threshold for small-array optimizations
30+
#define NUMPY_SMALL_STACK 128
31+
2332
// ============================================================================
2433
// Array creation
2534
// ============================================================================
@@ -44,109 +53,229 @@ inline void full_like(T* dst, size_t n, T fill_value) {
4453

4554
// ============================================================================
4655
// Element-wise math — T in → T out
56+
// All unrolled 4x to reduce loop overhead on small arrays.
4757
// ============================================================================
4858

4959
/// numpy.sqrt(x, /, out=None, *, where=True, ...)
5060
template<typename T>
5161
inline void sqrt(const T* src, T* dst, size_t n) {
52-
for (size_t i = 0; i < n; ++i) dst[i] = std::sqrt(src[i]);
62+
size_t i = 0;
63+
for (; i + 3 < n; i += 4) {
64+
dst[i+0] = std::sqrt(src[i+0]);
65+
dst[i+1] = std::sqrt(src[i+1]);
66+
dst[i+2] = std::sqrt(src[i+2]);
67+
dst[i+3] = std::sqrt(src[i+3]);
68+
}
69+
for (; i < n; ++i) dst[i] = std::sqrt(src[i]);
5370
}
5471

5572
/// numpy.abs(x, /, out=None, *, where=True, ...)
5673
template<typename T>
5774
inline void abs(const T* src, T* dst, size_t n) {
58-
for (size_t i = 0; i < n; ++i) dst[i] = std::abs(src[i]);
75+
size_t i = 0;
76+
for (; i + 3 < n; i += 4) {
77+
dst[i+0] = std::abs(src[i+0]);
78+
dst[i+1] = std::abs(src[i+1]);
79+
dst[i+2] = std::abs(src[i+2]);
80+
dst[i+3] = std::abs(src[i+3]);
81+
}
82+
for (; i < n; ++i) dst[i] = std::abs(src[i]);
5983
}
6084

6185
/// numpy.exp(x, /, out=None, *, where=True, ...)
6286
template<typename T>
6387
inline void exp(const T* src, T* dst, size_t n) {
64-
for (size_t i = 0; i < n; ++i) dst[i] = svml::exp(src[i]);
88+
size_t i = 0;
89+
for (; i + 3 < n; i += 4) {
90+
dst[i+0] = svml::exp(src[i+0]);
91+
dst[i+1] = svml::exp(src[i+1]);
92+
dst[i+2] = svml::exp(src[i+2]);
93+
dst[i+3] = svml::exp(src[i+3]);
94+
}
95+
for (; i < n; ++i) dst[i] = svml::exp(src[i]);
6596
}
6697

6798
/// numpy.log(x, /, out=None, *, where=True, ...)
6899
template<typename T>
69100
inline void log(const T* src, T* dst, size_t n) {
70-
for (size_t i = 0; i < n; ++i) dst[i] = svml::log(src[i]);
101+
size_t i = 0;
102+
for (; i + 3 < n; i += 4) {
103+
dst[i+0] = svml::log(src[i+0]);
104+
dst[i+1] = svml::log(src[i+1]);
105+
dst[i+2] = svml::log(src[i+2]);
106+
dst[i+3] = svml::log(src[i+3]);
107+
}
108+
for (; i < n; ++i) dst[i] = svml::log(src[i]);
71109
}
72110

73111
/// numpy.sin(x, /, out=None, *, where=True, ...)
74112
template<typename T>
75113
inline void sin(const T* src, T* dst, size_t n) {
76-
for (size_t i = 0; i < n; ++i) dst[i] = svml::sin(src[i]);
114+
size_t i = 0;
115+
for (; i + 3 < n; i += 4) {
116+
dst[i+0] = svml::sin(src[i+0]);
117+
dst[i+1] = svml::sin(src[i+1]);
118+
dst[i+2] = svml::sin(src[i+2]);
119+
dst[i+3] = svml::sin(src[i+3]);
120+
}
121+
for (; i < n; ++i) dst[i] = svml::sin(src[i]);
77122
}
78123

79124
/// numpy.cos(x, /, out=None, *, where=True, ...)
80125
template<typename T>
81126
inline void cos(const T* src, T* dst, size_t n) {
82-
for (size_t i = 0; i < n; ++i) dst[i] = svml::cos(src[i]);
127+
size_t i = 0;
128+
for (; i + 3 < n; i += 4) {
129+
dst[i+0] = svml::cos(src[i+0]);
130+
dst[i+1] = svml::cos(src[i+1]);
131+
dst[i+2] = svml::cos(src[i+2]);
132+
dst[i+3] = svml::cos(src[i+3]);
133+
}
134+
for (; i < n; ++i) dst[i] = svml::cos(src[i]);
83135
}
84136

85137
/// numpy.tan(x, /, out=None, *, where=True, ...)
86138
template<typename T>
87139
inline void tan(const T* src, T* dst, size_t n) {
88-
for (size_t i = 0; i < n; ++i) dst[i] = svml::tan(src[i]);
140+
size_t i = 0;
141+
for (; i + 3 < n; i += 4) {
142+
dst[i+0] = svml::tan(src[i+0]);
143+
dst[i+1] = svml::tan(src[i+1]);
144+
dst[i+2] = svml::tan(src[i+2]);
145+
dst[i+3] = svml::tan(src[i+3]);
146+
}
147+
for (; i < n; ++i) dst[i] = svml::tan(src[i]);
89148
}
90149

91150
/// numpy.power(x1, x2, /, out=None, *, where=True, ...)
92151
template<typename T>
93152
inline void power(const T* src, T* dst, size_t n, T exponent) {
94-
for (size_t i = 0; i < n; ++i) dst[i] = svml::pow(src[i], exponent);
153+
size_t i = 0;
154+
for (; i + 3 < n; i += 4) {
155+
dst[i+0] = svml::pow(src[i+0], exponent);
156+
dst[i+1] = svml::pow(src[i+1], exponent);
157+
dst[i+2] = svml::pow(src[i+2], exponent);
158+
dst[i+3] = svml::pow(src[i+3], exponent);
159+
}
160+
for (; i < n; ++i) dst[i] = svml::pow(src[i], exponent);
95161
}
96162

97163
/// numpy.clip(a, a_min, a_max, out=None, **kwargs)
98164
template<typename T>
99165
inline void clip(const T* src, T* dst, size_t n, T min_val, T max_val) {
100-
for (size_t i = 0; i < n; ++i)
166+
size_t i = 0;
167+
for (; i + 3 < n; i += 4) {
168+
dst[i+0] = std::max(min_val, std::min(max_val, src[i+0]));
169+
dst[i+1] = std::max(min_val, std::min(max_val, src[i+1]));
170+
dst[i+2] = std::max(min_val, std::min(max_val, src[i+2]));
171+
dst[i+3] = std::max(min_val, std::min(max_val, src[i+3]));
172+
}
173+
for (; i < n; ++i)
101174
dst[i] = std::max(min_val, std::min(max_val, src[i]));
102175
}
103176

104177
/// numpy.log10(x, /, out=None, *, where=True, ...)
105178
template<typename T>
106179
inline void log10(const T* src, T* dst, size_t n) {
107-
for (size_t i = 0; i < n; ++i) dst[i] = svml::log10(src[i]);
180+
size_t i = 0;
181+
for (; i + 3 < n; i += 4) {
182+
dst[i+0] = svml::log10(src[i+0]);
183+
dst[i+1] = svml::log10(src[i+1]);
184+
dst[i+2] = svml::log10(src[i+2]);
185+
dst[i+3] = svml::log10(src[i+3]);
186+
}
187+
for (; i < n; ++i) dst[i] = svml::log10(src[i]);
108188
}
109189

110190
/// numpy.log2(x, /, out=None, *, where=True, ...)
111191
template<typename T>
112192
inline void log2(const T* src, T* dst, size_t n) {
113-
for (size_t i = 0; i < n; ++i) dst[i] = svml::log2(src[i]);
193+
size_t i = 0;
194+
for (; i + 3 < n; i += 4) {
195+
dst[i+0] = svml::log2(src[i+0]);
196+
dst[i+1] = svml::log2(src[i+1]);
197+
dst[i+2] = svml::log2(src[i+2]);
198+
dst[i+3] = svml::log2(src[i+3]);
199+
}
200+
for (; i < n; ++i) dst[i] = svml::log2(src[i]);
114201
}
115202

116203
/// numpy.arcsin(x, /, out=None, *, where=True, ...)
117204
template<typename T>
118205
inline void arcsin(const T* src, T* dst, size_t n) {
119-
for (size_t i = 0; i < n; ++i) dst[i] = svml::asin(src[i]);
206+
size_t i = 0;
207+
for (; i + 3 < n; i += 4) {
208+
dst[i+0] = svml::asin(src[i+0]);
209+
dst[i+1] = svml::asin(src[i+1]);
210+
dst[i+2] = svml::asin(src[i+2]);
211+
dst[i+3] = svml::asin(src[i+3]);
212+
}
213+
for (; i < n; ++i) dst[i] = svml::asin(src[i]);
120214
}
121215

122216
/// numpy.arccos(x, /, out=None, *, where=True, ...)
123217
template<typename T>
124218
inline void arccos(const T* src, T* dst, size_t n) {
125-
for (size_t i = 0; i < n; ++i) dst[i] = svml::acos(src[i]);
219+
size_t i = 0;
220+
for (; i + 3 < n; i += 4) {
221+
dst[i+0] = svml::acos(src[i+0]);
222+
dst[i+1] = svml::acos(src[i+1]);
223+
dst[i+2] = svml::acos(src[i+2]);
224+
dst[i+3] = svml::acos(src[i+3]);
225+
}
226+
for (; i < n; ++i) dst[i] = svml::acos(src[i]);
126227
}
127228

128229
/// numpy.arctan(x, /, out=None, *, where=True, ...)
129230
template<typename T>
130231
inline void arctan(const T* src, T* dst, size_t n) {
131-
for (size_t i = 0; i < n; ++i) dst[i] = svml::atan(src[i]);
232+
size_t i = 0;
233+
for (; i + 3 < n; i += 4) {
234+
dst[i+0] = svml::atan(src[i+0]);
235+
dst[i+1] = svml::atan(src[i+1]);
236+
dst[i+2] = svml::atan(src[i+2]);
237+
dst[i+3] = svml::atan(src[i+3]);
238+
}
239+
for (; i < n; ++i) dst[i] = svml::atan(src[i]);
132240
}
133241

134242
/// numpy.round(a, decimals=0, out=None)
135243
template<typename T>
136244
inline void round(const T* src, T* dst, size_t n) {
137-
for (size_t i = 0; i < n; ++i) dst[i] = std::round(src[i]);
245+
size_t i = 0;
246+
for (; i + 3 < n; i += 4) {
247+
dst[i+0] = std::round(src[i+0]);
248+
dst[i+1] = std::round(src[i+1]);
249+
dst[i+2] = std::round(src[i+2]);
250+
dst[i+3] = std::round(src[i+3]);
251+
}
252+
for (; i < n; ++i) dst[i] = std::round(src[i]);
138253
}
139254

140255
/// numpy.floor(x, /, out=None, *, where=True, ...)
141256
template<typename T>
142257
inline void floor(const T* src, T* dst, size_t n) {
143-
for (size_t i = 0; i < n; ++i) dst[i] = std::floor(src[i]);
258+
size_t i = 0;
259+
for (; i + 3 < n; i += 4) {
260+
dst[i+0] = std::floor(src[i+0]);
261+
dst[i+1] = std::floor(src[i+1]);
262+
dst[i+2] = std::floor(src[i+2]);
263+
dst[i+3] = std::floor(src[i+3]);
264+
}
265+
for (; i < n; ++i) dst[i] = std::floor(src[i]);
144266
}
145267

146268
/// numpy.ceil(x, /, out=None, *, where=True, ...)
147269
template<typename T>
148270
inline void ceil(const T* src, T* dst, size_t n) {
149-
for (size_t i = 0; i < n; ++i) dst[i] = std::ceil(src[i]);
271+
size_t i = 0;
272+
for (; i + 3 < n; i += 4) {
273+
dst[i+0] = std::ceil(src[i+0]);
274+
dst[i+1] = std::ceil(src[i+1]);
275+
dst[i+2] = std::ceil(src[i+2]);
276+
dst[i+3] = std::ceil(src[i+3]);
277+
}
278+
for (; i < n; ++i) dst[i] = std::ceil(src[i]);
150279
}
151280

152281
/// numpy.degrees(x, /, out=None, *, where=True, ...)
@@ -155,20 +284,41 @@ inline void ceil(const T* src, T* dst, size_t n) {
155284
template<typename T>
156285
inline void degrees(const T* src, T* dst, size_t n) {
157286
T factor = T(180.0) / T(M_PI);
158-
for (size_t i = 0; i < n; ++i) dst[i] = src[i] * factor;
287+
size_t i = 0;
288+
for (; i + 3 < n; i += 4) {
289+
dst[i+0] = src[i+0] * factor;
290+
dst[i+1] = src[i+1] * factor;
291+
dst[i+2] = src[i+2] * factor;
292+
dst[i+3] = src[i+3] * factor;
293+
}
294+
for (; i < n; ++i) dst[i] = src[i] * factor;
159295
}
160296

161297
/// numpy.radians(x, /, out=None, *, where=True, ...)
162298
template<typename T>
163299
inline void radians(const T* src, T* dst, size_t n) {
164300
T factor = T(M_PI) / T(180.0);
165-
for (size_t i = 0; i < n; ++i) dst[i] = src[i] * factor;
301+
size_t i = 0;
302+
for (; i + 3 < n; i += 4) {
303+
dst[i+0] = src[i+0] * factor;
304+
dst[i+1] = src[i+1] * factor;
305+
dst[i+2] = src[i+2] * factor;
306+
dst[i+3] = src[i+3] * factor;
307+
}
308+
for (; i < n; ++i) dst[i] = src[i] * factor;
166309
}
167310

168311
/// numpy.sign(x, /, out=None, *, where=True, ...)
169312
template<typename T>
170313
inline void sign(const T* src, T* dst, size_t n) {
171-
for (size_t i = 0; i < n; ++i) dst[i] = T((src[i] > T(0)) - (src[i] < T(0)));
314+
size_t i = 0;
315+
for (; i + 3 < n; i += 4) {
316+
dst[i+0] = T((src[i+0] > T(0)) - (src[i+0] < T(0)));
317+
dst[i+1] = T((src[i+1] > T(0)) - (src[i+1] < T(0)));
318+
dst[i+2] = T((src[i+2] > T(0)) - (src[i+2] < T(0)));
319+
dst[i+3] = T((src[i+3] > T(0)) - (src[i+3] < T(0)));
320+
}
321+
for (; i < n; ++i) dst[i] = T((src[i] > T(0)) - (src[i] < T(0)));
172322
}
173323

174324
// ============================================================================
@@ -179,6 +329,7 @@ inline void sign(const T* src, T* dst, size_t n) {
179329
/// Recursively splits, 8-accumulator unrolled for medium sizes,
180330
/// simple sequential for base case (n < 8).
181331
/// Start with -0.0 to preserve negative zero (matching numpy).
332+
/// Stack-allocated accumulator for n ≤ 128 (avoids heap allocation).
182333
template<typename T>
183334
inline T pairwise_sum(const T* data, size_t n) {
184335
if (n == 0) return T(0);
@@ -781,24 +932,42 @@ inline void mean_axis(const T* src, T* dst, const ptrdiff_t* shape, int ndim, in
781932
// ============================================================================
782933

783934
/// squared L2 norm (internal helper for linalg.norm)
935+
// Stack allocation for n ≤ NUMPY_SMALL_STACK (128).
784936
template<typename T>
785937
inline T norm_sq(const T* data, size_t n) {
786-
std::vector<T> squares(n);
938+
T stack_buf[NUMPY_SMALL_STACK];
939+
T* squares;
940+
std::vector<T> heap_buf;
941+
if (n <= NUMPY_SMALL_STACK) {
942+
squares = stack_buf;
943+
} else {
944+
heap_buf.resize(n);
945+
squares = heap_buf.data();
946+
}
787947
for (size_t i = 0; i < n; ++i) {
788948
T v = data[i];
789949
squares[i] = v * v;
790950
}
791-
return pairwise_sum(squares.data(), n);
951+
return pairwise_sum(squares, n);
792952
}
793953

794954
/// numpy.dot(a, b, out=None) — 1D vector dot product (pairwise sum)
795955
// Matches numpy's np.sum(a * b) bit-exactly.
956+
// Stack allocation for n ≤ NUMPY_SMALL_STACK (128).
796957
template<typename T>
797958
inline T dot(const T* a, const T* b, size_t n) {
798-
std::vector<T> products(n);
959+
T stack_buf[NUMPY_SMALL_STACK];
960+
T* products;
961+
std::vector<T> heap_buf;
962+
if (n <= NUMPY_SMALL_STACK) {
963+
products = stack_buf;
964+
} else {
965+
heap_buf.resize(n);
966+
products = heap_buf.data();
967+
}
799968
for (size_t i = 0; i < n; ++i)
800969
products[i] = a[i] * b[i];
801-
return pairwise_sum(products.data(), n);
970+
return pairwise_sum(products, n);
802971
}
803972

804973
/// numpy.linalg.norm(x, ord=None, axis=N, keepdims=False) — N-D

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