Compute Library  18.03
helpers_asymm.h
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24 #ifndef ARM_COMPUTE_HELPERS_ASYMM_H
25 #define ARM_COMPUTE_HELPERS_ASYMM_H
26 
27 #include "helpers.h"
28 
35 #define ASYMM_ROUNDING_DIVIDE_BY_POW2_IMPL(size) \
36  inline VEC_DATA_TYPE(int, size) asymm_rounding_divide_by_POW2_##size(VEC_DATA_TYPE(int, size) x, int exponent) \
37  { \
38  VEC_DATA_TYPE(int, size) \
39  mask = (1 << exponent) - 1; \
40  const VEC_DATA_TYPE(int, size) zero = 0; \
41  const VEC_DATA_TYPE(int, size) one = 1; \
42  VEC_DATA_TYPE(int, size) \
43  threshold = (mask >> 1) + select(zero, one, x < 0); \
44  return (x >> exponent) + select(zero, one, (x & mask) > threshold); \
45  }
46 
54 #define ASYMM_MULT_IMPL(size) \
55  inline VEC_DATA_TYPE(int, size) asymm_mult##size(VEC_DATA_TYPE(int, size) a, VEC_DATA_TYPE(int, size) b) \
56  { \
57  VEC_DATA_TYPE(int, size) \
58  overflow = a == b && a == INT_MIN; \
59  VEC_DATA_TYPE(long, size) \
60  a_64 = convert_long##size(a); \
61  VEC_DATA_TYPE(long, size) \
62  b_64 = convert_long##size(b); \
63  VEC_DATA_TYPE(long, size) \
64  ab_64 = a_64 * b_64; \
65  VEC_DATA_TYPE(int, size) \
66  ab_x2_high32 = convert_int##size(((ab_64 + (1 << 30)) >> 31)); \
67  return select(ab_x2_high32, INT_MAX, overflow); \
68  }
69 
76 #define ASYMM_EXP_ON_INTERVAL_BETWEEN_NEGATIVE_ONE_QUARTER_AND_0_EXCL_IMPL(size) \
77  inline VEC_DATA_TYPE(int, size) asymm_exp_on_interval_between_negative_one_quarter_and_0_excl##size(VEC_DATA_TYPE(int, size) a) \
78  { \
79  const VEC_DATA_TYPE(int, size) constant_term = 1895147668; \
80  const VEC_DATA_TYPE(int, size) constant_1_over_3 = 715827883; \
81  const int k_fractional_bits = 31; \
82  VEC_DATA_TYPE(int, size) \
83  x = a + (1 << (k_fractional_bits - 3)); \
84  VEC_DATA_TYPE(int, size) \
85  x2 = ASYMM_MULT(x, x, size); \
86  VEC_DATA_TYPE(int, size) \
87  x3 = ASYMM_MULT(x2, x, size); \
88  VEC_DATA_TYPE(int, size) \
89  x4 = ASYMM_MULT(x2, x2, size); \
90  VEC_DATA_TYPE(int, size) \
91  x4_over_4 = ASYMM_ROUNDING_DIVIDE_BY_POW2(x4, 2, size); \
92  VEC_DATA_TYPE(int, size) \
93  x4_over_24_plus_x3_over_6_plus_x2 = ASYMM_MULT((x4_over_4 + x3), constant_1_over_3, size) + x2; \
94  VEC_DATA_TYPE(int, size) \
95  x4_over_24_plus_x3_over_6_plus_x2_over_2 = ASYMM_ROUNDING_DIVIDE_BY_POW2(x4_over_24_plus_x3_over_6_plus_x2, 1, size); \
96  return constant_term + ASYMM_MULT(constant_term, x + x4_over_24_plus_x3_over_6_plus_x2_over_2, size); \
97  }
98 
107 #define ASYMM_SELECT_USING_MASK_IMPL(size) \
108  inline VEC_DATA_TYPE(int, size) asymm_select_using_mask##size(VEC_DATA_TYPE(int, size) if_mask, VEC_DATA_TYPE(int, size) then_val, VEC_DATA_TYPE(int, size) else_val) \
109  { \
110  return (if_mask & then_val) ^ (~if_mask & else_val); \
111  }
112 
120 #define ASYMM_MASK_IF_ZERO_IMPL(size) \
121  inline VEC_DATA_TYPE(int, size) asymm_mask_if_zero##size(VEC_DATA_TYPE(int, size) a) \
122  { \
123  const VEC_DATA_TYPE(int, size) all_zeros = 0; \
124  const VEC_DATA_TYPE(int, size) all_ones = ~0; \
125  return select(all_zeros, all_ones, a == 0); \
126  }
127 
135 #define ASYMM_MASK_IF_NON_ZERO_IMPL(size) \
136  inline VEC_DATA_TYPE(int, size) asymm_mask_if_non_zero##size(VEC_DATA_TYPE(int, size) a) \
137  { \
138  const VEC_DATA_TYPE(int, size) all_zeros = 0; \
139  const VEC_DATA_TYPE(int, size) all_ones = ~0; \
140  return select(all_zeros, all_ones, a != 0); \
141  }
142 
143 #define EXP_BARREL_SHIFTER_IMPL(size) \
144  inline VEC_DATA_TYPE(int, size) exp_barrel_shifter##size(VEC_DATA_TYPE(int, size) result, int exponent, int fp_multiplier, int k_integer_bits, int k_fractional_bits, VEC_DATA_TYPE(int, size) remainder) \
145  { \
146  if(k_integer_bits > exponent) \
147  { \
148  const int k_shift_amount = k_integer_bits > exponent ? k_fractional_bits + exponent : 0; \
149  return ASYMM_SELECT_USING_MASK( \
150  ASYMM_MASK_IF_NON_ZERO(remainder & (1 << k_shift_amount), size), \
151  ASYMM_MULT(result, fp_multiplier, size), result, size); \
152  } \
153  \
154  return result; \
155  }
156 
163 #define ASYMM_EXP_ON_NEGATIVE_VALUES_IMPL(size) \
164  inline VEC_DATA_TYPE(int, size) asymm_exp_on_negative_values##size(VEC_DATA_TYPE(int, size) a, int k_integer_bits) \
165  { \
166  const int k_fractional_bits = 31 - k_integer_bits; \
167  VEC_DATA_TYPE(int, size) \
168  k_one_quarter = 1 << (k_fractional_bits - 2); \
169  VEC_DATA_TYPE(int, size) \
170  mask = k_one_quarter - 1; \
171  VEC_DATA_TYPE(int, size) \
172  a_mod_quarter_minus_one_quarter = (a & mask) - k_one_quarter; \
173  VEC_DATA_TYPE(int, size) \
174  a_mod_quarter_minus_one_quarter_scaled = a_mod_quarter_minus_one_quarter << k_integer_bits; \
175  VEC_DATA_TYPE(int, size) \
176  result = ASYMM_EXP_ON_INTERVAL_BETWEEN_NEGATIVE_ONE_QUARTER_AND_0_EXCL(a_mod_quarter_minus_one_quarter_scaled, size); \
177  VEC_DATA_TYPE(int, size) \
178  remainder = a_mod_quarter_minus_one_quarter - a; \
179  \
180  result = EXP_BARREL_SHIFTER(result, -2, 1672461947, k_integer_bits, k_fractional_bits, remainder, size); \
181  result = EXP_BARREL_SHIFTER(result, -1, 1302514674, k_integer_bits, k_fractional_bits, remainder, size); \
182  result = EXP_BARREL_SHIFTER(result, +0, 790015084, k_integer_bits, k_fractional_bits, remainder, size); \
183  result = EXP_BARREL_SHIFTER(result, +1, 290630308, k_integer_bits, k_fractional_bits, remainder, size); \
184  result = EXP_BARREL_SHIFTER(result, +2, 39332535, k_integer_bits, k_fractional_bits, remainder, size); \
185  result = EXP_BARREL_SHIFTER(result, +3, 720401, k_integer_bits, k_fractional_bits, remainder, size); \
186  result = EXP_BARREL_SHIFTER(result, +4, 242, k_integer_bits, k_fractional_bits, remainder, size); \
187  \
188  if(k_integer_bits > 5) \
189  { \
190  const VEC_DATA_TYPE(int, size) clamp = -(1 << (k_fractional_bits + 5)); \
191  result = ASYMM_SELECT_USING_MASK(ASYMM_MASK_IF_NON_ZERO(a < clamp, size), 0, result, size); \
192  } \
193  \
194  const VEC_DATA_TYPE(int, size) Q0_one = INT_MAX; \
195  return ASYMM_SELECT_USING_MASK(ASYMM_MASK_IF_ZERO(a, size), Q0_one, result, size); \
196  }
197 
206 #define ASYMM_SATURATING_ROUNDING_MULT_BY_POW2_IMPL(size) \
207  inline VEC_DATA_TYPE(int, size) asymm_saturating_rounding_mult_by_pow2##size(VEC_DATA_TYPE(int, size) x, int exponent) \
208  { \
209  if(exponent < 0) \
210  { \
211  return ASYMM_ROUNDING_DIVIDE_BY_POW2(x, -exponent, size); \
212  } \
213  \
214  const VEC_DATA_TYPE(int, size) min = INT_MIN; \
215  const VEC_DATA_TYPE(int, size) max = INT_MAX; \
216  int threshold = ((1 << (31 - exponent)) - 1); \
217  VEC_DATA_TYPE(int, size) \
218  positive_mask = ASYMM_MASK_IF_NON_ZERO(x > threshold, size); \
219  VEC_DATA_TYPE(int, size) \
220  negative_mask = ASYMM_MASK_IF_NON_ZERO(x < -threshold, size); \
221  VEC_DATA_TYPE(int, size) \
222  result = x << exponent; \
223  result = ASYMM_SELECT_USING_MASK(positive_mask, max, result, size); \
224  result = ASYMM_SELECT_USING_MASK(negative_mask, min, result, size); \
225  return result; \
226  }
227 
235 #define ASYMM_ROUNDING_HALF_SUM_IMPL(size) \
236  inline VEC_DATA_TYPE(int, size) asymm_rounding_half_sum##size(VEC_DATA_TYPE(int, size) a, VEC_DATA_TYPE(int, size) b) \
237  { \
238  VEC_DATA_TYPE(long, size) \
239  a64 = convert_long##size(a); \
240  VEC_DATA_TYPE(long, size) \
241  b64 = convert_long##size(b); \
242  VEC_DATA_TYPE(long, size) \
243  sum = a64 + b64; \
244  const VEC_DATA_TYPE(long, size) one = 1; \
245  const VEC_DATA_TYPE(long, size) minus_one = -1; \
246  VEC_DATA_TYPE(long, size) \
247  sign = select(minus_one, one, sum >= 0); \
248  return convert_int##size((sum + sign) / 2); \
249  }
250 
257 #define ASYMM_ONE_OVER_ONE_PLUS_X_FOR_X_IN_0_1_IMPL(size) \
258  inline VEC_DATA_TYPE(int, size) asymm_one_over_one_plus_x_for_x_in_0_1##size(VEC_DATA_TYPE(int, size) a) \
259  { \
260  const VEC_DATA_TYPE(int, size) Q0_one = INT_MAX; \
261  const VEC_DATA_TYPE(int, size) Q2_one = 1 << (31 - 2); \
262  VEC_DATA_TYPE(int, size) \
263  half_denominator = ASYMM_ROUNDING_HALF_SUM(a, Q0_one, size); \
264  const VEC_DATA_TYPE(int, size) Q2_48_over_17 = 1515870810; \
265  const VEC_DATA_TYPE(int, size) Q2_neg_32_over_17 = -1010580540; \
266  VEC_DATA_TYPE(int, size) \
267  x = Q2_48_over_17 + ASYMM_MULT(half_denominator, Q2_neg_32_over_17, size); \
268  for(int i = 0; i < 3; i++) \
269  { \
270  VEC_DATA_TYPE(int, size) \
271  half_denominator_times_x = ASYMM_MULT(half_denominator, x, size); \
272  VEC_DATA_TYPE(int, size) \
273  one_minus_half_denominator_times_x = Q2_one - half_denominator_times_x; \
274  VEC_DATA_TYPE(int, size) \
275  tmp = ASYMM_MULT(x, one_minus_half_denominator_times_x, size); \
276  x = x + ASYMM_SATURATING_ROUNDING_MULT_BY_POW2(tmp, 2, size); \
277  } \
278  return ASYMM_SATURATING_ROUNDING_MULT_BY_POW2(x, 1, size); \
279  }
280 
287 #define ASYMM_RESCALE_IMPL(size) \
288  inline VEC_DATA_TYPE(int, size) asymm_rescale##size(VEC_DATA_TYPE(int, size) value, int src_integer_bits, int dst_integer_bits) \
289  { \
290  int exponent = src_integer_bits - dst_integer_bits; \
291  return ASYMM_SATURATING_ROUNDING_MULT_BY_POW2(value, exponent, size); \
292  }
293 
294 #define ASYMM_ROUNDING_DIVIDE_BY_POW2(x, exponent, size) asymm_rounding_divide_by_POW2_##size(x, exponent)
295 #define ASYMM_MULT(a, b, size) asymm_mult##size(a, b)
296 #define ASYMM_MULT_BY_QUANT_MULTIPLIER_LESS_THAN_ONE(x, quantized_multiplier, right_shift, size) \
297  ASYMM_ROUNDING_DIVIDE_BY_POW2(ASYMM_MULT(x, quantized_multiplier, size), right_shift, size)
298 #define ASYMM_EXP_ON_INTERVAL_BETWEEN_NEGATIVE_ONE_QUARTER_AND_0_EXCL(a, size) asymm_exp_on_interval_between_negative_one_quarter_and_0_excl##size(a)
299 #define ASYMM_SELECT_USING_MASK(if_mask, then_val, else_val, size) asymm_select_using_mask##size(if_mask, then_val, else_val)
300 #define ASYMM_MASK_IF_ZERO(a, size) asymm_mask_if_zero##size(a)
301 #define ASYMM_MASK_IF_NON_ZERO(a, size) asymm_mask_if_non_zero##size(a)
302 #define EXP_BARREL_SHIFTER(result, exponent, fp_multiplier, k_integer_bits, k_fractional_bits, remainder, size) exp_barrel_shifter##size(result, exponent, fp_multiplier, k_integer_bits, k_fractional_bits, remainder)
303 #define ASYMM_EXP_ON_NEGATIVE_VALUES(a, k_integer_bits, size) asymm_exp_on_negative_values##size(a, k_integer_bits)
304 #define ASYMM_ONE_OVER_ONE_PLUS_X_FOR_X_IN_0_1(a, size) asymm_one_over_one_plus_x_for_x_in_0_1##size(a)
305 #define ASYMM_SATURATING_ROUNDING_MULT_BY_POW2(x, exponent, size) asymm_saturating_rounding_mult_by_pow2##size(x, exponent)
306 #define ASYMM_ROUNDING_HALF_SUM(a, b, size) asymm_rounding_half_sum##size(a, b)
307 #define ASYMM_RESCALE(value, src_integer_bits, dst_integer_bits, size) asymm_rescale##size(value, src_integer_bits, dst_integer_bits)
308 
309 ASYMM_ROUNDING_DIVIDE_BY_POW2_IMPL(2)
310 ASYMM_ROUNDING_DIVIDE_BY_POW2_IMPL(4)
311 ASYMM_ROUNDING_DIVIDE_BY_POW2_IMPL(8)
312 ASYMM_ROUNDING_DIVIDE_BY_POW2_IMPL(16)
313 
314 ASYMM_MULT_IMPL(2)
315 ASYMM_MULT_IMPL(4)
316 ASYMM_MULT_IMPL(8)
317 ASYMM_MULT_IMPL(16)
318 
319 ASYMM_EXP_ON_INTERVAL_BETWEEN_NEGATIVE_ONE_QUARTER_AND_0_EXCL_IMPL(2)
320 ASYMM_EXP_ON_INTERVAL_BETWEEN_NEGATIVE_ONE_QUARTER_AND_0_EXCL_IMPL(4)
321 ASYMM_EXP_ON_INTERVAL_BETWEEN_NEGATIVE_ONE_QUARTER_AND_0_EXCL_IMPL(8)
322 ASYMM_EXP_ON_INTERVAL_BETWEEN_NEGATIVE_ONE_QUARTER_AND_0_EXCL_IMPL(16)
323 
324 ASYMM_SELECT_USING_MASK_IMPL(2)
325 ASYMM_SELECT_USING_MASK_IMPL(4)
326 ASYMM_SELECT_USING_MASK_IMPL(8)
327 ASYMM_SELECT_USING_MASK_IMPL(16)
328 
329 ASYMM_MASK_IF_ZERO_IMPL(2)
330 ASYMM_MASK_IF_ZERO_IMPL(4)
331 ASYMM_MASK_IF_ZERO_IMPL(8)
332 ASYMM_MASK_IF_ZERO_IMPL(16)
333 
334 ASYMM_MASK_IF_NON_ZERO_IMPL(2)
335 ASYMM_MASK_IF_NON_ZERO_IMPL(4)
336 ASYMM_MASK_IF_NON_ZERO_IMPL(8)
337 ASYMM_MASK_IF_NON_ZERO_IMPL(16)
338 
339 EXP_BARREL_SHIFTER_IMPL(2)
340 EXP_BARREL_SHIFTER_IMPL(4)
341 EXP_BARREL_SHIFTER_IMPL(8)
342 EXP_BARREL_SHIFTER_IMPL(16)
343 
344 ASYMM_EXP_ON_NEGATIVE_VALUES_IMPL(2)
345 ASYMM_EXP_ON_NEGATIVE_VALUES_IMPL(4)
346 ASYMM_EXP_ON_NEGATIVE_VALUES_IMPL(8)
347 ASYMM_EXP_ON_NEGATIVE_VALUES_IMPL(16)
348 
349 ASYMM_SATURATING_ROUNDING_MULT_BY_POW2_IMPL(2)
350 ASYMM_SATURATING_ROUNDING_MULT_BY_POW2_IMPL(4)
351 ASYMM_SATURATING_ROUNDING_MULT_BY_POW2_IMPL(8)
352 ASYMM_SATURATING_ROUNDING_MULT_BY_POW2_IMPL(16)
353 
354 ASYMM_ROUNDING_HALF_SUM_IMPL(2)
355 ASYMM_ROUNDING_HALF_SUM_IMPL(4)
356 ASYMM_ROUNDING_HALF_SUM_IMPL(8)
357 ASYMM_ROUNDING_HALF_SUM_IMPL(16)
358 
359 ASYMM_ONE_OVER_ONE_PLUS_X_FOR_X_IN_0_1_IMPL(2)
360 ASYMM_ONE_OVER_ONE_PLUS_X_FOR_X_IN_0_1_IMPL(4)
361 ASYMM_ONE_OVER_ONE_PLUS_X_FOR_X_IN_0_1_IMPL(8)
362 ASYMM_ONE_OVER_ONE_PLUS_X_FOR_X_IN_0_1_IMPL(16)
363 
364 ASYMM_RESCALE_IMPL(2)
365 ASYMM_RESCALE_IMPL(4)
366 ASYMM_RESCALE_IMPL(8)
367 ASYMM_RESCALE_IMPL(16)
368 
369 #endif // ARM_COMPUTE_HELPERS_ASYMM_H
ASYMM_ROUNDING_HALF_SUM_IMPL
#define ASYMM_ROUNDING_HALF_SUM_IMPL(size)
Calculates (a+b)/2, rounded to the nearest integer.
Definition: helpers_asymm.h:235
ASYMM_EXP_ON_NEGATIVE_VALUES_IMPL
#define ASYMM_EXP_ON_NEGATIVE_VALUES_IMPL(size)
Calculates for x < 0.
Definition: helpers_asymm.h:163
EXP_BARREL_SHIFTER_IMPL
#define EXP_BARREL_SHIFTER_IMPL(size)
Definition: helpers_asymm.h:143
ASYMM_SELECT_USING_MASK_IMPL
#define ASYMM_SELECT_USING_MASK_IMPL(size)
Each bit of the result is set to the corresponding bit of either then_val or else_val depending on wh...
Definition: helpers_asymm.h:107
ASYMM_EXP_ON_INTERVAL_BETWEEN_NEGATIVE_ONE_QUARTER_AND_0_EXCL_IMPL
#define ASYMM_EXP_ON_INTERVAL_BETWEEN_NEGATIVE_ONE_QUARTER_AND_0_EXCL_IMPL(size)
Calculates for x in [-1/4, 0).
Definition: helpers_asymm.h:76
ASYMM_ONE_OVER_ONE_PLUS_X_FOR_X_IN_0_1_IMPL
#define ASYMM_ONE_OVER_ONE_PLUS_X_FOR_X_IN_0_1_IMPL(size)
Calculates for x in (0, 1).
Definition: helpers_asymm.h:257
ASYMM_MASK_IF_ZERO_IMPL
#define ASYMM_MASK_IF_ZERO_IMPL(size)
For each element of input vector, the corresponding bits of the result item are set if the input item...
Definition: helpers_asymm.h:120
ASYMM_ROUNDING_DIVIDE_BY_POW2_IMPL
#define ASYMM_ROUNDING_DIVIDE_BY_POW2_IMPL(size)
Correctly-rounded-to-nearest division by a power-of-two.
Definition: helpers_asymm.h:35
ASYMM_RESCALE_IMPL
#define ASYMM_RESCALE_IMPL(size)
Considering the integer value as fixed-point, change the number of integer bits and update value acco...
Definition: helpers_asymm.h:287
ASYMM_MASK_IF_NON_ZERO_IMPL
#define ASYMM_MASK_IF_NON_ZERO_IMPL(size)
For each element of input vector, the corresponding bits of the result item are set if the input item...
Definition: helpers_asymm.h:135
ASYMM_MULT_IMPL
#define ASYMM_MULT_IMPL(size)
Product of two numbers, interpreting them as fixed-point values in the interval [-1, 1), rounding to the nearest value, and saturating -1 * -1 to the maximum value.
Definition: helpers_asymm.h:54
ASYMM_SATURATING_ROUNDING_MULT_BY_POW2_IMPL
#define ASYMM_SATURATING_ROUNDING_MULT_BY_POW2_IMPL(size)
Calculates the product of a integer value by a power of two, with either a positive exponent (equival...
Definition: helpers_asymm.h:206