Compute Library
 20.08
AsymmHelpers.cpp
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27 
28 #include <cmath>
29 #include <limits>
30 #include <numeric>
31 
32 namespace arm_compute
33 {
34 namespace quantization
35 {
36 constexpr int64_t fixed_point_one_Q0 = (1LL << 31);
37 constexpr float epsilon = 0.00001f;
38 
39 Status calculate_quantized_multiplier(float multiplier, int32_t *quant_multiplier, int32_t *shift, bool ignore_epsilon)
40 {
41  if(multiplier >= 1.f)
42  {
43  Status status = calculate_quantized_multiplier_greater_than_one(multiplier, quant_multiplier, shift);
44  *shift *= -1;
45  return status;
46  }
47  else
48  {
49  return calculate_quantized_multiplier_less_than_one(multiplier, quant_multiplier, shift, ignore_epsilon);
50  }
51 }
52 
54  int32_t *quant_multiplier,
55  int32_t *right_shift,
56  bool ignore_epsilon)
57 {
58  const float internal_epsilon = ignore_epsilon ? 0.0f : epsilon;
59 
60  ARM_COMPUTE_RETURN_ERROR_ON(quant_multiplier == nullptr);
61  ARM_COMPUTE_RETURN_ERROR_ON(right_shift == nullptr);
62  ARM_COMPUTE_RETURN_ERROR_ON(multiplier < -internal_epsilon);
63  ARM_COMPUTE_RETURN_ERROR_ON(multiplier > 1.0f + internal_epsilon);
64  if(std::fabs(0.0f - multiplier) < internal_epsilon)
65  {
66  *quant_multiplier = 0;
67  *right_shift = 0;
68  return Status{};
69  }
70 
71  int shift_exp = 0;
72  const double q = std::frexp(multiplier, &shift_exp);
73  *right_shift = -1 * shift_exp;
74  auto q_fixed = static_cast<int64_t>(support::cpp11::round(q * fixed_point_one_Q0));
76  if(q_fixed == fixed_point_one_Q0)
77  {
78  q_fixed /= 2;
79  --*right_shift;
80  }
81 
82  if(ignore_epsilon && *right_shift > 31)
83  {
84  *right_shift = 0;
85  q_fixed = 0;
86  }
87 
88  ARM_COMPUTE_RETURN_ERROR_ON(*right_shift < 0);
89  ARM_COMPUTE_RETURN_ERROR_ON(q_fixed > std::numeric_limits<int32_t>::max());
90  *quant_multiplier = static_cast<int32_t>(q_fixed);
91 
92  return Status{};
93 }
94 
96  int32_t *quantized_multiplier,
97  int32_t *left_shift)
98 {
99  ARM_COMPUTE_RETURN_ERROR_ON(quantized_multiplier == nullptr);
100  ARM_COMPUTE_RETURN_ERROR_ON(left_shift == nullptr);
101  ARM_COMPUTE_RETURN_ERROR_ON(multiplier < 1.f);
102 
103  int shift_exp = 0;
104  const double q = std::frexp(multiplier, &shift_exp);
105  *left_shift = shift_exp;
106  auto q_fixed = static_cast<int64_t>(support::cpp11::round(q * fixed_point_one_Q0));
108  if(q_fixed == fixed_point_one_Q0)
109  {
110  q_fixed /= 2;
111  ++*left_shift;
112  }
113  ARM_COMPUTE_RETURN_ERROR_ON(*left_shift < 0);
114  ARM_COMPUTE_RETURN_ERROR_ON(q_fixed > std::numeric_limits<int32_t>::max());
115  *quantized_multiplier = static_cast<int32_t>(q_fixed);
116 
117  return Status{};
118 }
119 
121  const QuantizationInfo &wq_info,
122  const QuantizationInfo &oq_info,
123  GEMMLowpOutputStageInfo &stage_info)
124 {
125  ARM_COMPUTE_RETURN_ERROR_ON(iq_info.scale().empty());
126  ARM_COMPUTE_RETURN_ERROR_ON(wq_info.scale().empty());
127  ARM_COMPUTE_RETURN_ERROR_ON(oq_info.scale().empty());
128 
129  const unsigned int size = wq_info.scale().size();
130 
131  auto &quant_multipliers = stage_info.gemmlowp_multipliers;
132  auto &quant_shifts = stage_info.gemmlowp_shifts;
133  quant_multipliers.resize(size);
134  quant_shifts.resize(size);
135 
136  const auto &w_scales = wq_info.scale();
137  const float i_scale = iq_info.scale().at(0);
138  const float o_scale = oq_info.scale().at(0);
139 
140  for(unsigned int i = 0; i < size; ++i)
141  {
142  const float multiplier = i_scale * w_scales[i] / o_scale;
143  int32_t quant_multiplier = 0;
144  int32_t quant_shift = 0;
145  ARM_COMPUTE_RETURN_ON_ERROR(calculate_quantized_multiplier(multiplier, &quant_multiplier, &quant_shift));
146  quant_multipliers[i] = quant_multiplier;
147  quant_shifts[i] = quant_shift;
148  }
149 
150  // Legacy part
151  stage_info.gemmlowp_shift = quant_shifts[0];
152  stage_info.gemmlowp_multiplier = quant_multipliers[0];
153 
154  return Status{};
155 }
156 
158 {
159  int min_quant_val = 0;
160  int max_quant_val = 0;
161  switch(data_type)
162  {
163  case DataType::QASYMM8:
164  min_quant_val = std::numeric_limits<uint8_t>::min();
165  max_quant_val = std::numeric_limits<uint8_t>::max();
166  break;
167  case DataType::QSYMM8:
169  min_quant_val = std::numeric_limits<int8_t>::min();
170  max_quant_val = std::numeric_limits<int8_t>::max();
171  break;
172  case DataType::QASYMM16:
173  min_quant_val = std::numeric_limits<uint16_t>::min();
174  max_quant_val = std::numeric_limits<uint16_t>::max();
175  break;
176  case DataType::QSYMM16:
177  min_quant_val = std::numeric_limits<int16_t>::min();
178  max_quant_val = std::numeric_limits<int16_t>::max();
179  break;
180  default:
181  ARM_COMPUTE_ERROR("Unsupported data type");
182  }
183  return std::make_pair(min_quant_val, max_quant_val);
184 }
186  const ITensorInfo *weights,
187  const ITensorInfo *output,
188  unsigned int idx_ofms,
189  int32_t *output_multipliers_ptr,
190  int32_t *output_shifts_ptr)
191 {
192  const unsigned int num_filters = is_data_type_quantized_per_channel(weights->data_type()) ? weights->dimension(idx_ofms) : 1;
193 
194  const UniformQuantizationInfo iq_info = input->quantization_info().uniform();
195  const QuantizationInfo wq_info = weights->quantization_info();
196  const UniformQuantizationInfo oq_info = output->quantization_info().uniform();
197 
198  for(unsigned int i = 0; i < num_filters; ++i)
199  {
200  int32_t output_multiplier = 0;
201  int32_t output_shift = 0;
202  const float multiplier = iq_info.scale * wq_info.scale()[i] / oq_info.scale;
203  calculate_quantized_multiplier(multiplier, &output_multiplier, &output_shift);
204 
205  output_multipliers_ptr[i] = output_multiplier;
206  output_shifts_ptr[i] = output_shift;
207  }
208 }
209 
210 int32_t saturating_rounding_doubling_highmul(int32_t a, int32_t b)
211 {
212  bool overflow = a == b && a == std::numeric_limits<int32_t>::min();
213  int64_t a_64(a);
214  int64_t b_64(b);
215  int64_t ab_64 = a_64 * b_64;
216  bool is_positive_or_zero = a == 0 || b == 0 || (std::signbit(a) == std::signbit(b));
217  int32_t nudge = is_positive_or_zero ? (1 << 30) : (1 - (1 << 30));
218  int32_t ab_x2_high32 = static_cast<int32_t>((ab_64 + nudge) / (1ll << 31));
219  return overflow ? std::numeric_limits<int32_t>::max() : ab_x2_high32;
220 }
221 
222 inline int32_t rounding_divide_by_pow2(int32_t x, int exponent)
223 {
224  const int32_t mask = (1 << exponent) - 1;
225  const int32_t threshold = (mask >> 1) + (x < 0 ? 1 : 0);
226  return (x >> exponent) + ((x & mask) > threshold ? 1 : 0);
227 }
228 
229 int32_t multiply_by_quantized_multiplier(int32_t input, int32_t qmul, int32_t shift)
230 {
231  const auto left_shift = shift > 0 ? shift : 0;
232  const auto right_shift = shift > 0 ? 0 : -shift;
233  return rounding_divide_by_pow2(saturating_rounding_doubling_highmul(input * (1 << left_shift), qmul), right_shift);
234 }
235 
236 int32_t saturating_rounding_multiply_by_pow2(int32_t exponent, int32_t v)
237 {
238  if(exponent == 0)
239  {
240  return v;
241  }
242  else if(exponent < 0)
243  {
244  return rounding_divide_by_pow2(v, -exponent);
245  }
246  else
247  {
248  constexpr auto min = std::numeric_limits<int32_t>::min();
249  constexpr auto max = std::numeric_limits<int32_t>::max();
250  const auto width = sizeof(int32_t) * 8;
251 
252  const int32_t threshold = ((1 << (width - 1 - exponent)) - 1);
253  bool pos_mask = v > threshold;
254  bool neg_mask = v < -threshold;
255  int32_t result = v << exponent;
256  result = pos_mask ? max : result;
257  result = neg_mask ? min : result;
258  return result;
259  }
260 }
261 
262 void get_invsqrt_quantized_multiplier_exp(int32_t input, int32_t reverse_shift, int32_t &output_inv_sqrt, int32_t &output_shift)
263 {
265 
266  if(input <= 1)
267  {
268  // dealing the inputs (0 and 1) separately to avoid overflow
269  output_inv_sqrt = std::numeric_limits<std::int32_t>::max();
270  output_shift = 0;
271  return;
272  }
273 
274  // prepare input for fixed point operation and compute shift value
275  output_shift = 11;
276  while(input >= (1 << 29))
277  {
278  input /= 4;
279  ++output_shift;
280  }
281 
282  const uint32_t max_left_shift_bits = __builtin_clz(static_cast<uint32_t>(input)) - 1;
283  const uint32_t max_left_shift_bits_pairs = max_left_shift_bits / 2;
284  const uint32_t left_shift_bit_pairs = max_left_shift_bits_pairs - 1;
285  output_shift -= left_shift_bit_pairs;
286  input <<= 2 * left_shift_bit_pairs;
287 
288  // Calculation in fixed point domain with 3 integer bits.
289  using FixedPointRawType = int32_t;
290  constexpr uint32_t fixedpoint_position = 3;
291  constexpr uint32_t fixedpoint_int_position = sizeof(FixedPointRawType) * 8 - 1 - fixedpoint_position;
292  using FixedPoint3 = FixedPointRawType;
293  using FixedPoint0 = FixedPointRawType;
294 
295  // fixed point representation of input divided by 2 and 1.5 for Newton-Raphson iteration
296  const FixedPoint3 fixedpoint_input = (input >> 1);
297  const FixedPoint3 fixedpoint_half_input = rounding_divide_by_pow2(fixedpoint_input, 1);
298  const FixedPoint3 fixedpoint_half_three = (0x1 << fixedpoint_int_position) + (0x1 << (fixedpoint_int_position - 1));
299 
300  // initial guess (1) in fixed point representation
301  FixedPoint3 x = 0x1 << fixedpoint_int_position;
302 
303  // multiplication of two fixed point numbers, defined for readability
304  auto fixed_point_mul = [](FixedPointRawType a, FixedPointRawType b) -> FixedPointRawType
305  {
307  };
308 
309  // rescaling of fixed point to have dst_bit integer bits, defined for readability
310  auto fixed_point_rescale = [](FixedPointRawType a, uint32_t src_bit, uint32_t dst_bit) -> FixedPointRawType
311  {
312  const uint32_t exponent = src_bit - dst_bit;
313  return saturating_rounding_multiply_by_pow2(exponent, a);
314  };
315 
316  // 5 iterations of Newton-Raphson method for inverse square root - 1.5 * x_n = input/2 * (x_n)^3
317  constexpr int32_t num_iteration = 5;
318  for(int32_t i = 0; i < num_iteration; ++i)
319  {
320  const auto x3 = fixed_point_rescale(fixed_point_mul(fixed_point_mul(x, x), x), 9, fixedpoint_position);
321  x = fixed_point_rescale(fixed_point_mul(fixedpoint_half_three, x) - fixed_point_mul(fixedpoint_half_input, x3), 6, fixedpoint_position);
322  }
323 
324  // fixed point representation of sqrt(1/2)
325  const FixedPoint0 fixedpoint_half_sqrt_2 = 1518500250;
326  x = fixed_point_mul(fixedpoint_half_sqrt_2, x);
327  output_inv_sqrt = x;
328  if(output_shift < 0)
329  {
330  output_inv_sqrt <<= -output_shift;
331  output_shift = 0;
332  }
333  // convert right shift to left shift
334  output_shift *= reverse_shift;
335 }
336 } // quantization
337 } // arm_compute
int32_t gemmlowp_multiplier
GEMMLowp output stage multiplier used for quantizing to QASYMM8.
Definition: Types.h:1885
quantized, symmetric fixed-point 16-bit number
void compute_quantized_multipliers_and_shifts(const ITensorInfo *input, const ITensorInfo *weights, const ITensorInfo *output, unsigned int idx_ofms, int32_t *output_multipliers_ptr, int32_t *output_shifts_ptr)
Compute quantized per-channel multipliers and shifts.
SimpleTensor< float > b
Definition: DFT.cpp:157
#define ARM_COMPUTE_ERROR(msg)
Print the given message then throw an std::runtime_error.
Definition: Error.h:352
#define ARM_COMPUTE_RETURN_ON_ERROR(status)
Checks if a status contains an error and returns it.
Definition: Error.h:204
#define ARM_COMPUTE_ERROR_ON(cond)
If the condition is true then an error message is printed and an exception thrown.
Definition: Error.h:466
Store the tensor's metadata.
Definition: ITensorInfo.h:40
Quantization info when assuming per layer quantization.
quantized, asymmetric fixed-point 16-bit number
Status calculate_quantized_multiplier(float multiplier, int32_t *quant_multiplier, int32_t *shift, bool ignore_epsilon=false)
Calculate quantized representation of multiplier.
Status class.
Definition: Error.h:52
Status calculate_quantized_multiplier_greater_than_one(float multiplier, int32_t *quantized_multiplier, int32_t *left_shift)
Calculate quantized representation of multiplier having value greater than one.
#define ARM_COMPUTE_RETURN_ERROR_ON(cond)
If the condition is true, an error is returned.
Definition: Error.h:296
Copyright (c) 2017-2020 Arm Limited.
std::vector< int32_t > gemmlowp_shifts
GEMMLowp output stage multiplier used for quantizing to QASYMM8.
Definition: Types.h:1890
Quantization information.
std::pair< int, int > get_min_max_values_from_quantized_data_type(DataType data_type)
Get minimum and maximum values for the input quantized data type.
void get_invsqrt_quantized_multiplier_exp(int32_t input, int32_t reverse_shift, int32_t &output_inv_sqrt, int32_t &output_shift)
Compute quantized multiplier and shift for the inverse square root of input.
int32_t saturating_rounding_doubling_highmul(int32_t a, int32_t b)
Compute multiplication of two integers.
bool is_data_type_quantized_per_channel(DataType dt)
Check if a given data type is of per channel type.
Definition: Utils.h:1198
Status calculate_quantized_multipliers(const QuantizationInfo &iq_info, const QuantizationInfo &wq_info, const QuantizationInfo &oq_info, GEMMLowpOutputStageInfo &stage_info)
Calculate quantized representation of per-channel multipliers.
int32_t multiply_by_quantized_multiplier(int32_t input, int32_t qmul, int32_t shift)
Compute the value multiplied by given quantized multiplier and shift.
quantized, asymmetric fixed-point 8-bit number unsigned
std::vector< int32_t > gemmlowp_multipliers
GEMMLowp output stage multiplier used for quantizing to QASYMM8.
Definition: Types.h:1889
UniformQuantizationInfo uniform() const
Return per layer quantization info.
GEMMLowp output stage info.
Definition: Types.h:1881
const std::vector< float > & scale() const
Scale vector accessor.
virtual QuantizationInfo quantization_info() const =0
Get the quantization settings (scale and offset) of the tensor.
quantized, symmetric fixed-point 8-bit number
int32_t rounding_divide_by_pow2(int32_t x, int exponent)
Round to the nearest division by a power-of-two using exponent, copied from NEMath.
int32_t gemmlowp_shift
GEMMLowp output stage shift used for quantizing to uint8.
Definition: Types.h:1886
constexpr int64_t fixed_point_one_Q0
T round(T value)
Round floating-point value with half value rounding away from zero.
int32_t saturating_rounding_multiply_by_pow2(int32_t exponent, int32_t v)
Compute the value multiplied the power-of-two.
quantized, asymmetric fixed-point 8-bit number signed
Status calculate_quantized_multiplier_less_than_one(float multiplier, int32_t *quant_multiplier, int32_t *right_shift, bool ignore_epsilon=false)
Calculate quantized representation of multiplier with value less than one.
DataType
Available data types.
Definition: Types.h:77
SimpleTensor< T > threshold(const SimpleTensor< T > &src, T threshold, T false_value, T true_value, ThresholdType type, T upper)
Definition: Threshold.cpp:35