1// Copyright 2019 Google LLC
2//
3// This source code is licensed under the BSD-style license found in the
4// LICENSE file in the root directory of this source tree.
5
6$assert ELEMENTS_TILE % 16 == 0
7$assert ELEMENTS_TILE >= 16
8$SIMD_TILE = ELEMENTS_TILE // 16
9$ABC = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ"
10#include <assert.h>
11#include <math.h>
12
13#include <immintrin.h>
14
15#include <xnnpack/common.h>
16#include <xnnpack/intrinsics-polyfill.h>
17#include <xnnpack/raddextexp.h>
18
19
20void xnn_f32_raddextexp_ukernel__avx512f_p5_scalef_x${ELEMENTS_TILE}${"" if ACCUMULATORS == 1 else "_acc%d" % ACCUMULATORS}(
21    size_t elements,
22    const float* x,
23    float* sum)
24{
25  assert(elements % sizeof(float) == 0);
26
27  const __m512 vlog2e = _mm512_set1_ps(0x1.715476p+0f);
28  const __m512 vminus_ln2_hi = _mm512_set1_ps(-0x1.62E43p-1f);
29  const __m512 vminus_ln2_lo = _mm512_set1_ps(0x1.05C61p-29f);
30
31  const __m512 vc0 = _mm512_set1_ps(1.0f);
32  const __m512 vc1 = _mm512_set1_ps(0x1.FFFFF6p-1f);
33  const __m512 vc2 = _mm512_set1_ps(0x1.FFFDC6p-2f);
34  const __m512 vc3 = _mm512_set1_ps(0x1.555A80p-3f);
35  const __m512 vc4 = _mm512_set1_ps(0x1.573A1Ap-5f);
36  const __m512 vc5 = _mm512_set1_ps(0x1.0F9F9Cp-7f);
37
38  const __m512 vminus_inf = _mm512_set1_ps(-INFINITY);
39
40  $for K in range(ACCUMULATORS):
41    __m512 vaccv${K} = _mm512_setzero_ps();
42  $for K in range(ACCUMULATORS):
43    __m512 vacce${K} = vminus_inf;
44  for (; elements >= ${ELEMENTS_TILE} * sizeof(float); elements -= ${ELEMENTS_TILE} * sizeof(float)) {
45    // Load ${ELEMENTS_TILE} (${SIMD_TILE}x16) inputs at a time.
46    const __m512 vx0 = _mm512_loadu_ps(x);
47    $for N in range(1, SIMD_TILE):
48      const __m512 vx${N} = _mm512_loadu_ps(x + ${N * 16});
49    x += ${ELEMENTS_TILE};
50
51    // Compute reduced argument elements := round(x / log(2)).
52    $for N in range(SIMD_TILE):
53      const __m512 vn${N} = _mm512_roundscale_ps(_mm512_mul_ps(vx${N}, vlog2e), 0);
54
55    // Compute reduced argument t := x - elements * log(2).
56    // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
57    $for N in range(SIMD_TILE):
58      __m512 vt${N} = _mm512_fmadd_ps(vn${N}, vminus_ln2_hi, vx${N});
59
60    $for N in range(SIMD_TILE):
61      vt${N} = _mm512_fmadd_ps(vn${N}, vminus_ln2_lo, vt${N});
62
63    // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
64    $for N in range(SIMD_TILE):
65      __m512 vp${N} = _mm512_fmadd_ps(vc5, vt${N}, vc4);
66
67    $for N in range(SIMD_TILE):
68      vp${N} = _mm512_fmadd_ps(vp${N}, vt${N}, vc3);
69
70    $for N in range(SIMD_TILE):
71      vp${N} = _mm512_fmadd_ps(vp${N}, vt${N}, vc2);
72
73    $for N in range(SIMD_TILE):
74      vp${N} = _mm512_fmadd_ps(vp${N}, vt${N}, vc1);
75
76    $for N in range(SIMD_TILE):
77      vp${N} = _mm512_fmadd_ps(vp${N}, vt${N}, vc0);
78
79    // Accumulate "extended" floating-point numbers in ("mantissa", "exponent") representation where
80    //  - vnX is "exponent"
81    //  - vpX is "mantissa"
82    //
83    // exp2(ae) * av + exp2(be) * bv =
84    //   = exp2(max(ae, be)) * exp2(ae - max(ae, be)) * av + exp2(max(ae, be)) * exp2(be - max(ae, be)) * bv
85    //   = exp2(max_e) * (exp2(ae - max_e) * av + exp2(be - max_e) * bv)
86    //   = exp2(max_e) * (exp2(delta_ae) * av + exp2(delta_be) * bv)
87    //
88    // For computational efficiency we add three "extended" floating-point numbers at a time.
89    $for N in range(SIMD_TILE):
90      $if N < ACCUMULATORS:
91        __m512 vmax_e${N} = _mm512_max_ps(vacce${N}, vn${N});
92      $else:
93        vmax_e${N % ACCUMULATORS} = _mm512_max_ps(vmax_e${N % ACCUMULATORS}, vn${N});
94
95    $for K in range(ACCUMULATORS):
96      const __m512 vdelta_acce${K} = _mm512_sub_ps(vacce${K}, vmax_e${K});
97    $for N in range(SIMD_TILE):
98      const __m512 vdelta_e${N} = _mm512_sub_ps(vn${N}, vmax_e${N % ACCUMULATORS});
99
100    // Update accumulated "mantissa" and "exponent" values
101    $for K in range(ACCUMULATORS):
102      vaccv${K} = _mm512_scalef_ps(vaccv${K}, vdelta_acce${K});
103    $for N in range(SIMD_TILE):
104      vaccv${N % ACCUMULATORS} = _mm512_add_ps(vaccv${N % ACCUMULATORS}, _mm512_scalef_ps(vp${N}, vdelta_e${N}));
105
106    $for K in range(ACCUMULATORS):
107      vacce${K} = vmax_e${K};
108  }
109
110  // Reduce partial sums of "extended" floating-point numbers into a single "extended" SIMD vector of sums.
111  $if ACCUMULATORS > 1:
112    $for A in range(0, ACCUMULATORS, 2):
113      $if A + 1 < ACCUMULATORS:
114        const __m512 vmax_acce${ABC[A:A+2]} = _mm512_max_ps(vacce${A}, vacce${A+1});
115      $else:
116        const __m512 vmax_acce${ABC[A]} = vacce${A};
117    $ACC_SLICE = 2
118    $while ACC_SLICE < ACCUMULATORS:
119      $for A in range(0, ACCUMULATORS, ACC_SLICE * 2):
120        $if A + ACC_SLICE < ACCUMULATORS:
121          const __m512 vmax_acce${ABC[A:min(A+ACC_SLICE*2, ACCUMULATORS)]} = _mm512_max_ps(vmax_acce${ABC[A:A+ACC_SLICE]}, vmax_acce${ABC[A+ACC_SLICE:min(ACCUMULATORS,A+ACC_SLICE*2)]});
122      $ACC_SLICE *= 2
123
124    $for K in range(ACCUMULATORS):
125      const __m512 vdelta_acce${K} = _mm512_sub_ps(vacce${K}, vmax_acce${ABC[0:ACCUMULATORS]});
126
127    __m512 vaccv = _mm512_scalef_ps(vaccv0, vdelta_acce0);
128    $for K in range(1, ACCUMULATORS):
129      vaccv = _mm512_add_ps(vaccv, _mm512_scalef_ps(vaccv${K}, vdelta_acce${K}));
130    __m512 vacce = vmax_acce${ABC[0:ACCUMULATORS]};
131  $else:
132    __m512 vaccv = vaccv0;
133    __m512 vacce = vacce0;
134
135  for (; elements >= 16 * sizeof(float); elements -= 16 * sizeof(float)) {
136    // Load 16 inputs at a time.
137    const __m512 vx = _mm512_loadu_ps(x);
138    x += 16;
139
140    // Compute reduced argument elements := round(x / log(2)).
141    const __m512 vn = _mm512_roundscale_ps(_mm512_mul_ps(vx, vlog2e), 0);
142
143    // Compute reduced argument t := x - elements * log(2).
144    // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
145    __m512 vt = _mm512_fmadd_ps(vn, vminus_ln2_hi, vx);
146    vt = _mm512_fmadd_ps(vn, vminus_ln2_lo, vt);
147
148    // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
149    __m512 vp = _mm512_fmadd_ps(vc5, vt, vc4);
150    vp = _mm512_fmadd_ps(vp, vt, vc3);
151    vp = _mm512_fmadd_ps(vp, vt, vc2);
152    vp = _mm512_fmadd_ps(vp, vt, vc1);
153    vp = _mm512_fmadd_ps(vp, vt, vc0);
154
155    // Accumulate "extended" floating-point numbers in ("mantissa", "exponent") representation.
156    const __m512 vmax_e = _mm512_max_ps(vacce, vn);
157    const __m512 vdelta_acce = _mm512_sub_ps(vacce, vmax_e);
158    const __m512 vdelta_e = _mm512_sub_ps(vn, vmax_e);
159    vaccv = _mm512_scalef_ps(vaccv, vdelta_acce);
160    vaccv = _mm512_add_ps(vaccv, _mm512_scalef_ps(vp, vdelta_e));
161
162    vacce = vmax_e;
163  }
164  if XNN_UNLIKELY(elements != 0) {
165    // Prepare mask for valid 32-bit elements (depends on elements).
166    elements >>= 2 /* log2(sizeof(float)) */;
167    const __mmask16 vmask = _cvtu32_mask16((uint16_t) ((uint32_t) (UINT32_C(1) << elements) - UINT32_C(1)));
168
169    // Load up to 15 inputs at a time.
170    const __m512 vx = _mm512_maskz_loadu_ps(vmask, x);
171
172    // Compute reduced argument elements := round(x / log(2)).
173    const __m512 vn = _mm512_roundscale_ps(_mm512_mul_ps(vx, vlog2e), 0);
174
175    // Compute reduced argument t := x - elements * log(2).
176    // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
177    __m512 vt = _mm512_fmadd_ps(vn, vminus_ln2_hi, vx);
178    vt = _mm512_fmadd_ps(vn, vminus_ln2_lo, vt);
179
180    // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
181    __m512 vp = _mm512_fmadd_ps(vc5, vt, vc4);
182    vp = _mm512_fmadd_ps(vp, vt, vc3);
183    vp = _mm512_fmadd_ps(vp, vt, vc2);
184    vp = _mm512_fmadd_ps(vp, vt, vc1);
185    vp = _mm512_fmadd_ps(vp, vt, vc0);
186
187    // Accumulate "extended" floating-point numbers in ("mantissa", "exponent") representation.
188    const __m512 vmax_e = _mm512_mask_max_ps(vacce, vmask, vacce, vn);
189    const __m512 vdelta_acce = _mm512_sub_ps(vacce, vmax_e);
190    const __m512 vdelta_e = _mm512_sub_ps(vn, vmax_e);
191    vaccv = _mm512_mask_scalef_ps(vaccv, vmask, vaccv, vdelta_acce);
192    vaccv = _mm512_mask_add_ps(vaccv, vmask, vaccv, _mm512_maskz_scalef_ps(vmask, vp, vdelta_e));
193    vacce = vmax_e;
194  }
195
196  // Reduce partial sums of "extended" floating-point numbers into a single "extended" floating-point sum.
197  const float vmax_acce = _mm512_reduce_max_ps(vacce);
198  const __m512 vdelta_acce = _mm512_sub_ps(vacce, _mm512_set1_ps(vmax_acce));
199
200  sum[0] = _mm512_reduce_add_ps(_mm512_scalef_ps(vaccv, vdelta_acce));
201  sum[1] = vmax_acce;
202
203  _mm256_zeroupper();
204}
205