1 // Auto-generated file. Do not edit!
2 // Template: src/f32-raddstoreexpminusmax/scalar-rr2-p5.c.in
3 // Generator: tools/xngen
4 //
5 // Copyright 2020 Google LLC
6 //
7 // This source code is licensed under the BSD-style license found in the
8 // LICENSE file in the root directory of this source tree.
9
10 #include <assert.h>
11
12 #include <xnnpack/common.h>
13 #include <xnnpack/raddstoreexpminusmax.h>
14
15 #include <fp16/bitcasts.h>
16
17
xnn_f32_raddstoreexpminusmax_ukernel__scalar_rr2_p5_x1(size_t elements,const float * input,const float * max,float * output,float * sum,const union xnn_f32_expminus_params params[restrict XNN_MIN_ELEMENTS (1)])18 void xnn_f32_raddstoreexpminusmax_ukernel__scalar_rr2_p5_x1(
19 size_t elements,
20 const float* input,
21 const float* max,
22 float* output,
23 float* sum,
24 const union xnn_f32_expminus_params params[restrict XNN_MIN_ELEMENTS(1)])
25 {
26 assert(elements % sizeof(float) == 0);
27
28 const float vi_max = *max;
29 const float vlog2e = params->scalar_rr2_p5.log2e;
30 const float vmagic_bias = params->scalar_rr2_p5.magic_bias;
31 const float vminus_ln2_hi = params->scalar_rr2_p5.minus_ln2_hi;
32 const float vminus_ln2_lo = params->scalar_rr2_p5.minus_ln2_lo;
33 const float vc5 = params->scalar_rr2_p5.c5;
34 const float vc4 = params->scalar_rr2_p5.c4;
35 const float vc3 = params->scalar_rr2_p5.c3;
36 const float vc2 = params->scalar_rr2_p5.c2;
37 const float vc1 = params->scalar_rr2_p5.c1;
38 const float vdenorm_cutoff = params->scalar_rr2_p5.denorm_cutoff;
39
40 float vacc = 0.0f;
41 for (; elements >= sizeof(float); elements -= sizeof(float)) {
42 // Load 1 input at a time.
43 const float vi = *input++;
44
45 // Subtract maximum input x := i - i_max. This implies x <= 0.
46 const float vx = vi - vi_max;
47
48 // Compute reduced argument n := round(x / log(2)).
49 // We do it by adding a large number (magic bias) to the product x * (1/log(2)), which cause rounding of the result
50 // to an integer, then subtracing the large number back. The trick with adding large number is valid only within
51 // certain bounds (|x| <= 2**22), but that's ok, because inputs outside of [-87.336540, 0.0] underflow expf(x)
52 // anyway. We fixup the result for such inputs at the very end of the algorithm.
53 float vn = vx * vlog2e + vmagic_bias;
54
55 // Create a floating-point number s (scale) such that s == 2**n for inputs which don't cause underflow, i.e.
56 // -87.33642 <= x <= 0.0, and -126 <= n <= 0 accordingly.
57 const float vs = fp32_from_bits(fp32_to_bits(vn) << 23);
58
59 // Subtract the large number back to get final n := round(x / log(2)).
60 vn -= vmagic_bias;
61
62 // Compute reduced argument t := x - n * log(2).
63 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
64 float vt = vn * vminus_ln2_hi + vx;
65 vt = vn * vminus_ln2_lo + vt;
66
67 // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
68 float vp = vc5 * vt + vc4;
69 vp = vp * vt + vc3;
70 vp = vp * vt + vc2;
71 vp = vp * vt + vc1;
72
73 // Reconstruct the final f value:
74 // f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
75 // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
76 // = s + (t * s) * p
77 vt *= vs;
78 float vf = vt * vp + vs;
79
80 // For inputs below denormal cutoff, replace output with +0.0f.
81 // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
82 if XNN_UNPREDICTABLE(vx < vdenorm_cutoff) {
83 vf = 0.0f;
84 }
85
86 // Store 1 output at a time.
87 *output++ = vf;
88
89 // Accumulate computed exponents.
90 vacc += vf;
91 }
92 *sum = vacc;
93 }
94