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/math.h>
14 #include <xnnpack/raddstoreexpminusmax.h>
15
16
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)])17 void xnn_f32_raddstoreexpminusmax_ukernel__scalar_rr2_p5_x1(
18 size_t elements,
19 const float* input,
20 const float* max,
21 float* output,
22 float* sum,
23 const union xnn_f32_expminus_params params[restrict XNN_MIN_ELEMENTS(1)])
24 {
25 assert(elements % sizeof(float) == 0);
26
27 const float vi_max = *max;
28 const float vlog2e = params->scalar_rr2_p5.log2e;
29 const float vmagic_bias = params->scalar_rr2_p5.magic_bias;
30 const float vminus_ln2_hi = params->scalar_rr2_p5.minus_ln2_hi;
31 const float vminus_ln2_lo = params->scalar_rr2_p5.minus_ln2_lo;
32 const float vc5 = params->scalar_rr2_p5.c5;
33 const float vc4 = params->scalar_rr2_p5.c4;
34 const float vc3 = params->scalar_rr2_p5.c3;
35 const float vc2 = params->scalar_rr2_p5.c2;
36 const float vc1 = params->scalar_rr2_p5.c1;
37 const float vdenorm_cutoff = params->scalar_rr2_p5.denorm_cutoff;
38
39 float vacc = 0.0f;
40 for (; elements >= sizeof(float); elements -= sizeof(float)) {
41 // Load 1 input at a time.
42 const float vi = *input++;
43
44 // Subtract maximum input x := i - i_max. This implies x <= 0.
45 const float vx = vi - vi_max;
46
47 // Compute reduced argument n := round(x / log(2)).
48 // We do it by adding a large number (magic bias) to the product x * (1/log(2)), which cause rounding of the result
49 // to an integer, then subtracing the large number back. The trick with adding large number is valid only within
50 // certain bounds (|x| <= 2**22), but that's ok, because inputs outside of [-87.336540, 0.0] underflow expf(x)
51 // anyway. We fixup the result for such inputs at the very end of the algorithm.
52 float vn = vx * vlog2e + vmagic_bias;
53
54 // Create a floating-point number s (scale) such that s == 2**n for inputs which don't cause underflow, i.e.
55 // -87.33642 <= x <= 0.0, and -126 <= n <= 0 accordingly.
56 const float vs = uint32_as_float(float_as_uint32(vn) << 23);
57
58 // Subtract the large number back to get final n := round(x / log(2)).
59 vn -= vmagic_bias;
60
61 // Compute reduced argument t := x - n * log(2).
62 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
63 float vt = vn * vminus_ln2_hi + vx;
64 vt = vn * vminus_ln2_lo + vt;
65
66 // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
67 float vp = vc5 * vt + vc4;
68 vp = vp * vt + vc3;
69 vp = vp * vt + vc2;
70 vp = vp * vt + vc1;
71
72 // Reconstruct the final f value:
73 // f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
74 // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
75 // = s + (t * s) * p
76 vt *= vs;
77 float vf = vt * vp + vs;
78
79 // For inputs below denormal cutoff, replace output with +0.0f.
80 // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
81 if XNN_UNPREDICTABLE(vx < vdenorm_cutoff) {
82 vf = 0.0f;
83 }
84
85 // Store 1 output at a time.
86 *output++ = vf;
87
88 // Accumulate computed exponents.
89 vacc += vf;
90 }
91 *sum = vacc;
92 }
93