1 // Copyright 2020 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 #include <assert.h>
7 #include <stddef.h>
8
9 #include <wasm_simd128.h>
10
11 #include <xnnpack/common.h>
12 #include <xnnpack/math-stubs.h>
13
14
15 // Table of exp2(k / 16) values decremented (as integer) by (k << 19), k = 0..15
16 extern XNN_INTERNAL const float xnn_table_exp2minus_k_over_16[16];
17
xnn_math_f32_expm1minus__wasmsimd_rr2_lut16_p3_andnot(size_t n,const float * input,float * output)18 void xnn_math_f32_expm1minus__wasmsimd_rr2_lut16_p3_andnot(
19 size_t n,
20 const float* input,
21 float* output)
22 {
23 assert(n % (4 * sizeof(float)) == 0);
24
25 // Large number such that ulp(magic bias) == exp2(-4)
26 const v128_t vmagic_bias = wasm_f32x4_splat(0x1.800000p19f);
27 const v128_t vlog2e = wasm_f32x4_splat(0x1.715476p+0f);
28 // Mask for the lowest 4 bits
29 const v128_t vindex_mask = wasm_i32x4_splat(0xF);
30 // The largest x for which expm1f(x) is saturated at -1.0f.
31 const v128_t vsat_cutoff = wasm_f32x4_splat(-0x1.154246p+4f);
32 // Last 9 bits are zeroes
33 const v128_t vminus_ln2_hi = wasm_f32x4_splat(-0x1.62E400p-1f);
34 const v128_t vminus_ln2_lo = wasm_f32x4_splat(-0x1.7F7D1Cp-20f);
35 // Coefficient of polynomial approximation
36 // exp(t) - 1 ~ t * (1 + t * (c2 + t * c3))
37 // on [-log(2)/32, log(2)/32]
38 const v128_t vc3 = wasm_f32x4_splat(0x1.55561Cp-3f);
39 const v128_t vc2 = wasm_f32x4_splat(0x1.0001ECp-1f);
40 const v128_t vone = wasm_f32x4_splat(1.0f);
41
42 for (; n != 0; n -= 4 * sizeof(float)) {
43 v128_t vx = wasm_v128_load(input);
44
45 // Compute reduced argument n := round(x / log(2), 4).
46 // We do it by adding a large number (magic bias), which cause rounding of the result to 4 fractional bits, then
47 // subtracing the large number back. The trick with adding large number is valid only within certain bounds
48 // (|x / log(2)| <= 2**18, i.e. |x| <= 0x1.62E43p+17 = 181704.375), but that is acceptable, because inputs x are
49 // restricted to [-17.328680, 0].
50 // Note that addition-subtraction of the large number doesn't cause overflow for inputs in this range.
51 v128_t vn = wasm_f32x4_add(wasm_f32x4_mul(vx, vlog2e), vmagic_bias);
52
53 // Create a floating-point number s (scale) such that s := 2**n for valid inputs, i.e. -17.328680 <= x <= 0.0. As n
54 // has 4 fractional bits, we split s == 2**n = 2**int(n) * 2**frac(n). We create s in two steps:
55 // 1. Fetch 2**frac(n) from the table using the 4 low bits of n, as integer. Note that the fetched values are in
56 // the [1.0, 2.0) range, i.e. their floating-point exponent is 0.
57 // 2. Adjust fecthed value by addition of int(n) to its floating-point exponent. The result is always a normalized
58 // number, because for -17.328680 <= x <= 0.0 we have -25 <= int(n) <= 0, and thus the adjusted exponent is not
59 // lower than -25.
60 //
61 // Shift bits 4:12 into 23:31 (position of floating-point exponent).
62 const v128_t ven = wasm_i32x4_shl(vn, 19);
63
64 // Use bits 0:4 bits of n, as integer, as an index for table lookup of l := 2**frac(n).
65 const v128_t vidx = wasm_i32x4_shl(wasm_v128_and(vn, vindex_mask), 2);
66 const uint64_t vidx_lo = wasm_i64x2_extract_lane(vidx, 0);
67 const uint64_t vidx_hi = wasm_i64x2_extract_lane(vidx, 1);
68 const float vl0 = *((const float*) ((uintptr_t) xnn_table_exp2minus_k_over_16 + (uint32_t) vidx_lo));
69 const float vl1 = *((const float*) ((uintptr_t) xnn_table_exp2minus_k_over_16 + (uint32_t) (vidx_lo >> 32)));
70 const float vl2 = *((const float*) ((uintptr_t) xnn_table_exp2minus_k_over_16 + (uint32_t) vidx_hi));
71 const float vl3 = *((const float*) ((uintptr_t) xnn_table_exp2minus_k_over_16 + (uint32_t) (vidx_hi >> 32)));
72 const v128_t vl = wasm_f32x4_make(vl0, vl1, vl2, vl3);
73 // Adjust exponent of the value l fetched from the table to get the final s value.
74 v128_t vs = wasm_i32x4_add(vl, ven);
75
76 // Subtract the large number back to get final n := round(x / log(2), 4).
77 vn = wasm_f32x4_sub(vn, vmagic_bias);
78
79 // Compute reduced argument t := x - n * log(2).
80 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
81 v128_t vt = wasm_f32x4_add(wasm_f32x4_mul(vn, vminus_ln2_hi), vx);
82 vt = wasm_f32x4_add(wasm_f32x4_mul(vn, vminus_ln2_lo), vt);
83
84 // The function saturates at -1 for large negative inputs: expm1f(x) == -1.0f for x <= sat_cutoff ~= -17.328680.
85 // To guarantee this behaviour, we zero out s (scale) and t (reduced argument) for x <= sat_cutoff.
86 const v128_t vm = wasm_f32x4_le(vx, vsat_cutoff);
87 vs = wasm_v128_andnot(vs, vm);
88 vt = wasm_v128_andnot(vt, vm);
89
90 // Compute degree-3 polynomial approximation for exp(t) - 1 on [-log(2)/32, log(2)/32].
91 // P(t) = t * (1 + t * (c2 + t * c3)) = t + t * (t * (c2 + t * c3)) = t + t * p
92 v128_t vp = wasm_f32x4_add(wasm_f32x4_mul(vc3, vt), vc2);
93 vp = wasm_f32x4_mul(vp, vt);
94
95 // Reconstruct the exp(x) - 1 value:
96 // exp(x) - 1 = s * (1 + t * (1 + t * (c2 + t * c3))) - 1
97 // = (s - 1) + s * (t + t * p)
98 // = ((t * s) + (t * s) * p) + (s - 1)
99 vt = wasm_f32x4_mul(vt, vs);
100 const v128_t vsm1 = wasm_f32x4_sub(vs, vone);
101 vp = wasm_f32x4_add(wasm_f32x4_mul(vp, vt), vt);
102 const v128_t vf = wasm_f32x4_add(vp, vsm1);
103
104 wasm_v128_store(output, vf);
105
106 input += 4;
107 output += 4;
108 }
109 }
110