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 #include <stdint.h>
9
10 #include <arm_neon.h>
11
12 #include <xnnpack/math-stubs.h>
13
14
xnn_math_f32_roundd__neon_addsub(size_t n,const float * input,float * output)15 void xnn_math_f32_roundd__neon_addsub(
16 size_t n,
17 const float* input,
18 float* output)
19 {
20 assert(n % (4 * sizeof(float)) == 0);
21
22 // Addition of this number to a floating-point number x cause rounding of the result to an integer. Then this magic
23 // number is subtracted back from the result to get original x rounded to integer. This trick works only for
24 // 0 <= x < 2**24, but all numbers in 2**23 <= x < 2**24 range are integers, so we can further restrict it to
25 // 0 <= x < 2**23. Then the upper bound of the validity interval is conveniently the same as the magic number.
26 const float32x4_t vmagic_number = vmovq_n_f32(0x1.000000p+23f);
27 // Mask for the sign bit of a floating-point number.
28 const uint32x4_t vsign_mask = vmovq_n_u32(UINT32_C(0x80000000));
29 // Unit constant to decrement results rounded "wrong way" (i.e. up) in the round-to-nearest-even operation.
30 const uint32x4_t vone = vmovq_n_u32(UINT32_C(0x3F800000));
31
32 for (; n != 0; n -= 4 * sizeof(float)) {
33 const float32x4_t vx = vld1q_f32(input); input += 4;
34
35 // The rounding trick works only for x >= 0, so we compute absolute value of x, round it, and restore the sign in
36 // the end. This method works for round-to-nearest-even because it is an odd function.
37 const float32x4_t vabsx = vabsq_f32(vx);
38 // Compute bitmask for the bits we want to copy from the rounded abs(x). Other bits will be copied from x.
39 // If abs(x) >= 2**23, we want all bits from x.
40 // If abs(x) < 2**23 or x is NaN, we want all but the sign bit from the rounded abs(x) and the sign bit from x.
41 // Note: we do vcaltq_f32(vmagic_number, vx) instead of vcltq_f32(vmagic_number, vabsx) to reduce dependency chain.
42 const uint32x4_t vrndmask = vorrq_u32(vcaltq_f32(vmagic_number, vx), vsign_mask);
43
44 // Addition-subtraction trick with the magic number to cause rounding to the nearest-even integer for abs(x).
45 // Note: the result is valid only for 0 <= abs(x) < 2**23.
46 // Note: addition-subtraction implicitly converts SNaN inputs to QNaNs.
47 const float32x4_t vrndabsx = vsubq_f32(vaddq_f32(vabsx, vmagic_number), vmagic_number);
48
49 // Combine abs(x) rounded via addition-subtraction trick and the input x value.
50 // For abs(x) < 2**23, the result is abs(x) rounded via addition-subtraction trick with the sign of x.
51 // For NaN inputs, the result is x converted to QNaN as a side-effect of addition-subtraction.
52 // For abs(x) >= 2**23, the result is x itself.
53 const float32x4_t vrndx = vbslq_f32(vrndmask, vx, vrndabsx);
54
55 // Adjust x rounded towards nearest-even to get x rounded down.
56 // Note: subtraction implicitly converts SNaN inputs to QNaNs.
57 const float32x4_t vy = vsubq_f32(vrndx, vreinterpretq_f32_u32(vandq_u32(vcgtq_f32(vrndx, vx), vone)));
58
59 vst1q_f32(output, vy); output += 4;
60 }
61 }
62