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 <math.h>
8 #include <stddef.h>
9
10 #include <xnnpack/common.h>
11 #include <xnnpack/math-stubs.h>
12
13
xnn_math_f32_roundz__scalar_addsub(size_t n,const float * input,float * output)14 void xnn_math_f32_roundz__scalar_addsub(
15 size_t n,
16 const float* input,
17 float* output)
18 {
19 assert(n % sizeof(float) == 0);
20
21 // Addition of this number to a floating-point number x cause rounding of the result to an integer. Then this magic
22 // number is subtracted back from the result to get original x rounded to integer. This trick works only for
23 // 0 <= x < 2**24, but all numbers in 2**23 <= x < 2**24 range are integers, so we can further restrict it to
24 // 0 <= x < 2**23. Then the upper bound of the validity interval is conveniently the same as the magic number.
25 const float vmagic_number = 0x1.000000p+23f;
26 // Unit constant to decrement absolute values rounded "wrong way" (i.e. away from zero) in the round-to-nearest-even
27 // operation.
28 const float vone = 1.0f;
29
30 for (; n != 0; n -= sizeof(float)) {
31 const float vx = *input++;
32
33 // The rounding trick works only for x >= 0, so we compute absolute value of x, round it, and restore the sign in
34 // the end. This method works for round-towards-zero because it is an odd function.
35 const float vabsx = fabsf(vx);
36 // Addition-subtraction trick with the magic number to cause rounding to the nearest-even integer for abs(x).
37 // Note: the result is valid only for 0 <= abs(x) < 2**23.
38 // Note: addition-subtraction implicitly converts SNaN inputs to QNaNs.
39 const float vrndabsx = (vabsx + vmagic_number) - vmagic_number;
40
41 // Adjust abs(x) rounded to nearest-even via the addition-subtraction trick to get abs(x) rounded down.
42 // Note: subtraction implicitly converts SNaN inputs to QNaNs.
43 const float vflrabsx = XNN_UNPREDICTABLE(vrndabsx <= vabsx) ? vrndabsx : vrndabsx - vone;
44
45 // Select between the abs(x) rounded down using addition-subtraction trick with adjustment and the abs(x) value.
46 // For abs(x) < 2**23, the result is abs(x) rounded via addition-subtraction trick.
47 // For abs(x) >= 2**23, the result is abs(x) itself (already an integer).
48 // For NaN inputs, the result is abs(x) converted to QNaN as a side-effect of addition-subtraction.
49 const float vabsy = XNN_UNPREDICTABLE(vabsx >= vmagic_number) ? vabsx : vflrabsx;
50 // Restore the sign of the rounded value.
51 const float vy = copysignf(vabsy, vx);
52
53 *output++ = vy;
54 }
55 }
56