1 /*
2  * Helper for single-precision routines which calculate exp(x) and do not
3  * need special-case handling
4  *
5  * Copyright (c) 2019-2023, Arm Limited.
6  * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
7  */
8 
9 #ifndef PL_MATH_V_EXPF_INLINE_H
10 #define PL_MATH_V_EXPF_INLINE_H
11 
12 #include "v_math.h"
13 
14 struct v_expf_data
15 {
16   float32x4_t poly[5];
17   float32x4_t shift, invln2_and_ln2;
18 };
19 
20 /* maxerr: 1.45358 +0.5 ulp.  */
21 #define V_EXPF_DATA                                                           \
22   {                                                                           \
23     .poly = { V4 (0x1.0e4020p-7f), V4 (0x1.573e2ep-5f), V4 (0x1.555e66p-3f),  \
24 	      V4 (0x1.fffdb6p-2f), V4 (0x1.ffffecp-1f) },                     \
25     .shift = V4 (0x1.8p23f),                                                  \
26     .invln2_and_ln2 = { 0x1.715476p+0f, 0x1.62e4p-1f, 0x1.7f7d1cp-20f, 0 },   \
27   }
28 
29 #define ExponentBias v_u32 (0x3f800000) /* asuint(1.0f).  */
30 #define C(i) d->poly[i]
31 
32 static inline float32x4_t
33 v_expf_inline (float32x4_t x, const struct v_expf_data *d)
34 {
35   /* Helper routine for calculating exp(x).
36      Copied from v_expf.c, with all special-case handling removed - the
37      calling routine should handle special values if required.  */
38 
39   /* exp(x) = 2^n (1 + poly(r)), with 1 + poly(r) in [1/sqrt(2),sqrt(2)]
40      x = ln2*n + r, with r in [-ln2/2, ln2/2].  */
41   float32x4_t n, r, z;
42   z = vfmaq_laneq_f32 (d->shift, x, d->invln2_and_ln2, 0);
43   n = vsubq_f32 (z, d->shift);
44   r = vfmsq_laneq_f32 (x, n, d->invln2_and_ln2, 1);
45   r = vfmsq_laneq_f32 (r, n, d->invln2_and_ln2, 2);
46   uint32x4_t e = vshlq_n_u32 (vreinterpretq_u32_f32 (z), 23);
47   float32x4_t scale = vreinterpretq_f32_u32 (vaddq_u32 (e, ExponentBias));
48 
49   /* Custom order-4 Estrin avoids building high order monomial.  */
50   float32x4_t r2 = vmulq_f32 (r, r);
51   float32x4_t p, q, poly;
52   p = vfmaq_f32 (C (1), C (0), r);
53   q = vfmaq_f32 (C (3), C (2), r);
54   q = vfmaq_f32 (q, p, r2);
55   p = vmulq_f32 (C (4), r);
56   poly = vfmaq_f32 (p, q, r2);
57   return vfmaq_f32 (scale, poly, scale);
58 }
59 
60 #endif // PL_MATH_V_EXPF_INLINE_H
61