1 /*
2 * Helper for single-precision routines which calculate exp(x) and do not
3 * need special-case handling
4 *
5 * Copyright (c) 2019-2024, 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;
18 float invln2_and_ln2[4];
19 };
20
21 /* maxerr: 1.45358 +0.5 ulp. */
22 #define V_EXPF_DATA \
23 { \
24 .poly = { V4 (0x1.0e4020p-7f), V4 (0x1.573e2ep-5f), V4 (0x1.555e66p-3f), \
25 V4 (0x1.fffdb6p-2f), V4 (0x1.ffffecp-1f) }, \
26 .shift = V4 (0x1.8p23f), \
27 .invln2_and_ln2 = { 0x1.715476p+0f, 0x1.62e4p-1f, 0x1.7f7d1cp-20f, 0 }, \
28 }
29
30 #define ExponentBias v_u32 (0x3f800000) /* asuint(1.0f). */
31 #define C(i) d->poly[i]
32
33 static inline float32x4_t
v_expf_inline(float32x4_t x,const struct v_expf_data * d)34 v_expf_inline (float32x4_t x, const struct v_expf_data *d)
35 {
36 /* Helper routine for calculating exp(x).
37 Copied from v_expf.c, with all special-case handling removed - the
38 calling routine should handle special values if required. */
39
40 /* exp(x) = 2^n (1 + poly(r)), with 1 + poly(r) in [1/sqrt(2),sqrt(2)]
41 x = ln2*n + r, with r in [-ln2/2, ln2/2]. */
42 float32x4_t n, r, z;
43 float32x4_t invln2_and_ln2 = vld1q_f32 (d->invln2_and_ln2);
44 z = vfmaq_laneq_f32 (d->shift, x, invln2_and_ln2, 0);
45 n = vsubq_f32 (z, d->shift);
46 r = vfmsq_laneq_f32 (x, n, invln2_and_ln2, 1);
47 r = vfmsq_laneq_f32 (r, n, invln2_and_ln2, 2);
48 uint32x4_t e = vshlq_n_u32 (vreinterpretq_u32_f32 (z), 23);
49 float32x4_t scale = vreinterpretq_f32_u32 (vaddq_u32 (e, ExponentBias));
50
51 /* Custom order-4 Estrin avoids building high order monomial. */
52 float32x4_t r2 = vmulq_f32 (r, r);
53 float32x4_t p, q, poly;
54 p = vfmaq_f32 (C (1), C (0), r);
55 q = vfmaq_f32 (C (3), C (2), r);
56 q = vfmaq_f32 (q, p, r2);
57 p = vmulq_f32 (C (4), r);
58 poly = vfmaq_f32 (p, q, r2);
59 return vfmaq_f32 (scale, poly, scale);
60 }
61
62 #endif // PL_MATH_V_EXPF_INLINE_H
63