1 /*
2 * Helper for single-precision routines which calculate exp(x) - 1 and do not
3 * need special-case handling
4 *
5 * Copyright (c) 2022-2024, Arm Limited.
6 * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
7 */
8
9 #ifndef MATH_V_EXPM1F_INLINE_H
10 #define MATH_V_EXPM1F_INLINE_H
11
12 #include "v_math.h"
13
14 struct v_expm1f_data
15 {
16 float32x4_t c0, c2;
17 int32x4_t exponent_bias;
18 float c1, c3, inv_ln2, c4;
19 float ln2_hi, ln2_lo;
20 };
21
22 /* Coefficients generated using fpminimax with degree=5 in [-log(2)/2,
23 log(2)/2]. Exponent bias is asuint(1.0f). */
24 #define V_EXPM1F_DATA \
25 { \
26 .c0 = V4 (0x1.fffffep-2), .c1 = 0x1.5554aep-3, .c2 = V4 (0x1.555736p-5), \
27 .c3 = 0x1.12287cp-7, .c4 = 0x1.6b55a2p-10, \
28 .exponent_bias = V4 (0x3f800000), .inv_ln2 = 0x1.715476p+0f, \
29 .ln2_hi = 0x1.62e4p-1f, .ln2_lo = 0x1.7f7d1cp-20f, \
30 }
31
32 static inline float32x4_t
expm1f_inline(float32x4_t x,const struct v_expm1f_data * d)33 expm1f_inline (float32x4_t x, const struct v_expm1f_data *d)
34 {
35 /* Helper routine for calculating exp(x) - 1. */
36
37 float32x2_t ln2 = vld1_f32 (&d->ln2_hi);
38 float32x4_t lane_consts = vld1q_f32 (&d->c1);
39
40 /* Reduce argument: f in [-ln2/2, ln2/2], i is exact. */
41 float32x4_t j = vrndaq_f32 (vmulq_laneq_f32 (x, lane_consts, 2));
42 int32x4_t i = vcvtq_s32_f32 (j);
43 float32x4_t f = vfmsq_lane_f32 (x, j, ln2, 0);
44 f = vfmsq_lane_f32 (f, j, ln2, 1);
45
46 /* Approximate expm1(f) with polynomial P, expm1(f) ~= f + f^2 * P(f). */
47 float32x4_t f2 = vmulq_f32 (f, f);
48 float32x4_t f4 = vmulq_f32 (f2, f2);
49 float32x4_t p01 = vfmaq_laneq_f32 (d->c0, f, lane_consts, 0);
50 float32x4_t p23 = vfmaq_laneq_f32 (d->c2, f, lane_consts, 1);
51 float32x4_t p = vfmaq_f32 (p01, f2, p23);
52 p = vfmaq_laneq_f32 (p, f4, lane_consts, 3);
53 p = vfmaq_f32 (f, f2, p);
54
55 /* t = 2^i. */
56 int32x4_t u = vaddq_s32 (vshlq_n_s32 (i, 23), d->exponent_bias);
57 float32x4_t t = vreinterpretq_f32_s32 (u);
58 /* expm1(x) ~= p * t + (t - 1). */
59 return vfmaq_f32 (vsubq_f32 (t, v_f32 (1.0f)), p, t);
60 }
61
62 #endif // MATH_V_EXPM1F_INLINE_H
63