1*f3087befSAndrew Turner /*
2*f3087befSAndrew Turner * Helper for single-precision routines which calculate exp(x) - 1 and do not
3*f3087befSAndrew Turner * need special-case handling
4*f3087befSAndrew Turner *
5*f3087befSAndrew Turner * Copyright (c) 2022-2024, Arm Limited.
6*f3087befSAndrew Turner * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
7*f3087befSAndrew Turner */
8*f3087befSAndrew Turner
9*f3087befSAndrew Turner #ifndef MATH_V_EXPM1F_INLINE_H
10*f3087befSAndrew Turner #define MATH_V_EXPM1F_INLINE_H
11*f3087befSAndrew Turner
12*f3087befSAndrew Turner #include "v_math.h"
13*f3087befSAndrew Turner
14*f3087befSAndrew Turner struct v_expm1f_data
15*f3087befSAndrew Turner {
16*f3087befSAndrew Turner float32x4_t c0, c2;
17*f3087befSAndrew Turner int32x4_t exponent_bias;
18*f3087befSAndrew Turner float c1, c3, inv_ln2, c4;
19*f3087befSAndrew Turner float ln2_hi, ln2_lo;
20*f3087befSAndrew Turner };
21*f3087befSAndrew Turner
22*f3087befSAndrew Turner /* Coefficients generated using fpminimax with degree=5 in [-log(2)/2,
23*f3087befSAndrew Turner log(2)/2]. Exponent bias is asuint(1.0f). */
24*f3087befSAndrew Turner #define V_EXPM1F_DATA \
25*f3087befSAndrew Turner { \
26*f3087befSAndrew Turner .c0 = V4 (0x1.fffffep-2), .c1 = 0x1.5554aep-3, .c2 = V4 (0x1.555736p-5), \
27*f3087befSAndrew Turner .c3 = 0x1.12287cp-7, .c4 = 0x1.6b55a2p-10, \
28*f3087befSAndrew Turner .exponent_bias = V4 (0x3f800000), .inv_ln2 = 0x1.715476p+0f, \
29*f3087befSAndrew Turner .ln2_hi = 0x1.62e4p-1f, .ln2_lo = 0x1.7f7d1cp-20f, \
30*f3087befSAndrew Turner }
31*f3087befSAndrew Turner
32*f3087befSAndrew Turner static inline float32x4_t
expm1f_inline(float32x4_t x,const struct v_expm1f_data * d)33*f3087befSAndrew Turner expm1f_inline (float32x4_t x, const struct v_expm1f_data *d)
34*f3087befSAndrew Turner {
35*f3087befSAndrew Turner /* Helper routine for calculating exp(x) - 1. */
36*f3087befSAndrew Turner
37*f3087befSAndrew Turner float32x2_t ln2 = vld1_f32 (&d->ln2_hi);
38*f3087befSAndrew Turner float32x4_t lane_consts = vld1q_f32 (&d->c1);
39*f3087befSAndrew Turner
40*f3087befSAndrew Turner /* Reduce argument: f in [-ln2/2, ln2/2], i is exact. */
41*f3087befSAndrew Turner float32x4_t j = vrndaq_f32 (vmulq_laneq_f32 (x, lane_consts, 2));
42*f3087befSAndrew Turner int32x4_t i = vcvtq_s32_f32 (j);
43*f3087befSAndrew Turner float32x4_t f = vfmsq_lane_f32 (x, j, ln2, 0);
44*f3087befSAndrew Turner f = vfmsq_lane_f32 (f, j, ln2, 1);
45*f3087befSAndrew Turner
46*f3087befSAndrew Turner /* Approximate expm1(f) with polynomial P, expm1(f) ~= f + f^2 * P(f). */
47*f3087befSAndrew Turner float32x4_t f2 = vmulq_f32 (f, f);
48*f3087befSAndrew Turner float32x4_t f4 = vmulq_f32 (f2, f2);
49*f3087befSAndrew Turner float32x4_t p01 = vfmaq_laneq_f32 (d->c0, f, lane_consts, 0);
50*f3087befSAndrew Turner float32x4_t p23 = vfmaq_laneq_f32 (d->c2, f, lane_consts, 1);
51*f3087befSAndrew Turner float32x4_t p = vfmaq_f32 (p01, f2, p23);
52*f3087befSAndrew Turner p = vfmaq_laneq_f32 (p, f4, lane_consts, 3);
53*f3087befSAndrew Turner p = vfmaq_f32 (f, f2, p);
54*f3087befSAndrew Turner
55*f3087befSAndrew Turner /* t = 2^i. */
56*f3087befSAndrew Turner int32x4_t u = vaddq_s32 (vshlq_n_s32 (i, 23), d->exponent_bias);
57*f3087befSAndrew Turner float32x4_t t = vreinterpretq_f32_s32 (u);
58*f3087befSAndrew Turner /* expm1(x) ~= p * t + (t - 1). */
59*f3087befSAndrew Turner return vfmaq_f32 (vsubq_f32 (t, v_f32 (1.0f)), p, t);
60*f3087befSAndrew Turner }
61*f3087befSAndrew Turner
62*f3087befSAndrew Turner #endif // MATH_V_EXPM1F_INLINE_H
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