1072a4ba8SAndrew Turner /*
2072a4ba8SAndrew Turner * Helper for single-precision routines which calculate exp(x) - 1 and do not
3072a4ba8SAndrew Turner * need special-case handling
4072a4ba8SAndrew Turner *
5072a4ba8SAndrew Turner * Copyright (c) 2022-2023, Arm Limited.
6072a4ba8SAndrew Turner * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
7072a4ba8SAndrew Turner */
8072a4ba8SAndrew Turner
9072a4ba8SAndrew Turner #ifndef PL_MATH_V_EXPM1F_INLINE_H
10072a4ba8SAndrew Turner #define PL_MATH_V_EXPM1F_INLINE_H
11072a4ba8SAndrew Turner
12072a4ba8SAndrew Turner #include "v_math.h"
13072a4ba8SAndrew Turner #include "math_config.h"
14*5a02ffc3SAndrew Turner #include "poly_advsimd_f32.h"
15072a4ba8SAndrew Turner
16*5a02ffc3SAndrew Turner struct v_expm1f_data
17*5a02ffc3SAndrew Turner {
18*5a02ffc3SAndrew Turner float32x4_t poly[5];
19*5a02ffc3SAndrew Turner float32x4_t invln2_and_ln2, shift;
20*5a02ffc3SAndrew Turner int32x4_t exponent_bias;
21*5a02ffc3SAndrew Turner };
22072a4ba8SAndrew Turner
23*5a02ffc3SAndrew Turner /* Coefficients generated using fpminimax with degree=5 in [-log(2)/2,
24*5a02ffc3SAndrew Turner log(2)/2]. Exponent bias is asuint(1.0f).
25*5a02ffc3SAndrew Turner invln2_and_ln2 Stores constants: invln2, ln2_lo, ln2_hi, 0. */
26*5a02ffc3SAndrew Turner #define V_EXPM1F_DATA \
27*5a02ffc3SAndrew Turner { \
28*5a02ffc3SAndrew Turner .poly = { V4 (0x1.fffffep-2), V4 (0x1.5554aep-3), V4 (0x1.555736p-5), \
29*5a02ffc3SAndrew Turner V4 (0x1.12287cp-7), V4 (0x1.6b55a2p-10) }, \
30*5a02ffc3SAndrew Turner .shift = V4 (0x1.8p23f), .exponent_bias = V4 (0x3f800000), \
31*5a02ffc3SAndrew Turner .invln2_and_ln2 = { 0x1.715476p+0f, 0x1.62e4p-1f, 0x1.7f7d1cp-20f, 0 }, \
32*5a02ffc3SAndrew Turner }
33072a4ba8SAndrew Turner
34*5a02ffc3SAndrew Turner static inline float32x4_t
expm1f_inline(float32x4_t x,const struct v_expm1f_data * d)35*5a02ffc3SAndrew Turner expm1f_inline (float32x4_t x, const struct v_expm1f_data *d)
36072a4ba8SAndrew Turner {
37072a4ba8SAndrew Turner /* Helper routine for calculating exp(x) - 1.
38072a4ba8SAndrew Turner Copied from v_expm1f_1u6.c, with all special-case handling removed - the
39072a4ba8SAndrew Turner calling routine should handle special values if required. */
40072a4ba8SAndrew Turner
41072a4ba8SAndrew Turner /* Reduce argument: f in [-ln2/2, ln2/2], i is exact. */
42*5a02ffc3SAndrew Turner float32x4_t j = vsubq_f32 (
43*5a02ffc3SAndrew Turner vfmaq_laneq_f32 (d->shift, x, d->invln2_and_ln2, 0), d->shift);
44*5a02ffc3SAndrew Turner int32x4_t i = vcvtq_s32_f32 (j);
45*5a02ffc3SAndrew Turner float32x4_t f = vfmsq_laneq_f32 (x, j, d->invln2_and_ln2, 1);
46*5a02ffc3SAndrew Turner f = vfmsq_laneq_f32 (f, j, d->invln2_and_ln2, 2);
47072a4ba8SAndrew Turner
48072a4ba8SAndrew Turner /* Approximate expm1(f) with polynomial P, expm1(f) ~= f + f^2 * P(f).
49*5a02ffc3SAndrew Turner Uses Estrin scheme, where the main _ZGVnN4v_expm1f routine uses
50*5a02ffc3SAndrew Turner Horner. */
51*5a02ffc3SAndrew Turner float32x4_t f2 = vmulq_f32 (f, f);
52*5a02ffc3SAndrew Turner float32x4_t f4 = vmulq_f32 (f2, f2);
53*5a02ffc3SAndrew Turner float32x4_t p = v_estrin_4_f32 (f, f2, f4, d->poly);
54*5a02ffc3SAndrew Turner p = vfmaq_f32 (f, f2, p);
55072a4ba8SAndrew Turner
56072a4ba8SAndrew Turner /* t = 2^i. */
57*5a02ffc3SAndrew Turner int32x4_t u = vaddq_s32 (vshlq_n_s32 (i, 23), d->exponent_bias);
58*5a02ffc3SAndrew Turner float32x4_t t = vreinterpretq_f32_s32 (u);
59072a4ba8SAndrew Turner /* expm1(x) ~= p * t + (t - 1). */
60*5a02ffc3SAndrew Turner return vfmaq_f32 (vsubq_f32 (t, v_f32 (1.0f)), p, t);
61072a4ba8SAndrew Turner }
62072a4ba8SAndrew Turner
63072a4ba8SAndrew Turner #endif // PL_MATH_V_EXPM1F_INLINE_H
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