1 /*
2  * Helper for single-precision routines which calculate exp(x) - 1 and do not
3  * need special-case handling
4  *
5  * Copyright (c) 2022-2023, Arm Limited.
6  * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
7  */
8 
9 #ifndef PL_MATH_V_EXPM1F_INLINE_H
10 #define PL_MATH_V_EXPM1F_INLINE_H
11 
12 #include "v_math.h"
13 #include "math_config.h"
14 #include "poly_advsimd_f32.h"
15 
16 struct v_expm1f_data
17 {
18   float32x4_t poly[5];
19   float32x4_t invln2_and_ln2, shift;
20   int32x4_t exponent_bias;
21 };
22 
23 /* Coefficients generated using fpminimax with degree=5 in [-log(2)/2,
24    log(2)/2]. Exponent bias is asuint(1.0f).
25    invln2_and_ln2 Stores constants: invln2, ln2_lo, ln2_hi, 0.  */
26 #define V_EXPM1F_DATA                                                         \
27   {                                                                           \
28     .poly = { V4 (0x1.fffffep-2), V4 (0x1.5554aep-3), V4 (0x1.555736p-5),     \
29 	      V4 (0x1.12287cp-7), V4 (0x1.6b55a2p-10) },                      \
30     .shift = V4 (0x1.8p23f), .exponent_bias = V4 (0x3f800000),                \
31     .invln2_and_ln2 = { 0x1.715476p+0f, 0x1.62e4p-1f, 0x1.7f7d1cp-20f, 0 },   \
32   }
33 
34 static inline float32x4_t
35 expm1f_inline (float32x4_t x, const struct v_expm1f_data *d)
36 {
37   /* Helper routine for calculating exp(x) - 1.
38      Copied from v_expm1f_1u6.c, with all special-case handling removed - the
39      calling routine should handle special values if required.  */
40 
41   /* Reduce argument: f in [-ln2/2, ln2/2], i is exact.  */
42   float32x4_t j = vsubq_f32 (
43       vfmaq_laneq_f32 (d->shift, x, d->invln2_and_ln2, 0), d->shift);
44   int32x4_t i = vcvtq_s32_f32 (j);
45   float32x4_t f = vfmsq_laneq_f32 (x, j, d->invln2_and_ln2, 1);
46   f = vfmsq_laneq_f32 (f, j, d->invln2_and_ln2, 2);
47 
48   /* Approximate expm1(f) with polynomial P, expm1(f) ~= f + f^2 * P(f).
49      Uses Estrin scheme, where the main _ZGVnN4v_expm1f routine uses
50      Horner.  */
51   float32x4_t f2 = vmulq_f32 (f, f);
52   float32x4_t f4 = vmulq_f32 (f2, f2);
53   float32x4_t p = v_estrin_4_f32 (f, f2, f4, d->poly);
54   p = vfmaq_f32 (f, f2, p);
55 
56   /* t = 2^i.  */
57   int32x4_t u = vaddq_s32 (vshlq_n_s32 (i, 23), d->exponent_bias);
58   float32x4_t t = vreinterpretq_f32_s32 (u);
59   /* expm1(x) ~= p * t + (t - 1).  */
60   return vfmaq_f32 (vsubq_f32 (t, v_f32 (1.0f)), p, t);
61 }
62 
63 #endif // PL_MATH_V_EXPM1F_INLINE_H
64