1 /*
2 * SVE helper for single-precision routines which calculate exp(x) - 1 and do
3 * not need special-case handling
4 *
5 * Copyright (c) 2023, Arm Limited.
6 * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
7 */
8
9 #ifndef PL_MATH_SV_EXPM1F_INLINE_H
10 #define PL_MATH_SV_EXPM1F_INLINE_H
11
12 #include "sv_math.h"
13
14 struct sv_expm1f_data
15 {
16 /* These 4 are grouped together so they can be loaded as one quadword, then
17 used with _lane forms of svmla/svmls. */
18 float32_t c2, c4, ln2_hi, ln2_lo;
19 float32_t c0, c1, c3, inv_ln2, shift;
20 };
21
22 /* Coefficients generated using fpminimax. */
23 #define SV_EXPM1F_DATA \
24 { \
25 .c0 = 0x1.fffffep-2, .c1 = 0x1.5554aep-3, .c2 = 0x1.555736p-5, \
26 .c3 = 0x1.12287cp-7, .c4 = 0x1.6b55a2p-10, \
27 \
28 .shift = 0x1.8p23f, .inv_ln2 = 0x1.715476p+0f, .ln2_hi = 0x1.62e4p-1f, \
29 .ln2_lo = 0x1.7f7d1cp-20f, \
30 }
31
32 #define C(i) sv_f32 (d->c##i)
33
34 static inline svfloat32_t
expm1f_inline(svfloat32_t x,svbool_t pg,const struct sv_expm1f_data * d)35 expm1f_inline (svfloat32_t x, svbool_t pg, const struct sv_expm1f_data *d)
36 {
37 /* This vector is reliant on layout of data - it contains constants
38 that can be used with _lane forms of svmla/svmls. Values are:
39 [ coeff_2, coeff_4, ln2_hi, ln2_lo ]. */
40 svfloat32_t lane_constants = svld1rq (svptrue_b32 (), &d->c2);
41
42 /* Reduce argument to smaller range:
43 Let i = round(x / ln2)
44 and f = x - i * ln2, then f is in [-ln2/2, ln2/2].
45 exp(x) - 1 = 2^i * (expm1(f) + 1) - 1
46 where 2^i is exact because i is an integer. */
47 svfloat32_t j = svmla_x (pg, sv_f32 (d->shift), x, d->inv_ln2);
48 j = svsub_x (pg, j, d->shift);
49 svint32_t i = svcvt_s32_x (pg, j);
50
51 svfloat32_t f = svmls_lane (x, j, lane_constants, 2);
52 f = svmls_lane (f, j, lane_constants, 3);
53
54 /* Approximate expm1(f) using polynomial.
55 Taylor expansion for expm1(x) has the form:
56 x + ax^2 + bx^3 + cx^4 ....
57 So we calculate the polynomial P(f) = a + bf + cf^2 + ...
58 and assemble the approximation expm1(f) ~= f + f^2 * P(f). */
59 svfloat32_t p12 = svmla_lane (C (1), f, lane_constants, 0);
60 svfloat32_t p34 = svmla_lane (C (3), f, lane_constants, 1);
61 svfloat32_t f2 = svmul_x (pg, f, f);
62 svfloat32_t p = svmla_x (pg, p12, f2, p34);
63 p = svmla_x (pg, C (0), f, p);
64 p = svmla_x (pg, f, f2, p);
65
66 /* Assemble the result.
67 expm1(x) ~= 2^i * (p + 1) - 1
68 Let t = 2^i. */
69 svfloat32_t t = svscale_x (pg, sv_f32 (1), i);
70 return svmla_x (pg, svsub_x (pg, t, 1), p, t);
71 }
72
73 #endif // PL_MATH_SV_EXPM1F_INLINE_H