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git.ipfire.org Git - thirdparty/glibc.git/blob - sysdeps/aarch64/fpu/exp10_sve.c
1 /* Double-precision vector (SVE) exp10 function.
3 Copyright (C) 2023 Free Software Foundation, Inc.
4 This file is part of the GNU C Library.
6 The GNU C Library is free software; you can redistribute it and/or
7 modify it under the terms of the GNU Lesser General Public
8 License as published by the Free Software Foundation; either
9 version 2.1 of the License, or (at your option) any later version.
11 The GNU C Library is distributed in the hope that it will be useful,
12 but WITHOUT ANY WARRANTY; without even the implied warranty of
13 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
14 Lesser General Public License for more details.
16 You should have received a copy of the GNU Lesser General Public
17 License along with the GNU C Library; if not, see
18 <https://www.gnu.org/licenses/>. */
21 #include "poly_sve_f64.h"
23 #define SpecialBound 307.0 /* floor (log10 (2^1023)). */
25 static const struct data
28 double shift
, log10_2
, log2_10_hi
, log2_10_lo
, scale_thres
, special_bound
;
30 /* Coefficients generated using Remez algorithm.
31 rel error: 0x1.9fcb9b3p-60
32 abs error: 0x1.a20d9598p-60 in [ -log10(2)/128, log10(2)/128 ]
33 max ulp err 0.52 +0.5. */
34 .poly
= { 0x1.26bb1bbb55516p1
, 0x1.53524c73cd32ap1
, 0x1.0470591daeafbp1
,
35 0x1.2bd77b1361ef6p0
, 0x1.142b5d54e9621p
-1 },
36 /* 1.5*2^46+1023. This value is further explained below. */
37 .shift
= 0x1.800000000ffc0p
+46,
38 .log10_2
= 0x1.a934f0979a371p1
, /* 1/log2(10). */
39 .log2_10_hi
= 0x1.34413509f79ffp
-2, /* log2(10). */
40 .log2_10_lo
= -0x1.9dc1da994fd21p
-59,
41 .scale_thres
= 1280.0,
42 .special_bound
= SpecialBound
,
45 #define SpecialOffset 0x6000000000000000 /* 0x1p513. */
46 /* SpecialBias1 + SpecialBias1 = asuint(1.0). */
47 #define SpecialBias1 0x7000000000000000 /* 0x1p769. */
48 #define SpecialBias2 0x3010000000000000 /* 0x1p-254. */
50 /* Update of both special and non-special cases, if any special case is
52 static inline svfloat64_t
53 special_case (svbool_t pg
, svfloat64_t s
, svfloat64_t y
, svfloat64_t n
,
56 /* s=2^n may overflow, break it up into s=s1*s2,
57 such that exp = s + s*y can be computed as s1*(s2+s2*y)
58 and s1*s1 overflows only if n>0. */
60 /* If n<=0 then set b to 0x6, 0 otherwise. */
61 svbool_t p_sign
= svcmple (pg
, n
, 0.0); /* n <= 0. */
62 svuint64_t b
= svdup_u64_z (p_sign
, SpecialOffset
);
64 /* Set s1 to generate overflow depending on sign of exponent n. */
65 svfloat64_t s1
= svreinterpret_f64 (svsubr_x (pg
, b
, SpecialBias1
));
66 /* Offset s to avoid overflow in final result if n is below threshold. */
67 svfloat64_t s2
= svreinterpret_f64 (
68 svadd_x (pg
, svsub_x (pg
, svreinterpret_u64 (s
), SpecialBias2
), b
));
70 /* |n| > 1280 => 2^(n) overflows. */
71 svbool_t p_cmp
= svacgt (pg
, n
, d
->scale_thres
);
73 svfloat64_t r1
= svmul_x (pg
, s1
, s1
);
74 svfloat64_t r2
= svmla_x (pg
, s2
, s2
, y
);
75 svfloat64_t r0
= svmul_x (pg
, r2
, s1
);
77 return svsel (p_cmp
, r1
, r0
);
80 /* Fast vector implementation of exp10 using FEXPA instruction.
81 Maximum measured error is 1.02 ulp.
82 SV_NAME_D1 (exp10)(-0x1.2862fec805e58p+2) got 0x1.885a89551d782p-16
83 want 0x1.885a89551d781p-16. */
84 svfloat64_t
SV_NAME_D1 (exp10
) (svfloat64_t x
, svbool_t pg
)
86 const struct data
*d
= ptr_barrier (&data
);
87 svbool_t no_big_scale
= svacle (pg
, x
, d
->special_bound
);
88 svbool_t special
= svnot_z (pg
, no_big_scale
);
90 /* n = round(x/(log10(2)/N)). */
91 svfloat64_t shift
= sv_f64 (d
->shift
);
92 svfloat64_t z
= svmla_x (pg
, shift
, x
, d
->log10_2
);
93 svfloat64_t n
= svsub_x (pg
, z
, shift
);
95 /* r = x - n*log10(2)/N. */
96 svfloat64_t log2_10
= svld1rq (svptrue_b64 (), &d
->log2_10_hi
);
98 r
= svmls_lane (r
, n
, log2_10
, 0);
99 r
= svmls_lane (r
, n
, log2_10
, 1);
101 /* scale = 2^(n/N), computed using FEXPA. FEXPA does not propagate NaNs, so
102 for consistent NaN handling we have to manually propagate them. This
103 comes at significant performance cost. */
104 svuint64_t u
= svreinterpret_u64 (z
);
105 svfloat64_t scale
= svexpa (u
);
107 /* Approximate exp10(r) using polynomial. */
108 svfloat64_t r2
= svmul_x (pg
, r
, r
);
109 svfloat64_t y
= svmla_x (pg
, svmul_x (pg
, r
, d
->poly
[0]), r2
,
110 sv_pairwise_poly_3_f64_x (pg
, r
, r2
, d
->poly
+ 1));
112 /* Assemble result as exp10(x) = 2^n * exp10(r). If |x| > SpecialBound
113 multiplication may overflow, so use special case routine. */
114 if (__glibc_unlikely (svptest_any (pg
, special
)))
116 /* FEXPA zeroes the sign bit, however the sign is meaningful to the
117 special case function so needs to be copied.
118 e = sign bit of u << 46. */
119 svuint64_t e
= svand_x (pg
, svlsl_x (pg
, u
, 46), 0x8000000000000000);
120 /* Copy sign to scale. */
121 scale
= svreinterpret_f64 (svadd_x (pg
, e
, svreinterpret_u64 (scale
)));
122 return special_case (pg
, scale
, y
, n
, d
);
125 /* No special case. */
126 return svmla_x (pg
, scale
, scale
, y
);