1/*
2 * Single-precision e^x function.
3 *
4 * Copyright (c) 2017-2023, Arm Limited.
5 * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
6 */
7
8#include <math.h>
9#include <stdint.h>
10#include "math_config.h"
11
12/*
13EXPF_TABLE_BITS = 5
14EXPF_POLY_ORDER = 3
15
16ULP error: 0.502 (nearest rounding.)
17Relative error: 1.69 * 2^-34 in [-ln2/64, ln2/64] (before rounding.)
18Wrong count: 170635 (all nearest rounding wrong results with fma.)
19Non-nearest ULP error: 1 (rounded ULP error)
20*/
21
22#define N (1 << EXPF_TABLE_BITS)
23#define InvLn2N __expf_data.invln2_scaled
24#define T __expf_data.tab
25#define C __expf_data.poly_scaled
26
27static inline uint32_t
28top12 (float x)
29{
30  return asuint (x) >> 20;
31}
32
33float
34optr_aor_exp_f32 (float x)
35{
36  uint32_t abstop;
37  uint64_t ki, t;
38  /* double_t for better performance on targets with FLT_EVAL_METHOD==2.  */
39  double_t kd, xd, z, r, r2, y, s;
40
41  xd = (double_t) x;
42  abstop = top12 (x) & 0x7ff;
43  if (unlikely (abstop >= top12 (88.0f)))
44    {
45      /* |x| >= 88 or x is nan.  */
46      if (asuint (x) == asuint (-INFINITY))
47	return 0.0f;
48      if (abstop >= top12 (INFINITY))
49	return x + x;
50      if (x > 0x1.62e42ep6f) /* x > log(0x1p128) ~= 88.72 */
51	return __math_oflowf (0);
52      if (x < -0x1.9fe368p6f) /* x < log(0x1p-150) ~= -103.97 */
53	return __math_uflowf (0);
54    }
55
56  /* x*N/Ln2 = k + r with r in [-1/2, 1/2] and int k.  */
57  z = InvLn2N * xd;
58
59  /* Round and convert z to int, the result is in [-150*N, 128*N] and
60     ideally nearest int is used, otherwise the magnitude of r can be
61     bigger which gives larger approximation error.  */
62  kd = round (z);
63  ki = lround (z);
64  r = z - kd;
65
66  /* exp(x) = 2^(k/N) * 2^(r/N) ~= s * (C0*r^3 + C1*r^2 + C2*r + 1) */
67  t = T[ki % N];
68  t += ki << (52 - EXPF_TABLE_BITS);
69  s = asdouble (t);
70  z = C[0] * r + C[1];
71  r2 = r * r;
72  y = C[2] * r + 1;
73  y = z * r2 + y;
74  y = y * s;
75  return eval_as_float (y);
76}
77