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173
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1 /*
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2 * Double-precision vector log(x) function.
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3 *
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4 * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
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5 * See https://llvm.org/LICENSE.txt for license information.
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6 * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
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7 */
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8
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9 #include "mathlib.h"
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10 #include "v_math.h"
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11 #include "v_log.h"
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12 #if V_SUPPORTED
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13
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14 /* Worst-case error: 1.17 + 0.5 ulp. */
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15
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16 static const f64_t Poly[] = {
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17 /* rel error: 0x1.6272e588p-56 in [ -0x1.fc1p-9 0x1.009p-8 ]. */
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18 -0x1.ffffffffffff7p-2,
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19 0x1.55555555170d4p-2,
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20 -0x1.0000000399c27p-2,
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21 0x1.999b2e90e94cap-3,
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22 -0x1.554e550bd501ep-3,
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23 };
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24
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25 #define A0 v_f64 (Poly[0])
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26 #define A1 v_f64 (Poly[1])
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27 #define A2 v_f64 (Poly[2])
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28 #define A3 v_f64 (Poly[3])
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29 #define A4 v_f64 (Poly[4])
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30 #define Ln2 v_f64 (0x1.62e42fefa39efp-1)
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31 #define N (1 << V_LOG_TABLE_BITS)
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32 #define OFF v_u64 (0x3fe6900900000000)
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33
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34 struct entry
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35 {
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36 v_f64_t invc;
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37 v_f64_t logc;
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38 };
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39
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40 static inline struct entry
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41 lookup (v_u64_t i)
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42 {
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43 struct entry e;
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44 #ifdef SCALAR
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45 e.invc = __v_log_data[i].invc;
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46 e.logc = __v_log_data[i].logc;
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47 #else
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48 e.invc[0] = __v_log_data[i[0]].invc;
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49 e.logc[0] = __v_log_data[i[0]].logc;
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50 e.invc[1] = __v_log_data[i[1]].invc;
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51 e.logc[1] = __v_log_data[i[1]].logc;
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52 #endif
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53 return e;
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54 }
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55
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56 VPCS_ATTR
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57 __attribute__ ((noinline)) static v_f64_t
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58 specialcase (v_f64_t x, v_f64_t y, v_u64_t cmp)
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59 {
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60 return v_call_f64 (log, x, y, cmp);
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61 }
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62
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63 VPCS_ATTR
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64 v_f64_t
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65 V_NAME(log) (v_f64_t x)
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66 {
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67 v_f64_t z, r, r2, p, y, kd, hi;
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68 v_u64_t ix, iz, tmp, top, i, cmp;
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69 v_s64_t k;
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70 struct entry e;
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71
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72 ix = v_as_u64_f64 (x);
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73 top = ix >> 48;
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74 cmp = v_cond_u64 (top - v_u64 (0x0010) >= v_u64 (0x7ff0 - 0x0010));
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75
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76 /* x = 2^k z; where z is in range [OFF,2*OFF) and exact.
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77 The range is split into N subintervals.
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78 The ith subinterval contains z and c is near its center. */
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79 tmp = ix - OFF;
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80 i = (tmp >> (52 - V_LOG_TABLE_BITS)) % N;
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81 k = v_as_s64_u64 (tmp) >> 52; /* arithmetic shift */
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82 iz = ix - (tmp & v_u64 (0xfffULL << 52));
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83 z = v_as_f64_u64 (iz);
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84 e = lookup (i);
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85
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86 /* log(x) = log1p(z/c-1) + log(c) + k*Ln2. */
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87 r = v_fma_f64 (z, e.invc, v_f64 (-1.0));
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88 kd = v_to_f64_s64 (k);
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89
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90 /* hi = r + log(c) + k*Ln2. */
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91 hi = v_fma_f64 (kd, Ln2, e.logc + r);
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92 /* y = r2*(A0 + r*A1 + r2*(A2 + r*A3 + r2*A4)) + hi. */
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93 r2 = r * r;
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94 y = v_fma_f64 (A3, r, A2);
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95 p = v_fma_f64 (A1, r, A0);
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96 y = v_fma_f64 (A4, r2, y);
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97 y = v_fma_f64 (y, r2, p);
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98 y = v_fma_f64 (y, r2, hi);
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99
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100 if (unlikely (v_any_u64 (cmp)))
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101 return specialcase (x, y, cmp);
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102 return y;
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103 }
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104 VPCS_ALIAS
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105 #endif
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