1 | /* Single-precision log function. |
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2 | Copyright (c) 2017 ARM Ltd. All rights reserved. |
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3 | |
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4 | Redistribution and use in source and binary forms, with or without |
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5 | modification, are permitted provided that the following conditions |
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6 | are met: |
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7 | 1. Redistributions of source code must retain the above copyright |
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8 | notice, this list of conditions and the following disclaimer. |
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9 | 2. Redistributions in binary form must reproduce the above copyright |
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10 | notice, this list of conditions and the following disclaimer in the |
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11 | documentation and/or other materials provided with the distribution. |
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12 | 3. The name of the company may not be used to endorse or promote |
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13 | products derived from this software without specific prior written |
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14 | permission. |
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15 | |
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16 | THIS SOFTWARE IS PROVIDED BY ARM LTD ``AS IS AND ANY EXPRESS OR IMPLIED |
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17 | WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF |
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18 | MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. |
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19 | IN NO EVENT SHALL ARM LTD BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, |
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20 | SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED |
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21 | TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR |
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22 | PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF |
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23 | LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING |
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24 | NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS |
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25 | SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */ |
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26 | |
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27 | #include "fdlibm.h" |
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28 | #if !__OBSOLETE_MATH |
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29 | |
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30 | #include <math.h> |
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31 | #include <stdint.h> |
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32 | #include "math_config.h" |
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33 | |
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34 | /* |
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35 | LOGF_TABLE_BITS = 4 |
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36 | LOGF_POLY_ORDER = 4 |
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37 | |
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38 | ULP error: 0.818 (nearest rounding.) |
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39 | Relative error: 1.957 * 2^-26 (before rounding.) |
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40 | */ |
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41 | |
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42 | #define T __logf_data.tab |
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43 | #define A __logf_data.poly |
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44 | #define Ln2 __logf_data.ln2 |
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45 | #define N (1 << LOGF_TABLE_BITS) |
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46 | #define OFF 0x3f330000 |
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47 | |
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48 | float |
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49 | logf (float x) |
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50 | { |
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51 | /* double_t for better performance on targets with FLT_EVAL_METHOD==2. */ |
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52 | double_t z, r, r2, y, y0, invc, logc; |
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53 | uint32_t ix, iz, tmp; |
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54 | int k, i; |
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55 | |
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56 | ix = asuint (x); |
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57 | #if WANT_ROUNDING |
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58 | /* Fix sign of zero with downward rounding when x==1. */ |
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59 | if (__builtin_expect (ix == 0x3f800000, 0)) |
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60 | return 0; |
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61 | #endif |
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62 | if (__builtin_expect (ix - 0x00800000 >= 0x7f800000 - 0x00800000, 0)) |
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63 | { |
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64 | /* x < 0x1p-126 or inf or nan. */ |
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65 | if (ix * 2 == 0) |
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66 | return __math_divzerof (1); |
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67 | if (ix == 0x7f800000) /* log(inf) == inf. */ |
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68 | return x; |
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69 | if ((ix & 0x80000000) || ix * 2 >= 0xff000000) |
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70 | return __math_invalidf (x); |
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71 | /* x is subnormal, normalize it. */ |
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72 | ix = asuint (x * 0x1p23f); |
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73 | ix -= 23 << 23; |
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74 | } |
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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 >> (23 - LOGF_TABLE_BITS)) % N; |
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81 | k = (int32_t) tmp >> 23; /* arithmetic shift */ |
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82 | iz = ix - (tmp & 0x1ff << 23); |
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83 | invc = T[i].invc; |
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84 | logc = T[i].logc; |
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85 | z = (double_t) asfloat (iz); |
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86 | |
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87 | /* log(x) = log1p(z/c-1) + log(c) + k*Ln2 */ |
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88 | r = z * invc - 1; |
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89 | y0 = logc + (double_t) k * Ln2; |
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90 | |
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91 | /* Pipelined polynomial evaluation to approximate log1p(r). */ |
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92 | r2 = r * r; |
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93 | y = A[1] * r + A[2]; |
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94 | y = A[0] * r2 + y; |
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95 | y = y * r2 + (y0 + r); |
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96 | return (float) y; |
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97 | } |
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98 | #endif /* !__OBSOLETE_MATH */ |
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