projects / unix-history / blame
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|---|---|---|
| 9b525f39 | 1 | /* |
| e7a9c683 | 2 | * Copyright (c) 1985 Regents of the University of California. |
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3 | * All rights reserved. |
| 4 | * | |
| 5 | * Redistribution and use in source and binary forms are permitted | |
| 6 | * provided that this notice is preserved and that due credit is given | |
| 7 | * to the University of California at Berkeley. The name of the University | |
| 8 | * may not be used to endorse or promote products derived from this | |
| 9 | * software without specific prior written permission. This software | |
| 10 | * is provided ``as is'' without express or implied warranty. | |
| 11 | * | |
| 12 | * All recipients should regard themselves as participants in an ongoing | |
| 13 | * research project and hence should feel obligated to report their | |
| 14 | * experiences (good or bad) with these elementary function codes, using | |
| 15 | * the sendbug(8) program, to the authors. | |
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16 | */ |
| 17 | ||
| 18 | #ifndef lint | |
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19 | static char sccsid[] = "@(#)log__L.c 5.2 (Berkeley) %G%"; |
| 20 | #endif /* not lint */ | |
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21 | |
| 22 | /* log__L(Z) | |
| 23 | * LOG(1+X) - 2S X | |
| 24 | * RETURN --------------- WHERE Z = S*S, S = ------- , 0 <= Z <= .0294... | |
| 25 | * S 2 + X | |
| 26 | * | |
| 27 | * DOUBLE PRECISION (VAX D FORMAT 56 bits or IEEE DOUBLE 53 BITS) | |
| 28 | * KERNEL FUNCTION FOR LOG; TO BE USED IN LOG1P, LOG, AND POW FUNCTIONS | |
| 29 | * CODED IN C BY K.C. NG, 1/19/85; | |
| 30 | * REVISED BY K.C. Ng, 2/3/85, 4/16/85. | |
| 31 | * | |
| 32 | * Method : | |
| 33 | * 1. Polynomial approximation: let s = x/(2+x). | |
| 34 | * Based on log(1+x) = log(1+s) - log(1-s) | |
| 35 | * = 2s + 2/3 s**3 + 2/5 s**5 + ....., | |
| 36 | * | |
| 37 | * (log(1+x) - 2s)/s is computed by | |
| 38 | * | |
| 39 | * z*(L1 + z*(L2 + z*(... (L7 + z*L8)...))) | |
| 40 | * | |
| 41 | * where z=s*s. (See the listing below for Lk's values.) The | |
| 42 | * coefficients are obtained by a special Remez algorithm. | |
| 43 | * | |
| 44 | * Accuracy: | |
| 45 | * Assuming no rounding error, the maximum magnitude of the approximation | |
| 46 | * error (absolute) is 2**(-58.49) for IEEE double, and 2**(-63.63) | |
| 47 | * for VAX D format. | |
| 48 | * | |
| 49 | * Constants: | |
| 50 | * The hexadecimal values are the intended ones for the following constants. | |
| 51 | * The decimal values may be used, provided that the compiler will convert | |
| 52 | * from decimal to binary accurately enough to produce the hexadecimal values | |
| 53 | * shown. | |
| 54 | */ | |
| 55 | ||
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56 | #if defined(vax)||defined(tahoe) /* VAX D format (56 bits) */ |
| 57 | #ifdef vax | |
| 0e01cbea | 58 | #define _0x(A,B) 0x/**/A/**/B |
| 859dc438 | 59 | #else /* vax */ |
| 0e01cbea | 60 | #define _0x(A,B) 0x/**/B/**/A |
| 859dc438 | 61 | #endif /* vax */ |
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62 | /* static double */ |
| 63 | /* L1 = 6.6666666666666703212E-1 , Hex 2^ 0 * .AAAAAAAAAAAAC5 */ | |
| 64 | /* L2 = 3.9999999999970461961E-1 , Hex 2^ -1 * .CCCCCCCCCC2684 */ | |
| 65 | /* L3 = 2.8571428579395698188E-1 , Hex 2^ -1 * .92492492F85782 */ | |
| 66 | /* L4 = 2.2222221233634724402E-1 , Hex 2^ -2 * .E38E3839B7AF2C */ | |
| 67 | /* L5 = 1.8181879517064680057E-1 , Hex 2^ -2 * .BA2EB4CC39655E */ | |
| 68 | /* L6 = 1.5382888777946145467E-1 , Hex 2^ -2 * .9D8551E8C5781D */ | |
| 69 | /* L7 = 1.3338356561139403517E-1 , Hex 2^ -2 * .8895B3907FCD92 */ | |
| 70 | /* L8 = 1.2500000000000000000E-1 , Hex 2^ -2 * .80000000000000 */ | |
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71 | static long L1x[] = { _0x(aaaa,402a), _0x(aac5,aaaa)}; |
| 72 | static long L2x[] = { _0x(cccc,3fcc), _0x(2684,cccc)}; | |
| 73 | static long L3x[] = { _0x(4924,3f92), _0x(5782,92f8)}; | |
| 74 | static long L4x[] = { _0x(8e38,3f63), _0x(af2c,39b7)}; | |
| 75 | static long L5x[] = { _0x(2eb4,3f3a), _0x(655e,cc39)}; | |
| 76 | static long L6x[] = { _0x(8551,3f1d), _0x(781d,e8c5)}; | |
| 77 | static long L7x[] = { _0x(95b3,3f08), _0x(cd92,907f)}; | |
| 78 | static long L8x[] = { _0x(0000,3f00), _0x(0000,0000)}; | |
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79 | #define L1 (*(double*)L1x) |
| 80 | #define L2 (*(double*)L2x) | |
| 81 | #define L3 (*(double*)L3x) | |
| 82 | #define L4 (*(double*)L4x) | |
| 83 | #define L5 (*(double*)L5x) | |
| 84 | #define L6 (*(double*)L6x) | |
| 85 | #define L7 (*(double*)L7x) | |
| 86 | #define L8 (*(double*)L8x) | |
| 859dc438 | 87 | #else /* defined(vax)||defined(tahoe) */ |
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88 | static double |
| 89 | L1 = 6.6666666666667340202E-1 , /*Hex 2^ -1 * 1.5555555555592 */ | |
| 90 | L2 = 3.9999999999416702146E-1 , /*Hex 2^ -2 * 1.999999997FF24 */ | |
| 91 | L3 = 2.8571428742008753154E-1 , /*Hex 2^ -2 * 1.24924941E07B4 */ | |
| 92 | L4 = 2.2222198607186277597E-1 , /*Hex 2^ -3 * 1.C71C52150BEA6 */ | |
| 93 | L5 = 1.8183562745289935658E-1 , /*Hex 2^ -3 * 1.74663CC94342F */ | |
| 94 | L6 = 1.5314087275331442206E-1 , /*Hex 2^ -3 * 1.39A1EC014045B */ | |
| 95 | L7 = 1.4795612545334174692E-1 ; /*Hex 2^ -3 * 1.2F039F0085122 */ | |
| 859dc438 | 96 | #endif /* defined(vax)||defined(tahoe) */ |
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97 | |
| 98 | double log__L(z) | |
| 99 | double z; | |
| 100 | { | |
| 859dc438 | 101 | #if defined(vax)||defined(tahoe) |
| e7a9c683 | 102 | return(z*(L1+z*(L2+z*(L3+z*(L4+z*(L5+z*(L6+z*(L7+z*L8)))))))); |
| 859dc438 | 103 | #else /* defined(vax)||defined(tahoe) */ |
| e7a9c683 | 104 | return(z*(L1+z*(L2+z*(L3+z*(L4+z*(L5+z*(L6+z*L7))))))); |
| 859dc438 | 105 | #endif /* defined(vax)||defined(tahoe) */ |
| e7a9c683 | 106 | } |