[388] | 1 | /* origin: FreeBSD /usr/src/lib/msun/src/e_log10.c */
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| 2 | /*
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| 3 | * ====================================================
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| 4 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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| 5 | *
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| 6 | * Developed at SunSoft, a Sun Microsystems, Inc. business.
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| 7 | * Permission to use, copy, modify, and distribute this
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| 8 | * software is freely granted, provided that this notice
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| 9 | * is preserved.
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| 10 | * ====================================================
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| 11 | */
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| 12 | /*
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| 13 | * Return the base 10 logarithm of x. See log.c for most comments.
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| 14 | *
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| 15 | * Reduce x to 2^k (1+f) and calculate r = log(1+f) - f + f*f/2
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| 16 | * as in log.c, then combine and scale in extra precision:
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| 17 | * log10(x) = (f - f*f/2 + r)/log(10) + k*log10(2)
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| 18 | */
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| 19 |
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| 20 | #include <math.h>
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| 21 | #include <stdint.h>
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| 22 |
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| 23 | static const double
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| 24 | ivln10hi = 4.34294481878168880939e-01, /* 0x3fdbcb7b, 0x15200000 */
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| 25 | ivln10lo = 2.50829467116452752298e-11, /* 0x3dbb9438, 0xca9aadd5 */
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| 26 | log10_2hi = 3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */
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| 27 | log10_2lo = 3.69423907715893078616e-13, /* 0x3D59FEF3, 0x11F12B36 */
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| 28 | Lg1 = 6.666666666666735130e-01, /* 3FE55555 55555593 */
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| 29 | Lg2 = 3.999999999940941908e-01, /* 3FD99999 9997FA04 */
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| 30 | Lg3 = 2.857142874366239149e-01, /* 3FD24924 94229359 */
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| 31 | Lg4 = 2.222219843214978396e-01, /* 3FCC71C5 1D8E78AF */
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| 32 | Lg5 = 1.818357216161805012e-01, /* 3FC74664 96CB03DE */
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| 33 | Lg6 = 1.531383769920937332e-01, /* 3FC39A09 D078C69F */
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| 34 | Lg7 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */
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| 35 |
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| 36 | double log10(double x)
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| 37 | {
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| 38 | union {double f; uint64_t i;} u = {x};
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| 39 | double_t hfsq,f,s,z,R,w,t1,t2,dk,y,hi,lo,val_hi,val_lo;
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| 40 | uint32_t hx;
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| 41 | int k;
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| 42 |
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| 43 | hx = u.i>>32;
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| 44 | k = 0;
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| 45 | if (hx < 0x00100000 || hx>>31) {
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| 46 | if (u.i<<1 == 0)
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| 47 | return -1/(x*x); /* log(+-0)=-inf */
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| 48 | if (hx>>31)
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| 49 | return (x-x)/0.0; /* log(-#) = NaN */
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| 50 | /* subnormal number, scale x up */
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| 51 | k -= 54;
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| 52 | x *= 0x1p54;
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| 53 | u.f = x;
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| 54 | hx = u.i>>32;
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| 55 | } else if (hx >= 0x7ff00000) {
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| 56 | return x;
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| 57 | } else if (hx == 0x3ff00000 && u.i<<32 == 0)
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| 58 | return 0;
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| 59 |
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| 60 | /* reduce x into [sqrt(2)/2, sqrt(2)] */
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| 61 | hx += 0x3ff00000 - 0x3fe6a09e;
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| 62 | k += (int)(hx>>20) - 0x3ff;
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| 63 | hx = (hx&0x000fffff) + 0x3fe6a09e;
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| 64 | u.i = (uint64_t)hx<<32 | (u.i&0xffffffff);
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| 65 | x = u.f;
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| 66 |
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| 67 | f = x - 1.0;
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| 68 | hfsq = 0.5*f*f;
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| 69 | s = f/(2.0+f);
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| 70 | z = s*s;
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| 71 | w = z*z;
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| 72 | t1 = w*(Lg2+w*(Lg4+w*Lg6));
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| 73 | t2 = z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7)));
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| 74 | R = t2 + t1;
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| 75 |
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| 76 | /* See log2.c for details. */
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| 77 | /* hi+lo = f - hfsq + s*(hfsq+R) ~ log(1+f) */
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| 78 | hi = f - hfsq;
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| 79 | u.f = hi;
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| 80 | u.i &= (uint64_t)-1<<32;
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| 81 | hi = u.f;
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| 82 | lo = f - hi - hfsq + s*(hfsq+R);
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| 83 |
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| 84 | /* val_hi+val_lo ~ log10(1+f) + k*log10(2) */
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| 85 | val_hi = hi*ivln10hi;
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| 86 | dk = k;
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| 87 | y = dk*log10_2hi;
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| 88 | val_lo = dk*log10_2lo + (lo+hi)*ivln10lo + lo*ivln10hi;
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| 89 |
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| 90 | /*
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| 91 | * Extra precision in for adding y is not strictly needed
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| 92 | * since there is no very large cancellation near x = sqrt(2) or
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| 93 | * x = 1/sqrt(2), but we do it anyway since it costs little on CPUs
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| 94 | * with some parallelism and it reduces the error for many args.
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| 95 | */
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| 96 | w = y + val_hi;
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| 97 | val_lo += (y - w) + val_hi;
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| 98 | val_hi = w;
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| 99 |
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| 100 | return val_lo + val_hi;
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| 101 | }
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