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Last change
on this file since 573e7034 was
79492222,
checked in by krzywon, 10 years ago
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Changed the file and folder names to remove all SANS references.
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-
Property mode set to
100644
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File size:
1.6 KB
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Rev | Line | |
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[230f479] | 1 | /* expx2.c |
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| 2 | * |
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| 3 | * Exponential of squared argument |
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| 4 | * |
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| 5 | * |
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| 6 | * |
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| 7 | * SYNOPSIS: |
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| 8 | * |
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| 9 | * double x, y, expx2(); |
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| 10 | * int sign; |
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| 11 | * |
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| 12 | * y = expx2( x, sign ); |
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| 13 | * |
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| 14 | * |
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| 15 | * |
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| 16 | * DESCRIPTION: |
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| 17 | * |
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| 18 | * Computes y = exp(x*x) while suppressing error amplification |
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| 19 | * that would ordinarily arise from the inexactness of the |
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| 20 | * exponential argument x*x. |
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| 21 | * |
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| 22 | * If sign < 0, the result is inverted; i.e., y = exp(-x*x) . |
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| 23 | * |
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| 24 | * |
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| 25 | * ACCURACY: |
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| 26 | * |
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| 27 | * Relative error: |
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| 28 | * arithmetic domain # trials peak rms |
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| 29 | * IEEE -26.6, 26.6 10^7 3.9e-16 8.9e-17 |
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| 30 | * |
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| 31 | */ |
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| 32 | |
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| 33 | /* |
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| 34 | Cephes Math Library Release 2.9: June, 2000 |
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| 35 | Copyright 2000 by Stephen L. Moshier |
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| 36 | */ |
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| 37 | |
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| 38 | #include "mconf.h" |
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| 39 | |
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| 40 | #ifdef ANSIPROT |
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| 41 | extern double fabs (double); |
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| 42 | extern double floor (double); |
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| 43 | extern double exp (double); |
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| 44 | #else |
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| 45 | double fabs(); |
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| 46 | double floor(); |
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| 47 | double exp(); |
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| 48 | #endif |
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| 49 | |
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| 50 | #ifdef DEC |
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| 51 | #define M 32.0 |
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| 52 | #define MINV .03125 |
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| 53 | #else |
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| 54 | #define M 128.0 |
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| 55 | #define MINV .0078125 |
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| 56 | #endif |
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| 57 | |
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| 58 | extern double MAXLOG; |
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| 59 | extern double INFINITY; |
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| 60 | |
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| 61 | double expx2 (x, sign) |
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| 62 | double x; |
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| 63 | int sign; |
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| 64 | { |
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| 65 | double u, u1, m, f; |
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| 66 | |
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| 67 | x = fabs (x); |
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| 68 | if (sign < 0) |
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| 69 | x = -x; |
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| 70 | |
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| 71 | /* Represent x as an exact multiple of M plus a residual. |
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| 72 | M is a power of 2 chosen so that exp(m * m) does not overflow |
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| 73 | or underflow and so that |x - m| is small. */ |
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| 74 | m = MINV * floor(M * x + 0.5); |
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| 75 | f = x - m; |
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| 76 | |
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| 77 | /* x^2 = m^2 + 2mf + f^2 */ |
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| 78 | u = m * m; |
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| 79 | u1 = 2 * m * f + f * f; |
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| 80 | |
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| 81 | if (sign < 0) |
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| 82 | { |
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| 83 | u = -u; |
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| 84 | u1 = -u1; |
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| 85 | } |
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| 86 | |
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| 87 | if ((u+u1) > MAXLOG) |
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| 88 | return (INFINITY); |
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| 89 | |
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| 90 | /* u is exact, u1 is small. */ |
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| 91 | u = exp(u) * exp(u1); |
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| 92 | return(u); |
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| 93 | } |
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