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This commit is contained in:
Stefan Krah 2012-05-31 16:21:34 +02:00
parent 1ef17954cc
commit 9a5beece1b
1 changed files with 14 additions and 4 deletions
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18
Modules/_decimal/libmpdec/mpdecimal.c
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@ -3953,8 +3953,18 @@ _mpd_get_exp_iterations(const mpd_t *r, mpd_ssize_t p)
}
/*
* Internal function, specials have been dealt with. The result has a
* relative error of less than 0.5 * 10**(-ctx->prec).
* Internal function, specials have been dealt with. Apart from Overflow
* and Underflow, two cases must be considered for the error of the result:
*
* 1) abs(a) <= 9 * 10**(-prec-1) ==> result == 1
*
* Absolute error: abs(1 - e**x) < 10**(-prec)
* -------------------------------------------
*
* 2) abs(a) > 9 * 10**(-prec-1)
*
* Relative error: abs(result - e**x) < 0.5 * 10**(-prec) * e**x
* -------------------------------------------------------------
*
* The algorithm is from Hull&Abrham, Variable Precision Exponential Function,
* ACM Transactions on Mathematical Software, Vol. 12, No. 2, June 1986.
@ -3998,9 +4008,9 @@ _mpd_qexp(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx,
*
* MAX-EMAX+1 < log10(e^(0.1*10*t)) <= log10(e^(r*10^t)) < adjexp(e^(r*10^t))+1
*
* (2) -1 < r <= -0.1, so e^r <= e^-0.1. It t > MAX_T, underflow occurs:
* (2) -1 < r <= -0.1, so e^r <= e^-0.1. If t > MAX_T, underflow occurs:
*
* adjexp(e^(r*10^t)) <= log10(e^(r*10^t)) <= log10(e^(-0.1*10^t) < MIN-ETINY
* adjexp(e^(r*10^t)) <= log10(e^(r*10^t)) <= log10(e^(-0.1*10^t)) < MIN-ETINY
*/
#if defined(CONFIG_64)
#define MPD_EXP_MAX_T 19