/* * R : A Computer Language for Statistical Data Analysis * Copyright (C) 2000--2015 The R Core Team * * This program is free software; you can redistribute it and/or modify * it under the terms of the GNU General Public License as published by * the Free Software Foundation; either version 2 of the License, or * (at your option) any later version. * * This program is distributed in the hope that it will be useful, * but WITHOUT ANY WARRANTY; without even the implied warranty of * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the * GNU General Public License for more details. * * You should have received a copy of the GNU General Public License * along with this program; if not, a copy is available at * https://www.R-project.org/Licenses/ */ /* Utilities for `dpq' handling (density/probability/quantile) */ /* give_log in "d"; log_p in "p" & "q" : */ #define give_log log_p /* "DEFAULT" */ /* --------- */ #define R_D__0 (log_p ? ML_NEGINF : 0.) /* 0 */ #define R_D__1 (log_p ? 0. : 1.) /* 1 */ #define R_DT_0 (lower_tail ? R_D__0 : R_D__1) /* 0 */ #define R_DT_1 (lower_tail ? R_D__1 : R_D__0) /* 1 */ #define R_D_half (log_p ? -M_LN2 : 0.5) // 1/2 (lower- or upper tail) /* Use 0.5 - p + 0.5 to perhaps gain 1 bit of accuracy */ #define R_D_Lval(p) (lower_tail ? (p) : (0.5 - (p) + 0.5)) /* p */ #define R_D_Cval(p) (lower_tail ? (0.5 - (p) + 0.5) : (p)) /* 1 - p */ #define R_D_val(x) (log_p ? log(x) : (x)) /* x in pF(x,..) */ #define R_D_qIv(p) (log_p ? exp(p) : (p)) /* p in qF(p,..) */ #define R_D_exp(x) (log_p ? (x) : exp(x)) /* exp(x) */ #define R_D_log(p) (log_p ? (p) : log(p)) /* log(p) */ #define R_D_Clog(p) (log_p ? log1p(-(p)) : (0.5 - (p) + 0.5)) /* [log](1-p) */ // log(1 - exp(x)) in more stable form than log1p(- R_D_qIv(x)) : #define R_Log1_Exp(x) ((x) > -M_LN2 ? log(-expm1(x)) : log1p(-exp(x))) /* log(1-exp(x)): R_D_LExp(x) == (log1p(- R_D_qIv(x))) but even more stable:*/ #define R_D_LExp(x) (log_p ? R_Log1_Exp(x) : log1p(-x)) #define R_DT_val(x) (lower_tail ? R_D_val(x) : R_D_Clog(x)) #define R_DT_Cval(x) (lower_tail ? R_D_Clog(x) : R_D_val(x)) /*#define R_DT_qIv(p) R_D_Lval(R_D_qIv(p)) * p in qF ! */ #define R_DT_qIv(p) (log_p ? (lower_tail ? exp(p) : - expm1(p)) \ : R_D_Lval(p)) /*#define R_DT_CIv(p) R_D_Cval(R_D_qIv(p)) * 1 - p in qF */ #define R_DT_CIv(p) (log_p ? (lower_tail ? -expm1(p) : exp(p)) \ : R_D_Cval(p)) #define R_DT_exp(x) R_D_exp(R_D_Lval(x)) /* exp(x) */ #define R_DT_Cexp(x) R_D_exp(R_D_Cval(x)) /* exp(1 - x) */ #define R_DT_log(p) (lower_tail? R_D_log(p) : R_D_LExp(p))/* log(p) in qF */ #define R_DT_Clog(p) (lower_tail? R_D_LExp(p): R_D_log(p))/* log(1-p) in qF*/ #define R_DT_Log(p) (lower_tail? (p) : R_Log1_Exp(p)) // == R_DT_log when we already "know" log_p == TRUE #define R_Q_P01_check(p) \ if ((log_p && p > 0) || \ (!log_p && (p < 0 || p > 1)) ) \ ML_WARN_return_NAN /* Do the boundaries exactly for q*() functions : * Often _LEFT_ = ML_NEGINF , and very often _RIGHT_ = ML_POSINF; * * R_Q_P01_boundaries(p, _LEFT_, _RIGHT_) :<==> * * R_Q_P01_check(p); * if (p == R_DT_0) return _LEFT_ ; * if (p == R_DT_1) return _RIGHT_; * * the following implementation should be more efficient (less tests): */ #define R_Q_P01_boundaries(p, _LEFT_, _RIGHT_) \ if (log_p) { \ if(p > 0) \ ML_WARN_return_NAN; \ if(p == 0) /* upper bound*/ \ return lower_tail ? _RIGHT_ : _LEFT_; \ if(p == ML_NEGINF) \ return lower_tail ? _LEFT_ : _RIGHT_; \ } \ else { /* !log_p */ \ if(p < 0 || p > 1) \ ML_WARN_return_NAN; \ if(p == 0) \ return lower_tail ? _LEFT_ : _RIGHT_; \ if(p == 1) \ return lower_tail ? _RIGHT_ : _LEFT_; \ } #define R_P_bounds_01(x, x_min, x_max) \ if(x <= x_min) return R_DT_0; \ if(x >= x_max) return R_DT_1 /* is typically not quite optimal for (-Inf,Inf) where * you'd rather have */ #define R_P_bounds_Inf_01(x) \ if(!R_FINITE(x)) { \ if (x > 0) return R_DT_1; \ /* x < 0 */return R_DT_0; \ } /* additions for density functions (C.Loader) */ #define R_D_fexp(f,x) (give_log ? -0.5*log(f)+(x) : exp(x)/sqrt(f)) /* [neg]ative or [non int]eger : */ #define R_D_negInonint(x) (x < 0. || R_nonint(x)) // for discrete d(x, ...) : #define R_D_nonint_check(x) \ if(R_nonint(x)) { \ MATHLIB_WARNING(_("non-integer x = %f"), x); \ return R_D__0; \ }