1 /* 2 * R : A Computer Language for Statistical Data Analysis 3 * Copyright (C) 2000--2015 The R Core Team 4 * 5 * This program is free software; you can redistribute it and/or modify 6 * it under the terms of the GNU General Public License as published by 7 * the Free Software Foundation; either version 2 of the License, or 8 * (at your option) any later version. 9 * 10 * This program is distributed in the hope that it will be useful, 11 * but WITHOUT ANY WARRANTY; without even the implied warranty of 12 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 13 * GNU General Public License for more details. 14 * 15 * You should have received a copy of the GNU General Public License 16 * along with this program; if not, a copy is available at 17 * https://www.R-project.org/Licenses/ 18 */ 19 /* Utilities for `dpq' handling (density/probability/quantile) */ 20 21 /* give_log in "d"; log_p in "p" & "q" : */ 22 #define give_log log_p 23 /* "DEFAULT" */ 24 /* --------- */ 25 #define R_D__0 (log_p ? ML_NEGINF : 0.) /* 0 */ 26 #define R_D__1 (log_p ? 0. : 1.) /* 1 */ 27 #define R_DT_0 (lower_tail ? R_D__0 : R_D__1) /* 0 */ 28 #define R_DT_1 (lower_tail ? R_D__1 : R_D__0) /* 1 */ 29 #define R_D_half (log_p ? -M_LN2 : 0.5) // 1/2 (lower- or upper tail) 30 31 32 /* Use 0.5 - p + 0.5 to perhaps gain 1 bit of accuracy */ 33 #define R_D_Lval(p) (lower_tail ? (p) : (0.5 - (p) + 0.5)) /* p */ 34 #define R_D_Cval(p) (lower_tail ? (0.5 - (p) + 0.5) : (p)) /* 1 - p */ 35 36 #define R_D_val(x) (log_p ? log(x) : (x)) /* x in pF(x,..) */ 37 #define R_D_qIv(p) (log_p ? exp(p) : (p)) /* p in qF(p,..) */ 38 #define R_D_exp(x) (log_p ? (x) : exp(x)) /* exp(x) */ 39 #define R_D_log(p) (log_p ? (p) : log(p)) /* log(p) */ 40 #define R_D_Clog(p) (log_p ? log1p(-(p)) : (0.5 - (p) + 0.5)) /* [log](1-p) */ 41 42 // log(1 - exp(x)) in more stable form than log1p(- R_D_qIv(x)) : 43 #define R_Log1_Exp(x) ((x) > -M_LN2 ? log(-expm1(x)) : log1p(-exp(x))) 44 45 /* log(1-exp(x)): R_D_LExp(x) == (log1p(- R_D_qIv(x))) but even more stable:*/ 46 #define R_D_LExp(x) (log_p ? R_Log1_Exp(x) : log1p(-x)) 47 48 #define R_DT_val(x) (lower_tail ? R_D_val(x) : R_D_Clog(x)) 49 #define R_DT_Cval(x) (lower_tail ? R_D_Clog(x) : R_D_val(x)) 50 51 /*#define R_DT_qIv(p) R_D_Lval(R_D_qIv(p)) * p in qF ! */ 52 #define R_DT_qIv(p) (log_p ? (lower_tail ? exp(p) : - expm1(p)) \ 53 : R_D_Lval(p)) 54 55 /*#define R_DT_CIv(p) R_D_Cval(R_D_qIv(p)) * 1 - p in qF */ 56 #define R_DT_CIv(p) (log_p ? (lower_tail ? -expm1(p) : exp(p)) \ 57 : R_D_Cval(p)) 58 59 #define R_DT_exp(x) R_D_exp(R_D_Lval(x)) /* exp(x) */ 60 #define R_DT_Cexp(x) R_D_exp(R_D_Cval(x)) /* exp(1 - x) */ 61 62 #define R_DT_log(p) (lower_tail? R_D_log(p) : R_D_LExp(p))/* log(p) in qF */ 63 #define R_DT_Clog(p) (lower_tail? R_D_LExp(p): R_D_log(p))/* log(1-p) in qF*/ 64 #define R_DT_Log(p) (lower_tail? (p) : R_Log1_Exp(p)) 65 // == R_DT_log when we already "know" log_p == TRUE 66 67 68 #define R_Q_P01_check(p) \ 69 if ((log_p && p > 0) || \ 70 (!log_p && (p < 0 || p > 1)) ) \ 71 ML_WARN_return_NAN 72 73 /* Do the boundaries exactly for q*() functions : 74 * Often _LEFT_ = ML_NEGINF , and very often _RIGHT_ = ML_POSINF; 75 * 76 * R_Q_P01_boundaries(p, _LEFT_, _RIGHT_) :<==> 77 * 78 * R_Q_P01_check(p); 79 * if (p == R_DT_0) return _LEFT_ ; 80 * if (p == R_DT_1) return _RIGHT_; 81 * 82 * the following implementation should be more efficient (less tests): 83 */ 84 #define R_Q_P01_boundaries(p, _LEFT_, _RIGHT_) \ 85 if (log_p) { \ 86 if(p > 0) \ 87 ML_WARN_return_NAN; \ 88 if(p == 0) /* upper bound*/ \ 89 return lower_tail ? _RIGHT_ : _LEFT_; \ 90 if(p == ML_NEGINF) \ 91 return lower_tail ? _LEFT_ : _RIGHT_; \ 92 } \ 93 else { /* !log_p */ \ 94 if(p < 0 || p > 1) \ 95 ML_WARN_return_NAN; \ 96 if(p == 0) \ 97 return lower_tail ? _LEFT_ : _RIGHT_; \ 98 if(p == 1) \ 99 return lower_tail ? _RIGHT_ : _LEFT_; \ 100 } 101 102 #define R_P_bounds_01(x, x_min, x_max) \ 103 if(x <= x_min) return R_DT_0; \ 104 if(x >= x_max) return R_DT_1 105 /* is typically not quite optimal for (-Inf,Inf) where 106 * you'd rather have */ 107 #define R_P_bounds_Inf_01(x) \ 108 if(!R_FINITE(x)) { \ 109 if (x > 0) return R_DT_1; \ 110 /* x < 0 */return R_DT_0; \ 111 } 112 113 114 115 /* additions for density functions (C.Loader) */ 116 #define R_D_fexp(f,x) (give_log ? -0.5*log(f)+(x) : exp(x)/sqrt(f)) 117 118 /* [neg]ative or [non int]eger : */ 119 #define R_D_negInonint(x) (x < 0. || R_nonint(x)) 120 121 // for discrete d<distr>(x, ...) : 122 #define R_D_nonint_check(x) \ 123 if(R_nonint(x)) { \ 124 MATHLIB_WARNING(_("non-integer x = %f"), x); \ 125 return R_D__0; \ 126 } 127