rcl/math.lisp

   1 ;; Copyright (c) 2006-2007 Carlos Ungil
   2
   3 ;; Permission is hereby granted, free of charge, to any person obtaining
   4 ;; a copy of this software and associated documentation files (the
   5 ;; "Software"), to deal in the Software without restriction, including
   6 ;; without limitation the rights to use, copy, modify, merge, publish,
   7 ;; distribute, sublicense, and/or sell copies of the Software, and to
   8 ;; permit persons to whom the Software is furnished to do so, subject to
   9 ;; the following conditions:
  10
  11 ;; The above copyright notice and this permission notice shall be
  12 ;; included in all copies or substantial portions of the Software.
  13
  14 ;; THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
  15 ;; EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
  16 ;; MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
  17 ;; NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE
  18 ;; LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION
  19 ;; OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION
  20 ;; WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
  21
  22 (in-package :rcl)
  23
  24 ;; Rmath.h  should contain ALL headers from R's C code in `src/nmath'
  25 ;; -------  such that ``the Math library'' can be used by simply
  26 ;; #include <Rmath.h>
  27 ;; and nothing else.
  28
  29 ;; R_VERSION_STRING "2.2.1"
  30
  31 ;; See http://cran.r-project.org/doc/manuals/R-exts.html#Distribution-functions
  32
  33 (cffi:defcfun "Rf_d1mach" :double (a :int))
  34 (cffi:defcfun "Rf_i1mach" :double (a :int))
  35 #-linux
  36 (cffi:defcfun "Rf_gamma_cody" :double (a :double))
  37
  38 ;; search also for "undefined" aliens
  39
  40 ;; 6.3 Random number generation
  41
  42 ;; Random Number Generators
  43 (cffi:defcfun "norm_rand" :double)
  44 (cffi:defcfun "unif_rand" :double)
  45 (cffi:defcfun "exp_rand" :double)
  46
  47 ;;(cffi:defcfun "set_seed" :void (a :int) (b :int))
  48 ;;(cffi:defcfun "get_seed" :void (a :pointer) (b :pointer))
  49
  50 ;; 6.7.2 Mathematical functions
  51
  52 ;; Gamma and Related Functions
  53 (cffi:defcfun "Rf_gammafn" :double (x :double))
  54 (cffi:defcfun "Rf_lgammafn" :double (x :double))
  55 (cffi:defcfun "Rf_digamma" :double (x :double))
  56 (cffi:defcfun "Rf_trigamma" :double (x :double))
  57 (cffi:defcfun "Rf_tetragamma" :double (x :double))
  58 (cffi:defcfun "Rf_pentagamma" :double (x :double))
  59 (cffi:defcfun "Rf_psigamma" :double (x :double) (deriv :double))
  60 ;; The Gamma function, its natural logarithm and first four
  61 ;; derivatives and the n-th derivative of Psi, the digamma function.
  62
  63 ;;; void    dpsifn(double, int, int, int, double*, int*, int*);
  64
  65 (cffi:defcfun "Rf_beta" :double (a :double) (b :double))
  66 (cffi:defcfun "Rf_lbeta" :double (a :double) (b :double))
  67 ;; The (complete) Beta function and its natural logarithm.
  68
  69 (cffi:defcfun "Rf_choose" :double (a :double) (b :double))
  70 (cffi:defcfun "Rf_lchoose" :double (a :double) (b :double))
  71 ;; The number of combinations of k items chosen from from n and its
  72 ;; natural logarithm.  n and k are rounded to the nearest integer.
  73
  74 ;; Bessel Functions
  75 (cffi:defcfun "Rf_bessel_i" :double (x :double) (nu :double) (expo :double))
  76 (cffi:defcfun "Rf_bessel_j" :double (x :double) (nu :double))
  77 (cffi:defcfun "Rf_bessel_k" :double (x :double) (nu :double) (expo :double))
  78 (cffi:defcfun "Rf_bessel_y" :double (x :double) (nu :double))
  79 ;;  Bessel functions of types I, J, K and Y with index nu. For
  80 ;;  bessel_i and bessel_k there is the option to return
  81 ;;  exp(-x) I(x; nu) or exp(x) K(x; nu) if expo is 2.
  82 ;;  (Use expo == 1 for unscaled values.)
  83
  84
  85 ;; 6.7.3 Numerical Utilities
  86
  87 ;;undefined in newer versions (post 2.1.1)
  88 ;;(cffi:defcfun "R_log" :double (x :double))
  89
  90 (cffi:defcfun "R_pow" :double (x :double) (y :double))
  91 (cffi:defcfun "R_pow_di" :double (x :double) (i :int))
  92 ;; R_pow(x, y) and R_pow_di(x, i) compute x^y and x^i, respectively
  93 ;; using R_FINITE checks and returning the proper result (the same as
  94 ;; R) for the cases where x, y or i are 0 or missing or infinite or
  95 ;; NaN.
  96
  97 (cffi:defcfun "Rf_pythag" :double (a :double) (b :double))
  98 ;; pythag(a, b) computes sqrt(a^2 + b^2) without overflow or
  99 ;; destructive underflow: for example it still works when both a and b
 100 ;; are between 1e200 and 1e300 (in IEEE double precision).
 101
 102 ;;undefined
 103 ;;(cffi:defcfun "Rlog1p" :double (x :double))
 104 ;; = log(1+x) {care for small x}
 105 ;; Computes log(1 + x) (log 1 plus x), accurately even for small x,
 106 ;; i.e., |x| << 1.
 107 ;; This may be provided by your platform, in which case it is not
 108 ;; included in Rmath.h, but is (probably) in math.h which Rmath.h
 109 ;; includes. For backwards compatibility with R versions prior to
 110 ;; 1.5.0, the entry point Rf_log1p is still provided.
 111
 112 (cffi:defcfun "Rf_log1pmx" :double (x :double))
 113 ;; Accurate log(1+x) - x, {care for small x} */
 114 ;; Computes log(1 + x) - x (log 1 plus x minus x), accurately even for
 115 ;; small x, i.e., |x| << 1.
 116
 117 (cffi:defcfun "expm1" :double (x :double))
 118 ;; = exp(x)-1 {care for small x}
 119 ;; Computes exp(x) - 1 (exp x minus 1), accurately even for small x,
 120 ;; i.e., |x| << 1.
 121 ;; This may be provided by your platform, in which case it is not
 122 ;; included in Rmath.h, but is (probably) in math.h which Rmath.h
 123 ;; includes.
 124
 125 (cffi:defcfun "Rf_lgamma1p" :double (x :double))
 126 ;; accurate log(gamma(x+1)), small x (0 < x < 0.5)
 127 ;; Computes log(gamma(x + 1)) (log(gamma(1 plus x))), accurately even
 128 ;; for small x, i.e., 0 < x < 0.5.
 129
 130 (cffi:defcfun "Rf_logspace_add" :double (logx :double) (logy :double))
 131 (cffi:defcfun "Rf_logspace_sub" :double (logx :double) (logy :double))
 132 ;; Compute the log of a sum or difference from logs of terms, i.e.,
 133 ;; “x + y” as log (exp(logx) + exp(logy)) and “x - y” as log
 134 ;; (exp(logx) - exp(logy)), without causing overflows or throwing away
 135 ;; too much accuracy.
 136
 137 (cffi:defcfun "Rf_imax2" :int (x :int) (y :int))
 138 (cffi:defcfun "Rf_imin2" :int (x :int) (y :int))
 139 (cffi:defcfun "Rf_fmax2" :double (x :double) (y :double))
 140 (cffi:defcfun "Rf_fmin2" :double (x :double) (y :double))
 141 ;;  Return the larger (max) or smaller (min) of two integer or double
 142 ;;  numbers, respectively.
 143
 144 (cffi:defcfun "Rf_sign" :double (x :double))
 145 ;;  Compute the signum function, where sign(x) is 1, 0, or -1, when x
 146 ;;  is positive, 0, or negative, respectively.
 147
 148 (cffi:defcfun "Rf_fsign" :double (x :double) (y :double))
 149 ;;  Performs "transfer of sign" and is defined as |x| * sign(y).
 150
 151 (cffi:defcfun "Rf_fprec" :double (x :double) (digits :double))
 152 ;;  Returns the value of x rounded to digits decimal digits (after the
 153 ;;  decimal point).
 154
 155 (cffi:defcfun "Rf_fround" :double (x :double) (digits :double))
 156 ;;  Returns the value of x rounded to digits significant decimal
 157 ;;  digits.
 158
 159 (cffi:defcfun "Rf_ftrunc" :double (x :double))
 160 ;;  Returns the value of x truncated (to an integer value) towards zero.
 161
 162
 163 ;; 6.7.1 Distribution functions
 164
 165 #|The routines used to calculate densities, cumulative distribution
 166 functions and quantile functions for the standard statistical
 167 distributions are available as entry points.
 168
 169 The arguments for the entry points follow the pattern of those for the
 170 normal distribution:
 171      double dnorm(double x, double mu, double sigma, int give_log);
 172      double pnorm(double x, double mu, double sigma, int lower_tail, int give_log);
 173      double qnorm(double p, double mu, double sigma, int lower_tail, int log_p);
 174      double rnorm(double mu, double sigma);
 175
 176 That is, the first argument gives the position for the density and CDF
 177 and probability for the quantile function, followed by the
 178 distribution's parameters. Argument lower_tail should be TRUE (or 1)
 179 for normal use, but can be FALSE (or 0) if the probability of the
 180 upper tail is desired or specified.
 181
 182 Finally, give_log should be non-zero if the result is required on log
 183 scale, and log_p should be non-zero if p has been specified on log
 184 scale.
 185
 186 Note that you directly get the cumulative (or “integrated”) hazard
 187 function, H(t) = - log(1 - F(t)), by using
 188  - pdist(t, ..., /*lower_tail = */ FALSE, /* give_log = */ TRUE)
 189 or shorter (and more cryptic)
 190  - pdist(t, ..., 0, 1).
 191
 192 The random-variate generation routine rnorm returns one normal
 193 variate. See Random numbers, for the protocol in using the
 194 random-variate routines. Note that these argument sequences are (apart
 195 from the names and that rnorm has no n) exactly the same as the
 196 corresponding R functions of the same name, so the documentation of
 197 the R functions can be used.
 198
 199 For reference, the following table gives the basic name (to be
 200 prefixed by `d', `p', `q' or `r' apart from the exceptions noted) and
 201 distribution-specific arguments for the complete set of distributions.
 202
 203 ...
 204
 205 Entries marked with an asterisk only have `p' and `q' functions
 206 available, and none of the non-central distributions have `r'
 207 functions. After a call to dwilcox, pwilcox or qwilcox the function
 208 wilcox_free() should be called, and similarly for the signed rank
 209 functions.
 210
 211 The argument names are not all quite the same as the R ones.
 212 |#
 213
 214 ;; Normal Distribution
 215 ;; normal       norm    mu, sigma
 216 (cffi:defcfun "Rf_dnorm4" :double (x :double) (mu :double) (sigma :double) (give-log :int))
 217 (cffi:defcfun "Rf_pnorm5" :double (x :double) (mu :double) (sigma :double) (lower-tail :int) (give-log :int))
 218 (cffi:defcfun "Rf_qnorm5" :double (p :double) (mu :double) (sigma :double) (lower-tail :int) (log-p :int))
 219 (cffi:defcfun "Rf_rnorm" :double (mu :double) (sigma :double))
 220 (cffi:defcfun "Rf_pnorm_both" :void (x :double) (cum :pointer) (ccum :pointer) (lower-tail :int) (log-p :int))
 221
 222 ;; Uniform Distribution
 223 ;; unif a, b
 224 (cffi:defcfun "Rf_dunif" :double (x :double) (a :double) (b :double) (give-log :int))
 225 (cffi:defcfun "Rf_punif" :double (x :double) (a :double) (b :double) (lower-tail :int) (give-log :int))
 226 (cffi:defcfun "Rf_qunif" :double (p :double) (a :double) (b :double) (lower-tail :int) (log-p :int))
 227 (cffi:defcfun "Rf_runif" :double (a :double) (b :double))
 228
 229 ;; Gamma Distribution
 230 ;; gamma        shape, scale
 231 (cffi:defcfun "Rf_dgamma" :double (x :double) (shape :double) (scale :double) (give-log :int))
 232 (cffi:defcfun "Rf_pgamma" :double (x :double) (shape :double) (scale :double) (lower-tail :int) (give-log :int))
 233 (cffi:defcfun "Rf_qgamma" :double (p :double) (shape :double) (scale :double) (lower-tail :int) (log-p :int))
 234 (cffi:defcfun "Rf_rgamma" :double (shape :double) (scale :double))
 235
 236 ;; Beta Distribution
 237 ;; beta a, b
 238 (cffi:defcfun "Rf_dbeta" :double (x :double) (a :double) (b :double) (give-log :int))
 239 (cffi:defcfun "Rf_pbeta" :double (x :double) (a :double) (b :double) (lower-tail :int) (give-log :int))
 240 (cffi:defcfun "Rf_qbeta" :double (p :double) (a :double) (b :double) (lower-tail :int) (log-p :int))
 241 (cffi:defcfun "Rf_rbeta" :double (a :double) (b :double))
 242 #-linux
 243 (cffi:defcfun "Rf_pbeta_raw" :double (x :double) (a :double) (b :double) (lower-tail :int))
 244
 245 ;; Lognormal Distribution
 246 ;; lnorm        logmean, logsd
 247 (cffi:defcfun "Rf_dlnorm" :double (x :double) (logmean :double) (logsd :double) (give-log :int))
 248 (cffi:defcfun "Rf_plnorm" :double (x :double) (logmean :double) (logsd :double) (lower-tail :int) (give-log :int))
 249 (cffi:defcfun "Rf_qlnorm" :double (p :double) (logmean :double) (logsd :double) (lower-tail :int) (log-p :int))
 250 (cffi:defcfun "Rf_rlnorm" :double (logmean :double) (logsd :double))
 251
 252 ;; Chi-squared Distribution
 253 ;; chisq        df
 254 (cffi:defcfun "Rf_dchisq" :double (x :double) (df :double) (give-log :int))
 255 (cffi:defcfun "Rf_pchisq" :double (x :double) (df :double) (lower-tail :int) (give-log :int))
 256 (cffi:defcfun "Rf_qchisq" :double (p :double) (df :double) (lower-tail :int) (log-p :int))
 257 (cffi:defcfun "Rf_rchisq" :double (df :double))
 258 #-linux
 259 (cffi:defcfun "Rf_qchisq_appr" :double (p :double) (df :double) (lgamma :double) (lower-tail :int) (log-p :int) (tol :double))
 260
 261 ;; Non-central Chi-squared Distribution
 262 ;; nchisq       df, lambda
 263 (cffi:defcfun "Rf_dnchisq" :double (x :double) (df :double) (lambda :double) (give-log :int))
 264 (cffi:defcfun "Rf_pnchisq" :double (x :double) (df :double) (lambda :double) (lower-tail :int) (give-log :int))
 265 (cffi:defcfun "Rf_qnchisq" :double (p :double) (df :double) (lambda :double) (lower-tail :int) (log-p :int))
 266 (cffi:defcfun "Rf_rnchisq" :double (df :double) (lambda :double))
 267
 268 ;; F Distibution
 269 ;; f    n1, n2
 270 (cffi:defcfun "Rf_df" :double (x :double) (n1 :double) (n2 :double) (give-log :int))
 271 (cffi:defcfun "Rf_pf" :double (x :double) (n1 :double) (n2 :double) (lower-tail :int) (give-log :int))
 272 (cffi:defcfun "Rf_qf" :double (p :double) (n1 :double) (n2 :double) (lower-tail :int) (log-p :int))
 273 (cffi:defcfun "Rf_rf" :double (n1 :double) (n2 :double))
 274
 275 ;; Student t Distibution
 276 ;; t    n
 277 (cffi:defcfun "Rf_dt" :double (x :double) (n :double) (give-log :int))
 278 (cffi:defcfun "Rf_pt" :double (x :double) (n :double) (lower-tail :int) (give-log :int))
 279 (cffi:defcfun "Rf_qt" :double (p :double) (n :double) (lower-tail :int) (log-p :int))
 280 (cffi:defcfun "Rf_rt" :double (n :double))
 281
 282 ;; Binomial Distribution
 283 ;; binom        n, p
 284 (cffi:defcfun "Rf_dbinom" :double (x :double) (n :double) (p :double) (give-log :int))
 285 (cffi:defcfun "Rf_pbinom" :double (x :double) (n :double) (p :double) (lower-tail :int) (give-log :int))
 286 (cffi:defcfun "Rf_qbinom" :double (p :double) (n :double) (pp :double) (lower-tail :int) (log-p :int))
 287 (cffi:defcfun "Rf_rbinom" :double (n :double) (p :double))
 288
 289 ;; Multinomial Distribution
 290
 291 ;; void rmultinom(int, double*, int, int*);
 292
 293 ;; Cauchy Distribution
 294 ;;cauchy        location, scale
 295 (cffi:defcfun "Rf_dcauchy" :double (x :double) (location :double) (scale :double) (give-log :int))
 296 (cffi:defcfun "Rf_pcauchy" :double (x :double) (location :double) (scale :double) (lower-tail :int) (give-log :int))
 297 (cffi:defcfun "Rf_qcauchy" :double (p :double) (location :double) (scale :double) (lower-tail :int) (log-p :int))
 298 (cffi:defcfun "Rf_rcauchy" :double (location :double) (scale :double))
 299
 300 ;; Exponential Distribution
 301 ;; exp  scale
 302 (cffi:defcfun "Rf_dexp" :double (x :double) (scale :double) (give-log :int))
 303 (cffi:defcfun "Rf_pexp" :double (x :double) (scale :double) (lower-tail :int) (give-log :int))
 304 (cffi:defcfun "Rf_qexp" :double (p :double) (scale :double) (lower-tail :int) (log-p :int))
 305 (cffi:defcfun "Rf_rexp" :double (scale :double))
 306
 307 ;; Geometric Distribution
 308 ;; geom p
 309 (cffi:defcfun "Rf_dgeom" :double (x :double) (p :double) (give-log :int))
 310 (cffi:defcfun "Rf_pgeom" :double (x :double) (p :double) (lower-tail :int) (give-log :int))
 311 (cffi:defcfun "Rf_qgeom" :double (p :double) (pp :double) (lower-tail :int) (log-p :int))
 312 (cffi:defcfun "Rf_rgeom" :double (p :double))
 313
 314 ;; Hypergeometric Distibution
 315 ;; hyper        NR, NB, n
 316 (cffi:defcfun "Rf_dhyper" :double (x :double) (nr :double) (nb :double) (n :double) (give-log :int))
 317 (cffi:defcfun "Rf_phyper" :double (x :double) (nr :double) (nb :double) (n :double) (lower-tail :int) (give-log :int))
 318 (cffi:defcfun "Rf_qhyper" :double (p :double) (nr :double) (nb :double) (n :double) (lower-tail :int) (log-p :int))
 319 (cffi:defcfun "Rf_rhyper" :double (nr :double) (nb :double) (n :double))
 320
 321 ;; Negative Binomial Distribution
 322 ;; nbinom       n, p
 323 (cffi:defcfun "Rf_dnbinom" :double (x :double) (n :double) (p :double) (give-log :int))
 324 (cffi:defcfun "Rf_pnbinom" :double (x :double) (n :double) (p :double) (lower-tail :int) (give-log :int))
 325 (cffi:defcfun "Rf_qnbinom" :double (p :double) (n :double) (pp :double) (lower-tail :int) (log-p :int))
 326 (cffi:defcfun "Rf_rnbinom" :double (n :double) (p :double))
 327
 328 ;; Poisson Distribution
 329 ;; pois lambda
 330 (cffi:defcfun "Rf_dpois" :double (x :double) (lambda :double) (give-log :int))
 331 (cffi:defcfun "Rf_ppois" :double (x :double) (lambda :double) (lower-tail :int) (give-log :int))
 332 (cffi:defcfun "Rf_qpois" :double (p :double) (lambda :double) (lower-tail :int) (log-p :int))
 333 (cffi:defcfun "Rf_rpois" :double (lambdax :double))
 334
 335 ;; Weibull Distribution
 336 ;; weibull      shape, scale
 337 (cffi:defcfun "Rf_dweibull" :double (x :double) (shape :double) (scale :double) (give-log :int))
 338 (cffi:defcfun "Rf_pweibull" :double (x :double) (shape :double) (scale :double) (lower-tail :int) (give-log :int))
 339 (cffi:defcfun "Rf_qweibull" :double (p :double) (shape :double) (scale :double) (lower-tail :int) (log-p :int))
 340 (cffi:defcfun "Rf_rweibull" :double (shape :double) (scale :double))
 341
 342 ;; Logistic Distribution
 343 ;; logis        location, scale
 344 (cffi:defcfun "Rf_dlogis" :double (x :double) (location :double) (scale :double) (give-log :int))
 345 (cffi:defcfun "Rf_plogis" :double (x :double) (location :double) (scale :double) (lower-tail :int) (give-log :int))
 346 (cffi:defcfun "Rf_qlogis" :double (p :double) (location :double) (scale :double) (lower-tail :int) (log-p :int))
 347 (cffi:defcfun "Rf_rlogis" :double (location :double) (scale :double))
 348
 349 ;; Non-central Beta Distribution
 350 ;; nbeta        a, b, lambda
 351 (cffi:defcfun "Rf_dnbeta" :double (x :double) (a :double) (b :double) (lambda :double) (give-log :int))
 352 (cffi:defcfun "Rf_pnbeta" :double (x :double) (a :double) (b :double) (lambda :double) (lower-tail :int) (give-log :int))
 353 ;;undefined
 354 ;;(cffi:defcfun "Rf_qnbeta" :double (p :double) (a :double) (b :double) (lambda :double) (lower-tail :int) (log-p :int))
 355 ;;(cffi:defcfun "Rf_rnbeta" :double (a :double) (b :double) (lambda :double))
 356
 357 ;; Non-central F Distribution
 358 ;; nf (*)       n1, n2, ncp
 359 (cffi:defcfun "Rf_dnf" :double (x :double) (n1 :double) (n2 :double) (ncp :double) (give-log :int))
 360 (cffi:defcfun "Rf_pnf" :double (x :double) (n1 :double) (n2 :double) (ncp :double) (lower-tail :int) (give-log :int))
 361 (cffi:defcfun "Rf_qnf" :double (p :double) (n1 :double) (n2 :double) (ncp :double) (lower-tail :int) (log-p :int))
 362
 363 ;; Non-central Student t Distribution
 364 ;; nt   df, delta
 365 (cffi:defcfun "Rf_dnt" :double (x :double) (df :double) (delta :double) (give-log :int))
 366 (cffi:defcfun "Rf_pnt" :double (x :double) (df :double) (delta :double) (lower-tail :int) (give-log :int))
 367 (cffi:defcfun "Rf_qnt" :double (p :double) (df :double) (delta :double) (lower-tail :int) (log-p :int))
 368
 369 ;; Studentized Range Distribution
 370 ;; tukey (*)    rr, cc, df
 371 (cffi:defcfun "Rf_ptukey" :double (x :double) (rr :double) (cc :double) (df :double) (lower-tail :int) (give-log :int))
 372 (cffi:defcfun "Rf_qtukey" :double (p :double) (rr :double) (cc :double) (df :double) (lower-tail :int) (log-p :int))
 373
 374 ;; Wilcoxon Rank Sum Distribution
 375 ;; wilcox       m, n
 376 (cffi:defcfun "Rf_dwilcox" :double (x :double) (m :double) (n :double) (give-log :int))
 377 (cffi:defcfun "Rf_pwilcox" :double (x :double) (m :double) (n :double) (lower-tail :int) (give-log :int))
 378 (cffi:defcfun "Rf_qwilcox" :double (p :double) (m :double) (n :double) (lower-tail :int) (log-p :int))
 379 (cffi:defcfun "Rf_rwilcox" :double (m :double) (n :double))
 380
 381 ;; Wilcoxon Signed Rank Distribution
 382 ;; signrank     n
 383 (cffi:defcfun "Rf_dsignrank" :double (x :double) (n :double) (give-log :int))
 384 (cffi:defcfun "Rf_psignrank" :double (x :double) (n :double) (lower-tail :int) (give-log :int))
 385 (cffi:defcfun "Rf_qsignrank" :double (p :double) (n :double) (lower-tail :int) (log-p :int))
 386 (cffi:defcfun "Rf_rsignrank" :double (n :double))