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/** R : A Computer Language for Statistical Data Analysis* Copyright (C) 1995, 1996 Robert Gentleman and Ross Ihaka* Copyright (C) 1997--2014 The R Core Team.* Copyright (C) 2003--2011 The R Foundation** 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* http://www.r-project.org/Licenses/*** Object Formatting** See ./paste.c for do_paste() , do_format() and do_formatinfo() and* ./util.c for do_formatC()* See ./printutils.c for general remarks on Printing and the Encode.. utils.* See ./print.c for do_printdefault, do_prmatrix, etc.** Exports* formatString* formatLogical* formatInteger* formatReal* formatComplex** These formatFOO() functions determine the proper width, digits, etc.*/#ifdef HAVE_CONFIG_H#include <config.h>#endif#include <Defn.h>#include <float.h> /* for DBL_EPSILON */#include <Rmath.h>#include <Print.h>/* this is just for conformity with other types */attribute_hiddenvoid formatRaw(Rbyte *x, R_xlen_t n, int *fieldwidth){*fieldwidth = 2;}attribute_hiddenvoid formatString(SEXP *x, R_xlen_t n, int *fieldwidth, int quote){int xmax = 0;int l;for (R_xlen_t i = 0; i < n; i++) {if (IS_NA_STRING(x[i])) {l = quote ? R_print.na_width : R_print.na_width_noquote;} else l = Rstrlen(x[i], quote) + (quote ? 2 : 0);if (l > xmax) xmax = l;}*fieldwidth = xmax;}void formatLogical(int *x, R_xlen_t n, int *fieldwidth){*fieldwidth = 1;for(R_xlen_t i = 0 ; i < n; i++) {if (x[i] == NA_LOGICAL) {if(*fieldwidth < R_print.na_width)*fieldwidth = R_print.na_width;} else if (x[i] != 0 && *fieldwidth < 4) {*fieldwidth = 4;} else if (x[i] == 0 && *fieldwidth < 5 ) {*fieldwidth = 5;break;/* this is the widest it can be, so stop */}}}void formatInteger(int *x, R_xlen_t n, int *fieldwidth){int xmin = INT_MAX, xmax = INT_MIN, naflag = 0;int l;for (R_xlen_t i = 0; i < n; i++) {if (x[i] == NA_INTEGER)naflag = 1;else {if (x[i] < xmin) xmin = x[i];if (x[i] > xmax) xmax = x[i];}}if (naflag) *fieldwidth = R_print.na_width;else *fieldwidth = 1;if (xmin < 0) {l = IndexWidth(-xmin) + 1; /* +1 for sign */if (l > *fieldwidth) *fieldwidth = l;}if (xmax > 0) {l = IndexWidth(xmax);if (l > *fieldwidth) *fieldwidth = l;}}/*---------------------------------------------------------------------------* scientific format determination for real numbers.* This is time-critical code. It is worth optimizing.** nsig digits altogether* kpower+1 digits to the left of "."* kpower+1+sgn including sign** Using GLOBAL R_print.digits -- had #define MAXDIG R_print.digits*//* long double is C99, so should always be defined but may be slow */#if defined(HAVE_LONG_DOUBLE) && (SIZEOF_LONG_DOUBLE > SIZEOF_DOUBLE)# ifdef HAVE_NEARBYINTL# define R_nearbyintl nearbyintl/* Cygwin had rintl but not nearbyintl */# elif defined(HAVE_RINTL)# define R_nearbyintl rintl# else# define R_nearbyintl private_nearbyintlLDOUBLE private_nearbyintl(LDOUBLE x){LDOUBLE x1;x1 = - floorl(-x + 0.5);x = floorl(x + 0.5);if (x == x1) return(x);else {/* FIXME: we should really test for floorl, also C99.But FreeBSD 7.x does have it, but not nearbyintl */if (x/2.0 == floorl(x/2.0)) return(x); else return(x1);}}# endif# else /* no long double */# ifdef HAVE_NEARBYINT# define R_nearbyint nearbyint# elif defined(HAVE_RINT)# define R_nearbyint rint# else# define R_nearbyint private_rint# include "nmath2.h" // for private_rint# endif#endif#define NB 1000static void format_via_sprintf(double r, int d, int *kpower, int *nsig){static char buff[NB];int i;snprintf(buff, NB, "%#.*e", d - 1, r);*kpower = (int) strtol(buff + (d + 2), NULL, 10);for (i = d; i >= 2; i--)if (buff[i] != '0') break;*nsig = i;}#if defined(HAVE_LONG_DOUBLE) && (SIZEOF_LONG_DOUBLE > SIZEOF_DOUBLE)static const long double tbl[] ={/* Powers exactly representable with 64 bit mantissa (except the first, which is only used with digits=0) */1e-1,1e00, 1e01, 1e02, 1e03, 1e04, 1e05, 1e06, 1e07, 1e08, 1e09,1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19,1e20, 1e21, 1e22, 1e23, 1e24, 1e25, 1e26, 1e27};#define KP_MAX 27#elsestatic const double tbl[] ={1e-1,1e00, 1e01, 1e02, 1e03, 1e04, 1e05, 1e06, 1e07, 1e08, 1e09,1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19,1e20, 1e21, 1e22};#define KP_MAX 22#endifstatic voidscientific(double *x, int *sgn, int *kpower, int *nsig, int *roundingwidens){/* for a number x , determine* sgn = 1_{x < 0} {0/1}* kpower = Exponent of 10;* nsig = min(R_print.digits, #{significant digits of alpha})* roundingwidens = 1 if rounding causes x to increase in width, 0 otherwise** where |x| = alpha * 10^kpower and 1 <= alpha < 10*/register double alpha;register double r;register int kp;int j;if (*x == 0.0) {*kpower = 0;*nsig = 1;*sgn = 0;*roundingwidens = 0;} else {if(*x < 0.0) {*sgn = 1; r = -*x;} else {*sgn = 0; r = *x;}if (R_print.digits >= DBL_DIG + 1) {format_via_sprintf(r, R_print.digits, kpower, nsig);*roundingwidens = 0;return;}kp = (int) floor(log10(r)) - R_print.digits + 1;/* r = |x|; 10^(kp + digits - 1) <= r */#if defined(HAVE_LONG_DOUBLE) && (SIZEOF_LONG_DOUBLE > SIZEOF_DOUBLE)long double r_prec = r;/* use exact scaling factor in long double precision, if possible */if (abs(kp) <= 27) {if (kp > 0) r_prec /= tbl[kp+1]; else if (kp < 0) r_prec *= tbl[ -kp+1];}#ifdef HAVE_POWLelser_prec /= powl(10.0, (long double) kp);#elseelse if (kp <= R_dec_min_exponent)r_prec = (r_prec * 1e+303)/Rexp10((double)(kp+303));elser_prec /= Rexp10((double) kp);#endifif (r_prec < tbl[R_print.digits]) {r_prec *= 10.0;kp--;}/* round alpha to integer, 10^(digits-1) <= alpha <= 10^digitsaccuracy limited by double rounding problem,alpha already rounded to 64 bits */alpha = (double) R_nearbyintl(r_prec);#elsedouble r_prec = r;/* use exact scaling factor in double precision, if possible */if (abs(kp) <= 22) {if (kp >= 0) r_prec /= tbl[kp+1]; else r_prec *= tbl[ -kp+1];}/* on IEEE 1e-308 is not representable except by gradual underflow.Shifting by 303 allows for any potential denormalized numbers x,and makes the reasonable assumption that R_dec_min_exponent+303is in range. Representation of 1e+303 has low error.*/else if (kp <= R_dec_min_exponent)r_prec = (r_prec * 1e+303)/Rexp10((double)(kp+303));elser_prec /= Rexp10((double)kp);if (r_prec < tbl[R_print.digits]) {r_prec *= 10.0;kp--;}/* round alpha to integer, 10^(digits-1) <= alpha <= 10^digits *//* accuracy limited by double rounding problem,alpha already rounded to 53 bits */alpha = R_nearbyint(r_prec);#endif*nsig = R_print.digits;for (j = 1; j <= R_print.digits; j++) {alpha /= 10.0;if (alpha == floor(alpha)) {(*nsig)--;} else {break;}}if (*nsig == 0 && R_print.digits > 0) {*nsig = 1;kp += 1;}*kpower = kp + R_print.digits - 1;/* Scientific format may do more rounding than fixed format, e.g.9996 with 3 digits is 1e+04 in scientific, but 9996 in fixed.This happens when the true value r is less than 10^(kpower+1)and would not round up to it in fixed format.Here rgt is the decimal place that will be cut off by rounding */int rgt = R_print.digits - *kpower;/* bound rgt by 0 and KP_MAX */rgt = rgt < 0 ? 0 : rgt > KP_MAX ? KP_MAX : rgt;double fuzz = 0.5/(double)tbl[1 + rgt];// kpower can be bigger than the table.*roundingwidens = *kpower > 0 && *kpower <= KP_MAX && r < tbl[*kpower + 1] - fuzz;}}/*The return values arew : the required field widthd : use %w.df in fixed format, %#w.de in scientific formate : use scientific format if != 0, value is number of exp digits - 1nsmall specifies the minimum number of decimal digits in fixed format:it is 0 except when called from do_format.*/void formatReal(double *x, R_xlen_t n, int *w, int *d, int *e, int nsmall){int left, right, sleft;int mnl, mxl, rgt, mxsl, mxns, wF;int neg, sgn, kpower, nsig, roundingwidens;int naflag, nanflag, posinf, neginf;nanflag = 0;naflag = 0;posinf = 0;neginf = 0;neg = 0;rgt = mxl = mxsl = mxns = INT_MIN;mnl = INT_MAX;for (R_xlen_t i = 0; i < n; i++) {if (!R_FINITE(x[i])) {if(ISNA(x[i])) naflag = 1;else if(ISNAN(x[i])) nanflag = 1;else if(x[i] > 0) posinf = 1;else neginf = 1;} else {scientific(&x[i], &sgn, &kpower, &nsig, &roundingwidens);left = kpower + 1;if (roundingwidens) left--;sleft = sgn + ((left <= 0) ? 1 : left); /* >= 1 */right = nsig - left; /* #{digits} right of '.' ( > 0 often)*/if (sgn) neg = 1; /* if any < 0, need extra space for sign *//* Infinite precision "F" Format : */if (right > rgt) rgt = right; /* max digits to right of . */if (left > mxl) mxl = left; /* max digits to left of . */if (left < mnl) mnl = left; /* min digits to left of . */if (sleft> mxsl) mxsl = sleft; /* max left including sign(s)*/if (nsig > mxns) mxns = nsig; /* max sig digits */}}/* F Format: use "F" format WHENEVER we use not more space than 'E'* and still satisfy 'R_print.digits' {but as if nsmall==0 !}** E Format has the form [S]X[.XXX]E+XX[X]** This is indicated by setting *e to non-zero (usually 1)* If the additional exponent digit is required *e is set to 2*//*-- These 'mxsl' & 'rgt' are used in F Format* AND in the ____ if(.) "F" else "E" ___ below: */if (R_print.digits == 0) rgt = 0;if (mxl < 0) mxsl = 1 + neg; /* we use %#w.dg, so have leading zero *//* use nsmall only *after* comparing "F" vs "E": */if (rgt < 0) rgt = 0;wF = mxsl + rgt + (rgt != 0); /* width for F format *//*-- 'see' how "E" Exponential format would be like : */*e = (mxl > 100 || mnl <= -99) ? 2 /* 3 digit exponent */ : 1;if (mxns != INT_MIN) {*d = mxns - 1;*w = neg + (*d > 0) + *d + 4 + *e; /* width for E format */if (wF <= *w + R_print.scipen) { /* Fixpoint if it needs less space */*e = 0;if (nsmall > rgt) {rgt = nsmall;wF = mxsl + rgt + (rgt != 0);}*d = rgt;*w = wF;} /* else : "E" Exponential format -- all done above */}else { /* when all x[i] are non-finite */*w = 0;/* to be increased */*d = 0;*e = 0;}if (naflag && *w < R_print.na_width)*w = R_print.na_width;if (nanflag && *w < 3) *w = 3;if (posinf && *w < 3) *w = 3;if (neginf && *w < 4) *w = 4;}/* As from 2.2.0 the number of digits applies to real and imaginary partstogether, not separately */void z_prec_r(Rcomplex *r, Rcomplex *x, double digits);void formatComplex(Rcomplex *x, R_xlen_t n, int *wr, int *dr, int *er,int *wi, int *di, int *ei, int nsmall){/* format.info() or x[1..l] for both Re & Im */int left, right, sleft;int rt, mnl, mxl, mxsl, mxns, wF, i_wF;int i_rt, i_mnl, i_mxl, i_mxsl, i_mxns;int neg, sgn;int kpower, nsig, roundingwidens;int naflag;int rnanflag, rposinf, rneginf, inanflag, iposinf;Rcomplex tmp;Rboolean all_re_zero = TRUE, all_im_zero = TRUE;naflag = 0;rnanflag = 0;rposinf = 0;rneginf = 0;inanflag = 0;iposinf = 0;neg = 0;rt = mxl = mxsl = mxns = INT_MIN;i_rt= i_mxl= i_mxsl= i_mxns= INT_MIN;i_mnl = mnl = INT_MAX;for (R_xlen_t i = 0; i < n; i++) {/* Now round */z_prec_r(&tmp, &(x[i]), R_print.digits);if(ISNA(tmp.r) || ISNA(tmp.i)) {naflag = 1;} else {/* real part */if(!R_FINITE(tmp.r)) {if (ISNAN(tmp.r)) rnanflag = 1;else if (tmp.r > 0) rposinf = 1;else rneginf = 1;} else {if(x[i].r != 0) all_re_zero = FALSE;scientific(&(tmp.r), &sgn, &kpower, &nsig, &roundingwidens);left = kpower + 1;if (roundingwidens) left--;sleft = sgn + ((left <= 0) ? 1 : left); /* >= 1 */right = nsig - left; /* #{digits} right of '.' ( > 0 often)*/if (sgn) neg = 1; /* if any < 0, need extra space for sign */if (right > rt) rt = right; /* max digits to right of . */if (left > mxl) mxl = left; /* max digits to left of . */if (left < mnl) mnl = left; /* min digits to left of . */if (sleft> mxsl) mxsl = sleft; /* max left including sign(s) */if (nsig > mxns) mxns = nsig; /* max sig digits */}/* imaginary part *//* this is always unsigned *//* we explicitly put the sign in when we print */if(!R_FINITE(tmp.i)) {if (ISNAN(tmp.i)) inanflag = 1;else iposinf = 1;} else {if(x[i].i != 0) all_im_zero = FALSE;scientific(&(tmp.i), &sgn, &kpower, &nsig, &roundingwidens);left = kpower + 1;if (roundingwidens) left--;sleft = ((left <= 0) ? 1 : left);right = nsig - left;if (right > i_rt) i_rt = right;if (left > i_mxl) i_mxl = left;if (left < i_mnl) i_mnl = left;if (sleft> i_mxsl) i_mxsl = sleft;if (nsig > i_mxns) i_mxns = nsig;}/* done: ; */}}/* see comments in formatReal() for details on this *//* overall format for real part */if (R_print.digits == 0) rt = 0;if (mxl != INT_MIN) {if (mxl < 0) mxsl = 1 + neg;if (rt < 0) rt = 0;wF = mxsl + rt + (rt != 0);*er = (mxl > 100 || mnl < -99) ? 2 : 1;*dr = mxns - 1;*wr = neg + (*dr > 0) + *dr + 4 + *er;} else {*er = 0;*wr = 0;*dr = 0;wF = 0;}/* overall format for imaginary part */if (R_print.digits == 0) i_rt = 0;if (i_mxl != INT_MIN) {if (i_mxl < 0) i_mxsl = 1;if (i_rt < 0) i_rt = 0;i_wF = i_mxsl + i_rt + (i_rt != 0);*ei = (i_mxl > 100 || i_mnl < -99) ? 2 : 1;*di = i_mxns - 1;*wi = (*di > 0) + *di + 4 + *ei;} else {*ei = 0;*wi = 0;*di = 0;i_wF = 0;}/* Now make the fixed/scientific decision */if(all_re_zero) {*er = *dr = 0;*wr = wF;if (i_wF <= *wi + R_print.scipen) {*ei = 0;if (nsmall > i_rt) {i_rt = nsmall; i_wF = i_mxsl + i_rt + (i_rt != 0);}*di = i_rt;*wi = i_wF;}} else if(all_im_zero) {if (wF <= *wr + R_print.scipen) {*er = 0;if (nsmall > rt) {rt = nsmall; wF = mxsl + rt + (rt != 0);}*dr = rt;*wr = wF;}*ei = *di = 0;*wi = i_wF;} else if(wF + i_wF < *wr + *wi + 2*R_print.scipen) {*er = 0;if (nsmall > rt) {rt = nsmall; wF = mxsl + rt + (rt != 0);}*dr = rt;*wr = wF;*ei = 0;if (nsmall > i_rt) {i_rt = nsmall;i_wF = i_mxsl + i_rt + (i_rt != 0);}*di = i_rt;*wi = i_wF;} /* else scientific for both */if(*wr < 0) *wr = 0;if(*wi < 0) *wi = 0;/* Ensure space for Inf and NaN */if (rnanflag && *wr < 3) *wr = 3;if (rposinf && *wr < 3) *wr = 3;if (rneginf && *wr < 4) *wr = 4;if (inanflag && *wi < 3) *wi = 3;if (iposinf && *wi < 3) *wi = 3;/* finally, ensure that there is space for NA */if (naflag && *wr+*wi+2 < R_print.na_width)*wr += (R_print.na_width -(*wr + *wi + 2));}