/* Compute gnm_log(gamma(a+1)) accurately also for small a (0 < a < 0.5). */
gnm_float lgamma1p (gnm_float a)
{
const gnm_float eulers_const = GNM_const(0.5772156649015328606065120900824024);
/* coeffs[i] holds (zeta(i+2)-1)/(i+2) , i = 1:N, N = 40 : */
const int N = 40;
static const gnm_float coeffs[40] = {
GNM_const(0.3224670334241132182362075833230126e-0),
GNM_const(0.6735230105319809513324605383715000e-1),
GNM_const(0.2058080842778454787900092413529198e-1),
GNM_const(0.7385551028673985266273097291406834e-2),
GNM_const(0.2890510330741523285752988298486755e-2),
GNM_const(0.1192753911703260977113935692828109e-2),
GNM_const(0.5096695247430424223356548135815582e-3),
GNM_const(0.2231547584535793797614188036013401e-3),
GNM_const(0.9945751278180853371459589003190170e-4),
GNM_const(0.4492623673813314170020750240635786e-4),
GNM_const(0.2050721277567069155316650397830591e-4),
GNM_const(0.9439488275268395903987425104415055e-5),
GNM_const(0.4374866789907487804181793223952411e-5),
GNM_const(0.2039215753801366236781900709670839e-5),
GNM_const(0.9551412130407419832857179772951265e-6),
GNM_const(0.4492469198764566043294290331193655e-6),
GNM_const(0.2120718480555466586923135901077628e-6),
GNM_const(0.1004322482396809960872083050053344e-6),
GNM_const(0.4769810169363980565760193417246730e-7),
GNM_const(0.2271109460894316491031998116062124e-7),
GNM_const(0.1083865921489695409107491757968159e-7),
GNM_const(0.5183475041970046655121248647057669e-8),
GNM_const(0.2483674543802478317185008663991718e-8),
GNM_const(0.1192140140586091207442548202774640e-8),
GNM_const(0.5731367241678862013330194857961011e-9),
GNM_const(0.2759522885124233145178149692816341e-9),
GNM_const(0.1330476437424448948149715720858008e-9),
GNM_const(0.6422964563838100022082448087644648e-10),
GNM_const(0.3104424774732227276239215783404066e-10),
GNM_const(0.1502138408075414217093301048780668e-10),
GNM_const(0.7275974480239079662504549924814047e-11),
GNM_const(0.3527742476575915083615072228655483e-11),
GNM_const(0.1711991790559617908601084114443031e-11),
GNM_const(0.8315385841420284819798357793954418e-12),
GNM_const(0.4042200525289440065536008957032895e-12),
GNM_const(0.1966475631096616490411045679010286e-12),
GNM_const(0.9573630387838555763782200936508615e-13),
GNM_const(0.4664076026428374224576492565974577e-13),
GNM_const(0.2273736960065972320633279596737272e-13),
GNM_const(0.1109139947083452201658320007192334e-13)
};
const gnm_float c = GNM_const(0.2273736845824652515226821577978691e-12);/* zeta(N+2)-1 */
gnm_float lgam;
int i;
if (gnm_abs (a) >= 0.5)
return gnm_lgamma (a + 1);
/* Abramowitz & Stegun 6.1.33,
* also http://functions.wolfram.com/06.11.06.0008.01 */
lgam = c * gnm_logcf (-a / 2, N + 2, 1);
for (i = N - 1; i >= 0; i--)
lgam = coeffs[i] - a * lgam;
return (a * lgam - eulers_const) * a - log1pmx (a);
} /* lgamma1p */
gnm_float stirlerr(gnm_float n)
{
#define S0 GNM_const(0.083333333333333333333) /* 1/12 */
#define S1 GNM_const(0.00277777777777777777778) /* 1/360 */
#define S2 GNM_const(0.00079365079365079365079365) /* 1/1260 */
#define S3 GNM_const(0.000595238095238095238095238) /* 1/1680 */
#define S4 GNM_const(0.0008417508417508417508417508)/* 1/1188 */
/*
error for 0, 0.5, 1.0, 1.5, ..., 14.5, 15.0.
*/
static const gnm_float sferr_halves[31] = {
0.0, /* n=0 - wrong, place holder only */
GNM_const(0.1534264097200273452913848), /* 0.5 */
GNM_const(0.0810614667953272582196702), /* 1.0 */
GNM_const(0.0548141210519176538961390), /* 1.5 */
GNM_const(0.0413406959554092940938221), /* 2.0 */
GNM_const(0.03316287351993628748511048), /* 2.5 */
GNM_const(0.02767792568499833914878929), /* 3.0 */
GNM_const(0.02374616365629749597132920), /* 3.5 */
GNM_const(0.02079067210376509311152277), /* 4.0 */
GNM_const(0.01848845053267318523077934), /* 4.5 */
GNM_const(0.01664469118982119216319487), /* 5.0 */
GNM_const(0.01513497322191737887351255), /* 5.5 */
GNM_const(0.01387612882307074799874573), /* 6.0 */
GNM_const(0.01281046524292022692424986), /* 6.5 */
GNM_const(0.01189670994589177009505572), /* 7.0 */
GNM_const(0.01110455975820691732662991), /* 7.5 */
GNM_const(0.010411265261972096497478567), /* 8.0 */
GNM_const(0.009799416126158803298389475), /* 8.5 */
GNM_const(0.009255462182712732917728637), /* 9.0 */
GNM_const(0.008768700134139385462952823), /* 9.5 */
GNM_const(0.008330563433362871256469318), /* 10.0 */
GNM_const(0.007934114564314020547248100), /* 10.5 */
GNM_const(0.007573675487951840794972024), /* 11.0 */
GNM_const(0.007244554301320383179543912), /* 11.5 */
GNM_const(0.006942840107209529865664152), /* 12.0 */
GNM_const(0.006665247032707682442354394), /* 12.5 */
GNM_const(0.006408994188004207068439631), /* 13.0 */
GNM_const(0.006171712263039457647532867), /* 13.5 */
GNM_const(0.005951370112758847735624416), /* 14.0 */
GNM_const(0.005746216513010115682023589), /* 14.5 */
GNM_const(0.005554733551962801371038690) /* 15.0 */
};
gnm_float nn;
if (n <= 15.0) {
nn = n + n;
if (nn == (int)nn) return(sferr_halves[(int)nn]);
return(lgamma1p (n ) - (n + 0.5)*gnm_log(n) + n - M_LN_SQRT_2PI);
}
nn = n*n;
if (n>500) return((S0-S1/nn)/n);
if (n> 80) return((S0-(S1-S2/nn)/nn)/n);
if (n> 35) return((S0-(S1-(S2-S3/nn)/nn)/nn)/n);
/* 15 < n <= 35 : */
return((S0-(S1-(S2-(S3-S4/nn)/nn)/nn)/nn)/n);
}
gnm_float axm2 = gnm_fmod (-x, 2.0);
gnm_float y = gnm_sinpi (axm2) / M_PIgnum;
*signp = axm2 > 1.0 ? +1 : -1;
return y == 0
? gnm_nan
: - gnm_log (gnm_abs (y)) - lgamma1p (-x);
}
}
#endif
/* ------------------------------------------------------------------------- */
static const gnm_float lanczos_g = GNM_const (808618867.0) / 134217728;
/*
* This Mathematica sniplet computes the Lanczos gamma coefficients:
*
* Dr[k_]:=DiagonalMatrix[Join[{1},Array[-Binomial[2*#-1,#]*#&,k]]]
* c[k_]:= Array[If[#1+#2==2,1/2,If[#1>=#2,(-1)^(#1+#2)*4^(#2-1)*(#1-1)*(#1+#2-3)!/(#1-#2)!/(2*#2-2)!,0]]&,{k+1,k+1}]
* Dc[k_]:=DiagonalMatrix[Array[2*(2*#-3)!!&,k+1]]
* B[k_]:=Array[If[#1==1,1,If[#1<=#2,(-1)^(#2-#1)*Binomial[#1+#2-3,#1+#1-3],0]]&,{k+1,k+1}]
* M[k_]:=(Dr[k].B[k]).(c[k].Dc[k])
* f[g_,k_]:=Array[Sqrt[2]*(E/(2*(#-1+g)+1))^(#-1/2)&,k+1]
* a[g_,k_]:=M[k].f[g,k]*Exp[g]/Sqrt[2*Pi]
*
* The result of a[g,k] will contain both positive and negative constants.
* Most people using the Lanczos series do not understand that a naive
* implemetation will suffer significant cancellation errors. The error
static gnm_float
gnm_owent (gnm_float h, gnm_float a)
{
gnm_float weight[10] = { GNM_const(0.0666713443086881375935688098933),
GNM_const(0.149451349150580593145776339658),
GNM_const(0.219086362515982043995534934228),
GNM_const(0.269266719309996355091226921569),
GNM_const(0.295524224714752870173892994651),
GNM_const(0.295524224714752870173892994651),
GNM_const(0.269266719309996355091226921569),
GNM_const(0.219086362515982043995534934228),
GNM_const(0.149451349150580593145776339658),
GNM_const(0.0666713443086881375935688098933)
};
gnm_float xtab[10] = {GNM_const(0.026093471482828279922035987916),
GNM_const(0.134936633311015489267903311577),
GNM_const(0.320590431700975593765672634885),
GNM_const(0.566604605870752809200734056834),
GNM_const(0.85112566101836878911517399887),
GNM_const(1.148874338981631210884826001130),
GNM_const(1.433395394129247190799265943166),
GNM_const(1.679409568299024406234327365115),
GNM_const(1.865063366688984510732096688423),
GNM_const(1.973906528517171720077964012084)
};
gnm_float hs, h2, as, rt;
int i;
if (fabs(h) < LIM1) return atan(a) * TWOPI_INVERSE;
if (fabs(h) > LIM2 || fabs(a) < LIM1) return 0.0;
hs = -0.5 * h * h;
h2 = a;
as = a * a;
if (log(1.0 + as) - hs * as >= LIM3)
{
gnm_float h1 = 0.5 * a;
as *= 0.25;
for (;;)
{
gnm_float rt = as + 1.0;
h2 = h1 + (hs * as + LIM3 - log(rt))
/ (2.0 * h1 * (1.0 / rt - hs));
as = h2 * h2;
if (fabs(h2 - h1) < LIM4) break;
h1 = h2;
}
}
rt = 0.0;
for (i = 0; i < 10; i++)
{
gnm_float x = 0.5 * h2 * xtab[i], tmp = 1.0 + x * x;
rt += weight[i] * gnm_exp (hs * tmp) / tmp;
}
return 0.5 * rt * h2 * TWOPI_INVERSE;
}
#include <number-match.h>
#include <parse-util.h>
#include <workbook.h>
#include <workbook-control.h>
#include <wbc-gtk.h>
#include <workbook-view.h>
#include <goal-seek.h>
#include <mathfunc.h>
#include <widgets/gnumeric-expr-entry.h>
#include <selection.h>
#include <gtk/gtk.h>
#include <math.h>
#include <string.h>
static const gnm_float max_range_val = GNM_const(1e24);
#define MAX_CELL_NAME_LEN 20
#define GOALSEEK_KEY "goal-seek-dialog"
typedef struct {
GladeXML *gui;
GtkWidget *dialog;
GnmExprEntry *set_cell_entry;
GnmExprEntry *change_cell_entry;
GtkWidget *to_value_entry;
GtkWidget *at_least_entry;
GtkWidget *at_most_entry;
GtkWidget *close_button;
GtkWidget *cancel_button;
GtkWidget *apply_button;
static GnmValue *
gnumeric_convert (GnmFuncEvalInfo *ei, GnmValue const * const *argv)
{
/* Weight and mass constants */
#define one_g_to_sg 0.00006852205001
#define one_g_to_lbm 0.002204622915
#define one_g_to_u 6.02217e+23
#define one_g_to_ozm 0.035273972
/* Distance constants */
#define one_m_to_mi (one_m_to_yd / 1760)
#define one_m_to_Nmi (1 / GNM_const (1852.0))
#define one_m_to_in (10000 / GNM_const (254.0))
#define one_m_to_ft (one_m_to_in / 12)
#define one_m_to_yd (one_m_to_ft / 3)
#define one_m_to_ang GNM_const (1e10)
#define one_m_to_pica 236.2204724409449
#define one_m_to_Pica one_m_to_pica * 12
/* Time constants */
#define one_yr_to_day 365.25
#define one_yr_to_hr (24 * one_yr_to_day)
#define one_yr_to_mn (60 * one_yr_to_hr)
#define one_yr_to_sec (60 * one_yr_to_mn)
/* Pressure constants */
#define one_Pa_to_atm 0.9869233e-5
#define one_Pa_to_mmHg 0.00750061708
/* Force constants */
#define one_N_to_dyn 100000
#define one_N_to_lbf 0.224808924
/* Power constants */
#define one_HP_to_W 745.701
/* Energy constants */
#define one_J_to_e 9999995.193
#define one_J_to_c 0.239006249
#define one_J_to_cal 0.238846191
#define one_J_to_eV 6.2146e+18
#define one_J_to_HPh (GNM_const (1.0) / (3600 * one_HP_to_W))
#define one_J_to_Wh (GNM_const (1.0) / 3600)
#define one_J_to_flb 23.73042222
#define one_J_to_BTU 0.000947815
/* Magnetism constants */
#define one_T_to_ga 10000
/* Temperature constants */
const gnm_float C_K_offset = GNM_const (273.15);
/* Liquid measure constants */
#define one_tsp_to_tbs (GNM_const (1.0) / 3)
#define one_tsp_to_oz (GNM_const (1.0) / 6)
#define one_tsp_to_cup (GNM_const (1.0) / 48)
#define one_tsp_to_pt (GNM_const (1.0) / 96)
#define one_tsp_to_qt (GNM_const (1.0) / 192)
#define one_tsp_to_gal (GNM_const (1.0) / 768)
#define one_tsp_to_l 0.004929994
/* Prefixes */
#define yotta GNM_const (1e+24)
#define zetta GNM_const (1e+21)
#define exa GNM_const (1e+18)
#define peta GNM_const (1e+15)
#define tera GNM_const (1e+12)
#define giga GNM_const (1e+09)
#define mega GNM_const (1e+06)
#define kilo GNM_const (1e+03)
#define hecto GNM_const (1e+02)
#define deka GNM_const (1e+01)
#define deci GNM_const (1e-01)
#define centi GNM_const (1e-02)
#define milli GNM_const (1e-03)
#define micro GNM_const (1e-06)
#define nano GNM_const (1e-09)
#define pico GNM_const (1e-12)
#define femto GNM_const (1e-15)
#define atto GNM_const (1e-18)
#define zepto GNM_const (1e-21)
#define yocto GNM_const (1e-24)
static const eng_convert_unit_t weight_units[] = {
{ "g", 1.0 },
{ "sg", one_g_to_sg },
{ "lbm", one_g_to_lbm },
{ "u", one_g_to_u },
{ "ozm", one_g_to_ozm },
{ NULL, 0.0 }
};
static const eng_convert_unit_t distance_units[] = {
{ "m", 1.0 },
{ "mi", one_m_to_mi },
{ "Nmi", one_m_to_Nmi },
{ "in", one_m_to_in },
{ "ft", one_m_to_ft },
{ "yd", one_m_to_yd },
{ "ang", one_m_to_ang },
{ "Pica", one_m_to_Pica },
{ "picapt", one_m_to_Pica },
{ "pica", one_m_to_pica },
{ NULL, 0.0 }
};
static const eng_convert_unit_t time_units[] = {
{ "yr", 1.0 },
{ "day", one_yr_to_day },
{ "hr", one_yr_to_hr },
{ "mn", one_yr_to_mn },
{ "sec", one_yr_to_sec },
{ NULL, 0.0 }
};
static const eng_convert_unit_t pressure_units[] = {
{ "Pa", 1.0 },
{ "atm", one_Pa_to_atm },
{ "mmHg", one_Pa_to_mmHg },
{ NULL, 0.0 }
};
static const eng_convert_unit_t force_units[] = {
{ "N", 1.0 },
{ "dyn", one_N_to_dyn },
{ "lbf", one_N_to_lbf },
{ NULL, 0.0 }
};
static const eng_convert_unit_t energy_units[] = {
{ "J", 1.0 },
{ "e", one_J_to_e },
{ "c", one_J_to_c },
{ "cal", one_J_to_cal },
{ "eV", one_J_to_eV },
{ "HPh", one_J_to_HPh },
{ "Wh", one_J_to_Wh },
{ "flb", one_J_to_flb },
{ "BTU", one_J_to_BTU },
{ NULL, 0.0 }
};
static const eng_convert_unit_t power_units[] = {
{ "HP", 1.0 },
{ "W", one_HP_to_W },
{ NULL, 0.0 }
};
static const eng_convert_unit_t magnetism_units[] = {
{ "T", 1.0 },
{ "ga", one_T_to_ga },
{ NULL, 0.0 }
};
static const eng_convert_unit_t liquid_units[] = {
{ "tsp", 1.0 },
{ "tbs", one_tsp_to_tbs },
{ "oz", one_tsp_to_oz },
{ "cup", one_tsp_to_cup },
{ "pt", one_tsp_to_pt },
{ "qt", one_tsp_to_qt },
{ "gal", one_tsp_to_gal },
{ "l", one_tsp_to_l },
{ NULL, 0.0 }
};
static const eng_convert_unit_t prefixes[] = {
{ "Y", yotta },
{ "Z", zetta },
{ "E", exa },
{ "P", peta },
{ "T", tera },
{ "G", giga },
{ "M", mega },
{ "k", kilo },
{ "h", hecto },
{ "e", deka },
{ "d", deci },
{ "c", centi },
{ "m", milli },
{ "u", micro },
{ "n", nano },
{ "p", pico },
{ "f", femto },
{ "a", atto },
{ "z", zepto },
{ "y", yocto },
{ NULL,0.0 }
};
gnm_float n;
char const *from_unit, *to_unit;
GnmValue *v;
n = value_get_as_float (argv[0]);
from_unit = value_peek_string (argv[1]);
to_unit = value_peek_string (argv[2]);
if (strcmp (from_unit, "C") == 0 && strcmp (to_unit, "F") == 0)
return value_new_float (n * 9 / 5 + 32);
else if (strcmp (from_unit, "F") == 0 && strcmp (to_unit, "C") == 0)
return value_new_float ((n - 32) * 5 / 9);
else if (strcmp (from_unit, "F") == 0 && strcmp (to_unit, "F") == 0)
return value_new_float (n);
else if (strcmp (from_unit, "F") == 0 && strcmp (to_unit, "K") == 0)
return value_new_float ((n - 32) * 5 / 9 + C_K_offset);
else if (strcmp (from_unit, "K") == 0 && strcmp (to_unit, "F") == 0)
return value_new_float ((n - C_K_offset) * 9 / 5 + 32);
else if (strcmp (from_unit, "C") == 0 && strcmp (to_unit, "K") == 0)
return value_new_float (n + C_K_offset);
else if (strcmp (from_unit, "K") == 0 && strcmp (to_unit, "C") == 0)
return value_new_float (n - C_K_offset);
if (convert (weight_units, prefixes, from_unit, to_unit, n, &v,
ei->pos))
return v;
if (convert (distance_units, prefixes, from_unit, to_unit, n, &v,
ei->pos))
return v;
if (convert (time_units, NULL, from_unit, to_unit, n, &v,
ei->pos))
return v;
if (convert (pressure_units, prefixes, from_unit, to_unit, n, &v,
ei->pos))
return v;
if (convert (force_units, prefixes, from_unit, to_unit, n, &v,
ei->pos))
return v;
if (convert (energy_units, prefixes, from_unit, to_unit, n, &v,
ei->pos))
return v;
if (convert (power_units, prefixes, from_unit, to_unit, n, &v,
ei->pos))
return v;
if (convert (magnetism_units, prefixes, from_unit, to_unit, n, &v,
ei->pos))
return v;
if (convert (liquid_units, prefixes, from_unit, to_unit, n, &v,
ei->pos))
return v;
if (convert (magnetism_units, prefixes, from_unit, to_unit, n, &v,
ei->pos))
return v;
return value_new_error_NA (ei->pos);
}