File: ca.sh
   1 #!/bin/sh
   2 
   3 # The MIT License (MIT)
   4 #
   5 # Copyright (c) 2026 pacman64
   6 #
   7 # Permission is hereby granted, free of charge, to any person obtaining a copy
   8 # of this software and associated documentation files (the "Software"), to deal
   9 # in the Software without restriction, including without limitation the rights
  10 # to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
  11 # copies of the Software, and to permit persons to whom the Software is
  12 # furnished to do so, subject to the following conditions:
  13 #
  14 # The above copyright notice and this permission notice shall be included in
  15 # all copies or substantial portions of the Software.
  16 #
  17 # THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
  18 # IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
  19 # FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
  20 # AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
  21 # LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
  22 # OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
  23 # SOFTWARE.
  24 
  25 
  26 # ca [expressions...]
  27 #
  28 # CAlculator is an easier-to-use way of running `bc` (basic calculator) where
  29 #
  30 #   - you can calculate multiple different things in one run
  31 #   - you give the expressions as arguments, while `bc` uses stdin
  32 #   - you don't need quoting when avoiding parentheses and spaces
  33 #   - you can use either ** or ^ to raise powers
  34 #   - you can use [ and ] or ( and ) interchangeably
  35 #   - the number of max-accuracy decimals is 25 by default
  36 #   - automatically includes the extended bc math library via option -l
  37 #   - there are several extra predefined values, functions, and aliases
  38 #   - unneeded trailing decimal zeros are ignored for final outputs
  39 
  40 
  41 case "$1" in
  42     -h|--h|-help|--help)
  43         awk '/^# +ca /, /^$/ { gsub(/^# ?/, ""); print }' "$0"
  44         exit 0
  45     ;;
  46 esac
  47 
  48 [ "$1" = '--' ] && shift
  49 
  50 if [ $# -eq 0 ]; then
  51     awk '/^# +ca /, /^$/ { gsub(/^# ?/, ""); print }' "$0"
  52     exit 0
  53 fi
  54 
  55 # default max-accuracy decimals to use for calculations
  56 scale=25
  57 
  58 # ensure each output is all on 1 line, define several funcs and values, then
  59 # inject the expressions given as this script's arguments, transforming them
  60 # according to the rules described above
  61 for arg in "$@"; do
  62     # printf "\e[7m%s\e[0m\n" "${arg}" > /dev/stderr
  63     [ $# -ge 2 ] && printf "\e[7m%s\e[0m\n" "${arg}" > /dev/stderr
  64 
  65     BC_LINE_LENGTH=0 bc -l << ENDOFSCRIPT
  66 scale = ${scale};
  67 
  68 femto = 0.000000000000001;
  69 pico = 0.000000000001;
  70 nano = 0.000000001;
  71 micro = 0.000001;
  72 milli = 0.001;
  73 
  74 kilo = 1000;
  75 mega = 1000 * kilo;
  76 giga = 1000 * mega;
  77 tera = 1000 * giga;
  78 peta = 1000 * tera;
  79 exa =  1000 * peta;
  80 zetta =  1000 * exa;
  81 
  82 binkilo = 1024;
  83 binmega = 1024 * binkilo;
  84 bingiga = 1024 * binmega;
  85 bintera = 1024 * bingiga;
  86 binpeta = 1024 * bintera;
  87 binexa = 1024 * binpeta;
  88 binzetta = 1024 * binexa;
  89 
  90 kb = 1024;
  91 mb = 1024 * kb;
  92 gb = 1024 * mb;
  93 tb = 1024 * gb;
  94 pb = 1024 * tb;
  95 eb = 1024 * pb;
  96 zb = 1024 * eb;
  97 
  98 kib = 1024;
  99 mib = 1024 * kib;
 100 gib = 1024 * mib;
 101 tib = 1024 * gib;
 102 pib = 1024 * tib;
 103 zib = 1024 * pib;
 104 
 105 mol = 602214076000000000000000;
 106 mole = 602214076000000000000000;
 107 
 108 cup = 0.23658824;
 109 cup2l = 0.23658824;
 110 floz2l = 0.0295735295625;
 111 floz2ml = 29.5735295625;
 112 ft = 0.3048;
 113 ft2m = 0.3048;
 114 gal = 3.785411784;
 115 gal2l = 3.785411784;
 116 in = 2.54;
 117 in2cm = 2.54;
 118 lb = 0.45359237;
 119 lb2kg = 0.45359237;
 120 mi = 1.609344;
 121 mi2km = 1.609344;
 122 mpg = 0.425143707;
 123 mpg2kpl = 0.425143707;
 124 nm = 1.852;
 125 nm2km = 1.852;
 126 nmi = 1.852;
 127 nmi2km = 1.852;
 128 oz2g = 28.349523125
 129 psi2pa = 6894.757293168;
 130 ton = 907.18474;
 131 ton2kg = 907.18474;
 132 yd = 0.9144;
 133 yd2m = 0.9144;
 134 
 135 ga2l = gal2l;
 136 nm2km = nmi2km;
 137 tn2kg = ton2kg;
 138 
 139 million = 1000000
 140 billion = 1000 * million
 141 trillion = 1000 * billion
 142 
 143 hour = 3600;
 144 day = 24 * hour;
 145 week = 7 * day;
 146 
 147 hr = hour;
 148 wk = week;
 149 
 150 /* function "choose": "bc" uses "c" for the built-in cosine function */
 151 
 152 define abs(x) { if (x >= 0) return (x) else return (-x); }
 153 define atan(x) { return (a(x)); }
 154 define bits(x) { return (log2(x)); }
 155 define choose(n, k) { return (com(n, k)); }
 156 define circle(r) { return (4 * a(1) * r * r); } /* circle-area from radius */
 157 define circum(r) { return (8 * a(1) * r); } /* circumference from radius */
 158 define circumference(r) { return (8 * a(1) * r); }
 159 define com(n, k) { if (n < k) return (0) else return (per(n, k) / fac(k)); }
 160 define comb(n, k) { return (com(n, k)); }
 161 define combin(n, k) { return (com(n, k)); }
 162 define combinations(n, k) { return (com(n, k)); }
 163 define cos(x) { return (c(x)); }
 164 define cosh(x) { return ((e(x) + e(-x)) / 2); }
 165 define cot(x) { return (c(x) / s(x)); }
 166 define coth(x) { return ((e(x) + e(-x)) / (e(x) - e(-x))); }
 167 define dbin(x, n, p) { return (dbinom(x, n, p)); }
 168 define dbinom(x, n, p) { return (com(n, x) * (p ^ x) * ((1 - p) ^ (n - x))); }
 169 define deg(x) { return (180 * x / pi()); }
 170 define digits(x) { return (log10(x)); }
 171 define degrees(x) { return (deg(x)); }
 172 define dexp(x, r) { if (r < 0) return (0) else return (r * e(-r * x)); }
 173 define dpois(x, l) { return ((l ^ x) * e(-l) / fac(x)); }
 174 define gauss(x) { return (gaussian(x)); }
 175 define gaussian(x) { return (e(-(x * x))); }
 176 define epa(x) { return (epanechnikov(x)); }
 177 define eu() { return (e(1)); }
 178 define euler() { return (e(1)); }
 179 define exp(x) { return (e(x)); }
 180 define f(x) { return (fac(x)); }
 181 define fact(x) { return (fac(x)); }
 182 define factorial(x) { return (fac(x)); }
 183 define ftin(f, i) { return (0.3048 * f + 0.0254 * i); }
 184 define gcd(x, y) { return (x * y / lcm(x, y)); }
 185 define hypot(x, y) { return (sqrt(x*x + y*y)); }
 186 define j0(x) { return (j(0, x)); }
 187 define j1(x) { return (j(1, x)); }
 188 define lboz(l, o) { return (0.45359237 * l + 0.028349523 * o); }
 189 define ln(x) { return (l(x)); }
 190 define log(x) { return (l(x)); }
 191 define logistic(x) { return (1 / (1 + e(-x))); }
 192 define max(x, y) { if (x >= y) return (x) else return (y); }
 193 define min(x, y) { if (x <= y) return (x) else return (y); }
 194 define mix(x, y, k) { return (x * (1 - k) + y * k); }
 195 define mod1(x) { return (mod(x, 1)); }
 196 define modf(x) { return (mod(x, 1)); }
 197 define p(n, k) { return (per(n, k)); }
 198 define pbin(x, n, p) { return (pbinom(x, n, p)); }
 199 define perm(n, k) { return (per(n, k)); }
 200 define permut(n, k) { return (per(n, k)); }
 201 define permutations(n, k) { return (per(n, k)); }
 202 define pexp(x, r) { if (r < 0) return (0) else return (1 - e(-r * x)); }
 203 define pi() { return (4 * a(1)); }
 204 define r(x, d) { return (round(x, d)); }
 205 define r0(x) { return (round0(x)); }
 206 define rad(x) { return (pi() * x / 180); }
 207 define radians(x) { return (rad(x)); }
 208 define sgn(x) { return (sgn(x)); }
 209 define sin(x) { return (s(x)); }
 210 define sinc(x) { if (x == 0) return (1) else return (s(x) / x); }
 211 define sinh(x) { return ((e(x) - e(-x)) / 2); }
 212 define tan(x) { return (s(x) / c(x)); }
 213 define tanh(x) { return ((e(x) - e(-x)) / (e(x) + e(-x))); }
 214 define tau() { return (8 * a(1)); }
 215 
 216 define epanechnikov(x) {
 217     if ((x < -1) || (x > 1)) return (0);
 218     return (3 / 4 * (1 - (x * x)));
 219 }
 220 
 221 define fac(x) {
 222     auto f, i;
 223     if (x < 0) return (0);
 224     f = 1;
 225     for (i = x; i >= 2; i--) f *= i;
 226     return (f);
 227 }
 228 
 229 define lcm(x, y) {
 230     auto a, b, z;
 231 
 232     /* the LCM is defined only for positive integers */
 233     /* if (mod(x, 1) != 0 || x < 1 || mod(y, 1) != 0 || y < 1) return (0); */
 234     /* if (mod(x, 1) != 0) return (0); */
 235     if (x < 1) return (0);
 236     /* if (mod(y, 1) != 0) return (0); */
 237     if (y < 1) return (0);
 238 
 239     a = min(x, y);
 240     b = max(x, y);
 241 
 242     z = b;
 243     while (mod(z, a) != 0) { z += b; }
 244     return (z);
 245 }
 246 
 247 define log2(x) {
 248     auto r, n;
 249     if (x <= 0) return (l(x) / l(2));
 250 
 251     r = 0;
 252     for (n = x; n > 1; n /= 2) r += 1;
 253 
 254     if (n == 1) return (r);
 255     return (l(x) / l(2));
 256 }
 257 
 258 define log10(x) {
 259     auto r, n;
 260     if (x <= 0) return (l(x) / l(10));
 261 
 262     r = 0;
 263     for (n = x; n > 1; n /= 10) r += 1;
 264 
 265     if (n == 1) return (r);
 266     return (l(x) / l(10));
 267 }
 268 
 269 define mod(x, y) {
 270     auto s, m;
 271     s = scale;
 272     scale = 0;
 273     m = x % y;
 274     scale = s;
 275     return (m);
 276 }
 277 
 278 define per(n, k) {
 279     auto p, i;
 280     if (n < k) return (0);
 281     p = 1;
 282     for (i = n; i >= n - k + 1; i--) p *= i;
 283     return (p);
 284 }
 285 
 286 /* pbinom inefficiently repeats calculations for now, which keeps it simple */
 287 define pbinom(x, n, p) {
 288     auto k, t;
 289     t = 0;
 290     for (k = 0; k <= n; k++) t += dbinom(k, n, p);
 291     return (t);
 292 }
 293 
 294 /* pbinomfast may be wrong, while the simpler pbinom seems correct */
 295 define pbinomfast(x, n, p) {
 296     auto a, b, d, q, k, t;
 297     if ((p < 0) || (p > 1)) return (0);
 298     if (x < 0) return (0);
 299     if (x >= n) return (1);
 300     a = 1;
 301     q = 1 - p;
 302     b = b ^ n;
 303     d = 1;
 304     t = 0;
 305     for (k = 0; k < x;) {
 306         t += (per(n, k) / d) * a * b;
 307         a *= p;
 308         b /= q;
 309         k++;
 310         d *= k;
 311     }
 312     /* remember the last loop, where k == x */
 313     t += (per(n, k) / d) * a * b;
 314     return (t);
 315 }
 316 
 317 define ppois(x, l) {
 318     auto t, d, i;
 319     t = 1;
 320     d = 1;
 321     for (i = 1; i <= l; i++) {
 322         d *= i;
 323         t += (l ^ i) / d;
 324     }
 325     return (e(-l) * t);
 326 }
 327 
 328 define round(x, d) {
 329     auto k;
 330     k = 10 ^ d;
 331     return (round0(x * k) / k);
 332 }
 333 
 334 define round0(x) {
 335     auto i;
 336     i = x - mod(x, 1);
 337     if (x - i >= 0.5) {
 338         return (i + 1);
 339     }
 340     return (i);
 341 }
 342 
 343 define sign(x) {
 344     if (x > 0) return (1);
 345     if (x < 0) return (-1);
 346     return (0);
 347 }
 348 
 349 define tricube(x) {
 350     auto a, b, c, d;
 351     if ((x < -1) || (x > 1)) return (0);
 352     if (x >= 0) a = x else a = -x;
 353     b = a * a * a;
 354     c = 1 - b;
 355     d = c * c * c;
 356     return (70 / 81 * d);
 357 }
 358 
 359 $(echo "${arg}" | sed 's-^+--g; s-_--g; s-\*\*-^-g; s-\[-(-g; s-\]-)-g')
 360 ENDOFSCRIPT
 361 
 362 done |
 363 # ensure the result shows at least a zero before the decimal dot, then
 364 # rid the result of trailing zero decimals and/or trailing decimal dots
 365 sed -E 's-^\.-0.-; s/^-\./-0./; s-(\.[0-9]*[1-9])0+$-\1-; s-\.0*$--'