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+$-\1-; s-\.0*$--'