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 [ $# -ge 2 ] && printf "\e[7m%s\e[0m\n" "${arg}" > /dev/stderr 63 64 { 65 BC_LINE_LENGTH=0 bc -l | 66 # ensure the result shows at least a zero before the decimal dot, then 67 # rid the result of trailing zero decimals and/or trailing decimal dots 68 sed -E 's-^\.-0.-; s/^-\./-0./; s-(\.[0-9]*[1-9])0+$-\1-; s-\.0*$--' 69 } << ENDOFSCRIPT 70 scale = ${scale}; 71 72 femto = 0.000000000000001; 73 pico = 0.000000000001; 74 nano = 0.000000001; 75 micro = 0.000001; 76 milli = 0.001; 77 78 kilo = 1000; 79 mega = 1000 * kilo; 80 giga = 1000 * mega; 81 tera = 1000 * giga; 82 peta = 1000 * tera; 83 exa = 1000 * peta; 84 zetta = 1000 * exa; 85 86 binkilo = 1024; 87 binmega = 1024 * binkilo; 88 bingiga = 1024 * binmega; 89 bintera = 1024 * bingiga; 90 binpeta = 1024 * bintera; 91 binexa = 1024 * binpeta; 92 binzetta = 1024 * binexa; 93 94 kb = 1024; 95 mb = 1024 * kb; 96 gb = 1024 * mb; 97 tb = 1024 * gb; 98 pb = 1024 * tb; 99 eb = 1024 * pb; 100 zb = 1024 * eb; 101 102 kib = 1024; 103 mib = 1024 * kib; 104 gib = 1024 * mib; 105 tib = 1024 * gib; 106 pib = 1024 * tib; 107 zib = 1024 * pib; 108 109 mol = 602214076000000000000000; 110 mole = 602214076000000000000000; 111 112 cup = 0.23658824; 113 cup2l = 0.23658824; 114 floz2l = 0.0295735295625; 115 floz2ml = 29.5735295625; 116 ft = 0.3048; 117 ft2m = 0.3048; 118 gal = 3.785411784; 119 gal2l = 3.785411784; 120 in = 2.54; 121 in2cm = 2.54; 122 lb = 0.45359237; 123 lb2kg = 0.45359237; 124 mi = 1.609344; 125 mi2km = 1.609344; 126 mpg = 0.425143707; 127 mpg2kpl = 0.425143707; 128 nm = 1.852; 129 nm2km = 1.852; 130 nmi = 1.852; 131 nmi2km = 1.852; 132 oz2g = 28.349523125 133 psi2pa = 6894.757293168; 134 ton = 907.18474; 135 ton2kg = 907.18474; 136 yd = 0.9144; 137 yd2m = 0.9144; 138 139 ga2l = gal2l; 140 nm2km = nmi2km; 141 tn2kg = ton2kg; 142 143 million = 1000000 144 billion = 1000 * million 145 trillion = 1000 * billion 146 147 hour = 3600; 148 day = 24 * hour; 149 week = 7 * day; 150 151 hr = hour; 152 wk = week; 153 154 /* function "choose": "bc" uses "c" for the built-in cosine function */ 155 156 define abs(x) { if (x >= 0) return (x) else return (-x); } 157 define atan(x) { return (a(x)); } 158 define bits(x) { return (log2(x)); } 159 define choose(n, k) { return (com(n, k)); } 160 define circle(r) { return (4 * a(1) * r * r); } /* circle-area from radius */ 161 define circum(r) { return (8 * a(1) * r); } /* circumference from radius */ 162 define circumference(r) { return (8 * a(1) * r); } 163 define com(n, k) { if (n < k) return (0) else return (per(n, k) / fac(k)); } 164 define comb(n, k) { return (com(n, k)); } 165 define combin(n, k) { return (com(n, k)); } 166 define combinations(n, k) { return (com(n, k)); } 167 define cos(x) { return (c(x)); } 168 define cosh(x) { return ((e(x) + e(-x)) / 2); } 169 define cot(x) { return (c(x) / s(x)); } 170 define coth(x) { return ((e(x) + e(-x)) / (e(x) - e(-x))); } 171 define dbin(x, n, p) { return (dbinom(x, n, p)); } 172 define dbinom(x, n, p) { return (com(n, x) * (p ^ x) * ((1 - p) ^ (n - x))); } 173 define deg(x) { return (180 * x / pi()); } 174 define digits(x) { return (log10(x)); } 175 define degrees(x) { return (deg(x)); } 176 define dexp(x, r) { if (r < 0) return (0) else return (r * e(-r * x)); } 177 define dpois(x, l) { return ((l ^ x) * e(-l) / fac(x)); } 178 define gauss(x) { return (gaussian(x)); } 179 define gaussian(x) { return (e(-(x * x))); } 180 define epa(x) { return (epanechnikov(x)); } 181 define eu() { return (e(1)); } 182 define euler() { return (e(1)); } 183 define exp(x) { return (e(x)); } 184 define f(x) { return (fac(x)); } 185 define fact(x) { return (fac(x)); } 186 define factorial(x) { return (fac(x)); } 187 define ftin(f, i) { return (0.3048 * f + 0.0254 * i); } 188 define gcd(x, y) { return (x * y / lcm(x, y)); } 189 define hypot(x, y) { return (sqrt(x*x + y*y)); } 190 define j0(x) { return (j(0, x)); } 191 define j1(x) { return (j(1, x)); } 192 define lboz(l, o) { return (0.45359237 * l + 0.028349523 * o); } 193 define ln(x) { return (l(x)); } 194 define log(x) { return (l(x)); } 195 define logistic(x) { return (1 / (1 + e(-x))); } 196 define max(x, y) { if (x >= y) return (x) else return (y); } 197 define min(x, y) { if (x <= y) return (x) else return (y); } 198 define mix(x, y, k) { return (x * (1 - k) + y * k); } 199 define mod1(x) { return (mod(x, 1)); } 200 define modf(x) { return (mod(x, 1)); } 201 define p(n, k) { return (per(n, k)); } 202 define pbin(x, n, p) { return (pbinom(x, n, p)); } 203 define perm(n, k) { return (per(n, k)); } 204 define permut(n, k) { return (per(n, k)); } 205 define permutations(n, k) { return (per(n, k)); } 206 define pexp(x, r) { if (r < 0) return (0) else return (1 - e(-r * x)); } 207 define pi() { return (4 * a(1)); } 208 define r(x, d) { return (round(x, d)); } 209 define r0(x) { return (round0(x)); } 210 define rad(x) { return (pi() * x / 180); } 211 define radians(x) { return (rad(x)); } 212 define sgn(x) { return (sgn(x)); } 213 define sin(x) { return (s(x)); } 214 define sinc(x) { if (x == 0) return (1) else return (s(x) / x); } 215 define sinh(x) { return ((e(x) - e(-x)) / 2); } 216 define tan(x) { return (s(x) / c(x)); } 217 define tanh(x) { return ((e(x) - e(-x)) / (e(x) + e(-x))); } 218 define tau() { return (8 * a(1)); } 219 220 define epanechnikov(x) { 221 if ((x < -1) || (x > 1)) return (0); 222 return (3 / 4 * (1 - (x * x))); 223 } 224 225 define fac(x) { 226 auto f, i; 227 if (x < 0) return (0); 228 f = 1; 229 for (i = x; i >= 2; i--) f *= i; 230 return (f); 231 } 232 233 define lcm(x, y) { 234 auto a, b, z; 235 236 /* the LCM is defined only for positive integers */ 237 /* if (mod(x, 1) != 0 || x < 1 || mod(y, 1) != 0 || y < 1) return (0); */ 238 /* if (mod(x, 1) != 0) return (0); */ 239 if (x < 1) return (0); 240 /* if (mod(y, 1) != 0) return (0); */ 241 if (y < 1) return (0); 242 243 a = min(x, y); 244 b = max(x, y); 245 246 z = b; 247 while (mod(z, a) != 0) { z += b; } 248 return (z); 249 } 250 251 define log2(x) { 252 auto r, n; 253 if (x <= 0) return (l(x) / l(2)); 254 255 r = 0; 256 for (n = x; n > 1; n /= 2) r += 1; 257 258 if (n == 1) return (r); 259 return (l(x) / l(2)); 260 } 261 262 define log10(x) { 263 auto r, n; 264 if (x <= 0) return (l(x) / l(10)); 265 266 r = 0; 267 for (n = x; n > 1; n /= 10) r += 1; 268 269 if (n == 1) return (r); 270 return (l(x) / l(10)); 271 } 272 273 define mod(x, y) { 274 auto s, m; 275 s = scale; 276 scale = 0; 277 m = x % y; 278 scale = s; 279 return (m); 280 } 281 282 define per(n, k) { 283 auto p, i; 284 if (n < k) return (0); 285 p = 1; 286 for (i = n; i >= n - k + 1; i--) p *= i; 287 return (p); 288 } 289 290 /* pbinom inefficiently repeats calculations for now, which keeps it simple */ 291 define pbinom(x, n, p) { 292 auto k, t; 293 t = 0; 294 for (k = 0; k <= n; k++) t += dbinom(k, n, p); 295 return (t); 296 } 297 298 /* pbinomfast may be wrong, while the simpler pbinom seems correct */ 299 define pbinomfast(x, n, p) { 300 auto a, b, d, q, k, t; 301 if ((p < 0) || (p > 1)) return (0); 302 if (x < 0) return (0); 303 if (x >= n) return (1); 304 a = 1; 305 q = 1 - p; 306 b = b ^ n; 307 d = 1; 308 t = 0; 309 for (k = 0; k < x;) { 310 t += (per(n, k) / d) * a * b; 311 a *= p; 312 b /= q; 313 k++; 314 d *= k; 315 } 316 /* remember the last loop, where k == x */ 317 t += (per(n, k) / d) * a * b; 318 return (t); 319 } 320 321 define ppois(x, l) { 322 auto t, d, i; 323 t = 1; 324 d = 1; 325 for (i = 1; i <= l; i++) { 326 d *= i; 327 t += (l ^ i) / d; 328 } 329 return (e(-l) * t); 330 } 331 332 define round(x, d) { 333 auto k; 334 k = 10 ^ d; 335 return (round0(x * k) / k); 336 } 337 338 define round0(x) { 339 auto i; 340 i = x - mod(x, 1); 341 if (x - i >= 0.5) { 342 return (i + 1); 343 } 344 return (i); 345 } 346 347 define sign(x) { 348 if (x > 0) return (1); 349 if (x < 0) return (-1); 350 return (0); 351 } 352 353 define tricube(x) { 354 auto a, b, c, d; 355 if ((x < -1) || (x > 1)) return (0); 356 if (x >= 0) a = x else a = -x; 357 b = a * a * a; 358 c = 1 - b; 359 d = c * c * c; 360 return (70 / 81 * d); 361 } 362 363 $(echo "${arg}" | sed 's-^+--g; s-_--g; s-\*\*-^-g; s-\[-(-g; s-\]-)-g') 364 ENDOFSCRIPT 365 366 done