/* for standalone usage, compile with: cc -Os -Wall -Wextra -Wshadow -march=native qrpn.c -lm -o qrpn */ #define _DEFAULT_SOURCE #define _XOPEN_SOURCE #include "qrpn.h" #include #include #include #include #include #include #include #include #include /* begin simple math functions we want to expose via the interpreter */ static double crd(const double theta) { return 2.0 * sin(theta / 2.0); } static double hav(const double theta) { const double a = sin(theta / 2.0); return a * a; } static double ahav(const double x) { return 2.0 * asin(sqrt(x)); } static double acrd(const double x) { return 2.0 * asin(x * 0.5); } static double versine(const double x) { return (fabs(x) > M_PI * 0.125) ? (2.0 * sin(x * 0.5)) : (1.0 - cos(x)); } static double exsecant(const double x) { return versine(x) / cos(x); } static double arcexsecant(const double x) { return atan(sqrt(x * x + x * 2.0)); } static double tenlog(double x) { return 10.0 * log10(x); } static double itenlog(double x) { return pow(10.0, x * 0.1); } static double complex cpow_checked(const double complex a, const double complex b) { /* cpow() cannot be trusted to have as much precision as pow() even for integer arguments that fit in 32 bits */ if (!cimag(a) && !cimag(b)) { const double ar = creal(a), br = creal(b); if (rint(br) == br) return __builtin_powi(ar, br); else return pow(ar, br); } else return cpow(a, b); } static unsigned long long gcd(unsigned long long a, unsigned long long b) { while (b) { const unsigned long long t = b; b = a % b; a = t; } return a; } static unsigned long long nchoosek(const unsigned long long n, const unsigned long long k) { if (1 == k) return n; if (k > n - k) return nchoosek(n, n - k); unsigned long long n_choose_k = n * (n - 1) / 2; for (size_t kr = 3; kr <= k; kr++) n_choose_k *= (n + 1 - kr) / kr; return n_choose_k; } static unsigned long long ceil_isqrt(unsigned long long n) { unsigned long long this = n / 2; if (!this) return n; for (unsigned long long next = this; (next = (this + n / this) / 2) < this; this = next); return this * this < n ? this + 1 : this; } static int isprime(const unsigned long long n) { if (2 == n) return 1; else if (1 == n || !(n % 2)) return 0; const unsigned long long stop = ceil_isqrt(n); for (unsigned long long m = 3; m < stop; m += 2) if (!(n % m)) return 0; return 1; } /* end simple math functions */ struct named_quantity { double value; int8_t units[BASEUNITS]; /* metre, kilogram, second, ampere, kelvin, candela, mol */ uint8_t flags; char * name; char * abrv; char * alt_spelling; }; struct si_prefix { double scale; char * name; char * abrv; }; static const struct si_prefix si_prefixes[] = { { 1e-24, "yocto", "y", }, { 1e-21, "zepto", "z", }, { 1e-18, "atto", "a", }, { 1e-15, "femto", "f", }, { 1e-12, "pico", "p", }, { 1e-9, "nano", "n" }, { 1e-6, "micro", "u" }, { 1e-3, "milli", "m" }, { 1e-2, "centi", "c" }, { 1e-1, "deci", "d" }, { 1e2, "hecto", "h" }, { 1e3, "kilo", "k" }, { 1e6, "mega", "M" }, { 1e9, "giga", "G" }, { 1e12, "tera", "T" }, { 1e15, "peta", "P" }, { 1e18, "exa", "E" }, { 1e21, "zetta", "Z" }, { 1e24, "yotta", "Y" }, { 1e27, "hella", "H" } }; static const int8_t units_of_time[BASEUNITS] = { 0, 0, 1, 0, 0, 0, 0 }; static const int8_t dimensionless[BASEUNITS] = { 0, 0, 0, 0, 0, 0, 0 }; #define FLAG_UNIT_ENTERS_AS_OPERAND 1 #define FLAG_SI_BASE_UNIT 4 #define FLAG_SI_DERIVED_UNIT 8 static const struct named_quantity named_quantities[] = { /* si base units */ { .value = 1.0, .units = { 1, 0, 0, 0, 0, 0, 0 }, .name = "metre", .abrv = "m", .flags = FLAG_SI_BASE_UNIT, .alt_spelling = "meter" }, { .value = 1.0, .units = { 0, 1, 0, 0, 0, 0, 0 }, .name = "kilogram", .abrv = "kg", .flags = FLAG_SI_BASE_UNIT }, { .value = 1.0, .units = { 0, 0, 1, 0, 0, 0, 0 }, .name = "second", .abrv = "s", .flags = FLAG_SI_BASE_UNIT }, { .value = 1.0, .units = { 0, 0, 0, 1, 0, 0, 0 }, .name = "ampere", .abrv = "A", .flags = FLAG_SI_BASE_UNIT }, { .value = 1.0, .units = { 0, 0, 0, 0, 1, 0, 0 }, .name = "kelvin", .abrv = "K", .flags = FLAG_SI_BASE_UNIT }, { .value = 1.0, .units = { 0, 0, 0, 0, 0, 1, 0 }, .name = "candela", .abrv = "Cd", .flags = FLAG_SI_BASE_UNIT }, { .value = 1.0, .units = { 0, 0, 0, 0, 0, 0, 1 }, .name = "mole", .abrv = "mol", .flags = FLAG_SI_BASE_UNIT }, /* si derived units */ { .value = 1.0, .units = { 0, 0, -1, 0, 0, 0, 0 }, .name = "hertz", .abrv = "Hz", .flags = FLAG_SI_DERIVED_UNIT }, { .value = 1.0, .units = { 1, 1, -2, 0, 0, 0, 0 }, .name = "newton", .abrv = "N", .flags = FLAG_SI_DERIVED_UNIT }, { .value = 1.0, .units = { -1, 1, -2, 0, 0, 0, 0 }, .name = "pascal", .abrv = "Pa", .flags = FLAG_SI_DERIVED_UNIT }, { .value = 1.0, .units = { 2, 1, -2, 0, 0, 0, 0 }, .name = "joule", .abrv = "J", .flags = FLAG_SI_DERIVED_UNIT }, { .value = 1.0, .units = { 2, 1, -3, 0, 0, 0, 0 }, .name = "watt", .abrv = "W", .flags = FLAG_SI_DERIVED_UNIT }, { .value = 1.0, .units = { 0, 0, 1, 1, 0, 0, 0 }, .name = "coulomb", .abrv = "C", .flags = FLAG_SI_DERIVED_UNIT }, { .value = 1.0, .units = { 2, 1, -3, -1, 0, 0, 0 }, .name = "volt", .abrv = "V", .flags = FLAG_SI_DERIVED_UNIT }, { .value = 1.0, .units = { -2, -1, 4, 2, 0, 0, 0 }, .name = "farad", .abrv = "F", .flags = FLAG_SI_DERIVED_UNIT }, { .value = 1.0, .units = { 2, 1, -3, -2, 0, 0, 0 }, .name = "ohm", .abrv = "ohm", .flags = FLAG_SI_DERIVED_UNIT }, { .value = 1.0, .units = { -2, -1, 3, 2, 0, 0, 0 }, .name = "siemens", .abrv = "S", .flags = FLAG_SI_DERIVED_UNIT }, { .value = 1.0, .units = { 2, 1, -2, -1, 0, 0, 0 }, .name = "weber", .abrv = "Wb", .flags = FLAG_SI_DERIVED_UNIT }, { .value = 1.0, .units = { 0, 1, -2, -1, 0, 0, 0 }, .name = "tesla", .abrv = "T", .flags = FLAG_SI_DERIVED_UNIT }, { .value = 1.0, .units = { 2, 1, -2, -2, 0, 0, 0 }, .name = "henry", .abrv = "H", .flags = FLAG_SI_DERIVED_UNIT }, { .value = 1.0, .units = { 0, 0, -1, 0, 0, 0, 1 }, .name = "katal", .abrv = "kat", .flags = FLAG_SI_DERIVED_UNIT }, { .value = 1.0, .units = { -2, 1, -1, 0, 0, 0, 0 }, .name = "rayl" }, /* todo keep the print thing from displaying these */ // { .value = 1.0, .units = { 0, 0, -1, 0, 0, 0, 0 }, .name = "becquerel", .abrv = "Bq" }, // { .value = 1.0, .units = { 2, 0, -2, 0, 0, 0, 0 }, .name = "gray", .abrv = "Gy" }, { .value = 100e3, { -1, 1, -2, 0, 0, 0, 0 }, .name = "bar" }, { .value = 60.0, .units = { 0, 0, 1, 0, 0, 0, 0 }, .name = "minute", .abrv = "min" }, { .value = 3600.0, .units = { 0, 0, 1, 0, 0, 0, 0 }, .name = "hour", .abrv = "h" }, { .value = 86400.0, .units = { 0, 0, 1, 0, 0, 0, 0 }, .name = "day" }, { .value = 1209600.0, .units = { 0, 0, 1, 0, 0, 0, 0 }, .name = "fortnight" }, { .value = 1.0e-15, .units = { 1, 0, 0, 0, 0, 0, 0 }, .name = "fermi", }, { .value = 1.0e-6, .units = { 1, 0, 0, 0, 0, 0, 0 }, .name = "micron", }, { .value = 1.0e-28, .units = { 2, 0, 0, 0, 0, 0, 0 }, .name = "barn", .abrv = "b", }, { .value = 1e-3, .units = { 0, 1, 0, 0, 0, 0, 0 }, .name = "gram", .abrv = "gm" }, { .value = 1e3, .units = { 0, 1, 0, 0, 0, 0, 0 }, .name = "tonne", .abrv = "t", .alt_spelling = "ton" }, { .value = 1e-3, .units = { 3, 0, 0, 0, 0, 0, 0 }, .name = "litre", .abrv = "L" }, { .value = 1e-6, .units = { 3, 0, 0, 0, 0, 0, 0 }, .name = "cc" }, { .value = 10e3, .units = { 2, 0, 0, 0, 0, 0, 0 }, .name = "hectare", .abrv = "ha" }, { .value = 3600.0, .units = { 2, 1, -2, 0, 0, 0, 0 }, .abrv = "Wh" }, { .value = 3600.0, .units = { 0, 0, 1, 1, 0, 0, 0 }, .abrv = "Ah" }, { .value = 1.0e-2, .units = { 2, 0, -2, 0, 0, 0, 0 }, .name = "rad" }, { .value = 10e-6, .units = { 1, 1, -2, 0, 0, 0, 0 }, .name = "dyne" }, { .value = 3.7e10, .units = { 0, 0, -1, 0, 0, 0, 0 }, .name = "curie", .abrv = "Ci" }, { .value = 4.92892159375e-6, .units = { 3, 0, 0, 0, 0, 0, 0 }, .name = "teaspoon", .abrv = "tsp" }, { .value = 14.78676478125e-6, .units = { 3, 0, 0, 0, 0, 0, 0 }, .name = "tablespoon", .abrv = "Tbsp" }, { .value = 29.5735295625e-6, .units = { 3, 0, 0, 0, 0, 0, 0 }, .name = "floz" }, { .value = 236.5882365e-6, .units = { 3, 0, 0, 0, 0, 0, 0 }, .name = "cup" }, { .value = 473.176473e-6, .units = { 3, 0, 0, 0, 0, 0, 0 }, .name = "pint" }, { .value = 0.946352946e-3, .units = { 3, 0, 0, 0, 0, 0, 0 }, .name = "quart" }, { .value = 3.785411784e-3, .units = { 3, 0, 0, 0, 0, 0, 0 }, .name = "gallon" }, { .value = 1.60217657e-19, .units = { 2, 1, -2, 0, 0, 0, 0 }, .abrv = "eV" }, { .value = 4046.8564224, .units = { 2, 0, 0, 0, 0, 0, 0 }, .name = "acre" }, { .value = 4.184, .units = { 2, 1, -2, 0, 0, 0, 0 }, .name = "calorie", .abrv = "cal" }, { .value = 4.184e3, .units = { 2, 1, -2, 0, 0, 0, 0 }, .abrv = "Cal" }, { .value = 4.184e6, .units = { 2, 0, -2, 0, 0, 0, 0 }, .name = "TNT" }, { .value = 1852.0, .units = { 1, 0, 0, 0, 0, 0, 0 }, .name = "nmi" }, { .value = 0.514444444, .units = { 1, 0, -1, 0, 0, 0, 0 }, .name = "knot", .abrv = "kt", }, { .value = 1609.344, .units = { 1, 0, 0, 0, 0, 0, 0 }, .name = "mile" }, { .value = 1609.344 / 3600, .units = { 1, 0, -1, 0, 0, 0, 0 }, .abrv = "mph" }, { .value = 86400.0 * 365.2425, .units = { 0, 0, 1, 0, 0, 0, 0 }, .name = "year", .abrv = "a" }, { .value = 1852.0 * 3, .units = { 1, 0, 0, 0, 0, 0, 0 }, .name = "league" }, { .value = 9.8066, .units = { 1, 0, -2, 0, 0, 0, 0 }, .name = "g" }, { .value = 0.01, .units = { 1, 0, -2, 0, 0, 0, 0 }, .name = "gal", .abrv = "Gal" }, { .value = 1.3806488e-23, .units = { 2, 1, -2, 0, -1, 0, 0 }, .flags = FLAG_UNIT_ENTERS_AS_OPERAND, .name = "Boltzmann", .abrv = "k" }, { .value = 6371000, .units = { 1, 0, 0, 0, 0, 0, 0 }, .flags = FLAG_UNIT_ENTERS_AS_OPERAND, .name = "Earth radius", .abrv = "Re" }, { .value = 6.02214129e23, .units = { 0, 0, 0, 0, 0, 0, -1 }, .name = "avogadro" }, { .value = 6.6738480e-11, .units = { 3, -1, -2, 0, 0, 0, 0 }, .flags = FLAG_UNIT_ENTERS_AS_OPERAND, .name = "G" }, { .value = 5.97219e24, .units = { 0, 1, 0, 0, 0, 0, 0 }, .flags = FLAG_UNIT_ENTERS_AS_OPERAND, .name = "Me" }, { .value = 8.3144621, .units = { 2, 1, -2, 0, -1, 0, -1 }, .flags = FLAG_UNIT_ENTERS_AS_OPERAND, .name = "Rc" }, { .value = 299792458.0, .units = { 1, 0, -1, 0, 0, 0, 0 }, .flags = FLAG_UNIT_ENTERS_AS_OPERAND, .name = "c", .abrv = "c0" }, { .value = 1.3806488e-23, .units = { 2, 1, -2, 0, -1, 0, 0 }, .flags = FLAG_UNIT_ENTERS_AS_OPERAND, .name = "Bc" }, { .value = 8.854187817620e-12, .units = { -3, -1, 4, 2, 0, 0, 0 }, .flags = FLAG_UNIT_ENTERS_AS_OPERAND, .name = "e0" }, { .value = 4.0e-7 * M_PI, .units = { 1, 1, -2, -2, 0, 0, 0 }, .flags = FLAG_UNIT_ENTERS_AS_OPERAND, .name = "u0" }, { .value = 20.779e9, .units = { 2, 0, 0, 0, 0, 0, 0 }, .name = "Wales" }, { .value = 0.0283495, .units = { 0, 1, 0, 0, 0, 0, 0 }, .name = "ounce", .abrv = "oz" }, { .value = 0.0311034768, .units = { 0, 1, 0, 0, 0, 0, 0 }, .name = "troyoz" }, { .value = 64.79891e-6, .units = { 0, 1, 0, 0, 0, 0, 0 }, .name = "grain" }, { .value = 101.325e3, .units = { -1, 1, -2, 0, 0, 0, 0 }, .name = "atmosphere", .abrv = "atm" }, { .value = 745.699872, .units = { 2, 1, -3, 0, 0, 0, 0 }, .name = "horsepower", .abrv = "hp" }, { .value = 0.3048 * 6.0, .units = { 1, 0, 0, 0, 0, 0, 0 }, .name = "fathom" }, { .value = 0.0254, .units = { 1, 0, 0, 0, 0, 0, 0 }, .name = "inch", .abrv = "in" }, { .value = 0.3048, .units = { 1, 0, 0, 0, 0, 0, 0 }, .name = "foot", .abrv = "ft" }, { .value = 0.9144, .units = { 1, 0, 0, 0, 0, 0, 0 }, .name = "yard", .abrv = "yd" }, { .value = 201.168, .units = { 1, 0, 0, 0, 0, 0, 0 }, .name = "furlong" }, { .value = 3.08567758e16, .units = { 1, 0, 0, 0, 0, 0, 0 }, .name = "parsec", .abrv = "pc" }, { .value = 0.45359237, .units = { 0, 1, 0, 0, 0, 0, 0 }, .name = "lbm" }, { .value = 4.448222, .units = { 1, 1, -2, 0, 0, 0, 0 }, .name = "lbf" }, { .value = 6.35029318, .units = { 0, 1, 0, 0, 0, 0, 0 }, .name = "stone", .abrv = "st" }, }; static const size_t named_quantity_count = sizeof(named_quantities) / sizeof(named_quantities[0]); static int units_are_power_of(const struct quantity * const test, const struct named_quantity * const base) { int exponent = 0; for (size_t iu = 0; iu < BASEUNITS; iu++) if (test->units[iu] && base->units[iu]) { exponent = test->units[iu] / base->units[iu]; break; } if (!exponent) return 0; for (size_t iu = 0; iu < BASEUNITS; iu++) if (test->units[iu] != base->units[iu] * exponent) return 0; return exponent; } static int units_are_equivalent(const int8_t a[BASEUNITS], const int8_t b[BASEUNITS]) { return !memcmp(a, b, sizeof(int8_t[BASEUNITS])); } static int units_are_dimensionless(const int8_t in[BASEUNITS]) { return !memcmp(in, dimensionless, sizeof(int8_t[BASEUNITS])); } static double datestr_to_unix_seconds(const char * const datestr) { int64_t seconds = 0, microseconds_after_decimal = 0; if (strchr(datestr, 'T') && strchr(datestr, 'Z')) { /* if input is a date string */ struct tm unixtime_struct = { 0 }; /* if input has colons and dashes, and a subsecond portion... */ if (strchr(datestr, '-') && strchr(datestr, ':') && strchr(datestr, '.')) { const uint64_t microseconds_remainder_with_integer = strtod(datestr + 18, NULL) * 1000000; microseconds_after_decimal = microseconds_remainder_with_integer % 1000000; strptime(datestr, "%Y-%m-%dT%H:%M:%S.", &unixtime_struct); } /* if input has colons and dashes */ else if (strchr(datestr, '-') && strchr(datestr, ':')) strptime(datestr, "%Y-%m-%dT%H:%M:%SZ", &unixtime_struct); /* if input has a subsecond portion */ else if (strchr(datestr, '.')) { const uint64_t microseconds_remainder_with_integer = strtod(datestr + 14, NULL) * 1000000; microseconds_after_decimal = microseconds_remainder_with_integer % 1000000; strptime(datestr, "%Y%m%dT%H%M%S.", &unixtime_struct); } else strptime(datestr, "%Y%m%dT%H%M%SZ", &unixtime_struct); seconds = timegm(&unixtime_struct); } else { /* otherwise, input is a number */ char * after = NULL; microseconds_after_decimal = llrint(strtod(datestr, &after) * 1000000); if (after && *after != '\0') fprintf(stderr, "warning: %s: ignoring \"%s\"\n", __func__, after); } return (seconds * 1000000 + microseconds_after_decimal) * 1e-6; } static int evaluate_unit(struct quantity stack[static QRPN_STACK_SIZE_MAX], int S, const char * const token, const int exponent_sign) { const char * slash = strchr(token, '/'); if (slash && exponent_sign < 0) return QRPN_ERROR_TOKEN_UNRECOGNIZED; const char * const carat = strrchr(token, '^'); const size_t bytes_before_carat = carat ? (size_t)(carat - token) : (slash ? (size_t)(slash - token) : strlen(token)); const long long unit_exponent = exponent_sign * (carat ? strtoll(carat + 1, NULL, 10) : 1); const struct named_quantity * quantity = NULL; const struct si_prefix * prefix = NULL; /* loop over all known units and prefixes looking for a match */ for (const struct named_quantity * possible_quantity = named_quantities; !quantity && possible_quantity < named_quantities + named_quantity_count; possible_quantity++) /* loop over [full name, abbreviation, alt spelling] of each unit. this is a bit of a mess */ for (int ipass = 0; !quantity && ipass < 3; ipass++) { const char * const unit_name = 2 == ipass ? possible_quantity->alt_spelling : 1 == ipass ? possible_quantity->abrv : possible_quantity->name; if (!unit_name) continue; /* get number of bytes in unit name because we're gonna need it many times */ const size_t unit_len = strlen(unit_name); if (bytes_before_carat < unit_len || memcmp(token + bytes_before_carat - unit_len, unit_name, unit_len)) continue; const size_t bytes_before_unit = bytes_before_carat - unit_len; prefix = NULL; /* loop over known si prefixes */ for (const struct si_prefix * possible_prefix = si_prefixes; !prefix && possible_prefix < si_prefixes + sizeof(si_prefixes) / sizeof(si_prefixes[0]); possible_prefix++) { /* if looking for SI unit abbreviations, admit SI prefix abbreviations */ const char * const prefix_name = 1 == ipass ? possible_prefix->abrv : possible_prefix->name; const size_t prefix_len = prefix_name ? strlen(prefix_name) : 0; if (bytes_before_unit == prefix_len && !memcmp(token, prefix_name, bytes_before_unit)) prefix = possible_prefix; } /* if there were bytes before the unit but they didn't match any known prefix, then dont treat as a unit */ if (!bytes_before_unit || prefix) quantity = possible_quantity; } /* not finding anything above is only an error if there was both a numerator and denominator */ if (!quantity) return QRPN_ERROR_TOKEN_UNRECOGNIZED; if (quantity->flags & FLAG_UNIT_ENTERS_AS_OPERAND) { if (S >= QRPN_STACK_SIZE_MAX) return QRPN_ERROR_TOO_MUCH_STACK; S++; stack[S - 1] = (struct quantity) { .value = 1 }; } if (!S) return QRPN_ERROR_NOT_ENOUGH_STACK; int units_out[BASEUNITS]; for (size_t iu = 0; iu < BASEUNITS; iu++) { units_out[iu] = (int8_t)(stack[S - 1].units[iu] + quantity->units[iu] * unit_exponent); if (units_out[iu] > INT8_MAX || units_out[iu] < INT8_MIN) return QRPN_ERROR_DIMENSION_OVERFLOW; } for (size_t iu = 0; iu < BASEUNITS; iu++) stack[S - 1].units[iu] = units_out[iu]; stack[S - 1].value *= pow(prefix ? prefix->scale * quantity->value : quantity->value, unit_exponent); if (slash) return evaluate_unit(stack, S, slash + 1, -exponent_sign); else return S; } static int evaluate_literal(struct quantity * stack, int S, const char * const token) { struct quantity tmp = { 0 }; char * endptr = NULL; const double dv = strtod(token, &endptr); /* check for special things or units if endptr doesn't move OR if the first character is not number-like (necessary to differentiate "nan" from "nano*") */ if (endptr == token || token[0] >= 'A') { if (!strcmp(token, "pi")) tmp.value = M_PI; else if (!strcmp(token, "-pi")) tmp.value = -M_PI; else if (!strcmp(token, "i")) tmp.value = I; else if (!strcmp(token, "-i")) tmp.value = -I; else if (!strcmp(token, "nan")) tmp.value = NAN; else return evaluate_unit(stack, S, token, 1); } else { /* otherwise, token was not a unit name, parse it as a simple literal */ double d = 0, m = 0, s = 0; if (strpbrk(token + 1, "d°") && sscanf(token, "%lf%*[d°]%lf%*[m']%lf%*[s\"]", &d, &m, &s)) tmp.value = copysign(fabs(d) + m / 60.0 + s / 3600.0, d) * M_PI / 180.0; else if (strpbrk(token, "T") && strpbrk(token, "Z")) { tmp.value = datestr_to_unix_seconds(token); tmp.units[2] = 1; } else { tmp.value = dv; if (!strcmp(endptr, "i")) tmp.value *= I; else if (endptr == token) return evaluate_unit(stack, S, token, 1); else if (endptr[0] != '\0' && endptr[1] == '\0') { double prefix_scale = 1.0; /* only allow k, M, G to be used in this position */ if ('k' == endptr[0]) prefix_scale = 1e3; else if ('M' == endptr[0]) prefix_scale = 1e6; else if ('G' == endptr[0]) prefix_scale = 1e9; /* special case: trailing 'f' from floating point literals copied and pasted from C code should be ignored */ else if ('f' == endptr[0]) prefix_scale = 1.0; else return QRPN_ERROR_TOKEN_UNRECOGNIZED; tmp.value *= prefix_scale; } } } if (S >= QRPN_STACK_SIZE_MAX) return QRPN_ERROR_TOO_MUCH_STACK; stack[S] = tmp; return S + 1; } static int evaluate_one_argument_must_be_unitless(struct quantity * const stack, int S, double complex (* op)(double complex)) { if (S < 1) return QRPN_ERROR_NOT_ENOUGH_STACK; if (!units_are_dimensionless(stack[S - 1].units)) return QRPN_ERROR_MUST_BE_UNITLESS; stack[S - 1].value = op(stack[S - 1].value); return S; } static int evaluate_one_argument_must_be_unitless_real(struct quantity * const stack, int S, double (* op)(double)) { if (S < 1) return QRPN_ERROR_NOT_ENOUGH_STACK; if (!units_are_dimensionless(stack[S - 1].units)) return QRPN_ERROR_MUST_BE_UNITLESS; stack[S - 1].value = op(creal(stack[S - 1].value)); return S; } static int evaluate_one_argument_must_be_unitless_real_nonnegative(struct quantity * const stack, int S, double (* op)(double)) { if (S < 1) return QRPN_ERROR_NOT_ENOUGH_STACK; if (!units_are_dimensionless(stack[S - 1].units)) return QRPN_ERROR_MUST_BE_UNITLESS; if (cimag(stack[S - 1].value) != 0) return QRPN_ERROR_MUST_BE_REAL; if (creal(stack[S - 1].value) < 0) return QRPN_ERROR_MUST_BE_NONNEGATIVE; stack[S - 1].value = op(creal(stack[S - 1].value)); return S; } int qrpn_evaluate_token(struct quantity * const stack, int S, const char * const token) { if (!strcmp(token, "mul") || !strcmp(token, "*")) { if (S < 2) return QRPN_ERROR_NOT_ENOUGH_STACK; /* calculate and validate output units */ int units_out[BASEUNITS]; for (size_t iu = 0; iu < BASEUNITS; iu++) { units_out[iu] = stack[S - 2].units[iu] + stack[S - 1].units[iu]; if (units_out[iu] > INT8_MAX || units_out[iu] < INT8_MIN) return QRPN_ERROR_DIMENSION_OVERFLOW; } /* note that we perform all possible validation before we mutate any state */ stack[S - 2].value *= stack[S - 1].value; for (size_t iu = 0; iu < BASEUNITS; iu++) stack[S - 2].units[iu] = units_out[iu]; return S - 1; } else if (!strcmp(token, "div") || !strcmp(token, "/")) { if (S < 2) return QRPN_ERROR_NOT_ENOUGH_STACK; int units_out[BASEUNITS]; for (size_t iu = 0; iu < BASEUNITS; iu++) { units_out[iu] = stack[S - 2].units[iu] - stack[S - 1].units[iu]; if (units_out[iu] > INT8_MAX || units_out[iu] < INT8_MIN) return QRPN_ERROR_DIMENSION_OVERFLOW; } stack[S - 2].value /= stack[S - 1].value; for (size_t iu = 0; iu < BASEUNITS; iu++) stack[S - 2].units[iu] = units_out[iu]; return S - 1; } else if (!strcmp(token, "idiv")) { if (S < 2) return QRPN_ERROR_NOT_ENOUGH_STACK; if (!units_are_dimensionless(stack[S - 1].units) || !units_are_dimensionless(stack[S - 2].units)) return QRPN_ERROR_MUST_BE_UNITLESS; const long long a = llrint(creal(stack[S - 2].value)); const long long b = llrint(creal(stack[S - 1].value)); if (!b) return QRPN_ERROR_DOMAIN; const long long c = a / b; stack[S - 2].value = c; return S - 1; } else if (!strcmp(token, "add") || !strcmp(token, "+")) { if (S < 2) return QRPN_ERROR_NOT_ENOUGH_STACK; if (!units_are_equivalent(stack[S - 2].units, stack[S - 1].units)) return QRPN_ERROR_INCONSISTENT_UNITS; stack[S - 2].value += stack[S - 1].value; return S - 1; } else if (!strcmp(token, "sub") || !strcmp(token, "-")) { if (S < 2) return QRPN_ERROR_NOT_ENOUGH_STACK; if (!units_are_equivalent(stack[S - 2].units, stack[S - 1].units)) return QRPN_ERROR_INCONSISTENT_UNITS; stack[S - 2].value -= stack[S - 1].value; return S - 1; } else if (!strcmp(token, "mod") || !strcmp(token, "%")) { if (S < 2) return QRPN_ERROR_NOT_ENOUGH_STACK; if (!units_are_equivalent(stack[S - 2].units, stack[S - 1].units)) return QRPN_ERROR_INCONSISTENT_UNITS; if (cimag(stack[S - 2].value) || cimag(stack[S - 1].value) ) return QRPN_ERROR_MUST_BE_REAL; stack[S - 2].value = fmod(creal(stack[S - 2].value), creal(stack[S - 1].value)); return S - 1; } else if (!strcmp(token, "hypot")) { if (S < 2) return QRPN_ERROR_NOT_ENOUGH_STACK; if (!units_are_equivalent(stack[S - 2].units, stack[S - 1].units)) return QRPN_ERROR_INCONSISTENT_UNITS; if (cimag(stack[S - 2].value) || cimag(stack[S - 1].value) ) return QRPN_ERROR_MUST_BE_REAL; stack[S - 2].value = hypot(creal(stack[S - 2].value), creal(stack[S - 1].value)); return S - 1; } else if (!strcmp(token, "atan2")) { if (S < 2) return QRPN_ERROR_NOT_ENOUGH_STACK; if (!units_are_equivalent(stack[S - 2].units, stack[S - 1].units)) return QRPN_ERROR_INCONSISTENT_UNITS; if (cimag(stack[S - 2].value) || cimag(stack[S - 1].value) ) return QRPN_ERROR_MUST_BE_REAL; stack[S - 2].value = atan2(creal(stack[S - 2].value), creal(stack[S - 1].value)); memset(stack[S - 2].units, 0, sizeof(int8_t[BASEUNITS])); return S - 1; } else if (!strcmp(token, "rcp")) { if (S < 1) return QRPN_ERROR_NOT_ENOUGH_STACK; for (size_t iu = 0; iu < BASEUNITS; iu++) if (stack[S - 1].units[iu] < -INT8_MAX) return QRPN_ERROR_DIMENSION_OVERFLOW; stack[S - 1].value = 1.0 / stack[S - 1].value; for (size_t iu = 0; iu < BASEUNITS; iu++) stack[S - 1].units[iu] *= -1; return S; } else if (!strcmp(token, "chs")) { if (S < 1) return QRPN_ERROR_NOT_ENOUGH_STACK; stack[S - 1].value *= -1; /* always choose positive imaginary side of negative real line because [1] [chs] [sqrt] is pretty common */ if (__imag__ stack[S - 1].value == -0) __imag__ stack[S - 1].value = 0; return S; } else if (!strcmp(token, "choose")) { if (S < 2) return QRPN_ERROR_NOT_ENOUGH_STACK; if (!units_are_equivalent(stack[S - 2].units, stack[S - 1].units)) return QRPN_ERROR_INCONSISTENT_UNITS; if (cimag(stack[S - 2].value) || cimag(stack[S - 1].value) ) return QRPN_ERROR_MUST_BE_REAL; const unsigned long long n = (unsigned long long)llrint(creal(stack[S - 2].value)); const unsigned long long k = (unsigned long long)llrint(creal(stack[S - 1].value)); if ((double)n != stack[S - 2].value || (double)k != stack[S - 1].value) return QRPN_ERROR_MUST_BE_INTEGER; stack[S - 2].value = nchoosek(n, k); return S - 1; } else if (!strcmp(token, "gcd")) { if (S < 2) return QRPN_ERROR_NOT_ENOUGH_STACK; if (!units_are_dimensionless(stack[S - 1].units) || !units_are_dimensionless(stack[S - 2].units)) return QRPN_ERROR_MUST_BE_UNITLESS; if (cimag(stack[S - 2].value) || cimag(stack[S - 1].value) ) return QRPN_ERROR_MUST_BE_REAL; if (creal(stack[S - 2].value) < 0 || creal(stack[S - 1].value) < 0 ) return QRPN_ERROR_MUST_BE_NONNEGATIVE; const unsigned long long a = (unsigned long long)llrint(creal(stack[S - 2].value)); const unsigned long long b = (unsigned long long)llrint(creal(stack[S - 1].value)); if ((double)a != stack[S - 2].value || (double)b != stack[S - 1].value) return QRPN_ERROR_MUST_BE_INTEGER; stack[S - 2].value = gcd(a, b); return S - 1; } else if (!strcmp(token, "lcm")) { if (S < 2) return QRPN_ERROR_NOT_ENOUGH_STACK; if (!units_are_dimensionless(stack[S - 1].units) || !units_are_dimensionless(stack[S - 2].units)) return QRPN_ERROR_MUST_BE_UNITLESS; if (cimag(stack[S - 2].value) || cimag(stack[S - 1].value) ) return QRPN_ERROR_MUST_BE_REAL; if (creal(stack[S - 2].value) < 0 || creal(stack[S - 1].value) < 0 ) return QRPN_ERROR_MUST_BE_NONNEGATIVE; const unsigned long long a = (unsigned long long)llrint(creal(stack[S - 2].value)); const unsigned long long b = (unsigned long long)llrint(creal(stack[S - 1].value)); if ((double)a != stack[S - 2].value || (double)b != stack[S - 1].value) return QRPN_ERROR_MUST_BE_INTEGER; stack[S - 2].value = a * b / gcd(a, b); return S - 1; } else if (!strcmp(token, "isprime")) { if (S < 1) return QRPN_ERROR_NOT_ENOUGH_STACK; if (cimag(stack[S - 1].value) != 0) return QRPN_ERROR_MUST_BE_REAL; if (creal(stack[S - 1].value) < 0) return QRPN_ERROR_MUST_BE_NONNEGATIVE; if (!units_are_dimensionless(stack[S - 1].units)) return QRPN_ERROR_MUST_BE_UNITLESS; const unsigned long long x = (unsigned long long)llrint(creal(stack[S - 1].value)); if (x > 1ULL << 53) return QRPN_ERROR_DOMAIN; if ((double)x != (double)creal(stack[S - 1].value)) return QRPN_ERROR_MUST_BE_INTEGER; stack[S - 1].value = isprime(x); return S; } else if (!strcmp(token, "swap")) { if (S < 2) return QRPN_ERROR_NOT_ENOUGH_STACK; struct quantity tmp = stack[S - 1]; stack[S - 1] = stack[S - 2]; stack[S - 2] = tmp; return S; } else if (!strcmp(token, "drop")) { if (S < 1) return QRPN_ERROR_NOT_ENOUGH_STACK; return S - 1; } else if (!strcmp(token, "dup")) { if (S < 1) return QRPN_ERROR_NOT_ENOUGH_STACK; if (S >= QRPN_STACK_SIZE_MAX) return QRPN_ERROR_TOO_MUCH_STACK; stack[S] = stack[S - 1]; return S + 1; } else if (!strcmp(token, "over")) { if (S < 2) return QRPN_ERROR_NOT_ENOUGH_STACK; if (S >= QRPN_STACK_SIZE_MAX) return QRPN_ERROR_TOO_MUCH_STACK; stack[S] = stack[S - 2]; return S + 1; } else if (!strcmp(token, "pick")) { if (S < 2) return QRPN_ERROR_NOT_ENOUGH_STACK; if (!units_are_dimensionless(stack[S - 1].units)) return QRPN_ERROR_MUST_BE_UNITLESS; if (cimag(stack[S - 1].value)) return QRPN_ERROR_MUST_BE_REAL; if (creal(stack[S - 1].value) < 0) return QRPN_ERROR_MUST_BE_NONNEGATIVE; const long arg = lrint(creal(stack[S - 1].value)); if (S < 2 + arg) return QRPN_ERROR_NOT_ENOUGH_STACK; stack[S - 1] = stack[S - arg - 2]; return S; } else if (!strcmp(token, "roll")) { if (S < 2) return QRPN_ERROR_NOT_ENOUGH_STACK; if (!units_are_dimensionless(stack[S - 1].units)) return QRPN_ERROR_MUST_BE_UNITLESS; if (cimag(stack[S - 1].value)) return QRPN_ERROR_MUST_BE_REAL; if (creal(stack[S - 1].value) < 0) return QRPN_ERROR_MUST_BE_NONNEGATIVE; const long arg = lrint(creal(stack[S - 1].value)); if (S < 2 + arg) return QRPN_ERROR_NOT_ENOUGH_STACK; const struct quantity tmp = stack[S - arg - 2]; memmove(stack + S - arg - 2, stack + S - arg - 1, sizeof(struct quantity) * arg); stack[S - 2] = tmp; return S - 1; } else if (!strcmp(token, "and")) { if (S < 2) return QRPN_ERROR_NOT_ENOUGH_STACK; if (!units_are_dimensionless(stack[S - 1].units) || !units_are_dimensionless(stack[S - 2].units)) return QRPN_ERROR_MUST_BE_UNITLESS; stack[S - 2].value = (!!stack[S - 2].value) && (!!stack[S - 1].value); return S - 1; } else if (!strcmp(token, "or")) { if (S < 2) return QRPN_ERROR_NOT_ENOUGH_STACK; if (!units_are_dimensionless(stack[S - 1].units) || !units_are_dimensionless(stack[S - 2].units)) return QRPN_ERROR_MUST_BE_UNITLESS; stack[S - 2].value = (!!stack[S - 2].value) || (!!stack[S - 1].value); return S - 1; } else if (!strcmp(token, "not")) { if (S < 1) return QRPN_ERROR_NOT_ENOUGH_STACK; if (!units_are_dimensionless(stack[S - 1].units)) return QRPN_ERROR_MUST_BE_UNITLESS; stack[S - 1].value = !stack[S - 1].value; return S; } else if (!strcmp(token, "eq")) { if (S < 2) return QRPN_ERROR_NOT_ENOUGH_STACK; if (!units_are_equivalent(stack[S - 2].units, stack[S - 1].units)) return QRPN_ERROR_INCONSISTENT_UNITS; stack[S - 2].value = stack[S - 2].value == stack[S - 1].value; memset(stack[S - 2].units, 0, sizeof(int8_t[BASEUNITS])); return S - 1; } else if (!strcmp(token, "le") || !strcmp(token, "lt") || !strcmp(token, "ge") || !strcmp(token, "gt")) { if (S < 2) return QRPN_ERROR_NOT_ENOUGH_STACK; if (!units_are_equivalent(stack[S - 2].units, stack[S - 1].units)) return QRPN_ERROR_INCONSISTENT_UNITS; if (cimag(stack[S - 1].value) || cimag(stack[S - 2].value) ) return QRPN_ERROR_DOMAIN; memset(stack[S - 2].units, 0, sizeof(int8_t[BASEUNITS])); if (!strcmp(token, "le")) stack[S - 2].value = creal(stack[S - 2].value) <= creal(stack[S - 1].value); else if (!strcmp(token, "lt")) stack[S - 2].value = creal(stack[S - 2].value) < creal(stack[S - 1].value); else if (!strcmp(token, "ge")) stack[S - 2].value = creal(stack[S - 2].value) >= creal(stack[S - 1].value); else if (!strcmp(token, "gt")) stack[S - 2].value = creal(stack[S - 2].value) > creal(stack[S - 1].value); return S - 1; } else if (!strcmp(token, "quadratic")) { if (S < 3) return QRPN_ERROR_NOT_ENOUGH_STACK; int units_out[BASEUNITS]; for (size_t iu = 0; iu < BASEUNITS; iu++) { if (stack[S - 1].units[iu] != stack[S - 2].units[iu] * 2 - stack[S - 3].units[iu]) return QRPN_ERROR_INCONSISTENT_UNITS; units_out[iu] = stack[S - 2].units[iu] - stack[S - 3].units[iu]; if (units_out[iu] > INT8_MAX || units_out[iu] < INT8_MIN) return QRPN_ERROR_DIMENSION_OVERFLOW; } const double complex a = stack[S - 3].value; const double complex b = stack[S - 2].value; const double complex c = stack[S - 1].value; const double complex discriminant = b * b - 4.0 * a * c; const double complex d = 0.5 / a; const double complex e = csqrt(discriminant); /* well-conditioned floating point method of getting roots, which avoids subtracting two nearly equal magnitude numbers */ const double complex r1 = __real__ e > 0 ? (-b - e) * d : (-b + e) * d; const double complex r0 = c / (r1 * a); stack[S - 3].value = r1; stack[S - 2].value = r0; for (size_t iu = 0; iu < BASEUNITS; iu++) { stack[S - 3].units[iu] = units_out[iu]; stack[S - 2].units[iu] = units_out[iu]; } return S - 1; } else if (!strcmp(token, "rot")) { if (S < 3) return QRPN_ERROR_NOT_ENOUGH_STACK; struct quantity tmp = stack[S - 3]; stack[S - 3] = stack[S - 2]; stack[S - 2] = stack[S - 1]; stack[S - 1] = tmp; return S; } else if (!strcmp(token, "pow")) { if (S < 2) return QRPN_ERROR_NOT_ENOUGH_STACK; if (!units_are_dimensionless(stack[S - 1].units)) return QRPN_ERROR_MUST_BE_UNITLESS; if (cimag(stack[S - 1].value)) return QRPN_ERROR_DOMAIN; if (units_are_dimensionless(stack[S - 2].units)) stack[S - 2].value = cpow_checked(stack[S - 2].value, creal(stack[S - 1].value)); else { const long ipowarg = lrint(creal(stack[S - 1].value)); if ((double)ipowarg != stack[S - 1].value) return QRPN_ERROR_MUST_BE_INTEGER; long long units_out[BASEUNITS]; for (size_t iu = 0; iu < BASEUNITS; iu++) { units_out[iu] = stack[S - 2].units[iu] * ipowarg; if (units_out[iu] > INT8_MAX || units_out[iu] < INT8_MIN) return QRPN_ERROR_DIMENSION_OVERFLOW; } stack[S - 2].value = cpow_checked(stack[S - 2].value, stack[S - 1].value); for (size_t iu = 0; iu < BASEUNITS; iu++) stack[S - 2].units[iu] = units_out[iu]; } return S - 1; } else if (!strcmp(token, "rpow")) { if (S < 2) return QRPN_ERROR_NOT_ENOUGH_STACK; if (!units_are_dimensionless(stack[S - 1].units)) return QRPN_ERROR_MUST_BE_UNITLESS; if (cimag(stack[S - 1].value)) return QRPN_ERROR_DOMAIN; if (units_are_dimensionless(stack[S - 2].units)) stack[S - 2].value = cpow_checked(stack[S - 2].value, 1.0 / stack[S - 1].value); else { const long long ipowarg = llrint(creal(stack[S - 1].value)); if ((double)ipowarg != stack[S - 1].value) return QRPN_ERROR_MUST_BE_INTEGER; for (size_t iu = 0; iu < BASEUNITS; iu++) if ((stack[S - 2].units[iu] / ipowarg) * ipowarg != stack[S - 2].units[iu]) return QRPN_ERROR_RATIONAL_NOT_IMPLEMENTED; stack[S - 2].value = cpow_checked(stack[S - 2].value, 1.0 / stack[S - 1].value); for (size_t iu = 0; iu < BASEUNITS; iu++) stack[S - 2].units[iu] /= ipowarg; } return S - 1; } else if (!strcmp(token, "gamma")) { if (S < 1) return QRPN_ERROR_NOT_ENOUGH_STACK; if (!units_are_dimensionless(stack[S - 1].units)) return QRPN_ERROR_MUST_BE_UNITLESS; if (cimag(stack[S - 1].value)) return QRPN_ERROR_DOMAIN; stack[S - 1].value = tgamma(creal(stack[S - 1].value)); return S; } else if (!strcmp(token, "br")) { if (S < 4) return QRPN_ERROR_NOT_ENOUGH_STACK; if (!units_are_dimensionless(stack[S - 1].units) || !units_are_dimensionless(stack[S - 2].units) || !units_are_dimensionless(stack[S - 3].units) || !units_are_dimensionless(stack[S - 4].units)) return QRPN_ERROR_MUST_BE_UNITLESS; if (cimag(stack[S - 1].value) || cimag(stack[S - 2].value) || cimag(stack[S - 3].value) || cimag(stack[S - 4].value)) return QRPN_ERROR_DOMAIN; const double a[2] = { creal(stack[S - 4].value), creal(stack[S - 3].value) }; const double b[2] = { creal(stack[S - 2].value), creal(stack[S - 1].value) }; const double d[2] = { b[0] - a[0], b[1] - a[1] }; double bearing = 0, range = 0; if (d[0] || d[1]) { /* todo */ const double cosa1 = cos(a[1]), cosb1 = cos(b[1]); bearing = atan2( sin(d[0]) * cosb1, cosa1 * sin(b[1]) - sin(a[1]) * cosb1 * cos(d[0]) ); if (bearing < 0.0) bearing += 2.0 * M_PI; range = ahav( hav(d[1]) + cosb1 * cosa1 * hav(d[0]) ); } stack[S - 4].value = bearing; stack[S - 3].value = range * 6371000.0; stack[S - 3].units[0] = 1; return S - 2; } else if (!strcmp(token, "travel")) { if (S < 4) return QRPN_ERROR_NOT_ENOUGH_STACK; if (stack[S - 1].units[0] == 1) { /* sketchy */ stack[S - 1].units[0] = 0; stack[S - 1].value /= 6371000.0; } if (!units_are_dimensionless(stack[S - 1].units) || !units_are_dimensionless(stack[S - 2].units) || !units_are_dimensionless(stack[S - 3].units) || !units_are_dimensionless(stack[S - 4].units)) return QRPN_ERROR_MUST_BE_UNITLESS; if (cimag(stack[S - 1].value) || cimag(stack[S - 2].value) || cimag(stack[S - 3].value) || cimag(stack[S - 4].value)) return QRPN_ERROR_DOMAIN; /* todo */ const double in[2] = { creal(stack[S - 4].value), creal(stack[S - 3].value) }; const double bearing = creal(stack[S - 2].value), range = creal(stack[S - 1].value); /* range, bearing, and declination of start point */ const double a = range, B = bearing, c = M_PI_2 - in[1]; /* declination of endpoint */ const double b = ahav( hav(a - c) + sin(a) * sin(c) * hav(B) ); /* change in longitude */ const double A = atan2( sin(B) * sin(a) * sin(c), cos(a) - cos(c) * cos(b) ); /* endpoint longitude is start plus delta */ stack[S - 4].value = in[0] + A; /* endpoint latitude is 90 degrees minus endpoint declination */ stack[S - 3].value = M_PI_2 - b; return S - 2; } else if (!strcmp(token, "nextafter")) { if (S < 1) return QRPN_ERROR_NOT_ENOUGH_STACK; if (cimag(stack[S - 1].value)) return QRPN_ERROR_DOMAIN; stack[S - 1].value = nextafter(creal(stack[S - 1].value), DBL_MAX); return S; } else if (!strcmp(token, "nextafterf")) { if (S < 1) return QRPN_ERROR_NOT_ENOUGH_STACK; if (cimag(stack[S - 1].value)) return QRPN_ERROR_DOMAIN; stack[S - 1].value = nextafterf(crealf(stack[S - 1].value), FLT_MAX); return S; } else if (!strcmp(token, "arg")) { if (S < 1) return QRPN_ERROR_NOT_ENOUGH_STACK; stack[S - 1].value = carg(stack[S - 1].value); return S; } else if (!strcmp(token, "real")) { if (S < 1) return QRPN_ERROR_NOT_ENOUGH_STACK; stack[S - 1].value = creal(stack[S - 1].value); return S; } else if (!strcmp(token, "imaginary")) { if (S < 1) return QRPN_ERROR_NOT_ENOUGH_STACK; stack[S - 1].value = cimag(stack[S - 1].value); return S; } else if (!strcmp(token, "hav")) return evaluate_one_argument_must_be_unitless_real(stack, S, hav); else if (!strcmp(token, "crd")) return evaluate_one_argument_must_be_unitless_real(stack, S, crd); else if (!strcmp(token, "exsec")) return evaluate_one_argument_must_be_unitless_real(stack, S, exsecant); else if (!strcmp(token, "ahav")) return evaluate_one_argument_must_be_unitless_real(stack, S, ahav); else if (!strcmp(token, "acrd")) return evaluate_one_argument_must_be_unitless_real(stack, S, acrd); else if (!strcmp(token, "aexsec")) return evaluate_one_argument_must_be_unitless_real(stack, S, arcexsecant); else if (!strcmp(token, "floor")) return evaluate_one_argument_must_be_unitless_real(stack, S, floor); else if (!strcmp(token, "ceil")) return evaluate_one_argument_must_be_unitless_real(stack, S, ceil); else if (!strcmp(token, "round")) return evaluate_one_argument_must_be_unitless_real(stack, S, round); else if (!strcmp(token, "erfc")) return evaluate_one_argument_must_be_unitless_real(stack, S, erfc); else if (!strcmp(token, "cos")) return evaluate_one_argument_must_be_unitless(stack, S, ccos); else if (!strcmp(token, "sin")) return evaluate_one_argument_must_be_unitless(stack, S, csin); else if (!strcmp(token, "tan")) return evaluate_one_argument_must_be_unitless(stack, S, ctan); else if (!strcmp(token, "tanh")) return evaluate_one_argument_must_be_unitless(stack, S, ctanh); else if (!strcmp(token, "acos")) return evaluate_one_argument_must_be_unitless(stack, S, cacos); else if (!strcmp(token, "asin")) return evaluate_one_argument_must_be_unitless(stack, S, casin); else if (!strcmp(token, "atan")) return evaluate_one_argument_must_be_unitless(stack, S, catan); else if (!strcmp(token, "exp")) return evaluate_one_argument_must_be_unitless(stack, S, cexp); else if (!strcmp(token, "log")) return evaluate_one_argument_must_be_unitless(stack, S, clog); else if (!strcmp(token, "log2")) return evaluate_one_argument_must_be_unitless_real_nonnegative(stack, S, log2); else if (!strcmp(token, "log10")) return evaluate_one_argument_must_be_unitless_real_nonnegative(stack, S, log10); else if (!strcmp(token, "tenlog")) return evaluate_one_argument_must_be_unitless_real_nonnegative(stack, S, tenlog); else if (!strcmp(token, "itenlog")) return evaluate_one_argument_must_be_unitless_real(stack, S, itenlog); else if (!strcmp(token, "square")) { if (S < 1) return QRPN_ERROR_NOT_ENOUGH_STACK; for (size_t iu = 0; iu < BASEUNITS; iu++) if (stack[S - 1].units[iu] * 2 > INT8_MAX || stack[S - 1].units[iu] * 2 < INT8_MIN) return QRPN_ERROR_DIMENSION_OVERFLOW; stack[S - 1].value = stack[S - 1].value * stack[S - 1].value; for (size_t iu = 0; iu < BASEUNITS; iu++) stack[S - 1].units[iu] *= 2; return S; } else if (!strcmp(token, "sqrt")) { if (S < 1) return QRPN_ERROR_NOT_ENOUGH_STACK; for (size_t iu = 0; iu < BASEUNITS; iu++) if ((stack[S - 1].units[iu] / 2) * 2 != stack[S - 1].units[iu]) return QRPN_ERROR_RATIONAL_NOT_IMPLEMENTED; stack[S - 1].value = csqrt(stack[S - 1].value); for (size_t iu = 0; iu < BASEUNITS; iu++) stack[S - 1].units[iu] /= 2; return S; } else if (!strcmp(token, "date")) { if (S < 1) return QRPN_ERROR_NOT_ENOUGH_STACK; if (!units_are_equivalent(stack[S - 1].units, units_of_time)) return QRPN_ERROR_INCONSISTENT_UNITS; if (cimag(stack[S - 1].value)) return QRPN_ERROR_DOMAIN; /* year, month, day, hour, minute, second */ time_t unixtime = floor(creal(stack[S - 1].value)); const double remainder = creal(stack[S - 1].value) - unixtime; struct tm unixtime_struct; gmtime_r(&unixtime, &unixtime_struct); if (S + 5 > QRPN_STACK_SIZE_MAX) return QRPN_ERROR_TOO_MUCH_STACK; S += 5; memset(stack + S - 6, 0, sizeof(struct quantity) * 6); stack[S - 6].value = unixtime_struct.tm_year + 1900; stack[S - 5].value = unixtime_struct.tm_mon + 1; stack[S - 4].value = unixtime_struct.tm_mday; stack[S - 3].value = unixtime_struct.tm_hour; stack[S - 2].value = unixtime_struct.tm_min; stack[S - 1].value = unixtime_struct.tm_sec + remainder; return S; } else if (!strcmp(token, "abs")) { if (S < 1) return QRPN_ERROR_NOT_ENOUGH_STACK; stack[S - 1].value = cabs(stack[S - 1].value); return S; } else if (!strcmp(token, "sum")) { if (S < 2) return QRPN_ERROR_NOT_ENOUGH_STACK; while (S > 1) { if (!units_are_equivalent(stack[S - 2].units, stack[S - 1].units)) return QRPN_ERROR_INCONSISTENT_UNITS; stack[S - 2].value += stack[S - 1].value; S--; } return S; } else if (!strcmp(token, "print")) { if (S < 1) return QRPN_ERROR_NOT_ENOUGH_STACK; fprintf_quantity(stderr, stack[S - 1]); fprintf(stderr, "\n"); return S; } else return evaluate_literal(stack, S, token); } static void fprintf_value(FILE * fh, const double complex value) { if (fabs(creal(value)) >= 1e6 && !cimag(value)) fprintf(fh, "%.16g", creal(value)); else if ((!creal(value) && cimag(value)) || fabs(creal(value)) * 1e14 < fabs(cimag(value))) { if (1.0 == cimag(value)) fprintf(fh, "i"); else if (-1.0 == cimag(value)) fprintf(fh, "-i"); else fprintf(fh, "%gi", cimag(value)); } else { fprintf(fh, "%g", creal(value)); if (cimag(value) && fabs(cimag(value)) * 1e14 > fabs(creal(value))) { fprintf(fh, " %c ", cimag(value) > 0 ? '+' : '-'); fprintf(fh, "%gi", fabs(cimag(value))); } } } static void fprintf_quantity_si_base(FILE * fh, const struct quantity quantity) { /* only use si base units */ fprintf_value(fh, quantity.value); static const char * si_base_unit_abbreviations[BASEUNITS] = { "m", "kg", "s", "A", "K", "Cd", "mol" }; for (size_t iu = 0; iu < BASEUNITS; iu++) { if (quantity.units[iu] > 0) fprintf(fh, " %s", si_base_unit_abbreviations[iu]); if (quantity.units[iu] > 1) fprintf(fh, "^%d", quantity.units[iu]); } for (size_t iu = 0; iu < BASEUNITS; iu++) if (quantity.units[iu] < 0) fprintf(fh, " %s^%d", si_base_unit_abbreviations[iu], quantity.units[iu]); } static void fprintf_quantity_si(FILE * fh, const struct quantity quantity) { /* look for SI-derived units with first positive, then negative exponents */ for (int sign = 1; sign > -3; sign -= 2) for (const struct named_quantity * named = named_quantities; named < named_quantities + named_quantity_count; named++) { int exponent; /* i hate everything about this and so should you */ if (named->flags & (FLAG_SI_BASE_UNIT | FLAG_SI_DERIVED_UNIT) && (exponent = units_are_power_of(&quantity, named)) * sign > 0) { fprintf_value(fh, quantity.value / named->value); fprintf(fh, " %s", named->name ? named->name : named->abrv); if (1 != exponent) fprintf(fh, "^%d", exponent); return; } } /* if we get here we're just looping through the SI base units */ fprintf_quantity_si_base(fh, quantity); } void fprintf_quantity(FILE * fh, const struct quantity quantity) { /* goofy shit that needs work: look for non-SI-base units which roughly match the quantity */ for (const struct named_quantity * named = named_quantities; named < named_quantities + named_quantity_count; named++) if (!(named->flags & (FLAG_SI_BASE_UNIT | FLAG_SI_DERIVED_UNIT)) && units_are_equivalent(quantity.units, named->units) && creal(quantity.value) && /* don't look at it marian */ cabs(quantity.value / named->value) < 1.000001 && cabs(named->value / quantity.value) < 1.000001) { if (!(named->flags & FLAG_UNIT_ENTERS_AS_OPERAND)) { fprintf_value(fh, quantity.value / named->value); fprintf(fh, " "); } fprintf(fh, "%s (", named->name ? named->name : named->abrv); fprintf_quantity_si(fh, quantity); fprintf(fh, ")"); return; } fprintf_quantity_si(fh, quantity); } void fprintf_stack(FILE * fh, struct quantity * stack, const int S) { if (!S) fprintf(fh, "[stack is empty]"); else for (int is = 0; is < S; is++) { fprintf_quantity(fh, stack[is]); if (is + 1 < S) fprintf(fh, ", "); } } char * qrpn_strerror(const int status) { if (status >= 0) return "success"; else if (QRPN_ERROR_TOKEN_UNRECOGNIZED == status) return "unrecognized"; else if (QRPN_ERROR_NOT_ENOUGH_STACK == status) return "not enough args"; else if (QRPN_ERROR_INCONSISTENT_UNITS == status) return "inconsistent units"; else if (QRPN_ERROR_MUST_BE_INTEGER == status) return "arg must be integer"; else if (QRPN_ERROR_MUST_BE_UNITLESS == status) return "arg must be unitless"; else if (QRPN_ERROR_MUST_BE_REAL == status) return "arg must be real-valued"; else if (QRPN_ERROR_MUST_BE_NONNEGATIVE == status) return "arg must be nonnegative"; else if (QRPN_ERROR_RATIONAL_NOT_IMPLEMENTED == status) return "noninteger units"; else if (QRPN_ERROR_DOMAIN == status) return "domain error"; else if (QRPN_ERROR_DIMENSION_OVERFLOW == status) return "dimension overflow"; else if (QRPN_ERROR_TOO_MUCH_STACK == status) return "insufficient stack space"; else if (QRPN_ERROR_UNMATCHED_CONTROL_STATEMENT == status) return "unmatched control statement"; else if (QRPN_ERROR_INEXACT_LITERAL == status) return "unrepresentable literal"; else return "undefined error"; } enum control_statement { NONE, ELSE_OR_ENDIF, ENDIF, UNTIL_OR_WHILE, REPEAT }; const char ** find_matching_control_statement(const char ** tp, const enum control_statement looking_for) { /* used to skip over branches not taken */ for (const char * token; (token = *tp); tp++) { if (!strcmp(token, "until") || !strcmp(token, "while")) return UNTIL_OR_WHILE == looking_for ? tp : NULL; else if (!strcmp(token, "repeat")) return REPEAT == looking_for ? tp : NULL; else if (!strcmp(token, "else") || !strcmp(token, "endif")) return ELSE_OR_ENDIF == looking_for || ENDIF == looking_for ? tp : NULL; else if (!strcmp(token, "if")) { tp = find_matching_control_statement(tp + 1, ELSE_OR_ENDIF); if (!tp) return NULL; else if (!strcmp(*tp, "else")) { tp = find_matching_control_statement(tp + 1, ENDIF); if (!tp) return NULL; } } else if (!strcmp(token, "begin")) { tp = find_matching_control_statement(tp + 1, UNTIL_OR_WHILE); if (!tp) return NULL; else if (!strcmp(*tp, "while")) { tp = find_matching_control_statement(tp + 1, REPEAT); if (!tp) return NULL; } } } return NULL; } int qrpn_evaluate_tokens(struct quantity * const stack, int S, const char ** const tokens, const size_t nest_level) { for (const char ** tp = tokens, * token; (token = *tp); tp++) { if (!strcmp(token, "else") || !strcmp(token, "endif") || !strcmp(token, "until") || !strcmp(token, "while") || !strcmp(token, "repeat")) return nest_level ? S : QRPN_ERROR_UNMATCHED_CONTROL_STATEMENT; else if (!strcmp(token, "begin")) { const char ** tp_until_or_while = find_matching_control_statement(tp + 1, UNTIL_OR_WHILE); if (!tp_until_or_while) return QRPN_ERROR_UNMATCHED_CONTROL_STATEMENT; else if (!strcmp(*tp_until_or_while, "while")) { const char ** tp_while = tp_until_or_while; const char ** tp_repeat = find_matching_control_statement(tp_while + 1, REPEAT); if (!tp_repeat) return QRPN_ERROR_UNMATCHED_CONTROL_STATEMENT; while (1) { S = qrpn_evaluate_tokens(stack, S, tp + 1, nest_level + 1); if (S < 0) return S; if (S < 1) return QRPN_ERROR_NOT_ENOUGH_STACK; if (!units_are_dimensionless(stack[S - 1].units)) return QRPN_ERROR_MUST_BE_UNITLESS; S--; if (!stack[S].value) break; S = qrpn_evaluate_tokens(stack, S, tp_while + 1, nest_level + 1); } tp = tp_repeat; } else { do { S = qrpn_evaluate_tokens(stack, S, tp + 1, nest_level + 1); if (S < 0) return S; if (S < 1) return QRPN_ERROR_NOT_ENOUGH_STACK; if (!units_are_dimensionless(stack[S - 1].units)) return QRPN_ERROR_MUST_BE_UNITLESS; S--; } while (!stack[S].value); tp = tp_until_or_while; } } else if (!strcmp(token, "if")) { if (S < 1) return QRPN_ERROR_NOT_ENOUGH_STACK; if (!units_are_dimensionless(stack[S - 1].units)) return QRPN_ERROR_MUST_BE_UNITLESS; const char ** tp_else_or_endif = find_matching_control_statement(tp + 1, ELSE_OR_ENDIF); const char ** tp_else = NULL, ** tp_endif; if (!tp_else_or_endif) return QRPN_ERROR_UNMATCHED_CONTROL_STATEMENT; else if (!strcmp(*tp_else_or_endif, "else")) { tp_else = tp_else_or_endif; tp_endif = find_matching_control_statement(tp_else + 1, ENDIF); if (!tp_endif) return QRPN_ERROR_UNMATCHED_CONTROL_STATEMENT; } else tp_endif = tp_else_or_endif; /* choose which branch to take */ const char ** tp_branch = stack[S - 1].value ? tp : tp_else; S--; S = qrpn_evaluate_tokens(stack, S, tp_branch + 1, nest_level + 1); tp = tp_endif; } else { S = qrpn_evaluate_token(stack, S, token); if (S < 0) return S; } } return S; } int qrpn_evaluate_string(struct quantity * const stack, int S, const char * string) { const char ** tokens = NULL; size_t T = 0; char * const copy = strdup(string); for (char * token, * p = copy; (token = strsep(&p, " ")); ) { T++; tokens = realloc(tokens, sizeof(char *) * (T + 1)); tokens[T - 1] = token; } tokens[T] = NULL; S = qrpn_evaluate_tokens(stack, S, tokens, 0); free(tokens); free(copy); return S; } int qrpn_try_token(const struct quantity stack[static QRPN_STACK_SIZE_MAX], const int S, const char * const token) { /* ideally we would have a strong guarantee that qrpn_evaluate_token would not mutate the input if it would result in an error */ struct quantity stack_copy[QRPN_STACK_SIZE_MAX]; memcpy(stack_copy, stack, sizeof(struct quantity) * S); return qrpn_evaluate_token(stack_copy, S, token); } int qrpn_try_string(const struct quantity stack[static QRPN_STACK_SIZE_MAX], const int S, const char * const string) { /* ideally we would have a strong guarantee that qrpn_evaluate_token would not mutate the input if it would result in an error */ struct quantity stack_copy[QRPN_STACK_SIZE_MAX]; memcpy(stack_copy, stack, sizeof(struct quantity) * S); return qrpn_evaluate_string(stack_copy, S, string); } #include /* if no other main() is linked, this one will be, and provides a simple command line interface */ __attribute((weak)) int main(const int argc, const char ** const argv) { if (isatty(STDIN_FILENO) && argc < 2) { /* never reached */ fprintf(stderr, "%s: Evaluates an RPN expression with units\n", argv[0]); exit(EXIT_FAILURE); } struct quantity stack[QRPN_STACK_SIZE_MAX]; int S = qrpn_evaluate_tokens(stack, 0, argv + 1, 0); if (S < 0) { fprintf(stderr, "error: %s\n", qrpn_strerror(S)); exit(EXIT_FAILURE); } fprintf_stack(stdout, stack, S); fprintf(stdout, "\n"); return 0; }