diff options
Diffstat (limited to 'source/luametatex/source/luacore/lua54/src/lmathlib.c')
-rw-r--r-- | source/luametatex/source/luacore/lua54/src/lmathlib.c | 764 |
1 files changed, 764 insertions, 0 deletions
diff --git a/source/luametatex/source/luacore/lua54/src/lmathlib.c b/source/luametatex/source/luacore/lua54/src/lmathlib.c new file mode 100644 index 000000000..e0c61a168 --- /dev/null +++ b/source/luametatex/source/luacore/lua54/src/lmathlib.c @@ -0,0 +1,764 @@ +/* +** $Id: lmathlib.c $ +** Standard mathematical library +** See Copyright Notice in lua.h +*/ + +#define lmathlib_c +#define LUA_LIB + +#include "lprefix.h" + + +#include <float.h> +#include <limits.h> +#include <math.h> +#include <stdlib.h> +#include <time.h> + +#include "lua.h" + +#include "lauxlib.h" +#include "lualib.h" + + +#undef PI +#define PI (l_mathop(3.141592653589793238462643383279502884)) + + +static int math_abs (lua_State *L) { + if (lua_isinteger(L, 1)) { + lua_Integer n = lua_tointeger(L, 1); + if (n < 0) n = (lua_Integer)(0u - (lua_Unsigned)n); + lua_pushinteger(L, n); + } + else + lua_pushnumber(L, l_mathop(fabs)(luaL_checknumber(L, 1))); + return 1; +} + +static int math_sin (lua_State *L) { + lua_pushnumber(L, l_mathop(sin)(luaL_checknumber(L, 1))); + return 1; +} + +static int math_cos (lua_State *L) { + lua_pushnumber(L, l_mathop(cos)(luaL_checknumber(L, 1))); + return 1; +} + +static int math_tan (lua_State *L) { + lua_pushnumber(L, l_mathop(tan)(luaL_checknumber(L, 1))); + return 1; +} + +static int math_asin (lua_State *L) { + lua_pushnumber(L, l_mathop(asin)(luaL_checknumber(L, 1))); + return 1; +} + +static int math_acos (lua_State *L) { + lua_pushnumber(L, l_mathop(acos)(luaL_checknumber(L, 1))); + return 1; +} + +static int math_atan (lua_State *L) { + lua_Number y = luaL_checknumber(L, 1); + lua_Number x = luaL_optnumber(L, 2, 1); + lua_pushnumber(L, l_mathop(atan2)(y, x)); + return 1; +} + + +static int math_toint (lua_State *L) { + int valid; + lua_Integer n = lua_tointegerx(L, 1, &valid); + if (l_likely(valid)) + lua_pushinteger(L, n); + else { + luaL_checkany(L, 1); + luaL_pushfail(L); /* value is not convertible to integer */ + } + return 1; +} + + +static void pushnumint (lua_State *L, lua_Number d) { + lua_Integer n; + if (lua_numbertointeger(d, &n)) /* does 'd' fit in an integer? */ + lua_pushinteger(L, n); /* result is integer */ + else + lua_pushnumber(L, d); /* result is float */ +} + + +static int math_floor (lua_State *L) { + if (lua_isinteger(L, 1)) + lua_settop(L, 1); /* integer is its own floor */ + else { + lua_Number d = l_mathop(floor)(luaL_checknumber(L, 1)); + pushnumint(L, d); + } + return 1; +} + + +static int math_ceil (lua_State *L) { + if (lua_isinteger(L, 1)) + lua_settop(L, 1); /* integer is its own ceil */ + else { + lua_Number d = l_mathop(ceil)(luaL_checknumber(L, 1)); + pushnumint(L, d); + } + return 1; +} + + +static int math_fmod (lua_State *L) { + if (lua_isinteger(L, 1) && lua_isinteger(L, 2)) { + lua_Integer d = lua_tointeger(L, 2); + if ((lua_Unsigned)d + 1u <= 1u) { /* special cases: -1 or 0 */ + luaL_argcheck(L, d != 0, 2, "zero"); + lua_pushinteger(L, 0); /* avoid overflow with 0x80000... / -1 */ + } + else + lua_pushinteger(L, lua_tointeger(L, 1) % d); + } + else + lua_pushnumber(L, l_mathop(fmod)(luaL_checknumber(L, 1), + luaL_checknumber(L, 2))); + return 1; +} + + +/* +** next function does not use 'modf', avoiding problems with 'double*' +** (which is not compatible with 'float*') when lua_Number is not +** 'double'. +*/ +static int math_modf (lua_State *L) { + if (lua_isinteger(L ,1)) { + lua_settop(L, 1); /* number is its own integer part */ + lua_pushnumber(L, 0); /* no fractional part */ + } + else { + lua_Number n = luaL_checknumber(L, 1); + /* integer part (rounds toward zero) */ + lua_Number ip = (n < 0) ? l_mathop(ceil)(n) : l_mathop(floor)(n); + pushnumint(L, ip); + /* fractional part (test needed for inf/-inf) */ + lua_pushnumber(L, (n == ip) ? l_mathop(0.0) : (n - ip)); + } + return 2; +} + + +static int math_sqrt (lua_State *L) { + lua_pushnumber(L, l_mathop(sqrt)(luaL_checknumber(L, 1))); + return 1; +} + + +static int math_ult (lua_State *L) { + lua_Integer a = luaL_checkinteger(L, 1); + lua_Integer b = luaL_checkinteger(L, 2); + lua_pushboolean(L, (lua_Unsigned)a < (lua_Unsigned)b); + return 1; +} + +static int math_log (lua_State *L) { + lua_Number x = luaL_checknumber(L, 1); + lua_Number res; + if (lua_isnoneornil(L, 2)) + res = l_mathop(log)(x); + else { + lua_Number base = luaL_checknumber(L, 2); +#if !defined(LUA_USE_C89) + if (base == l_mathop(2.0)) + res = l_mathop(log2)(x); + else +#endif + if (base == l_mathop(10.0)) + res = l_mathop(log10)(x); + else + res = l_mathop(log)(x)/l_mathop(log)(base); + } + lua_pushnumber(L, res); + return 1; +} + +static int math_exp (lua_State *L) { + lua_pushnumber(L, l_mathop(exp)(luaL_checknumber(L, 1))); + return 1; +} + +static int math_deg (lua_State *L) { + lua_pushnumber(L, luaL_checknumber(L, 1) * (l_mathop(180.0) / PI)); + return 1; +} + +static int math_rad (lua_State *L) { + lua_pushnumber(L, luaL_checknumber(L, 1) * (PI / l_mathop(180.0))); + return 1; +} + + +static int math_min (lua_State *L) { + int n = lua_gettop(L); /* number of arguments */ + int imin = 1; /* index of current minimum value */ + int i; + luaL_argcheck(L, n >= 1, 1, "value expected"); + for (i = 2; i <= n; i++) { + if (lua_compare(L, i, imin, LUA_OPLT)) + imin = i; + } + lua_pushvalue(L, imin); + return 1; +} + + +static int math_max (lua_State *L) { + int n = lua_gettop(L); /* number of arguments */ + int imax = 1; /* index of current maximum value */ + int i; + luaL_argcheck(L, n >= 1, 1, "value expected"); + for (i = 2; i <= n; i++) { + if (lua_compare(L, imax, i, LUA_OPLT)) + imax = i; + } + lua_pushvalue(L, imax); + return 1; +} + + +static int math_type (lua_State *L) { + if (lua_type(L, 1) == LUA_TNUMBER) + lua_pushstring(L, (lua_isinteger(L, 1)) ? "integer" : "float"); + else { + luaL_checkany(L, 1); + luaL_pushfail(L); + } + return 1; +} + + + +/* +** {================================================================== +** Pseudo-Random Number Generator based on 'xoshiro256**'. +** =================================================================== +*/ + +/* number of binary digits in the mantissa of a float */ +#define FIGS l_floatatt(MANT_DIG) + +#if FIGS > 64 +/* there are only 64 random bits; use them all */ +#undef FIGS +#define FIGS 64 +#endif + + +/* +** LUA_RAND32 forces the use of 32-bit integers in the implementation +** of the PRN generator (mainly for testing). +*/ +#if !defined(LUA_RAND32) && !defined(Rand64) + +/* try to find an integer type with at least 64 bits */ + +#if (ULONG_MAX >> 31 >> 31) >= 3 + +/* 'long' has at least 64 bits */ +#define Rand64 unsigned long + +#elif !defined(LUA_USE_C89) && defined(LLONG_MAX) + +/* there is a 'long long' type (which must have at least 64 bits) */ +#define Rand64 unsigned long long + +#elif (LUA_MAXUNSIGNED >> 31 >> 31) >= 3 + +/* 'lua_Integer' has at least 64 bits */ +#define Rand64 lua_Unsigned + +#endif + +#endif + + +#if defined(Rand64) /* { */ + +/* +** Standard implementation, using 64-bit integers. +** If 'Rand64' has more than 64 bits, the extra bits do not interfere +** with the 64 initial bits, except in a right shift. Moreover, the +** final result has to discard the extra bits. +*/ + +/* avoid using extra bits when needed */ +#define trim64(x) ((x) & 0xffffffffffffffffu) + + +/* rotate left 'x' by 'n' bits */ +static Rand64 rotl (Rand64 x, int n) { + return (x << n) | (trim64(x) >> (64 - n)); +} + +static Rand64 nextrand (Rand64 *state) { + Rand64 state0 = state[0]; + Rand64 state1 = state[1]; + Rand64 state2 = state[2] ^ state0; + Rand64 state3 = state[3] ^ state1; + Rand64 res = rotl(state1 * 5, 7) * 9; + state[0] = state0 ^ state3; + state[1] = state1 ^ state2; + state[2] = state2 ^ (state1 << 17); + state[3] = rotl(state3, 45); + return res; +} + + +/* must take care to not shift stuff by more than 63 slots */ + + +/* +** Convert bits from a random integer into a float in the +** interval [0,1), getting the higher FIG bits from the +** random unsigned integer and converting that to a float. +*/ + +/* must throw out the extra (64 - FIGS) bits */ +#define shift64_FIG (64 - FIGS) + +/* to scale to [0, 1), multiply by scaleFIG = 2^(-FIGS) */ +#define scaleFIG (l_mathop(0.5) / ((Rand64)1 << (FIGS - 1))) + +static lua_Number I2d (Rand64 x) { + return (lua_Number)(trim64(x) >> shift64_FIG) * scaleFIG; +} + +/* convert a 'Rand64' to a 'lua_Unsigned' */ +#define I2UInt(x) ((lua_Unsigned)trim64(x)) + +/* convert a 'lua_Unsigned' to a 'Rand64' */ +#define Int2I(x) ((Rand64)(x)) + + +#else /* no 'Rand64' }{ */ + +/* get an integer with at least 32 bits */ +#if LUAI_IS32INT +typedef unsigned int lu_int32; +#else +typedef unsigned long lu_int32; +#endif + + +/* +** Use two 32-bit integers to represent a 64-bit quantity. +*/ +typedef struct Rand64 { + lu_int32 h; /* higher half */ + lu_int32 l; /* lower half */ +} Rand64; + + +/* +** If 'lu_int32' has more than 32 bits, the extra bits do not interfere +** with the 32 initial bits, except in a right shift and comparisons. +** Moreover, the final result has to discard the extra bits. +*/ + +/* avoid using extra bits when needed */ +#define trim32(x) ((x) & 0xffffffffu) + + +/* +** basic operations on 'Rand64' values +*/ + +/* build a new Rand64 value */ +static Rand64 packI (lu_int32 h, lu_int32 l) { + Rand64 result; + result.h = h; + result.l = l; + return result; +} + +/* return i << n */ +static Rand64 Ishl (Rand64 i, int n) { + lua_assert(n > 0 && n < 32); + return packI((i.h << n) | (trim32(i.l) >> (32 - n)), i.l << n); +} + +/* i1 ^= i2 */ +static void Ixor (Rand64 *i1, Rand64 i2) { + i1->h ^= i2.h; + i1->l ^= i2.l; +} + +/* return i1 + i2 */ +static Rand64 Iadd (Rand64 i1, Rand64 i2) { + Rand64 result = packI(i1.h + i2.h, i1.l + i2.l); + if (trim32(result.l) < trim32(i1.l)) /* carry? */ + result.h++; + return result; +} + +/* return i * 5 */ +static Rand64 times5 (Rand64 i) { + return Iadd(Ishl(i, 2), i); /* i * 5 == (i << 2) + i */ +} + +/* return i * 9 */ +static Rand64 times9 (Rand64 i) { + return Iadd(Ishl(i, 3), i); /* i * 9 == (i << 3) + i */ +} + +/* return 'i' rotated left 'n' bits */ +static Rand64 rotl (Rand64 i, int n) { + lua_assert(n > 0 && n < 32); + return packI((i.h << n) | (trim32(i.l) >> (32 - n)), + (trim32(i.h) >> (32 - n)) | (i.l << n)); +} + +/* for offsets larger than 32, rotate right by 64 - offset */ +static Rand64 rotl1 (Rand64 i, int n) { + lua_assert(n > 32 && n < 64); + n = 64 - n; + return packI((trim32(i.h) >> n) | (i.l << (32 - n)), + (i.h << (32 - n)) | (trim32(i.l) >> n)); +} + +/* +** implementation of 'xoshiro256**' algorithm on 'Rand64' values +*/ +static Rand64 nextrand (Rand64 *state) { + Rand64 res = times9(rotl(times5(state[1]), 7)); + Rand64 t = Ishl(state[1], 17); + Ixor(&state[2], state[0]); + Ixor(&state[3], state[1]); + Ixor(&state[1], state[2]); + Ixor(&state[0], state[3]); + Ixor(&state[2], t); + state[3] = rotl1(state[3], 45); + return res; +} + + +/* +** Converts a 'Rand64' into a float. +*/ + +/* an unsigned 1 with proper type */ +#define UONE ((lu_int32)1) + + +#if FIGS <= 32 + +/* 2^(-FIGS) */ +#define scaleFIG (l_mathop(0.5) / (UONE << (FIGS - 1))) + +/* +** get up to 32 bits from higher half, shifting right to +** throw out the extra bits. +*/ +static lua_Number I2d (Rand64 x) { + lua_Number h = (lua_Number)(trim32(x.h) >> (32 - FIGS)); + return h * scaleFIG; +} + +#else /* 32 < FIGS <= 64 */ + +/* must take care to not shift stuff by more than 31 slots */ + +/* 2^(-FIGS) = 1.0 / 2^30 / 2^3 / 2^(FIGS-33) */ +#define scaleFIG \ + (l_mathop(1.0) / (UONE << 30) / l_mathop(8.0) / (UONE << (FIGS - 33))) + +/* +** use FIGS - 32 bits from lower half, throwing out the other +** (32 - (FIGS - 32)) = (64 - FIGS) bits +*/ +#define shiftLOW (64 - FIGS) + +/* +** higher 32 bits go after those (FIGS - 32) bits: shiftHI = 2^(FIGS - 32) +*/ +#define shiftHI ((lua_Number)(UONE << (FIGS - 33)) * l_mathop(2.0)) + + +static lua_Number I2d (Rand64 x) { + lua_Number h = (lua_Number)trim32(x.h) * shiftHI; + lua_Number l = (lua_Number)(trim32(x.l) >> shiftLOW); + return (h + l) * scaleFIG; +} + +#endif + + +/* convert a 'Rand64' to a 'lua_Unsigned' */ +static lua_Unsigned I2UInt (Rand64 x) { + return ((lua_Unsigned)trim32(x.h) << 31 << 1) | (lua_Unsigned)trim32(x.l); +} + +/* convert a 'lua_Unsigned' to a 'Rand64' */ +static Rand64 Int2I (lua_Unsigned n) { + return packI((lu_int32)(n >> 31 >> 1), (lu_int32)n); +} + +#endif /* } */ + + +/* +** A state uses four 'Rand64' values. +*/ +typedef struct { + Rand64 s[4]; +} RanState; + + +/* +** Project the random integer 'ran' into the interval [0, n]. +** Because 'ran' has 2^B possible values, the projection can only be +** uniform when the size of the interval is a power of 2 (exact +** division). Otherwise, to get a uniform projection into [0, n], we +** first compute 'lim', the smallest Mersenne number not smaller than +** 'n'. We then project 'ran' into the interval [0, lim]. If the result +** is inside [0, n], we are done. Otherwise, we try with another 'ran', +** until we have a result inside the interval. +*/ +static lua_Unsigned project (lua_Unsigned ran, lua_Unsigned n, + RanState *state) { + if ((n & (n + 1)) == 0) /* is 'n + 1' a power of 2? */ + return ran & n; /* no bias */ + else { + lua_Unsigned lim = n; + /* compute the smallest (2^b - 1) not smaller than 'n' */ + lim |= (lim >> 1); + lim |= (lim >> 2); + lim |= (lim >> 4); + lim |= (lim >> 8); + lim |= (lim >> 16); +#if (LUA_MAXUNSIGNED >> 31) >= 3 + lim |= (lim >> 32); /* integer type has more than 32 bits */ +#endif + lua_assert((lim & (lim + 1)) == 0 /* 'lim + 1' is a power of 2, */ + && lim >= n /* not smaller than 'n', */ + && (lim >> 1) < n); /* and it is the smallest one */ + while ((ran &= lim) > n) /* project 'ran' into [0..lim] */ + ran = I2UInt(nextrand(state->s)); /* not inside [0..n]? try again */ + return ran; + } +} + + +static int math_random (lua_State *L) { + lua_Integer low, up; + lua_Unsigned p; + RanState *state = (RanState *)lua_touserdata(L, lua_upvalueindex(1)); + Rand64 rv = nextrand(state->s); /* next pseudo-random value */ + switch (lua_gettop(L)) { /* check number of arguments */ + case 0: { /* no arguments */ + lua_pushnumber(L, I2d(rv)); /* float between 0 and 1 */ + return 1; + } + case 1: { /* only upper limit */ + low = 1; + up = luaL_checkinteger(L, 1); + if (up == 0) { /* single 0 as argument? */ + lua_pushinteger(L, I2UInt(rv)); /* full random integer */ + return 1; + } + break; + } + case 2: { /* lower and upper limits */ + low = luaL_checkinteger(L, 1); + up = luaL_checkinteger(L, 2); + break; + } + default: return luaL_error(L, "wrong number of arguments"); + } + /* random integer in the interval [low, up] */ + luaL_argcheck(L, low <= up, 1, "interval is empty"); + /* project random integer into the interval [0, up - low] */ + p = project(I2UInt(rv), (lua_Unsigned)up - (lua_Unsigned)low, state); + lua_pushinteger(L, p + (lua_Unsigned)low); + return 1; +} + + +static void setseed (lua_State *L, Rand64 *state, + lua_Unsigned n1, lua_Unsigned n2) { + int i; + state[0] = Int2I(n1); + state[1] = Int2I(0xff); /* avoid a zero state */ + state[2] = Int2I(n2); + state[3] = Int2I(0); + for (i = 0; i < 16; i++) + nextrand(state); /* discard initial values to "spread" seed */ + lua_pushinteger(L, n1); + lua_pushinteger(L, n2); +} + + +/* +** Set a "random" seed. To get some randomness, use the current time +** and the address of 'L' (in case the machine does address space layout +** randomization). +*/ +static void randseed (lua_State *L, RanState *state) { + lua_Unsigned seed1 = (lua_Unsigned)time(NULL); + lua_Unsigned seed2 = (lua_Unsigned)(size_t)L; + setseed(L, state->s, seed1, seed2); +} + + +static int math_randomseed (lua_State *L) { + RanState *state = (RanState *)lua_touserdata(L, lua_upvalueindex(1)); + if (lua_isnone(L, 1)) { + randseed(L, state); + } + else { + lua_Integer n1 = luaL_checkinteger(L, 1); + lua_Integer n2 = luaL_optinteger(L, 2, 0); + setseed(L, state->s, n1, n2); + } + return 2; /* return seeds */ +} + + +static const luaL_Reg randfuncs[] = { + {"random", math_random}, + {"randomseed", math_randomseed}, + {NULL, NULL} +}; + + +/* +** Register the random functions and initialize their state. +*/ +static void setrandfunc (lua_State *L) { + RanState *state = (RanState *)lua_newuserdatauv(L, sizeof(RanState), 0); + randseed(L, state); /* initialize with a "random" seed */ + lua_pop(L, 2); /* remove pushed seeds */ + luaL_setfuncs(L, randfuncs, 1); +} + +/* }================================================================== */ + + +/* +** {================================================================== +** Deprecated functions (for compatibility only) +** =================================================================== +*/ +#if defined(LUA_COMPAT_MATHLIB) + +static int math_cosh (lua_State *L) { + lua_pushnumber(L, l_mathop(cosh)(luaL_checknumber(L, 1))); + return 1; +} + +static int math_sinh (lua_State *L) { + lua_pushnumber(L, l_mathop(sinh)(luaL_checknumber(L, 1))); + return 1; +} + +static int math_tanh (lua_State *L) { + lua_pushnumber(L, l_mathop(tanh)(luaL_checknumber(L, 1))); + return 1; +} + +static int math_pow (lua_State *L) { + lua_Number x = luaL_checknumber(L, 1); + lua_Number y = luaL_checknumber(L, 2); + lua_pushnumber(L, l_mathop(pow)(x, y)); + return 1; +} + +static int math_frexp (lua_State *L) { + int e; + lua_pushnumber(L, l_mathop(frexp)(luaL_checknumber(L, 1), &e)); + lua_pushinteger(L, e); + return 2; +} + +static int math_ldexp (lua_State *L) { + lua_Number x = luaL_checknumber(L, 1); + int ep = (int)luaL_checkinteger(L, 2); + lua_pushnumber(L, l_mathop(ldexp)(x, ep)); + return 1; +} + +static int math_log10 (lua_State *L) { + lua_pushnumber(L, l_mathop(log10)(luaL_checknumber(L, 1))); + return 1; +} + +#endif +/* }================================================================== */ + + + +static const luaL_Reg mathlib[] = { + {"abs", math_abs}, + {"acos", math_acos}, + {"asin", math_asin}, + {"atan", math_atan}, + {"ceil", math_ceil}, + {"cos", math_cos}, + {"deg", math_deg}, + {"exp", math_exp}, + {"tointeger", math_toint}, + {"floor", math_floor}, + {"fmod", math_fmod}, + {"ult", math_ult}, + {"log", math_log}, + {"max", math_max}, + {"min", math_min}, + {"modf", math_modf}, + {"rad", math_rad}, + {"sin", math_sin}, + {"sqrt", math_sqrt}, + {"tan", math_tan}, + {"type", math_type}, +#if defined(LUA_COMPAT_MATHLIB) + {"atan2", math_atan}, + {"cosh", math_cosh}, + {"sinh", math_sinh}, + {"tanh", math_tanh}, + {"pow", math_pow}, + {"frexp", math_frexp}, + {"ldexp", math_ldexp}, + {"log10", math_log10}, +#endif + /* placeholders */ + {"random", NULL}, + {"randomseed", NULL}, + {"pi", NULL}, + {"huge", NULL}, + {"maxinteger", NULL}, + {"mininteger", NULL}, + {NULL, NULL} +}; + + +/* +** Open math library +*/ +LUAMOD_API int luaopen_math (lua_State *L) { + luaL_newlib(L, mathlib); + lua_pushnumber(L, PI); + lua_setfield(L, -2, "pi"); + lua_pushnumber(L, (lua_Number)HUGE_VAL); + lua_setfield(L, -2, "huge"); + lua_pushinteger(L, LUA_MAXINTEGER); + lua_setfield(L, -2, "maxinteger"); + lua_pushinteger(L, LUA_MININTEGER); + lua_setfield(L, -2, "mininteger"); + setrandfunc(L); + return 1; +} + |