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/*
* Math built-ins
*/
#include "duk_internal.h"
#if defined(DUK_USE_MATH_BUILTIN)
/*
* Use static helpers which can work with math.h functions matching
* the following signatures. This is not portable if any of these math
* functions is actually a macro.
*
* Typing here is intentionally 'double' wherever values interact with
* the standard library APIs.
*/
typedef double (*duk__one_arg_func)(double);
typedef double (*duk__two_arg_func)(double, double);
DUK_LOCAL duk_ret_t duk__math_minmax(duk_hthread *thr, duk_double_t initial, duk__two_arg_func min_max) {
duk_idx_t n = duk_get_top(thr);
duk_idx_t i;
duk_double_t res = initial;
duk_double_t t;
/*
* Note: fmax() does not match the E5 semantics. E5 requires
* that if -any- input to Math.max() is a NaN, the result is a
* NaN. fmax() will return a NaN only if -both- inputs are NaN.
* Same applies to fmin().
*
* Note: every input value must be coerced with ToNumber(), even
* if we know the result will be a NaN anyway: ToNumber() may have
* side effects for which even order of evaluation matters.
*/
for (i = 0; i < n; i++) {
t = duk_to_number(thr, i);
if (DUK_FPCLASSIFY(t) == DUK_FP_NAN || DUK_FPCLASSIFY(res) == DUK_FP_NAN) {
/* Note: not normalized, but duk_push_number() will normalize */
res = (duk_double_t) DUK_DOUBLE_NAN;
} else {
res = (duk_double_t) min_max(res, (double) t);
}
}
duk_push_number(thr, res);
return 1;
}
DUK_LOCAL double duk__fmin_fixed(double x, double y) {
/* fmin() with args -0 and +0 is not guaranteed to return
* -0 as ECMAScript requires.
*/
if (duk_double_equals(x, 0.0) && duk_double_equals(y, 0.0)) {
duk_double_union du1, du2;
du1.d = x;
du2.d = y;
/* Already checked to be zero so these must hold, and allow us
* to check for "x is -0 or y is -0" by ORing the high parts
* for comparison.
*/
DUK_ASSERT(du1.ui[DUK_DBL_IDX_UI0] == 0 || du1.ui[DUK_DBL_IDX_UI0] == 0x80000000UL);
DUK_ASSERT(du2.ui[DUK_DBL_IDX_UI0] == 0 || du2.ui[DUK_DBL_IDX_UI0] == 0x80000000UL);
/* XXX: what's the safest way of creating a negative zero? */
if ((du1.ui[DUK_DBL_IDX_UI0] | du2.ui[DUK_DBL_IDX_UI0]) != 0) {
/* Enter here if either x or y (or both) is -0. */
return -0.0;
} else {
return +0.0;
}
}
return duk_double_fmin(x, y);
}
DUK_LOCAL double duk__fmax_fixed(double x, double y) {
/* fmax() with args -0 and +0 is not guaranteed to return
* +0 as ECMAScript requires.
*/
if (duk_double_equals(x, 0.0) && duk_double_equals(y, 0.0)) {
if (DUK_SIGNBIT(x) == 0 || DUK_SIGNBIT(y) == 0) {
return +0.0;
} else {
return -0.0;
}
}
return duk_double_fmax(x, y);
}
#if defined(DUK_USE_ES6)
DUK_LOCAL double duk__cbrt(double x) {
/* cbrt() is C99. To avoid hassling embedders with the need to provide a
* cube root function, we can get by with pow(). The result is not
* identical, but that's OK: ES2015 says it's implementation-dependent.
*/
#if defined(DUK_CBRT)
/* cbrt() matches ES2015 requirements. */
return DUK_CBRT(x);
#else
duk_small_int_t c = (duk_small_int_t) DUK_FPCLASSIFY(x);
/* pow() does not, however. */
if (c == DUK_FP_NAN || c == DUK_FP_INFINITE || c == DUK_FP_ZERO) {
return x;
}
if (DUK_SIGNBIT(x)) {
return -DUK_POW(-x, 1.0 / 3.0);
} else {
return DUK_POW(x, 1.0 / 3.0);
}
#endif
}
DUK_LOCAL double duk__log2(double x) {
#if defined(DUK_LOG2)
return DUK_LOG2(x);
#else
return DUK_LOG(x) * DUK_DOUBLE_LOG2E;
#endif
}
DUK_LOCAL double duk__log10(double x) {
#if defined(DUK_LOG10)
return DUK_LOG10(x);
#else
return DUK_LOG(x) * DUK_DOUBLE_LOG10E;
#endif
}
DUK_LOCAL double duk__trunc(double x) {
#if defined(DUK_TRUNC)
return DUK_TRUNC(x);
#else
/* Handles -0 correctly: -0.0 matches 'x >= 0.0' but floor()
* is required to return -0 when the argument is -0.
*/
return x >= 0.0 ? DUK_FLOOR(x) : DUK_CEIL(x);
#endif
}
#endif /* DUK_USE_ES6 */
DUK_LOCAL double duk__round_fixed(double x) {
/* Numbers half-way between integers must be rounded towards +Infinity,
* e.g. -3.5 must be rounded to -3 (not -4). When rounded to zero, zero
* sign must be set appropriately. E5.1 Section 15.8.2.15.
*
* Note that ANSI C round() is "round to nearest integer, away from zero",
* which is incorrect for negative values. Here we make do with floor().
*/
duk_small_int_t c = (duk_small_int_t) DUK_FPCLASSIFY(x);
if (c == DUK_FP_NAN || c == DUK_FP_INFINITE || c == DUK_FP_ZERO) {
return x;
}
/*
* x is finite and non-zero
*
* -1.6 -> floor(-1.1) -> -2
* -1.5 -> floor(-1.0) -> -1 (towards +Inf)
* -1.4 -> floor(-0.9) -> -1
* -0.5 -> -0.0 (special case)
* -0.1 -> -0.0 (special case)
* +0.1 -> +0.0 (special case)
* +0.5 -> floor(+1.0) -> 1 (towards +Inf)
* +1.4 -> floor(+1.9) -> 1
* +1.5 -> floor(+2.0) -> 2 (towards +Inf)
* +1.6 -> floor(+2.1) -> 2
*/
if (x >= -0.5 && x < 0.5) {
/* +0.5 is handled by floor, this is on purpose */
if (x < 0.0) {
return -0.0;
} else {
return +0.0;
}
}
return DUK_FLOOR(x + 0.5);
}
/* Wrappers for calling standard math library methods. These may be required
* on platforms where one or more of the math built-ins are defined as macros
* or inline functions and are thus not suitable to be used as function pointers.
*/
#if defined(DUK_USE_AVOID_PLATFORM_FUNCPTRS)
DUK_LOCAL double duk__fabs(double x) {
return DUK_FABS(x);
}
DUK_LOCAL double duk__acos(double x) {
return DUK_ACOS(x);
}
DUK_LOCAL double duk__asin(double x) {
return DUK_ASIN(x);
}
DUK_LOCAL double duk__atan(double x) {
return DUK_ATAN(x);
}
DUK_LOCAL double duk__ceil(double x) {
return DUK_CEIL(x);
}
DUK_LOCAL double duk__cos(double x) {
return DUK_COS(x);
}
DUK_LOCAL double duk__exp(double x) {
return DUK_EXP(x);
}
DUK_LOCAL double duk__floor(double x) {
return DUK_FLOOR(x);
}
DUK_LOCAL double duk__log(double x) {
return DUK_LOG(x);
}
DUK_LOCAL double duk__sin(double x) {
return DUK_SIN(x);
}
DUK_LOCAL double duk__sqrt(double x) {
return DUK_SQRT(x);
}
DUK_LOCAL double duk__tan(double x) {
return DUK_TAN(x);
}
DUK_LOCAL double duk__atan2_fixed(double x, double y) {
#if defined(DUK_USE_ATAN2_WORKAROUNDS)
/* Specific fixes to common atan2() implementation issues:
* - test-bug-mingw-math-issues.js
*/
if (DUK_ISINF(x) && DUK_ISINF(y)) {
if (DUK_SIGNBIT(x)) {
if (DUK_SIGNBIT(y)) {
return -2.356194490192345;
} else {
return -0.7853981633974483;
}
} else {
if (DUK_SIGNBIT(y)) {
return 2.356194490192345;
} else {
return 0.7853981633974483;
}
}
}
#else
/* Some ISO C assumptions. */
DUK_ASSERT(duk_double_equals(DUK_ATAN2(DUK_DOUBLE_INFINITY, DUK_DOUBLE_INFINITY), 0.7853981633974483));
DUK_ASSERT(duk_double_equals(DUK_ATAN2(-DUK_DOUBLE_INFINITY, DUK_DOUBLE_INFINITY), -0.7853981633974483));
DUK_ASSERT(duk_double_equals(DUK_ATAN2(DUK_DOUBLE_INFINITY, -DUK_DOUBLE_INFINITY), 2.356194490192345));
DUK_ASSERT(duk_double_equals(DUK_ATAN2(-DUK_DOUBLE_INFINITY, -DUK_DOUBLE_INFINITY), -2.356194490192345));
#endif
return DUK_ATAN2(x, y);
}
#endif /* DUK_USE_AVOID_PLATFORM_FUNCPTRS */
/* order must match constants in configure tooling */
DUK_LOCAL const duk__one_arg_func duk__one_arg_funcs[] = {
#if defined(DUK_USE_AVOID_PLATFORM_FUNCPTRS)
duk__fabs, duk__acos, duk__asin, duk__atan, duk__ceil, duk__cos, duk__exp,
duk__floor, duk__log, duk__round_fixed, duk__sin, duk__sqrt, duk__tan,
#if defined(DUK_USE_ES6)
duk__cbrt, duk__log2, duk__log10, duk__trunc
#endif
#else /* DUK_USE_AVOID_PLATFORM_FUNCPTRS */
DUK_FABS, DUK_ACOS, DUK_ASIN, DUK_ATAN, DUK_CEIL, DUK_COS, DUK_EXP,
DUK_FLOOR, DUK_LOG, duk__round_fixed, DUK_SIN, DUK_SQRT, DUK_TAN,
#if defined(DUK_USE_ES6)
duk__cbrt, duk__log2, duk__log10, duk__trunc
#endif
#endif /* DUK_USE_AVOID_PLATFORM_FUNCPTRS */
};
/* order must match constants in configure tooling */
DUK_LOCAL const duk__two_arg_func duk__two_arg_funcs[] = {
#if defined(DUK_USE_AVOID_PLATFORM_FUNCPTRS)
duk__atan2_fixed,
duk_js_arith_pow
#else
duk__atan2_fixed,
duk_js_arith_pow
#endif
};
DUK_INTERNAL duk_ret_t duk_bi_math_object_onearg_shared(duk_hthread *thr) {
duk_small_int_t fun_idx = duk_get_current_magic(thr);
duk__one_arg_func fun;
duk_double_t arg1;
DUK_ASSERT(fun_idx >= 0);
DUK_ASSERT(fun_idx < (duk_small_int_t) (sizeof(duk__one_arg_funcs) / sizeof(duk__one_arg_func)));
arg1 = duk_to_number(thr, 0);
fun = duk__one_arg_funcs[fun_idx];
duk_push_number(thr, (duk_double_t) fun((double) arg1));
return 1;
}
DUK_INTERNAL duk_ret_t duk_bi_math_object_twoarg_shared(duk_hthread *thr) {
duk_small_int_t fun_idx = duk_get_current_magic(thr);
duk__two_arg_func fun;
duk_double_t arg1;
duk_double_t arg2;
DUK_ASSERT(fun_idx >= 0);
DUK_ASSERT(fun_idx < (duk_small_int_t) (sizeof(duk__two_arg_funcs) / sizeof(duk__two_arg_func)));
arg1 = duk_to_number(thr, 0); /* explicit ordered evaluation to match coercion semantics */
arg2 = duk_to_number(thr, 1);
fun = duk__two_arg_funcs[fun_idx];
duk_push_number(thr, (duk_double_t) fun((double) arg1, (double) arg2));
return 1;
}
DUK_INTERNAL duk_ret_t duk_bi_math_object_max(duk_hthread *thr) {
return duk__math_minmax(thr, -DUK_DOUBLE_INFINITY, duk__fmax_fixed);
}
DUK_INTERNAL duk_ret_t duk_bi_math_object_min(duk_hthread *thr) {
return duk__math_minmax(thr, DUK_DOUBLE_INFINITY, duk__fmin_fixed);
}
DUK_INTERNAL duk_ret_t duk_bi_math_object_random(duk_hthread *thr) {
duk_push_number(thr, (duk_double_t) duk_util_get_random_double(thr));
return 1;
}
#if defined(DUK_USE_ES6)
DUK_INTERNAL duk_ret_t duk_bi_math_object_hypot(duk_hthread *thr) {
/*
* E6 Section 20.2.2.18: Math.hypot
*
* - If no arguments are passed, the result is +0.
* - If any argument is +inf, the result is +inf.
* - If any argument is -inf, the result is +inf.
* - If no argument is +inf or -inf, and any argument is NaN, the result is
* NaN.
* - If all arguments are either +0 or -0, the result is +0.
*/
duk_idx_t nargs;
duk_idx_t i;
duk_bool_t found_nan;
duk_double_t max;
duk_double_t sum, summand;
duk_double_t comp, prelim;
duk_double_t t;
nargs = duk_get_top(thr);
/* Find the highest value. Also ToNumber() coerces. */
max = 0.0;
found_nan = 0;
for (i = 0; i < nargs; i++) {
t = DUK_FABS(duk_to_number(thr, i));
if (DUK_FPCLASSIFY(t) == DUK_FP_NAN) {
found_nan = 1;
} else {
max = duk_double_fmax(max, t);
}
}
/* Early return cases. */
if (duk_double_equals(max, DUK_DOUBLE_INFINITY)) {
duk_push_number(thr, DUK_DOUBLE_INFINITY);
return 1;
} else if (found_nan) {
duk_push_number(thr, DUK_DOUBLE_NAN);
return 1;
} else if (duk_double_equals(max, 0.0)) {
duk_push_number(thr, 0.0);
/* Otherwise we'd divide by zero. */
return 1;
}
/* Use Kahan summation and normalize to the highest value to minimize
* floating point rounding error and avoid overflow.
*
* https://en.wikipedia.org/wiki/Kahan_summation_algorithm
*/
sum = 0.0;
comp = 0.0;
for (i = 0; i < nargs; i++) {
t = DUK_FABS(duk_get_number(thr, i)) / max;
summand = (t * t) - comp;
prelim = sum + summand;
comp = (prelim - sum) - summand;
sum = prelim;
}
duk_push_number(thr, (duk_double_t) DUK_SQRT(sum) * max);
return 1;
}
#endif /* DUK_USE_ES6 */
#if defined(DUK_USE_ES6)
DUK_INTERNAL duk_ret_t duk_bi_math_object_sign(duk_hthread *thr) {
duk_double_t d;
d = duk_to_number(thr, 0);
if (duk_double_is_nan(d)) {
DUK_ASSERT(duk_is_nan(thr, -1));
return 1; /* NaN input -> return NaN */
}
if (duk_double_equals(d, 0.0)) {
/* Zero sign kept, i.e. -0 -> -0, +0 -> +0. */
return 1;
}
duk_push_int(thr, (d > 0.0 ? 1 : -1));
return 1;
}
#endif /* DUK_USE_ES6 */
#if defined(DUK_USE_ES6)
DUK_INTERNAL duk_ret_t duk_bi_math_object_clz32(duk_hthread *thr) {
duk_uint32_t x;
duk_small_uint_t i;
#if defined(DUK_USE_PREFER_SIZE)
duk_uint32_t mask;
x = duk_to_uint32(thr, 0);
for (i = 0, mask = 0x80000000UL; mask != 0; mask >>= 1) {
if (x & mask) {
break;
}
i++;
}
DUK_ASSERT(i <= 32);
duk_push_uint(thr, i);
return 1;
#else /* DUK_USE_PREFER_SIZE */
i = 0;
x = duk_to_uint32(thr, 0);
if (x & 0xffff0000UL) {
x >>= 16;
} else {
i += 16;
}
if (x & 0x0000ff00UL) {
x >>= 8;
} else {
i += 8;
}
if (x & 0x000000f0UL) {
x >>= 4;
} else {
i += 4;
}
if (x & 0x0000000cUL) {
x >>= 2;
} else {
i += 2;
}
if (x & 0x00000002UL) {
x >>= 1;
} else {
i += 1;
}
if (x & 0x00000001UL) {
;
} else {
i += 1;
}
DUK_ASSERT(i <= 32);
duk_push_uint(thr, i);
return 1;
#endif /* DUK_USE_PREFER_SIZE */
}
#endif /* DUK_USE_ES6 */
#if defined(DUK_USE_ES6)
DUK_INTERNAL duk_ret_t duk_bi_math_object_imul(duk_hthread *thr) {
duk_uint32_t x, y, z;
x = duk_to_uint32(thr, 0);
y = duk_to_uint32(thr, 1);
z = x * y;
/* While arguments are ToUint32() coerced and the multiplication
* is unsigned as such, the final result is curiously interpreted
* as a signed 32-bit value.
*/
duk_push_i32(thr, (duk_int32_t) z);
return 1;
}
#endif /* DUK_USE_ES6 */
#endif /* DUK_USE_MATH_BUILTIN */