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_ATAN2(DUK_DOUBLE_INFINITY, DUK_DOUBLE_INFINITY) == 0.7853981633974483);
DUK_ASSERT(DUK_ATAN2(-DUK_DOUBLE_INFINITY, DUK_DOUBLE_INFINITY) == -0.7853981633974483);
DUK_ASSERT(DUK_ATAN2(DUK_DOUBLE_INFINITY, -DUK_DOUBLE_INFINITY) == 2.356194490192345);
DUK_ASSERT(DUK_ATAN2(-DUK_DOUBLE_INFINITY, -DUK_DOUBLE_INFINITY) == -2.356194490192345);
#endif
return DUK_ATAN2(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 (x == 0 && y == 0) {
if (DUK_SIGNBIT(x) == 0 || DUK_SIGNBIT(y) == 0) {
return +0.0;
} else {
return -0.0;
}
}
return duk_double_fmax(x, y);
}
static double fmax_fixed(double x, double y) {
/* fmax() with args -0 and +0 is not guaranteed to return
* +0 as Ecmascript requires.
*/
if (x == 0 && y == 0) {
if (DUK_SIGNBIT(x) == 0 || DUK_SIGNBIT(y) == 0) {
return +0.0;
} else {
return -0.0;
}
}
#ifdef DUK_USE_MATH_FMAX
return fmax(x, y);
#else
return (x > y ? x : y);
#endif
}
static double fmin_fixed(double x, double y) {
/* fmin() with args -0 and +0 is not guaranteed to return
* -0 as Ecmascript requires.
*/
if (x == 0 && y == 0) {
/* XXX: what's the safest way of creating a negative zero? */
if (DUK_SIGNBIT(x) != 0 || DUK_SIGNBIT(y) != 0) {
return -0.0;
} else {
return +0.0;
}
}
#ifdef DUK_USE_MATH_FMIN
return fmin(x, y);
#else
return (x < y ? x : y);
#endif
}
/* exposed, used by e.g. duk_bi_date.c */
DUK_INTERNAL duk_double_t duk_js_tointeger_number(duk_double_t x) {
duk_small_int_t c = (duk_small_int_t) DUK_FPCLASSIFY(x);
if (c == DUK_FP_NAN) {
return 0.0;
} else if (c == DUK_FP_ZERO || c == DUK_FP_INFINITE) {
/* XXX: FP_ZERO check can be removed, the else clause handles it
* correctly (preserving sign).
*/
return x;
} else {
duk_small_int_t s = (duk_small_int_t) DUK_SIGNBIT(x);
x = DUK_FLOOR(DUK_FABS(x)); /* truncate towards zero */
if (s) {
x = -x;
}
return x;
}
}
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
}
/* combined algorithm matching E5 Sections 9.5 and 9.6 */
DUK_LOCAL duk_double_t duk__toint32_touint32_helper(duk_double_t x, duk_bool_t is_toint32) {
duk_small_int_t c = (duk_small_int_t) DUK_FPCLASSIFY(x);
duk_small_int_t s;
if (c == DUK_FP_NAN || c == DUK_FP_ZERO || c == DUK_FP_INFINITE) {
return 0.0;
}
/* x = sign(x) * floor(abs(x)), i.e. truncate towards zero, keep sign */
s = (duk_small_int_t) DUK_SIGNBIT(x);
x = DUK_FLOOR(DUK_FABS(x));
if (s) {
x = -x;
}
/* NOTE: fmod(x) result sign is same as sign of x, which
* differs from what Javascript wants (see Section 9.6).
*/
x = DUK_FMOD(x, DUK_DOUBLE_2TO32); /* -> x in ]-2**32, 2**32[ */
if (x < 0.0) {
x += DUK_DOUBLE_2TO32;
}
/* -> x in [0, 2**32[ */
if (is_toint32) {
if (x >= DUK_DOUBLE_2TO31) {
/* x in [2**31, 2**32[ */
x -= DUK_DOUBLE_2TO32; /* -> x in [-2**31,2**31[ */
}
}
return x;
}
DUK_INTERNAL duk_bool_t duk_js_compare_helper(duk_hthread *thr, duk_tval *tv_x, duk_tval *tv_y, duk_small_int_t flags) {
duk_context *ctx = (duk_context *) thr;
duk_double_t d1, d2;
duk_small_int_t c1, c2;
duk_small_int_t s1, s2;
duk_small_int_t rc;
duk_bool_t retval;
/* Fast path for fastints */
#if defined(DUK_USE_FASTINT)
if (DUK_TVAL_IS_FASTINT(tv_x) && DUK_TVAL_IS_FASTINT(tv_y)) {
duk_int64_t v1 = DUK_TVAL_GET_FASTINT(tv_x);
duk_int64_t v2 = DUK_TVAL_GET_FASTINT(tv_y);
if (v1 < v2) {
/* 'lt is true' */
retval = 1;
} else {
retval = 0;
}
if (flags & DUK_COMPARE_FLAG_NEGATE) {
retval ^= 1;
}
return retval;
}
#endif /* DUK_USE_FASTINT */
/* Fast path for numbers (one of which may be a fastint) */
#if 1 /* XXX: make fast paths optional for size minimization? */
if (DUK_TVAL_IS_NUMBER(tv_x) && DUK_TVAL_IS_NUMBER(tv_y)) {
d1 = DUK_TVAL_GET_NUMBER(tv_x);
d2 = DUK_TVAL_GET_NUMBER(tv_y);
c1 = DUK_FPCLASSIFY(d1);
c2 = DUK_FPCLASSIFY(d2);
if (c1 == DUK_FP_NORMAL && c2 == DUK_FP_NORMAL) {
/* XXX: this is a very narrow check, and doesn't cover
* zeroes, subnormals, infinities, which compare normally.
*/
if (d1 < d2) {
/* 'lt is true' */
retval = 1;
} else {
retval = 0;
}
if (flags & DUK_COMPARE_FLAG_NEGATE) {
retval ^= 1;
}
return retval;
}
}
#endif
/* Slow path */
duk_push_tval(ctx, tv_x);
duk_push_tval(ctx, tv_y);
if (flags & DUK_COMPARE_FLAG_EVAL_LEFT_FIRST) {
duk_to_primitive(ctx, -2, DUK_HINT_NUMBER);
duk_to_primitive(ctx, -1, DUK_HINT_NUMBER);
} else {
duk_to_primitive(ctx, -1, DUK_HINT_NUMBER);
duk_to_primitive(ctx, -2, DUK_HINT_NUMBER);
}
/* Note: reuse variables */
tv_x = duk_get_tval(ctx, -2);
tv_y = duk_get_tval(ctx, -1);
if (DUK_TVAL_IS_STRING(tv_x) && DUK_TVAL_IS_STRING(tv_y)) {
duk_hstring *h1 = DUK_TVAL_GET_STRING(tv_x);
duk_hstring *h2 = DUK_TVAL_GET_STRING(tv_y);
DUK_ASSERT(h1 != NULL);
DUK_ASSERT(h2 != NULL);
rc = duk_js_string_compare(h1, h2);
if (rc < 0) {
goto lt_true;
} else {
goto lt_false;
}
} else {
/* Ordering should not matter (E5 Section 11.8.5, step 3.a) but
* preserve it just in case.
*/
if (flags & DUK_COMPARE_FLAG_EVAL_LEFT_FIRST) {
d1 = duk_to_number(ctx, -2);
d2 = duk_to_number(ctx, -1);
} else {
d2 = duk_to_number(ctx, -1);
d1 = duk_to_number(ctx, -2);
}
c1 = (duk_small_int_t) DUK_FPCLASSIFY(d1);
s1 = (duk_small_int_t) DUK_SIGNBIT(d1);
c2 = (duk_small_int_t) DUK_FPCLASSIFY(d2);
s2 = (duk_small_int_t) DUK_SIGNBIT(d2);
if (c1 == DUK_FP_NAN || c2 == DUK_FP_NAN) {
goto lt_undefined;
}
if (c1 == DUK_FP_ZERO && c2 == DUK_FP_ZERO) {
/* For all combinations: +0 < +0, +0 < -0, -0 < +0, -0 < -0,
* steps e, f, and g.
*/
goto lt_false;
}
if (d1 == d2) {
goto lt_false;
}
if (c1 == DUK_FP_INFINITE && s1 == 0) {
/* x == +Infinity */
goto lt_false;
}
if (c2 == DUK_FP_INFINITE && s2 == 0) {
/* y == +Infinity */
goto lt_true;
}
if (c2 == DUK_FP_INFINITE && s2 != 0) {
/* y == -Infinity */
goto lt_false;
}
if (c1 == DUK_FP_INFINITE && s1 != 0) {
/* x == -Infinity */
goto lt_true;
}
if (d1 < d2) {
goto lt_true;
}
goto lt_false;
}
lt_undefined:
/* Note: undefined from Section 11.8.5 always results in false
* return (see e.g. Section 11.8.3) - hence special treatment here.
*/
retval = 0;
goto cleanup;
lt_true:
if (flags & DUK_COMPARE_FLAG_NEGATE) {
retval = 0;
goto cleanup;
} else {
retval = 1;
goto cleanup;
}
/* never here */
lt_false:
if (flags & DUK_COMPARE_FLAG_NEGATE) {
retval = 1;
goto cleanup;
} else {
retval = 0;
goto cleanup;
}
/* never here */
cleanup:
duk_pop_2(ctx);
return retval;
}
DUK_LOCAL duk_bool_t duk__js_samevalue_number(duk_double_t x, duk_double_t y) {
#if defined(DUK_USE_PARANOID_MATH)
duk_small_int_t cx = (duk_small_int_t) DUK_FPCLASSIFY(x);
duk_small_int_t cy = (duk_small_int_t) DUK_FPCLASSIFY(y);
if (cx == DUK_FP_NAN && cy == DUK_FP_NAN) {
/* SameValue(NaN, NaN) = true, regardless of NaN sign or extra bits */
return 1;
}
if (cx == DUK_FP_ZERO && cy == DUK_FP_ZERO) {
/* Note: cannot assume that a non-zero return value of signbit() would
* always be the same -- hence cannot (portably) use something like:
*
* signbit(x) == signbit(y)
*/
duk_small_int_t sx = (DUK_SIGNBIT(x) ? 1 : 0);
duk_small_int_t sy = (DUK_SIGNBIT(y) ? 1 : 0);
return (sx == sy);
}
/* normal comparison; known:
* - both x and y are not NaNs (but one of them can be)
* - both x and y are not zero (but one of them can be)
* - x and y may be denormal or infinite
*/
return (x == y);
#else /* DUK_USE_PARANOID_MATH */
duk_small_int_t cx = (duk_small_int_t) DUK_FPCLASSIFY(x);
duk_small_int_t cy = (duk_small_int_t) DUK_FPCLASSIFY(y);
if (x == y) {
/* IEEE requires that NaNs compare false */
DUK_ASSERT(DUK_FPCLASSIFY(x) != DUK_FP_NAN);
DUK_ASSERT(DUK_FPCLASSIFY(y) != DUK_FP_NAN);
/* Using classification has smaller footprint than direct comparison. */
if (DUK_UNLIKELY(cx == DUK_FP_ZERO && cy == DUK_FP_ZERO)) {
/* Note: cannot assume that a non-zero return value of signbit() would
* always be the same -- hence cannot (portably) use something like:
*
* signbit(x) == signbit(y)
*/
duk_small_int_t sx = (DUK_SIGNBIT(x) ? 1 : 0);
duk_small_int_t sy = (DUK_SIGNBIT(y) ? 1 : 0);
return (sx == sy);
}
return 1;
} else {
/* IEEE requires that zeros compare the same regardless
* of their signed, so if both x and y are zeroes, they
* are caught above.
*/
DUK_ASSERT(!(DUK_FPCLASSIFY(x) == DUK_FP_ZERO && DUK_FPCLASSIFY(y) == DUK_FP_ZERO));
/* Difference to non-strict/strict comparison is that NaNs compare
* equal and signed zero signs matter.
*/
if (DUK_UNLIKELY(cx == DUK_FP_NAN && cy == DUK_FP_NAN)) {
/* SameValue(NaN, NaN) = true, regardless of NaN sign or extra bits */
return 1;
}
return 0;
}
#endif /* DUK_USE_PARANOID_MATH */
}
static double duk__pow_fixed(double x, double y) {
/* The ANSI C pow() semantics differ from Ecmascript.
*
* E.g. when x==1 and y is +/- infinite, the Ecmascript required
* result is NaN, while at least Linux pow() returns 1.
*/
int cx, cy, sx;
DUK_UNREF(cx);
DUK_UNREF(sx);
cy = DUK_FPCLASSIFY(y);
if (cy == DUK_FP_NAN) {
goto ret_nan;
}
if (DUK_FABS(x) == 1.0 && cy == DUK_FP_INFINITE) {
goto ret_nan;
}
#if defined(DUK_USE_POW_NETBSD_WORKAROUND)
/* See test-bug-netbsd-math-pow.js: NetBSD 6.0 on x86 (at least) does not
* correctly handle some cases where x=+/-0. Specific fixes to these
* here.
*/
cx = DUK_FPCLASSIFY(x);
if (cx == DUK_FP_ZERO && y < 0.0) {
sx = DUK_SIGNBIT(x);
if (sx == 0) {
/* Math.pow(+0,y) should be Infinity when y<0. NetBSD pow()
* returns -Infinity instead when y is <0 and finite. The
* if-clause also catches y == -Infinity (which works even
* without the fix).
*/
return DUK_DOUBLE_INFINITY;
} else {
/* Math.pow(-0,y) where y<0 should be:
* - -Infinity if y<0 and an odd integer
* - Infinity otherwise
* NetBSD pow() returns -Infinity for all finite y<0. The
* if-clause also catches y == -Infinity (which works even
* without the fix).
*/
/* fmod() return value has same sign as input (negative) so
* the result here will be in the range ]-2,0], 1 indicates
* odd. If x is -Infinity, NaN is returned and the odd check
* always concludes "not odd" which results in desired outcome.
*/
double tmp = DUK_FMOD(y, 2);
if (tmp == -1.0) {
return -DUK_DOUBLE_INFINITY;
} else {
/* Not odd, or y == -Infinity */
return DUK_DOUBLE_INFINITY;
}
}
}
#endif
return DUK_POW(x, y);
ret_nan:
return DUK_DOUBLE_NAN;
}
duk_bool_t duk_js_compare_helper(duk_hthread *thr, duk_tval *tv_x, duk_tval *tv_y, duk_small_int_t flags) {
duk_context *ctx = (duk_context *) thr;
duk_double_t d1, d2;
duk_small_int_t c1, c2;
duk_small_int_t s1, s2;
duk_small_int_t rc;
duk_bool_t retval;
duk_push_tval(ctx, tv_x);
duk_push_tval(ctx, tv_y);
if (flags & DUK_COMPARE_FLAG_EVAL_LEFT_FIRST) {
duk_to_primitive(ctx, -2, DUK_HINT_NUMBER);
duk_to_primitive(ctx, -1, DUK_HINT_NUMBER);
} else {
duk_to_primitive(ctx, -1, DUK_HINT_NUMBER);
duk_to_primitive(ctx, -2, DUK_HINT_NUMBER);
}
/* Note: reuse variables */
tv_x = duk_get_tval(ctx, -2);
tv_y = duk_get_tval(ctx, -1);
if (DUK_TVAL_IS_STRING(tv_x) && DUK_TVAL_IS_STRING(tv_y)) {
duk_hstring *h1 = DUK_TVAL_GET_STRING(tv_x);
duk_hstring *h2 = DUK_TVAL_GET_STRING(tv_y);
DUK_ASSERT(h1 != NULL);
DUK_ASSERT(h2 != NULL);
rc = duk_js_string_compare(h1, h2);
if (rc < 0) {
goto lt_true;
} else {
goto lt_false;
}
} else {
/* Ordering should not matter (E5 Section 11.8.5, step 3.a) but
* preserve it just in case.
*/
if (flags & DUK_COMPARE_FLAG_EVAL_LEFT_FIRST) {
d1 = duk_to_number(ctx, -2);
d2 = duk_to_number(ctx, -1);
} else {
d2 = duk_to_number(ctx, -1);
d1 = duk_to_number(ctx, -2);
}
c1 = (duk_small_int_t) DUK_FPCLASSIFY(d1);
s1 = (duk_small_int_t) DUK_SIGNBIT(d1);
c2 = (duk_small_int_t) DUK_FPCLASSIFY(d2);
s2 = (duk_small_int_t) DUK_SIGNBIT(d2);
if (c1 == DUK_FP_NAN || c2 == DUK_FP_NAN) {
goto lt_undefined;
}
if (c1 == DUK_FP_ZERO && c2 == DUK_FP_ZERO) {
/* For all combinations: +0 < +0, +0 < -0, -0 < +0, -0 < -0,
* steps e, f, and g.
*/
goto lt_false;
}
if (d1 == d2) {
goto lt_false;
}
if (c1 == DUK_FP_INFINITE && s1 == 0) {
/* x == +Infinity */
goto lt_false;
}
if (c2 == DUK_FP_INFINITE && s2 == 0) {
/* y == +Infinity */
goto lt_true;
}
if (c2 == DUK_FP_INFINITE && s2 != 0) {
/* y == -Infinity */
goto lt_false;
}
if (c1 == DUK_FP_INFINITE && s1 != 0) {
/* x == -Infinity */
goto lt_true;
}
if (d1 < d2) {
goto lt_true;
}
goto lt_false;
}
lt_undefined:
/* Note: undefined from Section 11.8.5 always results in false
* return (see e.g. Section 11.8.3) - hence special treatment here.
*/
retval = 0;
goto cleanup;
lt_true:
if (flags & DUK_COMPARE_FLAG_NEGATE) {
retval = 0;
goto cleanup;
} else {
retval = 1;
goto cleanup;
}
/* never here */
lt_false:
if (flags & DUK_COMPARE_FLAG_NEGATE) {
retval = 1;
goto cleanup;
} else {
retval = 0;
goto cleanup;
}
/* never here */
cleanup:
duk_pop_2(ctx);
return retval;
}