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/* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
*
* ***** BEGIN LICENSE BLOCK *****
* Version: MPL 1.1/GPL 2.0/LGPL 2.1
*
* The contents of this file are subject to the Mozilla Public License Version
* 1.1 (the "License"); you may not use this file except in compliance with
* the License. You may obtain a copy of the License at
* http://www.mozilla.org/MPL/
*
* Software distributed under the License is distributed on an "AS IS" basis,
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the License
* for the specific language governing rights and limitations under the
* License.
*
* The Original Code is Mozilla Communicator client code, released
* March 31, 1998.
*
* The Initial Developer of the Original Code is
* Netscape Communications Corporation.
* Portions created by the Initial Developer are Copyright (C) 1998
* the Initial Developer. All Rights Reserved.
*
* Contributor(s):
*
* Alternatively, the contents of this file may be used under the terms of
* either of the GNU General Public License Version 2 or later (the "GPL"),
* or the GNU Lesser General Public License Version 2.1 or later (the "LGPL"),
* in which case the provisions of the GPL or the LGPL are applicable instead
* of those above. If you wish to allow use of your version of this file only
* under the terms of either the GPL or the LGPL, and not to allow others to
* use your version of this file under the terms of the MPL, indicate your
* decision by deleting the provisions above and replace them with the notice
* and other provisions required by the GPL or the LGPL. If you do not delete
* the provisions above, a recipient may use your version of this file under
* the terms of any one of the MPL, the GPL or the LGPL.
*
* ***** END LICENSE BLOCK ***** */
#ifndef jsnum_h___
#define jsnum_h___
#include <math.h>
#include "jsobj.h"
/*
* JS number (IEEE double) interface.
*
* JS numbers are optimistically stored in the top 31 bits of 32-bit integers,
* but floating point literals, results that overflow 31 bits, and division and
* modulus operands and results require a 64-bit IEEE double. These are GC'ed
* and pointed to by 32-bit jsvals on the stack and in object properties.
*/
/*
* The ARM architecture supports two floating point models: VFP and FPA. When
* targetting FPA, doubles are mixed-endian on little endian ARMs (meaning that
* the high and low words are in big endian order).
*/
#if defined(__arm) || defined(__arm32__) || defined(__arm26__) || defined(__arm__)
#if !defined(__VFP_FP__)
#define FPU_IS_ARM_FPA
#endif
#endif
/* Low-level floating-point predicates. See bug 640494. */
#define JSDOUBLE_HI32_SIGNBIT 0x80000000
#define JSDOUBLE_HI32_EXPMASK 0x7ff00000
#define JSDOUBLE_HI32_MANTMASK 0x000fffff
#define JSDOUBLE_HI32_NAN 0x7ff80000
#define JSDOUBLE_LO32_NAN 0x00000000
#define JSDOUBLE_HI32_EXPSHIFT 20
#define JSDOUBLE_EXPBIAS 1023
union jsdpun {
struct {
#if defined(IS_LITTLE_ENDIAN) && !defined(FPU_IS_ARM_FPA)
uint32_t lo, hi;
#else
uint32_t hi, lo;
#endif
} s;
uint64_t u64;
double d;
};
static inline int
JSDOUBLE_IS_NaN(double d)
{
jsdpun u;
u.d = d;
return (u.u64 & JSDOUBLE_EXPMASK) == JSDOUBLE_EXPMASK &&
(u.u64 & JSDOUBLE_MANTMASK) != 0;
}
static inline int
JSDOUBLE_IS_FINITE(double d)
{
/* -0 is finite. NaNs are not. */
jsdpun u;
u.d = d;
return (u.u64 & JSDOUBLE_EXPMASK) != JSDOUBLE_EXPMASK;
}
static inline int
JSDOUBLE_IS_INFINITE(double d)
{
jsdpun u;
u.d = d;
return (u.u64 & ~JSDOUBLE_SIGNBIT) == JSDOUBLE_EXPMASK;
}
static inline bool
JSDOUBLE_IS_NEG(double d)
{
jsdpun u;
u.d = d;
return (u.s.hi & JSDOUBLE_HI32_SIGNBIT) != 0;
}
static inline uint32_t
JS_HASH_DOUBLE(double d)
{
jsdpun u;
u.d = d;
return u.s.lo ^ u.s.hi;
}
extern double js_NaN;
extern double js_PositiveInfinity;
extern double js_NegativeInfinity;
namespace js {
extern bool
InitRuntimeNumberState(JSRuntime *rt);
extern void
FinishRuntimeNumberState(JSRuntime *rt);
} /* namespace js */
/* Initialize the Number class, returning its prototype object. */
extern JSObject *
js_InitNumberClass(JSContext *cx, JSObject *obj);
/*
* String constants for global function names, used in jsapi.c and jsnum.c.
*/
extern const char js_isNaN_str[];
extern const char js_isFinite_str[];
extern const char js_parseFloat_str[];
extern const char js_parseInt_str[];
class JSString;
class JSFixedString;
extern JSString * JS_FASTCALL
js_IntToString(JSContext *cx, int i);
/*
* When base == 10, this function implements ToString() as specified by
* ECMA-262-5 section 9.8.1; but note that it handles integers specially for
* performance. See also js::NumberToCString().
*/
extern JSString * JS_FASTCALL
js_NumberToString(JSContext *cx, double d);
namespace js {
/*
* Convert an integer or double (contained in the given value) to a string and
* append to the given buffer.
*/
extern bool JS_FASTCALL
NumberValueToStringBuffer(JSContext *cx, const Value &v, StringBuffer &sb);
/* Same as js_NumberToString, different signature. */
extern JSFixedString *
NumberToString(JSContext *cx, double d);
extern JSFixedString *
IndexToString(JSContext *cx, uint32_t index);
/*
* Usually a small amount of static storage is enough, but sometimes we need
* to dynamically allocate much more. This struct encapsulates that.
* Dynamically allocated memory will be freed when the object is destroyed.
*/
struct ToCStringBuf
{
/*
* The longest possible result that would need to fit in sbuf is
* (-0x80000000).toString(2), which has length 33. Longer cases are
* possible, but they'll go in dbuf.
*/
static const size_t sbufSize = 34;
char sbuf[sbufSize];
char *dbuf;
ToCStringBuf();
~ToCStringBuf();
};
/*
* Convert a number to a C string. When base==10, this function implements
* ToString() as specified by ECMA-262-5 section 9.8.1. It handles integral
* values cheaply. Return NULL if we ran out of memory. See also
* js_NumberToCString().
*/
extern char *
NumberToCString(JSContext *cx, ToCStringBuf *cbuf, double d, int base = 10);
/*
* The largest positive integer such that all positive integers less than it
* may be precisely represented using the IEEE-754 double-precision format.
*/
const double DOUBLE_INTEGRAL_PRECISION_LIMIT = uint64_t(1) << 53;
/*
* Compute the positive integer of the given base described immediately at the
* start of the range [start, end) -- no whitespace-skipping, no magical
* leading-"0" octal or leading-"0x" hex behavior, no "+"/"-" parsing, just
* reading the digits of the integer. Return the index one past the end of the
* digits of the integer in *endp, and return the integer itself in *dp. If
* base is 10 or a power of two the returned integer is the closest possible
* double; otherwise extremely large integers may be slightly inaccurate.
*
* If [start, end) does not begin with a number with the specified base,
* *dp == 0 and *endp == start upon return.
*/
extern bool
GetPrefixInteger(JSContext *cx, const jschar *start, const jschar *end, int base,
const jschar **endp, double *dp);
/* ES5 9.3 ToNumber, overwriting *vp with the appropriate number value. */
JS_ALWAYS_INLINE bool
ToNumber(JSContext *cx, Value *vp)
{
if (vp->isNumber())
return true;
double d;
extern bool ToNumberSlow(JSContext *cx, js::Value v, double *dp);
if (!ToNumberSlow(cx, *vp, &d))
return false;
vp->setNumber(d);
return true;
}
/*
* Convert a value to a uint32_t, according to the ECMA rules for
* ToUint32. Return converted value in *out on success, !ok on
* failure.
*/
JS_ALWAYS_INLINE bool
ToUint32(JSContext *cx, const js::Value &v, uint32_t *out)
{
if (v.isInt32()) {
*out = (uint32_t)v.toInt32();
return true;
}
extern bool ToUint32Slow(JSContext *cx, const js::Value &v, uint32_t *ip);
return ToUint32Slow(cx, v, out);
}
/*
* Convert a value to a number, then to an int32_t if it fits by rounding to
* nearest. Return converted value in *out on success, !ok on failure. As a
* side effect, *vp will be mutated to match *out.
*/
JS_ALWAYS_INLINE bool
NonstandardToInt32(JSContext *cx, const js::Value &v, int32_t *out)
{
if (v.isInt32()) {
*out = v.toInt32();
return true;
}
extern bool NonstandardToInt32Slow(JSContext *cx, const js::Value &v, int32_t *ip);
return NonstandardToInt32Slow(cx, v, out);
}
/*
* Convert a value to a number, then to a uint16_t according to the ECMA rules
* for ToUint16. Return converted value on success, !ok on failure. v must be a
* copy of a rooted value.
*/
JS_ALWAYS_INLINE bool
ValueToUint16(JSContext *cx, const js::Value &v, uint16_t *out)
{
if (v.isInt32()) {
*out = uint16_t(v.toInt32());
return true;
}
extern bool ValueToUint16Slow(JSContext *cx, const js::Value &v, uint16_t *out);
return ValueToUint16Slow(cx, v, out);
}
JSBool
num_parseInt(JSContext *cx, unsigned argc, Value *vp);
} /* namespace js */
/*
* Specialized ToInt32 and ToUint32 converters for doubles.
*/
/*
* From the ES3 spec, 9.5
* 2. If Result(1) is NaN, +0, -0, +Inf, or -Inf, return +0.
* 3. Compute sign(Result(1)) * floor(abs(Result(1))).
* 4. Compute Result(3) modulo 2^32; that is, a finite integer value k of Number
* type with positive sign and less than 2^32 in magnitude such the mathematical
* difference of Result(3) and k is mathematically an integer multiple of 2^32.
* 5. If Result(4) is greater than or equal to 2^31, return Result(4)- 2^32,
* otherwise return Result(4).
*/
static inline int32_t
js_DoubleToECMAInt32(double d)
{
#if defined(__i386__) || defined(__i386) || defined(__x86_64__) || \
defined(_M_IX86) || defined(_M_X64)
jsdpun du, duh, two32;
uint32_t di_h, u_tmp, expon, shift_amount;
int32_t mask32;
/*
* Algorithm Outline
* Step 1. If d is NaN, +/-Inf or |d|>=2^84 or |d|<1, then return 0
* All of this is implemented based on an exponent comparison.
* Step 2. If |d|<2^31, then return (int)d
* The cast to integer (conversion in RZ mode) returns the correct result.
* Step 3. If |d|>=2^32, d:=fmod(d, 2^32) is taken -- but without a call
* Step 4. If |d|>=2^31, then the fractional bits are cleared before
* applying the correction by 2^32: d - sign(d)*2^32
* Step 5. Return (int)d
*/
du.d = d;
di_h = du.s.hi;
u_tmp = (di_h & 0x7ff00000) - 0x3ff00000;
if (u_tmp >= (0x45300000-0x3ff00000)) {
// d is Nan, +/-Inf or +/-0, or |d|>=2^(32+52) or |d|<1, in which case result=0
return 0;
}
if (u_tmp < 0x01f00000) {
// |d|<2^31
return int32_t(d);
}
if (u_tmp > 0x01f00000) {
// |d|>=2^32
expon = u_tmp >> 20;
shift_amount = expon - 21;
duh.u64 = du.u64;
mask32 = 0x80000000;
if (shift_amount < 32) {
mask32 >>= shift_amount;
duh.s.hi = du.s.hi & mask32;
duh.s.lo = 0;
} else {
mask32 >>= (shift_amount-32);
duh.s.hi = du.s.hi;
duh.s.lo = du.s.lo & mask32;
}
du.d -= duh.d;
}
di_h = du.s.hi;
// eliminate fractional bits
u_tmp = (di_h & 0x7ff00000);
if (u_tmp >= 0x41e00000) {
// |d|>=2^31
expon = u_tmp >> 20;
shift_amount = expon - (0x3ff - 11);
mask32 = 0x80000000;
if (shift_amount < 32) {
mask32 >>= shift_amount;
du.s.hi &= mask32;
du.s.lo = 0;
} else {
mask32 >>= (shift_amount-32);
du.s.lo &= mask32;
}
two32.s.hi = 0x41f00000 ^ (du.s.hi & 0x80000000);
two32.s.lo = 0;
du.d -= two32.d;
}
return int32_t(du.d);
#elif defined (__arm__) && defined (__GNUC__)
int32_t i;
uint32_t tmp0;
uint32_t tmp1;
uint32_t tmp2;
asm (
// We use a pure integer solution here. In the 'softfp' ABI, the argument
// will start in r0 and r1, and VFP can't do all of the necessary ECMA
// conversions by itself so some integer code will be required anyway. A
// hybrid solution is faster on A9, but this pure integer solution is
// notably faster for A8.
// %0 is the result register, and may alias either of the %[QR]1 registers.
// %Q4 holds the lower part of the mantissa.
// %R4 holds the sign, exponent, and the upper part of the mantissa.
// %1, %2 and %3 are used as temporary values.
// Extract the exponent.
" mov %1, %R4, LSR #20\n"
" bic %1, %1, #(1 << 11)\n" // Clear the sign.
// Set the implicit top bit of the mantissa. This clobbers a bit of the
// exponent, but we have already extracted that.
" orr %R4, %R4, #(1 << 20)\n"
// Special Cases
// We should return zero in the following special cases:
// - Exponent is 0x000 - 1023: +/-0 or subnormal.
// - Exponent is 0x7ff - 1023: +/-INFINITY or NaN
// - This case is implicitly handled by the standard code path anyway,
// as shifting the mantissa up by the exponent will result in '0'.
//
// The result is composed of the mantissa, prepended with '1' and
// bit-shifted left by the (decoded) exponent. Note that because the r1[20]
// is the bit with value '1', r1 is effectively already shifted (left) by
// 20 bits, and r0 is already shifted by 52 bits.
// Adjust the exponent to remove the encoding offset. If the decoded
// exponent is negative, quickly bail out with '0' as such values round to
// zero anyway. This also catches +/-0 and subnormals.
" sub %1, %1, #0xff\n"
" subs %1, %1, #0x300\n"
" bmi 8f\n"
// %1 = (decoded) exponent >= 0
// %R4 = upper mantissa and sign
// ---- Lower Mantissa ----
" subs %3, %1, #52\n" // Calculate exp-52
" bmi 1f\n"
// Shift r0 left by exp-52.
// Ensure that we don't overflow ARM's 8-bit shift operand range.
// We need to handle anything up to an 11-bit value here as we know that
// 52 <= exp <= 1024 (0x400). Any shift beyond 31 bits results in zero
// anyway, so as long as we don't touch the bottom 5 bits, we can use
// a logical OR to push long shifts into the 32 <= (exp&0xff) <= 255 range.
" bic %2, %3, #0xff\n"
" orr %3, %3, %2, LSR #3\n"
// We can now perform a straight shift, avoiding the need for any
// conditional instructions or extra branches.
" mov %Q4, %Q4, LSL %3\n"
" b 2f\n"
"1:\n" // Shift r0 right by 52-exp.
// We know that 0 <= exp < 52, and we can shift up to 255 bits so 52-exp
// will always be a valid shift and we can sk%3 the range check for this case.
" rsb %3, %1, #52\n"
" mov %Q4, %Q4, LSR %3\n"
// %1 = (decoded) exponent
// %R4 = upper mantissa and sign
// %Q4 = partially-converted integer
"2:\n"
// ---- Upper Mantissa ----
// This is much the same as the lower mantissa, with a few different
// boundary checks and some masking to hide the exponent & sign bit in the
// upper word.
// Note that the upper mantissa is pre-shifted by 20 in %R4, but we shift
// it left more to remove the sign and exponent so it is effectively
// pre-shifted by 31 bits.
" subs %3, %1, #31\n" // Calculate exp-31
" mov %1, %R4, LSL #11\n" // Re-use %1 as a temporary register.
" bmi 3f\n"
// Shift %R4 left by exp-31.
// Avoid overflowing the 8-bit shift range, as before.
" bic %2, %3, #0xff\n"
" orr %3, %3, %2, LSR #3\n"
// Perform the shift.
" mov %2, %1, LSL %3\n"
" b 4f\n"
"3:\n" // Shift r1 right by 31-exp.
// We know that 0 <= exp < 31, and we can shift up to 255 bits so 31-exp
// will always be a valid shift and we can skip the range check for this case.
" rsb %3, %3, #0\n" // Calculate 31-exp from -(exp-31)
" mov %2, %1, LSR %3\n" // Thumb-2 can't do "LSR %3" in "orr".
// %Q4 = partially-converted integer (lower)
// %R4 = upper mantissa and sign
// %2 = partially-converted integer (upper)
"4:\n"
// Combine the converted parts.
" orr %Q4, %Q4, %2\n"
// Negate the result if we have to, and move it to %0 in the process. To
// avoid conditionals, we can do this by inverting on %R4[31], then adding
// %R4[31]>>31.
" eor %Q4, %Q4, %R4, ASR #31\n"
" add %0, %Q4, %R4, LSR #31\n"
" b 9f\n"
"8:\n"
// +/-INFINITY, +/-0, subnormals, NaNs, and anything else out-of-range that
// will result in a conversion of '0'.
" mov %0, #0\n"
"9:\n"
: "=r" (i), "=&r" (tmp0), "=&r" (tmp1), "=&r" (tmp2)
: "r" (d)
: "cc"
);
return i;
#else
int32_t i;
double two32, two31;
if (!JSDOUBLE_IS_FINITE(d))
return 0;
i = (int32_t) d;
if ((double) i == d)
return i;
two32 = 4294967296.0;
two31 = 2147483648.0;
d = fmod(d, two32);
d = (d >= 0) ? floor(d) : ceil(d) + two32;
return (int32_t) (d >= two31 ? d - two32 : d);
#endif
}
inline uint32_t
js_DoubleToECMAUint32(double d)
{
return uint32_t(js_DoubleToECMAInt32(d));
}
/*
* Convert a double to an integral number, stored in a double.
* If d is NaN, return 0. If d is an infinity, return it without conversion.
*/
static inline double
js_DoubleToInteger(double d)
{
if (d == 0)
return d;
if (!JSDOUBLE_IS_FINITE(d)) {
if (JSDOUBLE_IS_NaN(d))
return 0;
return d;
}
JSBool neg = (d < 0);
d = floor(neg ? -d : d);
return neg ? -d : d;
}
/*
* Similar to strtod except that it replaces overflows with infinities of the
* correct sign, and underflows with zeros of the correct sign. Guaranteed to
* return the closest double number to the given input in dp.
*
* Also allows inputs of the form [+|-]Infinity, which produce an infinity of
* the appropriate sign. The case of the "Infinity" string must match exactly.
* If the string does not contain a number, set *ep to s and return 0.0 in dp.
* Return false if out of memory.
*/
extern JSBool
js_strtod(JSContext *cx, const jschar *s, const jschar *send,
const jschar **ep, double *dp);
extern JSBool
js_num_valueOf(JSContext *cx, unsigned argc, js::Value *vp);
namespace js {
static JS_ALWAYS_INLINE bool
ValueFitsInInt32(const Value &v, int32_t *pi)
{
if (v.isInt32()) {
*pi = v.toInt32();
return true;
}
return v.isDouble() && JSDOUBLE_IS_INT32(v.toDouble(), pi);
}
/*
* Returns true if the given value is definitely an index: that is, the value
* is a number that's an unsigned 32-bit integer.
*
* This method prioritizes common-case speed over accuracy in every case. It
* can produce false negatives (but not false positives): some values which are
* indexes will be reported not to be indexes by this method. Users must
* consider this possibility when using this method.
*/
static JS_ALWAYS_INLINE bool
IsDefinitelyIndex(const Value &v, uint32_t *indexp)
{
if (v.isInt32() && v.toInt32() >= 0) {
*indexp = v.toInt32();
return true;
}
int32_t i;
if (v.isDouble() && JSDOUBLE_IS_INT32(v.toDouble(), &i) && i >= 0) {
*indexp = uint32_t(i);
return true;
}
return false;
}
/* ES5 9.4 ToInteger. */
static inline bool
ToInteger(JSContext *cx, const js::Value &v, double *dp)
{
if (v.isInt32()) {
*dp = v.toInt32();
return true;
}
if (v.isDouble()) {
*dp = v.toDouble();
} else {
extern bool ToNumberSlow(JSContext *cx, Value v, double *dp);
if (!ToNumberSlow(cx, v, dp))
return false;
}
*dp = js_DoubleToInteger(*dp);
return true;
}
} /* namespace js */
#endif /* jsnum_h___ */
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