blob: e2b761f60e4af5d7374133559be93630761fac10 [file] [log] [blame]
/*
* Copyright (C) 2015-2016 Apple Inc. All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
* 1. Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
*
* THIS SOFTWARE IS PROVIDED BY APPLE INC. ``AS IS'' AND ANY
* EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
* PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL APPLE INC. OR
* CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
* EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
* PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
* PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY
* OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
* OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*/
#include "config.h"
#include "MathCommon.h"
#include "PureNaN.h"
namespace JSC {
#if PLATFORM(IOS_FAMILY) && CPU(ARM_THUMB2)
// The following code is taken from netlib.org:
// http://www.netlib.org/fdlibm/fdlibm.h
// http://www.netlib.org/fdlibm/e_pow.c
// http://www.netlib.org/fdlibm/s_scalbn.c
//
// And was originally distributed under the following license:
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/*
* ====================================================
* Copyright (C) 2004 by Sun Microsystems, Inc. All rights reserved.
*
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/* __ieee754_pow(x,y) return x**y
*
* n
* Method: Let x = 2 * (1+f)
* 1. Compute and return log2(x) in two pieces:
* log2(x) = w1 + w2,
* where w1 has 53-24 = 29 bit trailing zeros.
* 2. Perform y*log2(x) = n+y' by simulating muti-precision
* arithmetic, where |y'|<=0.5.
* 3. Return x**y = 2**n*exp(y'*log2)
*
* Special cases:
* 1. (anything) ** 0 is 1
* 2. (anything) ** 1 is itself
* 3. (anything) ** NAN is NAN
* 4. NAN ** (anything except 0) is NAN
* 5. +-(|x| > 1) ** +INF is +INF
* 6. +-(|x| > 1) ** -INF is +0
* 7. +-(|x| < 1) ** +INF is +0
* 8. +-(|x| < 1) ** -INF is +INF
* 9. +-1 ** +-INF is NAN
* 10. +0 ** (+anything except 0, NAN) is +0
* 11. -0 ** (+anything except 0, NAN, odd integer) is +0
* 12. +0 ** (-anything except 0, NAN) is +INF
* 13. -0 ** (-anything except 0, NAN, odd integer) is +INF
* 14. -0 ** (odd integer) = -( +0 ** (odd integer) )
* 15. +INF ** (+anything except 0,NAN) is +INF
* 16. +INF ** (-anything except 0,NAN) is +0
* 17. -INF ** (anything) = -0 ** (-anything)
* 18. (-anything) ** (integer) is (-1)**(integer)*(+anything**integer)
* 19. (-anything except 0 and inf) ** (non-integer) is NAN
*
* Accuracy:
* pow(x,y) returns x**y nearly rounded. In particular
* pow(integer,integer)
* always returns the correct integer provided it is
* representable.
*
* Constants :
* The hexadecimal values are the intended ones for the following
* constants. The decimal values may be used, provided that the
* compiler will convert from decimal to binary accurately enough
* to produce the hexadecimal values shown.
*/
#define __HI(x) *(1+(int*)&x)
#define __LO(x) *(int*)&x
static const double
bp[] = {1.0, 1.5,},
dp_h[] = { 0.0, 5.84962487220764160156e-01,}, /* 0x3FE2B803, 0x40000000 */
dp_l[] = { 0.0, 1.35003920212974897128e-08,}, /* 0x3E4CFDEB, 0x43CFD006 */
zero = 0.0,
one = 1.0,
two = 2.0,
two53 = 9007199254740992.0, /* 0x43400000, 0x00000000 */
huge = 1.0e300,
tiny = 1.0e-300,
/* for scalbn */
two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */
twom54 = 5.55111512312578270212e-17, /* 0x3C900000, 0x00000000 */
/* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */
L1 = 5.99999999999994648725e-01, /* 0x3FE33333, 0x33333303 */
L2 = 4.28571428578550184252e-01, /* 0x3FDB6DB6, 0xDB6FABFF */
L3 = 3.33333329818377432918e-01, /* 0x3FD55555, 0x518F264D */
L4 = 2.72728123808534006489e-01, /* 0x3FD17460, 0xA91D4101 */
L5 = 2.30660745775561754067e-01, /* 0x3FCD864A, 0x93C9DB65 */
L6 = 2.06975017800338417784e-01, /* 0x3FCA7E28, 0x4A454EEF */
P1 = 1.66666666666666019037e-01, /* 0x3FC55555, 0x5555553E */
P2 = -2.77777777770155933842e-03, /* 0xBF66C16C, 0x16BEBD93 */
P3 = 6.61375632143793436117e-05, /* 0x3F11566A, 0xAF25DE2C */
P4 = -1.65339022054652515390e-06, /* 0xBEBBBD41, 0xC5D26BF1 */
P5 = 4.13813679705723846039e-08, /* 0x3E663769, 0x72BEA4D0 */
lg2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */
lg2_h = 6.93147182464599609375e-01, /* 0x3FE62E43, 0x00000000 */
lg2_l = -1.90465429995776804525e-09, /* 0xBE205C61, 0x0CA86C39 */
ovt = 8.0085662595372944372e-0017, /* -(1024-log2(ovfl+.5ulp)) */
cp = 9.61796693925975554329e-01, /* 0x3FEEC709, 0xDC3A03FD =2/(3ln2) */
cp_h = 9.61796700954437255859e-01, /* 0x3FEEC709, 0xE0000000 =(float)cp */
cp_l = -7.02846165095275826516e-09, /* 0xBE3E2FE0, 0x145B01F5 =tail of cp_h*/
ivln2 = 1.44269504088896338700e+00, /* 0x3FF71547, 0x652B82FE =1/ln2 */
ivln2_h = 1.44269502162933349609e+00, /* 0x3FF71547, 0x60000000 =24b 1/ln2*/
ivln2_l = 1.92596299112661746887e-08; /* 0x3E54AE0B, 0xF85DDF44 =1/ln2 tail*/
inline double fdlibmScalbn (double x, int n)
{
int k,hx,lx;
hx = __HI(x);
lx = __LO(x);
k = (hx&0x7ff00000)>>20; /* extract exponent */
if (k==0) { /* 0 or subnormal x */
if ((lx|(hx&0x7fffffff))==0) return x; /* +-0 */
x *= two54;
hx = __HI(x);
k = ((hx&0x7ff00000)>>20) - 54;
if (n< -50000) return tiny*x; /*underflow*/
}
if (k==0x7ff) return x+x; /* NaN or Inf */
k = k+n;
if (k > 0x7fe) return huge*copysign(huge,x); /* overflow */
if (k > 0) /* normal result */
{__HI(x) = (hx&0x800fffff)|(k<<20); return x;}
if (k <= -54) {
if (n > 50000) /* in case integer overflow in n+k */
return huge*copysign(huge,x); /*overflow*/
else return tiny*copysign(tiny,x); /*underflow*/
}
k += 54; /* subnormal result */
__HI(x) = (hx&0x800fffff)|(k<<20);
return x*twom54;
}
static double fdlibmPow(double x, double y)
{
double z,ax,z_h,z_l,p_h,p_l;
double y1,t1,t2,r,s,t,u,v,w;
int i0,i1,i,j,k,yisint,n;
int hx,hy,ix,iy;
unsigned lx,ly;
i0 = ((*(const int*)&one)>>29)^1; i1=1-i0;
hx = __HI(x); lx = __LO(x);
hy = __HI(y); ly = __LO(y);
ix = hx&0x7fffffff; iy = hy&0x7fffffff;
/* y==zero: x**0 = 1 */
if((iy|ly)==0) return one;
/* +-NaN return x+y */
if(ix > 0x7ff00000 || ((ix==0x7ff00000)&&(lx!=0)) ||
iy > 0x7ff00000 || ((iy==0x7ff00000)&&(ly!=0)))
return x+y;
/* determine if y is an odd int when x < 0
* yisint = 0 ... y is not an integer
* yisint = 1 ... y is an odd int
* yisint = 2 ... y is an even int
*/
yisint = 0;
if(hx<0) {
if(iy>=0x43400000) yisint = 2; /* even integer y */
else if(iy>=0x3ff00000) {
k = (iy>>20)-0x3ff; /* exponent */
if(k>20) {
j = ly>>(52-k);
if(static_cast<unsigned>(j<<(52-k))==ly) yisint = 2-(j&1);
} else if(ly==0) {
j = iy>>(20-k);
if((j<<(20-k))==iy) yisint = 2-(j&1);
}
}
}
/* special value of y */
if(ly==0) {
if (iy==0x7ff00000) { /* y is +-inf */
if(((ix-0x3ff00000)|lx)==0)
return y - y; /* inf**+-1 is NaN */
else if (ix >= 0x3ff00000)/* (|x|>1)**+-inf = inf,0 */
return (hy>=0)? y: zero;
else /* (|x|<1)**-,+inf = inf,0 */
return (hy<0)?-y: zero;
}
if(iy==0x3ff00000) { /* y is +-1 */
if(hy<0) return one/x; else return x;
}
if(hy==0x40000000) return x*x; /* y is 2 */
if(hy==0x3fe00000) { /* y is 0.5 */
if(hx>=0) /* x >= +0 */
return sqrt(x);
}
}
ax = fabs(x);
/* special value of x */
if(lx==0) {
if(ix==0x7ff00000||ix==0||ix==0x3ff00000){
z = ax; /*x is +-0,+-inf,+-1*/
if(hy<0) z = one/z; /* z = (1/|x|) */
if(hx<0) {
if(((ix-0x3ff00000)|yisint)==0) {
z = (z-z)/(z-z); /* (-1)**non-int is NaN */
} else if(yisint==1)
z = -z; /* (x<0)**odd = -(|x|**odd) */
}
return z;
}
}
n = (hx>>31)+1;
/* (x<0)**(non-int) is NaN */
if((n|yisint)==0) return (x-x)/(x-x);
s = one; /* s (sign of result -ve**odd) = -1 else = 1 */
if((n|(yisint-1))==0) s = -one;/* (-ve)**(odd int) */
/* |y| is huge */
if(iy>0x41e00000) { /* if |y| > 2**31 */
if(iy>0x43f00000){ /* if |y| > 2**64, must o/uflow */
if(ix<=0x3fefffff) return (hy<0)? huge*huge:tiny*tiny;
if(ix>=0x3ff00000) return (hy>0)? huge*huge:tiny*tiny;
}
/* over/underflow if x is not close to one */
if(ix<0x3fefffff) return (hy<0)? s*huge*huge:s*tiny*tiny;
if(ix>0x3ff00000) return (hy>0)? s*huge*huge:s*tiny*tiny;
/* now |1-x| is tiny <= 2**-20, suffice to compute
log(x) by x-x^2/2+x^3/3-x^4/4 */
t = ax-one; /* t has 20 trailing zeros */
w = (t*t)*(0.5-t*(0.3333333333333333333333-t*0.25));
u = ivln2_h*t; /* ivln2_h has 21 sig. bits */
v = t*ivln2_l-w*ivln2;
t1 = u+v;
__LO(t1) = 0;
t2 = v-(t1-u);
} else {
double ss,s2,s_h,s_l,t_h,t_l;
n = 0;
/* take care subnormal number */
if(ix<0x00100000)
{ax *= two53; n -= 53; ix = __HI(ax); }
n += ((ix)>>20)-0x3ff;
j = ix&0x000fffff;
/* determine interval */
ix = j|0x3ff00000; /* normalize ix */
if(j<=0x3988E) k=0; /* |x|<sqrt(3/2) */
else if(j<0xBB67A) k=1; /* |x|<sqrt(3) */
else {k=0;n+=1;ix -= 0x00100000;}
__HI(ax) = ix;
/* compute ss = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
u = ax-bp[k]; /* bp[0]=1.0, bp[1]=1.5 */
v = one/(ax+bp[k]);
ss = u*v;
s_h = ss;
__LO(s_h) = 0;
/* t_h=ax+bp[k] High */
t_h = zero;
__HI(t_h)=((ix>>1)|0x20000000)+0x00080000+(k<<18);
t_l = ax - (t_h-bp[k]);
s_l = v*((u-s_h*t_h)-s_h*t_l);
/* compute log(ax) */
s2 = ss*ss;
r = s2*s2*(L1+s2*(L2+s2*(L3+s2*(L4+s2*(L5+s2*L6)))));
r += s_l*(s_h+ss);
s2 = s_h*s_h;
t_h = 3.0+s2+r;
__LO(t_h) = 0;
t_l = r-((t_h-3.0)-s2);
/* u+v = ss*(1+...) */
u = s_h*t_h;
v = s_l*t_h+t_l*ss;
/* 2/(3log2)*(ss+...) */
p_h = u+v;
__LO(p_h) = 0;
p_l = v-(p_h-u);
z_h = cp_h*p_h; /* cp_h+cp_l = 2/(3*log2) */
z_l = cp_l*p_h+p_l*cp+dp_l[k];
/* log2(ax) = (ss+..)*2/(3*log2) = n + dp_h + z_h + z_l */
t = (double)n;
t1 = (((z_h+z_l)+dp_h[k])+t);
__LO(t1) = 0;
t2 = z_l-(((t1-t)-dp_h[k])-z_h);
}
/* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */
y1 = y;
__LO(y1) = 0;
p_l = (y-y1)*t1+y*t2;
p_h = y1*t1;
z = p_l+p_h;
j = __HI(z);
i = __LO(z);
if (j>=0x40900000) { /* z >= 1024 */
if(((j-0x40900000)|i)!=0) /* if z > 1024 */
return s*huge*huge; /* overflow */
else {
if(p_l+ovt>z-p_h) return s*huge*huge; /* overflow */
}
} else if((j&0x7fffffff)>=0x4090cc00 ) { /* z <= -1075 */
if(((j-0xc090cc00)|i)!=0) /* z < -1075 */
return s*tiny*tiny; /* underflow */
else {
if(p_l<=z-p_h) return s*tiny*tiny; /* underflow */
}
}
/*
* compute 2**(p_h+p_l)
*/
i = j&0x7fffffff;
k = (i>>20)-0x3ff;
n = 0;
if(i>0x3fe00000) { /* if |z| > 0.5, set n = [z+0.5] */
n = j+(0x00100000>>(k+1));
k = ((n&0x7fffffff)>>20)-0x3ff; /* new k for n */
t = zero;
__HI(t) = (n&~(0x000fffff>>k));
n = ((n&0x000fffff)|0x00100000)>>(20-k);
if(j<0) n = -n;
p_h -= t;
}
t = p_l+p_h;
__LO(t) = 0;
u = t*lg2_h;
v = (p_l-(t-p_h))*lg2+t*lg2_l;
z = u+v;
w = v-(z-u);
t = z*z;
t1 = z - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
r = (z*t1)/(t1-two)-(w+z*w);
z = one-(r-z);
j = __HI(z);
j += (n<<20);
if((j>>20)<=0) z = fdlibmScalbn(z,n); /* subnormal output */
else __HI(z) += (n<<20);
return s*z;
}
static ALWAYS_INLINE bool isDenormal(double x)
{
static const uint64_t signbit = 0x8000000000000000ULL;
static const uint64_t minNormal = 0x0001000000000000ULL;
return (bitwise_cast<uint64_t>(x) & ~signbit) - 1 < minNormal - 1;
}
static ALWAYS_INLINE bool isEdgeCase(double x)
{
static const uint64_t signbit = 0x8000000000000000ULL;
static const uint64_t infinity = 0x7fffffffffffffffULL;
return (bitwise_cast<uint64_t>(x) & ~signbit) - 1 >= infinity - 1;
}
static ALWAYS_INLINE double mathPowInternal(double x, double y)
{
if (!isDenormal(x) && !isDenormal(y)) {
double libmResult = std::pow(x, y);
if (libmResult || isEdgeCase(x) || isEdgeCase(y))
return libmResult;
}
return fdlibmPow(x, y);
}
#else
ALWAYS_INLINE double mathPowInternal(double x, double y)
{
return pow(x, y);
}
#endif
double JIT_OPERATION operationMathPow(double x, double y)
{
if (std::isnan(y))
return PNaN;
double absoluteBase = fabs(x);
if (absoluteBase == 1 && std::isinf(y))
return PNaN;
if (y == 0.5) {
if (!absoluteBase)
return 0;
if (absoluteBase == std::numeric_limits<double>::infinity())
return std::numeric_limits<double>::infinity();
return sqrt(x);
}
if (y == -0.5) {
if (!absoluteBase)
return std::numeric_limits<double>::infinity();
if (absoluteBase == std::numeric_limits<double>::infinity())
return 0.;
return 1. / sqrt(x);
}
int32_t yAsInt = y;
if (static_cast<double>(yAsInt) == y && yAsInt >= 0 && yAsInt <= maxExponentForIntegerMathPow) {
// If the exponent is a small positive int32 integer, we do a fast exponentiation
double result = 1;
double xd = x;
while (yAsInt) {
if (yAsInt & 1)
result *= xd;
xd *= xd;
yAsInt >>= 1;
}
return result;
}
return mathPowInternal(x, y);
}
int32_t JIT_OPERATION operationToInt32(double value)
{
return JSC::toInt32(value);
}
int32_t JIT_OPERATION operationToInt32SensibleSlow(double number)
{
return toInt32Internal<ToInt32Mode::AfterSensibleConversionAttempt>(number);
}
#if HAVE(ARM_IDIV_INSTRUCTIONS)
static inline bool isStrictInt32(double value)
{
int32_t valueAsInt32 = static_cast<int32_t>(value);
if (value != valueAsInt32)
return false;
if (!valueAsInt32) {
if (std::signbit(value))
return false;
}
return true;
}
#endif
extern "C" {
double jsRound(double value)
{
double integer = ceil(value);
return integer - (integer - value > 0.5);
}
#if CALLING_CONVENTION_IS_STDCALL || CPU(ARM_THUMB2)
double jsMod(double x, double y)
{
#if HAVE(ARM_IDIV_INSTRUCTIONS)
// fmod() does not have exact results for integer on ARMv7.
// When DFG/FTL use IDIV, the result of op_mod can change if we use fmod().
//
// We implement here the same algorithm and conditions as the upper tier to keep
// a stable result when tiering up.
if (y) {
if (isStrictInt32(x) && isStrictInt32(y)) {
int32_t xAsInt32 = static_cast<int32_t>(x);
int32_t yAsInt32 = static_cast<int32_t>(y);
int32_t quotient = xAsInt32 / yAsInt32;
if (!productOverflows<int32_t>(quotient, yAsInt32)) {
int32_t remainder = xAsInt32 - (quotient * yAsInt32);
if (remainder || xAsInt32 >= 0)
return remainder;
}
}
}
#endif
return fmod(x, y);
}
#endif
} // extern "C"
namespace Math {
double JIT_OPERATION log1p(double value)
{
if (value == 0.0)
return value;
return std::log1p(value);
}
} // namespace Math
} // namespace JSC