/* * 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) && 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 = ((*(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(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|>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(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(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::infinity()) return std::numeric_limits::infinity(); return sqrt(x); } if (y == -0.5) { if (!absoluteBase) return std::numeric_limits::infinity(); if (absoluteBase == std::numeric_limits::infinity()) return 0.; return 1. / sqrt(x); } int32_t yAsInt = y; if (static_cast(yAsInt) == y && yAsInt >= 0 && yAsInt <= maxExponentForIntegerMathPow) { // If the exponent is a small positive int32 integer, we do a fast exponentiation // Do not use x87 values for accumulation. x87 values has 80bit precision. // The result produced by x87's 80bit double precision differs from the one calculated with SSE2 in DFG. // Using volatile double is workaround for this problem. By specifying volatile, we expect that `result` and `xd` // are stored in the stack. And at that time, we expect that they are rounded by fst/fstp[1, 2]. // [1]: https://gcc.gnu.org/wiki/x87note // [2]: https://gcc.gnu.org/bugzilla/show_bug.cgi?id=323 #if !CPU(X86) || (defined(__SSE2_MATH__) && defined(__SSE2__)) typedef double DoubleValue; #else typedef volatile double DoubleValue; #endif DoubleValue result = 1; DoubleValue 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); } #if HAVE(ARM_IDIV_INSTRUCTIONS) static inline bool isStrictInt32(double value) { int32_t valueAsInt32 = static_cast(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(x); int32_t yAsInt32 = static_cast(y); int32_t quotient = xAsInt32 / yAsInt32; if (!productOverflows(quotient, yAsInt32)) { int32_t remainder = xAsInt32 - (quotient * yAsInt32); if (remainder || xAsInt32 >= 0) return remainder; } } } #endif return fmod(x, y); } #endif } // extern "C" } // namespace JSC