1/*
2 * Copyright (C) 2015-2016 Apple Inc. All rights reserved.
3 *
4 * Redistribution and use in source and binary forms, with or without
5 * modification, are permitted provided that the following conditions
6 * are met:
7 * 1. Redistributions of source code must retain the above copyright
8 * notice, this list of conditions and the following disclaimer.
9 * 2. Redistributions in binary form must reproduce the above copyright
10 * notice, this list of conditions and the following disclaimer in the
11 * documentation and/or other materials provided with the distribution.
12 *
13 * THIS SOFTWARE IS PROVIDED BY APPLE INC. ``AS IS'' AND ANY
14 * EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
15 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
16 * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL APPLE INC. OR
17 * CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
18 * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
19 * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
20 * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY
21 * OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
22 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
23 * OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
24 */
25
26#include "config.h"
27#include "MathCommon.h"
28
29#include "PureNaN.h"
30
31namespace JSC {
32
33#if PLATFORM(IOS_FAMILY) && CPU(ARM_THUMB2)
34
35// The following code is taken from netlib.org:
36// http://www.netlib.org/fdlibm/fdlibm.h
37// http://www.netlib.org/fdlibm/e_pow.c
38// http://www.netlib.org/fdlibm/s_scalbn.c
39//
40// And was originally distributed under the following license:
41
42/*
43 * ====================================================
44 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
45 *
46 * Developed at SunSoft, a Sun Microsystems, Inc. business.
47 * Permission to use, copy, modify, and distribute this
48 * software is freely granted, provided that this notice
49 * is preserved.
50 * ====================================================
51 */
52/*
53 * ====================================================
54 * Copyright (C) 2004 by Sun Microsystems, Inc. All rights reserved.
55 *
56 * Permission to use, copy, modify, and distribute this
57 * software is freely granted, provided that this notice
58 * is preserved.
59 * ====================================================
60 */
61
62/* __ieee754_pow(x,y) return x**y
63 *
64 * n
65 * Method: Let x = 2 * (1+f)
66 * 1. Compute and return log2(x) in two pieces:
67 * log2(x) = w1 + w2,
68 * where w1 has 53-24 = 29 bit trailing zeros.
69 * 2. Perform y*log2(x) = n+y' by simulating muti-precision
70 * arithmetic, where |y'|<=0.5.
71 * 3. Return x**y = 2**n*exp(y'*log2)
72 *
73 * Special cases:
74 * 1. (anything) ** 0 is 1
75 * 2. (anything) ** 1 is itself
76 * 3. (anything) ** NAN is NAN
77 * 4. NAN ** (anything except 0) is NAN
78 * 5. +-(|x| > 1) ** +INF is +INF
79 * 6. +-(|x| > 1) ** -INF is +0
80 * 7. +-(|x| < 1) ** +INF is +0
81 * 8. +-(|x| < 1) ** -INF is +INF
82 * 9. +-1 ** +-INF is NAN
83 * 10. +0 ** (+anything except 0, NAN) is +0
84 * 11. -0 ** (+anything except 0, NAN, odd integer) is +0
85 * 12. +0 ** (-anything except 0, NAN) is +INF
86 * 13. -0 ** (-anything except 0, NAN, odd integer) is +INF
87 * 14. -0 ** (odd integer) = -( +0 ** (odd integer) )
88 * 15. +INF ** (+anything except 0,NAN) is +INF
89 * 16. +INF ** (-anything except 0,NAN) is +0
90 * 17. -INF ** (anything) = -0 ** (-anything)
91 * 18. (-anything) ** (integer) is (-1)**(integer)*(+anything**integer)
92 * 19. (-anything except 0 and inf) ** (non-integer) is NAN
93 *
94 * Accuracy:
95 * pow(x,y) returns x**y nearly rounded. In particular
96 * pow(integer,integer)
97 * always returns the correct integer provided it is
98 * representable.
99 *
100 * Constants :
101 * The hexadecimal values are the intended ones for the following
102 * constants. The decimal values may be used, provided that the
103 * compiler will convert from decimal to binary accurately enough
104 * to produce the hexadecimal values shown.
105 */
106
107#define __HI(x) *(1+(int*)&x)
108#define __LO(x) *(int*)&x
109
110static const double
111bp[] = {1.0, 1.5,},
112dp_h[] = { 0.0, 5.84962487220764160156e-01,}, /* 0x3FE2B803, 0x40000000 */
113dp_l[] = { 0.0, 1.35003920212974897128e-08,}, /* 0x3E4CFDEB, 0x43CFD006 */
114zero = 0.0,
115one = 1.0,
116two = 2.0,
117two53 = 9007199254740992.0, /* 0x43400000, 0x00000000 */
118huge = 1.0e300,
119tiny = 1.0e-300,
120/* for scalbn */
121two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */
122twom54 = 5.55111512312578270212e-17, /* 0x3C900000, 0x00000000 */
123/* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */
124L1 = 5.99999999999994648725e-01, /* 0x3FE33333, 0x33333303 */
125L2 = 4.28571428578550184252e-01, /* 0x3FDB6DB6, 0xDB6FABFF */
126L3 = 3.33333329818377432918e-01, /* 0x3FD55555, 0x518F264D */
127L4 = 2.72728123808534006489e-01, /* 0x3FD17460, 0xA91D4101 */
128L5 = 2.30660745775561754067e-01, /* 0x3FCD864A, 0x93C9DB65 */
129L6 = 2.06975017800338417784e-01, /* 0x3FCA7E28, 0x4A454EEF */
130P1 = 1.66666666666666019037e-01, /* 0x3FC55555, 0x5555553E */
131P2 = -2.77777777770155933842e-03, /* 0xBF66C16C, 0x16BEBD93 */
132P3 = 6.61375632143793436117e-05, /* 0x3F11566A, 0xAF25DE2C */
133P4 = -1.65339022054652515390e-06, /* 0xBEBBBD41, 0xC5D26BF1 */
134P5 = 4.13813679705723846039e-08, /* 0x3E663769, 0x72BEA4D0 */
135lg2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */
136lg2_h = 6.93147182464599609375e-01, /* 0x3FE62E43, 0x00000000 */
137lg2_l = -1.90465429995776804525e-09, /* 0xBE205C61, 0x0CA86C39 */
138ovt = 8.0085662595372944372e-0017, /* -(1024-log2(ovfl+.5ulp)) */
139cp = 9.61796693925975554329e-01, /* 0x3FEEC709, 0xDC3A03FD =2/(3ln2) */
140cp_h = 9.61796700954437255859e-01, /* 0x3FEEC709, 0xE0000000 =(float)cp */
141cp_l = -7.02846165095275826516e-09, /* 0xBE3E2FE0, 0x145B01F5 =tail of cp_h*/
142ivln2 = 1.44269504088896338700e+00, /* 0x3FF71547, 0x652B82FE =1/ln2 */
143ivln2_h = 1.44269502162933349609e+00, /* 0x3FF71547, 0x60000000 =24b 1/ln2*/
144ivln2_l = 1.92596299112661746887e-08; /* 0x3E54AE0B, 0xF85DDF44 =1/ln2 tail*/
145
146inline double fdlibmScalbn (double x, int n)
147{
148 int k,hx,lx;
149 hx = __HI(x);
150 lx = __LO(x);
151 k = (hx&0x7ff00000)>>20; /* extract exponent */
152 if (k==0) { /* 0 or subnormal x */
153 if ((lx|(hx&0x7fffffff))==0) return x; /* +-0 */
154 x *= two54;
155 hx = __HI(x);
156 k = ((hx&0x7ff00000)>>20) - 54;
157 if (n< -50000) return tiny*x; /*underflow*/
158 }
159 if (k==0x7ff) return x+x; /* NaN or Inf */
160 k = k+n;
161 if (k > 0x7fe) return huge*copysign(huge,x); /* overflow */
162 if (k > 0) /* normal result */
163 {__HI(x) = (hx&0x800fffff)|(k<<20); return x;}
164 if (k <= -54) {
165 if (n > 50000) /* in case integer overflow in n+k */
166 return huge*copysign(huge,x); /*overflow*/
167 else return tiny*copysign(tiny,x); /*underflow*/
168 }
169 k += 54; /* subnormal result */
170 __HI(x) = (hx&0x800fffff)|(k<<20);
171 return x*twom54;
172}
173
174static double fdlibmPow(double x, double y)
175{
176 double z,ax,z_h,z_l,p_h,p_l;
177 double y1,t1,t2,r,s,t,u,v,w;
178 int i0,i1,i,j,k,yisint,n;
179 int hx,hy,ix,iy;
180 unsigned lx,ly;
181
182 i0 = ((*(const int*)&one)>>29)^1; i1=1-i0;
183 hx = __HI(x); lx = __LO(x);
184 hy = __HI(y); ly = __LO(y);
185 ix = hx&0x7fffffff; iy = hy&0x7fffffff;
186
187 /* y==zero: x**0 = 1 */
188 if((iy|ly)==0) return one;
189
190 /* +-NaN return x+y */
191 if(ix > 0x7ff00000 || ((ix==0x7ff00000)&&(lx!=0)) ||
192 iy > 0x7ff00000 || ((iy==0x7ff00000)&&(ly!=0)))
193 return x+y;
194
195 /* determine if y is an odd int when x < 0
196 * yisint = 0 ... y is not an integer
197 * yisint = 1 ... y is an odd int
198 * yisint = 2 ... y is an even int
199 */
200 yisint = 0;
201 if(hx<0) {
202 if(iy>=0x43400000) yisint = 2; /* even integer y */
203 else if(iy>=0x3ff00000) {
204 k = (iy>>20)-0x3ff; /* exponent */
205 if(k>20) {
206 j = ly>>(52-k);
207 if(static_cast<unsigned>(j<<(52-k))==ly) yisint = 2-(j&1);
208 } else if(ly==0) {
209 j = iy>>(20-k);
210 if((j<<(20-k))==iy) yisint = 2-(j&1);
211 }
212 }
213 }
214
215 /* special value of y */
216 if(ly==0) {
217 if (iy==0x7ff00000) { /* y is +-inf */
218 if(((ix-0x3ff00000)|lx)==0)
219 return y - y; /* inf**+-1 is NaN */
220 else if (ix >= 0x3ff00000)/* (|x|>1)**+-inf = inf,0 */
221 return (hy>=0)? y: zero;
222 else /* (|x|<1)**-,+inf = inf,0 */
223 return (hy<0)?-y: zero;
224 }
225 if(iy==0x3ff00000) { /* y is +-1 */
226 if(hy<0) return one/x; else return x;
227 }
228 if(hy==0x40000000) return x*x; /* y is 2 */
229 if(hy==0x3fe00000) { /* y is 0.5 */
230 if(hx>=0) /* x >= +0 */
231 return sqrt(x);
232 }
233 }
234
235 ax = fabs(x);
236 /* special value of x */
237 if(lx==0) {
238 if(ix==0x7ff00000||ix==0||ix==0x3ff00000){
239 z = ax; /*x is +-0,+-inf,+-1*/
240 if(hy<0) z = one/z; /* z = (1/|x|) */
241 if(hx<0) {
242 if(((ix-0x3ff00000)|yisint)==0) {
243 z = (z-z)/(z-z); /* (-1)**non-int is NaN */
244 } else if(yisint==1)
245 z = -z; /* (x<0)**odd = -(|x|**odd) */
246 }
247 return z;
248 }
249 }
250
251 n = (hx>>31)+1;
252
253 /* (x<0)**(non-int) is NaN */
254 if((n|yisint)==0) return (x-x)/(x-x);
255
256 s = one; /* s (sign of result -ve**odd) = -1 else = 1 */
257 if((n|(yisint-1))==0) s = -one;/* (-ve)**(odd int) */
258
259 /* |y| is huge */
260 if(iy>0x41e00000) { /* if |y| > 2**31 */
261 if(iy>0x43f00000){ /* if |y| > 2**64, must o/uflow */
262 if(ix<=0x3fefffff) return (hy<0)? huge*huge:tiny*tiny;
263 if(ix>=0x3ff00000) return (hy>0)? huge*huge:tiny*tiny;
264 }
265 /* over/underflow if x is not close to one */
266 if(ix<0x3fefffff) return (hy<0)? s*huge*huge:s*tiny*tiny;
267 if(ix>0x3ff00000) return (hy>0)? s*huge*huge:s*tiny*tiny;
268 /* now |1-x| is tiny <= 2**-20, suffice to compute
269 log(x) by x-x^2/2+x^3/3-x^4/4 */
270 t = ax-one; /* t has 20 trailing zeros */
271 w = (t*t)*(0.5-t*(0.3333333333333333333333-t*0.25));
272 u = ivln2_h*t; /* ivln2_h has 21 sig. bits */
273 v = t*ivln2_l-w*ivln2;
274 t1 = u+v;
275 __LO(t1) = 0;
276 t2 = v-(t1-u);
277 } else {
278 double ss,s2,s_h,s_l,t_h,t_l;
279 n = 0;
280 /* take care subnormal number */
281 if(ix<0x00100000)
282 {ax *= two53; n -= 53; ix = __HI(ax); }
283 n += ((ix)>>20)-0x3ff;
284 j = ix&0x000fffff;
285 /* determine interval */
286 ix = j|0x3ff00000; /* normalize ix */
287 if(j<=0x3988E) k=0; /* |x|<sqrt(3/2) */
288 else if(j<0xBB67A) k=1; /* |x|<sqrt(3) */
289 else {k=0;n+=1;ix -= 0x00100000;}
290 __HI(ax) = ix;
291
292 /* compute ss = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
293 u = ax-bp[k]; /* bp[0]=1.0, bp[1]=1.5 */
294 v = one/(ax+bp[k]);
295 ss = u*v;
296 s_h = ss;
297 __LO(s_h) = 0;
298 /* t_h=ax+bp[k] High */
299 t_h = zero;
300 __HI(t_h)=((ix>>1)|0x20000000)+0x00080000+(k<<18);
301 t_l = ax - (t_h-bp[k]);
302 s_l = v*((u-s_h*t_h)-s_h*t_l);
303 /* compute log(ax) */
304 s2 = ss*ss;
305 r = s2*s2*(L1+s2*(L2+s2*(L3+s2*(L4+s2*(L5+s2*L6)))));
306 r += s_l*(s_h+ss);
307 s2 = s_h*s_h;
308 t_h = 3.0+s2+r;
309 __LO(t_h) = 0;
310 t_l = r-((t_h-3.0)-s2);
311 /* u+v = ss*(1+...) */
312 u = s_h*t_h;
313 v = s_l*t_h+t_l*ss;
314 /* 2/(3log2)*(ss+...) */
315 p_h = u+v;
316 __LO(p_h) = 0;
317 p_l = v-(p_h-u);
318 z_h = cp_h*p_h; /* cp_h+cp_l = 2/(3*log2) */
319 z_l = cp_l*p_h+p_l*cp+dp_l[k];
320 /* log2(ax) = (ss+..)*2/(3*log2) = n + dp_h + z_h + z_l */
321 t = (double)n;
322 t1 = (((z_h+z_l)+dp_h[k])+t);
323 __LO(t1) = 0;
324 t2 = z_l-(((t1-t)-dp_h[k])-z_h);
325 }
326
327 /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */
328 y1 = y;
329 __LO(y1) = 0;
330 p_l = (y-y1)*t1+y*t2;
331 p_h = y1*t1;
332 z = p_l+p_h;
333 j = __HI(z);
334 i = __LO(z);
335 if (j>=0x40900000) { /* z >= 1024 */
336 if(((j-0x40900000)|i)!=0) /* if z > 1024 */
337 return s*huge*huge; /* overflow */
338 else {
339 if(p_l+ovt>z-p_h) return s*huge*huge; /* overflow */
340 }
341 } else if((j&0x7fffffff)>=0x4090cc00 ) { /* z <= -1075 */
342 if(((j-0xc090cc00)|i)!=0) /* z < -1075 */
343 return s*tiny*tiny; /* underflow */
344 else {
345 if(p_l<=z-p_h) return s*tiny*tiny; /* underflow */
346 }
347 }
348 /*
349 * compute 2**(p_h+p_l)
350 */
351 i = j&0x7fffffff;
352 k = (i>>20)-0x3ff;
353 n = 0;
354 if(i>0x3fe00000) { /* if |z| > 0.5, set n = [z+0.5] */
355 n = j+(0x00100000>>(k+1));
356 k = ((n&0x7fffffff)>>20)-0x3ff; /* new k for n */
357 t = zero;
358 __HI(t) = (n&~(0x000fffff>>k));
359 n = ((n&0x000fffff)|0x00100000)>>(20-k);
360 if(j<0) n = -n;
361 p_h -= t;
362 }
363 t = p_l+p_h;
364 __LO(t) = 0;
365 u = t*lg2_h;
366 v = (p_l-(t-p_h))*lg2+t*lg2_l;
367 z = u+v;
368 w = v-(z-u);
369 t = z*z;
370 t1 = z - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
371 r = (z*t1)/(t1-two)-(w+z*w);
372 z = one-(r-z);
373 j = __HI(z);
374 j += (n<<20);
375 if((j>>20)<=0) z = fdlibmScalbn(z,n); /* subnormal output */
376 else __HI(z) += (n<<20);
377 return s*z;
378}
379
380static ALWAYS_INLINE bool isDenormal(double x)
381{
382 static const uint64_t signbit = 0x8000000000000000ULL;
383 static const uint64_t minNormal = 0x0001000000000000ULL;
384 return (bitwise_cast<uint64_t>(x) & ~signbit) - 1 < minNormal - 1;
385}
386
387static ALWAYS_INLINE bool isEdgeCase(double x)
388{
389 static const uint64_t signbit = 0x8000000000000000ULL;
390 static const uint64_t infinity = 0x7fffffffffffffffULL;
391 return (bitwise_cast<uint64_t>(x) & ~signbit) - 1 >= infinity - 1;
392}
393
394static ALWAYS_INLINE double mathPowInternal(double x, double y)
395{
396 if (!isDenormal(x) && !isDenormal(y)) {
397 double libmResult = std::pow(x, y);
398 if (libmResult || isEdgeCase(x) || isEdgeCase(y))
399 return libmResult;
400 }
401 return fdlibmPow(x, y);
402}
403
404#else
405
406ALWAYS_INLINE double mathPowInternal(double x, double y)
407{
408 return pow(x, y);
409}
410
411#endif
412
413double JIT_OPERATION operationMathPow(double x, double y)
414{
415 if (std::isnan(y))
416 return PNaN;
417 double absoluteBase = fabs(x);
418 if (absoluteBase == 1 && std::isinf(y))
419 return PNaN;
420
421 if (y == 0.5) {
422 if (!absoluteBase)
423 return 0;
424 if (absoluteBase == std::numeric_limits<double>::infinity())
425 return std::numeric_limits<double>::infinity();
426 return sqrt(x);
427 }
428
429 if (y == -0.5) {
430 if (!absoluteBase)
431 return std::numeric_limits<double>::infinity();
432 if (absoluteBase == std::numeric_limits<double>::infinity())
433 return 0.;
434 return 1. / sqrt(x);
435 }
436
437 int32_t yAsInt = y;
438 if (static_cast<double>(yAsInt) == y && yAsInt >= 0 && yAsInt <= maxExponentForIntegerMathPow) {
439 // If the exponent is a small positive int32 integer, we do a fast exponentiation
440 double result = 1;
441 double xd = x;
442 while (yAsInt) {
443 if (yAsInt & 1)
444 result *= xd;
445 xd *= xd;
446 yAsInt >>= 1;
447 }
448 return result;
449 }
450 return mathPowInternal(x, y);
451}
452
453int32_t JIT_OPERATION operationToInt32(double value)
454{
455 return JSC::toInt32(value);
456}
457
458int32_t JIT_OPERATION operationToInt32SensibleSlow(double number)
459{
460 return toInt32Internal<ToInt32Mode::AfterSensibleConversionAttempt>(number);
461}
462
463#if HAVE(ARM_IDIV_INSTRUCTIONS)
464static inline bool isStrictInt32(double value)
465{
466 int32_t valueAsInt32 = static_cast<int32_t>(value);
467 if (value != valueAsInt32)
468 return false;
469
470 if (!valueAsInt32) {
471 if (std::signbit(value))
472 return false;
473 }
474 return true;
475}
476#endif
477
478extern "C" {
479double jsRound(double value)
480{
481 double integer = ceil(value);
482 return integer - (integer - value > 0.5);
483}
484
485#if CALLING_CONVENTION_IS_STDCALL || CPU(ARM_THUMB2)
486double jsMod(double x, double y)
487{
488#if HAVE(ARM_IDIV_INSTRUCTIONS)
489 // fmod() does not have exact results for integer on ARMv7.
490 // When DFG/FTL use IDIV, the result of op_mod can change if we use fmod().
491 //
492 // We implement here the same algorithm and conditions as the upper tier to keep
493 // a stable result when tiering up.
494 if (y) {
495 if (isStrictInt32(x) && isStrictInt32(y)) {
496 int32_t xAsInt32 = static_cast<int32_t>(x);
497 int32_t yAsInt32 = static_cast<int32_t>(y);
498 int32_t quotient = xAsInt32 / yAsInt32;
499 if (!productOverflows<int32_t>(quotient, yAsInt32)) {
500 int32_t remainder = xAsInt32 - (quotient * yAsInt32);
501 if (remainder || xAsInt32 >= 0)
502 return remainder;
503 }
504 }
505 }
506#endif
507 return fmod(x, y);
508}
509#endif
510} // extern "C"
511
512namespace Math {
513
514double JIT_OPERATION log1p(double value)
515{
516 if (value == 0.0)
517 return value;
518 return std::log1p(value);
519}
520
521} // namespace Math
522} // namespace JSC
523