/*

 * Copyright (c) 2005, 2017, Oracle and/or its affiliates. All rights reserved.

 * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.

 *

 * This code is free software; you can redistribute it and/or modify it

 * under the terms of the GNU General Public License version 2 only, as

 * published by the Free Software Foundation.

 *

 * This code is distributed in the hope that it will be useful, but WITHOUT

 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or

 * FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License

 * version 2 for more details (a copy is included in the LICENSE file that

 * accompanied this code).

 *

 * You should have received a copy of the GNU General Public License version

 * 2 along with this work; if not, write to the Free Software Foundation,

 * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.

 *

 * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA

 * or visit www.oracle.com if you need additional information or have any

 * questions.

 *

 */

#include "precompiled.hpp"

#include "jni.h"

#include "runtime/sharedRuntime.hpp"

// This file contains copies of the fdlibm routines used by

// StrictMath. It turns out that it is almost always required to use

// these runtime routines; the Intel CPU doesn't meet the Java

// specification for sin/cos outside a certain limited argument range,

// and the SPARC CPU doesn't appear to have sin/cos instructions. It

// also turns out that avoiding the indirect call through function

// pointer out to libjava.so in SharedRuntime speeds these routines up

// by roughly 15% on both Win32/x86 and Solaris/SPARC.

// Enabling optimizations in this file causes incorrect code to be

// generated; can not figure out how to turn down optimization for one

// file in the IDE on Windows

#ifdef WIN32

# pragma warning( disable: 4748 ) // /GS can not protect parameters and local variables from local buffer overrun because optimizations are disabled in function

# pragma optimize ( "", off )

#endif

#include "runtime/sharedRuntimeMath.hpp"

/* __ieee754_log(x)

 * Return the logarithm of x

 *

 * Method :

 *   1. Argument Reduction: find k and f such that

 *                    x = 2^k * (1+f),

 *       where  sqrt(2)/2 < 1+f < sqrt(2) .

 *

 *   2. Approximation of log(1+f).

 *    Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s)

 *             = 2s + 2/3 s**3 + 2/5 s**5 + .....,

 *             = 2s + s*R

 *      We use a special Reme algorithm on [0,0.1716] to generate

 *    a polynomial of degree 14 to approximate R The maximum error

 *    of this polynomial approximation is bounded by 2**-58.45. In

 *    other words,

 *                    2      4      6      8      10      12      14

 *        R(z) ~ Lg1*s +Lg2*s +Lg3*s +Lg4*s +Lg5*s  +Lg6*s  +Lg7*s

 *    (the values of Lg1 to Lg7 are listed in the program)

 *    and

 *        |      2          14          |     -58.45

 *        | Lg1*s +...+Lg7*s    -  R(z) | <= 2

 *        |                             |

 *    Note that 2s = f - s*f = f - hfsq + s*hfsq, where hfsq = f*f/2.

 *    In order to guarantee error in log below 1ulp, we compute log

 *    by

 *            log(1+f) = f - s*(f - R)        (if f is not too large)

 *            log(1+f) = f - (hfsq - s*(hfsq+R)).     (better accuracy)

 *

 *    3. Finally,  log(x) = k*ln2 + log(1+f).

 *                        = k*ln2_hi+(f-(hfsq-(s*(hfsq+R)+k*ln2_lo)))

 *       Here ln2 is split into two floating point number:

 *                    ln2_hi + ln2_lo,

 *       where n*ln2_hi is always exact for |n| < 2000.

 *

 * Special cases:

 *    log(x) is NaN with signal if x < 0 (including -INF) ;

 *    log(+INF) is +INF; log(0) is -INF with signal;

 *    log(NaN) is that NaN with no signal.

 *

 * Accuracy:

 *    according to an error analysis, the error is always less than

 *    1 ulp (unit in the last place).

 *

 * 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.

 */

static const double

ln2_hi  =  6.93147180369123816490e-01,        /* 3fe62e42 fee00000 */

  ln2_lo  =  1.90821492927058770002e-10,        /* 3dea39ef 35793c76 */

  Lg1 = 6.666666666666735130e-01,  /* 3FE55555 55555593 */

  Lg2 = 3.999999999940941908e-01,  /* 3FD99999 9997FA04 */

  Lg3 = 2.857142874366239149e-01,  /* 3FD24924 94229359 */

  Lg4 = 2.222219843214978396e-01,  /* 3FCC71C5 1D8E78AF */

  Lg5 = 1.818357216161805012e-01,  /* 3FC74664 96CB03DE */

  Lg6 = 1.531383769920937332e-01,  /* 3FC39A09 D078C69F */

  Lg7 = 1.479819860511658591e-01;  /* 3FC2F112 DF3E5244 */

static double zero = 0.0;

static double __ieee754_log(double x) {

  double hfsq,f,s,z,R,w,t1,t2,dk;

  int k,hx,i,j;

  unsigned lx;

  hx = high(x);               /* high word of x */

  lx = low(x);                /* low  word of x */

  k=0;

  if (hx < 0x00100000) {                   /* x < 2**-1022  */

    if (((hx&0x7fffffff)|lx)==0)

      return -two54/zero;             /* log(+-0)=-inf */

    if (hx<0) return (x-x)/zero;   /* log(-#) = NaN */

    k -= 54; x *= two54; /* subnormal number, scale up x */

    hx = high(x);             /* high word of x */

  }

  if (hx >= 0x7ff00000) return x+x;

  k += (hx>>20)-1023;

  hx &= 0x000fffff;

  i = (hx+0x95f64)&0x100000;

  set_high(&x, hx|(i^0x3ff00000)); /* normalize x or x/2 */

  k += (i>>20);

  f = x-1.0;

  if((0x000fffff&(2+hx))<3) {  /* |f| < 2**-20 */

    if(f==zero) {

      if (k==0) return zero;

      else {dk=(double)k; return dk*ln2_hi+dk*ln2_lo;}

    }

    R = f*f*(0.5-0.33333333333333333*f);

    if(k==0) return f-R; else {dk=(double)k;

    return dk*ln2_hi-((R-dk*ln2_lo)-f);}

  }

  s = f/(2.0+f);

  dk = (double)k;

  z = s*s;

  i = hx-0x6147a;

  w = z*z;

  j = 0x6b851-hx;

  t1= w*(Lg2+w*(Lg4+w*Lg6));

  t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7)));

  i |= j;

  R = t2+t1;

  if(i>0) {

    hfsq=0.5*f*f;

    if(k==0) return f-(hfsq-s*(hfsq+R)); else

      return dk*ln2_hi-((hfsq-(s*(hfsq+R)+dk*ln2_lo))-f);

  } else {

    if(k==0) return f-s*(f-R); else

      return dk*ln2_hi-((s*(f-R)-dk*ln2_lo)-f);

  }

}

JRT_LEAF(jdouble, SharedRuntime::dlog(jdouble x))

  return __ieee754_log(x);

JRT_END

/* __ieee754_log10(x)

 * Return the base 10 logarithm of x

 *

 * Method :

 *    Let log10_2hi = leading 40 bits of log10(2) and

 *        log10_2lo = log10(2) - log10_2hi,

 *        ivln10   = 1/log(10) rounded.

 *    Then

 *            n = ilogb(x),

 *            if(n<0)  n = n+1;

 *            x = scalbn(x,-n);

 *            log10(x) := n*log10_2hi + (n*log10_2lo + ivln10*log(x))

 *

 * Note 1:

 *    To guarantee log10(10**n)=n, where 10**n is normal, the rounding

 *    mode must set to Round-to-Nearest.

 * Note 2:

 *    [1/log(10)] rounded to 53 bits has error  .198   ulps;

 *    log10 is monotonic at all binary break points.

 *

 * Special cases:

 *    log10(x) is NaN with signal if x < 0;

 *    log10(+INF) is +INF with no signal; log10(0) is -INF with signal;

 *    log10(NaN) is that NaN with no signal;

 *    log10(10**N) = N  for N=0,1,...,22.

 *

 * 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.

 */

static const double

ivln10     =  4.34294481903251816668e-01, /* 0x3FDBCB7B, 0x1526E50E */

  log10_2hi  =  3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */

  log10_2lo  =  3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */

static double __ieee754_log10(double x) {

  double y,z;

  int i,k,hx;

  unsigned lx;

  hx = high(x);       /* high word of x */

  lx = low(x);        /* low word of x */

  k=0;

  if (hx < 0x00100000) {                  /* x < 2**-1022  */

    if (((hx&0x7fffffff)|lx)==0)

      return -two54/zero;             /* log(+-0)=-inf */

    if (hx<0) return (x-x)/zero;        /* log(-#) = NaN */

    k -= 54; x *= two54; /* subnormal number, scale up x */

    hx = high(x);                /* high word of x */

  }

  if (hx >= 0x7ff00000) return x+x;

  k += (hx>>20)-1023;

  i  = ((unsigned)k&0x80000000)>>31;

  hx = (hx&0x000fffff)|((0x3ff-i)<<20);

  y  = (double)(k+i);

  set_high(&x, hx);

  z  = y*log10_2lo + ivln10*__ieee754_log(x);

  return  z+y*log10_2hi;

}

JRT_LEAF(jdouble, SharedRuntime::dlog10(jdouble x))

  return __ieee754_log10(x);

JRT_END

/* __ieee754_exp(x)

 * Returns the exponential of x.

 *

 * Method

 *   1. Argument reduction:

 *      Reduce x to an r so that |r| <= 0.5*ln2 ~ 0.34658.

 *      Given x, find r and integer k such that

 *

 *               x = k*ln2 + r,  |r| <= 0.5*ln2.

 *

 *      Here r will be represented as r = hi-lo for better

 *      accuracy.

 *

 *   2. Approximation of exp(r) by a special rational function on

 *      the interval [0,0.34658]:

 *      Write

 *          R(r**2) = r*(exp(r)+1)/(exp(r)-1) = 2 + r*r/6 - r**4/360 + ...

 *      We use a special Reme algorithm on [0,0.34658] to generate

 *      a polynomial of degree 5 to approximate R. The maximum error

 *      of this polynomial approximation is bounded by 2**-59. In

 *      other words,

 *          R(z) ~ 2.0 + P1*z + P2*z**2 + P3*z**3 + P4*z**4 + P5*z**5

 *      (where z=r*r, and the values of P1 to P5 are listed below)

 *      and

 *          |                  5          |     -59

 *          | 2.0+P1*z+...+P5*z   -  R(z) | <= 2

 *          |                             |

 *      The computation of exp(r) thus becomes

 *                             2*r

 *              exp(r) = 1 + -------

 *                            R - r

 *                                 r*R1(r)

 *                     = 1 + r + ----------- (for better accuracy)

 *                                2 - R1(r)

 *      where

 *                               2       4             10

 *              R1(r) = r - (P1*r  + P2*r  + ... + P5*r   ).

 *

 *   3. Scale back to obtain exp(x):

 *      From step 1, we have

 *         exp(x) = 2^k * exp(r)

 *

 * Special cases:

 *      exp(INF) is INF, exp(NaN) is NaN;

 *      exp(-INF) is 0, and

 *      for finite argument, only exp(0)=1 is exact.

 *

 * Accuracy:

 *      according to an error analysis, the error is always less than

 *      1 ulp (unit in the last place).

 *

 * Misc. info.

 *      For IEEE double

 *          if x >  7.09782712893383973096e+02 then exp(x) overflow

 *          if x < -7.45133219101941108420e+02 then exp(x) underflow

 *

 * 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.

 */

static const double

one     = 1.0,

  halF[2]       = {0.5,-0.5,},

  twom1000= 9.33263618503218878990e-302,     /* 2**-1000=0x01700000,0*/

    o_threshold=  7.09782712893383973096e+02,  /* 0x40862E42, 0xFEFA39EF */

    u_threshold= -7.45133219101941108420e+02,  /* 0xc0874910, 0xD52D3051 */

    ln2HI[2]   ={ 6.93147180369123816490e-01,  /* 0x3fe62e42, 0xfee00000 */

                  -6.93147180369123816490e-01,},/* 0xbfe62e42, 0xfee00000 */

    ln2LO[2]   ={ 1.90821492927058770002e-10,  /* 0x3dea39ef, 0x35793c76 */

                  -1.90821492927058770002e-10,},/* 0xbdea39ef, 0x35793c76 */

      invln2 =  1.44269504088896338700e+00, /* 0x3ff71547, 0x652b82fe */

        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 */

static double __ieee754_exp(double x) {

  double y,hi=0,lo=0,c,t;

  int k=0,xsb;

  unsigned hx;

  hx  = high(x);                /* high word of x */

  xsb = (hx>>31)&1;             /* sign bit of x */

  hx &= 0x7fffffff;             /* high word of |x| */

  /* filter out non-finite argument */

  if(hx >= 0x40862E42) {                        /* if |x|>=709.78... */

    if(hx>=0x7ff00000) {

      if(((hx&0xfffff)|low(x))!=0)

        return x+x;             /* NaN */

      else return (xsb==0)? x:0.0;      /* exp(+-inf)={inf,0} */

    }

    if(x > o_threshold) return hugeX*hugeX; /* overflow */

    if(x < u_threshold) return twom1000*twom1000; /* underflow */

  }

  /* argument reduction */

  if(hx > 0x3fd62e42) {         /* if  |x| > 0.5 ln2 */

    if(hx < 0x3FF0A2B2) {       /* and |x| < 1.5 ln2 */

      hi = x-ln2HI[xsb]; lo=ln2LO[xsb]; k = 1-xsb-xsb;

    } else {

      k  = (int)(invln2*x+halF[xsb]);

      t  = k;

      hi = x - t*ln2HI[0];      /* t*ln2HI is exact here */

      lo = t*ln2LO[0];

    }

    x  = hi - lo;

  }

  else if(hx < 0x3e300000)  {   /* when |x|<2**-28 */

    if(hugeX+x>one) return one+x;/* trigger inexact */

  }

  else k = 0;

  /* x is now in primary range */

  t  = x*x;

  c  = x - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));

  if(k==0)      return one-((x*c)/(c-2.0)-x);

  else          y = one-((lo-(x*c)/(2.0-c))-hi);

  if(k >= -1021) {

    set_high(&y, high(y) + (k<<20)); /* add k to y's exponent */

    return y;

  } else {

    set_high(&y, high(y) + ((k+1000)<<20)); /* add k to y's exponent */

    return y*twom1000;

  }

}

JRT_LEAF(jdouble, SharedRuntime::dexp(jdouble x))

  return __ieee754_exp(x);

JRT_END

/* __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.

 */

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 */

      zeroX    =  0.0,

        two     =  2.0,

        two53   =  9007199254740992.0,  /* 0x43400000, 0x00000000 */

        /* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */

        L1X  =  5.99999999999994648725e-01, /* 0x3FE33333, 0x33333303 */

        L2X  =  4.28571428578550184252e-01, /* 0x3FDB6DB6, 0xDB6FABFF */

        L3X  =  3.33333329818377432918e-01, /* 0x3FD55555, 0x518F264D */

        L4X  =  2.72728123808534006489e-01, /* 0x3FD17460, 0xA91D4101 */

        L5X  =  2.30660745775561754067e-01, /* 0x3FCD864A, 0x93C9DB65 */

        L6X  =  2.06975017800338417784e-01, /* 0x3FCA7E28, 0x4A454EEF */

        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*/

double __ieee754_pow(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 = high(x); lx = low(x);

  hy = high(y); ly = low(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((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: zeroX;

      else                      /* (|x|<1)**-,+inf = inf,0 */

        return (hy<0)?-y: zeroX;

    }

    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   = fabsd(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) {

#ifdef CAN_USE_NAN_DEFINE

          z = NAN;

#else

          z = (z-z)/(z-z); /* (-1)**non-int is NaN */

#endif

        } else if(yisint==1)

          z = -1.0*z;           /* (x<0)**odd = -(|x|**odd) */

      }

      return z;

    }

  }

  n = (hx>>31)+1;