/*

 * Copyright (c) 2001, 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/interfaceSupport.inline.hpp"

#include "runtime/sharedRuntime.hpp"

#include "runtime/sharedRuntimeMath.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.

/*

 * __kernel_rem_pio2(x,y,e0,nx,prec,ipio2)

 * double x[],y[]; int e0,nx,prec; int ipio2[];

 *

 * __kernel_rem_pio2 return the last three digits of N with

 *              y = x - N*pi/2

 * so that |y| < pi/2.

 *

 * The method is to compute the integer (mod 8) and fraction parts of

 * (2/pi)*x without doing the full multiplication. In general we

 * skip the part of the product that are known to be a huge integer (

 * more accurately, = 0 mod 8 ). Thus the number of operations are

 * independent of the exponent of the input.

 *

 * (2/pi) is represented by an array of 24-bit integers in ipio2[].

 *

 * Input parameters:

 *      x[]     The input value (must be positive) is broken into nx

 *              pieces of 24-bit integers in double precision format.

 *              x[i] will be the i-th 24 bit of x. The scaled exponent

 *              of x[0] is given in input parameter e0 (i.e., x[0]*2^e0

 *              match x's up to 24 bits.

 *

 *              Example of breaking a double positive z into x[0]+x[1]+x[2]:

 *                      e0 = ilogb(z)-23

 *                      z  = scalbn(z,-e0)

 *              for i = 0,1,2

 *                      x[i] = floor(z)

 *                      z    = (z-x[i])*2**24

 *

 *

 *      y[]     ouput result in an array of double precision numbers.

 *              The dimension of y[] is:

 *                      24-bit  precision       1

 *                      53-bit  precision       2

 *                      64-bit  precision       2

 *                      113-bit precision       3

 *              The actual value is the sum of them. Thus for 113-bit

 *              precsion, one may have to do something like:

 *

 *              long double t,w,r_head, r_tail;

 *              t = (long double)y[2] + (long double)y[1];

 *              w = (long double)y[0];

 *              r_head = t+w;

 *              r_tail = w - (r_head - t);

 *

 *      e0      The exponent of x[0]

 *

 *      nx      dimension of x[]

 *

 *      prec    an interger indicating the precision:

 *                      0       24  bits (single)

 *                      1       53  bits (double)

 *                      2       64  bits (extended)

 *                      3       113 bits (quad)

 *

 *      ipio2[]

 *              integer array, contains the (24*i)-th to (24*i+23)-th

 *              bit of 2/pi after binary point. The corresponding

 *              floating value is

 *

 *                      ipio2[i] * 2^(-24(i+1)).

 *

 * External function:

 *      double scalbn(), floor();

 *

 *

 * Here is the description of some local variables:

 *

 *      jk      jk+1 is the initial number of terms of ipio2[] needed

 *              in the computation. The recommended value is 2,3,4,

 *              6 for single, double, extended,and quad.

 *

 *      jz      local integer variable indicating the number of

 *              terms of ipio2[] used.

 *

 *      jx      nx - 1

 *

 *      jv      index for pointing to the suitable ipio2[] for the

 *              computation. In general, we want

 *                      ( 2^e0*x[0] * ipio2[jv-1]*2^(-24jv) )/8

 *              is an integer. Thus

 *                      e0-3-24*jv >= 0 or (e0-3)/24 >= jv

 *              Hence jv = max(0,(e0-3)/24).

 *

 *      jp      jp+1 is the number of terms in PIo2[] needed, jp = jk.

 *

 *      q[]     double array with integral value, representing the

 *              24-bits chunk of the product of x and 2/pi.

 *

 *      q0      the corresponding exponent of q[0]. Note that the

 *              exponent for q[i] would be q0-24*i.

 *

 *      PIo2[]  double precision array, obtained by cutting pi/2

 *              into 24 bits chunks.

 *

 *      f[]     ipio2[] in floating point

 *

 *      iq[]    integer array by breaking up q[] in 24-bits chunk.

 *

 *      fq[]    final product of x*(2/pi) in fq[0],..,fq[jk]

 *

 *      ih      integer. If >0 it indicates q[] is >= 0.5, hence

 *              it also indicates the *sign* of the result.

 *

 */

/*

 * 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 int init_jk[] = {2,3,4,6}; /* initial value for jk */

static const double PIo2[] = {

  1.57079625129699707031e+00, /* 0x3FF921FB, 0x40000000 */

  7.54978941586159635335e-08, /* 0x3E74442D, 0x00000000 */

  5.39030252995776476554e-15, /* 0x3CF84698, 0x80000000 */

  3.28200341580791294123e-22, /* 0x3B78CC51, 0x60000000 */

  1.27065575308067607349e-29, /* 0x39F01B83, 0x80000000 */

  1.22933308981111328932e-36, /* 0x387A2520, 0x40000000 */

  2.73370053816464559624e-44, /* 0x36E38222, 0x80000000 */

  2.16741683877804819444e-51, /* 0x3569F31D, 0x00000000 */

};

static const double

zeroB   = 0.0,

one     = 1.0,

two24B  = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */

twon24  = 5.96046447753906250000e-08; /* 0x3E700000, 0x00000000 */

static int __kernel_rem_pio2(double *x, double *y, int e0, int nx, int prec, const int *ipio2) {

  int jz,jx,jv,jp,jk,carry,n,iq[20],i,j,k,m,q0,ih;

  double z,fw,f[20],fq[20],q[20];

  /* initialize jk*/

  jk = init_jk[prec];

  jp = jk;

  /* determine jx,jv,q0, note that 3>q0 */

  jx =  nx-1;

  jv = (e0-3)/24; if(jv<0) jv=0;

  q0 =  e0-24*(jv+1);

  /* set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk] */

  j = jv-jx; m = jx+jk;

  for(i=0;i<=m;i++,j++) f[i] = (j<0)? zeroB : (double) ipio2[j];

  /* compute q[0],q[1],...q[jk] */

  for (i=0;i<=jk;i++) {

    for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; q[i] = fw;

  }

  jz = jk;

recompute:

  /* distill q[] into iq[] reversingly */

  for(i=0,j=jz,z=q[jz];j>0;i++,j--) {

    fw    =  (double)((int)(twon24* z));

    iq[i] =  (int)(z-two24B*fw);

    z     =  q[j-1]+fw;

  }

  /* compute n */

  z  = scalbnA(z,q0);           /* actual value of z */

  z -= 8.0*floor(z*0.125);              /* trim off integer >= 8 */

  n  = (int) z;

  z -= (double)n;

  ih = 0;

  if(q0>0) {    /* need iq[jz-1] to determine n */

    i  = (iq[jz-1]>>(24-q0)); n += i;

    iq[jz-1] -= i<<(24-q0);

    ih = iq[jz-1]>>(23-q0);

  }

  else if(q0==0) ih = iq[jz-1]>>23;

  else if(z>=0.5) ih=2;

  if(ih>0) {    /* q > 0.5 */

    n += 1; carry = 0;

    for(i=0;i<jz ;i++) {        /* compute 1-q */

      j = iq[i];

      if(carry==0) {

        if(j!=0) {

          carry = 1; iq[i] = 0x1000000- j;

        }

      } else  iq[i] = 0xffffff - j;

    }

    if(q0>0) {          /* rare case: chance is 1 in 12 */

      switch(q0) {

      case 1:

        iq[jz-1] &= 0x7fffff; break;

      case 2:

        iq[jz-1] &= 0x3fffff; break;

      }

    }

    if(ih==2) {

      z = one - z;

      if(carry!=0) z -= scalbnA(one,q0);

    }

  }

  /* check if recomputation is needed */

  if(z==zeroB) {

    j = 0;

    for (i=jz-1;i>=jk;i--) j |= iq[i];

    if(j==0) { /* need recomputation */

      for(k=1;iq[jk-k]==0;k++);   /* k = no. of terms needed */

      for(i=jz+1;i<=jz+k;i++) {   /* add q[jz+1] to q[jz+k] */

        f[jx+i] = (double) ipio2[jv+i];

        for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j];

        q[i] = fw;

      }

      jz += k;

      goto recompute;

    }

  }

  /* chop off zero terms */

  if(z==0.0) {

    jz -= 1; q0 -= 24;

    while(iq[jz]==0) { jz--; q0-=24;}

  } else { /* break z into 24-bit if necessary */

    z = scalbnA(z,-q0);

    if(z>=two24B) {

      fw = (double)((int)(twon24*z));

      iq[jz] = (int)(z-two24B*fw);

      jz += 1; q0 += 24;

      iq[jz] = (int) fw;

    } else iq[jz] = (int) z ;

  }

  /* convert integer "bit" chunk to floating-point value */

  fw = scalbnA(one,q0);

  for(i=jz;i>=0;i--) {

    q[i] = fw*(double)iq[i]; fw*=twon24;

  }

  /* compute PIo2[0,...,jp]*q[jz,...,0] */

  for(i=jz;i>=0;i--) {

    for(fw=0.0,k=0;k<=jp&&k<=jz-i;k++) fw += PIo2[k]*q[i+k];

    fq[jz-i] = fw;

  }

  /* compress fq[] into y[] */

  switch(prec) {

  case 0:

    fw = 0.0;

    for (i=jz;i>=0;i--) fw += fq[i];

    y[0] = (ih==0)? fw: -fw;

    break;

  case 1:

  case 2:

    fw = 0.0;

    for (i=jz;i>=0;i--) fw += fq[i];

    y[0] = (ih==0)? fw: -fw;

    fw = fq[0]-fw;

    for (i=1;i<=jz;i++) fw += fq[i];

    y[1] = (ih==0)? fw: -fw;

    break;

  case 3:       /* painful */

    for (i=jz;i>0;i--) {

      fw      = fq[i-1]+fq[i];

      fq[i]  += fq[i-1]-fw;

      fq[i-1] = fw;

    }

    for (i=jz;i>1;i--) {

      fw      = fq[i-1]+fq[i];

      fq[i]  += fq[i-1]-fw;

      fq[i-1] = fw;

    }

    for (fw=0.0,i=jz;i>=2;i--) fw += fq[i];

    if(ih==0) {

      y[0] =  fq[0]; y[1] =  fq[1]; y[2] =  fw;

    } else {

      y[0] = -fq[0]; y[1] = -fq[1]; y[2] = -fw;

    }

  }

  return n&7;

}

/*

 * ====================================================

 * Copyright (c) 1993 Oracle and/or its affiliates. All rights reserved.

 *

 * Developed at SunPro, a Sun Microsystems, Inc. business.

 * Permission to use, copy, modify, and distribute this

 * software is freely granted, provided that this notice

 * is preserved.

 * ====================================================

 *

 */

/* __ieee754_rem_pio2(x,y)

 *

 * return the remainder of x rem pi/2 in y[0]+y[1]

 * use __kernel_rem_pio2()

 */

/*

 * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi

 */

static const int two_over_pi[] = {

  0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62,

  0x95993C, 0x439041, 0xFE5163, 0xABDEBB, 0xC561B7, 0x246E3A,

  0x424DD2, 0xE00649, 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129,

  0xA73EE8, 0x8235F5, 0x2EBB44, 0x84E99C, 0x7026B4, 0x5F7E41,

  0x3991D6, 0x398353, 0x39F49C, 0x845F8B, 0xBDF928, 0x3B1FF8,

  0x97FFDE, 0x05980F, 0xEF2F11, 0x8B5A0A, 0x6D1F6D, 0x367ECF,

  0x27CB09, 0xB74F46, 0x3F669E, 0x5FEA2D, 0x7527BA, 0xC7EBE5,

  0xF17B3D, 0x0739F7, 0x8A5292, 0xEA6BFB, 0x5FB11F, 0x8D5D08,

  0x560330, 0x46FC7B, 0x6BABF0, 0xCFBC20, 0x9AF436, 0x1DA9E3,

  0x91615E, 0xE61B08, 0x659985, 0x5F14A0, 0x68408D, 0xFFD880,

  0x4D7327, 0x310606, 0x1556CA, 0x73A8C9, 0x60E27B, 0xC08C6B,

};

static const int npio2_hw[] = {

  0x3FF921FB, 0x400921FB, 0x4012D97C, 0x401921FB, 0x401F6A7A, 0x4022D97C,

  0x4025FDBB, 0x402921FB, 0x402C463A, 0x402F6A7A, 0x4031475C, 0x4032D97C,

  0x40346B9C, 0x4035FDBB, 0x40378FDB, 0x403921FB, 0x403AB41B, 0x403C463A,

  0x403DD85A, 0x403F6A7A, 0x40407E4C, 0x4041475C, 0x4042106C, 0x4042D97C,

  0x4043A28C, 0x40446B9C, 0x404534AC, 0x4045FDBB, 0x4046C6CB, 0x40478FDB,

  0x404858EB, 0x404921FB,

};

/*

 * invpio2:  53 bits of 2/pi

 * pio2_1:   first  33 bit of pi/2

 * pio2_1t:  pi/2 - pio2_1

 * pio2_2:   second 33 bit of pi/2

 * pio2_2t:  pi/2 - (pio2_1+pio2_2)

 * pio2_3:   third  33 bit of pi/2

 * pio2_3t:  pi/2 - (pio2_1+pio2_2+pio2_3)

 */

static const double

zeroA =  0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */

half =  5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */

two24A =  1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */

invpio2 =  6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */

pio2_1  =  1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */

pio2_1t =  6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */

pio2_2  =  6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */

pio2_2t =  2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */

pio2_3  =  2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */

pio2_3t =  8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */

static int __ieee754_rem_pio2(double x, double *y) {

  double z,w,t,r,fn;

  double tx[3];

  int e0,i,j,nx,n,ix,hx,i0;

  i0 = ((*(int*)&two24A)>>30)^1;        /* high word index */

  hx = *(i0+(int*)&x);          /* high word of x */

  ix = hx&0x7fffffff;

  if(ix<=0x3fe921fb)   /* |x| ~<= pi/4 , no need for reduction */

    {y[0] = x; y[1] = 0; return 0;}

  if(ix<0x4002d97c) {  /* |x| < 3pi/4, special case with n=+-1 */

    if(hx>0) {

      z = x - pio2_1;

      if(ix!=0x3ff921fb) {    /* 33+53 bit pi is good enough */

        y[0] = z - pio2_1t;

        y[1] = (z-y[0])-pio2_1t;

      } else {                /* near pi/2, use 33+33+53 bit pi */

        z -= pio2_2;

        y[0] = z - pio2_2t;

        y[1] = (z-y[0])-pio2_2t;

      }

      return 1;

    } else {    /* negative x */

      z = x + pio2_1;

      if(ix!=0x3ff921fb) {    /* 33+53 bit pi is good enough */

        y[0] = z + pio2_1t;

        y[1] = (z-y[0])+pio2_1t;

      } else {                /* near pi/2, use 33+33+53 bit pi */

        z += pio2_2;

        y[0] = z + pio2_2t;

        y[1] = (z-y[0])+pio2_2t;

      }

      return -1;

    }

  }

  if(ix<=0x413921fb) { /* |x| ~<= 2^19*(pi/2), medium size */

    t  = fabsd(x);

    n  = (int) (t*invpio2+half);

    fn = (double)n;

    r  = t-fn*pio2_1;

    w  = fn*pio2_1t;    /* 1st round good to 85 bit */

    if(n<32&&ix!=npio2_hw[n-1]) {

      y[0] = r-w;       /* quick check no cancellation */

    } else {

      j  = ix>>20;

      y[0] = r-w;

      i = j-(((*(i0+(int*)&y[0]))>>20)&0x7ff);

      if(i>16) {  /* 2nd iteration needed, good to 118 */

        t  = r;

        w  = fn*pio2_2;

        r  = t-w;

        w  = fn*pio2_2t-((t-r)-w);

        y[0] = r-w;

        i = j-(((*(i0+(int*)&y[0]))>>20)&0x7ff);

        if(i>49)  {     /* 3rd iteration need, 151 bits acc */

          t  = r;       /* will cover all possible cases */

          w  = fn*pio2_3;

          r  = t-w;

          w  = fn*pio2_3t-((t-r)-w);

          y[0] = r-w;

        }

      }

    }

    y[1] = (r-y[0])-w;

    if(hx<0)    {y[0] = -y[0]; y[1] = -y[1]; return -n;}

    else         return n;

  }

  /*

   * all other (large) arguments

   */

  if(ix>=0x7ff00000) {          /* x is inf or NaN */

    y[0]=y[1]=x-x; return 0;

  }

  /* set z = scalbn(|x|,ilogb(x)-23) */

  *(1-i0+(int*)&z) = *(1-i0+(int*)&x);

  e0    = (ix>>20)-1046;        /* e0 = ilogb(z)-23; */

  *(i0+(int*)&z) = ix - (e0<<20);

  for(i=0;i<2;i++) {

    tx[i] = (double)((int)(z));

    z     = (z-tx[i])*two24A;

  }

  tx[2] = z;

  nx = 3;

  while(tx[nx-1]==zeroA) nx--;  /* skip zero term */

  n  =  __kernel_rem_pio2(tx,y,e0,nx,2,two_over_pi);

  if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;}

  return n;

}

/* __kernel_sin( x, y, iy)

 * kernel sin function on [-pi/4, pi/4], pi/4 ~ 0.7854

 * Input x is assumed to be bounded by ~pi/4 in magnitude.

 * Input y is the tail of x.

 * Input iy indicates whether y is 0. (if iy=0, y assume to be 0).

 *

 * Algorithm

 *      1. Since sin(-x) = -sin(x), we need only to consider positive x.

 *      2. if x < 2^-27 (hx<0x3e400000 0), return x with inexact if x!=0.

 *      3. sin(x) is approximated by a polynomial of degree 13 on

 *         [0,pi/4]

 *                               3            13

 *              sin(x) ~ x + S1*x + ... + S6*x

 *         where

 *

 *      |sin(x)         2     4     6     8     10     12  |     -58

 *      |----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x  +S6*x   )| <= 2

 *      |  x                                               |

 *

 *      4. sin(x+y) = sin(x) + sin'(x')*y

 *                  ~ sin(x) + (1-x*x/2)*y

 *         For better accuracy, let

 *                   3      2      2      2      2

 *              r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6))))

 *         then                   3    2

 *              sin(x) = x + (S1*x + (x *(r-y/2)+y))

 */

static const double

S1  = -1.66666666666666324348e-01, /* 0xBFC55555, 0x55555549 */

S2  =  8.33333333332248946124e-03, /* 0x3F811111, 0x1110F8A6 */

S3  = -1.98412698298579493134e-04, /* 0xBF2A01A0, 0x19C161D5 */

S4  =  2.75573137070700676789e-06, /* 0x3EC71DE3, 0x57B1FE7D */

S5  = -2.50507602534068634195e-08, /* 0xBE5AE5E6, 0x8A2B9CEB */

S6  =  1.58969099521155010221e-10; /* 0x3DE5D93A, 0x5ACFD57C */

static double __kernel_sin(double x, double y, int iy)

{

        double z,r,v;

        int ix;

        ix = high(x)&0x7fffffff;                /* high word of x */

        if(ix<0x3e400000)                       /* |x| < 2**-27 */

           {if((int)x==0) return x;}            /* generate inexact */

        z       =  x*x;

        v       =  z*x;