src/hotspot/share/runtime/sharedRuntimeTrig.cpp
author erikj
Tue, 12 Sep 2017 19:03:39 +0200
changeset 47216 71c04702a3d5
parent 25919 hotspot/src/share/vm/runtime/sharedRuntimeTrig.cpp@d4e4f72b49fc
child 47659 a8e9aff89f7b
permissions -rw-r--r--
8187443: Forest Consolidation: Move files to unified layout Reviewed-by: darcy, ihse
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/*
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 * Copyright (c) 2001, 2014, Oracle and/or its affiliates. All rights reserved.
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 * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
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 *
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 * This code is free software; you can redistribute it and/or modify it
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 * under the terms of the GNU General Public License version 2 only, as
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 * published by the Free Software Foundation.
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 *
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 * This code is distributed in the hope that it will be useful, but WITHOUT
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 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
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 * FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
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 * version 2 for more details (a copy is included in the LICENSE file that
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 * accompanied this code).
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 *
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 * You should have received a copy of the GNU General Public License version
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 * 2 along with this work; if not, write to the Free Software Foundation,
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 * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
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 *
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 * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
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 * or visit www.oracle.com if you need additional information or have any
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 * questions.
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 *
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 */
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#include "precompiled.hpp"
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#include "prims/jni.h"
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#include "runtime/interfaceSupport.hpp"
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#include "runtime/sharedRuntime.hpp"
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#include "runtime/sharedRuntimeMath.hpp"
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// This file contains copies of the fdlibm routines used by
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// StrictMath. It turns out that it is almost always required to use
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// these runtime routines; the Intel CPU doesn't meet the Java
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// specification for sin/cos outside a certain limited argument range,
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// and the SPARC CPU doesn't appear to have sin/cos instructions. It
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// also turns out that avoiding the indirect call through function
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// pointer out to libjava.so in SharedRuntime speeds these routines up
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// by roughly 15% on both Win32/x86 and Solaris/SPARC.
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/*
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 * __kernel_rem_pio2(x,y,e0,nx,prec,ipio2)
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 * double x[],y[]; int e0,nx,prec; int ipio2[];
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 *
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 * __kernel_rem_pio2 return the last three digits of N with
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 *              y = x - N*pi/2
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 * so that |y| < pi/2.
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 *
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 * The method is to compute the integer (mod 8) and fraction parts of
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 * (2/pi)*x without doing the full multiplication. In general we
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 * skip the part of the product that are known to be a huge integer (
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 * more accurately, = 0 mod 8 ). Thus the number of operations are
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 * independent of the exponent of the input.
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 *
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 * (2/pi) is represented by an array of 24-bit integers in ipio2[].
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 *
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 * Input parameters:
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 *      x[]     The input value (must be positive) is broken into nx
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 *              pieces of 24-bit integers in double precision format.
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 *              x[i] will be the i-th 24 bit of x. The scaled exponent
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 *              of x[0] is given in input parameter e0 (i.e., x[0]*2^e0
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 *              match x's up to 24 bits.
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 *
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 *              Example of breaking a double positive z into x[0]+x[1]+x[2]:
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 *                      e0 = ilogb(z)-23
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 *                      z  = scalbn(z,-e0)
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 *              for i = 0,1,2
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 *                      x[i] = floor(z)
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 *                      z    = (z-x[i])*2**24
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 *
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 *
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 *      y[]     ouput result in an array of double precision numbers.
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 *              The dimension of y[] is:
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 *                      24-bit  precision       1
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 *                      53-bit  precision       2
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 *                      64-bit  precision       2
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 *                      113-bit precision       3
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 *              The actual value is the sum of them. Thus for 113-bit
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 *              precsion, one may have to do something like:
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 *
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 *              long double t,w,r_head, r_tail;
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 *              t = (long double)y[2] + (long double)y[1];
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 *              w = (long double)y[0];
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 *              r_head = t+w;
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 *              r_tail = w - (r_head - t);
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 *
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 *      e0      The exponent of x[0]
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 *
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 *      nx      dimension of x[]
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 *
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 *      prec    an interger indicating the precision:
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 *                      0       24  bits (single)
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 *                      1       53  bits (double)
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 *                      2       64  bits (extended)
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 *                      3       113 bits (quad)
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 *
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 *      ipio2[]
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 *              integer array, contains the (24*i)-th to (24*i+23)-th
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 *              bit of 2/pi after binary point. The corresponding
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 *              floating value is
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 *
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 *                      ipio2[i] * 2^(-24(i+1)).
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 *
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 * External function:
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 *      double scalbn(), floor();
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 *
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 *
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 * Here is the description of some local variables:
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 *
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 *      jk      jk+1 is the initial number of terms of ipio2[] needed
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 *              in the computation. The recommended value is 2,3,4,
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 *              6 for single, double, extended,and quad.
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 *
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 *      jz      local integer variable indicating the number of
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 *              terms of ipio2[] used.
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 *
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 *      jx      nx - 1
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 *
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 *      jv      index for pointing to the suitable ipio2[] for the
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 *              computation. In general, we want
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 *                      ( 2^e0*x[0] * ipio2[jv-1]*2^(-24jv) )/8
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 *              is an integer. Thus
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 *                      e0-3-24*jv >= 0 or (e0-3)/24 >= jv
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 *              Hence jv = max(0,(e0-3)/24).
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 *
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 *      jp      jp+1 is the number of terms in PIo2[] needed, jp = jk.
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 *
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 *      q[]     double array with integral value, representing the
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 *              24-bits chunk of the product of x and 2/pi.
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 *
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 *      q0      the corresponding exponent of q[0]. Note that the
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 *              exponent for q[i] would be q0-24*i.
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 *
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 *      PIo2[]  double precision array, obtained by cutting pi/2
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 *              into 24 bits chunks.
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 *
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 *      f[]     ipio2[] in floating point
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 *
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 *      iq[]    integer array by breaking up q[] in 24-bits chunk.
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 *
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 *      fq[]    final product of x*(2/pi) in fq[0],..,fq[jk]
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 *
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 *      ih      integer. If >0 it indicates q[] is >= 0.5, hence
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 *              it also indicates the *sign* of the result.
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 *
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 */
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/*
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 * Constants:
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 * The hexadecimal values are the intended ones for the following
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 * constants. The decimal values may be used, provided that the
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 * compiler will convert from decimal to binary accurately enough
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 * to produce the hexadecimal values shown.
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 */
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static const int init_jk[] = {2,3,4,6}; /* initial value for jk */
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static const double PIo2[] = {
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  1.57079625129699707031e+00, /* 0x3FF921FB, 0x40000000 */
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  7.54978941586159635335e-08, /* 0x3E74442D, 0x00000000 */
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  5.39030252995776476554e-15, /* 0x3CF84698, 0x80000000 */
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  3.28200341580791294123e-22, /* 0x3B78CC51, 0x60000000 */
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  1.27065575308067607349e-29, /* 0x39F01B83, 0x80000000 */
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  1.22933308981111328932e-36, /* 0x387A2520, 0x40000000 */
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  2.73370053816464559624e-44, /* 0x36E38222, 0x80000000 */
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  2.16741683877804819444e-51, /* 0x3569F31D, 0x00000000 */
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};
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static const double
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zeroB   = 0.0,
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one     = 1.0,
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two24B  = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */
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twon24  = 5.96046447753906250000e-08; /* 0x3E700000, 0x00000000 */
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static int __kernel_rem_pio2(double *x, double *y, int e0, int nx, int prec, const int *ipio2) {
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  int jz,jx,jv,jp,jk,carry,n,iq[20],i,j,k,m,q0,ih;
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  double z,fw,f[20],fq[20],q[20];
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  /* initialize jk*/
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  jk = init_jk[prec];
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  jp = jk;
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  /* determine jx,jv,q0, note that 3>q0 */
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  jx =  nx-1;
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  jv = (e0-3)/24; if(jv<0) jv=0;
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   187
  q0 =  e0-24*(jv+1);
489c9b5090e2 Initial load
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diff changeset
   188
489c9b5090e2 Initial load
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   189
  /* set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk] */
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   190
  j = jv-jx; m = jx+jk;
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   191
  for(i=0;i<=m;i++,j++) f[i] = (j<0)? zeroB : (double) ipio2[j];
489c9b5090e2 Initial load
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diff changeset
   192
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parents:
diff changeset
   193
  /* compute q[0],q[1],...q[jk] */
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diff changeset
   194
  for (i=0;i<=jk;i++) {
489c9b5090e2 Initial load
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   195
    for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; q[i] = fw;
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   196
  }
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diff changeset
   197
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diff changeset
   198
  jz = jk;
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   199
recompute:
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   200
  /* distill q[] into iq[] reversingly */
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   201
  for(i=0,j=jz,z=q[jz];j>0;i++,j--) {
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   202
    fw    =  (double)((int)(twon24* z));
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   203
    iq[i] =  (int)(z-two24B*fw);
489c9b5090e2 Initial load
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   204
    z     =  q[j-1]+fw;
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   205
  }
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   206
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   207
  /* compute n */
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diff changeset
   208
  z  = scalbnA(z,q0);           /* actual value of z */
489c9b5090e2 Initial load
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diff changeset
   209
  z -= 8.0*floor(z*0.125);              /* trim off integer >= 8 */
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   210
  n  = (int) z;
489c9b5090e2 Initial load
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   211
  z -= (double)n;
489c9b5090e2 Initial load
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   212
  ih = 0;
489c9b5090e2 Initial load
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parents:
diff changeset
   213
  if(q0>0) {    /* need iq[jz-1] to determine n */
489c9b5090e2 Initial load
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parents:
diff changeset
   214
    i  = (iq[jz-1]>>(24-q0)); n += i;
489c9b5090e2 Initial load
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parents:
diff changeset
   215
    iq[jz-1] -= i<<(24-q0);
489c9b5090e2 Initial load
duke
parents:
diff changeset
   216
    ih = iq[jz-1]>>(23-q0);
489c9b5090e2 Initial load
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parents:
diff changeset
   217
  }
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diff changeset
   218
  else if(q0==0) ih = iq[jz-1]>>23;
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diff changeset
   219
  else if(z>=0.5) ih=2;
489c9b5090e2 Initial load
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parents:
diff changeset
   220
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parents:
diff changeset
   221
  if(ih>0) {    /* q > 0.5 */
489c9b5090e2 Initial load
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parents:
diff changeset
   222
    n += 1; carry = 0;
489c9b5090e2 Initial load
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parents:
diff changeset
   223
    for(i=0;i<jz ;i++) {        /* compute 1-q */
489c9b5090e2 Initial load
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parents:
diff changeset
   224
      j = iq[i];
489c9b5090e2 Initial load
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parents:
diff changeset
   225
      if(carry==0) {
489c9b5090e2 Initial load
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parents:
diff changeset
   226
        if(j!=0) {
489c9b5090e2 Initial load
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parents:
diff changeset
   227
          carry = 1; iq[i] = 0x1000000- j;
489c9b5090e2 Initial load
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diff changeset
   228
        }
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parents:
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   229
      } else  iq[i] = 0xffffff - j;
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   230
    }
489c9b5090e2 Initial load
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parents:
diff changeset
   231
    if(q0>0) {          /* rare case: chance is 1 in 12 */
489c9b5090e2 Initial load
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parents:
diff changeset
   232
      switch(q0) {
489c9b5090e2 Initial load
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parents:
diff changeset
   233
      case 1:
489c9b5090e2 Initial load
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parents:
diff changeset
   234
        iq[jz-1] &= 0x7fffff; break;
489c9b5090e2 Initial load
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parents:
diff changeset
   235
      case 2:
489c9b5090e2 Initial load
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parents:
diff changeset
   236
        iq[jz-1] &= 0x3fffff; break;
489c9b5090e2 Initial load
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parents:
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   237
      }
489c9b5090e2 Initial load
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parents:
diff changeset
   238
    }
489c9b5090e2 Initial load
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parents:
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   239
    if(ih==2) {
489c9b5090e2 Initial load
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parents:
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   240
      z = one - z;
489c9b5090e2 Initial load
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parents:
diff changeset
   241
      if(carry!=0) z -= scalbnA(one,q0);
489c9b5090e2 Initial load
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parents:
diff changeset
   242
    }
489c9b5090e2 Initial load
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parents:
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   243
  }
489c9b5090e2 Initial load
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parents:
diff changeset
   244
489c9b5090e2 Initial load
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parents:
diff changeset
   245
  /* check if recomputation is needed */
489c9b5090e2 Initial load
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parents:
diff changeset
   246
  if(z==zeroB) {
489c9b5090e2 Initial load
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parents:
diff changeset
   247
    j = 0;
489c9b5090e2 Initial load
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parents:
diff changeset
   248
    for (i=jz-1;i>=jk;i--) j |= iq[i];
489c9b5090e2 Initial load
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parents:
diff changeset
   249
    if(j==0) { /* need recomputation */
489c9b5090e2 Initial load
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parents:
diff changeset
   250
      for(k=1;iq[jk-k]==0;k++);   /* k = no. of terms needed */
489c9b5090e2 Initial load
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parents:
diff changeset
   251
489c9b5090e2 Initial load
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parents:
diff changeset
   252
      for(i=jz+1;i<=jz+k;i++) {   /* add q[jz+1] to q[jz+k] */
489c9b5090e2 Initial load
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parents:
diff changeset
   253
        f[jx+i] = (double) ipio2[jv+i];
489c9b5090e2 Initial load
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parents:
diff changeset
   254
        for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j];
489c9b5090e2 Initial load
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parents:
diff changeset
   255
        q[i] = fw;
489c9b5090e2 Initial load
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parents:
diff changeset
   256
      }
489c9b5090e2 Initial load
duke
parents:
diff changeset
   257
      jz += k;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   258
      goto recompute;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   259
    }
489c9b5090e2 Initial load
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parents:
diff changeset
   260
  }
489c9b5090e2 Initial load
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parents:
diff changeset
   261
489c9b5090e2 Initial load
duke
parents:
diff changeset
   262
  /* chop off zero terms */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   263
  if(z==0.0) {
489c9b5090e2 Initial load
duke
parents:
diff changeset
   264
    jz -= 1; q0 -= 24;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   265
    while(iq[jz]==0) { jz--; q0-=24;}
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parents: 7397
diff changeset
   266
  } else { /* break z into 24-bit if necessary */
1
489c9b5090e2 Initial load
duke
parents:
diff changeset
   267
    z = scalbnA(z,-q0);
489c9b5090e2 Initial load
duke
parents:
diff changeset
   268
    if(z>=two24B) {
489c9b5090e2 Initial load
duke
parents:
diff changeset
   269
      fw = (double)((int)(twon24*z));
489c9b5090e2 Initial load
duke
parents:
diff changeset
   270
      iq[jz] = (int)(z-two24B*fw);
489c9b5090e2 Initial load
duke
parents:
diff changeset
   271
      jz += 1; q0 += 24;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   272
      iq[jz] = (int) fw;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   273
    } else iq[jz] = (int) z ;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   274
  }
489c9b5090e2 Initial load
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parents:
diff changeset
   275
489c9b5090e2 Initial load
duke
parents:
diff changeset
   276
  /* convert integer "bit" chunk to floating-point value */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   277
  fw = scalbnA(one,q0);
489c9b5090e2 Initial load
duke
parents:
diff changeset
   278
  for(i=jz;i>=0;i--) {
489c9b5090e2 Initial load
duke
parents:
diff changeset
   279
    q[i] = fw*(double)iq[i]; fw*=twon24;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   280
  }
489c9b5090e2 Initial load
duke
parents:
diff changeset
   281
489c9b5090e2 Initial load
duke
parents:
diff changeset
   282
  /* compute PIo2[0,...,jp]*q[jz,...,0] */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   283
  for(i=jz;i>=0;i--) {
489c9b5090e2 Initial load
duke
parents:
diff changeset
   284
    for(fw=0.0,k=0;k<=jp&&k<=jz-i;k++) fw += PIo2[k]*q[i+k];
489c9b5090e2 Initial load
duke
parents:
diff changeset
   285
    fq[jz-i] = fw;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   286
  }
489c9b5090e2 Initial load
duke
parents:
diff changeset
   287
489c9b5090e2 Initial load
duke
parents:
diff changeset
   288
  /* compress fq[] into y[] */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   289
  switch(prec) {
489c9b5090e2 Initial load
duke
parents:
diff changeset
   290
  case 0:
489c9b5090e2 Initial load
duke
parents:
diff changeset
   291
    fw = 0.0;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   292
    for (i=jz;i>=0;i--) fw += fq[i];
489c9b5090e2 Initial load
duke
parents:
diff changeset
   293
    y[0] = (ih==0)? fw: -fw;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   294
    break;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   295
  case 1:
489c9b5090e2 Initial load
duke
parents:
diff changeset
   296
  case 2:
489c9b5090e2 Initial load
duke
parents:
diff changeset
   297
    fw = 0.0;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   298
    for (i=jz;i>=0;i--) fw += fq[i];
489c9b5090e2 Initial load
duke
parents:
diff changeset
   299
    y[0] = (ih==0)? fw: -fw;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   300
    fw = fq[0]-fw;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   301
    for (i=1;i<=jz;i++) fw += fq[i];
489c9b5090e2 Initial load
duke
parents:
diff changeset
   302
    y[1] = (ih==0)? fw: -fw;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   303
    break;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   304
  case 3:       /* painful */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   305
    for (i=jz;i>0;i--) {
489c9b5090e2 Initial load
duke
parents:
diff changeset
   306
      fw      = fq[i-1]+fq[i];
489c9b5090e2 Initial load
duke
parents:
diff changeset
   307
      fq[i]  += fq[i-1]-fw;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   308
      fq[i-1] = fw;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   309
    }
489c9b5090e2 Initial load
duke
parents:
diff changeset
   310
    for (i=jz;i>1;i--) {
489c9b5090e2 Initial load
duke
parents:
diff changeset
   311
      fw      = fq[i-1]+fq[i];
489c9b5090e2 Initial load
duke
parents:
diff changeset
   312
      fq[i]  += fq[i-1]-fw;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   313
      fq[i-1] = fw;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   314
    }
489c9b5090e2 Initial load
duke
parents:
diff changeset
   315
    for (fw=0.0,i=jz;i>=2;i--) fw += fq[i];
489c9b5090e2 Initial load
duke
parents:
diff changeset
   316
    if(ih==0) {
489c9b5090e2 Initial load
duke
parents:
diff changeset
   317
      y[0] =  fq[0]; y[1] =  fq[1]; y[2] =  fw;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   318
    } else {
489c9b5090e2 Initial load
duke
parents:
diff changeset
   319
      y[0] = -fq[0]; y[1] = -fq[1]; y[2] = -fw;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   320
    }
489c9b5090e2 Initial load
duke
parents:
diff changeset
   321
  }
489c9b5090e2 Initial load
duke
parents:
diff changeset
   322
  return n&7;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   323
}
489c9b5090e2 Initial load
duke
parents:
diff changeset
   324
489c9b5090e2 Initial load
duke
parents:
diff changeset
   325
489c9b5090e2 Initial load
duke
parents:
diff changeset
   326
/*
489c9b5090e2 Initial load
duke
parents:
diff changeset
   327
 * ====================================================
22551
9bf46d16dcc6 8025856: Fix typos in the GC code
jwilhelm
parents: 7397
diff changeset
   328
 * Copyright (c) 1993 Oracle and/or its affiliates. All rights reserved.
1
489c9b5090e2 Initial load
duke
parents:
diff changeset
   329
 *
489c9b5090e2 Initial load
duke
parents:
diff changeset
   330
 * Developed at SunPro, a Sun Microsystems, Inc. business.
489c9b5090e2 Initial load
duke
parents:
diff changeset
   331
 * Permission to use, copy, modify, and distribute this
489c9b5090e2 Initial load
duke
parents:
diff changeset
   332
 * software is freely granted, provided that this notice
489c9b5090e2 Initial load
duke
parents:
diff changeset
   333
 * is preserved.
489c9b5090e2 Initial load
duke
parents:
diff changeset
   334
 * ====================================================
489c9b5090e2 Initial load
duke
parents:
diff changeset
   335
 *
489c9b5090e2 Initial load
duke
parents:
diff changeset
   336
 */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   337
489c9b5090e2 Initial load
duke
parents:
diff changeset
   338
/* __ieee754_rem_pio2(x,y)
489c9b5090e2 Initial load
duke
parents:
diff changeset
   339
 *
489c9b5090e2 Initial load
duke
parents:
diff changeset
   340
 * return the remainder of x rem pi/2 in y[0]+y[1]
489c9b5090e2 Initial load
duke
parents:
diff changeset
   341
 * use __kernel_rem_pio2()
489c9b5090e2 Initial load
duke
parents:
diff changeset
   342
 */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   343
489c9b5090e2 Initial load
duke
parents:
diff changeset
   344
/*
489c9b5090e2 Initial load
duke
parents:
diff changeset
   345
 * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi
489c9b5090e2 Initial load
duke
parents:
diff changeset
   346
 */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   347
static const int two_over_pi[] = {
489c9b5090e2 Initial load
duke
parents:
diff changeset
   348
  0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62,
489c9b5090e2 Initial load
duke
parents:
diff changeset
   349
  0x95993C, 0x439041, 0xFE5163, 0xABDEBB, 0xC561B7, 0x246E3A,
489c9b5090e2 Initial load
duke
parents:
diff changeset
   350
  0x424DD2, 0xE00649, 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129,
489c9b5090e2 Initial load
duke
parents:
diff changeset
   351
  0xA73EE8, 0x8235F5, 0x2EBB44, 0x84E99C, 0x7026B4, 0x5F7E41,
489c9b5090e2 Initial load
duke
parents:
diff changeset
   352
  0x3991D6, 0x398353, 0x39F49C, 0x845F8B, 0xBDF928, 0x3B1FF8,
489c9b5090e2 Initial load
duke
parents:
diff changeset
   353
  0x97FFDE, 0x05980F, 0xEF2F11, 0x8B5A0A, 0x6D1F6D, 0x367ECF,
489c9b5090e2 Initial load
duke
parents:
diff changeset
   354
  0x27CB09, 0xB74F46, 0x3F669E, 0x5FEA2D, 0x7527BA, 0xC7EBE5,
489c9b5090e2 Initial load
duke
parents:
diff changeset
   355
  0xF17B3D, 0x0739F7, 0x8A5292, 0xEA6BFB, 0x5FB11F, 0x8D5D08,
489c9b5090e2 Initial load
duke
parents:
diff changeset
   356
  0x560330, 0x46FC7B, 0x6BABF0, 0xCFBC20, 0x9AF436, 0x1DA9E3,
489c9b5090e2 Initial load
duke
parents:
diff changeset
   357
  0x91615E, 0xE61B08, 0x659985, 0x5F14A0, 0x68408D, 0xFFD880,
489c9b5090e2 Initial load
duke
parents:
diff changeset
   358
  0x4D7327, 0x310606, 0x1556CA, 0x73A8C9, 0x60E27B, 0xC08C6B,
489c9b5090e2 Initial load
duke
parents:
diff changeset
   359
};
489c9b5090e2 Initial load
duke
parents:
diff changeset
   360
489c9b5090e2 Initial load
duke
parents:
diff changeset
   361
static const int npio2_hw[] = {
489c9b5090e2 Initial load
duke
parents:
diff changeset
   362
  0x3FF921FB, 0x400921FB, 0x4012D97C, 0x401921FB, 0x401F6A7A, 0x4022D97C,
489c9b5090e2 Initial load
duke
parents:
diff changeset
   363
  0x4025FDBB, 0x402921FB, 0x402C463A, 0x402F6A7A, 0x4031475C, 0x4032D97C,
489c9b5090e2 Initial load
duke
parents:
diff changeset
   364
  0x40346B9C, 0x4035FDBB, 0x40378FDB, 0x403921FB, 0x403AB41B, 0x403C463A,
489c9b5090e2 Initial load
duke
parents:
diff changeset
   365
  0x403DD85A, 0x403F6A7A, 0x40407E4C, 0x4041475C, 0x4042106C, 0x4042D97C,
489c9b5090e2 Initial load
duke
parents:
diff changeset
   366
  0x4043A28C, 0x40446B9C, 0x404534AC, 0x4045FDBB, 0x4046C6CB, 0x40478FDB,
489c9b5090e2 Initial load
duke
parents:
diff changeset
   367
  0x404858EB, 0x404921FB,
489c9b5090e2 Initial load
duke
parents:
diff changeset
   368
};
489c9b5090e2 Initial load
duke
parents:
diff changeset
   369
489c9b5090e2 Initial load
duke
parents:
diff changeset
   370
/*
489c9b5090e2 Initial load
duke
parents:
diff changeset
   371
 * invpio2:  53 bits of 2/pi
489c9b5090e2 Initial load
duke
parents:
diff changeset
   372
 * pio2_1:   first  33 bit of pi/2
489c9b5090e2 Initial load
duke
parents:
diff changeset
   373
 * pio2_1t:  pi/2 - pio2_1
489c9b5090e2 Initial load
duke
parents:
diff changeset
   374
 * pio2_2:   second 33 bit of pi/2
489c9b5090e2 Initial load
duke
parents:
diff changeset
   375
 * pio2_2t:  pi/2 - (pio2_1+pio2_2)
489c9b5090e2 Initial load
duke
parents:
diff changeset
   376
 * pio2_3:   third  33 bit of pi/2
489c9b5090e2 Initial load
duke
parents:
diff changeset
   377
 * pio2_3t:  pi/2 - (pio2_1+pio2_2+pio2_3)
489c9b5090e2 Initial load
duke
parents:
diff changeset
   378
 */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   379
489c9b5090e2 Initial load
duke
parents:
diff changeset
   380
static const double
489c9b5090e2 Initial load
duke
parents:
diff changeset
   381
zeroA =  0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   382
half =  5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   383
two24A =  1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   384
invpio2 =  6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   385
pio2_1  =  1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   386
pio2_1t =  6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   387
pio2_2  =  6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   388
pio2_2t =  2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   389
pio2_3  =  2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   390
pio2_3t =  8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   391
25060
fab862c73f1c 6961433: Revisit need to disable Windows C++ compiler optimisation of sharedRuntimeTrig.cpp.
lfoltan
parents: 24660
diff changeset
   392
static int __ieee754_rem_pio2(double x, double *y) {
1
489c9b5090e2 Initial load
duke
parents:
diff changeset
   393
  double z,w,t,r,fn;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   394
  double tx[3];
489c9b5090e2 Initial load
duke
parents:
diff changeset
   395
  int e0,i,j,nx,n,ix,hx,i0;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   396
489c9b5090e2 Initial load
duke
parents:
diff changeset
   397
  i0 = ((*(int*)&two24A)>>30)^1;        /* high word index */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   398
  hx = *(i0+(int*)&x);          /* high word of x */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   399
  ix = hx&0x7fffffff;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   400
  if(ix<=0x3fe921fb)   /* |x| ~<= pi/4 , no need for reduction */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   401
    {y[0] = x; y[1] = 0; return 0;}
489c9b5090e2 Initial load
duke
parents:
diff changeset
   402
  if(ix<0x4002d97c) {  /* |x| < 3pi/4, special case with n=+-1 */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   403
    if(hx>0) {
489c9b5090e2 Initial load
duke
parents:
diff changeset
   404
      z = x - pio2_1;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   405
      if(ix!=0x3ff921fb) {    /* 33+53 bit pi is good enough */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   406
        y[0] = z - pio2_1t;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   407
        y[1] = (z-y[0])-pio2_1t;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   408
      } else {                /* near pi/2, use 33+33+53 bit pi */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   409
        z -= pio2_2;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   410
        y[0] = z - pio2_2t;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   411
        y[1] = (z-y[0])-pio2_2t;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   412
      }
489c9b5090e2 Initial load
duke
parents:
diff changeset
   413
      return 1;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   414
    } else {    /* negative x */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   415
      z = x + pio2_1;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   416
      if(ix!=0x3ff921fb) {    /* 33+53 bit pi is good enough */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   417
        y[0] = z + pio2_1t;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   418
        y[1] = (z-y[0])+pio2_1t;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   419
      } else {                /* near pi/2, use 33+33+53 bit pi */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   420
        z += pio2_2;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   421
        y[0] = z + pio2_2t;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   422
        y[1] = (z-y[0])+pio2_2t;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   423
      }
489c9b5090e2 Initial load
duke
parents:
diff changeset
   424
      return -1;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   425
    }
489c9b5090e2 Initial load
duke
parents:
diff changeset
   426
  }
489c9b5090e2 Initial load
duke
parents:
diff changeset
   427
  if(ix<=0x413921fb) { /* |x| ~<= 2^19*(pi/2), medium size */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   428
    t  = fabsd(x);
489c9b5090e2 Initial load
duke
parents:
diff changeset
   429
    n  = (int) (t*invpio2+half);
489c9b5090e2 Initial load
duke
parents:
diff changeset
   430
    fn = (double)n;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   431
    r  = t-fn*pio2_1;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   432
    w  = fn*pio2_1t;    /* 1st round good to 85 bit */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   433
    if(n<32&&ix!=npio2_hw[n-1]) {
489c9b5090e2 Initial load
duke
parents:
diff changeset
   434
      y[0] = r-w;       /* quick check no cancellation */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   435
    } else {
489c9b5090e2 Initial load
duke
parents:
diff changeset
   436
      j  = ix>>20;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   437
      y[0] = r-w;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   438
      i = j-(((*(i0+(int*)&y[0]))>>20)&0x7ff);
489c9b5090e2 Initial load
duke
parents:
diff changeset
   439
      if(i>16) {  /* 2nd iteration needed, good to 118 */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   440
        t  = r;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   441
        w  = fn*pio2_2;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   442
        r  = t-w;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   443
        w  = fn*pio2_2t-((t-r)-w);
489c9b5090e2 Initial load
duke
parents:
diff changeset
   444
        y[0] = r-w;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   445
        i = j-(((*(i0+(int*)&y[0]))>>20)&0x7ff);
489c9b5090e2 Initial load
duke
parents:
diff changeset
   446
        if(i>49)  {     /* 3rd iteration need, 151 bits acc */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   447
          t  = r;       /* will cover all possible cases */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   448
          w  = fn*pio2_3;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   449
          r  = t-w;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   450
          w  = fn*pio2_3t-((t-r)-w);
489c9b5090e2 Initial load
duke
parents:
diff changeset
   451
          y[0] = r-w;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   452
        }
489c9b5090e2 Initial load
duke
parents:
diff changeset
   453
      }
489c9b5090e2 Initial load
duke
parents:
diff changeset
   454
    }
489c9b5090e2 Initial load
duke
parents:
diff changeset
   455
    y[1] = (r-y[0])-w;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   456
    if(hx<0)    {y[0] = -y[0]; y[1] = -y[1]; return -n;}
489c9b5090e2 Initial load
duke
parents:
diff changeset
   457
    else         return n;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   458
  }
489c9b5090e2 Initial load
duke
parents:
diff changeset
   459
  /*
489c9b5090e2 Initial load
duke
parents:
diff changeset
   460
   * all other (large) arguments
489c9b5090e2 Initial load
duke
parents:
diff changeset
   461
   */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   462
  if(ix>=0x7ff00000) {          /* x is inf or NaN */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   463
    y[0]=y[1]=x-x; return 0;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   464
  }
489c9b5090e2 Initial load
duke
parents:
diff changeset
   465
  /* set z = scalbn(|x|,ilogb(x)-23) */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   466
  *(1-i0+(int*)&z) = *(1-i0+(int*)&x);
489c9b5090e2 Initial load
duke
parents:
diff changeset
   467
  e0    = (ix>>20)-1046;        /* e0 = ilogb(z)-23; */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   468
  *(i0+(int*)&z) = ix - (e0<<20);
489c9b5090e2 Initial load
duke
parents:
diff changeset
   469
  for(i=0;i<2;i++) {
489c9b5090e2 Initial load
duke
parents:
diff changeset
   470
    tx[i] = (double)((int)(z));
489c9b5090e2 Initial load
duke
parents:
diff changeset
   471
    z     = (z-tx[i])*two24A;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   472
  }
489c9b5090e2 Initial load
duke
parents:
diff changeset
   473
  tx[2] = z;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   474
  nx = 3;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   475
  while(tx[nx-1]==zeroA) nx--;  /* skip zero term */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   476
  n  =  __kernel_rem_pio2(tx,y,e0,nx,2,two_over_pi);
489c9b5090e2 Initial load
duke
parents:
diff changeset
   477
  if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;}
489c9b5090e2 Initial load
duke
parents:
diff changeset
   478
  return n;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   479
}
489c9b5090e2 Initial load
duke
parents:
diff changeset
   480
489c9b5090e2 Initial load
duke
parents:
diff changeset
   481
489c9b5090e2 Initial load
duke
parents:
diff changeset
   482
/* __kernel_sin( x, y, iy)
489c9b5090e2 Initial load
duke
parents:
diff changeset
   483
 * kernel sin function on [-pi/4, pi/4], pi/4 ~ 0.7854
489c9b5090e2 Initial load
duke
parents:
diff changeset
   484
 * Input x is assumed to be bounded by ~pi/4 in magnitude.
489c9b5090e2 Initial load
duke
parents:
diff changeset
   485
 * Input y is the tail of x.
489c9b5090e2 Initial load
duke
parents:
diff changeset
   486
 * Input iy indicates whether y is 0. (if iy=0, y assume to be 0).
489c9b5090e2 Initial load
duke
parents:
diff changeset
   487
 *
489c9b5090e2 Initial load
duke
parents:
diff changeset
   488
 * Algorithm
489c9b5090e2 Initial load
duke
parents:
diff changeset
   489
 *      1. Since sin(-x) = -sin(x), we need only to consider positive x.
489c9b5090e2 Initial load
duke
parents:
diff changeset
   490
 *      2. if x < 2^-27 (hx<0x3e400000 0), return x with inexact if x!=0.
489c9b5090e2 Initial load
duke
parents:
diff changeset
   491
 *      3. sin(x) is approximated by a polynomial of degree 13 on
489c9b5090e2 Initial load
duke
parents:
diff changeset
   492
 *         [0,pi/4]
489c9b5090e2 Initial load
duke
parents:
diff changeset
   493
 *                               3            13
489c9b5090e2 Initial load
duke
parents:
diff changeset
   494
 *              sin(x) ~ x + S1*x + ... + S6*x
489c9b5090e2 Initial load
duke
parents:
diff changeset
   495
 *         where
489c9b5090e2 Initial load
duke
parents:
diff changeset
   496
 *
489c9b5090e2 Initial load
duke
parents:
diff changeset
   497
 *      |sin(x)         2     4     6     8     10     12  |     -58
489c9b5090e2 Initial load
duke
parents:
diff changeset
   498
 *      |----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x  +S6*x   )| <= 2
489c9b5090e2 Initial load
duke
parents:
diff changeset
   499
 *      |  x                                               |
489c9b5090e2 Initial load
duke
parents:
diff changeset
   500
 *
489c9b5090e2 Initial load
duke
parents:
diff changeset
   501
 *      4. sin(x+y) = sin(x) + sin'(x')*y
489c9b5090e2 Initial load
duke
parents:
diff changeset
   502
 *                  ~ sin(x) + (1-x*x/2)*y
489c9b5090e2 Initial load
duke
parents:
diff changeset
   503
 *         For better accuracy, let
489c9b5090e2 Initial load
duke
parents:
diff changeset
   504
 *                   3      2      2      2      2
489c9b5090e2 Initial load
duke
parents:
diff changeset
   505
 *              r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6))))
489c9b5090e2 Initial load
duke
parents:
diff changeset
   506
 *         then                   3    2
489c9b5090e2 Initial load
duke
parents:
diff changeset
   507
 *              sin(x) = x + (S1*x + (x *(r-y/2)+y))
489c9b5090e2 Initial load
duke
parents:
diff changeset
   508
 */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   509
489c9b5090e2 Initial load
duke
parents:
diff changeset
   510
static const double
489c9b5090e2 Initial load
duke
parents:
diff changeset
   511
S1  = -1.66666666666666324348e-01, /* 0xBFC55555, 0x55555549 */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   512
S2  =  8.33333333332248946124e-03, /* 0x3F811111, 0x1110F8A6 */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   513
S3  = -1.98412698298579493134e-04, /* 0xBF2A01A0, 0x19C161D5 */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   514
S4  =  2.75573137070700676789e-06, /* 0x3EC71DE3, 0x57B1FE7D */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   515
S5  = -2.50507602534068634195e-08, /* 0xBE5AE5E6, 0x8A2B9CEB */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   516
S6  =  1.58969099521155010221e-10; /* 0x3DE5D93A, 0x5ACFD57C */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   517
489c9b5090e2 Initial load
duke
parents:
diff changeset
   518
static double __kernel_sin(double x, double y, int iy)
489c9b5090e2 Initial load
duke
parents:
diff changeset
   519
{
489c9b5090e2 Initial load
duke
parents:
diff changeset
   520
        double z,r,v;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   521
        int ix;
25919
d4e4f72b49fc 8049043: Load variable through a pointer of an incompatible type in hotspot/src/share/vm/runtime/sharedRuntimeMath.hpp
thartmann
parents: 25060
diff changeset
   522
        ix = high(x)&0x7fffffff;                /* high word of x */
1
489c9b5090e2 Initial load
duke
parents:
diff changeset
   523
        if(ix<0x3e400000)                       /* |x| < 2**-27 */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   524
           {if((int)x==0) return x;}            /* generate inexact */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   525
        z       =  x*x;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   526
        v       =  z*x;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   527
        r       =  S2+z*(S3+z*(S4+z*(S5+z*S6)));
489c9b5090e2 Initial load
duke
parents:
diff changeset
   528
        if(iy==0) return x+v*(S1+z*r);
489c9b5090e2 Initial load
duke
parents:
diff changeset
   529
        else      return x-((z*(half*y-v*r)-y)-v*S1);
489c9b5090e2 Initial load
duke
parents:
diff changeset
   530
}
489c9b5090e2 Initial load
duke
parents:
diff changeset
   531
489c9b5090e2 Initial load
duke
parents:
diff changeset
   532
/*
489c9b5090e2 Initial load
duke
parents:
diff changeset
   533
 * __kernel_cos( x,  y )
489c9b5090e2 Initial load
duke
parents:
diff changeset
   534
 * kernel cos function on [-pi/4, pi/4], pi/4 ~ 0.785398164
489c9b5090e2 Initial load
duke
parents:
diff changeset
   535
 * Input x is assumed to be bounded by ~pi/4 in magnitude.
489c9b5090e2 Initial load
duke
parents:
diff changeset
   536
 * Input y is the tail of x.
489c9b5090e2 Initial load
duke
parents:
diff changeset
   537
 *
489c9b5090e2 Initial load
duke
parents:
diff changeset
   538
 * Algorithm
489c9b5090e2 Initial load
duke
parents:
diff changeset
   539
 *      1. Since cos(-x) = cos(x), we need only to consider positive x.
489c9b5090e2 Initial load
duke
parents:
diff changeset
   540
 *      2. if x < 2^-27 (hx<0x3e400000 0), return 1 with inexact if x!=0.
489c9b5090e2 Initial load
duke
parents:
diff changeset
   541
 *      3. cos(x) is approximated by a polynomial of degree 14 on
489c9b5090e2 Initial load
duke
parents:
diff changeset
   542
 *         [0,pi/4]
489c9b5090e2 Initial load
duke
parents:
diff changeset
   543
 *                                       4            14
489c9b5090e2 Initial load
duke
parents:
diff changeset
   544
 *              cos(x) ~ 1 - x*x/2 + C1*x + ... + C6*x
489c9b5090e2 Initial load
duke
parents:
diff changeset
   545
 *         where the remez error is
489c9b5090e2 Initial load
duke
parents:
diff changeset
   546
 *
489c9b5090e2 Initial load
duke
parents:
diff changeset
   547
 *      |              2     4     6     8     10    12     14 |     -58
489c9b5090e2 Initial load
duke
parents:
diff changeset
   548
 *      |cos(x)-(1-.5*x +C1*x +C2*x +C3*x +C4*x +C5*x  +C6*x  )| <= 2
489c9b5090e2 Initial load
duke
parents:
diff changeset
   549
 *      |                                                      |
489c9b5090e2 Initial load
duke
parents:
diff changeset
   550
 *
489c9b5090e2 Initial load
duke
parents:
diff changeset
   551
 *                     4     6     8     10    12     14
489c9b5090e2 Initial load
duke
parents:
diff changeset
   552
 *      4. let r = C1*x +C2*x +C3*x +C4*x +C5*x  +C6*x  , then
489c9b5090e2 Initial load
duke
parents:
diff changeset
   553
 *             cos(x) = 1 - x*x/2 + r
489c9b5090e2 Initial load
duke
parents:
diff changeset
   554
 *         since cos(x+y) ~ cos(x) - sin(x)*y
489c9b5090e2 Initial load
duke
parents:
diff changeset
   555
 *                        ~ cos(x) - x*y,
489c9b5090e2 Initial load
duke
parents:
diff changeset
   556
 *         a correction term is necessary in cos(x) and hence
489c9b5090e2 Initial load
duke
parents:
diff changeset
   557
 *              cos(x+y) = 1 - (x*x/2 - (r - x*y))
489c9b5090e2 Initial load
duke
parents:
diff changeset
   558
 *         For better accuracy when x > 0.3, let qx = |x|/4 with
489c9b5090e2 Initial load
duke
parents:
diff changeset
   559
 *         the last 32 bits mask off, and if x > 0.78125, let qx = 0.28125.
489c9b5090e2 Initial load
duke
parents:
diff changeset
   560
 *         Then
489c9b5090e2 Initial load
duke
parents:
diff changeset
   561
 *              cos(x+y) = (1-qx) - ((x*x/2-qx) - (r-x*y)).
489c9b5090e2 Initial load
duke
parents:
diff changeset
   562
 *         Note that 1-qx and (x*x/2-qx) is EXACT here, and the
489c9b5090e2 Initial load
duke
parents:
diff changeset
   563
 *         magnitude of the latter is at least a quarter of x*x/2,
489c9b5090e2 Initial load
duke
parents:
diff changeset
   564
 *         thus, reducing the rounding error in the subtraction.
489c9b5090e2 Initial load
duke
parents:
diff changeset
   565
 */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   566
489c9b5090e2 Initial load
duke
parents:
diff changeset
   567
static const double
489c9b5090e2 Initial load
duke
parents:
diff changeset
   568
C1  =  4.16666666666666019037e-02, /* 0x3FA55555, 0x5555554C */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   569
C2  = -1.38888888888741095749e-03, /* 0xBF56C16C, 0x16C15177 */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   570
C3  =  2.48015872894767294178e-05, /* 0x3EFA01A0, 0x19CB1590 */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   571
C4  = -2.75573143513906633035e-07, /* 0xBE927E4F, 0x809C52AD */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   572
C5  =  2.08757232129817482790e-09, /* 0x3E21EE9E, 0xBDB4B1C4 */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   573
C6  = -1.13596475577881948265e-11; /* 0xBDA8FAE9, 0xBE8838D4 */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   574
489c9b5090e2 Initial load
duke
parents:
diff changeset
   575
static double __kernel_cos(double x, double y)
489c9b5090e2 Initial load
duke
parents:
diff changeset
   576
{
25919
d4e4f72b49fc 8049043: Load variable through a pointer of an incompatible type in hotspot/src/share/vm/runtime/sharedRuntimeMath.hpp
thartmann
parents: 25060
diff changeset
   577
  double a,h,z,r,qx=0;
1
489c9b5090e2 Initial load
duke
parents:
diff changeset
   578
  int ix;
25919
d4e4f72b49fc 8049043: Load variable through a pointer of an incompatible type in hotspot/src/share/vm/runtime/sharedRuntimeMath.hpp
thartmann
parents: 25060
diff changeset
   579
  ix = high(x)&0x7fffffff;              /* ix = |x|'s high word*/
1
489c9b5090e2 Initial load
duke
parents:
diff changeset
   580
  if(ix<0x3e400000) {                   /* if x < 2**27 */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   581
    if(((int)x)==0) return one;         /* generate inexact */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   582
  }
489c9b5090e2 Initial load
duke
parents:
diff changeset
   583
  z  = x*x;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   584
  r  = z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*C6)))));
489c9b5090e2 Initial load
duke
parents:
diff changeset
   585
  if(ix < 0x3FD33333)                   /* if |x| < 0.3 */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   586
    return one - (0.5*z - (z*r - x*y));
489c9b5090e2 Initial load
duke
parents:
diff changeset
   587
  else {
489c9b5090e2 Initial load
duke
parents:
diff changeset
   588
    if(ix > 0x3fe90000) {               /* x > 0.78125 */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   589
      qx = 0.28125;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   590
    } else {
25919
d4e4f72b49fc 8049043: Load variable through a pointer of an incompatible type in hotspot/src/share/vm/runtime/sharedRuntimeMath.hpp
thartmann
parents: 25060
diff changeset
   591
      set_high(&qx, ix-0x00200000); /* x/4 */
d4e4f72b49fc 8049043: Load variable through a pointer of an incompatible type in hotspot/src/share/vm/runtime/sharedRuntimeMath.hpp
thartmann
parents: 25060
diff changeset
   592
      set_low(&qx, 0);
1
489c9b5090e2 Initial load
duke
parents:
diff changeset
   593
    }
22827
07d991d45a51 8023033: PPC64 (part 13): basic changes for AIX
goetz
parents: 7397
diff changeset
   594
    h = 0.5*z-qx;
07d991d45a51 8023033: PPC64 (part 13): basic changes for AIX
goetz
parents: 7397
diff changeset
   595
    a = one-qx;
07d991d45a51 8023033: PPC64 (part 13): basic changes for AIX
goetz
parents: 7397
diff changeset
   596
    return a - (h - (z*r-x*y));
1
489c9b5090e2 Initial load
duke
parents:
diff changeset
   597
  }
489c9b5090e2 Initial load
duke
parents:
diff changeset
   598
}
489c9b5090e2 Initial load
duke
parents:
diff changeset
   599
489c9b5090e2 Initial load
duke
parents:
diff changeset
   600
/* __kernel_tan( x, y, k )
489c9b5090e2 Initial load
duke
parents:
diff changeset
   601
 * kernel tan function on [-pi/4, pi/4], pi/4 ~ 0.7854
489c9b5090e2 Initial load
duke
parents:
diff changeset
   602
 * Input x is assumed to be bounded by ~pi/4 in magnitude.
489c9b5090e2 Initial load
duke
parents:
diff changeset
   603
 * Input y is the tail of x.
489c9b5090e2 Initial load
duke
parents:
diff changeset
   604
 * Input k indicates whether tan (if k=1) or
489c9b5090e2 Initial load
duke
parents:
diff changeset
   605
 * -1/tan (if k= -1) is returned.
489c9b5090e2 Initial load
duke
parents:
diff changeset
   606
 *
489c9b5090e2 Initial load
duke
parents:
diff changeset
   607
 * Algorithm
489c9b5090e2 Initial load
duke
parents:
diff changeset
   608
 *      1. Since tan(-x) = -tan(x), we need only to consider positive x.
489c9b5090e2 Initial load
duke
parents:
diff changeset
   609
 *      2. if x < 2^-28 (hx<0x3e300000 0), return x with inexact if x!=0.
489c9b5090e2 Initial load
duke
parents:
diff changeset
   610
 *      3. tan(x) is approximated by a odd polynomial of degree 27 on
489c9b5090e2 Initial load
duke
parents:
diff changeset
   611
 *         [0,0.67434]
489c9b5090e2 Initial load
duke
parents:
diff changeset
   612
 *                               3             27
489c9b5090e2 Initial load
duke
parents:
diff changeset
   613
 *              tan(x) ~ x + T1*x + ... + T13*x
489c9b5090e2 Initial load
duke
parents:
diff changeset
   614
 *         where
489c9b5090e2 Initial load
duke
parents:
diff changeset
   615
 *
489c9b5090e2 Initial load
duke
parents:
diff changeset
   616
 *              |tan(x)         2     4            26   |     -59.2
489c9b5090e2 Initial load
duke
parents:
diff changeset
   617
 *              |----- - (1+T1*x +T2*x +.... +T13*x    )| <= 2
489c9b5090e2 Initial load
duke
parents:
diff changeset
   618
 *              |  x                                    |
489c9b5090e2 Initial load
duke
parents:
diff changeset
   619
 *
489c9b5090e2 Initial load
duke
parents:
diff changeset
   620
 *         Note: tan(x+y) = tan(x) + tan'(x)*y
489c9b5090e2 Initial load
duke
parents:
diff changeset
   621
 *                        ~ tan(x) + (1+x*x)*y
489c9b5090e2 Initial load
duke
parents:
diff changeset
   622
 *         Therefore, for better accuracy in computing tan(x+y), let
489c9b5090e2 Initial load
duke
parents:
diff changeset
   623
 *                   3      2      2       2       2
489c9b5090e2 Initial load
duke
parents:
diff changeset
   624
 *              r = x *(T2+x *(T3+x *(...+x *(T12+x *T13))))
489c9b5090e2 Initial load
duke
parents:
diff changeset
   625
 *         then
489c9b5090e2 Initial load
duke
parents:
diff changeset
   626
 *                                  3    2
489c9b5090e2 Initial load
duke
parents:
diff changeset
   627
 *              tan(x+y) = x + (T1*x + (x *(r+y)+y))
489c9b5090e2 Initial load
duke
parents:
diff changeset
   628
 *
489c9b5090e2 Initial load
duke
parents:
diff changeset
   629
 *      4. For x in [0.67434,pi/4],  let y = pi/4 - x, then
489c9b5090e2 Initial load
duke
parents:
diff changeset
   630
 *              tan(x) = tan(pi/4-y) = (1-tan(y))/(1+tan(y))
489c9b5090e2 Initial load
duke
parents:
diff changeset
   631
 *                     = 1 - 2*(tan(y) - (tan(y)^2)/(1+tan(y)))
489c9b5090e2 Initial load
duke
parents:
diff changeset
   632
 */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   633
489c9b5090e2 Initial load
duke
parents:
diff changeset
   634
static const double
489c9b5090e2 Initial load
duke
parents:
diff changeset
   635
pio4  =  7.85398163397448278999e-01, /* 0x3FE921FB, 0x54442D18 */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   636
pio4lo=  3.06161699786838301793e-17, /* 0x3C81A626, 0x33145C07 */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   637
T[] =  {
489c9b5090e2 Initial load
duke
parents:
diff changeset
   638
  3.33333333333334091986e-01, /* 0x3FD55555, 0x55555563 */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   639
  1.33333333333201242699e-01, /* 0x3FC11111, 0x1110FE7A */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   640
  5.39682539762260521377e-02, /* 0x3FABA1BA, 0x1BB341FE */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   641
  2.18694882948595424599e-02, /* 0x3F9664F4, 0x8406D637 */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   642
  8.86323982359930005737e-03, /* 0x3F8226E3, 0xE96E8493 */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   643
  3.59207910759131235356e-03, /* 0x3F6D6D22, 0xC9560328 */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   644
  1.45620945432529025516e-03, /* 0x3F57DBC8, 0xFEE08315 */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   645
  5.88041240820264096874e-04, /* 0x3F4344D8, 0xF2F26501 */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   646
  2.46463134818469906812e-04, /* 0x3F3026F7, 0x1A8D1068 */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   647
  7.81794442939557092300e-05, /* 0x3F147E88, 0xA03792A6 */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   648
  7.14072491382608190305e-05, /* 0x3F12B80F, 0x32F0A7E9 */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   649
 -1.85586374855275456654e-05, /* 0xBEF375CB, 0xDB605373 */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   650
  2.59073051863633712884e-05, /* 0x3EFB2A70, 0x74BF7AD4 */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   651
};
489c9b5090e2 Initial load
duke
parents:
diff changeset
   652
489c9b5090e2 Initial load
duke
parents:
diff changeset
   653
static double __kernel_tan(double x, double y, int iy)
489c9b5090e2 Initial load
duke
parents:
diff changeset
   654
{
489c9b5090e2 Initial load
duke
parents:
diff changeset
   655
  double z,r,v,w,s;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   656
  int ix,hx;
25919
d4e4f72b49fc 8049043: Load variable through a pointer of an incompatible type in hotspot/src/share/vm/runtime/sharedRuntimeMath.hpp
thartmann
parents: 25060
diff changeset
   657
  hx = high(x);           /* high word of x */
1
489c9b5090e2 Initial load
duke
parents:
diff changeset
   658
  ix = hx&0x7fffffff;     /* high word of |x| */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   659
  if(ix<0x3e300000) {                     /* x < 2**-28 */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   660
    if((int)x==0) {                       /* generate inexact */
25919
d4e4f72b49fc 8049043: Load variable through a pointer of an incompatible type in hotspot/src/share/vm/runtime/sharedRuntimeMath.hpp
thartmann
parents: 25060
diff changeset
   661
      if (((ix | low(x)) | (iy + 1)) == 0)
1
489c9b5090e2 Initial load
duke
parents:
diff changeset
   662
        return one / fabsd(x);
489c9b5090e2 Initial load
duke
parents:
diff changeset
   663
      else {
489c9b5090e2 Initial load
duke
parents:
diff changeset
   664
        if (iy == 1)
489c9b5090e2 Initial load
duke
parents:
diff changeset
   665
          return x;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   666
        else {    /* compute -1 / (x+y) carefully */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   667
          double a, t;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   668
489c9b5090e2 Initial load
duke
parents:
diff changeset
   669
          z = w = x + y;
25919
d4e4f72b49fc 8049043: Load variable through a pointer of an incompatible type in hotspot/src/share/vm/runtime/sharedRuntimeMath.hpp
thartmann
parents: 25060
diff changeset
   670
          set_low(&z, 0);
1
489c9b5090e2 Initial load
duke
parents:
diff changeset
   671
          v = y - (z - x);
489c9b5090e2 Initial load
duke
parents:
diff changeset
   672
          t = a = -one / w;
25919
d4e4f72b49fc 8049043: Load variable through a pointer of an incompatible type in hotspot/src/share/vm/runtime/sharedRuntimeMath.hpp
thartmann
parents: 25060
diff changeset
   673
          set_low(&t, 0);
1
489c9b5090e2 Initial load
duke
parents:
diff changeset
   674
          s = one + t * z;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   675
          return t + a * (s + t * v);
489c9b5090e2 Initial load
duke
parents:
diff changeset
   676
        }
489c9b5090e2 Initial load
duke
parents:
diff changeset
   677
      }
489c9b5090e2 Initial load
duke
parents:
diff changeset
   678
    }
489c9b5090e2 Initial load
duke
parents:
diff changeset
   679
  }
489c9b5090e2 Initial load
duke
parents:
diff changeset
   680
  if(ix>=0x3FE59428) {                    /* |x|>=0.6744 */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   681
    if(hx<0) {x = -x; y = -y;}
489c9b5090e2 Initial load
duke
parents:
diff changeset
   682
    z = pio4-x;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   683
    w = pio4lo-y;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   684
    x = z+w; y = 0.0;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   685
  }
489c9b5090e2 Initial load
duke
parents:
diff changeset
   686
  z       =  x*x;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   687
  w       =  z*z;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   688
  /* Break x^5*(T[1]+x^2*T[2]+...) into
489c9b5090e2 Initial load
duke
parents:
diff changeset
   689
   *    x^5(T[1]+x^4*T[3]+...+x^20*T[11]) +
489c9b5090e2 Initial load
duke
parents:
diff changeset
   690
   *    x^5(x^2*(T[2]+x^4*T[4]+...+x^22*[T12]))
489c9b5090e2 Initial load
duke
parents:
diff changeset
   691
   */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   692
  r = T[1]+w*(T[3]+w*(T[5]+w*(T[7]+w*(T[9]+w*T[11]))));
489c9b5090e2 Initial load
duke
parents:
diff changeset
   693
  v = z*(T[2]+w*(T[4]+w*(T[6]+w*(T[8]+w*(T[10]+w*T[12])))));
489c9b5090e2 Initial load
duke
parents:
diff changeset
   694
  s = z*x;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   695
  r = y + z*(s*(r+v)+y);
489c9b5090e2 Initial load
duke
parents:
diff changeset
   696
  r += T[0]*s;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   697
  w = x+r;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   698
  if(ix>=0x3FE59428) {
489c9b5090e2 Initial load
duke
parents:
diff changeset
   699
    v = (double)iy;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   700
    return (double)(1-((hx>>30)&2))*(v-2.0*(x-(w*w/(w+v)-r)));
489c9b5090e2 Initial load
duke
parents:
diff changeset
   701
  }
489c9b5090e2 Initial load
duke
parents:
diff changeset
   702
  if(iy==1) return w;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   703
  else {          /* if allow error up to 2 ulp,
489c9b5090e2 Initial load
duke
parents:
diff changeset
   704
                     simply return -1.0/(x+r) here */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   705
    /*  compute -1.0/(x+r) accurately */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   706
    double a,t;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   707
    z  = w;
25919
d4e4f72b49fc 8049043: Load variable through a pointer of an incompatible type in hotspot/src/share/vm/runtime/sharedRuntimeMath.hpp
thartmann
parents: 25060
diff changeset
   708
    set_low(&z, 0);
1
489c9b5090e2 Initial load
duke
parents:
diff changeset
   709
    v  = r-(z - x);     /* z+v = r+x */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   710
    t = a  = -1.0/w;    /* a = -1.0/w */
25919
d4e4f72b49fc 8049043: Load variable through a pointer of an incompatible type in hotspot/src/share/vm/runtime/sharedRuntimeMath.hpp
thartmann
parents: 25060
diff changeset
   711
    set_low(&t, 0);
1
489c9b5090e2 Initial load
duke
parents:
diff changeset
   712
    s  = 1.0+t*z;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   713
    return t+a*(s+t*v);
489c9b5090e2 Initial load
duke
parents:
diff changeset
   714
  }
489c9b5090e2 Initial load
duke
parents:
diff changeset
   715
}
489c9b5090e2 Initial load
duke
parents:
diff changeset
   716
489c9b5090e2 Initial load
duke
parents:
diff changeset
   717
489c9b5090e2 Initial load
duke
parents:
diff changeset
   718
//----------------------------------------------------------------------
489c9b5090e2 Initial load
duke
parents:
diff changeset
   719
//
489c9b5090e2 Initial load
duke
parents:
diff changeset
   720
// Routines for new sin/cos implementation
489c9b5090e2 Initial load
duke
parents:
diff changeset
   721
//
489c9b5090e2 Initial load
duke
parents:
diff changeset
   722
//----------------------------------------------------------------------
489c9b5090e2 Initial load
duke
parents:
diff changeset
   723
489c9b5090e2 Initial load
duke
parents:
diff changeset
   724
/* sin(x)
489c9b5090e2 Initial load
duke
parents:
diff changeset
   725
 * Return sine function of x.
489c9b5090e2 Initial load
duke
parents:
diff changeset
   726
 *
489c9b5090e2 Initial load
duke
parents:
diff changeset
   727
 * kernel function:
489c9b5090e2 Initial load
duke
parents:
diff changeset
   728
 *      __kernel_sin            ... sine function on [-pi/4,pi/4]
489c9b5090e2 Initial load
duke
parents:
diff changeset
   729
 *      __kernel_cos            ... cose function on [-pi/4,pi/4]
489c9b5090e2 Initial load
duke
parents:
diff changeset
   730
 *      __ieee754_rem_pio2      ... argument reduction routine
489c9b5090e2 Initial load
duke
parents:
diff changeset
   731
 *
489c9b5090e2 Initial load
duke
parents:
diff changeset
   732
 * Method.
489c9b5090e2 Initial load
duke
parents:
diff changeset
   733
 *      Let S,C and T denote the sin, cos and tan respectively on
489c9b5090e2 Initial load
duke
parents:
diff changeset
   734
 *      [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
489c9b5090e2 Initial load
duke
parents:
diff changeset
   735
 *      in [-pi/4 , +pi/4], and let n = k mod 4.
489c9b5090e2 Initial load
duke
parents:
diff changeset
   736
 *      We have
489c9b5090e2 Initial load
duke
parents:
diff changeset
   737
 *
489c9b5090e2 Initial load
duke
parents:
diff changeset
   738
 *          n        sin(x)      cos(x)        tan(x)
489c9b5090e2 Initial load
duke
parents:
diff changeset
   739
 *     ----------------------------------------------------------
489c9b5090e2 Initial load
duke
parents:
diff changeset
   740
 *          0          S           C             T
489c9b5090e2 Initial load
duke
parents:
diff changeset
   741
 *          1          C          -S            -1/T
489c9b5090e2 Initial load
duke
parents:
diff changeset
   742
 *          2         -S          -C             T
489c9b5090e2 Initial load
duke
parents:
diff changeset
   743
 *          3         -C           S            -1/T
489c9b5090e2 Initial load
duke
parents:
diff changeset
   744
 *     ----------------------------------------------------------
489c9b5090e2 Initial load
duke
parents:
diff changeset
   745
 *
489c9b5090e2 Initial load
duke
parents:
diff changeset
   746
 * Special cases:
489c9b5090e2 Initial load
duke
parents:
diff changeset
   747
 *      Let trig be any of sin, cos, or tan.
489c9b5090e2 Initial load
duke
parents:
diff changeset
   748
 *      trig(+-INF)  is NaN, with signals;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   749
 *      trig(NaN)    is that NaN;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   750
 *
489c9b5090e2 Initial load
duke
parents:
diff changeset
   751
 * Accuracy:
489c9b5090e2 Initial load
duke
parents:
diff changeset
   752
 *      TRIG(x) returns trig(x) nearly rounded
489c9b5090e2 Initial load
duke
parents:
diff changeset
   753
 */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   754
489c9b5090e2 Initial load
duke
parents:
diff changeset
   755
JRT_LEAF(jdouble, SharedRuntime::dsin(jdouble x))
489c9b5090e2 Initial load
duke
parents:
diff changeset
   756
  double y[2],z=0.0;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   757
  int n, ix;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   758
489c9b5090e2 Initial load
duke
parents:
diff changeset
   759
  /* High word of x. */
25919
d4e4f72b49fc 8049043: Load variable through a pointer of an incompatible type in hotspot/src/share/vm/runtime/sharedRuntimeMath.hpp
thartmann
parents: 25060
diff changeset
   760
  ix = high(x);
1
489c9b5090e2 Initial load
duke
parents:
diff changeset
   761
489c9b5090e2 Initial load
duke
parents:
diff changeset
   762
  /* |x| ~< pi/4 */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   763
  ix &= 0x7fffffff;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   764
  if(ix <= 0x3fe921fb) return __kernel_sin(x,z,0);
489c9b5090e2 Initial load
duke
parents:
diff changeset
   765
489c9b5090e2 Initial load
duke
parents:
diff changeset
   766
  /* sin(Inf or NaN) is NaN */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   767
  else if (ix>=0x7ff00000) return x-x;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   768
489c9b5090e2 Initial load
duke
parents:
diff changeset
   769
  /* argument reduction needed */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   770
  else {
489c9b5090e2 Initial load
duke
parents:
diff changeset
   771
    n = __ieee754_rem_pio2(x,y);
489c9b5090e2 Initial load
duke
parents:
diff changeset
   772
    switch(n&3) {
489c9b5090e2 Initial load
duke
parents:
diff changeset
   773
    case 0: return  __kernel_sin(y[0],y[1],1);
489c9b5090e2 Initial load
duke
parents:
diff changeset
   774
    case 1: return  __kernel_cos(y[0],y[1]);
489c9b5090e2 Initial load
duke
parents:
diff changeset
   775
    case 2: return -__kernel_sin(y[0],y[1],1);
489c9b5090e2 Initial load
duke
parents:
diff changeset
   776
    default:
489c9b5090e2 Initial load
duke
parents:
diff changeset
   777
      return -__kernel_cos(y[0],y[1]);
489c9b5090e2 Initial load
duke
parents:
diff changeset
   778
    }
489c9b5090e2 Initial load
duke
parents:
diff changeset
   779
  }
489c9b5090e2 Initial load
duke
parents:
diff changeset
   780
JRT_END
489c9b5090e2 Initial load
duke
parents:
diff changeset
   781
489c9b5090e2 Initial load
duke
parents:
diff changeset
   782
/* cos(x)
489c9b5090e2 Initial load
duke
parents:
diff changeset
   783
 * Return cosine function of x.
489c9b5090e2 Initial load
duke
parents:
diff changeset
   784
 *
489c9b5090e2 Initial load
duke
parents:
diff changeset
   785
 * kernel function:
489c9b5090e2 Initial load
duke
parents:
diff changeset
   786
 *      __kernel_sin            ... sine function on [-pi/4,pi/4]
489c9b5090e2 Initial load
duke
parents:
diff changeset
   787
 *      __kernel_cos            ... cosine function on [-pi/4,pi/4]
489c9b5090e2 Initial load
duke
parents:
diff changeset
   788
 *      __ieee754_rem_pio2      ... argument reduction routine
489c9b5090e2 Initial load
duke
parents:
diff changeset
   789
 *
489c9b5090e2 Initial load
duke
parents:
diff changeset
   790
 * Method.
489c9b5090e2 Initial load
duke
parents:
diff changeset
   791
 *      Let S,C and T denote the sin, cos and tan respectively on
489c9b5090e2 Initial load
duke
parents:
diff changeset
   792
 *      [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
489c9b5090e2 Initial load
duke
parents:
diff changeset
   793
 *      in [-pi/4 , +pi/4], and let n = k mod 4.
489c9b5090e2 Initial load
duke
parents:
diff changeset
   794
 *      We have
489c9b5090e2 Initial load
duke
parents:
diff changeset
   795
 *
489c9b5090e2 Initial load
duke
parents:
diff changeset
   796
 *          n        sin(x)      cos(x)        tan(x)
489c9b5090e2 Initial load
duke
parents:
diff changeset
   797
 *     ----------------------------------------------------------
489c9b5090e2 Initial load
duke
parents:
diff changeset
   798
 *          0          S           C             T
489c9b5090e2 Initial load
duke
parents:
diff changeset
   799
 *          1          C          -S            -1/T
489c9b5090e2 Initial load
duke
parents:
diff changeset
   800
 *          2         -S          -C             T
489c9b5090e2 Initial load
duke
parents:
diff changeset
   801
 *          3         -C           S            -1/T
489c9b5090e2 Initial load
duke
parents:
diff changeset
   802
 *     ----------------------------------------------------------
489c9b5090e2 Initial load
duke
parents:
diff changeset
   803
 *
489c9b5090e2 Initial load
duke
parents:
diff changeset
   804
 * Special cases:
489c9b5090e2 Initial load
duke
parents:
diff changeset
   805
 *      Let trig be any of sin, cos, or tan.
489c9b5090e2 Initial load
duke
parents:
diff changeset
   806
 *      trig(+-INF)  is NaN, with signals;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   807
 *      trig(NaN)    is that NaN;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   808
 *
489c9b5090e2 Initial load
duke
parents:
diff changeset
   809
 * Accuracy:
489c9b5090e2 Initial load
duke
parents:
diff changeset
   810
 *      TRIG(x) returns trig(x) nearly rounded
489c9b5090e2 Initial load
duke
parents:
diff changeset
   811
 */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   812
489c9b5090e2 Initial load
duke
parents:
diff changeset
   813
JRT_LEAF(jdouble, SharedRuntime::dcos(jdouble x))
489c9b5090e2 Initial load
duke
parents:
diff changeset
   814
  double y[2],z=0.0;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   815
  int n, ix;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   816
489c9b5090e2 Initial load
duke
parents:
diff changeset
   817
  /* High word of x. */
25919
d4e4f72b49fc 8049043: Load variable through a pointer of an incompatible type in hotspot/src/share/vm/runtime/sharedRuntimeMath.hpp
thartmann
parents: 25060
diff changeset
   818
  ix = high(x);
1
489c9b5090e2 Initial load
duke
parents:
diff changeset
   819
489c9b5090e2 Initial load
duke
parents:
diff changeset
   820
  /* |x| ~< pi/4 */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   821
  ix &= 0x7fffffff;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   822
  if(ix <= 0x3fe921fb) return __kernel_cos(x,z);
489c9b5090e2 Initial load
duke
parents:
diff changeset
   823
489c9b5090e2 Initial load
duke
parents:
diff changeset
   824
  /* cos(Inf or NaN) is NaN */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   825
  else if (ix>=0x7ff00000) return x-x;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   826
489c9b5090e2 Initial load
duke
parents:
diff changeset
   827
  /* argument reduction needed */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   828
  else {
489c9b5090e2 Initial load
duke
parents:
diff changeset
   829
    n = __ieee754_rem_pio2(x,y);
489c9b5090e2 Initial load
duke
parents:
diff changeset
   830
    switch(n&3) {
489c9b5090e2 Initial load
duke
parents:
diff changeset
   831
    case 0: return  __kernel_cos(y[0],y[1]);
489c9b5090e2 Initial load
duke
parents:
diff changeset
   832
    case 1: return -__kernel_sin(y[0],y[1],1);
489c9b5090e2 Initial load
duke
parents:
diff changeset
   833
    case 2: return -__kernel_cos(y[0],y[1]);
489c9b5090e2 Initial load
duke
parents:
diff changeset
   834
    default:
489c9b5090e2 Initial load
duke
parents:
diff changeset
   835
      return  __kernel_sin(y[0],y[1],1);
489c9b5090e2 Initial load
duke
parents:
diff changeset
   836
    }
489c9b5090e2 Initial load
duke
parents:
diff changeset
   837
  }
489c9b5090e2 Initial load
duke
parents:
diff changeset
   838
JRT_END
489c9b5090e2 Initial load
duke
parents:
diff changeset
   839
489c9b5090e2 Initial load
duke
parents:
diff changeset
   840
/* tan(x)
489c9b5090e2 Initial load
duke
parents:
diff changeset
   841
 * Return tangent function of x.
489c9b5090e2 Initial load
duke
parents:
diff changeset
   842
 *
489c9b5090e2 Initial load
duke
parents:
diff changeset
   843
 * kernel function:
489c9b5090e2 Initial load
duke
parents:
diff changeset
   844
 *      __kernel_tan            ... tangent function on [-pi/4,pi/4]
489c9b5090e2 Initial load
duke
parents:
diff changeset
   845
 *      __ieee754_rem_pio2      ... argument reduction routine
489c9b5090e2 Initial load
duke
parents:
diff changeset
   846
 *
489c9b5090e2 Initial load
duke
parents:
diff changeset
   847
 * Method.
489c9b5090e2 Initial load
duke
parents:
diff changeset
   848
 *      Let S,C and T denote the sin, cos and tan respectively on
489c9b5090e2 Initial load
duke
parents:
diff changeset
   849
 *      [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
489c9b5090e2 Initial load
duke
parents:
diff changeset
   850
 *      in [-pi/4 , +pi/4], and let n = k mod 4.
489c9b5090e2 Initial load
duke
parents:
diff changeset
   851
 *      We have
489c9b5090e2 Initial load
duke
parents:
diff changeset
   852
 *
489c9b5090e2 Initial load
duke
parents:
diff changeset
   853
 *          n        sin(x)      cos(x)        tan(x)
489c9b5090e2 Initial load
duke
parents:
diff changeset
   854
 *     ----------------------------------------------------------
489c9b5090e2 Initial load
duke
parents:
diff changeset
   855
 *          0          S           C             T
489c9b5090e2 Initial load
duke
parents:
diff changeset
   856
 *          1          C          -S            -1/T
489c9b5090e2 Initial load
duke
parents:
diff changeset
   857
 *          2         -S          -C             T
489c9b5090e2 Initial load
duke
parents:
diff changeset
   858
 *          3         -C           S            -1/T
489c9b5090e2 Initial load
duke
parents:
diff changeset
   859
 *     ----------------------------------------------------------
489c9b5090e2 Initial load
duke
parents:
diff changeset
   860
 *
489c9b5090e2 Initial load
duke
parents:
diff changeset
   861
 * Special cases:
489c9b5090e2 Initial load
duke
parents:
diff changeset
   862
 *      Let trig be any of sin, cos, or tan.
489c9b5090e2 Initial load
duke
parents:
diff changeset
   863
 *      trig(+-INF)  is NaN, with signals;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   864
 *      trig(NaN)    is that NaN;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   865
 *
489c9b5090e2 Initial load
duke
parents:
diff changeset
   866
 * Accuracy:
489c9b5090e2 Initial load
duke
parents:
diff changeset
   867
 *      TRIG(x) returns trig(x) nearly rounded
489c9b5090e2 Initial load
duke
parents:
diff changeset
   868
 */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   869
489c9b5090e2 Initial load
duke
parents:
diff changeset
   870
JRT_LEAF(jdouble, SharedRuntime::dtan(jdouble x))
489c9b5090e2 Initial load
duke
parents:
diff changeset
   871
  double y[2],z=0.0;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   872
  int n, ix;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   873
489c9b5090e2 Initial load
duke
parents:
diff changeset
   874
  /* High word of x. */
25919
d4e4f72b49fc 8049043: Load variable through a pointer of an incompatible type in hotspot/src/share/vm/runtime/sharedRuntimeMath.hpp
thartmann
parents: 25060
diff changeset
   875
  ix = high(x);
1
489c9b5090e2 Initial load
duke
parents:
diff changeset
   876
489c9b5090e2 Initial load
duke
parents:
diff changeset
   877
  /* |x| ~< pi/4 */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   878
  ix &= 0x7fffffff;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   879
  if(ix <= 0x3fe921fb) return __kernel_tan(x,z,1);
489c9b5090e2 Initial load
duke
parents:
diff changeset
   880
489c9b5090e2 Initial load
duke
parents:
diff changeset
   881
  /* tan(Inf or NaN) is NaN */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   882
  else if (ix>=0x7ff00000) return x-x;            /* NaN */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   883
489c9b5090e2 Initial load
duke
parents:
diff changeset
   884
  /* argument reduction needed */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   885
  else {
489c9b5090e2 Initial load
duke
parents:
diff changeset
   886
    n = __ieee754_rem_pio2(x,y);
489c9b5090e2 Initial load
duke
parents:
diff changeset
   887
    return __kernel_tan(y[0],y[1],1-((n&1)<<1)); /*   1 -- n even
489c9b5090e2 Initial load
duke
parents:
diff changeset
   888
                                                     -1 -- n odd */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   889
  }
489c9b5090e2 Initial load
duke
parents:
diff changeset
   890
JRT_END