hotspot/src/share/vm/runtime/sharedRuntimeTrig.cpp
author jwilhelm
Thu, 23 Jan 2014 14:47:23 +0100
changeset 22551 9bf46d16dcc6
parent 7397 5b173b4ca846
child 22876 57aa8995d43b
permissions -rw-r--r--
8025856: Fix typos in the GC code Summary: Fix about 440 typos in comments in the VM code Reviewed-by: mgerdin, tschatzl, coleenp, kmo, jcoomes
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/*
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 * Copyright (c) 2001, 2010, 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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// 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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// Enabling optimizations in this file causes incorrect code to be
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// generated; can not figure out how to turn down optimization for one
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// file in the IDE on Windows
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#ifdef WIN32
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# pragma optimize ( "", off )
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#endif
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/* The above workaround now causes more problems with the latest MS compiler.
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 * Visual Studio 2010's /GS option tries to guard against buffer overruns.
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 * /GS is on by default if you specify optimizations, which we do globally
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 * via /W3 /O2. However the above selective turning off of optimizations means
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 * that /GS issues a warning "4748". And since we treat warnings as errors (/WX)
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 * then the compilation fails. There are several possible solutions
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 * (1) Remove that pragma above as obsolete with VS2010 - requires testing.
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 * (2) Stop treating warnings as errors - would be a backward step
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 * (3) Disable /GS - may help performance but you lose the security checks
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 * (4) Disable the warning with "#pragma warning( disable : 4748 )"
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 * (5) Disable planting the code with  __declspec(safebuffers)
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 * I've opted for (5) although we should investigate the local performance
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 * benefits of (1) and global performance benefit of (3).
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 */
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#if defined(WIN32) && (defined(_MSC_VER) && (_MSC_VER >= 1600))
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#define SAFEBUF __declspec(safebuffers)
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#else
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#define SAFEBUF
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#endif
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#include <math.h>
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// VM_LITTLE_ENDIAN is #defined appropriately in the Makefiles
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// [jk] this is not 100% correct because the float word order may different
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// from the byte order (e.g. on ARM)
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#ifdef VM_LITTLE_ENDIAN
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# define __HI(x) *(1+(int*)&x)
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# define __LO(x) *(int*)&x
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#else
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# define __HI(x) *(int*)&x
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# define __LO(x) *(1+(int*)&x)
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#endif
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static double copysignA(double x, double y) {
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  __HI(x) = (__HI(x)&0x7fffffff)|(__HI(y)&0x80000000);
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  return x;
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}
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/*
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 * scalbn (double x, int n)
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 * scalbn(x,n) returns x* 2**n  computed by  exponent
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 * manipulation rather than by actually performing an
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 * exponentiation or a multiplication.
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 */
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static const double
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two54   =  1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */
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twom54  =  5.55111512312578270212e-17, /* 0x3C900000, 0x00000000 */
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hugeX  = 1.0e+300,
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tiny   = 1.0e-300;
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static double scalbnA (double x, int n) {
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  int  k,hx,lx;
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  hx = __HI(x);
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  lx = __LO(x);
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  k = (hx&0x7ff00000)>>20;              /* extract exponent */
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  if (k==0) {                           /* 0 or subnormal x */
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    if ((lx|(hx&0x7fffffff))==0) return x; /* +-0 */
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    x *= two54;
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    hx = __HI(x);
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    k = ((hx&0x7ff00000)>>20) - 54;
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    if (n< -50000) return tiny*x;       /*underflow*/
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  }
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  if (k==0x7ff) return x+x;             /* NaN or Inf */
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  k = k+n;
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  if (k >  0x7fe) return hugeX*copysignA(hugeX,x); /* overflow  */
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  if (k > 0)                            /* normal result */
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    {__HI(x) = (hx&0x800fffff)|(k<<20); return x;}
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  if (k <= -54) {
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    if (n > 50000)      /* in case integer overflow in n+k */
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      return hugeX*copysignA(hugeX,x);  /*overflow*/
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    else return tiny*copysignA(tiny,x); /*underflow*/
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  }
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  k += 54;                              /* subnormal result */
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  __HI(x) = (hx&0x800fffff)|(k<<20);
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  return x*twom54;
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}
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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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   221
 *
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 *      iq[]    integer array by breaking up q[] in 24-bits chunk.
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   223
 *
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   224
 *      fq[]    final product of x*(2/pi) in fq[0],..,fq[jk]
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   225
 *
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 *      ih      integer. If >0 it indicates q[] is >= 0.5, hence
1
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 *              it also indicates the *sign* of the result.
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   228
 *
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   229
 */
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   230
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   231
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   232
/*
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   233
 * Constants:
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   234
 * The hexadecimal values are the intended ones for the following
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   235
 * constants. The decimal values may be used, provided that the
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   236
 * compiler will convert from decimal to binary accurately enough
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 * to produce the hexadecimal values shown.
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   238
 */
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   240
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static const int init_jk[] = {2,3,4,6}; /* initial value for jk */
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   242
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   243
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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   246
  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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   249
  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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   252
};
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   253
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static const double
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zeroB   = 0.0,
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   256
one     = 1.0,
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two24B  = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */
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   258
twon24  = 5.96046447753906250000e-08; /* 0x3E700000, 0x00000000 */
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   259
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static SAFEBUF int __kernel_rem_pio2(double *x, double *y, int e0, int nx, int prec, const int *ipio2) {
1
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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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   263
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  /* initialize jk*/
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  jk = init_jk[prec];
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   266
  jp = jk;
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   267
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   268
  /* determine jx,jv,q0, note that 3>q0 */
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   269
  jx =  nx-1;
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   270
  jv = (e0-3)/24; if(jv<0) jv=0;
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   271
  q0 =  e0-24*(jv+1);
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   272
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   273
  /* set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk] */
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  j = jv-jx; m = jx+jk;
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  for(i=0;i<=m;i++,j++) f[i] = (j<0)? zeroB : (double) ipio2[j];
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   276
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   277
  /* compute q[0],q[1],...q[jk] */
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   278
  for (i=0;i<=jk;i++) {
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    for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; q[i] = fw;
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   280
  }
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   281
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  jz = jk;
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   283
recompute:
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   284
  /* distill q[] into iq[] reversingly */
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   285
  for(i=0,j=jz,z=q[jz];j>0;i++,j--) {
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   286
    fw    =  (double)((int)(twon24* z));
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    iq[i] =  (int)(z-two24B*fw);
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   288
    z     =  q[j-1]+fw;
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   289
  }
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   290
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   291
  /* compute n */
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   292
  z  = scalbnA(z,q0);           /* actual value of z */
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   293
  z -= 8.0*floor(z*0.125);              /* trim off integer >= 8 */
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   294
  n  = (int) z;
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   295
  z -= (double)n;
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   296
  ih = 0;
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   297
  if(q0>0) {    /* need iq[jz-1] to determine n */
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   298
    i  = (iq[jz-1]>>(24-q0)); n += i;
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   299
    iq[jz-1] -= i<<(24-q0);
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   300
    ih = iq[jz-1]>>(23-q0);
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   301
  }
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   302
  else if(q0==0) ih = iq[jz-1]>>23;
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   303
  else if(z>=0.5) ih=2;
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   304
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   305
  if(ih>0) {    /* q > 0.5 */
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   306
    n += 1; carry = 0;
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   307
    for(i=0;i<jz ;i++) {        /* compute 1-q */
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   308
      j = iq[i];
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   309
      if(carry==0) {
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   310
        if(j!=0) {
489c9b5090e2 Initial load
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   311
          carry = 1; iq[i] = 0x1000000- j;
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   312
        }
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   313
      } else  iq[i] = 0xffffff - j;
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   314
    }
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   315
    if(q0>0) {          /* rare case: chance is 1 in 12 */
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   316
      switch(q0) {
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   317
      case 1:
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   318
        iq[jz-1] &= 0x7fffff; break;
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   319
      case 2:
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   320
        iq[jz-1] &= 0x3fffff; break;
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   321
      }
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   322
    }
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   323
    if(ih==2) {
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   324
      z = one - z;
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   325
      if(carry!=0) z -= scalbnA(one,q0);
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   326
    }
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   327
  }
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   328
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   329
  /* check if recomputation is needed */
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   330
  if(z==zeroB) {
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   331
    j = 0;
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   332
    for (i=jz-1;i>=jk;i--) j |= iq[i];
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   333
    if(j==0) { /* need recomputation */
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   334
      for(k=1;iq[jk-k]==0;k++);   /* k = no. of terms needed */
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   335
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   336
      for(i=jz+1;i<=jz+k;i++) {   /* add q[jz+1] to q[jz+k] */
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   337
        f[jx+i] = (double) ipio2[jv+i];
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   338
        for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j];
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   339
        q[i] = fw;
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   340
      }
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   341
      jz += k;
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   342
      goto recompute;
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   343
    }
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   344
  }
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   345
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   346
  /* chop off zero terms */
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   347
  if(z==0.0) {
489c9b5090e2 Initial load
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   348
    jz -= 1; q0 -= 24;
489c9b5090e2 Initial load
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   349
    while(iq[jz]==0) { jz--; q0-=24;}
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   350
  } else { /* break z into 24-bit if necessary */
1
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   351
    z = scalbnA(z,-q0);
489c9b5090e2 Initial load
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diff changeset
   352
    if(z>=two24B) {
489c9b5090e2 Initial load
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   353
      fw = (double)((int)(twon24*z));
489c9b5090e2 Initial load
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   354
      iq[jz] = (int)(z-two24B*fw);
489c9b5090e2 Initial load
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   355
      jz += 1; q0 += 24;
489c9b5090e2 Initial load
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   356
      iq[jz] = (int) fw;
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   357
    } else iq[jz] = (int) z ;
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   358
  }
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   359
489c9b5090e2 Initial load
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   360
  /* convert integer "bit" chunk to floating-point value */
489c9b5090e2 Initial load
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   361
  fw = scalbnA(one,q0);
489c9b5090e2 Initial load
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   362
  for(i=jz;i>=0;i--) {
489c9b5090e2 Initial load
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diff changeset
   363
    q[i] = fw*(double)iq[i]; fw*=twon24;
489c9b5090e2 Initial load
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   364
  }
489c9b5090e2 Initial load
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parents:
diff changeset
   365
489c9b5090e2 Initial load
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parents:
diff changeset
   366
  /* compute PIo2[0,...,jp]*q[jz,...,0] */
489c9b5090e2 Initial load
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diff changeset
   367
  for(i=jz;i>=0;i--) {
489c9b5090e2 Initial load
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diff changeset
   368
    for(fw=0.0,k=0;k<=jp&&k<=jz-i;k++) fw += PIo2[k]*q[i+k];
489c9b5090e2 Initial load
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diff changeset
   369
    fq[jz-i] = fw;
489c9b5090e2 Initial load
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diff changeset
   370
  }
489c9b5090e2 Initial load
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diff changeset
   371
489c9b5090e2 Initial load
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parents:
diff changeset
   372
  /* compress fq[] into y[] */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   373
  switch(prec) {
489c9b5090e2 Initial load
duke
parents:
diff changeset
   374
  case 0:
489c9b5090e2 Initial load
duke
parents:
diff changeset
   375
    fw = 0.0;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   376
    for (i=jz;i>=0;i--) fw += fq[i];
489c9b5090e2 Initial load
duke
parents:
diff changeset
   377
    y[0] = (ih==0)? fw: -fw;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   378
    break;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   379
  case 1:
489c9b5090e2 Initial load
duke
parents:
diff changeset
   380
  case 2:
489c9b5090e2 Initial load
duke
parents:
diff changeset
   381
    fw = 0.0;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   382
    for (i=jz;i>=0;i--) fw += fq[i];
489c9b5090e2 Initial load
duke
parents:
diff changeset
   383
    y[0] = (ih==0)? fw: -fw;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   384
    fw = fq[0]-fw;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   385
    for (i=1;i<=jz;i++) fw += fq[i];
489c9b5090e2 Initial load
duke
parents:
diff changeset
   386
    y[1] = (ih==0)? fw: -fw;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   387
    break;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   388
  case 3:       /* painful */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   389
    for (i=jz;i>0;i--) {
489c9b5090e2 Initial load
duke
parents:
diff changeset
   390
      fw      = fq[i-1]+fq[i];
489c9b5090e2 Initial load
duke
parents:
diff changeset
   391
      fq[i]  += fq[i-1]-fw;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   392
      fq[i-1] = fw;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   393
    }
489c9b5090e2 Initial load
duke
parents:
diff changeset
   394
    for (i=jz;i>1;i--) {
489c9b5090e2 Initial load
duke
parents:
diff changeset
   395
      fw      = fq[i-1]+fq[i];
489c9b5090e2 Initial load
duke
parents:
diff changeset
   396
      fq[i]  += fq[i-1]-fw;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   397
      fq[i-1] = fw;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   398
    }
489c9b5090e2 Initial load
duke
parents:
diff changeset
   399
    for (fw=0.0,i=jz;i>=2;i--) fw += fq[i];
489c9b5090e2 Initial load
duke
parents:
diff changeset
   400
    if(ih==0) {
489c9b5090e2 Initial load
duke
parents:
diff changeset
   401
      y[0] =  fq[0]; y[1] =  fq[1]; y[2] =  fw;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   402
    } else {
489c9b5090e2 Initial load
duke
parents:
diff changeset
   403
      y[0] = -fq[0]; y[1] = -fq[1]; y[2] = -fw;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   404
    }
489c9b5090e2 Initial load
duke
parents:
diff changeset
   405
  }
489c9b5090e2 Initial load
duke
parents:
diff changeset
   406
  return n&7;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   407
}
489c9b5090e2 Initial load
duke
parents:
diff changeset
   408
489c9b5090e2 Initial load
duke
parents:
diff changeset
   409
489c9b5090e2 Initial load
duke
parents:
diff changeset
   410
/*
489c9b5090e2 Initial load
duke
parents:
diff changeset
   411
 * ====================================================
22551
9bf46d16dcc6 8025856: Fix typos in the GC code
jwilhelm
parents: 7397
diff changeset
   412
 * Copyright (c) 1993 Oracle and/or its affiliates. All rights reserved.
1
489c9b5090e2 Initial load
duke
parents:
diff changeset
   413
 *
489c9b5090e2 Initial load
duke
parents:
diff changeset
   414
 * Developed at SunPro, a Sun Microsystems, Inc. business.
489c9b5090e2 Initial load
duke
parents:
diff changeset
   415
 * Permission to use, copy, modify, and distribute this
489c9b5090e2 Initial load
duke
parents:
diff changeset
   416
 * software is freely granted, provided that this notice
489c9b5090e2 Initial load
duke
parents:
diff changeset
   417
 * is preserved.
489c9b5090e2 Initial load
duke
parents:
diff changeset
   418
 * ====================================================
489c9b5090e2 Initial load
duke
parents:
diff changeset
   419
 *
489c9b5090e2 Initial load
duke
parents:
diff changeset
   420
 */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   421
489c9b5090e2 Initial load
duke
parents:
diff changeset
   422
/* __ieee754_rem_pio2(x,y)
489c9b5090e2 Initial load
duke
parents:
diff changeset
   423
 *
489c9b5090e2 Initial load
duke
parents:
diff changeset
   424
 * return the remainder of x rem pi/2 in y[0]+y[1]
489c9b5090e2 Initial load
duke
parents:
diff changeset
   425
 * use __kernel_rem_pio2()
489c9b5090e2 Initial load
duke
parents:
diff changeset
   426
 */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   427
489c9b5090e2 Initial load
duke
parents:
diff changeset
   428
/*
489c9b5090e2 Initial load
duke
parents:
diff changeset
   429
 * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi
489c9b5090e2 Initial load
duke
parents:
diff changeset
   430
 */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   431
static const int two_over_pi[] = {
489c9b5090e2 Initial load
duke
parents:
diff changeset
   432
  0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62,
489c9b5090e2 Initial load
duke
parents:
diff changeset
   433
  0x95993C, 0x439041, 0xFE5163, 0xABDEBB, 0xC561B7, 0x246E3A,
489c9b5090e2 Initial load
duke
parents:
diff changeset
   434
  0x424DD2, 0xE00649, 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129,
489c9b5090e2 Initial load
duke
parents:
diff changeset
   435
  0xA73EE8, 0x8235F5, 0x2EBB44, 0x84E99C, 0x7026B4, 0x5F7E41,
489c9b5090e2 Initial load
duke
parents:
diff changeset
   436
  0x3991D6, 0x398353, 0x39F49C, 0x845F8B, 0xBDF928, 0x3B1FF8,
489c9b5090e2 Initial load
duke
parents:
diff changeset
   437
  0x97FFDE, 0x05980F, 0xEF2F11, 0x8B5A0A, 0x6D1F6D, 0x367ECF,
489c9b5090e2 Initial load
duke
parents:
diff changeset
   438
  0x27CB09, 0xB74F46, 0x3F669E, 0x5FEA2D, 0x7527BA, 0xC7EBE5,
489c9b5090e2 Initial load
duke
parents:
diff changeset
   439
  0xF17B3D, 0x0739F7, 0x8A5292, 0xEA6BFB, 0x5FB11F, 0x8D5D08,
489c9b5090e2 Initial load
duke
parents:
diff changeset
   440
  0x560330, 0x46FC7B, 0x6BABF0, 0xCFBC20, 0x9AF436, 0x1DA9E3,
489c9b5090e2 Initial load
duke
parents:
diff changeset
   441
  0x91615E, 0xE61B08, 0x659985, 0x5F14A0, 0x68408D, 0xFFD880,
489c9b5090e2 Initial load
duke
parents:
diff changeset
   442
  0x4D7327, 0x310606, 0x1556CA, 0x73A8C9, 0x60E27B, 0xC08C6B,
489c9b5090e2 Initial load
duke
parents:
diff changeset
   443
};
489c9b5090e2 Initial load
duke
parents:
diff changeset
   444
489c9b5090e2 Initial load
duke
parents:
diff changeset
   445
static const int npio2_hw[] = {
489c9b5090e2 Initial load
duke
parents:
diff changeset
   446
  0x3FF921FB, 0x400921FB, 0x4012D97C, 0x401921FB, 0x401F6A7A, 0x4022D97C,
489c9b5090e2 Initial load
duke
parents:
diff changeset
   447
  0x4025FDBB, 0x402921FB, 0x402C463A, 0x402F6A7A, 0x4031475C, 0x4032D97C,
489c9b5090e2 Initial load
duke
parents:
diff changeset
   448
  0x40346B9C, 0x4035FDBB, 0x40378FDB, 0x403921FB, 0x403AB41B, 0x403C463A,
489c9b5090e2 Initial load
duke
parents:
diff changeset
   449
  0x403DD85A, 0x403F6A7A, 0x40407E4C, 0x4041475C, 0x4042106C, 0x4042D97C,
489c9b5090e2 Initial load
duke
parents:
diff changeset
   450
  0x4043A28C, 0x40446B9C, 0x404534AC, 0x4045FDBB, 0x4046C6CB, 0x40478FDB,
489c9b5090e2 Initial load
duke
parents:
diff changeset
   451
  0x404858EB, 0x404921FB,
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
 * invpio2:  53 bits of 2/pi
489c9b5090e2 Initial load
duke
parents:
diff changeset
   456
 * pio2_1:   first  33 bit of pi/2
489c9b5090e2 Initial load
duke
parents:
diff changeset
   457
 * pio2_1t:  pi/2 - pio2_1
489c9b5090e2 Initial load
duke
parents:
diff changeset
   458
 * pio2_2:   second 33 bit of pi/2
489c9b5090e2 Initial load
duke
parents:
diff changeset
   459
 * pio2_2t:  pi/2 - (pio2_1+pio2_2)
489c9b5090e2 Initial load
duke
parents:
diff changeset
   460
 * pio2_3:   third  33 bit of pi/2
489c9b5090e2 Initial load
duke
parents:
diff changeset
   461
 * pio2_3t:  pi/2 - (pio2_1+pio2_2+pio2_3)
489c9b5090e2 Initial load
duke
parents:
diff changeset
   462
 */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   463
489c9b5090e2 Initial load
duke
parents:
diff changeset
   464
static const double
489c9b5090e2 Initial load
duke
parents:
diff changeset
   465
zeroA =  0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   466
half =  5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   467
two24A =  1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   468
invpio2 =  6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   469
pio2_1  =  1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   470
pio2_1t =  6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   471
pio2_2  =  6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   472
pio2_2t =  2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   473
pio2_3  =  2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   474
pio2_3t =  8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   475
5377
bcf55c5acf4e 6931180: Migration to recent versions of MS Platform SDK
prr
parents: 1
diff changeset
   476
static SAFEBUF int __ieee754_rem_pio2(double x, double *y) {
1
489c9b5090e2 Initial load
duke
parents:
diff changeset
   477
  double z,w,t,r,fn;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   478
  double tx[3];
489c9b5090e2 Initial load
duke
parents:
diff changeset
   479
  int e0,i,j,nx,n,ix,hx,i0;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   480
489c9b5090e2 Initial load
duke
parents:
diff changeset
   481
  i0 = ((*(int*)&two24A)>>30)^1;        /* high word index */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   482
  hx = *(i0+(int*)&x);          /* high word of x */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   483
  ix = hx&0x7fffffff;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   484
  if(ix<=0x3fe921fb)   /* |x| ~<= pi/4 , no need for reduction */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   485
    {y[0] = x; y[1] = 0; return 0;}
489c9b5090e2 Initial load
duke
parents:
diff changeset
   486
  if(ix<0x4002d97c) {  /* |x| < 3pi/4, special case with n=+-1 */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   487
    if(hx>0) {
489c9b5090e2 Initial load
duke
parents:
diff changeset
   488
      z = x - pio2_1;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   489
      if(ix!=0x3ff921fb) {    /* 33+53 bit pi is good enough */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   490
        y[0] = z - pio2_1t;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   491
        y[1] = (z-y[0])-pio2_1t;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   492
      } else {                /* near pi/2, use 33+33+53 bit pi */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   493
        z -= pio2_2;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   494
        y[0] = z - pio2_2t;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   495
        y[1] = (z-y[0])-pio2_2t;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   496
      }
489c9b5090e2 Initial load
duke
parents:
diff changeset
   497
      return 1;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   498
    } else {    /* negative x */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   499
      z = x + pio2_1;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   500
      if(ix!=0x3ff921fb) {    /* 33+53 bit pi is good enough */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   501
        y[0] = z + pio2_1t;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   502
        y[1] = (z-y[0])+pio2_1t;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   503
      } else {                /* near pi/2, use 33+33+53 bit pi */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   504
        z += pio2_2;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   505
        y[0] = z + pio2_2t;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   506
        y[1] = (z-y[0])+pio2_2t;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   507
      }
489c9b5090e2 Initial load
duke
parents:
diff changeset
   508
      return -1;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   509
    }
489c9b5090e2 Initial load
duke
parents:
diff changeset
   510
  }
489c9b5090e2 Initial load
duke
parents:
diff changeset
   511
  if(ix<=0x413921fb) { /* |x| ~<= 2^19*(pi/2), medium size */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   512
    t  = fabsd(x);
489c9b5090e2 Initial load
duke
parents:
diff changeset
   513
    n  = (int) (t*invpio2+half);
489c9b5090e2 Initial load
duke
parents:
diff changeset
   514
    fn = (double)n;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   515
    r  = t-fn*pio2_1;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   516
    w  = fn*pio2_1t;    /* 1st round good to 85 bit */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   517
    if(n<32&&ix!=npio2_hw[n-1]) {
489c9b5090e2 Initial load
duke
parents:
diff changeset
   518
      y[0] = r-w;       /* quick check no cancellation */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   519
    } else {
489c9b5090e2 Initial load
duke
parents:
diff changeset
   520
      j  = ix>>20;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   521
      y[0] = r-w;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   522
      i = j-(((*(i0+(int*)&y[0]))>>20)&0x7ff);
489c9b5090e2 Initial load
duke
parents:
diff changeset
   523
      if(i>16) {  /* 2nd iteration needed, good to 118 */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   524
        t  = r;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   525
        w  = fn*pio2_2;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   526
        r  = t-w;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   527
        w  = fn*pio2_2t-((t-r)-w);
489c9b5090e2 Initial load
duke
parents:
diff changeset
   528
        y[0] = r-w;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   529
        i = j-(((*(i0+(int*)&y[0]))>>20)&0x7ff);
489c9b5090e2 Initial load
duke
parents:
diff changeset
   530
        if(i>49)  {     /* 3rd iteration need, 151 bits acc */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   531
          t  = r;       /* will cover all possible cases */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   532
          w  = fn*pio2_3;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   533
          r  = t-w;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   534
          w  = fn*pio2_3t-((t-r)-w);
489c9b5090e2 Initial load
duke
parents:
diff changeset
   535
          y[0] = r-w;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   536
        }
489c9b5090e2 Initial load
duke
parents:
diff changeset
   537
      }
489c9b5090e2 Initial load
duke
parents:
diff changeset
   538
    }
489c9b5090e2 Initial load
duke
parents:
diff changeset
   539
    y[1] = (r-y[0])-w;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   540
    if(hx<0)    {y[0] = -y[0]; y[1] = -y[1]; return -n;}
489c9b5090e2 Initial load
duke
parents:
diff changeset
   541
    else         return n;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   542
  }
489c9b5090e2 Initial load
duke
parents:
diff changeset
   543
  /*
489c9b5090e2 Initial load
duke
parents:
diff changeset
   544
   * all other (large) arguments
489c9b5090e2 Initial load
duke
parents:
diff changeset
   545
   */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   546
  if(ix>=0x7ff00000) {          /* x is inf or NaN */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   547
    y[0]=y[1]=x-x; return 0;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   548
  }
489c9b5090e2 Initial load
duke
parents:
diff changeset
   549
  /* set z = scalbn(|x|,ilogb(x)-23) */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   550
  *(1-i0+(int*)&z) = *(1-i0+(int*)&x);
489c9b5090e2 Initial load
duke
parents:
diff changeset
   551
  e0    = (ix>>20)-1046;        /* e0 = ilogb(z)-23; */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   552
  *(i0+(int*)&z) = ix - (e0<<20);
489c9b5090e2 Initial load
duke
parents:
diff changeset
   553
  for(i=0;i<2;i++) {
489c9b5090e2 Initial load
duke
parents:
diff changeset
   554
    tx[i] = (double)((int)(z));
489c9b5090e2 Initial load
duke
parents:
diff changeset
   555
    z     = (z-tx[i])*two24A;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   556
  }
489c9b5090e2 Initial load
duke
parents:
diff changeset
   557
  tx[2] = z;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   558
  nx = 3;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   559
  while(tx[nx-1]==zeroA) nx--;  /* skip zero term */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   560
  n  =  __kernel_rem_pio2(tx,y,e0,nx,2,two_over_pi);
489c9b5090e2 Initial load
duke
parents:
diff changeset
   561
  if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;}
489c9b5090e2 Initial load
duke
parents:
diff changeset
   562
  return n;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   563
}
489c9b5090e2 Initial load
duke
parents:
diff changeset
   564
489c9b5090e2 Initial load
duke
parents:
diff changeset
   565
489c9b5090e2 Initial load
duke
parents:
diff changeset
   566
/* __kernel_sin( x, y, iy)
489c9b5090e2 Initial load
duke
parents:
diff changeset
   567
 * kernel sin function on [-pi/4, pi/4], pi/4 ~ 0.7854
489c9b5090e2 Initial load
duke
parents:
diff changeset
   568
 * Input x is assumed to be bounded by ~pi/4 in magnitude.
489c9b5090e2 Initial load
duke
parents:
diff changeset
   569
 * Input y is the tail of x.
489c9b5090e2 Initial load
duke
parents:
diff changeset
   570
 * Input iy indicates whether y is 0. (if iy=0, y assume to be 0).
489c9b5090e2 Initial load
duke
parents:
diff changeset
   571
 *
489c9b5090e2 Initial load
duke
parents:
diff changeset
   572
 * Algorithm
489c9b5090e2 Initial load
duke
parents:
diff changeset
   573
 *      1. Since sin(-x) = -sin(x), we need only to consider positive x.
489c9b5090e2 Initial load
duke
parents:
diff changeset
   574
 *      2. if x < 2^-27 (hx<0x3e400000 0), return x with inexact if x!=0.
489c9b5090e2 Initial load
duke
parents:
diff changeset
   575
 *      3. sin(x) is approximated by a polynomial of degree 13 on
489c9b5090e2 Initial load
duke
parents:
diff changeset
   576
 *         [0,pi/4]
489c9b5090e2 Initial load
duke
parents:
diff changeset
   577
 *                               3            13
489c9b5090e2 Initial load
duke
parents:
diff changeset
   578
 *              sin(x) ~ x + S1*x + ... + S6*x
489c9b5090e2 Initial load
duke
parents:
diff changeset
   579
 *         where
489c9b5090e2 Initial load
duke
parents:
diff changeset
   580
 *
489c9b5090e2 Initial load
duke
parents:
diff changeset
   581
 *      |sin(x)         2     4     6     8     10     12  |     -58
489c9b5090e2 Initial load
duke
parents:
diff changeset
   582
 *      |----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x  +S6*x   )| <= 2
489c9b5090e2 Initial load
duke
parents:
diff changeset
   583
 *      |  x                                               |
489c9b5090e2 Initial load
duke
parents:
diff changeset
   584
 *
489c9b5090e2 Initial load
duke
parents:
diff changeset
   585
 *      4. sin(x+y) = sin(x) + sin'(x')*y
489c9b5090e2 Initial load
duke
parents:
diff changeset
   586
 *                  ~ sin(x) + (1-x*x/2)*y
489c9b5090e2 Initial load
duke
parents:
diff changeset
   587
 *         For better accuracy, let
489c9b5090e2 Initial load
duke
parents:
diff changeset
   588
 *                   3      2      2      2      2
489c9b5090e2 Initial load
duke
parents:
diff changeset
   589
 *              r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6))))
489c9b5090e2 Initial load
duke
parents:
diff changeset
   590
 *         then                   3    2
489c9b5090e2 Initial load
duke
parents:
diff changeset
   591
 *              sin(x) = x + (S1*x + (x *(r-y/2)+y))
489c9b5090e2 Initial load
duke
parents:
diff changeset
   592
 */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   593
489c9b5090e2 Initial load
duke
parents:
diff changeset
   594
static const double
489c9b5090e2 Initial load
duke
parents:
diff changeset
   595
S1  = -1.66666666666666324348e-01, /* 0xBFC55555, 0x55555549 */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   596
S2  =  8.33333333332248946124e-03, /* 0x3F811111, 0x1110F8A6 */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   597
S3  = -1.98412698298579493134e-04, /* 0xBF2A01A0, 0x19C161D5 */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   598
S4  =  2.75573137070700676789e-06, /* 0x3EC71DE3, 0x57B1FE7D */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   599
S5  = -2.50507602534068634195e-08, /* 0xBE5AE5E6, 0x8A2B9CEB */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   600
S6  =  1.58969099521155010221e-10; /* 0x3DE5D93A, 0x5ACFD57C */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   601
489c9b5090e2 Initial load
duke
parents:
diff changeset
   602
static double __kernel_sin(double x, double y, int iy)
489c9b5090e2 Initial load
duke
parents:
diff changeset
   603
{
489c9b5090e2 Initial load
duke
parents:
diff changeset
   604
        double z,r,v;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   605
        int ix;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   606
        ix = __HI(x)&0x7fffffff;        /* high word of x */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   607
        if(ix<0x3e400000)                       /* |x| < 2**-27 */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   608
           {if((int)x==0) return x;}            /* generate inexact */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   609
        z       =  x*x;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   610
        v       =  z*x;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   611
        r       =  S2+z*(S3+z*(S4+z*(S5+z*S6)));
489c9b5090e2 Initial load
duke
parents:
diff changeset
   612
        if(iy==0) return x+v*(S1+z*r);
489c9b5090e2 Initial load
duke
parents:
diff changeset
   613
        else      return x-((z*(half*y-v*r)-y)-v*S1);
489c9b5090e2 Initial load
duke
parents:
diff changeset
   614
}
489c9b5090e2 Initial load
duke
parents:
diff changeset
   615
489c9b5090e2 Initial load
duke
parents:
diff changeset
   616
/*
489c9b5090e2 Initial load
duke
parents:
diff changeset
   617
 * __kernel_cos( x,  y )
489c9b5090e2 Initial load
duke
parents:
diff changeset
   618
 * kernel cos function on [-pi/4, pi/4], pi/4 ~ 0.785398164
489c9b5090e2 Initial load
duke
parents:
diff changeset
   619
 * Input x is assumed to be bounded by ~pi/4 in magnitude.
489c9b5090e2 Initial load
duke
parents:
diff changeset
   620
 * Input y is the tail of x.
489c9b5090e2 Initial load
duke
parents:
diff changeset
   621
 *
489c9b5090e2 Initial load
duke
parents:
diff changeset
   622
 * Algorithm
489c9b5090e2 Initial load
duke
parents:
diff changeset
   623
 *      1. Since cos(-x) = cos(x), we need only to consider positive x.
489c9b5090e2 Initial load
duke
parents:
diff changeset
   624
 *      2. if x < 2^-27 (hx<0x3e400000 0), return 1 with inexact if x!=0.
489c9b5090e2 Initial load
duke
parents:
diff changeset
   625
 *      3. cos(x) is approximated by a polynomial of degree 14 on
489c9b5090e2 Initial load
duke
parents:
diff changeset
   626
 *         [0,pi/4]
489c9b5090e2 Initial load
duke
parents:
diff changeset
   627
 *                                       4            14
489c9b5090e2 Initial load
duke
parents:
diff changeset
   628
 *              cos(x) ~ 1 - x*x/2 + C1*x + ... + C6*x
489c9b5090e2 Initial load
duke
parents:
diff changeset
   629
 *         where the remez error is
489c9b5090e2 Initial load
duke
parents:
diff changeset
   630
 *
489c9b5090e2 Initial load
duke
parents:
diff changeset
   631
 *      |              2     4     6     8     10    12     14 |     -58
489c9b5090e2 Initial load
duke
parents:
diff changeset
   632
 *      |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
   633
 *      |                                                      |
489c9b5090e2 Initial load
duke
parents:
diff changeset
   634
 *
489c9b5090e2 Initial load
duke
parents:
diff changeset
   635
 *                     4     6     8     10    12     14
489c9b5090e2 Initial load
duke
parents:
diff changeset
   636
 *      4. let r = C1*x +C2*x +C3*x +C4*x +C5*x  +C6*x  , then
489c9b5090e2 Initial load
duke
parents:
diff changeset
   637
 *             cos(x) = 1 - x*x/2 + r
489c9b5090e2 Initial load
duke
parents:
diff changeset
   638
 *         since cos(x+y) ~ cos(x) - sin(x)*y
489c9b5090e2 Initial load
duke
parents:
diff changeset
   639
 *                        ~ cos(x) - x*y,
489c9b5090e2 Initial load
duke
parents:
diff changeset
   640
 *         a correction term is necessary in cos(x) and hence
489c9b5090e2 Initial load
duke
parents:
diff changeset
   641
 *              cos(x+y) = 1 - (x*x/2 - (r - x*y))
489c9b5090e2 Initial load
duke
parents:
diff changeset
   642
 *         For better accuracy when x > 0.3, let qx = |x|/4 with
489c9b5090e2 Initial load
duke
parents:
diff changeset
   643
 *         the last 32 bits mask off, and if x > 0.78125, let qx = 0.28125.
489c9b5090e2 Initial load
duke
parents:
diff changeset
   644
 *         Then
489c9b5090e2 Initial load
duke
parents:
diff changeset
   645
 *              cos(x+y) = (1-qx) - ((x*x/2-qx) - (r-x*y)).
489c9b5090e2 Initial load
duke
parents:
diff changeset
   646
 *         Note that 1-qx and (x*x/2-qx) is EXACT here, and the
489c9b5090e2 Initial load
duke
parents:
diff changeset
   647
 *         magnitude of the latter is at least a quarter of x*x/2,
489c9b5090e2 Initial load
duke
parents:
diff changeset
   648
 *         thus, reducing the rounding error in the subtraction.
489c9b5090e2 Initial load
duke
parents:
diff changeset
   649
 */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   650
489c9b5090e2 Initial load
duke
parents:
diff changeset
   651
static const double
489c9b5090e2 Initial load
duke
parents:
diff changeset
   652
C1  =  4.16666666666666019037e-02, /* 0x3FA55555, 0x5555554C */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   653
C2  = -1.38888888888741095749e-03, /* 0xBF56C16C, 0x16C15177 */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   654
C3  =  2.48015872894767294178e-05, /* 0x3EFA01A0, 0x19CB1590 */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   655
C4  = -2.75573143513906633035e-07, /* 0xBE927E4F, 0x809C52AD */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   656
C5  =  2.08757232129817482790e-09, /* 0x3E21EE9E, 0xBDB4B1C4 */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   657
C6  = -1.13596475577881948265e-11; /* 0xBDA8FAE9, 0xBE8838D4 */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   658
489c9b5090e2 Initial load
duke
parents:
diff changeset
   659
static double __kernel_cos(double x, double y)
489c9b5090e2 Initial load
duke
parents:
diff changeset
   660
{
489c9b5090e2 Initial load
duke
parents:
diff changeset
   661
  double a,hz,z,r,qx;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   662
  int ix;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   663
  ix = __HI(x)&0x7fffffff;      /* ix = |x|'s high word*/
489c9b5090e2 Initial load
duke
parents:
diff changeset
   664
  if(ix<0x3e400000) {                   /* if x < 2**27 */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   665
    if(((int)x)==0) return one;         /* generate inexact */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   666
  }
489c9b5090e2 Initial load
duke
parents:
diff changeset
   667
  z  = x*x;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   668
  r  = z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*C6)))));
489c9b5090e2 Initial load
duke
parents:
diff changeset
   669
  if(ix < 0x3FD33333)                   /* if |x| < 0.3 */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   670
    return one - (0.5*z - (z*r - x*y));
489c9b5090e2 Initial load
duke
parents:
diff changeset
   671
  else {
489c9b5090e2 Initial load
duke
parents:
diff changeset
   672
    if(ix > 0x3fe90000) {               /* x > 0.78125 */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   673
      qx = 0.28125;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   674
    } else {
489c9b5090e2 Initial load
duke
parents:
diff changeset
   675
      __HI(qx) = ix-0x00200000; /* x/4 */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   676
      __LO(qx) = 0;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   677
    }
489c9b5090e2 Initial load
duke
parents:
diff changeset
   678
    hz = 0.5*z-qx;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   679
    a  = one-qx;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   680
    return a - (hz - (z*r-x*y));
489c9b5090e2 Initial load
duke
parents:
diff changeset
   681
  }
489c9b5090e2 Initial load
duke
parents:
diff changeset
   682
}
489c9b5090e2 Initial load
duke
parents:
diff changeset
   683
489c9b5090e2 Initial load
duke
parents:
diff changeset
   684
/* __kernel_tan( x, y, k )
489c9b5090e2 Initial load
duke
parents:
diff changeset
   685
 * kernel tan function on [-pi/4, pi/4], pi/4 ~ 0.7854
489c9b5090e2 Initial load
duke
parents:
diff changeset
   686
 * Input x is assumed to be bounded by ~pi/4 in magnitude.
489c9b5090e2 Initial load
duke
parents:
diff changeset
   687
 * Input y is the tail of x.
489c9b5090e2 Initial load
duke
parents:
diff changeset
   688
 * Input k indicates whether tan (if k=1) or
489c9b5090e2 Initial load
duke
parents:
diff changeset
   689
 * -1/tan (if k= -1) is returned.
489c9b5090e2 Initial load
duke
parents:
diff changeset
   690
 *
489c9b5090e2 Initial load
duke
parents:
diff changeset
   691
 * Algorithm
489c9b5090e2 Initial load
duke
parents:
diff changeset
   692
 *      1. Since tan(-x) = -tan(x), we need only to consider positive x.
489c9b5090e2 Initial load
duke
parents:
diff changeset
   693
 *      2. if x < 2^-28 (hx<0x3e300000 0), return x with inexact if x!=0.
489c9b5090e2 Initial load
duke
parents:
diff changeset
   694
 *      3. tan(x) is approximated by a odd polynomial of degree 27 on
489c9b5090e2 Initial load
duke
parents:
diff changeset
   695
 *         [0,0.67434]
489c9b5090e2 Initial load
duke
parents:
diff changeset
   696
 *                               3             27
489c9b5090e2 Initial load
duke
parents:
diff changeset
   697
 *              tan(x) ~ x + T1*x + ... + T13*x
489c9b5090e2 Initial load
duke
parents:
diff changeset
   698
 *         where
489c9b5090e2 Initial load
duke
parents:
diff changeset
   699
 *
489c9b5090e2 Initial load
duke
parents:
diff changeset
   700
 *              |tan(x)         2     4            26   |     -59.2
489c9b5090e2 Initial load
duke
parents:
diff changeset
   701
 *              |----- - (1+T1*x +T2*x +.... +T13*x    )| <= 2
489c9b5090e2 Initial load
duke
parents:
diff changeset
   702
 *              |  x                                    |
489c9b5090e2 Initial load
duke
parents:
diff changeset
   703
 *
489c9b5090e2 Initial load
duke
parents:
diff changeset
   704
 *         Note: tan(x+y) = tan(x) + tan'(x)*y
489c9b5090e2 Initial load
duke
parents:
diff changeset
   705
 *                        ~ tan(x) + (1+x*x)*y
489c9b5090e2 Initial load
duke
parents:
diff changeset
   706
 *         Therefore, for better accuracy in computing tan(x+y), let
489c9b5090e2 Initial load
duke
parents:
diff changeset
   707
 *                   3      2      2       2       2
489c9b5090e2 Initial load
duke
parents:
diff changeset
   708
 *              r = x *(T2+x *(T3+x *(...+x *(T12+x *T13))))
489c9b5090e2 Initial load
duke
parents:
diff changeset
   709
 *         then
489c9b5090e2 Initial load
duke
parents:
diff changeset
   710
 *                                  3    2
489c9b5090e2 Initial load
duke
parents:
diff changeset
   711
 *              tan(x+y) = x + (T1*x + (x *(r+y)+y))
489c9b5090e2 Initial load
duke
parents:
diff changeset
   712
 *
489c9b5090e2 Initial load
duke
parents:
diff changeset
   713
 *      4. For x in [0.67434,pi/4],  let y = pi/4 - x, then
489c9b5090e2 Initial load
duke
parents:
diff changeset
   714
 *              tan(x) = tan(pi/4-y) = (1-tan(y))/(1+tan(y))
489c9b5090e2 Initial load
duke
parents:
diff changeset
   715
 *                     = 1 - 2*(tan(y) - (tan(y)^2)/(1+tan(y)))
489c9b5090e2 Initial load
duke
parents:
diff changeset
   716
 */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   717
489c9b5090e2 Initial load
duke
parents:
diff changeset
   718
static const double
489c9b5090e2 Initial load
duke
parents:
diff changeset
   719
pio4  =  7.85398163397448278999e-01, /* 0x3FE921FB, 0x54442D18 */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   720
pio4lo=  3.06161699786838301793e-17, /* 0x3C81A626, 0x33145C07 */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   721
T[] =  {
489c9b5090e2 Initial load
duke
parents:
diff changeset
   722
  3.33333333333334091986e-01, /* 0x3FD55555, 0x55555563 */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   723
  1.33333333333201242699e-01, /* 0x3FC11111, 0x1110FE7A */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   724
  5.39682539762260521377e-02, /* 0x3FABA1BA, 0x1BB341FE */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   725
  2.18694882948595424599e-02, /* 0x3F9664F4, 0x8406D637 */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   726
  8.86323982359930005737e-03, /* 0x3F8226E3, 0xE96E8493 */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   727
  3.59207910759131235356e-03, /* 0x3F6D6D22, 0xC9560328 */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   728
  1.45620945432529025516e-03, /* 0x3F57DBC8, 0xFEE08315 */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   729
  5.88041240820264096874e-04, /* 0x3F4344D8, 0xF2F26501 */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   730
  2.46463134818469906812e-04, /* 0x3F3026F7, 0x1A8D1068 */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   731
  7.81794442939557092300e-05, /* 0x3F147E88, 0xA03792A6 */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   732
  7.14072491382608190305e-05, /* 0x3F12B80F, 0x32F0A7E9 */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   733
 -1.85586374855275456654e-05, /* 0xBEF375CB, 0xDB605373 */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   734
  2.59073051863633712884e-05, /* 0x3EFB2A70, 0x74BF7AD4 */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   735
};
489c9b5090e2 Initial load
duke
parents:
diff changeset
   736
489c9b5090e2 Initial load
duke
parents:
diff changeset
   737
static double __kernel_tan(double x, double y, int iy)
489c9b5090e2 Initial load
duke
parents:
diff changeset
   738
{
489c9b5090e2 Initial load
duke
parents:
diff changeset
   739
  double z,r,v,w,s;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   740
  int ix,hx;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   741
  hx = __HI(x);   /* high word of x */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   742
  ix = hx&0x7fffffff;     /* high word of |x| */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   743
  if(ix<0x3e300000) {                     /* x < 2**-28 */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   744
    if((int)x==0) {                       /* generate inexact */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   745
      if (((ix | __LO(x)) | (iy + 1)) == 0)
489c9b5090e2 Initial load
duke
parents:
diff changeset
   746
        return one / fabsd(x);
489c9b5090e2 Initial load
duke
parents:
diff changeset
   747
      else {
489c9b5090e2 Initial load
duke
parents:
diff changeset
   748
        if (iy == 1)
489c9b5090e2 Initial load
duke
parents:
diff changeset
   749
          return x;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   750
        else {    /* compute -1 / (x+y) carefully */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   751
          double a, t;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   752
489c9b5090e2 Initial load
duke
parents:
diff changeset
   753
          z = w = x + y;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   754
          __LO(z) = 0;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   755
          v = y - (z - x);
489c9b5090e2 Initial load
duke
parents:
diff changeset
   756
          t = a = -one / w;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   757
          __LO(t) = 0;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   758
          s = one + t * z;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   759
          return t + a * (s + t * v);
489c9b5090e2 Initial load
duke
parents:
diff changeset
   760
        }
489c9b5090e2 Initial load
duke
parents:
diff changeset
   761
      }
489c9b5090e2 Initial load
duke
parents:
diff changeset
   762
    }
489c9b5090e2 Initial load
duke
parents:
diff changeset
   763
  }
489c9b5090e2 Initial load
duke
parents:
diff changeset
   764
  if(ix>=0x3FE59428) {                    /* |x|>=0.6744 */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   765
    if(hx<0) {x = -x; y = -y;}
489c9b5090e2 Initial load
duke
parents:
diff changeset
   766
    z = pio4-x;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   767
    w = pio4lo-y;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   768
    x = z+w; y = 0.0;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   769
  }
489c9b5090e2 Initial load
duke
parents:
diff changeset
   770
  z       =  x*x;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   771
  w       =  z*z;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   772
  /* Break x^5*(T[1]+x^2*T[2]+...) into
489c9b5090e2 Initial load
duke
parents:
diff changeset
   773
   *    x^5(T[1]+x^4*T[3]+...+x^20*T[11]) +
489c9b5090e2 Initial load
duke
parents:
diff changeset
   774
   *    x^5(x^2*(T[2]+x^4*T[4]+...+x^22*[T12]))
489c9b5090e2 Initial load
duke
parents:
diff changeset
   775
   */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   776
  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
   777
  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
   778
  s = z*x;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   779
  r = y + z*(s*(r+v)+y);
489c9b5090e2 Initial load
duke
parents:
diff changeset
   780
  r += T[0]*s;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   781
  w = x+r;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   782
  if(ix>=0x3FE59428) {
489c9b5090e2 Initial load
duke
parents:
diff changeset
   783
    v = (double)iy;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   784
    return (double)(1-((hx>>30)&2))*(v-2.0*(x-(w*w/(w+v)-r)));
489c9b5090e2 Initial load
duke
parents:
diff changeset
   785
  }
489c9b5090e2 Initial load
duke
parents:
diff changeset
   786
  if(iy==1) return w;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   787
  else {          /* if allow error up to 2 ulp,
489c9b5090e2 Initial load
duke
parents:
diff changeset
   788
                     simply return -1.0/(x+r) here */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   789
    /*  compute -1.0/(x+r) accurately */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   790
    double a,t;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   791
    z  = w;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   792
    __LO(z) = 0;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   793
    v  = r-(z - x);     /* z+v = r+x */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   794
    t = a  = -1.0/w;    /* a = -1.0/w */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   795
    __LO(t) = 0;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   796
    s  = 1.0+t*z;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   797
    return t+a*(s+t*v);
489c9b5090e2 Initial load
duke
parents:
diff changeset
   798
  }
489c9b5090e2 Initial load
duke
parents:
diff changeset
   799
}
489c9b5090e2 Initial load
duke
parents:
diff changeset
   800
489c9b5090e2 Initial load
duke
parents:
diff changeset
   801
489c9b5090e2 Initial load
duke
parents:
diff changeset
   802
//----------------------------------------------------------------------
489c9b5090e2 Initial load
duke
parents:
diff changeset
   803
//
489c9b5090e2 Initial load
duke
parents:
diff changeset
   804
// Routines for new sin/cos implementation
489c9b5090e2 Initial load
duke
parents:
diff changeset
   805
//
489c9b5090e2 Initial load
duke
parents:
diff changeset
   806
//----------------------------------------------------------------------
489c9b5090e2 Initial load
duke
parents:
diff changeset
   807
489c9b5090e2 Initial load
duke
parents:
diff changeset
   808
/* sin(x)
489c9b5090e2 Initial load
duke
parents:
diff changeset
   809
 * Return sine function of x.
489c9b5090e2 Initial load
duke
parents:
diff changeset
   810
 *
489c9b5090e2 Initial load
duke
parents:
diff changeset
   811
 * kernel function:
489c9b5090e2 Initial load
duke
parents:
diff changeset
   812
 *      __kernel_sin            ... sine function on [-pi/4,pi/4]
489c9b5090e2 Initial load
duke
parents:
diff changeset
   813
 *      __kernel_cos            ... cose function on [-pi/4,pi/4]
489c9b5090e2 Initial load
duke
parents:
diff changeset
   814
 *      __ieee754_rem_pio2      ... argument reduction routine
489c9b5090e2 Initial load
duke
parents:
diff changeset
   815
 *
489c9b5090e2 Initial load
duke
parents:
diff changeset
   816
 * Method.
489c9b5090e2 Initial load
duke
parents:
diff changeset
   817
 *      Let S,C and T denote the sin, cos and tan respectively on
489c9b5090e2 Initial load
duke
parents:
diff changeset
   818
 *      [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
489c9b5090e2 Initial load
duke
parents:
diff changeset
   819
 *      in [-pi/4 , +pi/4], and let n = k mod 4.
489c9b5090e2 Initial load
duke
parents:
diff changeset
   820
 *      We have
489c9b5090e2 Initial load
duke
parents:
diff changeset
   821
 *
489c9b5090e2 Initial load
duke
parents:
diff changeset
   822
 *          n        sin(x)      cos(x)        tan(x)
489c9b5090e2 Initial load
duke
parents:
diff changeset
   823
 *     ----------------------------------------------------------
489c9b5090e2 Initial load
duke
parents:
diff changeset
   824
 *          0          S           C             T
489c9b5090e2 Initial load
duke
parents:
diff changeset
   825
 *          1          C          -S            -1/T
489c9b5090e2 Initial load
duke
parents:
diff changeset
   826
 *          2         -S          -C             T
489c9b5090e2 Initial load
duke
parents:
diff changeset
   827
 *          3         -C           S            -1/T
489c9b5090e2 Initial load
duke
parents:
diff changeset
   828
 *     ----------------------------------------------------------
489c9b5090e2 Initial load
duke
parents:
diff changeset
   829
 *
489c9b5090e2 Initial load
duke
parents:
diff changeset
   830
 * Special cases:
489c9b5090e2 Initial load
duke
parents:
diff changeset
   831
 *      Let trig be any of sin, cos, or tan.
489c9b5090e2 Initial load
duke
parents:
diff changeset
   832
 *      trig(+-INF)  is NaN, with signals;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   833
 *      trig(NaN)    is that NaN;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   834
 *
489c9b5090e2 Initial load
duke
parents:
diff changeset
   835
 * Accuracy:
489c9b5090e2 Initial load
duke
parents:
diff changeset
   836
 *      TRIG(x) returns trig(x) nearly rounded
489c9b5090e2 Initial load
duke
parents:
diff changeset
   837
 */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   838
489c9b5090e2 Initial load
duke
parents:
diff changeset
   839
JRT_LEAF(jdouble, SharedRuntime::dsin(jdouble x))
489c9b5090e2 Initial load
duke
parents:
diff changeset
   840
  double y[2],z=0.0;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   841
  int n, ix;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   842
489c9b5090e2 Initial load
duke
parents:
diff changeset
   843
  /* High word of x. */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   844
  ix = __HI(x);
489c9b5090e2 Initial load
duke
parents:
diff changeset
   845
489c9b5090e2 Initial load
duke
parents:
diff changeset
   846
  /* |x| ~< pi/4 */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   847
  ix &= 0x7fffffff;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   848
  if(ix <= 0x3fe921fb) return __kernel_sin(x,z,0);
489c9b5090e2 Initial load
duke
parents:
diff changeset
   849
489c9b5090e2 Initial load
duke
parents:
diff changeset
   850
  /* sin(Inf or NaN) is NaN */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   851
  else if (ix>=0x7ff00000) return x-x;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   852
489c9b5090e2 Initial load
duke
parents:
diff changeset
   853
  /* argument reduction needed */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   854
  else {
489c9b5090e2 Initial load
duke
parents:
diff changeset
   855
    n = __ieee754_rem_pio2(x,y);
489c9b5090e2 Initial load
duke
parents:
diff changeset
   856
    switch(n&3) {
489c9b5090e2 Initial load
duke
parents:
diff changeset
   857
    case 0: return  __kernel_sin(y[0],y[1],1);
489c9b5090e2 Initial load
duke
parents:
diff changeset
   858
    case 1: return  __kernel_cos(y[0],y[1]);
489c9b5090e2 Initial load
duke
parents:
diff changeset
   859
    case 2: return -__kernel_sin(y[0],y[1],1);
489c9b5090e2 Initial load
duke
parents:
diff changeset
   860
    default:
489c9b5090e2 Initial load
duke
parents:
diff changeset
   861
      return -__kernel_cos(y[0],y[1]);
489c9b5090e2 Initial load
duke
parents:
diff changeset
   862
    }
489c9b5090e2 Initial load
duke
parents:
diff changeset
   863
  }
489c9b5090e2 Initial load
duke
parents:
diff changeset
   864
JRT_END
489c9b5090e2 Initial load
duke
parents:
diff changeset
   865
489c9b5090e2 Initial load
duke
parents:
diff changeset
   866
/* cos(x)
489c9b5090e2 Initial load
duke
parents:
diff changeset
   867
 * Return cosine function of x.
489c9b5090e2 Initial load
duke
parents:
diff changeset
   868
 *
489c9b5090e2 Initial load
duke
parents:
diff changeset
   869
 * kernel function:
489c9b5090e2 Initial load
duke
parents:
diff changeset
   870
 *      __kernel_sin            ... sine function on [-pi/4,pi/4]
489c9b5090e2 Initial load
duke
parents:
diff changeset
   871
 *      __kernel_cos            ... cosine function on [-pi/4,pi/4]
489c9b5090e2 Initial load
duke
parents:
diff changeset
   872
 *      __ieee754_rem_pio2      ... argument reduction routine
489c9b5090e2 Initial load
duke
parents:
diff changeset
   873
 *
489c9b5090e2 Initial load
duke
parents:
diff changeset
   874
 * Method.
489c9b5090e2 Initial load
duke
parents:
diff changeset
   875
 *      Let S,C and T denote the sin, cos and tan respectively on
489c9b5090e2 Initial load
duke
parents:
diff changeset
   876
 *      [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
489c9b5090e2 Initial load
duke
parents:
diff changeset
   877
 *      in [-pi/4 , +pi/4], and let n = k mod 4.
489c9b5090e2 Initial load
duke
parents:
diff changeset
   878
 *      We have
489c9b5090e2 Initial load
duke
parents:
diff changeset
   879
 *
489c9b5090e2 Initial load
duke
parents:
diff changeset
   880
 *          n        sin(x)      cos(x)        tan(x)
489c9b5090e2 Initial load
duke
parents:
diff changeset
   881
 *     ----------------------------------------------------------
489c9b5090e2 Initial load
duke
parents:
diff changeset
   882
 *          0          S           C             T
489c9b5090e2 Initial load
duke
parents:
diff changeset
   883
 *          1          C          -S            -1/T
489c9b5090e2 Initial load
duke
parents:
diff changeset
   884
 *          2         -S          -C             T
489c9b5090e2 Initial load
duke
parents:
diff changeset
   885
 *          3         -C           S            -1/T
489c9b5090e2 Initial load
duke
parents:
diff changeset
   886
 *     ----------------------------------------------------------
489c9b5090e2 Initial load
duke
parents:
diff changeset
   887
 *
489c9b5090e2 Initial load
duke
parents:
diff changeset
   888
 * Special cases:
489c9b5090e2 Initial load
duke
parents:
diff changeset
   889
 *      Let trig be any of sin, cos, or tan.
489c9b5090e2 Initial load
duke
parents:
diff changeset
   890
 *      trig(+-INF)  is NaN, with signals;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   891
 *      trig(NaN)    is that NaN;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   892
 *
489c9b5090e2 Initial load
duke
parents:
diff changeset
   893
 * Accuracy:
489c9b5090e2 Initial load
duke
parents:
diff changeset
   894
 *      TRIG(x) returns trig(x) nearly rounded
489c9b5090e2 Initial load
duke
parents:
diff changeset
   895
 */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   896
489c9b5090e2 Initial load
duke
parents:
diff changeset
   897
JRT_LEAF(jdouble, SharedRuntime::dcos(jdouble x))
489c9b5090e2 Initial load
duke
parents:
diff changeset
   898
  double y[2],z=0.0;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   899
  int n, ix;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   900
489c9b5090e2 Initial load
duke
parents:
diff changeset
   901
  /* High word of x. */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   902
  ix = __HI(x);
489c9b5090e2 Initial load
duke
parents:
diff changeset
   903
489c9b5090e2 Initial load
duke
parents:
diff changeset
   904
  /* |x| ~< pi/4 */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   905
  ix &= 0x7fffffff;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   906
  if(ix <= 0x3fe921fb) return __kernel_cos(x,z);
489c9b5090e2 Initial load
duke
parents:
diff changeset
   907
489c9b5090e2 Initial load
duke
parents:
diff changeset
   908
  /* cos(Inf or NaN) is NaN */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   909
  else if (ix>=0x7ff00000) return x-x;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   910
489c9b5090e2 Initial load
duke
parents:
diff changeset
   911
  /* argument reduction needed */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   912
  else {
489c9b5090e2 Initial load
duke
parents:
diff changeset
   913
    n = __ieee754_rem_pio2(x,y);
489c9b5090e2 Initial load
duke
parents:
diff changeset
   914
    switch(n&3) {
489c9b5090e2 Initial load
duke
parents:
diff changeset
   915
    case 0: return  __kernel_cos(y[0],y[1]);
489c9b5090e2 Initial load
duke
parents:
diff changeset
   916
    case 1: return -__kernel_sin(y[0],y[1],1);
489c9b5090e2 Initial load
duke
parents:
diff changeset
   917
    case 2: return -__kernel_cos(y[0],y[1]);
489c9b5090e2 Initial load
duke
parents:
diff changeset
   918
    default:
489c9b5090e2 Initial load
duke
parents:
diff changeset
   919
      return  __kernel_sin(y[0],y[1],1);
489c9b5090e2 Initial load
duke
parents:
diff changeset
   920
    }
489c9b5090e2 Initial load
duke
parents:
diff changeset
   921
  }
489c9b5090e2 Initial load
duke
parents:
diff changeset
   922
JRT_END
489c9b5090e2 Initial load
duke
parents:
diff changeset
   923
489c9b5090e2 Initial load
duke
parents:
diff changeset
   924
/* tan(x)
489c9b5090e2 Initial load
duke
parents:
diff changeset
   925
 * Return tangent function of x.
489c9b5090e2 Initial load
duke
parents:
diff changeset
   926
 *
489c9b5090e2 Initial load
duke
parents:
diff changeset
   927
 * kernel function:
489c9b5090e2 Initial load
duke
parents:
diff changeset
   928
 *      __kernel_tan            ... tangent function on [-pi/4,pi/4]
489c9b5090e2 Initial load
duke
parents:
diff changeset
   929
 *      __ieee754_rem_pio2      ... argument reduction routine
489c9b5090e2 Initial load
duke
parents:
diff changeset
   930
 *
489c9b5090e2 Initial load
duke
parents:
diff changeset
   931
 * Method.
489c9b5090e2 Initial load
duke
parents:
diff changeset
   932
 *      Let S,C and T denote the sin, cos and tan respectively on
489c9b5090e2 Initial load
duke
parents:
diff changeset
   933
 *      [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
489c9b5090e2 Initial load
duke
parents:
diff changeset
   934
 *      in [-pi/4 , +pi/4], and let n = k mod 4.
489c9b5090e2 Initial load
duke
parents:
diff changeset
   935
 *      We have
489c9b5090e2 Initial load
duke
parents:
diff changeset
   936
 *
489c9b5090e2 Initial load
duke
parents:
diff changeset
   937
 *          n        sin(x)      cos(x)        tan(x)
489c9b5090e2 Initial load
duke
parents:
diff changeset
   938
 *     ----------------------------------------------------------
489c9b5090e2 Initial load
duke
parents:
diff changeset
   939
 *          0          S           C             T
489c9b5090e2 Initial load
duke
parents:
diff changeset
   940
 *          1          C          -S            -1/T
489c9b5090e2 Initial load
duke
parents:
diff changeset
   941
 *          2         -S          -C             T
489c9b5090e2 Initial load
duke
parents:
diff changeset
   942
 *          3         -C           S            -1/T
489c9b5090e2 Initial load
duke
parents:
diff changeset
   943
 *     ----------------------------------------------------------
489c9b5090e2 Initial load
duke
parents:
diff changeset
   944
 *
489c9b5090e2 Initial load
duke
parents:
diff changeset
   945
 * Special cases:
489c9b5090e2 Initial load
duke
parents:
diff changeset
   946
 *      Let trig be any of sin, cos, or tan.
489c9b5090e2 Initial load
duke
parents:
diff changeset
   947
 *      trig(+-INF)  is NaN, with signals;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   948
 *      trig(NaN)    is that NaN;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   949
 *
489c9b5090e2 Initial load
duke
parents:
diff changeset
   950
 * Accuracy:
489c9b5090e2 Initial load
duke
parents:
diff changeset
   951
 *      TRIG(x) returns trig(x) nearly rounded
489c9b5090e2 Initial load
duke
parents:
diff changeset
   952
 */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   953
489c9b5090e2 Initial load
duke
parents:
diff changeset
   954
JRT_LEAF(jdouble, SharedRuntime::dtan(jdouble x))
489c9b5090e2 Initial load
duke
parents:
diff changeset
   955
  double y[2],z=0.0;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   956
  int n, ix;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   957
489c9b5090e2 Initial load
duke
parents:
diff changeset
   958
  /* High word of x. */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   959
  ix = __HI(x);
489c9b5090e2 Initial load
duke
parents:
diff changeset
   960
489c9b5090e2 Initial load
duke
parents:
diff changeset
   961
  /* |x| ~< pi/4 */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   962
  ix &= 0x7fffffff;
489c9b5090e2 Initial load
duke
parents:
diff changeset
   963
  if(ix <= 0x3fe921fb) return __kernel_tan(x,z,1);
489c9b5090e2 Initial load
duke
parents:
diff changeset
   964
489c9b5090e2 Initial load
duke
parents:
diff changeset
   965
  /* tan(Inf or NaN) is NaN */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   966
  else if (ix>=0x7ff00000) return x-x;            /* NaN */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   967
489c9b5090e2 Initial load
duke
parents:
diff changeset
   968
  /* argument reduction needed */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   969
  else {
489c9b5090e2 Initial load
duke
parents:
diff changeset
   970
    n = __ieee754_rem_pio2(x,y);
489c9b5090e2 Initial load
duke
parents:
diff changeset
   971
    return __kernel_tan(y[0],y[1],1-((n&1)<<1)); /*   1 -- n even
489c9b5090e2 Initial load
duke
parents:
diff changeset
   972
                                                     -1 -- n odd */
489c9b5090e2 Initial load
duke
parents:
diff changeset
   973
  }
489c9b5090e2 Initial load
duke
parents:
diff changeset
   974
JRT_END
489c9b5090e2 Initial load
duke
parents:
diff changeset
   975
489c9b5090e2 Initial load
duke
parents:
diff changeset
   976
489c9b5090e2 Initial load
duke
parents:
diff changeset
   977
#ifdef WIN32
489c9b5090e2 Initial load
duke
parents:
diff changeset
   978
# pragma optimize ( "", on )
489c9b5090e2 Initial load
duke
parents:
diff changeset
   979
#endif