aoqi@0: /* aoqi@0: * Copyright (c) 2001, 2010, Oracle and/or its affiliates. All rights reserved. aoqi@0: * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. aoqi@0: * aoqi@0: * This code is free software; you can redistribute it and/or modify it aoqi@0: * under the terms of the GNU General Public License version 2 only, as aoqi@0: * published by the Free Software Foundation. aoqi@0: * aoqi@0: * This code is distributed in the hope that it will be useful, but WITHOUT aoqi@0: * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or aoqi@0: * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License aoqi@0: * version 2 for more details (a copy is included in the LICENSE file that aoqi@0: * accompanied this code). aoqi@0: * aoqi@0: * You should have received a copy of the GNU General Public License version aoqi@0: * 2 along with this work; if not, write to the Free Software Foundation, aoqi@0: * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. aoqi@0: * aoqi@0: * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA aoqi@0: * or visit www.oracle.com if you need additional information or have any aoqi@0: * questions. aoqi@0: * aoqi@0: */ aoqi@0: aoqi@1: /* aoqi@1: * This file has been modified by Loongson Technology in 2015. These aoqi@1: * modifications are Copyright (c) 2015 Loongson Technology, and are made aoqi@1: * available on the same license terms set forth above. aoqi@1: */ aoqi@1: aoqi@0: #include "precompiled.hpp" aoqi@0: #include "prims/jni.h" aoqi@0: #include "runtime/interfaceSupport.hpp" aoqi@0: #include "runtime/sharedRuntime.hpp" aoqi@0: aoqi@0: // This file contains copies of the fdlibm routines used by aoqi@0: // StrictMath. It turns out that it is almost always required to use aoqi@0: // these runtime routines; the Intel CPU doesn't meet the Java aoqi@0: // specification for sin/cos outside a certain limited argument range, aoqi@0: // and the SPARC CPU doesn't appear to have sin/cos instructions. It aoqi@0: // also turns out that avoiding the indirect call through function aoqi@0: // pointer out to libjava.so in SharedRuntime speeds these routines up aoqi@0: // by roughly 15% on both Win32/x86 and Solaris/SPARC. aoqi@0: aoqi@0: // Enabling optimizations in this file causes incorrect code to be aoqi@0: // generated; can not figure out how to turn down optimization for one aoqi@0: // file in the IDE on Windows aoqi@0: #ifdef WIN32 aoqi@0: # pragma optimize ( "", off ) aoqi@0: #endif aoqi@0: aoqi@0: /* The above workaround now causes more problems with the latest MS compiler. aoqi@0: * Visual Studio 2010's /GS option tries to guard against buffer overruns. aoqi@0: * /GS is on by default if you specify optimizations, which we do globally aoqi@0: * via /W3 /O2. However the above selective turning off of optimizations means aoqi@0: * that /GS issues a warning "4748". And since we treat warnings as errors (/WX) aoqi@0: * then the compilation fails. There are several possible solutions aoqi@0: * (1) Remove that pragma above as obsolete with VS2010 - requires testing. aoqi@0: * (2) Stop treating warnings as errors - would be a backward step aoqi@0: * (3) Disable /GS - may help performance but you lose the security checks aoqi@0: * (4) Disable the warning with "#pragma warning( disable : 4748 )" aoqi@0: * (5) Disable planting the code with __declspec(safebuffers) aoqi@0: * I've opted for (5) although we should investigate the local performance aoqi@0: * benefits of (1) and global performance benefit of (3). aoqi@0: */ aoqi@0: #if defined(WIN32) && (defined(_MSC_VER) && (_MSC_VER >= 1600)) aoqi@0: #define SAFEBUF __declspec(safebuffers) aoqi@0: #else aoqi@0: #define SAFEBUF aoqi@0: #endif aoqi@0: aoqi@0: #include aoqi@0: aoqi@0: // VM_LITTLE_ENDIAN is #defined appropriately in the Makefiles aoqi@0: // [jk] this is not 100% correct because the float word order may different aoqi@0: // from the byte order (e.g. on ARM) aoqi@0: #ifdef VM_LITTLE_ENDIAN aoqi@0: # define __HI(x) *(1+(int*)&x) aoqi@0: # define __LO(x) *(int*)&x aoqi@0: #else aoqi@0: # define __HI(x) *(int*)&x aoqi@0: # define __LO(x) *(1+(int*)&x) aoqi@0: #endif aoqi@0: aoqi@0: static double copysignA(double x, double y) { aoqi@0: __HI(x) = (__HI(x)&0x7fffffff)|(__HI(y)&0x80000000); aoqi@0: return x; aoqi@0: } aoqi@0: aoqi@0: /* aoqi@0: * scalbn (double x, int n) aoqi@0: * scalbn(x,n) returns x* 2**n computed by exponent aoqi@0: * manipulation rather than by actually performing an aoqi@0: * exponentiation or a multiplication. aoqi@0: */ aoqi@0: aoqi@0: static const double aoqi@0: two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */ aoqi@0: twom54 = 5.55111512312578270212e-17, /* 0x3C900000, 0x00000000 */ aoqi@0: hugeX = 1.0e+300, aoqi@0: tiny = 1.0e-300; aoqi@0: aoqi@0: static double scalbnA (double x, int n) { aoqi@0: int k,hx,lx; aoqi@0: hx = __HI(x); aoqi@0: lx = __LO(x); aoqi@0: k = (hx&0x7ff00000)>>20; /* extract exponent */ aoqi@0: if (k==0) { /* 0 or subnormal x */ aoqi@0: if ((lx|(hx&0x7fffffff))==0) return x; /* +-0 */ aoqi@0: x *= two54; aoqi@0: hx = __HI(x); aoqi@0: k = ((hx&0x7ff00000)>>20) - 54; aoqi@0: if (n< -50000) return tiny*x; /*underflow*/ aoqi@0: } aoqi@0: if (k==0x7ff) return x+x; /* NaN or Inf */ aoqi@0: k = k+n; aoqi@0: if (k > 0x7fe) return hugeX*copysignA(hugeX,x); /* overflow */ aoqi@0: if (k > 0) /* normal result */ aoqi@0: {__HI(x) = (hx&0x800fffff)|(k<<20); return x;} aoqi@0: if (k <= -54) { aoqi@0: if (n > 50000) /* in case integer overflow in n+k */ aoqi@0: return hugeX*copysignA(hugeX,x); /*overflow*/ aoqi@0: else return tiny*copysignA(tiny,x); /*underflow*/ aoqi@0: } aoqi@0: k += 54; /* subnormal result */ aoqi@0: __HI(x) = (hx&0x800fffff)|(k<<20); aoqi@0: return x*twom54; aoqi@0: } aoqi@0: aoqi@0: /* aoqi@0: * __kernel_rem_pio2(x,y,e0,nx,prec,ipio2) aoqi@0: * double x[],y[]; int e0,nx,prec; int ipio2[]; aoqi@0: * aoqi@0: * __kernel_rem_pio2 return the last three digits of N with aoqi@0: * y = x - N*pi/2 aoqi@0: * so that |y| < pi/2. aoqi@0: * aoqi@0: * The method is to compute the integer (mod 8) and fraction parts of aoqi@0: * (2/pi)*x without doing the full multiplication. In general we aoqi@0: * skip the part of the product that are known to be a huge integer ( aoqi@0: * more accurately, = 0 mod 8 ). Thus the number of operations are aoqi@0: * independent of the exponent of the input. aoqi@0: * aoqi@0: * (2/pi) is represented by an array of 24-bit integers in ipio2[]. aoqi@0: * aoqi@0: * Input parameters: aoqi@0: * x[] The input value (must be positive) is broken into nx aoqi@0: * pieces of 24-bit integers in double precision format. aoqi@0: * x[i] will be the i-th 24 bit of x. The scaled exponent aoqi@0: * of x[0] is given in input parameter e0 (i.e., x[0]*2^e0 aoqi@0: * match x's up to 24 bits. aoqi@0: * aoqi@0: * Example of breaking a double positive z into x[0]+x[1]+x[2]: aoqi@0: * e0 = ilogb(z)-23 aoqi@0: * z = scalbn(z,-e0) aoqi@0: * for i = 0,1,2 aoqi@0: * x[i] = floor(z) aoqi@0: * z = (z-x[i])*2**24 aoqi@0: * aoqi@0: * aoqi@0: * y[] ouput result in an array of double precision numbers. aoqi@0: * The dimension of y[] is: aoqi@0: * 24-bit precision 1 aoqi@0: * 53-bit precision 2 aoqi@0: * 64-bit precision 2 aoqi@0: * 113-bit precision 3 aoqi@0: * The actual value is the sum of them. Thus for 113-bit aoqi@0: * precsion, one may have to do something like: aoqi@0: * aoqi@0: * long double t,w,r_head, r_tail; aoqi@0: * t = (long double)y[2] + (long double)y[1]; aoqi@0: * w = (long double)y[0]; aoqi@0: * r_head = t+w; aoqi@0: * r_tail = w - (r_head - t); aoqi@0: * aoqi@0: * e0 The exponent of x[0] aoqi@0: * aoqi@0: * nx dimension of x[] aoqi@0: * aoqi@0: * prec an interger indicating the precision: aoqi@0: * 0 24 bits (single) aoqi@0: * 1 53 bits (double) aoqi@0: * 2 64 bits (extended) aoqi@0: * 3 113 bits (quad) aoqi@0: * aoqi@0: * ipio2[] aoqi@0: * integer array, contains the (24*i)-th to (24*i+23)-th aoqi@0: * bit of 2/pi after binary point. The corresponding aoqi@0: * floating value is aoqi@0: * aoqi@0: * ipio2[i] * 2^(-24(i+1)). aoqi@0: * aoqi@0: * External function: aoqi@0: * double scalbn(), floor(); aoqi@0: * aoqi@0: * aoqi@0: * Here is the description of some local variables: aoqi@0: * aoqi@0: * jk jk+1 is the initial number of terms of ipio2[] needed aoqi@0: * in the computation. The recommended value is 2,3,4, aoqi@0: * 6 for single, double, extended,and quad. aoqi@0: * aoqi@0: * jz local integer variable indicating the number of aoqi@0: * terms of ipio2[] used. aoqi@0: * aoqi@0: * jx nx - 1 aoqi@0: * aoqi@0: * jv index for pointing to the suitable ipio2[] for the aoqi@0: * computation. In general, we want aoqi@0: * ( 2^e0*x[0] * ipio2[jv-1]*2^(-24jv) )/8 aoqi@0: * is an integer. Thus aoqi@0: * e0-3-24*jv >= 0 or (e0-3)/24 >= jv aoqi@0: * Hence jv = max(0,(e0-3)/24). aoqi@0: * aoqi@0: * jp jp+1 is the number of terms in PIo2[] needed, jp = jk. aoqi@0: * aoqi@0: * q[] double array with integral value, representing the aoqi@0: * 24-bits chunk of the product of x and 2/pi. aoqi@0: * aoqi@0: * q0 the corresponding exponent of q[0]. Note that the aoqi@0: * exponent for q[i] would be q0-24*i. aoqi@0: * aoqi@0: * PIo2[] double precision array, obtained by cutting pi/2 aoqi@0: * into 24 bits chunks. aoqi@0: * aoqi@0: * f[] ipio2[] in floating point aoqi@0: * aoqi@0: * iq[] integer array by breaking up q[] in 24-bits chunk. aoqi@0: * aoqi@0: * fq[] final product of x*(2/pi) in fq[0],..,fq[jk] aoqi@0: * aoqi@0: * ih integer. If >0 it indicats q[] is >= 0.5, hence aoqi@0: * it also indicates the *sign* of the result. aoqi@0: * aoqi@0: */ aoqi@0: aoqi@0: aoqi@0: /* aoqi@0: * Constants: aoqi@0: * The hexadecimal values are the intended ones for the following aoqi@0: * constants. The decimal values may be used, provided that the aoqi@0: * compiler will convert from decimal to binary accurately enough aoqi@0: * to produce the hexadecimal values shown. aoqi@0: */ aoqi@0: aoqi@0: aoqi@0: static const int init_jk[] = {2,3,4,6}; /* initial value for jk */ aoqi@0: aoqi@0: static const double PIo2[] = { aoqi@0: 1.57079625129699707031e+00, /* 0x3FF921FB, 0x40000000 */ aoqi@0: 7.54978941586159635335e-08, /* 0x3E74442D, 0x00000000 */ aoqi@0: 5.39030252995776476554e-15, /* 0x3CF84698, 0x80000000 */ aoqi@0: 3.28200341580791294123e-22, /* 0x3B78CC51, 0x60000000 */ aoqi@0: 1.27065575308067607349e-29, /* 0x39F01B83, 0x80000000 */ aoqi@0: 1.22933308981111328932e-36, /* 0x387A2520, 0x40000000 */ aoqi@0: 2.73370053816464559624e-44, /* 0x36E38222, 0x80000000 */ aoqi@0: 2.16741683877804819444e-51, /* 0x3569F31D, 0x00000000 */ aoqi@0: }; aoqi@0: aoqi@0: static const double aoqi@0: zeroB = 0.0, aoqi@0: one = 1.0, aoqi@0: two24B = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */ aoqi@0: twon24 = 5.96046447753906250000e-08; /* 0x3E700000, 0x00000000 */ aoqi@0: aoqi@0: static SAFEBUF int __kernel_rem_pio2(double *x, double *y, int e0, int nx, int prec, const int *ipio2) { aoqi@0: int jz,jx,jv,jp,jk,carry,n,iq[20],i,j,k,m,q0,ih; aoqi@0: double z,fw,f[20],fq[20],q[20]; aoqi@0: aoqi@0: /* initialize jk*/ aoqi@0: jk = init_jk[prec]; aoqi@0: jp = jk; aoqi@0: aoqi@0: /* determine jx,jv,q0, note that 3>q0 */ aoqi@0: jx = nx-1; aoqi@0: jv = (e0-3)/24; if(jv<0) jv=0; aoqi@0: q0 = e0-24*(jv+1); aoqi@0: aoqi@0: /* set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk] */ aoqi@0: j = jv-jx; m = jx+jk; aoqi@0: for(i=0;i<=m;i++,j++) f[i] = (j<0)? zeroB : (double) ipio2[j]; aoqi@0: aoqi@0: /* compute q[0],q[1],...q[jk] */ aoqi@0: for (i=0;i<=jk;i++) { aoqi@0: for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; q[i] = fw; aoqi@0: } aoqi@0: aoqi@0: jz = jk; aoqi@0: recompute: aoqi@0: /* distill q[] into iq[] reversingly */ aoqi@0: for(i=0,j=jz,z=q[jz];j>0;i++,j--) { aoqi@0: fw = (double)((int)(twon24* z)); aoqi@0: iq[i] = (int)(z-two24B*fw); aoqi@0: z = q[j-1]+fw; aoqi@0: } aoqi@0: aoqi@0: /* compute n */ aoqi@0: z = scalbnA(z,q0); /* actual value of z */ aoqi@0: z -= 8.0*floor(z*0.125); /* trim off integer >= 8 */ aoqi@0: n = (int) z; aoqi@0: z -= (double)n; aoqi@0: ih = 0; aoqi@0: if(q0>0) { /* need iq[jz-1] to determine n */ aoqi@0: i = (iq[jz-1]>>(24-q0)); n += i; aoqi@0: iq[jz-1] -= i<<(24-q0); aoqi@0: ih = iq[jz-1]>>(23-q0); aoqi@0: } aoqi@0: else if(q0==0) ih = iq[jz-1]>>23; aoqi@0: else if(z>=0.5) ih=2; aoqi@0: aoqi@0: if(ih>0) { /* q > 0.5 */ aoqi@0: n += 1; carry = 0; aoqi@0: for(i=0;i0) { /* rare case: chance is 1 in 12 */ aoqi@0: switch(q0) { aoqi@0: case 1: aoqi@0: iq[jz-1] &= 0x7fffff; break; aoqi@0: case 2: aoqi@0: iq[jz-1] &= 0x3fffff; break; aoqi@0: } aoqi@0: } aoqi@0: if(ih==2) { aoqi@0: z = one - z; aoqi@0: if(carry!=0) z -= scalbnA(one,q0); aoqi@0: } aoqi@0: } aoqi@0: aoqi@0: /* check if recomputation is needed */ aoqi@0: if(z==zeroB) { aoqi@0: j = 0; aoqi@0: for (i=jz-1;i>=jk;i--) j |= iq[i]; aoqi@0: if(j==0) { /* need recomputation */ aoqi@0: for(k=1;iq[jk-k]==0;k++); /* k = no. of terms needed */ aoqi@0: aoqi@0: for(i=jz+1;i<=jz+k;i++) { /* add q[jz+1] to q[jz+k] */ aoqi@0: f[jx+i] = (double) ipio2[jv+i]; aoqi@0: for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; aoqi@0: q[i] = fw; aoqi@0: } aoqi@0: jz += k; aoqi@0: goto recompute; aoqi@0: } aoqi@0: } aoqi@0: aoqi@0: /* chop off zero terms */ aoqi@0: if(z==0.0) { aoqi@0: jz -= 1; q0 -= 24; aoqi@0: while(iq[jz]==0) { jz--; q0-=24;} aoqi@0: } else { /* break z into 24-bit if neccessary */ aoqi@0: z = scalbnA(z,-q0); aoqi@0: if(z>=two24B) { aoqi@0: fw = (double)((int)(twon24*z)); aoqi@0: iq[jz] = (int)(z-two24B*fw); aoqi@0: jz += 1; q0 += 24; aoqi@0: iq[jz] = (int) fw; aoqi@0: } else iq[jz] = (int) z ; aoqi@0: } aoqi@0: aoqi@0: /* convert integer "bit" chunk to floating-point value */ aoqi@0: fw = scalbnA(one,q0); aoqi@0: for(i=jz;i>=0;i--) { aoqi@0: q[i] = fw*(double)iq[i]; fw*=twon24; aoqi@0: } aoqi@0: aoqi@0: /* compute PIo2[0,...,jp]*q[jz,...,0] */ aoqi@0: for(i=jz;i>=0;i--) { aoqi@0: for(fw=0.0,k=0;k<=jp&&k<=jz-i;k++) fw += PIo2[k]*q[i+k]; aoqi@0: fq[jz-i] = fw; aoqi@0: } aoqi@0: aoqi@0: /* compress fq[] into y[] */ aoqi@0: switch(prec) { aoqi@0: case 0: aoqi@0: fw = 0.0; aoqi@0: for (i=jz;i>=0;i--) fw += fq[i]; aoqi@0: y[0] = (ih==0)? fw: -fw; aoqi@0: break; aoqi@0: case 1: aoqi@0: case 2: aoqi@0: fw = 0.0; aoqi@0: for (i=jz;i>=0;i--) fw += fq[i]; aoqi@0: y[0] = (ih==0)? fw: -fw; aoqi@0: fw = fq[0]-fw; aoqi@0: for (i=1;i<=jz;i++) fw += fq[i]; aoqi@0: y[1] = (ih==0)? fw: -fw; aoqi@0: break; aoqi@0: case 3: /* painful */ aoqi@0: for (i=jz;i>0;i--) { aoqi@0: fw = fq[i-1]+fq[i]; aoqi@0: fq[i] += fq[i-1]-fw; aoqi@0: fq[i-1] = fw; aoqi@0: } aoqi@0: for (i=jz;i>1;i--) { aoqi@0: fw = fq[i-1]+fq[i]; aoqi@0: fq[i] += fq[i-1]-fw; aoqi@0: fq[i-1] = fw; aoqi@0: } aoqi@0: for (fw=0.0,i=jz;i>=2;i--) fw += fq[i]; aoqi@0: if(ih==0) { aoqi@0: y[0] = fq[0]; y[1] = fq[1]; y[2] = fw; aoqi@0: } else { aoqi@0: y[0] = -fq[0]; y[1] = -fq[1]; y[2] = -fw; aoqi@0: } aoqi@0: } aoqi@0: return n&7; aoqi@0: } aoqi@0: aoqi@0: aoqi@0: /* aoqi@0: * ==================================================== aoqi@0: * Copyright (c) 1993 Oracle and/or its affilates. All rights reserved. aoqi@0: * aoqi@0: * Developed at SunPro, a Sun Microsystems, Inc. business. aoqi@0: * Permission to use, copy, modify, and distribute this aoqi@0: * software is freely granted, provided that this notice aoqi@0: * is preserved. aoqi@0: * ==================================================== aoqi@0: * aoqi@0: */ aoqi@0: aoqi@0: /* __ieee754_rem_pio2(x,y) aoqi@0: * aoqi@0: * return the remainder of x rem pi/2 in y[0]+y[1] aoqi@0: * use __kernel_rem_pio2() aoqi@0: */ aoqi@0: aoqi@0: /* aoqi@0: * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi aoqi@0: */ aoqi@0: static const int two_over_pi[] = { aoqi@0: 0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62, aoqi@0: 0x95993C, 0x439041, 0xFE5163, 0xABDEBB, 0xC561B7, 0x246E3A, aoqi@0: 0x424DD2, 0xE00649, 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129, aoqi@0: 0xA73EE8, 0x8235F5, 0x2EBB44, 0x84E99C, 0x7026B4, 0x5F7E41, aoqi@0: 0x3991D6, 0x398353, 0x39F49C, 0x845F8B, 0xBDF928, 0x3B1FF8, aoqi@0: 0x97FFDE, 0x05980F, 0xEF2F11, 0x8B5A0A, 0x6D1F6D, 0x367ECF, aoqi@0: 0x27CB09, 0xB74F46, 0x3F669E, 0x5FEA2D, 0x7527BA, 0xC7EBE5, aoqi@0: 0xF17B3D, 0x0739F7, 0x8A5292, 0xEA6BFB, 0x5FB11F, 0x8D5D08, aoqi@0: 0x560330, 0x46FC7B, 0x6BABF0, 0xCFBC20, 0x9AF436, 0x1DA9E3, aoqi@0: 0x91615E, 0xE61B08, 0x659985, 0x5F14A0, 0x68408D, 0xFFD880, aoqi@0: 0x4D7327, 0x310606, 0x1556CA, 0x73A8C9, 0x60E27B, 0xC08C6B, aoqi@0: }; aoqi@0: aoqi@0: static const int npio2_hw[] = { aoqi@0: 0x3FF921FB, 0x400921FB, 0x4012D97C, 0x401921FB, 0x401F6A7A, 0x4022D97C, aoqi@0: 0x4025FDBB, 0x402921FB, 0x402C463A, 0x402F6A7A, 0x4031475C, 0x4032D97C, aoqi@0: 0x40346B9C, 0x4035FDBB, 0x40378FDB, 0x403921FB, 0x403AB41B, 0x403C463A, aoqi@0: 0x403DD85A, 0x403F6A7A, 0x40407E4C, 0x4041475C, 0x4042106C, 0x4042D97C, aoqi@0: 0x4043A28C, 0x40446B9C, 0x404534AC, 0x4045FDBB, 0x4046C6CB, 0x40478FDB, aoqi@0: 0x404858EB, 0x404921FB, aoqi@0: }; aoqi@0: aoqi@0: /* aoqi@0: * invpio2: 53 bits of 2/pi aoqi@0: * pio2_1: first 33 bit of pi/2 aoqi@0: * pio2_1t: pi/2 - pio2_1 aoqi@0: * pio2_2: second 33 bit of pi/2 aoqi@0: * pio2_2t: pi/2 - (pio2_1+pio2_2) aoqi@0: * pio2_3: third 33 bit of pi/2 aoqi@0: * pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3) aoqi@0: */ aoqi@0: aoqi@0: static const double aoqi@0: zeroA = 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ aoqi@0: half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */ aoqi@0: two24A = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */ aoqi@0: invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */ aoqi@0: pio2_1 = 1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */ aoqi@0: pio2_1t = 6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */ aoqi@0: pio2_2 = 6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */ aoqi@0: pio2_2t = 2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */ aoqi@0: pio2_3 = 2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */ aoqi@0: pio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */ aoqi@0: aoqi@0: static SAFEBUF int __ieee754_rem_pio2(double x, double *y) { aoqi@0: double z,w,t,r,fn; aoqi@0: double tx[3]; aoqi@0: int e0,i,j,nx,n,ix,hx,i0; aoqi@0: aoqi@0: i0 = ((*(int*)&two24A)>>30)^1; /* high word index */ aoqi@0: hx = *(i0+(int*)&x); /* high word of x */ aoqi@0: ix = hx&0x7fffffff; aoqi@0: if(ix<=0x3fe921fb) /* |x| ~<= pi/4 , no need for reduction */ aoqi@0: {y[0] = x; y[1] = 0; return 0;} aoqi@0: if(ix<0x4002d97c) { /* |x| < 3pi/4, special case with n=+-1 */ aoqi@0: if(hx>0) { aoqi@0: z = x - pio2_1; aoqi@0: if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */ aoqi@0: y[0] = z - pio2_1t; aoqi@0: y[1] = (z-y[0])-pio2_1t; aoqi@0: } else { /* near pi/2, use 33+33+53 bit pi */ aoqi@0: z -= pio2_2; aoqi@0: y[0] = z - pio2_2t; aoqi@0: y[1] = (z-y[0])-pio2_2t; aoqi@0: } aoqi@0: return 1; aoqi@0: } else { /* negative x */ aoqi@0: z = x + pio2_1; aoqi@0: if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */ aoqi@0: y[0] = z + pio2_1t; aoqi@0: y[1] = (z-y[0])+pio2_1t; aoqi@0: } else { /* near pi/2, use 33+33+53 bit pi */ aoqi@0: z += pio2_2; aoqi@0: y[0] = z + pio2_2t; aoqi@0: y[1] = (z-y[0])+pio2_2t; aoqi@0: } aoqi@0: return -1; aoqi@0: } aoqi@0: } aoqi@0: if(ix<=0x413921fb) { /* |x| ~<= 2^19*(pi/2), medium size */ aoqi@0: t = fabsd(x); aoqi@0: n = (int) (t*invpio2+half); aoqi@0: fn = (double)n; aoqi@0: r = t-fn*pio2_1; aoqi@0: w = fn*pio2_1t; /* 1st round good to 85 bit */ aoqi@0: if(n<32&&ix!=npio2_hw[n-1]) { aoqi@0: y[0] = r-w; /* quick check no cancellation */ aoqi@0: } else { aoqi@0: j = ix>>20; aoqi@0: y[0] = r-w; aoqi@0: i = j-(((*(i0+(int*)&y[0]))>>20)&0x7ff); aoqi@0: if(i>16) { /* 2nd iteration needed, good to 118 */ aoqi@0: t = r; aoqi@0: w = fn*pio2_2; aoqi@0: r = t-w; aoqi@0: w = fn*pio2_2t-((t-r)-w); aoqi@0: y[0] = r-w; aoqi@0: i = j-(((*(i0+(int*)&y[0]))>>20)&0x7ff); aoqi@0: if(i>49) { /* 3rd iteration need, 151 bits acc */ aoqi@0: t = r; /* will cover all possible cases */ aoqi@0: w = fn*pio2_3; aoqi@0: r = t-w; aoqi@0: w = fn*pio2_3t-((t-r)-w); aoqi@0: y[0] = r-w; aoqi@0: } aoqi@0: } aoqi@0: } aoqi@0: y[1] = (r-y[0])-w; aoqi@0: if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;} aoqi@0: else return n; aoqi@0: } aoqi@0: /* aoqi@0: * all other (large) arguments aoqi@0: */ aoqi@0: if(ix>=0x7ff00000) { /* x is inf or NaN */ aoqi@0: y[0]=y[1]=x-x; return 0; aoqi@0: } aoqi@0: /* set z = scalbn(|x|,ilogb(x)-23) */ aoqi@0: *(1-i0+(int*)&z) = *(1-i0+(int*)&x); aoqi@0: e0 = (ix>>20)-1046; /* e0 = ilogb(z)-23; */ aoqi@0: *(i0+(int*)&z) = ix - (e0<<20); aoqi@0: for(i=0;i<2;i++) { aoqi@0: tx[i] = (double)((int)(z)); aoqi@0: z = (z-tx[i])*two24A; aoqi@0: } aoqi@0: tx[2] = z; aoqi@0: nx = 3; aoqi@0: while(tx[nx-1]==zeroA) nx--; /* skip zero term */ aoqi@0: n = __kernel_rem_pio2(tx,y,e0,nx,2,two_over_pi); aoqi@0: if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;} aoqi@0: return n; aoqi@0: } aoqi@0: aoqi@0: aoqi@0: /* __kernel_sin( x, y, iy) aoqi@0: * kernel sin function on [-pi/4, pi/4], pi/4 ~ 0.7854 aoqi@0: * Input x is assumed to be bounded by ~pi/4 in magnitude. aoqi@0: * Input y is the tail of x. aoqi@0: * Input iy indicates whether y is 0. (if iy=0, y assume to be 0). aoqi@0: * aoqi@0: * Algorithm aoqi@0: * 1. Since sin(-x) = -sin(x), we need only to consider positive x. aoqi@0: * 2. if x < 2^-27 (hx<0x3e400000 0), return x with inexact if x!=0. aoqi@0: * 3. sin(x) is approximated by a polynomial of degree 13 on aoqi@0: * [0,pi/4] aoqi@0: * 3 13 aoqi@0: * sin(x) ~ x + S1*x + ... + S6*x aoqi@0: * where aoqi@0: * aoqi@0: * |sin(x) 2 4 6 8 10 12 | -58 aoqi@0: * |----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x +S6*x )| <= 2 aoqi@0: * | x | aoqi@0: * aoqi@0: * 4. sin(x+y) = sin(x) + sin'(x')*y aoqi@0: * ~ sin(x) + (1-x*x/2)*y aoqi@0: * For better accuracy, let aoqi@0: * 3 2 2 2 2 aoqi@0: * r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6)))) aoqi@0: * then 3 2 aoqi@0: * sin(x) = x + (S1*x + (x *(r-y/2)+y)) aoqi@0: */ aoqi@1: #ifdef MIPS64 aoqi@1: #undef S1 aoqi@1: #undef S2 aoqi@1: #undef S3 aoqi@1: #undef S4 aoqi@1: #undef S5 aoqi@1: #undef S6 aoqi@1: #endif aoqi@0: aoqi@0: static const double aoqi@0: S1 = -1.66666666666666324348e-01, /* 0xBFC55555, 0x55555549 */ aoqi@0: S2 = 8.33333333332248946124e-03, /* 0x3F811111, 0x1110F8A6 */ aoqi@0: S3 = -1.98412698298579493134e-04, /* 0xBF2A01A0, 0x19C161D5 */ aoqi@0: S4 = 2.75573137070700676789e-06, /* 0x3EC71DE3, 0x57B1FE7D */ aoqi@0: S5 = -2.50507602534068634195e-08, /* 0xBE5AE5E6, 0x8A2B9CEB */ aoqi@0: S6 = 1.58969099521155010221e-10; /* 0x3DE5D93A, 0x5ACFD57C */ aoqi@0: aoqi@0: static double __kernel_sin(double x, double y, int iy) aoqi@0: { aoqi@0: double z,r,v; aoqi@0: int ix; aoqi@0: ix = __HI(x)&0x7fffffff; /* high word of x */ aoqi@0: if(ix<0x3e400000) /* |x| < 2**-27 */ aoqi@0: {if((int)x==0) return x;} /* generate inexact */ aoqi@0: z = x*x; aoqi@0: v = z*x; aoqi@0: r = S2+z*(S3+z*(S4+z*(S5+z*S6))); aoqi@0: if(iy==0) return x+v*(S1+z*r); aoqi@0: else return x-((z*(half*y-v*r)-y)-v*S1); aoqi@0: } aoqi@0: aoqi@0: /* aoqi@0: * __kernel_cos( x, y ) aoqi@0: * kernel cos function on [-pi/4, pi/4], pi/4 ~ 0.785398164 aoqi@0: * Input x is assumed to be bounded by ~pi/4 in magnitude. aoqi@0: * Input y is the tail of x. aoqi@0: * aoqi@0: * Algorithm aoqi@0: * 1. Since cos(-x) = cos(x), we need only to consider positive x. aoqi@0: * 2. if x < 2^-27 (hx<0x3e400000 0), return 1 with inexact if x!=0. aoqi@0: * 3. cos(x) is approximated by a polynomial of degree 14 on aoqi@0: * [0,pi/4] aoqi@0: * 4 14 aoqi@0: * cos(x) ~ 1 - x*x/2 + C1*x + ... + C6*x aoqi@0: * where the remez error is aoqi@0: * aoqi@0: * | 2 4 6 8 10 12 14 | -58 aoqi@0: * |cos(x)-(1-.5*x +C1*x +C2*x +C3*x +C4*x +C5*x +C6*x )| <= 2 aoqi@0: * | | aoqi@0: * aoqi@0: * 4 6 8 10 12 14 aoqi@0: * 4. let r = C1*x +C2*x +C3*x +C4*x +C5*x +C6*x , then aoqi@0: * cos(x) = 1 - x*x/2 + r aoqi@0: * since cos(x+y) ~ cos(x) - sin(x)*y aoqi@0: * ~ cos(x) - x*y, aoqi@0: * a correction term is necessary in cos(x) and hence aoqi@0: * cos(x+y) = 1 - (x*x/2 - (r - x*y)) aoqi@0: * For better accuracy when x > 0.3, let qx = |x|/4 with aoqi@0: * the last 32 bits mask off, and if x > 0.78125, let qx = 0.28125. aoqi@0: * Then aoqi@0: * cos(x+y) = (1-qx) - ((x*x/2-qx) - (r-x*y)). aoqi@0: * Note that 1-qx and (x*x/2-qx) is EXACT here, and the aoqi@0: * magnitude of the latter is at least a quarter of x*x/2, aoqi@0: * thus, reducing the rounding error in the subtraction. aoqi@0: */ aoqi@0: aoqi@0: static const double aoqi@0: C1 = 4.16666666666666019037e-02, /* 0x3FA55555, 0x5555554C */ aoqi@0: C2 = -1.38888888888741095749e-03, /* 0xBF56C16C, 0x16C15177 */ aoqi@0: C3 = 2.48015872894767294178e-05, /* 0x3EFA01A0, 0x19CB1590 */ aoqi@0: C4 = -2.75573143513906633035e-07, /* 0xBE927E4F, 0x809C52AD */ aoqi@0: C5 = 2.08757232129817482790e-09, /* 0x3E21EE9E, 0xBDB4B1C4 */ aoqi@0: C6 = -1.13596475577881948265e-11; /* 0xBDA8FAE9, 0xBE8838D4 */ aoqi@0: aoqi@0: static double __kernel_cos(double x, double y) aoqi@0: { aoqi@0: double a,h,z,r,qx; aoqi@0: int ix; aoqi@0: ix = __HI(x)&0x7fffffff; /* ix = |x|'s high word*/ aoqi@0: if(ix<0x3e400000) { /* if x < 2**27 */ aoqi@0: if(((int)x)==0) return one; /* generate inexact */ aoqi@0: } aoqi@0: z = x*x; aoqi@0: r = z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*C6))))); aoqi@0: if(ix < 0x3FD33333) /* if |x| < 0.3 */ aoqi@0: return one - (0.5*z - (z*r - x*y)); aoqi@0: else { aoqi@0: if(ix > 0x3fe90000) { /* x > 0.78125 */ aoqi@0: qx = 0.28125; aoqi@0: } else { aoqi@0: __HI(qx) = ix-0x00200000; /* x/4 */ aoqi@0: __LO(qx) = 0; aoqi@0: } aoqi@0: h = 0.5*z-qx; aoqi@0: a = one-qx; aoqi@0: return a - (h - (z*r-x*y)); aoqi@0: } aoqi@0: } aoqi@0: aoqi@0: /* __kernel_tan( x, y, k ) aoqi@0: * kernel tan function on [-pi/4, pi/4], pi/4 ~ 0.7854 aoqi@0: * Input x is assumed to be bounded by ~pi/4 in magnitude. aoqi@0: * Input y is the tail of x. aoqi@0: * Input k indicates whether tan (if k=1) or aoqi@0: * -1/tan (if k= -1) is returned. aoqi@0: * aoqi@0: * Algorithm aoqi@0: * 1. Since tan(-x) = -tan(x), we need only to consider positive x. aoqi@0: * 2. if x < 2^-28 (hx<0x3e300000 0), return x with inexact if x!=0. aoqi@0: * 3. tan(x) is approximated by a odd polynomial of degree 27 on aoqi@0: * [0,0.67434] aoqi@0: * 3 27 aoqi@0: * tan(x) ~ x + T1*x + ... + T13*x aoqi@0: * where aoqi@0: * aoqi@0: * |tan(x) 2 4 26 | -59.2 aoqi@0: * |----- - (1+T1*x +T2*x +.... +T13*x )| <= 2 aoqi@0: * | x | aoqi@0: * aoqi@0: * Note: tan(x+y) = tan(x) + tan'(x)*y aoqi@0: * ~ tan(x) + (1+x*x)*y aoqi@0: * Therefore, for better accuracy in computing tan(x+y), let aoqi@0: * 3 2 2 2 2 aoqi@0: * r = x *(T2+x *(T3+x *(...+x *(T12+x *T13)))) aoqi@0: * then aoqi@0: * 3 2 aoqi@0: * tan(x+y) = x + (T1*x + (x *(r+y)+y)) aoqi@0: * aoqi@0: * 4. For x in [0.67434,pi/4], let y = pi/4 - x, then aoqi@0: * tan(x) = tan(pi/4-y) = (1-tan(y))/(1+tan(y)) aoqi@0: * = 1 - 2*(tan(y) - (tan(y)^2)/(1+tan(y))) aoqi@0: */ aoqi@0: aoqi@0: static const double aoqi@0: pio4 = 7.85398163397448278999e-01, /* 0x3FE921FB, 0x54442D18 */ aoqi@0: pio4lo= 3.06161699786838301793e-17, /* 0x3C81A626, 0x33145C07 */ aoqi@0: T[] = { aoqi@0: 3.33333333333334091986e-01, /* 0x3FD55555, 0x55555563 */ aoqi@0: 1.33333333333201242699e-01, /* 0x3FC11111, 0x1110FE7A */ aoqi@0: 5.39682539762260521377e-02, /* 0x3FABA1BA, 0x1BB341FE */ aoqi@0: 2.18694882948595424599e-02, /* 0x3F9664F4, 0x8406D637 */ aoqi@0: 8.86323982359930005737e-03, /* 0x3F8226E3, 0xE96E8493 */ aoqi@0: 3.59207910759131235356e-03, /* 0x3F6D6D22, 0xC9560328 */ aoqi@0: 1.45620945432529025516e-03, /* 0x3F57DBC8, 0xFEE08315 */ aoqi@0: 5.88041240820264096874e-04, /* 0x3F4344D8, 0xF2F26501 */ aoqi@0: 2.46463134818469906812e-04, /* 0x3F3026F7, 0x1A8D1068 */ aoqi@0: 7.81794442939557092300e-05, /* 0x3F147E88, 0xA03792A6 */ aoqi@0: 7.14072491382608190305e-05, /* 0x3F12B80F, 0x32F0A7E9 */ aoqi@0: -1.85586374855275456654e-05, /* 0xBEF375CB, 0xDB605373 */ aoqi@0: 2.59073051863633712884e-05, /* 0x3EFB2A70, 0x74BF7AD4 */ aoqi@0: }; aoqi@0: aoqi@0: static double __kernel_tan(double x, double y, int iy) aoqi@0: { aoqi@0: double z,r,v,w,s; aoqi@0: int ix,hx; aoqi@0: hx = __HI(x); /* high word of x */ aoqi@0: ix = hx&0x7fffffff; /* high word of |x| */ aoqi@0: if(ix<0x3e300000) { /* x < 2**-28 */ aoqi@0: if((int)x==0) { /* generate inexact */ aoqi@0: if (((ix | __LO(x)) | (iy + 1)) == 0) aoqi@0: return one / fabsd(x); aoqi@0: else { aoqi@0: if (iy == 1) aoqi@0: return x; aoqi@0: else { /* compute -1 / (x+y) carefully */ aoqi@0: double a, t; aoqi@0: aoqi@0: z = w = x + y; aoqi@0: __LO(z) = 0; aoqi@0: v = y - (z - x); aoqi@0: t = a = -one / w; aoqi@0: __LO(t) = 0; aoqi@0: s = one + t * z; aoqi@0: return t + a * (s + t * v); aoqi@0: } aoqi@0: } aoqi@0: } aoqi@0: } aoqi@0: if(ix>=0x3FE59428) { /* |x|>=0.6744 */ aoqi@0: if(hx<0) {x = -x; y = -y;} aoqi@0: z = pio4-x; aoqi@0: w = pio4lo-y; aoqi@0: x = z+w; y = 0.0; aoqi@0: } aoqi@0: z = x*x; aoqi@0: w = z*z; aoqi@0: /* Break x^5*(T[1]+x^2*T[2]+...) into aoqi@0: * x^5(T[1]+x^4*T[3]+...+x^20*T[11]) + aoqi@0: * x^5(x^2*(T[2]+x^4*T[4]+...+x^22*[T12])) aoqi@0: */ aoqi@0: r = T[1]+w*(T[3]+w*(T[5]+w*(T[7]+w*(T[9]+w*T[11])))); aoqi@0: v = z*(T[2]+w*(T[4]+w*(T[6]+w*(T[8]+w*(T[10]+w*T[12]))))); aoqi@0: s = z*x; aoqi@0: r = y + z*(s*(r+v)+y); aoqi@0: r += T[0]*s; aoqi@0: w = x+r; aoqi@0: if(ix>=0x3FE59428) { aoqi@0: v = (double)iy; aoqi@0: return (double)(1-((hx>>30)&2))*(v-2.0*(x-(w*w/(w+v)-r))); aoqi@0: } aoqi@0: if(iy==1) return w; aoqi@0: else { /* if allow error up to 2 ulp, aoqi@0: simply return -1.0/(x+r) here */ aoqi@0: /* compute -1.0/(x+r) accurately */ aoqi@0: double a,t; aoqi@0: z = w; aoqi@0: __LO(z) = 0; aoqi@0: v = r-(z - x); /* z+v = r+x */ aoqi@0: t = a = -1.0/w; /* a = -1.0/w */ aoqi@0: __LO(t) = 0; aoqi@0: s = 1.0+t*z; aoqi@0: return t+a*(s+t*v); aoqi@0: } aoqi@0: } aoqi@0: aoqi@0: aoqi@0: //---------------------------------------------------------------------- aoqi@0: // aoqi@0: // Routines for new sin/cos implementation aoqi@0: // aoqi@0: //---------------------------------------------------------------------- aoqi@0: aoqi@0: /* sin(x) aoqi@0: * Return sine function of x. aoqi@0: * aoqi@0: * kernel function: aoqi@0: * __kernel_sin ... sine function on [-pi/4,pi/4] aoqi@0: * __kernel_cos ... cose function on [-pi/4,pi/4] aoqi@0: * __ieee754_rem_pio2 ... argument reduction routine aoqi@0: * aoqi@0: * Method. aoqi@0: * Let S,C and T denote the sin, cos and tan respectively on aoqi@0: * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2 aoqi@0: * in [-pi/4 , +pi/4], and let n = k mod 4. aoqi@0: * We have aoqi@0: * aoqi@0: * n sin(x) cos(x) tan(x) aoqi@0: * ---------------------------------------------------------- aoqi@0: * 0 S C T aoqi@0: * 1 C -S -1/T aoqi@0: * 2 -S -C T aoqi@0: * 3 -C S -1/T aoqi@0: * ---------------------------------------------------------- aoqi@0: * aoqi@0: * Special cases: aoqi@0: * Let trig be any of sin, cos, or tan. aoqi@0: * trig(+-INF) is NaN, with signals; aoqi@0: * trig(NaN) is that NaN; aoqi@0: * aoqi@0: * Accuracy: aoqi@0: * TRIG(x) returns trig(x) nearly rounded aoqi@0: */ aoqi@0: aoqi@0: JRT_LEAF(jdouble, SharedRuntime::dsin(jdouble x)) aoqi@0: double y[2],z=0.0; aoqi@0: int n, ix; aoqi@0: aoqi@0: /* High word of x. */ aoqi@0: ix = __HI(x); aoqi@0: aoqi@0: /* |x| ~< pi/4 */ aoqi@0: ix &= 0x7fffffff; aoqi@0: if(ix <= 0x3fe921fb) return __kernel_sin(x,z,0); aoqi@0: aoqi@0: /* sin(Inf or NaN) is NaN */ aoqi@0: else if (ix>=0x7ff00000) return x-x; aoqi@0: aoqi@0: /* argument reduction needed */ aoqi@0: else { aoqi@0: n = __ieee754_rem_pio2(x,y); aoqi@0: switch(n&3) { aoqi@0: case 0: return __kernel_sin(y[0],y[1],1); aoqi@0: case 1: return __kernel_cos(y[0],y[1]); aoqi@0: case 2: return -__kernel_sin(y[0],y[1],1); aoqi@0: default: aoqi@0: return -__kernel_cos(y[0],y[1]); aoqi@0: } aoqi@0: } aoqi@0: JRT_END aoqi@0: aoqi@0: /* cos(x) aoqi@0: * Return cosine function of x. aoqi@0: * aoqi@0: * kernel function: aoqi@0: * __kernel_sin ... sine function on [-pi/4,pi/4] aoqi@0: * __kernel_cos ... cosine function on [-pi/4,pi/4] aoqi@0: * __ieee754_rem_pio2 ... argument reduction routine aoqi@0: * aoqi@0: * Method. aoqi@0: * Let S,C and T denote the sin, cos and tan respectively on aoqi@0: * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2 aoqi@0: * in [-pi/4 , +pi/4], and let n = k mod 4. aoqi@0: * We have aoqi@0: * aoqi@0: * n sin(x) cos(x) tan(x) aoqi@0: * ---------------------------------------------------------- aoqi@0: * 0 S C T aoqi@0: * 1 C -S -1/T aoqi@0: * 2 -S -C T aoqi@0: * 3 -C S -1/T aoqi@0: * ---------------------------------------------------------- aoqi@0: * aoqi@0: * Special cases: aoqi@0: * Let trig be any of sin, cos, or tan. aoqi@0: * trig(+-INF) is NaN, with signals; aoqi@0: * trig(NaN) is that NaN; aoqi@0: * aoqi@0: * Accuracy: aoqi@0: * TRIG(x) returns trig(x) nearly rounded aoqi@0: */ aoqi@0: aoqi@0: JRT_LEAF(jdouble, SharedRuntime::dcos(jdouble x)) aoqi@0: double y[2],z=0.0; aoqi@0: int n, ix; aoqi@0: aoqi@0: /* High word of x. */ aoqi@0: ix = __HI(x); aoqi@0: aoqi@0: /* |x| ~< pi/4 */ aoqi@0: ix &= 0x7fffffff; aoqi@0: if(ix <= 0x3fe921fb) return __kernel_cos(x,z); aoqi@0: aoqi@0: /* cos(Inf or NaN) is NaN */ aoqi@0: else if (ix>=0x7ff00000) return x-x; aoqi@0: aoqi@0: /* argument reduction needed */ aoqi@0: else { aoqi@0: n = __ieee754_rem_pio2(x,y); aoqi@0: switch(n&3) { aoqi@0: case 0: return __kernel_cos(y[0],y[1]); aoqi@0: case 1: return -__kernel_sin(y[0],y[1],1); aoqi@0: case 2: return -__kernel_cos(y[0],y[1]); aoqi@0: default: aoqi@0: return __kernel_sin(y[0],y[1],1); aoqi@0: } aoqi@0: } aoqi@0: JRT_END aoqi@0: aoqi@0: /* tan(x) aoqi@0: * Return tangent function of x. aoqi@0: * aoqi@0: * kernel function: aoqi@0: * __kernel_tan ... tangent function on [-pi/4,pi/4] aoqi@0: * __ieee754_rem_pio2 ... argument reduction routine aoqi@0: * aoqi@0: * Method. aoqi@0: * Let S,C and T denote the sin, cos and tan respectively on aoqi@0: * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2 aoqi@0: * in [-pi/4 , +pi/4], and let n = k mod 4. aoqi@0: * We have aoqi@0: * aoqi@0: * n sin(x) cos(x) tan(x) aoqi@0: * ---------------------------------------------------------- aoqi@0: * 0 S C T aoqi@0: * 1 C -S -1/T aoqi@0: * 2 -S -C T aoqi@0: * 3 -C S -1/T aoqi@0: * ---------------------------------------------------------- aoqi@0: * aoqi@0: * Special cases: aoqi@0: * Let trig be any of sin, cos, or tan. aoqi@0: * trig(+-INF) is NaN, with signals; aoqi@0: * trig(NaN) is that NaN; aoqi@0: * aoqi@0: * Accuracy: aoqi@0: * TRIG(x) returns trig(x) nearly rounded aoqi@0: */ aoqi@0: aoqi@0: JRT_LEAF(jdouble, SharedRuntime::dtan(jdouble x)) aoqi@0: double y[2],z=0.0; aoqi@0: int n, ix; aoqi@0: aoqi@0: /* High word of x. */ aoqi@0: ix = __HI(x); aoqi@0: aoqi@0: /* |x| ~< pi/4 */ aoqi@0: ix &= 0x7fffffff; aoqi@0: if(ix <= 0x3fe921fb) return __kernel_tan(x,z,1); aoqi@0: aoqi@0: /* tan(Inf or NaN) is NaN */ aoqi@0: else if (ix>=0x7ff00000) return x-x; /* NaN */ aoqi@0: aoqi@0: /* argument reduction needed */ aoqi@0: else { aoqi@0: n = __ieee754_rem_pio2(x,y); aoqi@0: return __kernel_tan(y[0],y[1],1-((n&1)<<1)); /* 1 -- n even aoqi@0: -1 -- n odd */ aoqi@0: } aoqi@0: JRT_END aoqi@0: aoqi@0: aoqi@0: #ifdef WIN32 aoqi@0: # pragma optimize ( "", on ) aoqi@0: #endif