| |
| /* |
| * Copyright (c) 1998, 2001, Oracle and/or its affiliates. All rights reserved. |
| * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. |
| * |
| * This code is free software; you can redistribute it and/or modify it |
| * under the terms of the GNU General Public License version 2 only, as |
| * published by the Free Software Foundation. Oracle designates this |
| * particular file as subject to the "Classpath" exception as provided |
| * by Oracle in the LICENSE file that accompanied this code. |
| * |
| * This code is distributed in the hope that it will be useful, but WITHOUT |
| * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or |
| * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
| * version 2 for more details (a copy is included in the LICENSE file that |
| * accompanied this code). |
| * |
| * You should have received a copy of the GNU General Public License version |
| * 2 along with this work; if not, write to the Free Software Foundation, |
| * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. |
| * |
| * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA |
| * or visit www.oracle.com if you need additional information or have any |
| * questions. |
| */ |
| |
| /* __ieee754_rem_pio2(x,y) |
| * |
| * return the remainder of x rem pi/2 in y[0]+y[1] |
| * use __kernel_rem_pio2() |
| */ |
| |
| #include "fdlibm.h" |
| |
| /* |
| * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi |
| */ |
| #ifdef __STDC__ |
| static const int two_over_pi[] = { |
| #else |
| static int two_over_pi[] = { |
| #endif |
| 0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62, |
| 0x95993C, 0x439041, 0xFE5163, 0xABDEBB, 0xC561B7, 0x246E3A, |
| 0x424DD2, 0xE00649, 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129, |
| 0xA73EE8, 0x8235F5, 0x2EBB44, 0x84E99C, 0x7026B4, 0x5F7E41, |
| 0x3991D6, 0x398353, 0x39F49C, 0x845F8B, 0xBDF928, 0x3B1FF8, |
| 0x97FFDE, 0x05980F, 0xEF2F11, 0x8B5A0A, 0x6D1F6D, 0x367ECF, |
| 0x27CB09, 0xB74F46, 0x3F669E, 0x5FEA2D, 0x7527BA, 0xC7EBE5, |
| 0xF17B3D, 0x0739F7, 0x8A5292, 0xEA6BFB, 0x5FB11F, 0x8D5D08, |
| 0x560330, 0x46FC7B, 0x6BABF0, 0xCFBC20, 0x9AF436, 0x1DA9E3, |
| 0x91615E, 0xE61B08, 0x659985, 0x5F14A0, 0x68408D, 0xFFD880, |
| 0x4D7327, 0x310606, 0x1556CA, 0x73A8C9, 0x60E27B, 0xC08C6B, |
| }; |
| |
| #ifdef __STDC__ |
| static const int npio2_hw[] = { |
| #else |
| static int npio2_hw[] = { |
| #endif |
| 0x3FF921FB, 0x400921FB, 0x4012D97C, 0x401921FB, 0x401F6A7A, 0x4022D97C, |
| 0x4025FDBB, 0x402921FB, 0x402C463A, 0x402F6A7A, 0x4031475C, 0x4032D97C, |
| 0x40346B9C, 0x4035FDBB, 0x40378FDB, 0x403921FB, 0x403AB41B, 0x403C463A, |
| 0x403DD85A, 0x403F6A7A, 0x40407E4C, 0x4041475C, 0x4042106C, 0x4042D97C, |
| 0x4043A28C, 0x40446B9C, 0x404534AC, 0x4045FDBB, 0x4046C6CB, 0x40478FDB, |
| 0x404858EB, 0x404921FB, |
| }; |
| |
| /* |
| * invpio2: 53 bits of 2/pi |
| * pio2_1: first 33 bit of pi/2 |
| * pio2_1t: pi/2 - pio2_1 |
| * pio2_2: second 33 bit of pi/2 |
| * pio2_2t: pi/2 - (pio2_1+pio2_2) |
| * pio2_3: third 33 bit of pi/2 |
| * pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3) |
| */ |
| |
| #ifdef __STDC__ |
| static const double |
| #else |
| static double |
| #endif |
| zero = 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ |
| half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */ |
| two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */ |
| invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */ |
| pio2_1 = 1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */ |
| pio2_1t = 6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */ |
| pio2_2 = 6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */ |
| pio2_2t = 2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */ |
| pio2_3 = 2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */ |
| pio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */ |
| |
| #ifdef __STDC__ |
| int __ieee754_rem_pio2(double x, double *y) |
| #else |
| int __ieee754_rem_pio2(x,y) |
| double x,y[]; |
| #endif |
| { |
| double z,w,t,r,fn; |
| double tx[3]; |
| int e0,i,j,nx,n,ix,hx; |
| |
| hx = __HI(x); /* high word of x */ |
| ix = hx&0x7fffffff; |
| if(ix<=0x3fe921fb) /* |x| ~<= pi/4 , no need for reduction */ |
| {y[0] = x; y[1] = 0; return 0;} |
| if(ix<0x4002d97c) { /* |x| < 3pi/4, special case with n=+-1 */ |
| if(hx>0) { |
| z = x - pio2_1; |
| if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */ |
| y[0] = z - pio2_1t; |
| y[1] = (z-y[0])-pio2_1t; |
| } else { /* near pi/2, use 33+33+53 bit pi */ |
| z -= pio2_2; |
| y[0] = z - pio2_2t; |
| y[1] = (z-y[0])-pio2_2t; |
| } |
| return 1; |
| } else { /* negative x */ |
| z = x + pio2_1; |
| if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */ |
| y[0] = z + pio2_1t; |
| y[1] = (z-y[0])+pio2_1t; |
| } else { /* near pi/2, use 33+33+53 bit pi */ |
| z += pio2_2; |
| y[0] = z + pio2_2t; |
| y[1] = (z-y[0])+pio2_2t; |
| } |
| return -1; |
| } |
| } |
| if(ix<=0x413921fb) { /* |x| ~<= 2^19*(pi/2), medium size */ |
| t = fabs(x); |
| n = (int) (t*invpio2+half); |
| fn = (double)n; |
| r = t-fn*pio2_1; |
| w = fn*pio2_1t; /* 1st round good to 85 bit */ |
| if(n<32&&ix!=npio2_hw[n-1]) { |
| y[0] = r-w; /* quick check no cancellation */ |
| } else { |
| j = ix>>20; |
| y[0] = r-w; |
| i = j-(((__HI(y[0]))>>20)&0x7ff); |
| if(i>16) { /* 2nd iteration needed, good to 118 */ |
| t = r; |
| w = fn*pio2_2; |
| r = t-w; |
| w = fn*pio2_2t-((t-r)-w); |
| y[0] = r-w; |
| i = j-(((__HI(y[0]))>>20)&0x7ff); |
| if(i>49) { /* 3rd iteration need, 151 bits acc */ |
| t = r; /* will cover all possible cases */ |
| w = fn*pio2_3; |
| r = t-w; |
| w = fn*pio2_3t-((t-r)-w); |
| y[0] = r-w; |
| } |
| } |
| } |
| y[1] = (r-y[0])-w; |
| if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;} |
| else return n; |
| } |
| /* |
| * all other (large) arguments |
| */ |
| if(ix>=0x7ff00000) { /* x is inf or NaN */ |
| y[0]=y[1]=x-x; return 0; |
| } |
| /* set z = scalbn(|x|,ilogb(x)-23) */ |
| __LO(z) = __LO(x); |
| e0 = (ix>>20)-1046; /* e0 = ilogb(z)-23; */ |
| __HI(z) = ix - (e0<<20); |
| for(i=0;i<2;i++) { |
| tx[i] = (double)((int)(z)); |
| z = (z-tx[i])*two24; |
| } |
| tx[2] = z; |
| nx = 3; |
| while(tx[nx-1]==zero) nx--; /* skip zero term */ |
| n = __kernel_rem_pio2(tx,y,e0,nx,2,two_over_pi); |
| if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;} |
| return n; |
| } |
