e_rem_pio2f.c revision 151855
1/* e_rem_pio2f.c -- float version of e_rem_pio2.c 2 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. 3 */ 4 5/* 6 * ==================================================== 7 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 8 * 9 * Developed at SunPro, a Sun Microsystems, Inc. business. 10 * Permission to use, copy, modify, and distribute this 11 * software is freely granted, provided that this notice 12 * is preserved. 13 * ==================================================== 14 */ 15 16#ifndef lint 17static char rcsid[] = "$FreeBSD: head/lib/msun/src/e_rem_pio2f.c 151855 2005-10-29 08:15:29Z bde $"; 18#endif 19 20/* __ieee754_rem_pio2f(x,y) 21 * 22 * return the remainder of x rem pi/2 in y[0]+y[1] 23 * use __kernel_rem_pio2f() 24 */ 25 26#include "math.h" 27#include "math_private.h" 28 29/* Clip any extra precision in the float variable v. */ 30#define cliptofloat(v) (*(volatile float *)&(v)) 31 32/* 33 * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi 34 */ 35static const int32_t two_over_pi[] = { 360xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62, 370x95993C, 0x439041, 0xFE5163, 0xABDEBB, 0xC561B7, 0x246E3A, 380x424DD2, 0xE00649, 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129, 390xA73EE8, 0x8235F5, 0x2EBB44, 0x84E99C, 0x7026B4, 0x5F7E41, 400x3991D6, 0x398353, 0x39F49C, 0x845F8B, 0xBDF928, 0x3B1FF8, 410x97FFDE, 0x05980F, 0xEF2F11, 0x8B5A0A, 0x6D1F6D, 0x367ECF, 420x27CB09, 0xB74F46, 0x3F669E, 0x5FEA2D, 0x7527BA, 0xC7EBE5, 430xF17B3D, 0x0739F7, 0x8A5292, 0xEA6BFB, 0x5FB11F, 0x8D5D08, 440x560330, 0x46FC7B, 0x6BABF0, 0xCFBC20, 0x9AF436, 0x1DA9E3, 450x91615E, 0xE61B08, 0x659985, 0x5F14A0, 0x68408D, 0xFFD880, 460x4D7327, 0x310606, 0x1556CA, 0x73A8C9, 0x60E27B, 0xC08C6B, 47}; 48 49/* 50 * This array is like the one in e_rem_pio2.c, but the numbers are 51 * single precision and the last few bits (8 here) are ignored by 52 * masking them off in the float word instead of by omitting the low 53 * word. 54 * 55 * Masking off 8 bits is not enough, but we defer further masking to 56 * runtime so that the mask is easy to change. We now mask off 21 57 * bits, which is the smallest number that makes the "quick check no 58 * cancellation" detect all cancellations for cases that it is used. 59 * It doesn't detect all non-cancellations, especiallly for small 60 * multiples of pi/2, but then the non-quick code selects the best 61 * approximation of pi/2 to use. The result is that arg reduction is 62 * always done with between 8 or 9 and 17 bits of extra precision in 63 * the medium-multiple case. With only 8 bits masked of we had 64 * negative extra precision in some cases starting near +-13*pi/2. 65 */ 66static const int32_t npio2_hw[] = { 670x3fc90f00, 0x40490f00, 0x4096cb00, 0x40c90f00, 0x40fb5300, 0x4116cb00, 680x412fed00, 0x41490f00, 0x41623100, 0x417b5300, 0x418a3a00, 0x4196cb00, 690x41a35c00, 0x41afed00, 0x41bc7e00, 0x41c90f00, 0x41d5a000, 0x41e23100, 700x41eec200, 0x41fb5300, 0x4203f200, 0x420a3a00, 0x42108300, 0x4216cb00, 710x421d1400, 0x42235c00, 0x4229a500, 0x422fed00, 0x42363600, 0x423c7e00, 720x4242c700, 0x42490f00 73}; 74 75/* 76 * invpio2: 24 bits of 2/pi 77 * pio2_1: first 17 bit of pi/2 78 * pio2_1t: pi/2 - pio2_1 79 * pio2_2: second 17 bit of pi/2 80 * pio2_2t: pi/2 - (pio2_1+pio2_2) 81 * pio2_3: third 17 bit of pi/2 82 * pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3) 83 */ 84 85static const float 86zero = 0.0000000000e+00, /* 0x00000000 */ 87half = 5.0000000000e-01, /* 0x3f000000 */ 88invpio2 = 6.3661980629e-01, /* 0x3f22f984 */ 89pio2_1 = 1.5707855225e+00, /* 0x3fc90f80 */ 90pio2_1t = 1.0804334124e-05, /* 0x37354443 */ 91pio2_2 = 1.0804273188e-05, /* 0x37354400 */ 92pio2_2t = 6.0770999344e-11, /* 0x2e85a308 */ 93pio2_3 = 6.0770943833e-11, /* 0x2e85a300 */ 94pio2_3t = 6.1232342629e-17; /* 0x248d3132 */ 95 96static const double 97two24 = 1.67772160000000000000e+07; /* 0x41700000, 0x00000000 */ 98 99 int32_t __ieee754_rem_pio2f(float x, float *y) 100{ 101 double dz; 102 float z,w,t,r,fn; 103 double tx[3]; 104 int32_t e0,i,j,nx,n,ix,hx; 105 106 GET_FLOAT_WORD(hx,x); 107 ix = hx&0x7fffffff; 108 if(ix<=0x3f490fd8) /* |x| ~<= pi/4 , no need for reduction */ 109 {y[0] = x; y[1] = 0; return 0;} 110 if(ix<0x4016cbe4) { /* |x| < 3pi/4, special case with n=+-1 */ 111 if(hx>0) { 112 z = x - pio2_1; 113 if((ix&0xfffe0000)!=0x3fc80000) { /* 17+24 bit pi OK */ 114 y[0] = z - pio2_1t; 115 y[1] = (z-cliptofloat(y[0]))-pio2_1t; 116 } else { /* near pi/2, use 17+17+24 bit pi */ 117 z -= pio2_2; 118 y[0] = z - pio2_2t; 119 y[1] = (z-cliptofloat(y[0]))-pio2_2t; 120 } 121 return 1; 122 } else { /* negative x */ 123 z = x + pio2_1; 124 if((ix&0xfffe0000)!=0x3fc80000) { /* 17+24 bit pi OK */ 125 y[0] = z + pio2_1t; 126 y[1] = (z-cliptofloat(y[0]))+pio2_1t; 127 } else { /* near pi/2, use 17+17+24 bit pi */ 128 z += pio2_2; 129 y[0] = z + pio2_2t; 130 y[1] = (z-cliptofloat(y[0]))+pio2_2t; 131 } 132 return -1; 133 } 134 } 135 if(ix<=0x43490f80) { /* |x| ~<= 2^7*(pi/2), medium size */ 136 t = fabsf(x); 137 n = (int32_t) (t*invpio2+half); 138 fn = (float)n; 139 r = t-fn*pio2_1; 140 w = fn*pio2_1t; /* 1st round good to 40 bit */ 141 if(n<32&&(ix&0xffe00000)!=(npio2_hw[n-1]&0xffe00000)) { 142 y[0] = r-w; /* quick check no cancellation */ 143 } else { 144 u_int32_t high; 145 j = ix>>23; 146 y[0] = r-w; 147 GET_FLOAT_WORD(high,y[0]); 148 i = j-((high>>23)&0xff); 149 if(i>8) { /* 2nd iteration needed, good to 57 */ 150 t = r; 151 w = fn*pio2_2; 152 r = t-w; 153 w = fn*pio2_2t-((t-r)-w); 154 y[0] = r-w; 155 GET_FLOAT_WORD(high,y[0]); 156 i = j-((high>>23)&0xff); 157 if(i>25) { /* 3rd iteration need, 74 bits acc */ 158 t = r; /* will cover all possible cases */ 159 w = fn*pio2_3; 160 r = t-w; 161 w = fn*pio2_3t-((t-r)-w); 162 y[0] = r-w; 163 } 164 } 165 } 166 y[1] = (r-cliptofloat(y[0]))-w; 167 if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;} 168 else return n; 169 } 170 /* 171 * all other (large) arguments 172 */ 173 if(ix>=0x7f800000) { /* x is inf or NaN */ 174 y[0]=y[1]=x-x; return 0; 175 } 176#define z dz 177 /* set z = scalbn(|x|,ilogb(x)-23) */ 178 z = x; 179 GET_HIGH_WORD(hx,z); 180 ix = hx&0x7fffffff; 181 e0 = (ix>>20)-1046; /* e0 = ilogb(z)-23; */ 182 SET_HIGH_WORD(z, ix - ((int32_t)(e0<<20))); 183 for(i=0;i<2;i++) { 184 tx[i] = (double)((int32_t)(z)); 185 z = (z-tx[i])*two24; 186 } 187 tx[2] = z; 188 nx = 3; 189 while(tx[nx-1]==zero) nx--; /* skip zero term */ 190 n = __kernel_rem_pio2(tx,&z,e0,nx,1,two_over_pi); 191 y[0] = z; 192 y[1] = z - y[0]; 193 if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;} 194 return n; 195} 196