1 2 /* @(#)k_rem_pio2.c 1.3 95/01/18 */ 3 /* 4 * ==================================================== 5 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 6 * 7 * Developed at SunSoft, a Sun Microsystems, Inc. business. 8 * Permission to use, copy, modify, and distribute this 9 * software is freely granted, provided that this notice 10 * is preserved. 11 * ==================================================== 12 */ 13 14 #include <sys/cdefs.h> 15 __FBSDID("$FreeBSD$"); 16 17 /* 18 * __kernel_rem_pio2(x,y,e0,nx,prec) 19 * double x[],y[]; int e0,nx,prec; 20 * 21 * __kernel_rem_pio2 return the last three digits of N with 22 * y = x - N*pi/2 23 * so that |y| < pi/2. 24 * 25 * The method is to compute the integer (mod 8) and fraction parts of 26 * (2/pi)*x without doing the full multiplication. In general we 27 * skip the part of the product that are known to be a huge integer ( 28 * more accurately, = 0 mod 8 ). Thus the number of operations are 29 * independent of the exponent of the input. 30 * 31 * (2/pi) is represented by an array of 24-bit integers in ipio2[]. 32 * 33 * Input parameters: 34 * x[] The input value (must be positive) is broken into nx 35 * pieces of 24-bit integers in double precision format. 36 * x[i] will be the i-th 24 bit of x. The scaled exponent 37 * of x[0] is given in input parameter e0 (i.e., x[0]*2^e0 38 * match x's up to 24 bits. 39 * 40 * Example of breaking a double positive z into x[0]+x[1]+x[2]: 41 * e0 = ilogb(z)-23 42 * z = scalbn(z,-e0) 43 * for i = 0,1,2 44 * x[i] = floor(z) 45 * z = (z-x[i])*2**24 46 * 47 * 48 * y[] ouput result in an array of double precision numbers. 49 * The dimension of y[] is: 50 * 24-bit precision 1 51 * 53-bit precision 2 52 * 64-bit precision 2 53 * 113-bit precision 3 54 * The actual value is the sum of them. Thus for 113-bit 55 * precison, one may have to do something like: 56 * 57 * long double t,w,r_head, r_tail; 58 * t = (long double)y[2] + (long double)y[1]; 59 * w = (long double)y[0]; 60 * r_head = t+w; 61 * r_tail = w - (r_head - t); 62 * 63 * e0 The exponent of x[0]. Must be <= 16360 or you need to 64 * expand the ipio2 table. 65 * 66 * nx dimension of x[] 67 * 68 * prec an integer indicating the precision: 69 * 0 24 bits (single) 70 * 1 53 bits (double) 71 * 2 64 bits (extended) 72 * 3 113 bits (quad) 73 * 74 * External function: 75 * double scalbn(), floor(); 76 * 77 * 78 * Here is the description of some local variables: 79 * 80 * jk jk+1 is the initial number of terms of ipio2[] needed 81 * in the computation. The recommended value is 2,3,4, 82 * 6 for single, double, extended,and quad. 83 * 84 * jz local integer variable indicating the number of 85 * terms of ipio2[] used. 86 * 87 * jx nx - 1 88 * 89 * jv index for pointing to the suitable ipio2[] for the 90 * computation. In general, we want 91 * ( 2^e0*x[0] * ipio2[jv-1]*2^(-24jv) )/8 92 * is an integer. Thus 93 * e0-3-24*jv >= 0 or (e0-3)/24 >= jv 94 * Hence jv = max(0,(e0-3)/24). 95 * 96 * jp jp+1 is the number of terms in PIo2[] needed, jp = jk. 97 * 98 * q[] double array with integral value, representing the 99 * 24-bits chunk of the product of x and 2/pi. 100 * 101 * q0 the corresponding exponent of q[0]. Note that the 102 * exponent for q[i] would be q0-24*i. 103 * 104 * PIo2[] double precision array, obtained by cutting pi/2 105 * into 24 bits chunks. 106 * 107 * f[] ipio2[] in floating point 108 * 109 * iq[] integer array by breaking up q[] in 24-bits chunk. 110 * 111 * fq[] final product of x*(2/pi) in fq[0],..,fq[jk] 112 * 113 * ih integer. If >0 it indicates q[] is >= 0.5, hence 114 * it also indicates the *sign* of the result. 115 * 116 */ 117 118 119 /* 120 * Constants: 121 * The hexadecimal values are the intended ones for the following 122 * constants. The decimal values may be used, provided that the 123 * compiler will convert from decimal to binary accurately enough 124 * to produce the hexadecimal values shown. 125 */ 126 127 #include <float.h> 128 129 #include "math.h" 130 #include "math_private.h" 131 132 static const int init_jk[] = {2,3,4,6}; /* initial value for jk */ 133 134 /* 135 * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi 136 * 137 * integer array, contains the (24*i)-th to (24*i+23)-th 138 * bit of 2/pi after binary point. The corresponding 139 * floating value is 140 * 141 * ipio2[i] * 2^(-24(i+1)). 142 * 143 * NB: This table must have at least (e0-3)/24 + jk terms. 144 * For quad precision (e0 <= 16360, jk = 6), this is 686. 145 */ 146 static const int32_t ipio2[] = { 147 0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62, 148 0x95993C, 0x439041, 0xFE5163, 0xABDEBB, 0xC561B7, 0x246E3A, 149 0x424DD2, 0xE00649, 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129, 150 0xA73EE8, 0x8235F5, 0x2EBB44, 0x84E99C, 0x7026B4, 0x5F7E41, 151 0x3991D6, 0x398353, 0x39F49C, 0x845F8B, 0xBDF928, 0x3B1FF8, 152 0x97FFDE, 0x05980F, 0xEF2F11, 0x8B5A0A, 0x6D1F6D, 0x367ECF, 153 0x27CB09, 0xB74F46, 0x3F669E, 0x5FEA2D, 0x7527BA, 0xC7EBE5, 154 0xF17B3D, 0x0739F7, 0x8A5292, 0xEA6BFB, 0x5FB11F, 0x8D5D08, 155 0x560330, 0x46FC7B, 0x6BABF0, 0xCFBC20, 0x9AF436, 0x1DA9E3, 156 0x91615E, 0xE61B08, 0x659985, 0x5F14A0, 0x68408D, 0xFFD880, 157 0x4D7327, 0x310606, 0x1556CA, 0x73A8C9, 0x60E27B, 0xC08C6B, 158 159 #if LDBL_MAX_EXP > 1024 160 #if LDBL_MAX_EXP > 16384 161 #error "ipio2 table needs to be expanded" 162 #endif 163 0x47C419, 0xC367CD, 0xDCE809, 0x2A8359, 0xC4768B, 0x961CA6, 164 0xDDAF44, 0xD15719, 0x053EA5, 0xFF0705, 0x3F7E33, 0xE832C2, 165 0xDE4F98, 0x327DBB, 0xC33D26, 0xEF6B1E, 0x5EF89F, 0x3A1F35, 166 0xCAF27F, 0x1D87F1, 0x21907C, 0x7C246A, 0xFA6ED5, 0x772D30, 167 0x433B15, 0xC614B5, 0x9D19C3, 0xC2C4AD, 0x414D2C, 0x5D000C, 168 0x467D86, 0x2D71E3, 0x9AC69B, 0x006233, 0x7CD2B4, 0x97A7B4, 169 0xD55537, 0xF63ED7, 0x1810A3, 0xFC764D, 0x2A9D64, 0xABD770, 170 0xF87C63, 0x57B07A, 0xE71517, 0x5649C0, 0xD9D63B, 0x3884A7, 171 0xCB2324, 0x778AD6, 0x23545A, 0xB91F00, 0x1B0AF1, 0xDFCE19, 172 0xFF319F, 0x6A1E66, 0x615799, 0x47FBAC, 0xD87F7E, 0xB76522, 173 0x89E832, 0x60BFE6, 0xCDC4EF, 0x09366C, 0xD43F5D, 0xD7DE16, 174 0xDE3B58, 0x929BDE, 0x2822D2, 0xE88628, 0x4D58E2, 0x32CAC6, 175 0x16E308, 0xCB7DE0, 0x50C017, 0xA71DF3, 0x5BE018, 0x34132E, 176 0x621283, 0x014883, 0x5B8EF5, 0x7FB0AD, 0xF2E91E, 0x434A48, 177 0xD36710, 0xD8DDAA, 0x425FAE, 0xCE616A, 0xA4280A, 0xB499D3, 178 0xF2A606, 0x7F775C, 0x83C2A3, 0x883C61, 0x78738A, 0x5A8CAF, 179 0xBDD76F, 0x63A62D, 0xCBBFF4, 0xEF818D, 0x67C126, 0x45CA55, 180 0x36D9CA, 0xD2A828, 0x8D61C2, 0x77C912, 0x142604, 0x9B4612, 181 0xC459C4, 0x44C5C8, 0x91B24D, 0xF31700, 0xAD43D4, 0xE54929, 182 0x10D5FD, 0xFCBE00, 0xCC941E, 0xEECE70, 0xF53E13, 0x80F1EC, 183 0xC3E7B3, 0x28F8C7, 0x940593, 0x3E71C1, 0xB3092E, 0xF3450B, 184 0x9C1288, 0x7B20AB, 0x9FB52E, 0xC29247, 0x2F327B, 0x6D550C, 185 0x90A772, 0x1FE76B, 0x96CB31, 0x4A1679, 0xE27941, 0x89DFF4, 186 0x9794E8, 0x84E6E2, 0x973199, 0x6BED88, 0x365F5F, 0x0EFDBB, 187 0xB49A48, 0x6CA467, 0x427271, 0x325D8D, 0xB8159F, 0x09E5BC, 188 0x25318D, 0x3974F7, 0x1C0530, 0x010C0D, 0x68084B, 0x58EE2C, 189 0x90AA47, 0x02E774, 0x24D6BD, 0xA67DF7, 0x72486E, 0xEF169F, 190 0xA6948E, 0xF691B4, 0x5153D1, 0xF20ACF, 0x339820, 0x7E4BF5, 191 0x6863B2, 0x5F3EDD, 0x035D40, 0x7F8985, 0x295255, 0xC06437, 192 0x10D86D, 0x324832, 0x754C5B, 0xD4714E, 0x6E5445, 0xC1090B, 193 0x69F52A, 0xD56614, 0x9D0727, 0x50045D, 0xDB3BB4, 0xC576EA, 194 0x17F987, 0x7D6B49, 0xBA271D, 0x296996, 0xACCCC6, 0x5414AD, 195 0x6AE290, 0x89D988, 0x50722C, 0xBEA404, 0x940777, 0x7030F3, 196 0x27FC00, 0xA871EA, 0x49C266, 0x3DE064, 0x83DD97, 0x973FA3, 197 0xFD9443, 0x8C860D, 0xDE4131, 0x9D3992, 0x8C70DD, 0xE7B717, 198 0x3BDF08, 0x2B3715, 0xA0805C, 0x93805A, 0x921110, 0xD8E80F, 199 0xAF806C, 0x4BFFDB, 0x0F9038, 0x761859, 0x15A562, 0xBBCB61, 200 0xB989C7, 0xBD4010, 0x04F2D2, 0x277549, 0xF6B6EB, 0xBB22DB, 201 0xAA140A, 0x2F2689, 0x768364, 0x333B09, 0x1A940E, 0xAA3A51, 202 0xC2A31D, 0xAEEDAF, 0x12265C, 0x4DC26D, 0x9C7A2D, 0x9756C0, 203 0x833F03, 0xF6F009, 0x8C402B, 0x99316D, 0x07B439, 0x15200C, 204 0x5BC3D8, 0xC492F5, 0x4BADC6, 0xA5CA4E, 0xCD37A7, 0x36A9E6, 205 0x9492AB, 0x6842DD, 0xDE6319, 0xEF8C76, 0x528B68, 0x37DBFC, 206 0xABA1AE, 0x3115DF, 0xA1AE00, 0xDAFB0C, 0x664D64, 0xB705ED, 207 0x306529, 0xBF5657, 0x3AFF47, 0xB9F96A, 0xF3BE75, 0xDF9328, 208 0x3080AB, 0xF68C66, 0x15CB04, 0x0622FA, 0x1DE4D9, 0xA4B33D, 209 0x8F1B57, 0x09CD36, 0xE9424E, 0xA4BE13, 0xB52333, 0x1AAAF0, 210 0xA8654F, 0xA5C1D2, 0x0F3F0B, 0xCD785B, 0x76F923, 0x048B7B, 211 0x721789, 0x53A6C6, 0xE26E6F, 0x00EBEF, 0x584A9B, 0xB7DAC4, 212 0xBA66AA, 0xCFCF76, 0x1D02D1, 0x2DF1B1, 0xC1998C, 0x77ADC3, 213 0xDA4886, 0xA05DF7, 0xF480C6, 0x2FF0AC, 0x9AECDD, 0xBC5C3F, 214 0x6DDED0, 0x1FC790, 0xB6DB2A, 0x3A25A3, 0x9AAF00, 0x9353AD, 215 0x0457B6, 0xB42D29, 0x7E804B, 0xA707DA, 0x0EAA76, 0xA1597B, 216 0x2A1216, 0x2DB7DC, 0xFDE5FA, 0xFEDB89, 0xFDBE89, 0x6C76E4, 217 0xFCA906, 0x70803E, 0x156E85, 0xFF87FD, 0x073E28, 0x336761, 218 0x86182A, 0xEABD4D, 0xAFE7B3, 0x6E6D8F, 0x396795, 0x5BBF31, 219 0x48D784, 0x16DF30, 0x432DC7, 0x356125, 0xCE70C9, 0xB8CB30, 220 0xFD6CBF, 0xA200A4, 0xE46C05, 0xA0DD5A, 0x476F21, 0xD21262, 221 0x845CB9, 0x496170, 0xE0566B, 0x015299, 0x375550, 0xB7D51E, 222 0xC4F133, 0x5F6E13, 0xE4305D, 0xA92E85, 0xC3B21D, 0x3632A1, 223 0xA4B708, 0xD4B1EA, 0x21F716, 0xE4698F, 0x77FF27, 0x80030C, 224 0x2D408D, 0xA0CD4F, 0x99A520, 0xD3A2B3, 0x0A5D2F, 0x42F9B4, 225 0xCBDA11, 0xD0BE7D, 0xC1DB9B, 0xBD17AB, 0x81A2CA, 0x5C6A08, 226 0x17552E, 0x550027, 0xF0147F, 0x8607E1, 0x640B14, 0x8D4196, 227 0xDEBE87, 0x2AFDDA, 0xB6256B, 0x34897B, 0xFEF305, 0x9EBFB9, 228 0x4F6A68, 0xA82A4A, 0x5AC44F, 0xBCF82D, 0x985AD7, 0x95C7F4, 229 0x8D4D0D, 0xA63A20, 0x5F57A4, 0xB13F14, 0x953880, 0x0120CC, 230 0x86DD71, 0xB6DEC9, 0xF560BF, 0x11654D, 0x6B0701, 0xACB08C, 231 0xD0C0B2, 0x485551, 0x0EFB1E, 0xC37295, 0x3B06A3, 0x3540C0, 232 0x7BDC06, 0xCC45E0, 0xFA294E, 0xC8CAD6, 0x41F3E8, 0xDE647C, 233 0xD8649B, 0x31BED9, 0xC397A4, 0xD45877, 0xC5E369, 0x13DAF0, 234 0x3C3ABA, 0x461846, 0x5F7555, 0xF5BDD2, 0xC6926E, 0x5D2EAC, 235 0xED440E, 0x423E1C, 0x87C461, 0xE9FD29, 0xF3D6E7, 0xCA7C22, 236 0x35916F, 0xC5E008, 0x8DD7FF, 0xE26A6E, 0xC6FDB0, 0xC10893, 237 0x745D7C, 0xB2AD6B, 0x9D6ECD, 0x7B723E, 0x6A11C6, 0xA9CFF7, 238 0xDF7329, 0xBAC9B5, 0x5100B7, 0x0DB2E2, 0x24BA74, 0x607DE5, 239 0x8AD874, 0x2C150D, 0x0C1881, 0x94667E, 0x162901, 0x767A9F, 240 0xBEFDFD, 0xEF4556, 0x367ED9, 0x13D9EC, 0xB9BA8B, 0xFC97C4, 241 0x27A831, 0xC36EF1, 0x36C594, 0x56A8D8, 0xB5A8B4, 0x0ECCCF, 242 0x2D8912, 0x34576F, 0x89562C, 0xE3CE99, 0xB920D6, 0xAA5E6B, 243 0x9C2A3E, 0xCC5F11, 0x4A0BFD, 0xFBF4E1, 0x6D3B8E, 0x2C86E2, 244 0x84D4E9, 0xA9B4FC, 0xD1EEEF, 0xC9352E, 0x61392F, 0x442138, 245 0xC8D91B, 0x0AFC81, 0x6A4AFB, 0xD81C2F, 0x84B453, 0x8C994E, 246 0xCC2254, 0xDC552A, 0xD6C6C0, 0x96190B, 0xB8701A, 0x649569, 247 0x605A26, 0xEE523F, 0x0F117F, 0x11B5F4, 0xF5CBFC, 0x2DBC34, 248 0xEEBC34, 0xCC5DE8, 0x605EDD, 0x9B8E67, 0xEF3392, 0xB817C9, 249 0x9B5861, 0xBC57E1, 0xC68351, 0x103ED8, 0x4871DD, 0xDD1C2D, 250 0xA118AF, 0x462C21, 0xD7F359, 0x987AD9, 0xC0549E, 0xFA864F, 251 0xFC0656, 0xAE79E5, 0x362289, 0x22AD38, 0xDC9367, 0xAAE855, 252 0x382682, 0x9BE7CA, 0xA40D51, 0xB13399, 0x0ED7A9, 0x480569, 253 0xF0B265, 0xA7887F, 0x974C88, 0x36D1F9, 0xB39221, 0x4A827B, 254 0x21CF98, 0xDC9F40, 0x5547DC, 0x3A74E1, 0x42EB67, 0xDF9DFE, 255 0x5FD45E, 0xA4677B, 0x7AACBA, 0xA2F655, 0x23882B, 0x55BA41, 256 0x086E59, 0x862A21, 0x834739, 0xE6E389, 0xD49EE5, 0x40FB49, 257 0xE956FF, 0xCA0F1C, 0x8A59C5, 0x2BFA94, 0xC5C1D3, 0xCFC50F, 258 0xAE5ADB, 0x86C547, 0x624385, 0x3B8621, 0x94792C, 0x876110, 259 0x7B4C2A, 0x1A2C80, 0x12BF43, 0x902688, 0x893C78, 0xE4C4A8, 260 0x7BDBE5, 0xC23AC4, 0xEAF426, 0x8A67F7, 0xBF920D, 0x2BA365, 261 0xB1933D, 0x0B7CBD, 0xDC51A4, 0x63DD27, 0xDDE169, 0x19949A, 262 0x9529A8, 0x28CE68, 0xB4ED09, 0x209F44, 0xCA984E, 0x638270, 263 0x237C7E, 0x32B90F, 0x8EF5A7, 0xE75614, 0x08F121, 0x2A9DB5, 264 0x4D7E6F, 0x5119A5, 0xABF9B5, 0xD6DF82, 0x61DD96, 0x023616, 265 0x9F3AC4, 0xA1A283, 0x6DED72, 0x7A8D39, 0xA9B882, 0x5C326B, 266 0x5B2746, 0xED3400, 0x7700D2, 0x55F4FC, 0x4D5901, 0x8071E0, 267 #endif 268 269 }; 270 271 static const double PIo2[] = { 272 1.57079625129699707031e+00, /* 0x3FF921FB, 0x40000000 */ 273 7.54978941586159635335e-08, /* 0x3E74442D, 0x00000000 */ 274 5.39030252995776476554e-15, /* 0x3CF84698, 0x80000000 */ 275 3.28200341580791294123e-22, /* 0x3B78CC51, 0x60000000 */ 276 1.27065575308067607349e-29, /* 0x39F01B83, 0x80000000 */ 277 1.22933308981111328932e-36, /* 0x387A2520, 0x40000000 */ 278 2.73370053816464559624e-44, /* 0x36E38222, 0x80000000 */ 279 2.16741683877804819444e-51, /* 0x3569F31D, 0x00000000 */ 280 }; 281 282 static const double 283 zero = 0.0, 284 one = 1.0, 285 two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */ 286 twon24 = 5.96046447753906250000e-08; /* 0x3E700000, 0x00000000 */ 287 288 int 289 __kernel_rem_pio2(double *x, double *y, int e0, int nx, int prec) 290 { 291 int32_t jz,jx,jv,jp,jk,carry,n,iq[20],i,j,k,m,q0,ih; 292 double z,fw,f[20],fq[20],q[20]; 293 294 /* initialize jk*/ 295 jk = init_jk[prec]; 296 jp = jk; 297 298 /* determine jx,jv,q0, note that 3>q0 */ 299 jx = nx-1; 300 jv = (e0-3)/24; if(jv<0) jv=0; 301 q0 = e0-24*(jv+1); 302 303 /* set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk] */ 304 j = jv-jx; m = jx+jk; 305 for(i=0;i<=m;i++,j++) f[i] = (j<0)? zero : (double) ipio2[j]; 306 307 /* compute q[0],q[1],...q[jk] */ 308 for (i=0;i<=jk;i++) { 309 for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; q[i] = fw; 310 } 311 312 jz = jk; 313 recompute: 314 /* distill q[] into iq[] reversingly */ 315 for(i=0,j=jz,z=q[jz];j>0;i++,j--) { 316 fw = (double)((int32_t)(twon24* z)); 317 iq[i] = (int32_t)(z-two24*fw); 318 z = q[j-1]+fw; 319 } 320 321 /* compute n */ 322 z = scalbn(z,q0); /* actual value of z */ 323 z -= 8.0*floor(z*0.125); /* trim off integer >= 8 */ 324 n = (int32_t) z; 325 z -= (double)n; 326 ih = 0; 327 if(q0>0) { /* need iq[jz-1] to determine n */ 328 i = (iq[jz-1]>>(24-q0)); n += i; 329 iq[jz-1] -= i<<(24-q0); 330 ih = iq[jz-1]>>(23-q0); 331 } 332 else if(q0==0) ih = iq[jz-1]>>23; 333 else if(z>=0.5) ih=2; 334 335 if(ih>0) { /* q > 0.5 */ 336 n += 1; carry = 0; 337 for(i=0;i<jz ;i++) { /* compute 1-q */ 338 j = iq[i]; 339 if(carry==0) { 340 if(j!=0) { 341 carry = 1; iq[i] = 0x1000000- j; 342 } 343 } else iq[i] = 0xffffff - j; 344 } 345 if(q0>0) { /* rare case: chance is 1 in 12 */ 346 switch(q0) { 347 case 1: 348 iq[jz-1] &= 0x7fffff; break; 349 case 2: 350 iq[jz-1] &= 0x3fffff; break; 351 } 352 } 353 if(ih==2) { 354 z = one - z; 355 if(carry!=0) z -= scalbn(one,q0); 356 } 357 } 358 359 /* check if recomputation is needed */ 360 if(z==zero) { 361 j = 0; 362 for (i=jz-1;i>=jk;i--) j |= iq[i]; 363 if(j==0) { /* need recomputation */ 364 for(k=1;iq[jk-k]==0;k++); /* k = no. of terms needed */ 365 366 for(i=jz+1;i<=jz+k;i++) { /* add q[jz+1] to q[jz+k] */ 367 f[jx+i] = (double) ipio2[jv+i]; 368 for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; 369 q[i] = fw; 370 } 371 jz += k; 372 goto recompute; 373 } 374 } 375 376 /* chop off zero terms */ 377 if(z==0.0) { 378 jz -= 1; q0 -= 24; 379 while(iq[jz]==0) { jz--; q0-=24;} 380 } else { /* break z into 24-bit if necessary */ 381 z = scalbn(z,-q0); 382 if(z>=two24) { 383 fw = (double)((int32_t)(twon24*z)); 384 iq[jz] = (int32_t)(z-two24*fw); 385 jz += 1; q0 += 24; 386 iq[jz] = (int32_t) fw; 387 } else iq[jz] = (int32_t) z ; 388 } 389 390 /* convert integer "bit" chunk to floating-point value */ 391 fw = scalbn(one,q0); 392 for(i=jz;i>=0;i--) { 393 q[i] = fw*(double)iq[i]; fw*=twon24; 394 } 395 396 /* compute PIo2[0,...,jp]*q[jz,...,0] */ 397 for(i=jz;i>=0;i--) { 398 for(fw=0.0,k=0;k<=jp&&k<=jz-i;k++) fw += PIo2[k]*q[i+k]; 399 fq[jz-i] = fw; 400 } 401 402 /* compress fq[] into y[] */ 403 switch(prec) { 404 case 0: 405 fw = 0.0; 406 for (i=jz;i>=0;i--) fw += fq[i]; 407 y[0] = (ih==0)? fw: -fw; 408 break; 409 case 1: 410 case 2: 411 fw = 0.0; 412 for (i=jz;i>=0;i--) fw += fq[i]; 413 STRICT_ASSIGN(double,fw,fw); 414 y[0] = (ih==0)? fw: -fw; 415 fw = fq[0]-fw; 416 for (i=1;i<=jz;i++) fw += fq[i]; 417 y[1] = (ih==0)? fw: -fw; 418 break; 419 case 3: /* painful */ 420 for (i=jz;i>0;i--) { 421 fw = fq[i-1]+fq[i]; 422 fq[i] += fq[i-1]-fw; 423 fq[i-1] = fw; 424 } 425 for (i=jz;i>1;i--) { 426 fw = fq[i-1]+fq[i]; 427 fq[i] += fq[i-1]-fw; 428 fq[i-1] = fw; 429 } 430 for (fw=0.0,i=jz;i>=2;i--) fw += fq[i]; 431 if(ih==0) { 432 y[0] = fq[0]; y[1] = fq[1]; y[2] = fw; 433 } else { 434 y[0] = -fq[0]; y[1] = -fq[1]; y[2] = -fw; 435 } 436 } 437 return n&7; 438 } 439