1 /* @(#)k_rem_pio2.c 5.1 93/09/24 */ 2 /* 3 * ==================================================== 4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 5 * 6 * Developed at SunPro, a Sun Microsystems, Inc. business. 7 * Permission to use, copy, modify, and distribute this 8 * software is freely granted, provided that this notice 9 * is preserved. 10 * ==================================================== 11 */ 12 13 /* 14 * __kernel_rem_pio2(x,y,e0,nx,prec) 15 * double x[],y[]; int e0,nx,prec; 16 * 17 * __kernel_rem_pio2 return the last three digits of N with 18 * y = x - N*pi/2 19 * so that |y| < pi/2. 20 * 21 * The method is to compute the integer (mod 8) and fraction parts of 22 * (2/pi)*x without doing the full multiplication. In general we 23 * skip the part of the product that are known to be a huge integer ( 24 * more accurately, = 0 mod 8 ). Thus the number of operations are 25 * independent of the exponent of the input. 26 * 27 * (2/pi) is represented by an array of 24-bit integers in ipio2[]. 28 * 29 * Input parameters: 30 * x[] The input value (must be positive) is broken into nx 31 * pieces of 24-bit integers in double precision format. 32 * x[i] will be the i-th 24 bit of x. The scaled exponent 33 * of x[0] is given in input parameter e0 (i.e., x[0]*2^e0 34 * match x's up to 24 bits. 35 * 36 * Example of breaking a double positive z into x[0]+x[1]+x[2]: 37 * e0 = ilogb(z)-23 38 * z = scalbn(z,-e0) 39 * for i = 0,1,2 40 * x[i] = floor(z) 41 * z = (z-x[i])*2**24 42 * 43 * 44 * y[] output result in an array of double precision numbers. 45 * The dimension of y[] is: 46 * 24-bit precision 1 47 * 53-bit precision 2 48 * 64-bit precision 2 49 * 113-bit precision 3 50 * The actual value is the sum of them. Thus for 113-bit 51 * precison, one may have to do something like: 52 * 53 * long double t,w,r_head, r_tail; 54 * t = (long double)y[2] + (long double)y[1]; 55 * w = (long double)y[0]; 56 * r_head = t+w; 57 * r_tail = w - (r_head - t); 58 * 59 * e0 The exponent of x[0]. Must be <= 16360 or you need to 60 * expand the ipio2 table. 61 * 62 * nx dimension of x[] 63 * 64 * prec an integer indicating the precision: 65 * 0 24 bits (single) 66 * 1 53 bits (double) 67 * 2 64 bits (extended) 68 * 3 113 bits (quad) 69 * 70 * External function: 71 * double scalbn(), floor(); 72 * 73 * 74 * Here is the description of some local variables: 75 * 76 * jk jk+1 is the initial number of terms of ipio2[] needed 77 * in the computation. The recommended value is 2,3,4, 78 * 6 for single, double, extended,and quad. 79 * 80 * jz local integer variable indicating the number of 81 * terms of ipio2[] used. 82 * 83 * jx nx - 1 84 * 85 * jv index for pointing to the suitable ipio2[] for the 86 * computation. In general, we want 87 * ( 2^e0*x[0] * ipio2[jv-1]*2^(-24jv) )/8 88 * is an integer. Thus 89 * e0-3-24*jv >= 0 or (e0-3)/24 >= jv 90 * Hence jv = max(0,(e0-3)/24). 91 * 92 * jp jp+1 is the number of terms in PIo2[] needed, jp = jk. 93 * 94 * q[] double array with integral value, representing the 95 * 24-bits chunk of the product of x and 2/pi. 96 * 97 * q0 the corresponding exponent of q[0]. Note that the 98 * exponent for q[i] would be q0-24*i. 99 * 100 * PIo2[] double precision array, obtained by cutting pi/2 101 * into 24 bits chunks. 102 * 103 * f[] ipio2[] in floating point 104 * 105 * iq[] integer array by breaking up q[] in 24-bits chunk. 106 * 107 * fq[] final product of x*(2/pi) in fq[0],..,fq[jk] 108 * 109 * ih integer. If >0 it indicates q[] is >= 0.5, hence 110 * it also indicates the *sign* of the result. 111 * 112 */ 113 114 115 /* 116 * Constants: 117 * The hexadecimal values are the intended ones for the following 118 * constants. The decimal values may be used, provided that the 119 * compiler will convert from decimal to binary accurately enough 120 * to produce the hexadecimal values shown. 121 */ 122 123 #include <float.h> 124 #include <math.h> 125 126 #include "math_private.h" 127 128 static const int init_jk[] = {2,3,4,6}; /* initial value for jk */ 129 130 /* 131 * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi 132 * 133 * integer array, contains the (24*i)-th to (24*i+23)-th 134 * bit of 2/pi after binary point. The corresponding 135 * floating value is 136 * 137 * ipio2[i] * 2^(-24(i+1)). 138 * 139 * NB: This table must have at least (e0-3)/24 + jk terms. 140 * For quad precision (e0 <= 16360, jk = 6), this is 686. 141 */ 142 static const int32_t ipio2[] = { 143 0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62, 144 0x95993C, 0x439041, 0xFE5163, 0xABDEBB, 0xC561B7, 0x246E3A, 145 0x424DD2, 0xE00649, 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129, 146 0xA73EE8, 0x8235F5, 0x2EBB44, 0x84E99C, 0x7026B4, 0x5F7E41, 147 0x3991D6, 0x398353, 0x39F49C, 0x845F8B, 0xBDF928, 0x3B1FF8, 148 0x97FFDE, 0x05980F, 0xEF2F11, 0x8B5A0A, 0x6D1F6D, 0x367ECF, 149 0x27CB09, 0xB74F46, 0x3F669E, 0x5FEA2D, 0x7527BA, 0xC7EBE5, 150 0xF17B3D, 0x0739F7, 0x8A5292, 0xEA6BFB, 0x5FB11F, 0x8D5D08, 151 0x560330, 0x46FC7B, 0x6BABF0, 0xCFBC20, 0x9AF436, 0x1DA9E3, 152 0x91615E, 0xE61B08, 0x659985, 0x5F14A0, 0x68408D, 0xFFD880, 153 0x4D7327, 0x310606, 0x1556CA, 0x73A8C9, 0x60E27B, 0xC08C6B, 154 155 #if LDBL_MAX_EXP > 1024 156 #if LDBL_MAX_EXP > 16384 157 #error "ipio2 table needs to be expanded" 158 #endif 159 0x47C419, 0xC367CD, 0xDCE809, 0x2A8359, 0xC4768B, 0x961CA6, 160 0xDDAF44, 0xD15719, 0x053EA5, 0xFF0705, 0x3F7E33, 0xE832C2, 161 0xDE4F98, 0x327DBB, 0xC33D26, 0xEF6B1E, 0x5EF89F, 0x3A1F35, 162 0xCAF27F, 0x1D87F1, 0x21907C, 0x7C246A, 0xFA6ED5, 0x772D30, 163 0x433B15, 0xC614B5, 0x9D19C3, 0xC2C4AD, 0x414D2C, 0x5D000C, 164 0x467D86, 0x2D71E3, 0x9AC69B, 0x006233, 0x7CD2B4, 0x97A7B4, 165 0xD55537, 0xF63ED7, 0x1810A3, 0xFC764D, 0x2A9D64, 0xABD770, 166 0xF87C63, 0x57B07A, 0xE71517, 0x5649C0, 0xD9D63B, 0x3884A7, 167 0xCB2324, 0x778AD6, 0x23545A, 0xB91F00, 0x1B0AF1, 0xDFCE19, 168 0xFF319F, 0x6A1E66, 0x615799, 0x47FBAC, 0xD87F7E, 0xB76522, 169 0x89E832, 0x60BFE6, 0xCDC4EF, 0x09366C, 0xD43F5D, 0xD7DE16, 170 0xDE3B58, 0x929BDE, 0x2822D2, 0xE88628, 0x4D58E2, 0x32CAC6, 171 0x16E308, 0xCB7DE0, 0x50C017, 0xA71DF3, 0x5BE018, 0x34132E, 172 0x621283, 0x014883, 0x5B8EF5, 0x7FB0AD, 0xF2E91E, 0x434A48, 173 0xD36710, 0xD8DDAA, 0x425FAE, 0xCE616A, 0xA4280A, 0xB499D3, 174 0xF2A606, 0x7F775C, 0x83C2A3, 0x883C61, 0x78738A, 0x5A8CAF, 175 0xBDD76F, 0x63A62D, 0xCBBFF4, 0xEF818D, 0x67C126, 0x45CA55, 176 0x36D9CA, 0xD2A828, 0x8D61C2, 0x77C912, 0x142604, 0x9B4612, 177 0xC459C4, 0x44C5C8, 0x91B24D, 0xF31700, 0xAD43D4, 0xE54929, 178 0x10D5FD, 0xFCBE00, 0xCC941E, 0xEECE70, 0xF53E13, 0x80F1EC, 179 0xC3E7B3, 0x28F8C7, 0x940593, 0x3E71C1, 0xB3092E, 0xF3450B, 180 0x9C1288, 0x7B20AB, 0x9FB52E, 0xC29247, 0x2F327B, 0x6D550C, 181 0x90A772, 0x1FE76B, 0x96CB31, 0x4A1679, 0xE27941, 0x89DFF4, 182 0x9794E8, 0x84E6E2, 0x973199, 0x6BED88, 0x365F5F, 0x0EFDBB, 183 0xB49A48, 0x6CA467, 0x427271, 0x325D8D, 0xB8159F, 0x09E5BC, 184 0x25318D, 0x3974F7, 0x1C0530, 0x010C0D, 0x68084B, 0x58EE2C, 185 0x90AA47, 0x02E774, 0x24D6BD, 0xA67DF7, 0x72486E, 0xEF169F, 186 0xA6948E, 0xF691B4, 0x5153D1, 0xF20ACF, 0x339820, 0x7E4BF5, 187 0x6863B2, 0x5F3EDD, 0x035D40, 0x7F8985, 0x295255, 0xC06437, 188 0x10D86D, 0x324832, 0x754C5B, 0xD4714E, 0x6E5445, 0xC1090B, 189 0x69F52A, 0xD56614, 0x9D0727, 0x50045D, 0xDB3BB4, 0xC576EA, 190 0x17F987, 0x7D6B49, 0xBA271D, 0x296996, 0xACCCC6, 0x5414AD, 191 0x6AE290, 0x89D988, 0x50722C, 0xBEA404, 0x940777, 0x7030F3, 192 0x27FC00, 0xA871EA, 0x49C266, 0x3DE064, 0x83DD97, 0x973FA3, 193 0xFD9443, 0x8C860D, 0xDE4131, 0x9D3992, 0x8C70DD, 0xE7B717, 194 0x3BDF08, 0x2B3715, 0xA0805C, 0x93805A, 0x921110, 0xD8E80F, 195 0xAF806C, 0x4BFFDB, 0x0F9038, 0x761859, 0x15A562, 0xBBCB61, 196 0xB989C7, 0xBD4010, 0x04F2D2, 0x277549, 0xF6B6EB, 0xBB22DB, 197 0xAA140A, 0x2F2689, 0x768364, 0x333B09, 0x1A940E, 0xAA3A51, 198 0xC2A31D, 0xAEEDAF, 0x12265C, 0x4DC26D, 0x9C7A2D, 0x9756C0, 199 0x833F03, 0xF6F009, 0x8C402B, 0x99316D, 0x07B439, 0x15200C, 200 0x5BC3D8, 0xC492F5, 0x4BADC6, 0xA5CA4E, 0xCD37A7, 0x36A9E6, 201 0x9492AB, 0x6842DD, 0xDE6319, 0xEF8C76, 0x528B68, 0x37DBFC, 202 0xABA1AE, 0x3115DF, 0xA1AE00, 0xDAFB0C, 0x664D64, 0xB705ED, 203 0x306529, 0xBF5657, 0x3AFF47, 0xB9F96A, 0xF3BE75, 0xDF9328, 204 0x3080AB, 0xF68C66, 0x15CB04, 0x0622FA, 0x1DE4D9, 0xA4B33D, 205 0x8F1B57, 0x09CD36, 0xE9424E, 0xA4BE13, 0xB52333, 0x1AAAF0, 206 0xA8654F, 0xA5C1D2, 0x0F3F0B, 0xCD785B, 0x76F923, 0x048B7B, 207 0x721789, 0x53A6C6, 0xE26E6F, 0x00EBEF, 0x584A9B, 0xB7DAC4, 208 0xBA66AA, 0xCFCF76, 0x1D02D1, 0x2DF1B1, 0xC1998C, 0x77ADC3, 209 0xDA4886, 0xA05DF7, 0xF480C6, 0x2FF0AC, 0x9AECDD, 0xBC5C3F, 210 0x6DDED0, 0x1FC790, 0xB6DB2A, 0x3A25A3, 0x9AAF00, 0x9353AD, 211 0x0457B6, 0xB42D29, 0x7E804B, 0xA707DA, 0x0EAA76, 0xA1597B, 212 0x2A1216, 0x2DB7DC, 0xFDE5FA, 0xFEDB89, 0xFDBE89, 0x6C76E4, 213 0xFCA906, 0x70803E, 0x156E85, 0xFF87FD, 0x073E28, 0x336761, 214 0x86182A, 0xEABD4D, 0xAFE7B3, 0x6E6D8F, 0x396795, 0x5BBF31, 215 0x48D784, 0x16DF30, 0x432DC7, 0x356125, 0xCE70C9, 0xB8CB30, 216 0xFD6CBF, 0xA200A4, 0xE46C05, 0xA0DD5A, 0x476F21, 0xD21262, 217 0x845CB9, 0x496170, 0xE0566B, 0x015299, 0x375550, 0xB7D51E, 218 0xC4F133, 0x5F6E13, 0xE4305D, 0xA92E85, 0xC3B21D, 0x3632A1, 219 0xA4B708, 0xD4B1EA, 0x21F716, 0xE4698F, 0x77FF27, 0x80030C, 220 0x2D408D, 0xA0CD4F, 0x99A520, 0xD3A2B3, 0x0A5D2F, 0x42F9B4, 221 0xCBDA11, 0xD0BE7D, 0xC1DB9B, 0xBD17AB, 0x81A2CA, 0x5C6A08, 222 0x17552E, 0x550027, 0xF0147F, 0x8607E1, 0x640B14, 0x8D4196, 223 0xDEBE87, 0x2AFDDA, 0xB6256B, 0x34897B, 0xFEF305, 0x9EBFB9, 224 0x4F6A68, 0xA82A4A, 0x5AC44F, 0xBCF82D, 0x985AD7, 0x95C7F4, 225 0x8D4D0D, 0xA63A20, 0x5F57A4, 0xB13F14, 0x953880, 0x0120CC, 226 0x86DD71, 0xB6DEC9, 0xF560BF, 0x11654D, 0x6B0701, 0xACB08C, 227 0xD0C0B2, 0x485551, 0x0EFB1E, 0xC37295, 0x3B06A3, 0x3540C0, 228 0x7BDC06, 0xCC45E0, 0xFA294E, 0xC8CAD6, 0x41F3E8, 0xDE647C, 229 0xD8649B, 0x31BED9, 0xC397A4, 0xD45877, 0xC5E369, 0x13DAF0, 230 0x3C3ABA, 0x461846, 0x5F7555, 0xF5BDD2, 0xC6926E, 0x5D2EAC, 231 0xED440E, 0x423E1C, 0x87C461, 0xE9FD29, 0xF3D6E7, 0xCA7C22, 232 0x35916F, 0xC5E008, 0x8DD7FF, 0xE26A6E, 0xC6FDB0, 0xC10893, 233 0x745D7C, 0xB2AD6B, 0x9D6ECD, 0x7B723E, 0x6A11C6, 0xA9CFF7, 234 0xDF7329, 0xBAC9B5, 0x5100B7, 0x0DB2E2, 0x24BA74, 0x607DE5, 235 0x8AD874, 0x2C150D, 0x0C1881, 0x94667E, 0x162901, 0x767A9F, 236 0xBEFDFD, 0xEF4556, 0x367ED9, 0x13D9EC, 0xB9BA8B, 0xFC97C4, 237 0x27A831, 0xC36EF1, 0x36C594, 0x56A8D8, 0xB5A8B4, 0x0ECCCF, 238 0x2D8912, 0x34576F, 0x89562C, 0xE3CE99, 0xB920D6, 0xAA5E6B, 239 0x9C2A3E, 0xCC5F11, 0x4A0BFD, 0xFBF4E1, 0x6D3B8E, 0x2C86E2, 240 0x84D4E9, 0xA9B4FC, 0xD1EEEF, 0xC9352E, 0x61392F, 0x442138, 241 0xC8D91B, 0x0AFC81, 0x6A4AFB, 0xD81C2F, 0x84B453, 0x8C994E, 242 0xCC2254, 0xDC552A, 0xD6C6C0, 0x96190B, 0xB8701A, 0x649569, 243 0x605A26, 0xEE523F, 0x0F117F, 0x11B5F4, 0xF5CBFC, 0x2DBC34, 244 0xEEBC34, 0xCC5DE8, 0x605EDD, 0x9B8E67, 0xEF3392, 0xB817C9, 245 0x9B5861, 0xBC57E1, 0xC68351, 0x103ED8, 0x4871DD, 0xDD1C2D, 246 0xA118AF, 0x462C21, 0xD7F359, 0x987AD9, 0xC0549E, 0xFA864F, 247 0xFC0656, 0xAE79E5, 0x362289, 0x22AD38, 0xDC9367, 0xAAE855, 248 0x382682, 0x9BE7CA, 0xA40D51, 0xB13399, 0x0ED7A9, 0x480569, 249 0xF0B265, 0xA7887F, 0x974C88, 0x36D1F9, 0xB39221, 0x4A827B, 250 0x21CF98, 0xDC9F40, 0x5547DC, 0x3A74E1, 0x42EB67, 0xDF9DFE, 251 0x5FD45E, 0xA4677B, 0x7AACBA, 0xA2F655, 0x23882B, 0x55BA41, 252 0x086E59, 0x862A21, 0x834739, 0xE6E389, 0xD49EE5, 0x40FB49, 253 0xE956FF, 0xCA0F1C, 0x8A59C5, 0x2BFA94, 0xC5C1D3, 0xCFC50F, 254 0xAE5ADB, 0x86C547, 0x624385, 0x3B8621, 0x94792C, 0x876110, 255 0x7B4C2A, 0x1A2C80, 0x12BF43, 0x902688, 0x893C78, 0xE4C4A8, 256 0x7BDBE5, 0xC23AC4, 0xEAF426, 0x8A67F7, 0xBF920D, 0x2BA365, 257 0xB1933D, 0x0B7CBD, 0xDC51A4, 0x63DD27, 0xDDE169, 0x19949A, 258 0x9529A8, 0x28CE68, 0xB4ED09, 0x209F44, 0xCA984E, 0x638270, 259 0x237C7E, 0x32B90F, 0x8EF5A7, 0xE75614, 0x08F121, 0x2A9DB5, 260 0x4D7E6F, 0x5119A5, 0xABF9B5, 0xD6DF82, 0x61DD96, 0x023616, 261 0x9F3AC4, 0xA1A283, 0x6DED72, 0x7A8D39, 0xA9B882, 0x5C326B, 262 0x5B2746, 0xED3400, 0x7700D2, 0x55F4FC, 0x4D5901, 0x8071E0, 263 #endif 264 265 }; 266 267 static const double PIo2[] = { 268 1.57079625129699707031e+00, /* 0x3FF921FB, 0x40000000 */ 269 7.54978941586159635335e-08, /* 0x3E74442D, 0x00000000 */ 270 5.39030252995776476554e-15, /* 0x3CF84698, 0x80000000 */ 271 3.28200341580791294123e-22, /* 0x3B78CC51, 0x60000000 */ 272 1.27065575308067607349e-29, /* 0x39F01B83, 0x80000000 */ 273 1.22933308981111328932e-36, /* 0x387A2520, 0x40000000 */ 274 2.73370053816464559624e-44, /* 0x36E38222, 0x80000000 */ 275 2.16741683877804819444e-51, /* 0x3569F31D, 0x00000000 */ 276 }; 277 278 static const double 279 zero = 0.0, 280 one = 1.0, 281 two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */ 282 twon24 = 5.96046447753906250000e-08; /* 0x3E700000, 0x00000000 */ 283 284 int 285 __kernel_rem_pio2(double *x, double *y, int e0, int nx, int prec) 286 { 287 int32_t jz,jx,jv,jp,jk,carry,n,iq[20],i,j,k,m,q0,ih; 288 double z,fw,f[20],fq[20],q[20]; 289 290 /* initialize jk*/ 291 jk = init_jk[prec]; 292 jp = jk; 293 294 /* determine jx,jv,q0, note that 3>q0 */ 295 jx = nx-1; 296 jv = (e0-3)/24; if(jv<0) jv=0; 297 q0 = e0-24*(jv+1); 298 299 /* set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk] */ 300 j = jv-jx; m = jx+jk; 301 for(i=0;i<=m;i++,j++) f[i] = (j<0)? zero : (double) ipio2[j]; 302 303 /* compute q[0],q[1],...q[jk] */ 304 for (i=0;i<=jk;i++) { 305 for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; 306 q[i] = fw; 307 } 308 309 jz = jk; 310 recompute: 311 /* distill q[] into iq[] reversingly */ 312 for(i=0,j=jz,z=q[jz];j>0;i++,j--) { 313 fw = (double)((int32_t)(twon24* z)); 314 iq[i] = (int32_t)(z-two24*fw); 315 z = q[j-1]+fw; 316 } 317 318 /* compute n */ 319 z = scalbn(z,q0); /* actual value of z */ 320 z -= 8.0*floor(z*0.125); /* trim off integer >= 8 */ 321 n = (int32_t) z; 322 z -= (double)n; 323 ih = 0; 324 if(q0>0) { /* need iq[jz-1] to determine n */ 325 i = (iq[jz-1]>>(24-q0)); n += i; 326 iq[jz-1] -= i<<(24-q0); 327 ih = iq[jz-1]>>(23-q0); 328 } 329 else if(q0==0) ih = iq[jz-1]>>23; 330 else if(z>=0.5) ih=2; 331 332 if(ih>0) { /* q > 0.5 */ 333 n += 1; carry = 0; 334 for(i=0;i<jz ;i++) { /* compute 1-q */ 335 j = iq[i]; 336 if(carry==0) { 337 if(j!=0) { 338 carry = 1; iq[i] = 0x1000000- j; 339 } 340 } else iq[i] = 0xffffff - j; 341 } 342 if(q0>0) { /* rare case: chance is 1 in 12 */ 343 switch(q0) { 344 case 1: 345 iq[jz-1] &= 0x7fffff; break; 346 case 2: 347 iq[jz-1] &= 0x3fffff; break; 348 } 349 } 350 if(ih==2) { 351 z = one - z; 352 if(carry!=0) z -= scalbn(one,q0); 353 } 354 } 355 356 /* check if recomputation is needed */ 357 if(z==zero) { 358 j = 0; 359 for (i=jz-1;i>=jk;i--) j |= iq[i]; 360 if(j==0) { /* need recomputation */ 361 for(k=1;iq[jk-k]==0;k++); /* k = no. of terms needed */ 362 363 for(i=jz+1;i<=jz+k;i++) { /* add q[jz+1] to q[jz+k] */ 364 f[jx+i] = (double) ipio2[jv+i]; 365 for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; 366 q[i] = fw; 367 } 368 jz += k; 369 goto recompute; 370 } 371 } 372 373 /* chop off zero terms */ 374 if(z==0.0) { 375 jz -= 1; q0 -= 24; 376 while(iq[jz]==0) { jz--; q0-=24;} 377 } else { /* break z into 24-bit if necessary */ 378 z = scalbn(z,-q0); 379 if(z>=two24) { 380 fw = (double)((int32_t)(twon24*z)); 381 iq[jz] = (int32_t)(z-two24*fw); 382 jz += 1; q0 += 24; 383 iq[jz] = (int32_t) fw; 384 } else iq[jz] = (int32_t) z ; 385 } 386 387 /* convert integer "bit" chunk to floating-point value */ 388 fw = scalbn(one,q0); 389 for(i=jz;i>=0;i--) { 390 q[i] = fw*(double)iq[i]; fw*=twon24; 391 } 392 393 /* compute PIo2[0,...,jp]*q[jz,...,0] */ 394 for(i=jz;i>=0;i--) { 395 for(fw=0.0,k=0;k<=jp&&k<=jz-i;k++) fw += PIo2[k]*q[i+k]; 396 fq[jz-i] = fw; 397 } 398 399 /* compress fq[] into y[] */ 400 switch(prec) { 401 case 0: 402 fw = 0.0; 403 for (i=jz;i>=0;i--) fw += fq[i]; 404 y[0] = (ih==0)? fw: -fw; 405 break; 406 case 1: 407 case 2: 408 fw = 0.0; 409 for (i=jz;i>=0;i--) fw += fq[i]; 410 STRICT_ASSIGN(double,fw,fw); 411 y[0] = (ih==0)? fw: -fw; 412 fw = fq[0]-fw; 413 for (i=1;i<=jz;i++) fw += fq[i]; 414 y[1] = (ih==0)? fw: -fw; 415 break; 416 case 3: /* painful */ 417 for (i=jz;i>0;i--) { 418 fw = fq[i-1]+fq[i]; 419 fq[i] += fq[i-1]-fw; 420 fq[i-1] = fw; 421 } 422 for (i=jz;i>1;i--) { 423 fw = fq[i-1]+fq[i]; 424 fq[i] += fq[i-1]-fw; 425 fq[i-1] = fw; 426 } 427 for (fw=0.0,i=jz;i>=2;i--) fw += fq[i]; 428 if(ih==0) { 429 y[0] = fq[0]; y[1] = fq[1]; y[2] = fw; 430 } else { 431 y[0] = -fq[0]; y[1] = -fq[1]; y[2] = -fw; 432 } 433 } 434 return n&7; 435 } 436