1 2 /* 3 * ==================================================== 4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 5 * 6 * Developed at SunSoft, 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 #include <sys/cdefs.h> 14 /* 15 * __kernel_rem_pio2(x,y,e0,nx,prec) 16 * double x[],y[]; int e0,nx,prec; 17 * 18 * __kernel_rem_pio2 return the last three digits of N with 19 * y = x - N*pi/2 20 * so that |y| < pi/2. 21 * 22 * The method is to compute the integer (mod 8) and fraction parts of 23 * (2/pi)*x without doing the full multiplication. In general we 24 * skip the part of the product that are known to be a huge integer ( 25 * more accurately, = 0 mod 8 ). Thus the number of operations are 26 * independent of the exponent of the input. 27 * 28 * (2/pi) is represented by an array of 24-bit integers in ipio2[]. 29 * 30 * Input parameters: 31 * x[] The input value (must be positive) is broken into nx 32 * pieces of 24-bit integers in double precision format. 33 * x[i] will be the i-th 24 bit of x. The scaled exponent 34 * of x[0] is given in input parameter e0 (i.e., x[0]*2^e0 35 * match x's up to 24 bits. 36 * 37 * Example of breaking a double positive z into x[0]+x[1]+x[2]: 38 * e0 = ilogb(z)-23 39 * z = scalbn(z,-e0) 40 * for i = 0,1,2 41 * x[i] = floor(z) 42 * z = (z-x[i])*2**24 43 * 44 * 45 * y[] output result in an array of double precision numbers. 46 * The dimension of y[] is: 47 * 24-bit precision 1 48 * 53-bit precision 2 49 * 64-bit precision 2 50 * 113-bit precision 3 51 * The actual value is the sum of them. Thus for 113-bit 52 * precision, one may have to do something like: 53 * 54 * long double t,w,r_head, r_tail; 55 * t = (long double)y[2] + (long double)y[1]; 56 * w = (long double)y[0]; 57 * r_head = t+w; 58 * r_tail = w - (r_head - t); 59 * 60 * e0 The exponent of x[0]. Must be <= 16360 or you need to 61 * expand the ipio2 table. 62 * 63 * nx dimension of x[] 64 * 65 * prec an integer indicating the precision: 66 * 0 24 bits (single) 67 * 1 53 bits (double) 68 * 2 64 bits (extended) 69 * 3 113 bits (quad) 70 * 71 * External function: 72 * double scalbn(), floor(); 73 * 74 * 75 * Here is the description of some local variables: 76 * 77 * jk jk+1 is the initial number of terms of ipio2[] needed 78 * in the computation. The minimum and recommended value 79 * for jk is 3,4,4,6 for single, double, extended, and quad. 80 * jk+1 must be 2 larger than you might expect so that our 81 * recomputation test works. (Up to 24 bits in the integer 82 * part (the 24 bits of it that we compute) and 23 bits in 83 * the fraction part may be lost to cancellation before we 84 * recompute.) 85 * 86 * jz local integer variable indicating the number of 87 * terms of ipio2[] used. 88 * 89 * jx nx - 1 90 * 91 * jv index for pointing to the suitable ipio2[] for the 92 * computation. In general, we want 93 * ( 2^e0*x[0] * ipio2[jv-1]*2^(-24jv) )/8 94 * is an integer. Thus 95 * e0-3-24*jv >= 0 or (e0-3)/24 >= jv 96 * Hence jv = max(0,(e0-3)/24). 97 * 98 * jp jp+1 is the number of terms in PIo2[] needed, jp = jk. 99 * 100 * q[] double array with integral value, representing the 101 * 24-bits chunk of the product of x and 2/pi. 102 * 103 * q0 the corresponding exponent of q[0]. Note that the 104 * exponent for q[i] would be q0-24*i. 105 * 106 * PIo2[] double precision array, obtained by cutting pi/2 107 * into 24 bits chunks. 108 * 109 * f[] ipio2[] in floating point 110 * 111 * iq[] integer array by breaking up q[] in 24-bits chunk. 112 * 113 * fq[] final product of x*(2/pi) in fq[0],..,fq[jk] 114 * 115 * ih integer. If >0 it indicates q[] is >= 0.5, hence 116 * it also indicates the *sign* of the result. 117 * 118 */ 119 120 121 /* 122 * Constants: 123 * The hexadecimal values are the intended ones for the following 124 * constants. The decimal values may be used, provided that the 125 * compiler will convert from decimal to binary accurately enough 126 * to produce the hexadecimal values shown. 127 */ 128 129 #include <float.h> 130 131 #include "math.h" 132 #include "math_private.h" 133 134 static const int init_jk[] = {3,4,4,6}; /* initial value for jk */ 135 136 /* 137 * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi 138 * 139 * integer array, contains the (24*i)-th to (24*i+23)-th 140 * bit of 2/pi after binary point. The corresponding 141 * floating value is 142 * 143 * ipio2[i] * 2^(-24(i+1)). 144 * 145 * NB: This table must have at least (e0-3)/24 + jk terms. 146 * For quad precision (e0 <= 16360, jk = 6), this is 686. 147 */ 148 static const int32_t ipio2[] = { 149 0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62, 150 0x95993C, 0x439041, 0xFE5163, 0xABDEBB, 0xC561B7, 0x246E3A, 151 0x424DD2, 0xE00649, 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129, 152 0xA73EE8, 0x8235F5, 0x2EBB44, 0x84E99C, 0x7026B4, 0x5F7E41, 153 0x3991D6, 0x398353, 0x39F49C, 0x845F8B, 0xBDF928, 0x3B1FF8, 154 0x97FFDE, 0x05980F, 0xEF2F11, 0x8B5A0A, 0x6D1F6D, 0x367ECF, 155 0x27CB09, 0xB74F46, 0x3F669E, 0x5FEA2D, 0x7527BA, 0xC7EBE5, 156 0xF17B3D, 0x0739F7, 0x8A5292, 0xEA6BFB, 0x5FB11F, 0x8D5D08, 157 0x560330, 0x46FC7B, 0x6BABF0, 0xCFBC20, 0x9AF436, 0x1DA9E3, 158 0x91615E, 0xE61B08, 0x659985, 0x5F14A0, 0x68408D, 0xFFD880, 159 0x4D7327, 0x310606, 0x1556CA, 0x73A8C9, 0x60E27B, 0xC08C6B, 160 161 #if LDBL_MAX_EXP > 1024 162 #if LDBL_MAX_EXP > 16384 163 #error "ipio2 table needs to be expanded" 164 #endif 165 0x47C419, 0xC367CD, 0xDCE809, 0x2A8359, 0xC4768B, 0x961CA6, 166 0xDDAF44, 0xD15719, 0x053EA5, 0xFF0705, 0x3F7E33, 0xE832C2, 167 0xDE4F98, 0x327DBB, 0xC33D26, 0xEF6B1E, 0x5EF89F, 0x3A1F35, 168 0xCAF27F, 0x1D87F1, 0x21907C, 0x7C246A, 0xFA6ED5, 0x772D30, 169 0x433B15, 0xC614B5, 0x9D19C3, 0xC2C4AD, 0x414D2C, 0x5D000C, 170 0x467D86, 0x2D71E3, 0x9AC69B, 0x006233, 0x7CD2B4, 0x97A7B4, 171 0xD55537, 0xF63ED7, 0x1810A3, 0xFC764D, 0x2A9D64, 0xABD770, 172 0xF87C63, 0x57B07A, 0xE71517, 0x5649C0, 0xD9D63B, 0x3884A7, 173 0xCB2324, 0x778AD6, 0x23545A, 0xB91F00, 0x1B0AF1, 0xDFCE19, 174 0xFF319F, 0x6A1E66, 0x615799, 0x47FBAC, 0xD87F7E, 0xB76522, 175 0x89E832, 0x60BFE6, 0xCDC4EF, 0x09366C, 0xD43F5D, 0xD7DE16, 176 0xDE3B58, 0x929BDE, 0x2822D2, 0xE88628, 0x4D58E2, 0x32CAC6, 177 0x16E308, 0xCB7DE0, 0x50C017, 0xA71DF3, 0x5BE018, 0x34132E, 178 0x621283, 0x014883, 0x5B8EF5, 0x7FB0AD, 0xF2E91E, 0x434A48, 179 0xD36710, 0xD8DDAA, 0x425FAE, 0xCE616A, 0xA4280A, 0xB499D3, 180 0xF2A606, 0x7F775C, 0x83C2A3, 0x883C61, 0x78738A, 0x5A8CAF, 181 0xBDD76F, 0x63A62D, 0xCBBFF4, 0xEF818D, 0x67C126, 0x45CA55, 182 0x36D9CA, 0xD2A828, 0x8D61C2, 0x77C912, 0x142604, 0x9B4612, 183 0xC459C4, 0x44C5C8, 0x91B24D, 0xF31700, 0xAD43D4, 0xE54929, 184 0x10D5FD, 0xFCBE00, 0xCC941E, 0xEECE70, 0xF53E13, 0x80F1EC, 185 0xC3E7B3, 0x28F8C7, 0x940593, 0x3E71C1, 0xB3092E, 0xF3450B, 186 0x9C1288, 0x7B20AB, 0x9FB52E, 0xC29247, 0x2F327B, 0x6D550C, 187 0x90A772, 0x1FE76B, 0x96CB31, 0x4A1679, 0xE27941, 0x89DFF4, 188 0x9794E8, 0x84E6E2, 0x973199, 0x6BED88, 0x365F5F, 0x0EFDBB, 189 0xB49A48, 0x6CA467, 0x427271, 0x325D8D, 0xB8159F, 0x09E5BC, 190 0x25318D, 0x3974F7, 0x1C0530, 0x010C0D, 0x68084B, 0x58EE2C, 191 0x90AA47, 0x02E774, 0x24D6BD, 0xA67DF7, 0x72486E, 0xEF169F, 192 0xA6948E, 0xF691B4, 0x5153D1, 0xF20ACF, 0x339820, 0x7E4BF5, 193 0x6863B2, 0x5F3EDD, 0x035D40, 0x7F8985, 0x295255, 0xC06437, 194 0x10D86D, 0x324832, 0x754C5B, 0xD4714E, 0x6E5445, 0xC1090B, 195 0x69F52A, 0xD56614, 0x9D0727, 0x50045D, 0xDB3BB4, 0xC576EA, 196 0x17F987, 0x7D6B49, 0xBA271D, 0x296996, 0xACCCC6, 0x5414AD, 197 0x6AE290, 0x89D988, 0x50722C, 0xBEA404, 0x940777, 0x7030F3, 198 0x27FC00, 0xA871EA, 0x49C266, 0x3DE064, 0x83DD97, 0x973FA3, 199 0xFD9443, 0x8C860D, 0xDE4131, 0x9D3992, 0x8C70DD, 0xE7B717, 200 0x3BDF08, 0x2B3715, 0xA0805C, 0x93805A, 0x921110, 0xD8E80F, 201 0xAF806C, 0x4BFFDB, 0x0F9038, 0x761859, 0x15A562, 0xBBCB61, 202 0xB989C7, 0xBD4010, 0x04F2D2, 0x277549, 0xF6B6EB, 0xBB22DB, 203 0xAA140A, 0x2F2689, 0x768364, 0x333B09, 0x1A940E, 0xAA3A51, 204 0xC2A31D, 0xAEEDAF, 0x12265C, 0x4DC26D, 0x9C7A2D, 0x9756C0, 205 0x833F03, 0xF6F009, 0x8C402B, 0x99316D, 0x07B439, 0x15200C, 206 0x5BC3D8, 0xC492F5, 0x4BADC6, 0xA5CA4E, 0xCD37A7, 0x36A9E6, 207 0x9492AB, 0x6842DD, 0xDE6319, 0xEF8C76, 0x528B68, 0x37DBFC, 208 0xABA1AE, 0x3115DF, 0xA1AE00, 0xDAFB0C, 0x664D64, 0xB705ED, 209 0x306529, 0xBF5657, 0x3AFF47, 0xB9F96A, 0xF3BE75, 0xDF9328, 210 0x3080AB, 0xF68C66, 0x15CB04, 0x0622FA, 0x1DE4D9, 0xA4B33D, 211 0x8F1B57, 0x09CD36, 0xE9424E, 0xA4BE13, 0xB52333, 0x1AAAF0, 212 0xA8654F, 0xA5C1D2, 0x0F3F0B, 0xCD785B, 0x76F923, 0x048B7B, 213 0x721789, 0x53A6C6, 0xE26E6F, 0x00EBEF, 0x584A9B, 0xB7DAC4, 214 0xBA66AA, 0xCFCF76, 0x1D02D1, 0x2DF1B1, 0xC1998C, 0x77ADC3, 215 0xDA4886, 0xA05DF7, 0xF480C6, 0x2FF0AC, 0x9AECDD, 0xBC5C3F, 216 0x6DDED0, 0x1FC790, 0xB6DB2A, 0x3A25A3, 0x9AAF00, 0x9353AD, 217 0x0457B6, 0xB42D29, 0x7E804B, 0xA707DA, 0x0EAA76, 0xA1597B, 218 0x2A1216, 0x2DB7DC, 0xFDE5FA, 0xFEDB89, 0xFDBE89, 0x6C76E4, 219 0xFCA906, 0x70803E, 0x156E85, 0xFF87FD, 0x073E28, 0x336761, 220 0x86182A, 0xEABD4D, 0xAFE7B3, 0x6E6D8F, 0x396795, 0x5BBF31, 221 0x48D784, 0x16DF30, 0x432DC7, 0x356125, 0xCE70C9, 0xB8CB30, 222 0xFD6CBF, 0xA200A4, 0xE46C05, 0xA0DD5A, 0x476F21, 0xD21262, 223 0x845CB9, 0x496170, 0xE0566B, 0x015299, 0x375550, 0xB7D51E, 224 0xC4F133, 0x5F6E13, 0xE4305D, 0xA92E85, 0xC3B21D, 0x3632A1, 225 0xA4B708, 0xD4B1EA, 0x21F716, 0xE4698F, 0x77FF27, 0x80030C, 226 0x2D408D, 0xA0CD4F, 0x99A520, 0xD3A2B3, 0x0A5D2F, 0x42F9B4, 227 0xCBDA11, 0xD0BE7D, 0xC1DB9B, 0xBD17AB, 0x81A2CA, 0x5C6A08, 228 0x17552E, 0x550027, 0xF0147F, 0x8607E1, 0x640B14, 0x8D4196, 229 0xDEBE87, 0x2AFDDA, 0xB6256B, 0x34897B, 0xFEF305, 0x9EBFB9, 230 0x4F6A68, 0xA82A4A, 0x5AC44F, 0xBCF82D, 0x985AD7, 0x95C7F4, 231 0x8D4D0D, 0xA63A20, 0x5F57A4, 0xB13F14, 0x953880, 0x0120CC, 232 0x86DD71, 0xB6DEC9, 0xF560BF, 0x11654D, 0x6B0701, 0xACB08C, 233 0xD0C0B2, 0x485551, 0x0EFB1E, 0xC37295, 0x3B06A3, 0x3540C0, 234 0x7BDC06, 0xCC45E0, 0xFA294E, 0xC8CAD6, 0x41F3E8, 0xDE647C, 235 0xD8649B, 0x31BED9, 0xC397A4, 0xD45877, 0xC5E369, 0x13DAF0, 236 0x3C3ABA, 0x461846, 0x5F7555, 0xF5BDD2, 0xC6926E, 0x5D2EAC, 237 0xED440E, 0x423E1C, 0x87C461, 0xE9FD29, 0xF3D6E7, 0xCA7C22, 238 0x35916F, 0xC5E008, 0x8DD7FF, 0xE26A6E, 0xC6FDB0, 0xC10893, 239 0x745D7C, 0xB2AD6B, 0x9D6ECD, 0x7B723E, 0x6A11C6, 0xA9CFF7, 240 0xDF7329, 0xBAC9B5, 0x5100B7, 0x0DB2E2, 0x24BA74, 0x607DE5, 241 0x8AD874, 0x2C150D, 0x0C1881, 0x94667E, 0x162901, 0x767A9F, 242 0xBEFDFD, 0xEF4556, 0x367ED9, 0x13D9EC, 0xB9BA8B, 0xFC97C4, 243 0x27A831, 0xC36EF1, 0x36C594, 0x56A8D8, 0xB5A8B4, 0x0ECCCF, 244 0x2D8912, 0x34576F, 0x89562C, 0xE3CE99, 0xB920D6, 0xAA5E6B, 245 0x9C2A3E, 0xCC5F11, 0x4A0BFD, 0xFBF4E1, 0x6D3B8E, 0x2C86E2, 246 0x84D4E9, 0xA9B4FC, 0xD1EEEF, 0xC9352E, 0x61392F, 0x442138, 247 0xC8D91B, 0x0AFC81, 0x6A4AFB, 0xD81C2F, 0x84B453, 0x8C994E, 248 0xCC2254, 0xDC552A, 0xD6C6C0, 0x96190B, 0xB8701A, 0x649569, 249 0x605A26, 0xEE523F, 0x0F117F, 0x11B5F4, 0xF5CBFC, 0x2DBC34, 250 0xEEBC34, 0xCC5DE8, 0x605EDD, 0x9B8E67, 0xEF3392, 0xB817C9, 251 0x9B5861, 0xBC57E1, 0xC68351, 0x103ED8, 0x4871DD, 0xDD1C2D, 252 0xA118AF, 0x462C21, 0xD7F359, 0x987AD9, 0xC0549E, 0xFA864F, 253 0xFC0656, 0xAE79E5, 0x362289, 0x22AD38, 0xDC9367, 0xAAE855, 254 0x382682, 0x9BE7CA, 0xA40D51, 0xB13399, 0x0ED7A9, 0x480569, 255 0xF0B265, 0xA7887F, 0x974C88, 0x36D1F9, 0xB39221, 0x4A827B, 256 0x21CF98, 0xDC9F40, 0x5547DC, 0x3A74E1, 0x42EB67, 0xDF9DFE, 257 0x5FD45E, 0xA4677B, 0x7AACBA, 0xA2F655, 0x23882B, 0x55BA41, 258 0x086E59, 0x862A21, 0x834739, 0xE6E389, 0xD49EE5, 0x40FB49, 259 0xE956FF, 0xCA0F1C, 0x8A59C5, 0x2BFA94, 0xC5C1D3, 0xCFC50F, 260 0xAE5ADB, 0x86C547, 0x624385, 0x3B8621, 0x94792C, 0x876110, 261 0x7B4C2A, 0x1A2C80, 0x12BF43, 0x902688, 0x893C78, 0xE4C4A8, 262 0x7BDBE5, 0xC23AC4, 0xEAF426, 0x8A67F7, 0xBF920D, 0x2BA365, 263 0xB1933D, 0x0B7CBD, 0xDC51A4, 0x63DD27, 0xDDE169, 0x19949A, 264 0x9529A8, 0x28CE68, 0xB4ED09, 0x209F44, 0xCA984E, 0x638270, 265 0x237C7E, 0x32B90F, 0x8EF5A7, 0xE75614, 0x08F121, 0x2A9DB5, 266 0x4D7E6F, 0x5119A5, 0xABF9B5, 0xD6DF82, 0x61DD96, 0x023616, 267 0x9F3AC4, 0xA1A283, 0x6DED72, 0x7A8D39, 0xA9B882, 0x5C326B, 268 0x5B2746, 0xED3400, 0x7700D2, 0x55F4FC, 0x4D5901, 0x8071E0, 269 #endif 270 271 }; 272 273 static const double PIo2[] = { 274 1.57079625129699707031e+00, /* 0x3FF921FB, 0x40000000 */ 275 7.54978941586159635335e-08, /* 0x3E74442D, 0x00000000 */ 276 5.39030252995776476554e-15, /* 0x3CF84698, 0x80000000 */ 277 3.28200341580791294123e-22, /* 0x3B78CC51, 0x60000000 */ 278 1.27065575308067607349e-29, /* 0x39F01B83, 0x80000000 */ 279 1.22933308981111328932e-36, /* 0x387A2520, 0x40000000 */ 280 2.73370053816464559624e-44, /* 0x36E38222, 0x80000000 */ 281 2.16741683877804819444e-51, /* 0x3569F31D, 0x00000000 */ 282 }; 283 284 static const double 285 zero = 0.0, 286 one = 1.0, 287 two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */ 288 twon24 = 5.96046447753906250000e-08; /* 0x3E700000, 0x00000000 */ 289 290 int 291 __kernel_rem_pio2(double *x, double *y, int e0, int nx, int prec) 292 { 293 int32_t jz,jx,jv,jp,jk,carry,n,iq[20],i,j,k,m,q0,ih; 294 double z,fw,f[20],fq[20],q[20]; 295 296 /* initialize jk*/ 297 jk = init_jk[prec]; 298 jp = jk; 299 300 /* determine jx,jv,q0, note that 3>q0 */ 301 jx = nx-1; 302 jv = (e0-3)/24; if(jv<0) jv=0; 303 q0 = e0-24*(jv+1); 304 305 /* set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk] */ 306 j = jv-jx; m = jx+jk; 307 for(i=0;i<=m;i++,j++) f[i] = (j<0)? zero : (double) ipio2[j]; 308 309 /* compute q[0],q[1],...q[jk] */ 310 for (i=0;i<=jk;i++) { 311 for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; q[i] = fw; 312 } 313 314 jz = jk; 315 recompute: 316 /* distill q[] into iq[] reversingly */ 317 for(i=0,j=jz,z=q[jz];j>0;i++,j--) { 318 fw = (double)((int32_t)(twon24* z)); 319 iq[i] = (int32_t)(z-two24*fw); 320 z = q[j-1]+fw; 321 } 322 323 /* compute n */ 324 z = scalbn(z,q0); /* actual value of z */ 325 z -= 8.0*floor(z*0.125); /* trim off integer >= 8 */ 326 n = (int32_t) z; 327 z -= (double)n; 328 ih = 0; 329 if(q0>0) { /* need iq[jz-1] to determine n */ 330 i = (iq[jz-1]>>(24-q0)); n += i; 331 iq[jz-1] -= i<<(24-q0); 332 ih = iq[jz-1]>>(23-q0); 333 } 334 else if(q0==0) ih = iq[jz-1]>>23; 335 else if(z>=0.5) ih=2; 336 337 if(ih>0) { /* q > 0.5 */ 338 n += 1; carry = 0; 339 for(i=0;i<jz ;i++) { /* compute 1-q */ 340 j = iq[i]; 341 if(carry==0) { 342 if(j!=0) { 343 carry = 1; iq[i] = 0x1000000- j; 344 } 345 } else iq[i] = 0xffffff - j; 346 } 347 if(q0>0) { /* rare case: chance is 1 in 12 */ 348 switch(q0) { 349 case 1: 350 iq[jz-1] &= 0x7fffff; break; 351 case 2: 352 iq[jz-1] &= 0x3fffff; break; 353 } 354 } 355 if(ih==2) { 356 z = one - z; 357 if(carry!=0) z -= scalbn(one,q0); 358 } 359 } 360 361 /* check if recomputation is needed */ 362 if(z==zero) { 363 j = 0; 364 for (i=jz-1;i>=jk;i--) j |= iq[i]; 365 if(j==0) { /* need recomputation */ 366 for(k=1;iq[jk-k]==0;k++); /* k = no. of terms needed */ 367 368 for(i=jz+1;i<=jz+k;i++) { /* add q[jz+1] to q[jz+k] */ 369 f[jx+i] = (double) ipio2[jv+i]; 370 for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; 371 q[i] = fw; 372 } 373 jz += k; 374 goto recompute; 375 } 376 } 377 378 /* chop off zero terms */ 379 if(z==0.0) { 380 jz -= 1; q0 -= 24; 381 while(iq[jz]==0) { jz--; q0-=24;} 382 } else { /* break z into 24-bit if necessary */ 383 z = scalbn(z,-q0); 384 if(z>=two24) { 385 fw = (double)((int32_t)(twon24*z)); 386 iq[jz] = (int32_t)(z-two24*fw); 387 jz += 1; q0 += 24; 388 iq[jz] = (int32_t) fw; 389 } else iq[jz] = (int32_t) z ; 390 } 391 392 /* convert integer "bit" chunk to floating-point value */ 393 fw = scalbn(one,q0); 394 for(i=jz;i>=0;i--) { 395 q[i] = fw*(double)iq[i]; fw*=twon24; 396 } 397 398 /* compute PIo2[0,...,jp]*q[jz,...,0] */ 399 for(i=jz;i>=0;i--) { 400 for(fw=0.0,k=0;k<=jp&&k<=jz-i;k++) fw += PIo2[k]*q[i+k]; 401 fq[jz-i] = fw; 402 } 403 404 /* compress fq[] into y[] */ 405 switch(prec) { 406 case 0: 407 fw = 0.0; 408 for (i=jz;i>=0;i--) fw += fq[i]; 409 y[0] = (ih==0)? fw: -fw; 410 break; 411 case 1: 412 case 2: 413 fw = 0.0; 414 for (i=jz;i>=0;i--) fw += fq[i]; 415 STRICT_ASSIGN(double,fw,fw); 416 y[0] = (ih==0)? fw: -fw; 417 fw = fq[0]-fw; 418 for (i=1;i<=jz;i++) fw += fq[i]; 419 y[1] = (ih==0)? fw: -fw; 420 break; 421 case 3: /* painful */ 422 for (i=jz;i>0;i--) { 423 fw = fq[i-1]+fq[i]; 424 fq[i] += fq[i-1]-fw; 425 fq[i-1] = fw; 426 } 427 for (i=jz;i>1;i--) { 428 fw = fq[i-1]+fq[i]; 429 fq[i] += fq[i-1]-fw; 430 fq[i-1] = fw; 431 } 432 for (fw=0.0,i=jz;i>=2;i--) fw += fq[i]; 433 if(ih==0) { 434 y[0] = fq[0]; y[1] = fq[1]; y[2] = fw; 435 } else { 436 y[0] = -fq[0]; y[1] = -fq[1]; y[2] = -fw; 437 } 438 } 439 return n&7; 440 } 441