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| 1 /* origin: FreeBSD /usr/src/lib/msun/src/k_rem_pio2.c */ |
| 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 * __rem_pio2_large(x,y,e0,nx,prec) |
| 14 * double x[],y[]; int e0,nx,prec; |
| 15 * |
| 16 * __rem_pio2_large return the last three digits of N with |
| 17 * y = x - N*pi/2 |
| 18 * so that |y| < pi/2. |
| 19 * |
| 20 * The method is to compute the integer (mod 8) and fraction parts of |
| 21 * (2/pi)*x without doing the full multiplication. In general we |
| 22 * skip the part of the product that are known to be a huge integer ( |
| 23 * more accurately, = 0 mod 8 ). Thus the number of operations are |
| 24 * independent of the exponent of the input. |
| 25 * |
| 26 * (2/pi) is represented by an array of 24-bit integers in ipio2[]. |
| 27 * |
| 28 * Input parameters: |
| 29 * x[] The input value (must be positive) is broken into nx |
| 30 * pieces of 24-bit integers in double precision format. |
| 31 * x[i] will be the i-th 24 bit of x. The scaled exponent |
| 32 * of x[0] is given in input parameter e0 (i.e., x[0]*2^e0 |
| 33 * match x's up to 24 bits. |
| 34 * |
| 35 * Example of breaking a double positive z into x[0]+x[1]+x[2]: |
| 36 * e0 = ilogb(z)-23 |
| 37 * z = scalbn(z,-e0) |
| 38 * for i = 0,1,2 |
| 39 * x[i] = floor(z) |
| 40 * z = (z-x[i])*2**24 |
| 41 * |
| 42 * |
| 43 * y[] ouput result in an array of double precision numbers. |
| 44 * The dimension of y[] is: |
| 45 * 24-bit precision 1 |
| 46 * 53-bit precision 2 |
| 47 * 64-bit precision 2 |
| 48 * 113-bit precision 3 |
| 49 * The actual value is the sum of them. Thus for 113-bit |
| 50 * precison, one may have to do something like: |
| 51 * |
| 52 * long double t,w,r_head, r_tail; |
| 53 * t = (long double)y[2] + (long double)y[1]; |
| 54 * w = (long double)y[0]; |
| 55 * r_head = t+w; |
| 56 * r_tail = w - (r_head - t); |
| 57 * |
| 58 * e0 The exponent of x[0]. Must be <= 16360 or you need to |
| 59 * expand the ipio2 table. |
| 60 * |
| 61 * nx dimension of x[] |
| 62 * |
| 63 * prec an integer indicating the precision: |
| 64 * 0 24 bits (single) |
| 65 * 1 53 bits (double) |
| 66 * 2 64 bits (extended) |
| 67 * 3 113 bits (quad) |
| 68 * |
| 69 * External function: |
| 70 * double scalbn(), floor(); |
| 71 * |
| 72 * |
| 73 * Here is the description of some local variables: |
| 74 * |
| 75 * jk jk+1 is the initial number of terms of ipio2[] needed |
| 76 * in the computation. The minimum and recommended value |
| 77 * for jk is 3,4,4,6 for single, double, extended, and quad. |
| 78 * jk+1 must be 2 larger than you might expect so that our |
| 79 * recomputation test works. (Up to 24 bits in the integer |
| 80 * part (the 24 bits of it that we compute) and 23 bits in |
| 81 * the fraction part may be lost to cancelation before we |
| 82 * recompute.) |
| 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 * Constants: |
| 119 * The hexadecimal values are the intended ones for the following |
| 120 * constants. The decimal values may be used, provided that the |
| 121 * compiler will convert from decimal to binary accurately enough |
| 122 * to produce the hexadecimal values shown. |
| 123 */ |
| 124 |
| 125 #include "libm.h" |
| 126 |
| 127 static const int init_jk[] = {3,4,4,6}; /* initial value for jk */ |
| 128 |
| 129 /* |
| 130 * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi |
| 131 * |
| 132 * integer array, contains the (24*i)-th to (24*i+23)-th |
| 133 * bit of 2/pi after binary point. The corresponding |
| 134 * floating value is |
| 135 * |
| 136 * ipio2[i] * 2^(-24(i+1)). |
| 137 * |
| 138 * NB: This table must have at least (e0-3)/24 + jk terms. |
| 139 * For quad precision (e0 <= 16360, jk = 6), this is 686. |
| 140 */ |
| 141 static const int32_t ipio2[] = { |
| 142 0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62, |
| 143 0x95993C, 0x439041, 0xFE5163, 0xABDEBB, 0xC561B7, 0x246E3A, |
| 144 0x424DD2, 0xE00649, 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129, |
| 145 0xA73EE8, 0x8235F5, 0x2EBB44, 0x84E99C, 0x7026B4, 0x5F7E41, |
| 146 0x3991D6, 0x398353, 0x39F49C, 0x845F8B, 0xBDF928, 0x3B1FF8, |
| 147 0x97FFDE, 0x05980F, 0xEF2F11, 0x8B5A0A, 0x6D1F6D, 0x367ECF, |
| 148 0x27CB09, 0xB74F46, 0x3F669E, 0x5FEA2D, 0x7527BA, 0xC7EBE5, |
| 149 0xF17B3D, 0x0739F7, 0x8A5292, 0xEA6BFB, 0x5FB11F, 0x8D5D08, |
| 150 0x560330, 0x46FC7B, 0x6BABF0, 0xCFBC20, 0x9AF436, 0x1DA9E3, |
| 151 0x91615E, 0xE61B08, 0x659985, 0x5F14A0, 0x68408D, 0xFFD880, |
| 152 0x4D7327, 0x310606, 0x1556CA, 0x73A8C9, 0x60E27B, 0xC08C6B, |
| 153 |
| 154 #if LDBL_MAX_EXP > 1024 |
| 155 0x47C419, 0xC367CD, 0xDCE809, 0x2A8359, 0xC4768B, 0x961CA6, |
| 156 0xDDAF44, 0xD15719, 0x053EA5, 0xFF0705, 0x3F7E33, 0xE832C2, |
| 157 0xDE4F98, 0x327DBB, 0xC33D26, 0xEF6B1E, 0x5EF89F, 0x3A1F35, |
| 158 0xCAF27F, 0x1D87F1, 0x21907C, 0x7C246A, 0xFA6ED5, 0x772D30, |
| 159 0x433B15, 0xC614B5, 0x9D19C3, 0xC2C4AD, 0x414D2C, 0x5D000C, |
| 160 0x467D86, 0x2D71E3, 0x9AC69B, 0x006233, 0x7CD2B4, 0x97A7B4, |
| 161 0xD55537, 0xF63ED7, 0x1810A3, 0xFC764D, 0x2A9D64, 0xABD770, |
| 162 0xF87C63, 0x57B07A, 0xE71517, 0x5649C0, 0xD9D63B, 0x3884A7, |
| 163 0xCB2324, 0x778AD6, 0x23545A, 0xB91F00, 0x1B0AF1, 0xDFCE19, |
| 164 0xFF319F, 0x6A1E66, 0x615799, 0x47FBAC, 0xD87F7E, 0xB76522, |
| 165 0x89E832, 0x60BFE6, 0xCDC4EF, 0x09366C, 0xD43F5D, 0xD7DE16, |
| 166 0xDE3B58, 0x929BDE, 0x2822D2, 0xE88628, 0x4D58E2, 0x32CAC6, |
| 167 0x16E308, 0xCB7DE0, 0x50C017, 0xA71DF3, 0x5BE018, 0x34132E, |
| 168 0x621283, 0x014883, 0x5B8EF5, 0x7FB0AD, 0xF2E91E, 0x434A48, |
| 169 0xD36710, 0xD8DDAA, 0x425FAE, 0xCE616A, 0xA4280A, 0xB499D3, |
| 170 0xF2A606, 0x7F775C, 0x83C2A3, 0x883C61, 0x78738A, 0x5A8CAF, |
| 171 0xBDD76F, 0x63A62D, 0xCBBFF4, 0xEF818D, 0x67C126, 0x45CA55, |
| 172 0x36D9CA, 0xD2A828, 0x8D61C2, 0x77C912, 0x142604, 0x9B4612, |
| 173 0xC459C4, 0x44C5C8, 0x91B24D, 0xF31700, 0xAD43D4, 0xE54929, |
| 174 0x10D5FD, 0xFCBE00, 0xCC941E, 0xEECE70, 0xF53E13, 0x80F1EC, |
| 175 0xC3E7B3, 0x28F8C7, 0x940593, 0x3E71C1, 0xB3092E, 0xF3450B, |
| 176 0x9C1288, 0x7B20AB, 0x9FB52E, 0xC29247, 0x2F327B, 0x6D550C, |
| 177 0x90A772, 0x1FE76B, 0x96CB31, 0x4A1679, 0xE27941, 0x89DFF4, |
| 178 0x9794E8, 0x84E6E2, 0x973199, 0x6BED88, 0x365F5F, 0x0EFDBB, |
| 179 0xB49A48, 0x6CA467, 0x427271, 0x325D8D, 0xB8159F, 0x09E5BC, |
| 180 0x25318D, 0x3974F7, 0x1C0530, 0x010C0D, 0x68084B, 0x58EE2C, |
| 181 0x90AA47, 0x02E774, 0x24D6BD, 0xA67DF7, 0x72486E, 0xEF169F, |
| 182 0xA6948E, 0xF691B4, 0x5153D1, 0xF20ACF, 0x339820, 0x7E4BF5, |
| 183 0x6863B2, 0x5F3EDD, 0x035D40, 0x7F8985, 0x295255, 0xC06437, |
| 184 0x10D86D, 0x324832, 0x754C5B, 0xD4714E, 0x6E5445, 0xC1090B, |
| 185 0x69F52A, 0xD56614, 0x9D0727, 0x50045D, 0xDB3BB4, 0xC576EA, |
| 186 0x17F987, 0x7D6B49, 0xBA271D, 0x296996, 0xACCCC6, 0x5414AD, |
| 187 0x6AE290, 0x89D988, 0x50722C, 0xBEA404, 0x940777, 0x7030F3, |
| 188 0x27FC00, 0xA871EA, 0x49C266, 0x3DE064, 0x83DD97, 0x973FA3, |
| 189 0xFD9443, 0x8C860D, 0xDE4131, 0x9D3992, 0x8C70DD, 0xE7B717, |
| 190 0x3BDF08, 0x2B3715, 0xA0805C, 0x93805A, 0x921110, 0xD8E80F, |
| 191 0xAF806C, 0x4BFFDB, 0x0F9038, 0x761859, 0x15A562, 0xBBCB61, |
| 192 0xB989C7, 0xBD4010, 0x04F2D2, 0x277549, 0xF6B6EB, 0xBB22DB, |
| 193 0xAA140A, 0x2F2689, 0x768364, 0x333B09, 0x1A940E, 0xAA3A51, |
| 194 0xC2A31D, 0xAEEDAF, 0x12265C, 0x4DC26D, 0x9C7A2D, 0x9756C0, |
| 195 0x833F03, 0xF6F009, 0x8C402B, 0x99316D, 0x07B439, 0x15200C, |
| 196 0x5BC3D8, 0xC492F5, 0x4BADC6, 0xA5CA4E, 0xCD37A7, 0x36A9E6, |
| 197 0x9492AB, 0x6842DD, 0xDE6319, 0xEF8C76, 0x528B68, 0x37DBFC, |
| 198 0xABA1AE, 0x3115DF, 0xA1AE00, 0xDAFB0C, 0x664D64, 0xB705ED, |
| 199 0x306529, 0xBF5657, 0x3AFF47, 0xB9F96A, 0xF3BE75, 0xDF9328, |
| 200 0x3080AB, 0xF68C66, 0x15CB04, 0x0622FA, 0x1DE4D9, 0xA4B33D, |
| 201 0x8F1B57, 0x09CD36, 0xE9424E, 0xA4BE13, 0xB52333, 0x1AAAF0, |
| 202 0xA8654F, 0xA5C1D2, 0x0F3F0B, 0xCD785B, 0x76F923, 0x048B7B, |
| 203 0x721789, 0x53A6C6, 0xE26E6F, 0x00EBEF, 0x584A9B, 0xB7DAC4, |
| 204 0xBA66AA, 0xCFCF76, 0x1D02D1, 0x2DF1B1, 0xC1998C, 0x77ADC3, |
| 205 0xDA4886, 0xA05DF7, 0xF480C6, 0x2FF0AC, 0x9AECDD, 0xBC5C3F, |
| 206 0x6DDED0, 0x1FC790, 0xB6DB2A, 0x3A25A3, 0x9AAF00, 0x9353AD, |
| 207 0x0457B6, 0xB42D29, 0x7E804B, 0xA707DA, 0x0EAA76, 0xA1597B, |
| 208 0x2A1216, 0x2DB7DC, 0xFDE5FA, 0xFEDB89, 0xFDBE89, 0x6C76E4, |
| 209 0xFCA906, 0x70803E, 0x156E85, 0xFF87FD, 0x073E28, 0x336761, |
| 210 0x86182A, 0xEABD4D, 0xAFE7B3, 0x6E6D8F, 0x396795, 0x5BBF31, |
| 211 0x48D784, 0x16DF30, 0x432DC7, 0x356125, 0xCE70C9, 0xB8CB30, |
| 212 0xFD6CBF, 0xA200A4, 0xE46C05, 0xA0DD5A, 0x476F21, 0xD21262, |
| 213 0x845CB9, 0x496170, 0xE0566B, 0x015299, 0x375550, 0xB7D51E, |
| 214 0xC4F133, 0x5F6E13, 0xE4305D, 0xA92E85, 0xC3B21D, 0x3632A1, |
| 215 0xA4B708, 0xD4B1EA, 0x21F716, 0xE4698F, 0x77FF27, 0x80030C, |
| 216 0x2D408D, 0xA0CD4F, 0x99A520, 0xD3A2B3, 0x0A5D2F, 0x42F9B4, |
| 217 0xCBDA11, 0xD0BE7D, 0xC1DB9B, 0xBD17AB, 0x81A2CA, 0x5C6A08, |
| 218 0x17552E, 0x550027, 0xF0147F, 0x8607E1, 0x640B14, 0x8D4196, |
| 219 0xDEBE87, 0x2AFDDA, 0xB6256B, 0x34897B, 0xFEF305, 0x9EBFB9, |
| 220 0x4F6A68, 0xA82A4A, 0x5AC44F, 0xBCF82D, 0x985AD7, 0x95C7F4, |
| 221 0x8D4D0D, 0xA63A20, 0x5F57A4, 0xB13F14, 0x953880, 0x0120CC, |
| 222 0x86DD71, 0xB6DEC9, 0xF560BF, 0x11654D, 0x6B0701, 0xACB08C, |
| 223 0xD0C0B2, 0x485551, 0x0EFB1E, 0xC37295, 0x3B06A3, 0x3540C0, |
| 224 0x7BDC06, 0xCC45E0, 0xFA294E, 0xC8CAD6, 0x41F3E8, 0xDE647C, |
| 225 0xD8649B, 0x31BED9, 0xC397A4, 0xD45877, 0xC5E369, 0x13DAF0, |
| 226 0x3C3ABA, 0x461846, 0x5F7555, 0xF5BDD2, 0xC6926E, 0x5D2EAC, |
| 227 0xED440E, 0x423E1C, 0x87C461, 0xE9FD29, 0xF3D6E7, 0xCA7C22, |
| 228 0x35916F, 0xC5E008, 0x8DD7FF, 0xE26A6E, 0xC6FDB0, 0xC10893, |
| 229 0x745D7C, 0xB2AD6B, 0x9D6ECD, 0x7B723E, 0x6A11C6, 0xA9CFF7, |
| 230 0xDF7329, 0xBAC9B5, 0x5100B7, 0x0DB2E2, 0x24BA74, 0x607DE5, |
| 231 0x8AD874, 0x2C150D, 0x0C1881, 0x94667E, 0x162901, 0x767A9F, |
| 232 0xBEFDFD, 0xEF4556, 0x367ED9, 0x13D9EC, 0xB9BA8B, 0xFC97C4, |
| 233 0x27A831, 0xC36EF1, 0x36C594, 0x56A8D8, 0xB5A8B4, 0x0ECCCF, |
| 234 0x2D8912, 0x34576F, 0x89562C, 0xE3CE99, 0xB920D6, 0xAA5E6B, |
| 235 0x9C2A3E, 0xCC5F11, 0x4A0BFD, 0xFBF4E1, 0x6D3B8E, 0x2C86E2, |
| 236 0x84D4E9, 0xA9B4FC, 0xD1EEEF, 0xC9352E, 0x61392F, 0x442138, |
| 237 0xC8D91B, 0x0AFC81, 0x6A4AFB, 0xD81C2F, 0x84B453, 0x8C994E, |
| 238 0xCC2254, 0xDC552A, 0xD6C6C0, 0x96190B, 0xB8701A, 0x649569, |
| 239 0x605A26, 0xEE523F, 0x0F117F, 0x11B5F4, 0xF5CBFC, 0x2DBC34, |
| 240 0xEEBC34, 0xCC5DE8, 0x605EDD, 0x9B8E67, 0xEF3392, 0xB817C9, |
| 241 0x9B5861, 0xBC57E1, 0xC68351, 0x103ED8, 0x4871DD, 0xDD1C2D, |
| 242 0xA118AF, 0x462C21, 0xD7F359, 0x987AD9, 0xC0549E, 0xFA864F, |
| 243 0xFC0656, 0xAE79E5, 0x362289, 0x22AD38, 0xDC9367, 0xAAE855, |
| 244 0x382682, 0x9BE7CA, 0xA40D51, 0xB13399, 0x0ED7A9, 0x480569, |
| 245 0xF0B265, 0xA7887F, 0x974C88, 0x36D1F9, 0xB39221, 0x4A827B, |
| 246 0x21CF98, 0xDC9F40, 0x5547DC, 0x3A74E1, 0x42EB67, 0xDF9DFE, |
| 247 0x5FD45E, 0xA4677B, 0x7AACBA, 0xA2F655, 0x23882B, 0x55BA41, |
| 248 0x086E59, 0x862A21, 0x834739, 0xE6E389, 0xD49EE5, 0x40FB49, |
| 249 0xE956FF, 0xCA0F1C, 0x8A59C5, 0x2BFA94, 0xC5C1D3, 0xCFC50F, |
| 250 0xAE5ADB, 0x86C547, 0x624385, 0x3B8621, 0x94792C, 0x876110, |
| 251 0x7B4C2A, 0x1A2C80, 0x12BF43, 0x902688, 0x893C78, 0xE4C4A8, |
| 252 0x7BDBE5, 0xC23AC4, 0xEAF426, 0x8A67F7, 0xBF920D, 0x2BA365, |
| 253 0xB1933D, 0x0B7CBD, 0xDC51A4, 0x63DD27, 0xDDE169, 0x19949A, |
| 254 0x9529A8, 0x28CE68, 0xB4ED09, 0x209F44, 0xCA984E, 0x638270, |
| 255 0x237C7E, 0x32B90F, 0x8EF5A7, 0xE75614, 0x08F121, 0x2A9DB5, |
| 256 0x4D7E6F, 0x5119A5, 0xABF9B5, 0xD6DF82, 0x61DD96, 0x023616, |
| 257 0x9F3AC4, 0xA1A283, 0x6DED72, 0x7A8D39, 0xA9B882, 0x5C326B, |
| 258 0x5B2746, 0xED3400, 0x7700D2, 0x55F4FC, 0x4D5901, 0x8071E0, |
| 259 #endif |
| 260 }; |
| 261 |
| 262 static const double PIo2[] = { |
| 263 1.57079625129699707031e+00, /* 0x3FF921FB, 0x40000000 */ |
| 264 7.54978941586159635335e-08, /* 0x3E74442D, 0x00000000 */ |
| 265 5.39030252995776476554e-15, /* 0x3CF84698, 0x80000000 */ |
| 266 3.28200341580791294123e-22, /* 0x3B78CC51, 0x60000000 */ |
| 267 1.27065575308067607349e-29, /* 0x39F01B83, 0x80000000 */ |
| 268 1.22933308981111328932e-36, /* 0x387A2520, 0x40000000 */ |
| 269 2.73370053816464559624e-44, /* 0x36E38222, 0x80000000 */ |
| 270 2.16741683877804819444e-51, /* 0x3569F31D, 0x00000000 */ |
| 271 }; |
| 272 |
| 273 int __rem_pio2_large(double *x, double *y, int e0, int nx, int prec) |
| 274 { |
| 275 int32_t jz,jx,jv,jp,jk,carry,n,iq[20],i,j,k,m,q0,ih; |
| 276 double z,fw,f[20],fq[20],q[20]; |
| 277 |
| 278 /* initialize jk*/ |
| 279 jk = init_jk[prec]; |
| 280 jp = jk; |
| 281 |
| 282 /* determine jx,jv,q0, note that 3>q0 */ |
| 283 jx = nx-1; |
| 284 jv = (e0-3)/24; if(jv<0) jv=0; |
| 285 q0 = e0-24*(jv+1); |
| 286 |
| 287 /* set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk] */ |
| 288 j = jv-jx; m = jx+jk; |
| 289 for (i=0; i<=m; i++,j++) |
| 290 f[i] = j<0 ? 0.0 : (double)ipio2[j]; |
| 291 |
| 292 /* compute q[0],q[1],...q[jk] */ |
| 293 for (i=0; i<=jk; i++) { |
| 294 for (j=0,fw=0.0; j<=jx; j++) |
| 295 fw += x[j]*f[jx+i-j]; |
| 296 q[i] = fw; |
| 297 } |
| 298 |
| 299 jz = jk; |
| 300 recompute: |
| 301 /* distill q[] into iq[] reversingly */ |
| 302 for (i=0,j=jz,z=q[jz]; j>0; i++,j--) { |
| 303 fw = (double)(int32_t)(0x1p-24*z); |
| 304 iq[i] = (int32_t)(z - 0x1p24*fw); |
| 305 z = q[j-1]+fw; |
| 306 } |
| 307 |
| 308 /* compute n */ |
| 309 z = scalbn(z,q0); /* actual value of z */ |
| 310 z -= 8.0*floor(z*0.125); /* trim off integer >= 8 */ |
| 311 n = (int32_t)z; |
| 312 z -= (double)n; |
| 313 ih = 0; |
| 314 if (q0 > 0) { /* need iq[jz-1] to determine n */ |
| 315 i = iq[jz-1]>>(24-q0); n += i; |
| 316 iq[jz-1] -= i<<(24-q0); |
| 317 ih = iq[jz-1]>>(23-q0); |
| 318 } |
| 319 else if (q0 == 0) ih = iq[jz-1]>>23; |
| 320 else if (z >= 0.5) ih = 2; |
| 321 |
| 322 if (ih > 0) { /* q > 0.5 */ |
| 323 n += 1; carry = 0; |
| 324 for (i=0; i<jz; i++) { /* compute 1-q */ |
| 325 j = iq[i]; |
| 326 if (carry == 0) { |
| 327 if (j != 0) { |
| 328 carry = 1; |
| 329 iq[i] = 0x1000000 - j; |
| 330 } |
| 331 } else |
| 332 iq[i] = 0xffffff - j; |
| 333 } |
| 334 if (q0 > 0) { /* rare case: chance is 1 in 12 */ |
| 335 switch(q0) { |
| 336 case 1: |
| 337 iq[jz-1] &= 0x7fffff; break; |
| 338 case 2: |
| 339 iq[jz-1] &= 0x3fffff; break; |
| 340 } |
| 341 } |
| 342 if (ih == 2) { |
| 343 z = 1.0 - z; |
| 344 if (carry != 0) |
| 345 z -= scalbn(1.0,q0); |
| 346 } |
| 347 } |
| 348 |
| 349 /* check if recomputation is needed */ |
| 350 if (z == 0.0) { |
| 351 j = 0; |
| 352 for (i=jz-1; i>=jk; i--) j |= iq[i]; |
| 353 if (j == 0) { /* need recomputation */ |
| 354 for (k=1; iq[jk-k]==0; k++); /* k = no. of terms needed
*/ |
| 355 |
| 356 for (i=jz+1; i<=jz+k; i++) { /* add q[jz+1] to q[jz+k]
*/ |
| 357 f[jx+i] = (double)ipio2[jv+i]; |
| 358 for (j=0,fw=0.0; j<=jx; j++) |
| 359 fw += x[j]*f[jx+i-j]; |
| 360 q[i] = fw; |
| 361 } |
| 362 jz += k; |
| 363 goto recompute; |
| 364 } |
| 365 } |
| 366 |
| 367 /* chop off zero terms */ |
| 368 if (z == 0.0) { |
| 369 jz -= 1; |
| 370 q0 -= 24; |
| 371 while (iq[jz] == 0) { |
| 372 jz--; |
| 373 q0 -= 24; |
| 374 } |
| 375 } else { /* break z into 24-bit if necessary */ |
| 376 z = scalbn(z,-q0); |
| 377 if (z >= 0x1p24) { |
| 378 fw = (double)(int32_t)(0x1p-24*z); |
| 379 iq[jz] = (int32_t)(z - 0x1p24*fw); |
| 380 jz += 1; |
| 381 q0 += 24; |
| 382 iq[jz] = (int32_t)fw; |
| 383 } else |
| 384 iq[jz] = (int32_t)z; |
| 385 } |
| 386 |
| 387 /* convert integer "bit" chunk to floating-point value */ |
| 388 fw = scalbn(1.0,q0); |
| 389 for (i=jz; i>=0; i--) { |
| 390 q[i] = fw*(double)iq[i]; |
| 391 fw *= 0x1p-24; |
| 392 } |
| 393 |
| 394 /* compute PIo2[0,...,jp]*q[jz,...,0] */ |
| 395 for(i=jz; i>=0; i--) { |
| 396 for (fw=0.0,k=0; k<=jp && k<=jz-i; k++) |
| 397 fw += PIo2[k]*q[i+k]; |
| 398 fq[jz-i] = fw; |
| 399 } |
| 400 |
| 401 /* compress fq[] into y[] */ |
| 402 switch(prec) { |
| 403 case 0: |
| 404 fw = 0.0; |
| 405 for (i=jz; i>=0; i--) |
| 406 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--) |
| 413 fw += fq[i]; |
| 414 // TODO: drop excess precision here once double_t is used |
| 415 fw = (double)fw; |
| 416 y[0] = ih==0 ? fw : -fw; |
| 417 fw = fq[0]-fw; |
| 418 for (i=1; i<=jz; i++) |
| 419 fw += fq[i]; |
| 420 y[1] = ih==0 ? fw : -fw; |
| 421 break; |
| 422 case 3: /* painful */ |
| 423 for (i=jz; i>0; i--) { |
| 424 fw = fq[i-1]+fq[i]; |
| 425 fq[i] += fq[i-1]-fw; |
| 426 fq[i-1] = fw; |
| 427 } |
| 428 for (i=jz; i>1; i--) { |
| 429 fw = fq[i-1]+fq[i]; |
| 430 fq[i] += fq[i-1]-fw; |
| 431 fq[i-1] = fw; |
| 432 } |
| 433 for (fw=0.0,i=jz; i>=2; i--) |
| 434 fw += fq[i]; |
| 435 if (ih==0) { |
| 436 y[0] = fq[0]; y[1] = fq[1]; y[2] = fw; |
| 437 } else { |
| 438 y[0] = -fq[0]; y[1] = -fq[1]; y[2] = -fw; |
| 439 } |
| 440 } |
| 441 return n&7; |
| 442 } |
| OLD | NEW |
|---|
Chromium Code Reviews
Issue 1573973002:
Add a "fork" of musl as //fusl. (Closed)
Base URL: https://github.com/domokit/mojo.git@master