| /* origin: FreeBSD /usr/src/lib/msun/src/k_rem_pio2.c */ |
| /* |
| * ==================================================== |
| * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
| * |
| * Developed at SunSoft, a Sun Microsystems, Inc. business. |
| * Permission to use, copy, modify, and distribute this |
| * software is freely granted, provided that this notice |
| * is preserved. |
| * ==================================================== |
| */ |
| /* |
| * __rem_pio2_large(x,y,e0,nx,prec) |
| * double x[],y[]; int e0,nx,prec; |
| * |
| * __rem_pio2_large return the last three digits of N with |
| * y = x - N*pi/2 |
| * so that |y| < pi/2. |
| * |
| * The method is to compute the integer (mod 8) and fraction parts of |
| * (2/pi)*x without doing the full multiplication. In general we |
| * skip the part of the product that are known to be a huge integer ( |
| * more accurately, = 0 mod 8 ). Thus the number of operations are |
| * independent of the exponent of the input. |
| * |
| * (2/pi) is represented by an array of 24-bit integers in ipio2[]. |
| * |
| * Input parameters: |
| * x[] The input value (must be positive) is broken into nx |
| * pieces of 24-bit integers in double precision format. |
| * x[i] will be the i-th 24 bit of x. The scaled exponent |
| * of x[0] is given in input parameter e0 (i.e., x[0]*2^e0 |
| * match x's up to 24 bits. |
| * |
| * Example of breaking a double positive z into x[0]+x[1]+x[2]: |
| * e0 = ilogb(z)-23 |
| * z = scalbn(z,-e0) |
| * for i = 0,1,2 |
| * x[i] = floor(z) |
| * z = (z-x[i])*2**24 |
| * |
| * |
| * y[] ouput result in an array of double precision numbers. |
| * The dimension of y[] is: |
| * 24-bit precision 1 |
| * 53-bit precision 2 |
| * 64-bit precision 2 |
| * 113-bit precision 3 |
| * The actual value is the sum of them. Thus for 113-bit |
| * precison, one may have to do something like: |
| * |
| * long double t,w,r_head, r_tail; |
| * t = (long double)y[2] + (long double)y[1]; |
| * w = (long double)y[0]; |
| * r_head = t+w; |
| * r_tail = w - (r_head - t); |
| * |
| * e0 The exponent of x[0]. Must be <= 16360 or you need to |
| * expand the ipio2 table. |
| * |
| * nx dimension of x[] |
| * |
| * prec an integer indicating the precision: |
| * 0 24 bits (single) |
| * 1 53 bits (double) |
| * 2 64 bits (extended) |
| * 3 113 bits (quad) |
| * |
| * External function: |
| * double scalbn(), floor(); |
| * |
| * |
| * Here is the description of some local variables: |
| * |
| * jk jk+1 is the initial number of terms of ipio2[] needed |
| * in the computation. The minimum and recommended value |
| * for jk is 3,4,4,6 for single, double, extended, and quad. |
| * jk+1 must be 2 larger than you might expect so that our |
| * recomputation test works. (Up to 24 bits in the integer |
| * part (the 24 bits of it that we compute) and 23 bits in |
| * the fraction part may be lost to cancelation before we |
| * recompute.) |
| * |
| * jz local integer variable indicating the number of |
| * terms of ipio2[] used. |
| * |
| * jx nx - 1 |
| * |
| * jv index for pointing to the suitable ipio2[] for the |
| * computation. In general, we want |
| * ( 2^e0*x[0] * ipio2[jv-1]*2^(-24jv) )/8 |
| * is an integer. Thus |
| * e0-3-24*jv >= 0 or (e0-3)/24 >= jv |
| * Hence jv = max(0,(e0-3)/24). |
| * |
| * jp jp+1 is the number of terms in PIo2[] needed, jp = jk. |
| * |
| * q[] double array with integral value, representing the |
| * 24-bits chunk of the product of x and 2/pi. |
| * |
| * q0 the corresponding exponent of q[0]. Note that the |
| * exponent for q[i] would be q0-24*i. |
| * |
| * PIo2[] double precision array, obtained by cutting pi/2 |
| * into 24 bits chunks. |
| * |
| * f[] ipio2[] in floating point |
| * |
| * iq[] integer array by breaking up q[] in 24-bits chunk. |
| * |
| * fq[] final product of x*(2/pi) in fq[0],..,fq[jk] |
| * |
| * ih integer. If >0 it indicates q[] is >= 0.5, hence |
| * it also indicates the *sign* of the result. |
| * |
| */ |
| /* |
| * Constants: |
| * The hexadecimal values are the intended ones for the following |
| * constants. The decimal values may be used, provided that the |
| * compiler will convert from decimal to binary accurately enough |
| * to produce the hexadecimal values shown. |
| */ |
| |
| #include "libm.h" |
| |
| static const int init_jk[] = {3, 4, 4, 6}; /* initial value for jk */ |
| |
| /* |
| * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi |
| * |
| * integer array, contains the (24*i)-th to (24*i+23)-th |
| * bit of 2/pi after binary point. The corresponding |
| * floating value is |
| * |
| * ipio2[i] * 2^(-24(i+1)). |
| * |
| * NB: This table must have at least (e0-3)/24 + jk terms. |
| * For quad precision (e0 <= 16360, jk = 6), this is 686. |
| */ |
| static const int32_t ipio2[] = { |
| 0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62, 0x95993C, |
| 0x439041, 0xFE5163, 0xABDEBB, 0xC561B7, 0x246E3A, 0x424DD2, 0xE00649, |
| 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129, 0xA73EE8, 0x8235F5, 0x2EBB44, |
| 0x84E99C, 0x7026B4, 0x5F7E41, 0x3991D6, 0x398353, 0x39F49C, 0x845F8B, |
| 0xBDF928, 0x3B1FF8, 0x97FFDE, 0x05980F, 0xEF2F11, 0x8B5A0A, 0x6D1F6D, |
| 0x367ECF, 0x27CB09, 0xB74F46, 0x3F669E, 0x5FEA2D, 0x7527BA, 0xC7EBE5, |
| 0xF17B3D, 0x0739F7, 0x8A5292, 0xEA6BFB, 0x5FB11F, 0x8D5D08, 0x560330, |
| 0x46FC7B, 0x6BABF0, 0xCFBC20, 0x9AF436, 0x1DA9E3, 0x91615E, 0xE61B08, |
| 0x659985, 0x5F14A0, 0x68408D, 0xFFD880, 0x4D7327, 0x310606, 0x1556CA, |
| 0x73A8C9, 0x60E27B, 0xC08C6B, |
| |
| #if LDBL_MAX_EXP > 1024 |
| 0x47C419, 0xC367CD, 0xDCE809, 0x2A8359, 0xC4768B, 0x961CA6, 0xDDAF44, |
| 0xD15719, 0x053EA5, 0xFF0705, 0x3F7E33, 0xE832C2, 0xDE4F98, 0x327DBB, |
| 0xC33D26, 0xEF6B1E, 0x5EF89F, 0x3A1F35, 0xCAF27F, 0x1D87F1, 0x21907C, |
| 0x7C246A, 0xFA6ED5, 0x772D30, 0x433B15, 0xC614B5, 0x9D19C3, 0xC2C4AD, |
| 0x414D2C, 0x5D000C, 0x467D86, 0x2D71E3, 0x9AC69B, 0x006233, 0x7CD2B4, |
| 0x97A7B4, 0xD55537, 0xF63ED7, 0x1810A3, 0xFC764D, 0x2A9D64, 0xABD770, |
| 0xF87C63, 0x57B07A, 0xE71517, 0x5649C0, 0xD9D63B, 0x3884A7, 0xCB2324, |
| 0x778AD6, 0x23545A, 0xB91F00, 0x1B0AF1, 0xDFCE19, 0xFF319F, 0x6A1E66, |
| 0x615799, 0x47FBAC, 0xD87F7E, 0xB76522, 0x89E832, 0x60BFE6, 0xCDC4EF, |
| 0x09366C, 0xD43F5D, 0xD7DE16, 0xDE3B58, 0x929BDE, 0x2822D2, 0xE88628, |
| 0x4D58E2, 0x32CAC6, 0x16E308, 0xCB7DE0, 0x50C017, 0xA71DF3, 0x5BE018, |
| 0x34132E, 0x621283, 0x014883, 0x5B8EF5, 0x7FB0AD, 0xF2E91E, 0x434A48, |
| 0xD36710, 0xD8DDAA, 0x425FAE, 0xCE616A, 0xA4280A, 0xB499D3, 0xF2A606, |
| 0x7F775C, 0x83C2A3, 0x883C61, 0x78738A, 0x5A8CAF, 0xBDD76F, 0x63A62D, |
| 0xCBBFF4, 0xEF818D, 0x67C126, 0x45CA55, 0x36D9CA, 0xD2A828, 0x8D61C2, |
| 0x77C912, 0x142604, 0x9B4612, 0xC459C4, 0x44C5C8, 0x91B24D, 0xF31700, |
| 0xAD43D4, 0xE54929, 0x10D5FD, 0xFCBE00, 0xCC941E, 0xEECE70, 0xF53E13, |
| 0x80F1EC, 0xC3E7B3, 0x28F8C7, 0x940593, 0x3E71C1, 0xB3092E, 0xF3450B, |
| 0x9C1288, 0x7B20AB, 0x9FB52E, 0xC29247, 0x2F327B, 0x6D550C, 0x90A772, |
| 0x1FE76B, 0x96CB31, 0x4A1679, 0xE27941, 0x89DFF4, 0x9794E8, 0x84E6E2, |
| 0x973199, 0x6BED88, 0x365F5F, 0x0EFDBB, 0xB49A48, 0x6CA467, 0x427271, |
| 0x325D8D, 0xB8159F, 0x09E5BC, 0x25318D, 0x3974F7, 0x1C0530, 0x010C0D, |
| 0x68084B, 0x58EE2C, 0x90AA47, 0x02E774, 0x24D6BD, 0xA67DF7, 0x72486E, |
| 0xEF169F, 0xA6948E, 0xF691B4, 0x5153D1, 0xF20ACF, 0x339820, 0x7E4BF5, |
| 0x6863B2, 0x5F3EDD, 0x035D40, 0x7F8985, 0x295255, 0xC06437, 0x10D86D, |
| 0x324832, 0x754C5B, 0xD4714E, 0x6E5445, 0xC1090B, 0x69F52A, 0xD56614, |
| 0x9D0727, 0x50045D, 0xDB3BB4, 0xC576EA, 0x17F987, 0x7D6B49, 0xBA271D, |
| 0x296996, 0xACCCC6, 0x5414AD, 0x6AE290, 0x89D988, 0x50722C, 0xBEA404, |
| 0x940777, 0x7030F3, 0x27FC00, 0xA871EA, 0x49C266, 0x3DE064, 0x83DD97, |
| 0x973FA3, 0xFD9443, 0x8C860D, 0xDE4131, 0x9D3992, 0x8C70DD, 0xE7B717, |
| 0x3BDF08, 0x2B3715, 0xA0805C, 0x93805A, 0x921110, 0xD8E80F, 0xAF806C, |
| 0x4BFFDB, 0x0F9038, 0x761859, 0x15A562, 0xBBCB61, 0xB989C7, 0xBD4010, |
| 0x04F2D2, 0x277549, 0xF6B6EB, 0xBB22DB, 0xAA140A, 0x2F2689, 0x768364, |
| 0x333B09, 0x1A940E, 0xAA3A51, 0xC2A31D, 0xAEEDAF, 0x12265C, 0x4DC26D, |
| 0x9C7A2D, 0x9756C0, 0x833F03, 0xF6F009, 0x8C402B, 0x99316D, 0x07B439, |
| 0x15200C, 0x5BC3D8, 0xC492F5, 0x4BADC6, 0xA5CA4E, 0xCD37A7, 0x36A9E6, |
| 0x9492AB, 0x6842DD, 0xDE6319, 0xEF8C76, 0x528B68, 0x37DBFC, 0xABA1AE, |
| 0x3115DF, 0xA1AE00, 0xDAFB0C, 0x664D64, 0xB705ED, 0x306529, 0xBF5657, |
| 0x3AFF47, 0xB9F96A, 0xF3BE75, 0xDF9328, 0x3080AB, 0xF68C66, 0x15CB04, |
| 0x0622FA, 0x1DE4D9, 0xA4B33D, 0x8F1B57, 0x09CD36, 0xE9424E, 0xA4BE13, |
| 0xB52333, 0x1AAAF0, 0xA8654F, 0xA5C1D2, 0x0F3F0B, 0xCD785B, 0x76F923, |
| 0x048B7B, 0x721789, 0x53A6C6, 0xE26E6F, 0x00EBEF, 0x584A9B, 0xB7DAC4, |
| 0xBA66AA, 0xCFCF76, 0x1D02D1, 0x2DF1B1, 0xC1998C, 0x77ADC3, 0xDA4886, |
| 0xA05DF7, 0xF480C6, 0x2FF0AC, 0x9AECDD, 0xBC5C3F, 0x6DDED0, 0x1FC790, |
| 0xB6DB2A, 0x3A25A3, 0x9AAF00, 0x9353AD, 0x0457B6, 0xB42D29, 0x7E804B, |
| 0xA707DA, 0x0EAA76, 0xA1597B, 0x2A1216, 0x2DB7DC, 0xFDE5FA, 0xFEDB89, |
| 0xFDBE89, 0x6C76E4, 0xFCA906, 0x70803E, 0x156E85, 0xFF87FD, 0x073E28, |
| 0x336761, 0x86182A, 0xEABD4D, 0xAFE7B3, 0x6E6D8F, 0x396795, 0x5BBF31, |
| 0x48D784, 0x16DF30, 0x432DC7, 0x356125, 0xCE70C9, 0xB8CB30, 0xFD6CBF, |
| 0xA200A4, 0xE46C05, 0xA0DD5A, 0x476F21, 0xD21262, 0x845CB9, 0x496170, |
| 0xE0566B, 0x015299, 0x375550, 0xB7D51E, 0xC4F133, 0x5F6E13, 0xE4305D, |
| 0xA92E85, 0xC3B21D, 0x3632A1, 0xA4B708, 0xD4B1EA, 0x21F716, 0xE4698F, |
| 0x77FF27, 0x80030C, 0x2D408D, 0xA0CD4F, 0x99A520, 0xD3A2B3, 0x0A5D2F, |
| 0x42F9B4, 0xCBDA11, 0xD0BE7D, 0xC1DB9B, 0xBD17AB, 0x81A2CA, 0x5C6A08, |
| 0x17552E, 0x550027, 0xF0147F, 0x8607E1, 0x640B14, 0x8D4196, 0xDEBE87, |
| 0x2AFDDA, 0xB6256B, 0x34897B, 0xFEF305, 0x9EBFB9, 0x4F6A68, 0xA82A4A, |
| 0x5AC44F, 0xBCF82D, 0x985AD7, 0x95C7F4, 0x8D4D0D, 0xA63A20, 0x5F57A4, |
| 0xB13F14, 0x953880, 0x0120CC, 0x86DD71, 0xB6DEC9, 0xF560BF, 0x11654D, |
| 0x6B0701, 0xACB08C, 0xD0C0B2, 0x485551, 0x0EFB1E, 0xC37295, 0x3B06A3, |
| 0x3540C0, 0x7BDC06, 0xCC45E0, 0xFA294E, 0xC8CAD6, 0x41F3E8, 0xDE647C, |
| 0xD8649B, 0x31BED9, 0xC397A4, 0xD45877, 0xC5E369, 0x13DAF0, 0x3C3ABA, |
| 0x461846, 0x5F7555, 0xF5BDD2, 0xC6926E, 0x5D2EAC, 0xED440E, 0x423E1C, |
| 0x87C461, 0xE9FD29, 0xF3D6E7, 0xCA7C22, 0x35916F, 0xC5E008, 0x8DD7FF, |
| 0xE26A6E, 0xC6FDB0, 0xC10893, 0x745D7C, 0xB2AD6B, 0x9D6ECD, 0x7B723E, |
| 0x6A11C6, 0xA9CFF7, 0xDF7329, 0xBAC9B5, 0x5100B7, 0x0DB2E2, 0x24BA74, |
| 0x607DE5, 0x8AD874, 0x2C150D, 0x0C1881, 0x94667E, 0x162901, 0x767A9F, |
| 0xBEFDFD, 0xEF4556, 0x367ED9, 0x13D9EC, 0xB9BA8B, 0xFC97C4, 0x27A831, |
| 0xC36EF1, 0x36C594, 0x56A8D8, 0xB5A8B4, 0x0ECCCF, 0x2D8912, 0x34576F, |
| 0x89562C, 0xE3CE99, 0xB920D6, 0xAA5E6B, 0x9C2A3E, 0xCC5F11, 0x4A0BFD, |
| 0xFBF4E1, 0x6D3B8E, 0x2C86E2, 0x84D4E9, 0xA9B4FC, 0xD1EEEF, 0xC9352E, |
| 0x61392F, 0x442138, 0xC8D91B, 0x0AFC81, 0x6A4AFB, 0xD81C2F, 0x84B453, |
| 0x8C994E, 0xCC2254, 0xDC552A, 0xD6C6C0, 0x96190B, 0xB8701A, 0x649569, |
| 0x605A26, 0xEE523F, 0x0F117F, 0x11B5F4, 0xF5CBFC, 0x2DBC34, 0xEEBC34, |
| 0xCC5DE8, 0x605EDD, 0x9B8E67, 0xEF3392, 0xB817C9, 0x9B5861, 0xBC57E1, |
| 0xC68351, 0x103ED8, 0x4871DD, 0xDD1C2D, 0xA118AF, 0x462C21, 0xD7F359, |
| 0x987AD9, 0xC0549E, 0xFA864F, 0xFC0656, 0xAE79E5, 0x362289, 0x22AD38, |
| 0xDC9367, 0xAAE855, 0x382682, 0x9BE7CA, 0xA40D51, 0xB13399, 0x0ED7A9, |
| 0x480569, 0xF0B265, 0xA7887F, 0x974C88, 0x36D1F9, 0xB39221, 0x4A827B, |
| 0x21CF98, 0xDC9F40, 0x5547DC, 0x3A74E1, 0x42EB67, 0xDF9DFE, 0x5FD45E, |
| 0xA4677B, 0x7AACBA, 0xA2F655, 0x23882B, 0x55BA41, 0x086E59, 0x862A21, |
| 0x834739, 0xE6E389, 0xD49EE5, 0x40FB49, 0xE956FF, 0xCA0F1C, 0x8A59C5, |
| 0x2BFA94, 0xC5C1D3, 0xCFC50F, 0xAE5ADB, 0x86C547, 0x624385, 0x3B8621, |
| 0x94792C, 0x876110, 0x7B4C2A, 0x1A2C80, 0x12BF43, 0x902688, 0x893C78, |
| 0xE4C4A8, 0x7BDBE5, 0xC23AC4, 0xEAF426, 0x8A67F7, 0xBF920D, 0x2BA365, |
| 0xB1933D, 0x0B7CBD, 0xDC51A4, 0x63DD27, 0xDDE169, 0x19949A, 0x9529A8, |
| 0x28CE68, 0xB4ED09, 0x209F44, 0xCA984E, 0x638270, 0x237C7E, 0x32B90F, |
| 0x8EF5A7, 0xE75614, 0x08F121, 0x2A9DB5, 0x4D7E6F, 0x5119A5, 0xABF9B5, |
| 0xD6DF82, 0x61DD96, 0x023616, 0x9F3AC4, 0xA1A283, 0x6DED72, 0x7A8D39, |
| 0xA9B882, 0x5C326B, 0x5B2746, 0xED3400, 0x7700D2, 0x55F4FC, 0x4D5901, |
| 0x8071E0, |
| #endif |
| }; |
| |
| static const double PIo2[] = { |
| 1.57079625129699707031e+00, /* 0x3FF921FB, 0x40000000 */ |
| 7.54978941586159635335e-08, /* 0x3E74442D, 0x00000000 */ |
| 5.39030252995776476554e-15, /* 0x3CF84698, 0x80000000 */ |
| 3.28200341580791294123e-22, /* 0x3B78CC51, 0x60000000 */ |
| 1.27065575308067607349e-29, /* 0x39F01B83, 0x80000000 */ |
| 1.22933308981111328932e-36, /* 0x387A2520, 0x40000000 */ |
| 2.73370053816464559624e-44, /* 0x36E38222, 0x80000000 */ |
| 2.16741683877804819444e-51, /* 0x3569F31D, 0x00000000 */ |
| }; |
| |
| int __rem_pio2_large(double* x, double* y, int e0, int nx, int prec) { |
| int32_t jz, jx, jv, jp, jk, carry, n, iq[20], i, j, k, m, q0, ih; |
| double z, fw, f[20], fq[20], q[20]; |
| |
| /* initialize jk*/ |
| jk = init_jk[prec]; |
| jp = jk; |
| |
| /* determine jx,jv,q0, note that 3>q0 */ |
| jx = nx - 1; |
| jv = (e0 - 3) / 24; |
| if (jv < 0) |
| jv = 0; |
| q0 = e0 - 24 * (jv + 1); |
| |
| /* set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk] */ |
| j = jv - jx; |
| m = jx + jk; |
| for (i = 0; i <= m; i++, j++) |
| f[i] = j < 0 ? 0.0 : (double)ipio2[j]; |
| |
| /* compute q[0],q[1],...q[jk] */ |
| for (i = 0; i <= jk; i++) { |
| for (j = 0, fw = 0.0; j <= jx; j++) |
| fw += x[j] * f[jx + i - j]; |
| q[i] = fw; |
| } |
| |
| jz = jk; |
| recompute: |
| /* distill q[] into iq[] reversingly */ |
| for (i = 0, j = jz, z = q[jz]; j > 0; i++, j--) { |
| fw = (double)(int32_t)(0x1p-24 * z); |
| iq[i] = (int32_t)(z - 0x1p24 * fw); |
| z = q[j - 1] + fw; |
| } |
| |
| /* compute n */ |
| z = scalbn(z, q0); /* actual value of z */ |
| z -= 8.0 * floor(z * 0.125); /* trim off integer >= 8 */ |
| n = (int32_t)z; |
| z -= (double)n; |
| ih = 0; |
| if (q0 > 0) { /* need iq[jz-1] to determine n */ |
| i = iq[jz - 1] >> (24 - q0); |
| n += i; |
| iq[jz - 1] -= i << (24 - q0); |
| ih = iq[jz - 1] >> (23 - q0); |
| } else if (q0 == 0) |
| ih = iq[jz - 1] >> 23; |
| else if (z >= 0.5) |
| ih = 2; |
| |
| if (ih > 0) { /* q > 0.5 */ |
| n += 1; |
| carry = 0; |
| for (i = 0; i < jz; i++) { /* compute 1-q */ |
| j = iq[i]; |
| if (carry == 0) { |
| if (j != 0) { |
| carry = 1; |
| iq[i] = 0x1000000 - j; |
| } |
| } else |
| iq[i] = 0xffffff - j; |
| } |
| if (q0 > 0) { /* rare case: chance is 1 in 12 */ |
| switch (q0) { |
| case 1: |
| iq[jz - 1] &= 0x7fffff; |
| break; |
| case 2: |
| iq[jz - 1] &= 0x3fffff; |
| break; |
| } |
| } |
| if (ih == 2) { |
| z = 1.0 - z; |
| if (carry != 0) |
| z -= scalbn(1.0, q0); |
| } |
| } |
| |
| /* check if recomputation is needed */ |
| if (z == 0.0) { |
| j = 0; |
| for (i = jz - 1; i >= jk; i--) |
| j |= iq[i]; |
| if (j == 0) { /* need recomputation */ |
| for (k = 1; iq[jk - k] == 0; k++) |
| ; /* k = no. of terms needed */ |
| |
| for (i = jz + 1; i <= jz + k; i++) { /* add q[jz+1] to q[jz+k] */ |
| f[jx + i] = (double)ipio2[jv + i]; |
| for (j = 0, fw = 0.0; j <= jx; j++) |
| fw += x[j] * f[jx + i - j]; |
| q[i] = fw; |
| } |
| jz += k; |
| goto recompute; |
| } |
| } |
| |
| /* chop off zero terms */ |
| if (z == 0.0) { |
| jz -= 1; |
| q0 -= 24; |
| while (iq[jz] == 0) { |
| jz--; |
| q0 -= 24; |
| } |
| } else { /* break z into 24-bit if necessary */ |
| z = scalbn(z, -q0); |
| if (z >= 0x1p24) { |
| fw = (double)(int32_t)(0x1p-24 * z); |
| iq[jz] = (int32_t)(z - 0x1p24 * fw); |
| jz += 1; |
| q0 += 24; |
| iq[jz] = (int32_t)fw; |
| } else |
| iq[jz] = (int32_t)z; |
| } |
| |
| /* convert integer "bit" chunk to floating-point value */ |
| fw = scalbn(1.0, q0); |
| for (i = jz; i >= 0; i--) { |
| q[i] = fw * (double)iq[i]; |
| fw *= 0x1p-24; |
| } |
| |
| /* compute PIo2[0,...,jp]*q[jz,...,0] */ |
| for (i = jz; i >= 0; i--) { |
| for (fw = 0.0, k = 0; k <= jp && k <= jz - i; k++) |
| fw += PIo2[k] * q[i + k]; |
| fq[jz - i] = fw; |
| } |
| |
| /* compress fq[] into y[] */ |
| switch (prec) { |
| case 0: |
| fw = 0.0; |
| for (i = jz; i >= 0; i--) |
| fw += fq[i]; |
| y[0] = ih == 0 ? fw : -fw; |
| break; |
| case 1: |
| case 2: |
| fw = 0.0; |
| for (i = jz; i >= 0; i--) |
| fw += fq[i]; |
| // TODO: drop excess precision here once double_t is used |
| fw = (double)fw; |
| y[0] = ih == 0 ? fw : -fw; |
| fw = fq[0] - fw; |
| for (i = 1; i <= jz; i++) |
| fw += fq[i]; |
| y[1] = ih == 0 ? fw : -fw; |
| break; |
| case 3: /* painful */ |
| for (i = jz; i > 0; i--) { |
| fw = fq[i - 1] + fq[i]; |
| fq[i] += fq[i - 1] - fw; |
| fq[i - 1] = fw; |
| } |
| for (i = jz; i > 1; i--) { |
| fw = fq[i - 1] + fq[i]; |
| fq[i] += fq[i - 1] - fw; |
| fq[i - 1] = fw; |
| } |
| for (fw = 0.0, i = jz; i >= 2; i--) |
| fw += fq[i]; |
| if (ih == 0) { |
| y[0] = fq[0]; |
| y[1] = fq[1]; |
| y[2] = fw; |
| } else { |
| y[0] = -fq[0]; |
| y[1] = -fq[1]; |
| y[2] = -fw; |
| } |
| } |
| return n & 7; |
| } |
