path: root/third_party/rust/libm/src/math/rem_pio2_large.rs

#![allow(unused_unsafe)]
/* 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.
 * ====================================================
 */

use super::floor;
use super::scalbn;

// initial value for jk
const INIT_JK: [usize; 4] = [3, 4, 4, 6];

// 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.
#[cfg(any(target_pointer_width = "32", target_pointer_width = "16"))]
const IPIO2: [i32; 66] = [
    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,
];

#[cfg(target_pointer_width = "64")]
const IPIO2: [i32; 690] = [
    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, 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,
];

const PIO2: [f64; 8] = [
    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 */
];

// fn rem_pio2_large(x : &[f64], y : &mut [f64], e0 : i32, prec : usize) -> i32
//
// 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.
//
//      prec    an integer indicating the precision:
//                      0       24  bits (single)
//                      1       53  bits (double)
//                      2       64  bits (extended)
//                      3       113 bits (quad)
//
// 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.

/// 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.
#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
pub(crate) fn rem_pio2_large(x: &[f64], y: &mut [f64], e0: i32, prec: usize) -> i32 {
    let x1p24 = f64::from_bits(0x4170000000000000); // 0x1p24 === 2 ^ 24
    let x1p_24 = f64::from_bits(0x3e70000000000000); // 0x1p_24 === 2 ^ (-24)

    #[cfg(all(target_pointer_width = "64", feature = "checked"))]
    assert!(e0 <= 16360);

    let nx = x.len();

    let mut fw: f64;
    let mut n: i32;
    let mut ih: i32;
    let mut z: f64;
    let mut f: [f64; 20] = [0.; 20];
    let mut fq: [f64; 20] = [0.; 20];
    let mut q: [f64; 20] = [0.; 20];
    let mut iq: [i32; 20] = [0; 20];

    /* initialize jk*/
    let jk = i!(INIT_JK, prec);
    let jp = jk;

    /* determine jx,jv,q0, note that 3>q0 */
    let jx = nx - 1;
    let mut jv = div!(e0 - 3, 24);
    if jv < 0 {
        jv = 0;
    }
    let mut q0 = e0 - 24 * (jv + 1);
    let jv = jv as usize;

    /* set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk] */
    let mut j = (jv as i32) - (jx as i32);
    let m = jx + jk;
    for i in 0..=m {
        i!(f, i, =, if j < 0 {
            0.
        } else {
            i!(IPIO2, j as usize) as f64
        });
        j += 1;
    }

    /* compute q[0],q[1],...q[jk] */
    for i in 0..=jk {
        fw = 0f64;
        for j in 0..=jx {
            fw += i!(x, j) * i!(f, jx + i - j);
        }
        i!(q, i, =, fw);
    }

    let mut jz = jk;

    'recompute: loop {
        /* distill q[] into iq[] reversingly */
        let mut i = 0i32;
        z = i!(q, jz);
        for j in (1..=jz).rev() {
            fw = (x1p_24 * z) as i32 as f64;
            i!(iq, i as usize, =, (z - x1p24 * fw) as i32);
            z = i!(q, j - 1) + fw;
            i += 1;
        }

        /* compute n */
        z = scalbn(z, q0); /* actual value of z */
        z -= 8.0 * floor(z * 0.125); /* trim off integer >= 8 */
        n = z as i32;
        z -= n as f64;
        ih = 0;
        if q0 > 0 {
            /* need iq[jz-1] to determine n */
            i = i!(iq, jz - 1) >> (24 - q0);
            n += i;
            i!(iq, jz - 1, -=, i << (24 - q0));
            ih = i!(iq, jz - 1) >> (23 - q0);
        } else if q0 == 0 {
            ih = i!(iq, jz - 1) >> 23;
        } else if z >= 0.5 {
            ih = 2;
        }

        if ih > 0 {
            /* q > 0.5 */
            n += 1;
            let mut carry = 0i32;
            for i in 0..jz {
                /* compute 1-q */
                let j = i!(iq, i);
                if carry == 0 {
                    if j != 0 {
                        carry = 1;
                        i!(iq, i, =, 0x1000000 - j);
                    }
                } else {
                    i!(iq, i, =, 0xffffff - j);
                }
            }
            if q0 > 0 {
                /* rare case: chance is 1 in 12 */
                match q0 {
                    1 => {
                        i!(iq, jz - 1, &=, 0x7fffff);
                    }
                    2 => {
                        i!(iq, jz - 1, &=, 0x3fffff);
                    }
                    _ => {}
                }
            }
            if ih == 2 {
                z = 1. - z;
                if carry != 0 {
                    z -= scalbn(1., q0);
                }
            }
        }

        /* check if recomputation is needed */
        if z == 0. {
            let mut j = 0;
            for i in (jk..=jz - 1).rev() {
                j |= i!(iq, i);
            }
            if j == 0 {
                /* need recomputation */
                let mut k = 1;
                while i!(iq, jk - k, ==, 0) {
                    k += 1; /* k = no. of terms needed */
                }

                for i in (jz + 1)..=(jz + k) {
                    /* add q[jz+1] to q[jz+k] */
                    i!(f, jx + i, =, i!(IPIO2, jv + i) as f64);
                    fw = 0f64;
                    for j in 0..=jx {
                        fw += i!(x, j) * i!(f, jx + i - j);
                    }
                    i!(q, i, =, fw);
                }
                jz += k;
                continue 'recompute;
            }
        }

        break;
    }

    /* chop off zero terms */
    if z == 0. {
        jz -= 1;
        q0 -= 24;
        while i!(iq, jz) == 0 {
            jz -= 1;
            q0 -= 24;
        }
    } else {
        /* break z into 24-bit if necessary */
        z = scalbn(z, -q0);
        if z >= x1p24 {
            fw = (x1p_24 * z) as i32 as f64;
            i!(iq, jz, =, (z - x1p24 * fw) as i32);
            jz += 1;
            q0 += 24;
            i!(iq, jz, =, fw as i32);
        } else {
            i!(iq, jz, =, z as i32);
        }
    }

    /* convert integer "bit" chunk to floating-point value */
    fw = scalbn(1., q0);
    for i in (0..=jz).rev() {
        i!(q, i, =, fw * (i!(iq, i) as f64));
        fw *= x1p_24;
    }

    /* compute PIo2[0,...,jp]*q[jz,...,0] */
    for i in (0..=jz).rev() {
        fw = 0f64;
        let mut k = 0;
        while (k <= jp) && (k <= jz - i) {
            fw += i!(PIO2, k) * i!(q, i + k);
            k += 1;
        }
        i!(fq, jz - i, =, fw);
    }

    /* compress fq[] into y[] */
    match prec {
        0 => {
            fw = 0f64;
            for i in (0..=jz).rev() {
                fw += i!(fq, i);
            }
            i!(y, 0, =, if ih == 0 { fw } else { -fw });
        }
        1 | 2 => {
            fw = 0f64;
            for i in (0..=jz).rev() {
                fw += i!(fq, i);
            }
            // TODO: drop excess precision here once double_t is used
            fw = fw as f64;
            i!(y, 0, =, if ih == 0 { fw } else { -fw });
            fw = i!(fq, 0) - fw;
            for i in 1..=jz {
                fw += i!(fq, i);
            }
            i!(y, 1, =, if ih == 0 { fw } else { -fw });
        }
        3 => {
            /* painful */
            for i in (1..=jz).rev() {
                fw = i!(fq, i - 1) + i!(fq, i);
                i!(fq, i, +=, i!(fq, i - 1) - fw);
                i!(fq, i - 1, =, fw);
            }
            for i in (2..=jz).rev() {
                fw = i!(fq, i - 1) + i!(fq, i);
                i!(fq, i, +=, i!(fq, i - 1) - fw);
                i!(fq, i - 1, =, fw);
            }
            fw = 0f64;
            for i in (2..=jz).rev() {
                fw += i!(fq, i);
            }
            if ih == 0 {
                i!(y, 0, =, i!(fq, 0));
                i!(y, 1, =, i!(fq, 1));
                i!(y, 2, =, fw);
            } else {
                i!(y, 0, =, -i!(fq, 0));
                i!(y, 1, =, -i!(fq, 1));
                i!(y, 2, =, -fw);
            }
        }
        #[cfg(debug_assertions)]
        _ => unreachable!(),
        #[cfg(not(debug_assertions))]
        _ => {}
    }
    n & 7
}