path: root/target/m68k/softfloat.c

/*
 * Ported from a work by Andreas Grabher for Previous, NeXT Computer Emulator,
 * derived from NetBSD M68040 FPSP functions,
 * derived from release 2a of the SoftFloat IEC/IEEE Floating-point Arithmetic
 * Package. Those parts of the code (and some later contributions) are
 * provided under that license, as detailed below.
 * It has subsequently been modified by contributors to the QEMU Project,
 * so some portions are provided under:
 *  the SoftFloat-2a license
 *  the BSD license
 *  GPL-v2-or-later
 *
 * Any future contributions to this file will be taken to be licensed under
 * the Softfloat-2a license unless specifically indicated otherwise.
 */

/*
 * Portions of this work are licensed under the terms of the GNU GPL,
 * version 2 or later. See the COPYING file in the top-level directory.
 */

#include "qemu/osdep.h"
#include "softfloat.h"
#include "fpu/softfloat-macros.h"
#include "softfloat_fpsp_tables.h"

#define pi_exp      0x4000
#define piby2_exp   0x3FFF
#define pi_sig      UINT64_C(0xc90fdaa22168c235)

static floatx80 propagateFloatx80NaNOneArg(floatx80 a, float_status *status)
{
    if (floatx80_is_signaling_nan(a, status)) {
        float_raise(float_flag_invalid, status);
        a = floatx80_silence_nan(a, status);
    }

    if (status->default_nan_mode) {
        return floatx80_default_nan(status);
    }

    return a;
}

/*
 * Returns the mantissa of the extended double-precision floating-point
 * value `a'.
 */

floatx80 floatx80_getman(floatx80 a, float_status *status)
{
    bool aSign;
    int32_t aExp;
    uint64_t aSig;

    aSig = extractFloatx80Frac(a);
    aExp = extractFloatx80Exp(a);
    aSign = extractFloatx80Sign(a);

    if (aExp == 0x7FFF) {
        if ((uint64_t) (aSig << 1)) {
            return propagateFloatx80NaNOneArg(a , status);
        }
        float_raise(float_flag_invalid , status);
        return floatx80_default_nan(status);
    }

    if (aExp == 0) {
        if (aSig == 0) {
            return packFloatx80(aSign, 0, 0);
        }
        normalizeFloatx80Subnormal(aSig, &aExp, &aSig);
    }

    return roundAndPackFloatx80(status->floatx80_rounding_precision, aSign,
                                0x3FFF, aSig, 0, status);
}

/*
 * Returns the exponent of the extended double-precision floating-point
 * value `a' as an extended double-precision value.
 */

floatx80 floatx80_getexp(floatx80 a, float_status *status)
{
    bool aSign;
    int32_t aExp;
    uint64_t aSig;

    aSig = extractFloatx80Frac(a);
    aExp = extractFloatx80Exp(a);
    aSign = extractFloatx80Sign(a);

    if (aExp == 0x7FFF) {
        if ((uint64_t) (aSig << 1)) {
            return propagateFloatx80NaNOneArg(a , status);
        }
        float_raise(float_flag_invalid , status);
        return floatx80_default_nan(status);
    }

    if (aExp == 0) {
        if (aSig == 0) {
            return packFloatx80(aSign, 0, 0);
        }
        normalizeFloatx80Subnormal(aSig, &aExp, &aSig);
    }

    return int32_to_floatx80(aExp - 0x3FFF, status);
}

/*
 * Scales extended double-precision floating-point value in operand `a' by
 * value `b'. The function truncates the value in the second operand 'b' to
 * an integral value and adds that value to the exponent of the operand 'a'.
 * The operation performed according to the IEC/IEEE Standard for Binary
 * Floating-Point Arithmetic.
 */

floatx80 floatx80_scale(floatx80 a, floatx80 b, float_status *status)
{
    bool aSign, bSign;
    int32_t aExp, bExp, shiftCount;
    uint64_t aSig, bSig;

    aSig = extractFloatx80Frac(a);
    aExp = extractFloatx80Exp(a);
    aSign = extractFloatx80Sign(a);
    bSig = extractFloatx80Frac(b);
    bExp = extractFloatx80Exp(b);
    bSign = extractFloatx80Sign(b);

    if (bExp == 0x7FFF) {
        if ((uint64_t) (bSig << 1) ||
            ((aExp == 0x7FFF) && (uint64_t) (aSig << 1))) {
            return propagateFloatx80NaN(a, b, status);
        }
        float_raise(float_flag_invalid , status);
        return floatx80_default_nan(status);
    }
    if (aExp == 0x7FFF) {
        if ((uint64_t) (aSig << 1)) {
            return propagateFloatx80NaN(a, b, status);
        }
        return packFloatx80(aSign, floatx80_infinity.high,
                            floatx80_infinity.low);
    }
    if (aExp == 0) {
        if (aSig == 0) {
            return packFloatx80(aSign, 0, 0);
        }
        if (bExp < 0x3FFF) {
            return a;
        }
        normalizeFloatx80Subnormal(aSig, &aExp, &aSig);
    }

    if (bExp < 0x3FFF) {
        return a;
    }

    if (0x400F < bExp) {
        aExp = bSign ? -0x6001 : 0xE000;
        return roundAndPackFloatx80(status->floatx80_rounding_precision,
                                    aSign, aExp, aSig, 0, status);
    }

    shiftCount = 0x403E - bExp;
    bSig >>= shiftCount;
    aExp = bSign ? (aExp - bSig) : (aExp + bSig);

    return roundAndPackFloatx80(status->floatx80_rounding_precision,
                                aSign, aExp, aSig, 0, status);
}

floatx80 floatx80_move(floatx80 a, float_status *status)
{
    bool aSign;
    int32_t aExp;
    uint64_t aSig;

    aSig = extractFloatx80Frac(a);
    aExp = extractFloatx80Exp(a);
    aSign = extractFloatx80Sign(a);

    if (aExp == 0x7FFF) {
        if ((uint64_t)(aSig << 1)) {
            return propagateFloatx80NaNOneArg(a, status);
        }
        return a;
    }
    if (aExp == 0) {
        if (aSig == 0) {
            return a;
        }
        normalizeRoundAndPackFloatx80(status->floatx80_rounding_precision,
                                      aSign, aExp, aSig, 0, status);
    }
    return roundAndPackFloatx80(status->floatx80_rounding_precision, aSign,
                                aExp, aSig, 0, status);
}

/*
 * Algorithms for transcendental functions supported by MC68881 and MC68882
 * mathematical coprocessors. The functions are derived from FPSP library.
 */

#define one_exp     0x3FFF
#define one_sig     UINT64_C(0x8000000000000000)

/*
 * Function for compactifying extended double-precision floating point values.
 */

static int32_t floatx80_make_compact(int32_t aExp, uint64_t aSig)
{
    return (aExp << 16) | (aSig >> 48);
}

/*
 * Log base e of x plus 1
 */

floatx80 floatx80_lognp1(floatx80 a, float_status *status)
{
    bool aSign;
    int32_t aExp;
    uint64_t aSig, fSig;

    FloatRoundMode user_rnd_mode;
    FloatX80RoundPrec user_rnd_prec;

    int32_t compact, j, k;
    floatx80 fp0, fp1, fp2, fp3, f, logof2, klog2, saveu;

    aSig = extractFloatx80Frac(a);
    aExp = extractFloatx80Exp(a);
    aSign = extractFloatx80Sign(a);

    if (aExp == 0x7FFF) {
        if ((uint64_t) (aSig << 1)) {
            propagateFloatx80NaNOneArg(a, status);
        }
        if (aSign) {
            float_raise(float_flag_invalid, status);
            return floatx80_default_nan(status);
        }
        return packFloatx80(0, floatx80_infinity.high, floatx80_infinity.low);
    }

    if (aExp == 0 && aSig == 0) {
        return packFloatx80(aSign, 0, 0);
    }

    if (aSign && aExp >= one_exp) {
        if (aExp == one_exp && aSig == one_sig) {
            float_raise(float_flag_divbyzero, status);
            return packFloatx80(aSign, floatx80_infinity.high,
                                floatx80_infinity.low);
        }
        float_raise(float_flag_invalid, status);
        return floatx80_default_nan(status);
    }

    if (aExp < 0x3f99 || (aExp == 0x3f99 && aSig == one_sig)) {
        /* <= min threshold */
        float_raise(float_flag_inexact, status);
        return floatx80_move(a, status);
    }

    user_rnd_mode = status->float_rounding_mode;
    user_rnd_prec = status->floatx80_rounding_precision;
    status->float_rounding_mode = float_round_nearest_even;
    status->floatx80_rounding_precision = floatx80_precision_x;

    compact = floatx80_make_compact(aExp, aSig);

    fp0 = a; /* Z */
    fp1 = a;

    fp0 = floatx80_add(fp0, float32_to_floatx80(make_float32(0x3F800000),
                       status), status); /* X = (1+Z) */

    aExp = extractFloatx80Exp(fp0);
    aSig = extractFloatx80Frac(fp0);

    compact = floatx80_make_compact(aExp, aSig);

    if (compact < 0x3FFE8000 || compact > 0x3FFFC000) {
        /* |X| < 1/2 or |X| > 3/2 */
        k = aExp - 0x3FFF;
        fp1 = int32_to_floatx80(k, status);

        fSig = (aSig & UINT64_C(0xFE00000000000000)) | UINT64_C(0x0100000000000000);
        j = (fSig >> 56) & 0x7E; /* DISPLACEMENT FOR 1/F */

        f = packFloatx80(0, 0x3FFF, fSig); /* F */
        fp0 = packFloatx80(0, 0x3FFF, aSig); /* Y */

        fp0 = floatx80_sub(fp0, f, status); /* Y-F */

    lp1cont1:
        /* LP1CONT1 */
        fp0 = floatx80_mul(fp0, log_tbl[j], status); /* FP0 IS U = (Y-F)/F */
        logof2 = packFloatx80(0, 0x3FFE, UINT64_C(0xB17217F7D1CF79AC));
        klog2 = floatx80_mul(fp1, logof2, status); /* FP1 IS K*LOG2 */
        fp2 = floatx80_mul(fp0, fp0, status); /* FP2 IS V=U*U */

        fp3 = fp2;
        fp1 = fp2;

        fp1 = floatx80_mul(fp1, float64_to_floatx80(
                           make_float64(0x3FC2499AB5E4040B), status),
                           status); /* V*A6 */
        fp2 = floatx80_mul(fp2, float64_to_floatx80(
                           make_float64(0xBFC555B5848CB7DB), status),
                           status); /* V*A5 */
        fp1 = floatx80_add(fp1, float64_to_floatx80(
                           make_float64(0x3FC99999987D8730), status),
                           status); /* A4+V*A6 */
        fp2 = floatx80_add(fp2, float64_to_floatx80(
                           make_float64(0xBFCFFFFFFF6F7E97), status),
                           status); /* A3+V*A5 */
        fp1 = floatx80_mul(fp1, fp3, status); /* V*(A4+V*A6) */
        fp2 = floatx80_mul(fp2, fp3, status); /* V*(A3+V*A5) */
        fp1 = floatx80_add(fp1, float64_to_floatx80(
                           make_float64(0x3FD55555555555A4), status),
                           status); /* A2+V*(A4+V*A6) */
        fp2 = floatx80_add(fp2, float64_to_floatx80(
                           make_float64(0xBFE0000000000008), status),
                           status); /* A1+V*(A3+V*A5) */
        fp1 = floatx80_mul(fp1, fp3, status); /* V*(A2+V*(A4+V*A6)) */
        fp2 = floatx80_mul(fp2, fp3, status); /* V*(A1+V*(A3+V*A5)) */
        fp1 = floatx80_mul(fp1, fp0, status); /* U*V*(A2+V*(A4+V*A6)) */
        fp0 = floatx80_add(fp0, fp2, status); /* U+V*(A1+V*(A3+V*A5)) */

        fp1 = floatx80_add(fp1, log_tbl[j + 1],
                           status); /* LOG(F)+U*V*(A2+V*(A4+V*A6)) */
        fp0 = floatx80_add(fp0, fp1, status); /* FP0 IS LOG(F) + LOG(1+U) */

        status->float_rounding_mode = user_rnd_mode;
        status->floatx80_rounding_precision = user_rnd_prec;

        a = floatx80_add(fp0, klog2, status);

        float_raise(float_flag_inexact, status);

        return a;
    } else if (compact < 0x3FFEF07D || compact > 0x3FFF8841) {
        /* |X| < 1/16 or |X| > -1/16 */
        /* LP1CARE */
        fSig = (aSig & UINT64_C(0xFE00000000000000)) | UINT64_C(0x0100000000000000);
        f = packFloatx80(0, 0x3FFF, fSig); /* F */
        j = (fSig >> 56) & 0x7E; /* DISPLACEMENT FOR 1/F */

        if (compact >= 0x3FFF8000) { /* 1+Z >= 1 */
            /* KISZERO */
            fp0 = floatx80_sub(float32_to_floatx80(make_float32(0x3F800000),
                               status), f, status); /* 1-F */
            fp0 = floatx80_add(fp0, fp1, status); /* FP0 IS Y-F = (1-F)+Z */
            fp1 = packFloatx80(0, 0, 0); /* K = 0 */
        } else {
            /* KISNEG */
            fp0 = floatx80_sub(float32_to_floatx80(make_float32(0x40000000),
                               status), f, status); /* 2-F */
            fp1 = floatx80_add(fp1, fp1, status); /* 2Z */
            fp0 = floatx80_add(fp0, fp1, status); /* FP0 IS Y-F = (2-F)+2Z */
            fp1 = packFloatx80(1, one_exp, one_sig); /* K = -1 */
        }
        goto lp1cont1;
    } else {
        /* LP1ONE16 */
        fp1 = floatx80_add(fp1, fp1, status); /* FP1 IS 2Z */
        fp0 = floatx80_add(fp0, float32_to_floatx80(make_float32(0x3F800000),
                           status), status); /* FP0 IS 1+X */

        /* LP1CONT2 */
        fp1 = floatx80_div(fp1, fp0, status); /* U */
        saveu = fp1;
        fp0 = floatx80_mul(fp1, fp1, status); /* FP0 IS V = U*U */
        fp1 = floatx80_mul(fp0, fp0, status); /* FP1 IS W = V*V */

        fp3 = float64_to_floatx80(make_float64(0x3F175496ADD7DAD6),
                                  status); /* B5 */
        fp2 = float64_to_floatx80(make_float64(0x3F3C71C2FE80C7E0),
                                  status); /* B4 */
        fp3 = floatx80_mul(fp3, fp1, status); /* W*B5 */
        fp2 = floatx80_mul(fp2, fp1, status); /* W*B4 */
        fp3 = floatx80_add(fp3, float64_to_floatx80(
                           make_float64(0x3F624924928BCCFF), status),
                           status); /* B3+W*B5 */
        fp2 = floatx80_add(fp2, float64_to_floatx80(
                           make_float64(0x3F899999999995EC), status),
                           status); /* B2+W*B4 */
        fp1 = floatx80_mul(fp1, fp3, status); /* W*(B3+W*B5) */
        fp2 = floatx80_mul(fp2, fp0, status); /* V*(B2+W*B4) */
        fp1 = floatx80_add(fp1, float64_to_floatx80(
                           make_float64(0x3FB5555555555555), status),
                           status); /* B1+W*(B3+W*B5) */

        fp0 = floatx80_mul(fp0, saveu, status); /* FP0 IS U*V */
        fp1 = floatx80_add(fp1, fp2,
                           status); /* B1+W*(B3+W*B5) + V*(B2+W*B4) */
        fp0 = floatx80_mul(fp0, fp1,
                           status); /* U*V*([B1+W*(B3+W*B5)] + [V*(B2+W*B4)]) */

        status->float_rounding_mode = user_rnd_mode;
        status->floatx80_rounding_precision = user_rnd_prec;

        a = floatx80_add(fp0, saveu, status);

        /*if (!floatx80_is_zero(a)) { */
            float_raise(float_flag_inexact, status);
        /*} */

        return a;
    }
}

/*
 * Log base e
 */

floatx80 floatx80_logn(floatx80 a, float_status *status)
{
    bool aSign;
    int32_t aExp;
    uint64_t aSig, fSig;

    FloatRoundMode user_rnd_mode;
    FloatX80RoundPrec user_rnd_prec;

    int32_t compact, j, k, adjk;
    floatx80 fp0, fp1, fp2, fp3, f, logof2, klog2, saveu;

    aSig = extractFloatx80Frac(a);
    aExp = extractFloatx80Exp(a);
    aSign = extractFloatx80Sign(a);

    if (aExp == 0x7FFF) {
        if ((uint64_t) (aSig << 1)) {
            propagateFloatx80NaNOneArg(a, status);
        }
        if (aSign == 0) {
            return packFloatx80(0, floatx80_infinity.high,
                                floatx80_infinity.low);
        }
    }

    adjk = 0;

    if (aExp == 0) {
        if (aSig == 0) { /* zero */
            float_raise(float_flag_divbyzero, status);
            return packFloatx80(1, floatx80_infinity.high,
                                floatx80_infinity.low);
        }
        if ((aSig & one_sig) == 0) { /* denormal */
            normalizeFloatx80Subnormal(aSig, &aExp, &aSig);
            adjk = -100;
            aExp += 100;
            a = packFloatx80(aSign, aExp, aSig);
        }
    }

    if (aSign) {
        float_raise(float_flag_invalid, status);
        return floatx80_default_nan(status);
    }

    user_rnd_mode = status->float_rounding_mode;
    user_rnd_prec = status->floatx80_rounding_precision;
    status->float_rounding_mode = float_round_nearest_even;
    status->floatx80_rounding_precision = floatx80_precision_x;

    compact = floatx80_make_compact(aExp, aSig);

    if (compact < 0x3FFEF07D || compact > 0x3FFF8841) {
        /* |X| < 15/16 or |X| > 17/16 */
        k = aExp - 0x3FFF;
        k += adjk;
        fp1 = int32_to_floatx80(k, status);

        fSig = (aSig & UINT64_C(0xFE00000000000000)) | UINT64_C(0x0100000000000000);
        j = (fSig >> 56) & 0x7E; /* DISPLACEMENT FOR 1/F */

        f = packFloatx80(0, 0x3FFF, fSig); /* F */
        fp0 = packFloatx80(0, 0x3FFF, aSig); /* Y */

        fp0 = floatx80_sub(fp0, f, status); /* Y-F */

        /* LP1CONT1 */
        fp0 = floatx80_mul(fp0, log_tbl[j], status); /* FP0 IS U = (Y-F)/F */
        logof2 = packFloatx80(0, 0x3FFE, UINT64_C(0xB17217F7D1CF79AC));
        klog2 = floatx80_mul(fp1, logof2, status); /* FP1 IS K*LOG2 */
        fp2 = floatx80_mul(fp0, fp0, status); /* FP2 IS V=U*U */

        fp3 = fp2;
        fp1 = fp2;

        fp1 = floatx80_mul(fp1, float64_to_floatx80(
                           make_float64(0x3FC2499AB5E4040B), status),
                           status); /* V*A6 */
        fp2 = floatx80_mul(fp2, float64_to_floatx80(
                           make_float64(0xBFC555B5848CB7DB), status),
                           status); /* V*A5 */
        fp1 = floatx80_add(fp1, float64_to_floatx80(
                           make_float64(0x3FC99999987D8730), status),
                           status); /* A4+V*A6 */
        fp2 = floatx80_add(fp2, float64_to_floatx80(
                           make_float64(0xBFCFFFFFFF6F7E97), status),
                           status); /* A3+V*A5 */
        fp1 = floatx80_mul(fp1, fp3, status); /* V*(A4+V*A6) */
        fp2 = floatx80_mul(fp2, fp3, status); /* V*(A3+V*A5) */
        fp1 = floatx80_add(fp1, float64_to_floatx80(
                           make_float64(0x3FD55555555555A4), status),
                           status); /* A2+V*(A4+V*A6) */
        fp2 = floatx80_add(fp2, float64_to_floatx80(
                           make_float64(0xBFE0000000000008), status),
                           status); /* A1+V*(A3+V*A5) */
        fp1 = floatx80_mul(fp1, fp3, status); /* V*(A2+V*(A4+V*A6)) */
        fp2 = floatx80_mul(fp2, fp3, status); /* V*(A1+V*(A3+V*A5)) */
        fp1 = floatx80_mul(fp1, fp0, status); /* U*V*(A2+V*(A4+V*A6)) */
        fp0 = floatx80_add(fp0, fp2, status); /* U+V*(A1+V*(A3+V*A5)) */

        fp1 = floatx80_add(fp1, log_tbl[j + 1],
                           status); /* LOG(F)+U*V*(A2+V*(A4+V*A6)) */
        fp0 = floatx80_add(fp0, fp1, status); /* FP0 IS LOG(F) + LOG(1+U) */

        status->float_rounding_mode = user_rnd_mode;
        status->floatx80_rounding_precision = user_rnd_prec;

        a = floatx80_add(fp0, klog2, status);

        float_raise(float_flag_inexact, status);

        return a;
    } else { /* |X-1| >= 1/16 */
        fp0 = a;
        fp1 = a;
        fp1 = floatx80_sub(fp1, float32_to_floatx80(make_float32(0x3F800000),
                           status), status); /* FP1 IS X-1 */
        fp0 = floatx80_add(fp0, float32_to_floatx80(make_float32(0x3F800000),
                           status), status); /* FP0 IS X+1 */
        fp1 = floatx80_add(fp1, fp1, status); /* FP1 IS 2(X-1) */

        /* LP1CONT2 */
        fp1 = floatx80_div(fp1, fp0, status); /* U */
        saveu = fp1;
        fp0 = floatx80_mul(fp1, fp1, status); /* FP0 IS V = U*U */
        fp1 = floatx80_mul(fp0, fp0, status); /* FP1 IS W = V*V */

        fp3 = float64_to_floatx80(make_float64(0x3F175496ADD7DAD6),
                                  status); /* B5 */
        fp2 = float64_to_floatx80(make_float64(0x3F3C71C2FE80C7E0),
                                  status); /* B4 */
        fp3 = floatx80_mul(fp3, fp1, status); /* W*B5 */
        fp2 = floatx80_mul(fp2, fp1, status); /* W*B4 */
        fp3 = floatx80_add(fp3, float64_to_floatx80(
                           make_float64(0x3F624924928BCCFF), status),
                           status); /* B3+W*B5 */
        fp2 = floatx80_add(fp2, float64_to_floatx80(
                           make_float64(0x3F899999999995EC), status),
                           status); /* B2+W*B4 */
        fp1 = floatx80_mul(fp1, fp3, status); /* W*(B3+W*B5) */
        fp2 = floatx80_mul(fp2, fp0, status); /* V*(B2+W*B4) */
        fp1 = floatx80_add(fp1, float64_to_floatx80(
                           make_float64(0x3FB5555555555555), status),
                           status); /* B1+W*(B3+W*B5) */

        fp0 = floatx80_mul(fp0, saveu, status); /* FP0 IS U*V */
        fp1 = floatx80_add(fp1, fp2, status); /* B1+W*(B3+W*B5) + V*(B2+W*B4) */
        fp0 = floatx80_mul(fp0, fp1,
                           status); /* U*V*([B1+W*(B3+W*B5)] + [V*(B2+W*B4)]) */

        status->float_rounding_mode = user_rnd_mode;
        status->floatx80_rounding_precision = user_rnd_prec;

        a = floatx80_add(fp0, saveu, status);

        /*if (!floatx80_is_zero(a)) { */
            float_raise(float_flag_inexact, status);
        /*} */

        return a;
    }
}

/*
 * Log base 10
 */

floatx80 floatx80_log10(floatx80 a, float_status *status)
{
    bool aSign;
    int32_t aExp;
    uint64_t aSig;

    FloatRoundMode user_rnd_mode;
    FloatX80RoundPrec user_rnd_prec;

    floatx80 fp0, fp1;

    aSig = extractFloatx80Frac(a);
    aExp = extractFloatx80Exp(a);
    aSign = extractFloatx80Sign(a);

    if (aExp == 0x7FFF) {
        if ((uint64_t) (aSig << 1)) {
            propagateFloatx80NaNOneArg(a, status);
        }
        if (aSign == 0) {
            return packFloatx80(0, floatx80_infinity.high,
                                floatx80_infinity.low);
        }
    }

    if (aExp == 0 && aSig == 0) {
        float_raise(float_flag_divbyzero, status);
        return packFloatx80(1, floatx80_infinity.high,
                            floatx80_infinity.low);
    }

    if (aSign) {
        float_raise(float_flag_invalid, status);
        return floatx80_default_nan(status);
    }

    user_rnd_mode = status->float_rounding_mode;
    user_rnd_prec = status->floatx80_rounding_precision;
    status->float_rounding_mode = float_round_nearest_even;
    status->floatx80_rounding_precision = floatx80_precision_x;

    fp0 = floatx80_logn(a, status);
    fp1 = packFloatx80(0, 0x3FFD, UINT64_C(0xDE5BD8A937287195)); /* INV_L10 */

    status->float_rounding_mode = user_rnd_mode;
    status->floatx80_rounding_precision = user_rnd_prec;

    a = floatx80_mul(fp0, fp1, status); /* LOGN(X)*INV_L10 */

    float_raise(float_flag_inexact, status);

    return a;
}

/*
 * Log base 2
 */

floatx80 floatx80_log2(floatx80 a, float_status *status)
{
    bool aSign;
    int32_t aExp;
    uint64_t aSig;

    FloatRoundMode user_rnd_mode;
    FloatX80RoundPrec user_rnd_prec;

    floatx80 fp0, fp1;

    aSig = extractFloatx80Frac(a);
    aExp = extractFloatx80Exp(a);
    aSign = extractFloatx80Sign(a);

    if (aExp == 0x7FFF) {
        if ((uint64_t) (aSig << 1)) {
            propagateFloatx80NaNOneArg(a, status);
        }
        if (aSign == 0) {
            return packFloatx80(0, floatx80_infinity.high,
                                floatx80_infinity.low);
        }
    }

    if (aExp == 0) {
        if (aSig == 0) {
            float_raise(float_flag_divbyzero, status);
            return packFloatx80(1, floatx80_infinity.high,
                                floatx80_infinity.low);
        }
        normalizeFloatx80Subnormal(aSig, &aExp, &aSig);
    }

    if (aSign) {
        float_raise(float_flag_invalid, status);
        return floatx80_default_nan(status);
    }

    user_rnd_mode = status->float_rounding_mode;
    user_rnd_prec = status->floatx80_rounding_precision;
    status->float_rounding_mode = float_round_nearest_even;
    status->floatx80_rounding_precision = floatx80_precision_x;

    if (aSig == one_sig) { /* X is 2^k */
        status->float_rounding_mode = user_rnd_mode;
        status->floatx80_rounding_precision = user_rnd_prec;

        a = int32_to_floatx80(aExp - 0x3FFF, status);
    } else {
        fp0 = floatx80_logn(a, status);
        fp1 = packFloatx80(0, 0x3FFF, UINT64_C(0xB8AA3B295C17F0BC)); /* INV_L2 */

        status->float_rounding_mode = user_rnd_mode;
        status->floatx80_rounding_precision = user_rnd_prec;

        a = floatx80_mul(fp0, fp1, status); /* LOGN(X)*INV_L2 */
    }

    float_raise(float_flag_inexact, status);

    return a;
}

/*
 * e to x
 */

floatx80 floatx80_etox(floatx80 a, float_status *status)
{
    bool aSign;
    int32_t aExp;
    uint64_t aSig;

    FloatRoundMode user_rnd_mode;
    FloatX80RoundPrec user_rnd_prec;

    int32_t compact, n, j, k, m, m1;
    floatx80 fp0, fp1, fp2, fp3, l2, scale, adjscale;
    bool adjflag;

    aSig = extractFloatx80Frac(a);
    aExp = extractFloatx80Exp(a);
    aSign = extractFloatx80Sign(a);

    if (aExp == 0x7FFF) {
        if ((uint64_t) (aSig << 1)) {
            return propagateFloatx80NaNOneArg(a, status);
        }
        if (aSign) {
            return packFloatx80(0, 0, 0);
        }
        return packFloatx80(0, floatx80_infinity.high,
                            floatx80_infinity.low);
    }

    if (aExp == 0 && aSig == 0) {
        return packFloatx80(0, one_exp, one_sig);
    }

    user_rnd_mode = status->float_rounding_mode;
    user_rnd_prec = status->floatx80_rounding_precision;
    status->float_rounding_mode = float_round_nearest_even;
    status->floatx80_rounding_precision = floatx80_precision_x;

    adjflag = 0;

    if (aExp >= 0x3FBE) { /* |X| >= 2^(-65) */
        compact = floatx80_make_compact(aExp, aSig);

        if (compact < 0x400CB167) { /* |X| < 16380 log2 */
            fp0 = a;
            fp1 = a;
            fp0 = floatx80_mul(fp0, float32_to_floatx80(
                               make_float32(0x42B8AA3B), status),
                               status); /* 64/log2 * X */
            adjflag = 0;
            n = floatx80_to_int32(fp0, status); /* int(64/log2*X) */
            fp0 = int32_to_floatx80(n, status);

            j = n & 0x3F; /* J = N mod 64 */
            m = n / 64; /* NOTE: this is really arithmetic right shift by 6 */
            if (n < 0 && j) {
                /*
                 * arithmetic right shift is division and
                 * round towards minus infinity
                 */
                m--;
            }
            m += 0x3FFF; /* biased exponent of 2^(M) */

        expcont1:
            fp2 = fp0; /* N */
            fp0 = floatx80_mul(fp0, float32_to_floatx80(
                               make_float32(0xBC317218), status),
                               status); /* N * L1, L1 = lead(-log2/64) */
            l2 = packFloatx80(0, 0x3FDC, UINT64_C(0x82E308654361C4C6));
            fp2 = floatx80_mul(fp2, l2, status); /* N * L2, L1+L2 = -log2/64 */
            fp0 = floatx80_add(fp0, fp1, status); /* X + N*L1 */
            fp0 = floatx80_add(fp0, fp2, status); /* R */

            fp1 = floatx80_mul(fp0, fp0, status); /* S = R*R */
            fp2 = float32_to_floatx80(make_float32(0x3AB60B70),
                                      status); /* A5 */
            fp2 = floatx80_mul(fp2, fp1, status); /* fp2 is S*A5 */
            fp3 = floatx80_mul(float32_to_floatx80(make_float32(0x3C088895),
                               status), fp1,
                               status); /* fp3 is S*A4 */
            fp2 = floatx80_add(fp2, float64_to_floatx80(make_float64(
                               0x3FA5555555554431), status),
                               status); /* fp2 is A3+S*A5 */
            fp3 = floatx80_add(fp3, float64_to_floatx80(make_float64(
                               0x3FC5555555554018), status),
                               status); /* fp3 is A2+S*A4 */
            fp2 = floatx80_mul(fp2, fp1, status); /* fp2 is S*(A3+S*A5) */
            fp3 = floatx80_mul(fp3, fp1, status); /* fp3 is S*(A2+S*A4) */
            fp2 = floatx80_add(fp2, float32_to_floatx80(
                               make_float32(0x3F000000), status),
                               status); /* fp2 is A1+S*(A3+S*A5) */
            fp3 = floatx80_mul(fp3, fp0, status); /* fp3 IS R*S*(A2+S*A4) */
            fp2 = floatx80_mul(fp2, fp1,
                               status); /* fp2 IS S*(A1+S*(A3+S*A5)) */
            fp0 = floatx80_add(fp0, fp3, status); /* fp0 IS R+R*S*(A2+S*A4) */
            fp0 = floatx80_add(fp0, fp2, status); /* fp0 IS EXP(R) - 1 */

            fp1 = exp_tbl[j];
            fp0 = floatx80_mul(fp0, fp1, status); /* 2^(J/64)*(Exp(R)-1) */
            fp0 = floatx80_add(fp0, float32_to_floatx80(exp_tbl2[j], status),
                               status); /* accurate 2^(J/64) */
            fp0 = floatx80_add(fp0, fp1,
                               status); /* 2^(J/64) + 2^(J/64)*(Exp(R)-1) */

            scale = packFloatx80(0, m, one_sig);
            if (adjflag) {
                adjscale = packFloatx80(0, m1, one_sig);
                fp0 = floatx80_mul(fp0, adjscale, status);
            }

            status->float_rounding_mode = user_rnd_mode;
            status->floatx80_rounding_precision = user_rnd_prec;

            a = floatx80_mul(fp0, scale, status);

            float_raise(float_flag_inexact, status);

            return a;
        } else { /* |X| >= 16380 log2 */
            if (compact > 0x400CB27C) { /* |X| >= 16480 log2 */
                status->float_rounding_mode = user_rnd_mode;
                status->floatx80_rounding_precision = user_rnd_prec;
                if (aSign) {
                    a = roundAndPackFloatx80(
                                           status->floatx80_rounding_precision,
                                           0, -0x1000, aSig, 0, status);
                } else {
                    a = roundAndPackFloatx80(
                                           status->floatx80_rounding_precision,
                                           0, 0x8000, aSig, 0, status);
                }
                float_raise(float_flag_inexact, status);

                return a;
            } else {
                fp0 = a;
                fp1 = a;
                fp0 = floatx80_mul(fp0, float32_to_floatx80(
                                   make_float32(0x42B8AA3B), status),
                                   status); /* 64/log2 * X */
                adjflag = 1;
                n = floatx80_to_int32(fp0, status); /* int(64/log2*X) */
                fp0 = int32_to_floatx80(n, status);

                j = n & 0x3F; /* J = N mod 64 */
                /* NOTE: this is really arithmetic right shift by 6 */
                k = n / 64;
                if (n < 0 && j) {
                    /* arithmetic right shift is division and
                     * round towards minus infinity
                     */
                    k--;
                }
                /* NOTE: this is really arithmetic right shift by 1 */
                m1 = k / 2;
                if (k < 0 && (k & 1)) {
                    /* arithmetic right shift is division and
                     * round towards minus infinity
                     */
                    m1--;
                }
                m = k - m1;
                m1 += 0x3FFF; /* biased exponent of 2^(M1) */
                m += 0x3FFF; /* biased exponent of 2^(M) */

                goto expcont1;
            }
        }
    } else { /* |X| < 2^(-65) */
        status->float_rounding_mode = user_rnd_mode;
        status->floatx80_rounding_precision = user_rnd_prec;

        a = floatx80_add(a, float32_to_floatx80(make_float32(0x3F800000),
                         status), status); /* 1 + X */

        float_raise(float_flag_inexact, status);

        return a;
    }
}

/*
 * 2 to x
 */

floatx80 floatx80_twotox(floatx80 a, float_status *status)
{
    bool aSign;
    int32_t aExp;
    uint64_t aSig;

    FloatRoundMode user_rnd_mode;
    FloatX80RoundPrec user_rnd_prec;

    int32_t compact, n, j, l, m, m1;
    floatx80 fp0, fp1, fp2, fp3, adjfact, fact1, fact2;

    aSig = extractFloatx80Frac(a);
    aExp = extractFloatx80Exp(a);
    aSign = extractFloatx80Sign(a);

    if (aExp == 0x7FFF) {
        if ((uint64_t) (aSig << 1)) {
            return propagateFloatx80NaNOneArg(a, status);
        }
        if (aSign) {
            return packFloatx80(0, 0, 0);
        }
        return packFloatx80(0, floatx80_infinity.high,
                            floatx80_infinity.low);
    }

    if (aExp == 0 && aSig == 0) {
        return packFloatx80(0, one_exp, one_sig);
    }

    user_rnd_mode = status->float_rounding_mode;
    user_rnd_prec = status->floatx80_rounding_precision;
    status->float_rounding_mode = float_round_nearest_even;
    status->floatx80_rounding_precision = floatx80_precision_x;

    fp0 = a;

    compact = floatx80_make_compact(aExp, aSig);

    if (compact < 0x3FB98000 || compact > 0x400D80C0) {
        /* |X| > 16480 or |X| < 2^(-70) */
        if (compact > 0x3FFF8000) { /* |X| > 16480 */
            status->float_rounding_mode = user_rnd_mode;
            status->floatx80_rounding_precision = user_rnd_prec;

            if (aSign) {
                return roundAndPackFloatx80(status->floatx80_rounding_precision,
                                            0, -0x1000, aSig, 0, status);
            } else {
                return roundAndPackFloatx80(status->floatx80_rounding_precision,
                                            0, 0x8000, aSig, 0, status);
            }
        } else { /* |X| < 2^(-70) */
            status->float_rounding_mode = user_rnd_mode;
            status->floatx80_rounding_precision = user_rnd_prec;

            a = floatx80_add(fp0, float32_to_floatx80(
                             make_float32(0x3F800000), status),
                             status); /* 1 + X */

            float_raise(float_flag_inexact, status);

            return a;
        }
    } else { /* 2^(-70) <= |X| <= 16480 */
        fp1 = fp0; /* X */
        fp1 = floatx80_mul(fp1, float32_to_floatx80(
                           make_float32(0x42800000), status),
                           status); /* X * 64 */
        n = floatx80_to_int32(fp1, status);
        fp1 = int32_to_floatx80(n, status);
        j = n & 0x3F;
        l = n / 64; /* NOTE: this is really arithmetic right shift by 6 */
        if (n < 0 && j) {
            /*
             * arithmetic right shift is division and
             * round towards minus infinity
             */
            l--;
        }
        m = l / 2; /* NOTE: this is really arithmetic right shift by 1 */
        if (l < 0 && (l & 1)) {
            /*
             * arithmetic right shift is division and
             * round towards minus infinity
             */
            m--;
        }
        m1 = l - m;
        m1 += 0x3FFF; /* ADJFACT IS 2^(M') */

        adjfact = packFloatx80(0, m1, one_sig);
        fact1 = exp2_tbl[j];
        fact1.high += m;
        fact2.high = exp2_tbl2[j] >> 16;
        fact2.high += m;
        fact2.low = (uint64_t)(exp2_tbl2[j] & 0xFFFF);
        fact2.low <<= 48;

        fp1 = floatx80_mul(fp1, float32_to_floatx80(
                           make_float32(0x3C800000), status),
                           status); /* (1/64)*N */
        fp0 = floatx80_sub(fp0, fp1, status); /* X - (1/64)*INT(64 X) */
        fp2 = packFloatx80(0, 0x3FFE, UINT64_C(0xB17217F7D1CF79AC)); /* LOG2 */
        fp0 = floatx80_mul(fp0, fp2, status); /* R */

        /* EXPR */
        fp1 = floatx80_mul(fp0, fp0, status); /* S = R*R */
        fp2 = float64_to_floatx80(make_float64(0x3F56C16D6F7BD0B2),
                                  status); /* A5 */
        fp3 = float64_to_floatx80(make_float64(0x3F811112302C712C),
                                  status); /* A4 */
        fp2 = floatx80_mul(fp2, fp1, status); /* S*A5 */
        fp3 = floatx80_mul(fp3, fp1, status); /* S*A4 */
        fp2 = floatx80_add(fp2, float64_to_floatx80(
                           make_float64(0x3FA5555555554CC1), status),
                           status); /* A3+S*A5 */
        fp3 = floatx80_add(fp3, float64_to_floatx80(
                           make_float64(0x3FC5555555554A54), status),
                           status); /* A2+S*A4 */
        fp2 = floatx80_mul(fp2, fp1, status); /* S*(A3+S*A5) */
        fp3 = floatx80_mul(fp3, fp1, status); /* S*(A2+S*A4) */
        fp2 = floatx80_add(fp2, float64_to_floatx80(
                           make_float64(0x3FE0000000000000), status),
                           status); /* A1+S*(A3+S*A5) */
        fp3 = floatx80_mul(fp3, fp0, status); /* R*S*(A2+S*A4) */

        fp2 = floatx80_mul(fp2, fp1, status); /* S*(A1+S*(A3+S*A5)) */
        fp0 = floatx80_add(fp0, fp3, status); /* R+R*S*(A2+S*A4) */
        fp0 = floatx80_add(fp0, fp2, status); /* EXP(R) - 1 */

        fp0 = floatx80_mul(fp0, fact1, status);
        fp0 = floatx80_add(fp0, fact2, status);
        fp0 = floatx80_add(fp0, fact1, status);

        status->float_rounding_mode = user_rnd_mode;
        status->floatx80_rounding_precision = user_rnd_prec;

        a = floatx80_mul(fp0, adjfact, status);

        float_raise(float_flag_inexact, status);

        return a;
    }
}

/*
 * 10 to x
 */

floatx80 floatx80_tentox(floatx80 a, float_status *status)
{
    bool aSign;
    int32_t aExp;
    uint64_t aSig;

    FloatRoundMode user_rnd_mode;
    FloatX80RoundPrec user_rnd_prec;

    int32_t compact, n, j, l, m, m1;
    floatx80 fp0, fp1, fp2, fp3, adjfact, fact1, fact2;

    aSig = extractFloatx80Frac(a);
    aExp = extractFloatx80Exp(a);
    aSign = extractFloatx80Sign(a);

    if (aExp == 0x7FFF) {
        if ((uint64_t) (aSig << 1)) {
            return propagateFloatx80NaNOneArg(a, status);
        }
        if (aSign) {
            return packFloatx80(0, 0, 0);
        }
        return packFloatx80(0, floatx80_infinity.high,
                            floatx80_infinity.low);
    }

    if (aExp == 0 && aSig == 0) {
        return packFloatx80(0, one_exp, one_sig);
    }

    user_rnd_mode = status->float_rounding_mode;
    user_rnd_prec = status->floatx80_rounding_precision;
    status->float_rounding_mode = float_round_nearest_even;
    status->floatx80_rounding_precision = floatx80_precision_x;

    fp0 = a;

    compact = floatx80_make_compact(aExp, aSig);

    if (compact < 0x3FB98000 || compact > 0x400B9B07) {
        /* |X| > 16480 LOG2/LOG10 or |X| < 2^(-70) */
        if (compact > 0x3FFF8000) { /* |X| > 16480 */
            status->float_rounding_mode = user_rnd_mode;
            status->floatx80_rounding_precision = user_rnd_prec;

            if (aSign) {
                return roundAndPackFloatx80(status->floatx80_rounding_precision,
                                            0, -0x1000, aSig, 0, status);
            } else {
                return roundAndPackFloatx80(status->floatx80_rounding_precision,
                                            0, 0x8000, aSig, 0, status);
            }
        } else { /* |X| < 2^(-70) */
            status->float_rounding_mode = user_rnd_mode;
            status->floatx80_rounding_precision = user_rnd_prec;

            a = floatx80_add(fp0, float32_to_floatx80(
                             make_float32(0x3F800000), status),
                             status); /* 1 + X */

            float_raise(float_flag_inexact, status);

            return a;
        }
    } else { /* 2^(-70) <= |X| <= 16480 LOG 2 / LOG 10 */
        fp1 = fp0; /* X */
        fp1 = floatx80_mul(fp1, float64_to_floatx80(
                           make_float64(0x406A934F0979A371),
                           status), status); /* X*64*LOG10/LOG2 */
        n = floatx80_to_int32(fp1, status); /* N=INT(X*64*LOG10/LOG2) */
        fp1 = int32_to_floatx80(n, status);

        j = n & 0x3F;
        l = n / 64; /* NOTE: this is really arithmetic right shift by 6 */
        if (n < 0 && j) {
            /*
             * arithmetic right shift is division and
             * round towards minus infinity
             */
            l--;
        }
        m = l / 2; /* NOTE: this is really arithmetic right shift by 1 */
        if (l < 0 && (l & 1)) {
            /*
             * arithmetic right shift is division and
             * round towards minus infinity
             */
            m--;
        }
        m1 = l - m;
        m1 += 0x3FFF; /* ADJFACT IS 2^(M') */

        adjfact = packFloatx80(0, m1, one_sig);
        fact1 = exp2_tbl[j];
        fact1.high += m;
        fact2.high = exp2_tbl2[j] >> 16;
        fact2.high += m;
        fact2.low = (uint64_t)(exp2_tbl2[j] & 0xFFFF);
        fact2.low <<= 48;

        fp2 = fp1; /* N */
        fp1 = floatx80_mul(fp1, float64_to_floatx80(
                           make_float64(0x3F734413509F8000), status),
                           status); /* N*(LOG2/64LOG10)_LEAD */
        fp3 = packFloatx80(1, 0x3FCD, UINT64_C(0xC0219DC1DA994FD2));
        fp2 = floatx80_mul(fp2, fp3, status); /* N*(LOG2/64LOG10)_TRAIL */
        fp0 = floatx80_sub(fp0, fp1, status); /* X - N L_LEAD */
        fp0 = floatx80_sub(fp0, fp2, status); /* X - N L_TRAIL */
        fp2 = packFloatx80(0, 0x4000, UINT64_C(0x935D8DDDAAA8AC17)); /* LOG10 */
        fp0 = floatx80_mul(fp0, fp2, status); /* R */

        /* EXPR */
        fp1 = floatx80_mul(fp0, fp0, status); /* S = R*R */
        fp2 = float64_to_floatx80(make_float64(0x3F56C16D6F7BD0B2),
                                  status); /* A5 */
        fp3 = float64_to_floatx80(make_float64(0x3F811112302C712C),
                                  status); /* A4 */
        fp2 = floatx80_mul(fp2, fp1, status); /* S*A5 */
        fp3 = floatx80_mul(fp3, fp1, status); /* S*A4 */
        fp2 = floatx80_add(fp2, float64_to_floatx80(
                           make_float64(0x3FA5555555554CC1), status),
                           status); /* A3+S*A5 */
        fp3 = floatx80_add(fp3, float64_to_floatx80(
                           make_float64(0x3FC5555555554A54), status),
                           status); /* A2+S*A4 */
        fp2 = floatx80_mul(fp2, fp1, status); /* S*(A3+S*A5) */
        fp3 = floatx80_mul(fp3, fp1, status); /* S*(A2+S*A4) */
        fp2 = floatx80_add(fp2, float64_to_floatx80(
                           make_float64(0x3FE0000000000000), status),
                           status); /* A1+S*(A3+S*A5) */
        fp3 = floatx80_mul(fp3, fp0, status); /* R*S*(A2+S*A4) */

        fp2 = floatx80_mul(fp2, fp1, status); /* S*(A1+S*(A3+S*A5)) */
        fp0 = floatx80_add(fp0, fp3, status); /* R+R*S*(A2+S*A4) */
        fp0 = floatx80_add(fp0, fp2, status); /* EXP(R) - 1 */

        fp0 = floatx80_mul(fp0, fact1, status);
        fp0 = floatx80_add(fp0, fact2, status);
        fp0 = floatx80_add(fp0, fact1, status);

        status->float_rounding_mode = user_rnd_mode;
        status->floatx80_rounding_precision = user_rnd_prec;

        a = floatx80_mul(fp0, adjfact, status);

        float_raise(float_flag_inexact, status);

        return a;
    }
}

/*
 * Tangent
 */

floatx80 floatx80_tan(floatx80 a, float_status *status)
{
    bool aSign, xSign;
    int32_t aExp, xExp;
    uint64_t aSig, xSig;

    FloatRoundMode user_rnd_mode;
    FloatX80RoundPrec user_rnd_prec;

    int32_t compact, l, n, j;
    floatx80 fp0, fp1, fp2, fp3, fp4, fp5, invtwopi, twopi1, twopi2;
    float32 twoto63;
    bool endflag;

    aSig = extractFloatx80Frac(a);
    aExp = extractFloatx80Exp(a);
    aSign = extractFloatx80Sign(a);

    if (aExp == 0x7FFF) {
        if ((uint64_t) (aSig << 1)) {
            return propagateFloatx80NaNOneArg(a, status);
        }
        float_raise(float_flag_invalid, status);
        return floatx80_default_nan(status);
    }

    if (aExp == 0 && aSig == 0) {
        return packFloatx80(aSign, 0, 0);
    }

    user_rnd_mode = status->float_rounding_mode;
    user_rnd_prec = status->floatx80_rounding_precision;
    status->float_rounding_mode = float_round_nearest_even;
    status->floatx80_rounding_precision = floatx80_precision_x;

    compact = floatx80_make_compact(aExp, aSig);

    fp0 = a;

    if (compact < 0x3FD78000 || compact > 0x4004BC7E) {
        /* 2^(-40) > |X| > 15 PI */
        if (compact > 0x3FFF8000) { /* |X| >= 15 PI */
            /* REDUCEX */
            fp1 = packFloatx80(0, 0, 0);
            if (compact == 0x7FFEFFFF) {
                twopi1 = packFloatx80(aSign ^ 1, 0x7FFE,
                                      UINT64_C(0xC90FDAA200000000));
                twopi2 = packFloatx80(aSign ^ 1, 0x7FDC,
                                      UINT64_C(0x85A308D300000000));
                fp0 = floatx80_add(fp0, twopi1, status);
                fp1 = fp0;
                fp0 = floatx80_add(fp0, twopi2, status);
                fp1 = floatx80_sub(fp1, fp0, status);
                fp1 = floatx80_add(fp1, twopi2, status);
            }
        loop:
            xSign = extractFloatx80Sign(fp0);
            xExp = extractFloatx80Exp(fp0);
            xExp -= 0x3FFF;
            if (xExp <= 28) {
                l = 0;
                endflag = true;
            } else {
                l = xExp - 27;
                endflag = false;
            }
            invtwopi = packFloatx80(0, 0x3FFE - l,
                                    UINT64_C(0xA2F9836E4E44152A)); /* INVTWOPI */
            twopi1 = packFloatx80(0, 0x3FFF + l, UINT64_C(0xC90FDAA200000000));
            twopi2 = packFloatx80(0, 0x3FDD + l, UINT64_C(0x85A308D300000000));

            /* SIGN(INARG)*2^63 IN SGL */
            twoto63 = packFloat32(xSign, 0xBE, 0);

            fp2 = floatx80_mul(fp0, invtwopi, status);
            fp2 = floatx80_add(fp2, float32_to_floatx80(twoto63, status),
                               status); /* THE FRACT PART OF FP2 IS ROUNDED */
            fp2 = floatx80_sub(fp2, float32_to_floatx80(twoto63, status),
                               status); /* FP2 is N */
            fp4 = floatx80_mul(twopi1, fp2, status); /* W = N*P1 */
            fp5 = floatx80_mul(twopi2, fp2, status); /* w = N*P2 */
            fp3 = floatx80_add(fp4, fp5, status); /* FP3 is P */
            fp4 = floatx80_sub(fp4, fp3, status); /* W-P */
            fp0 = floatx80_sub(fp0, fp3, status); /* FP0 is A := R - P */
            fp4 = floatx80_add(fp4, fp5, status); /* FP4 is p = (W-P)+w */
            fp3 = fp0; /* FP3 is A */
            fp1 = floatx80_sub(fp1, fp4, status); /* FP1 is a := r - p */
            fp0 = floatx80_add(fp0, fp1, status); /* FP0 is R := A+a */

            if (endflag) {
                n = floatx80_to_int32(fp2, status);
                goto tancont;
            }
            fp3 = floatx80_sub(fp3, fp0, status); /* A-R */
            fp1 = floatx80_add(fp1, fp3, status); /* FP1 is r := (A-R)+a */
            goto loop;
        } else {
            status->float_rounding_mode = user_rnd_mode;
            status->floatx80_rounding_precision = user_rnd_prec;

            a = floatx80_move(a, status);

            float_raise(float_flag_inexact, status);

            return a;
        }
    } else {
        fp1 = floatx80_mul(fp0, float64_to_floatx80(
                           make_float64(0x3FE45F306DC9C883), status),
                           status); /* X*2/PI */

        n = floatx80_to_int32(fp1, status);
        j = 32 + n;

        fp0 = floatx80_sub(fp0, pi_tbl[j], status); /* X-Y1 */
        fp0 = floatx80_sub(fp0, float32_to_floatx80(pi_tbl2[j], status),
                           status); /* FP0 IS R = (X-Y1)-Y2 */

    tancont:
        if (n & 1) {
            /* NODD */
            fp1 = fp0; /* R */
            fp0 = floatx80_mul(fp0, fp0, status); /* S = R*R */
            fp3 = float64_to_floatx80(make_float64(0x3EA0B759F50F8688),
                                      status); /* Q4 */
            fp2 = float64_to_floatx80(make_float64(0xBEF2BAA5A8924F04),
                                      status); /* P3 */
            fp3 = floatx80_mul(fp3, fp0, status); /* SQ4 */
            fp2 = floatx80_mul(fp2, fp0, status); /* SP3 */
            fp3 = floatx80_add(fp3, float64_to_floatx80(
                               make_float64(0xBF346F59B39BA65F), status),
                               status); /* Q3+SQ4 */
            fp4 = packFloatx80(0, 0x3FF6, UINT64_C(0xE073D3FC199C4A00));
            fp2 = floatx80_add(fp2, fp4, status); /* P2+SP3 */
            fp3 = floatx80_mul(fp3, fp0, status); /* S(Q3+SQ4) */
            fp2 = floatx80_mul(fp2, fp0, status); /* S(P2+SP3) */
            fp4 = packFloatx80(0, 0x3FF9, UINT64_C(0xD23CD68415D95FA1));
            fp3 = floatx80_add(fp3, fp4, status); /* Q2+S(Q3+SQ4) */
            fp4 = packFloatx80(1, 0x3FFC, UINT64_C(0x8895A6C5FB423BCA));
            fp2 = floatx80_add(fp2, fp4, status); /* P1+S(P2+SP3) */
            fp3 = floatx80_mul(fp3, fp0, status); /* S(Q2+S(Q3+SQ4)) */
            fp2 = floatx80_mul(fp2, fp0, status); /* S(P1+S(P2+SP3)) */
            fp4 = packFloatx80(1, 0x3FFD, UINT64_C(0xEEF57E0DA84BC8CE));
            fp3 = floatx80_add(fp3, fp4, status); /* Q1+S(Q2+S(Q3+SQ4)) */
            fp2 = floatx80_mul(fp2, fp1, status); /* RS(P1+S(P2+SP3)) */
            fp0 = floatx80_mul(fp0, fp3, status); /* S(Q1+S(Q2+S(Q3+SQ4))) */
            fp1 = floatx80_add(fp1, fp2, status); /* R+RS(P1+S(P2+SP3)) */
            fp0 = floatx80_add(fp0, float32_to_floatx80(
                               make_float32(0x3F800000), status),
                               status); /* 1+S(Q1+S(Q2+S(Q3+SQ4))) */

            xSign = extractFloatx80Sign(fp1);
            xExp = extractFloatx80Exp(fp1);
            xSig = extractFloatx80Frac(fp1);
            xSign ^= 1;
            fp1 = packFloatx80(xSign, xExp, xSig);

            status->float_rounding_mode = user_rnd_mode;
            status->floatx80_rounding_precision = user_rnd_prec;

            a = floatx80_div(fp0, fp1, status);

            float_raise(float_flag_inexact, status);

            return a;
        } else {
            fp1 = floatx80_mul(fp0, fp0, status); /* S = R*R */
            fp3 = float64_to_floatx80(make_float64(0x3EA0B759F50F8688),
                                      status); /* Q4 */
            fp2 = float64_to_floatx80(make_float64(0xBEF2BAA5A8924F04),
                                      status); /* P3 */
            fp3 = floatx80_mul(fp3, fp1, status); /* SQ4 */
            fp2 = floatx80_mul(fp2, fp1, status); /* SP3 */
            fp3 = floatx80_add(fp3, float64_to_floatx80(
                               make_float64(0xBF346F59B39BA65F), status),
                               status); /* Q3+SQ4 */
            fp4 = packFloatx80(0, 0x3FF6, UINT64_C(0xE073D3FC199C4A00));
            fp2 = floatx80_add(fp2, fp4, status); /* P2+SP3 */
            fp3 = floatx80_mul(fp3, fp1, status); /* S(Q3+SQ4) */
            fp2 = floatx80_mul(fp2, fp1, status); /* S(P2+SP3) */
            fp4 = packFloatx80(0, 0x3FF9, UINT64_C(0xD23CD68415D95FA1));
            fp3 = floatx80_add(fp3, fp4, status); /* Q2+S(Q3+SQ4) */
            fp4 = packFloatx80(1, 0x3FFC, UINT64_C(0x8895A6C5FB423BCA));
            fp2 = floatx80_add(fp2, fp4, status); /* P1+S(P2+SP3) */
            fp3 = floatx80_mul(fp3, fp1, status); /* S(Q2+S(Q3+SQ4)) */
            fp2 = floatx80_mul(fp2, fp1, status); /* S(P1+S(P2+SP3)) */
            fp4 = packFloatx80(1, 0x3FFD, UINT64_C(0xEEF57E0DA84BC8CE));
            fp3 = floatx80_add(fp3, fp4, status); /* Q1+S(Q2+S(Q3+SQ4)) */
            fp2 = floatx80_mul(fp2, fp0, status); /* RS(P1+S(P2+SP3)) */
            fp1 = floatx80_mul(fp1, fp3, status); /* S(Q1+S(Q2+S(Q3+SQ4))) */
            fp0 = floatx80_add(fp0, fp2, status); /* R+RS(P1+S(P2+SP3)) */
            fp1 = floatx80_add(fp1, float32_to_floatx80(
                               make_float32(0x3F800000), status),
                               status); /* 1+S(Q1+S(Q2+S(Q3+SQ4))) */

            status->float_rounding_mode = user_rnd_mode;
            status->floatx80_rounding_precision = user_rnd_prec;

            a = floatx80_div(fp0, fp1, status);

            float_raise(float_flag_inexact, status);

            return a;
        }
    }
}

/*
 * Sine
 */

floatx80 floatx80_sin(floatx80 a, float_status *status)
{
    bool aSign, xSign;
    int32_t aExp, xExp;
    uint64_t aSig, xSig;

    FloatRoundMode user_rnd_mode;
    FloatX80RoundPrec user_rnd_prec;

    int32_t compact, l, n, j;
    floatx80 fp0, fp1, fp2, fp3, fp4, fp5, x, invtwopi, twopi1, twopi2;
    float32 posneg1, twoto63;
    bool endflag;

    aSig = extractFloatx80Frac(a);
    aExp = extractFloatx80Exp(a);
    aSign = extractFloatx80Sign(a);

    if (aExp == 0x7FFF) {
        if ((uint64_t) (aSig << 1)) {
            return propagateFloatx80NaNOneArg(a, status);
        }
        float_raise(float_flag_invalid, status);
        return floatx80_default_nan(status);
    }

    if (aExp == 0 && aSig == 0) {
        return packFloatx80(aSign, 0, 0);
    }

    user_rnd_mode = status->float_rounding_mode;
    user_rnd_prec = status->floatx80_rounding_precision;
    status->float_rounding_mode = float_round_nearest_even;
    status->floatx80_rounding_precision = floatx80_precision_x;

    compact = floatx80_make_compact(aExp, aSig);

    fp0 = a;

    if (compact < 0x3FD78000 || compact > 0x4004BC7E) {
        /* 2^(-40) > |X| > 15 PI */
        if (compact > 0x3FFF8000) { /* |X| >= 15 PI */
            /* REDUCEX */
            fp1 = packFloatx80(0, 0, 0);
            if (compact == 0x7FFEFFFF) {
                twopi1 = packFloatx80(aSign ^ 1, 0x7FFE,
                                      UINT64_C(0xC90FDAA200000000));
                twopi2 = packFloatx80(aSign ^ 1, 0x7FDC,
                                      UINT64_C(0x85A308D300000000));
                fp0 = floatx80_add(fp0, twopi1, status);
                fp1 = fp0;
                fp0 = floatx80_add(fp0, twopi2, status);
                fp1 = floatx80_sub(fp1, fp0, status);
                fp1 = floatx80_add(fp1, twopi2, status);
            }
        loop:
            xSign = extractFloatx80Sign(fp0);
            xExp = extractFloatx80Exp(fp0);
            xExp -= 0x3FFF;
            if (xExp <= 28) {
                l = 0;
                endflag = true;
            } else {
                l = xExp - 27;
                endflag = false;
            }
            invtwopi = packFloatx80(0, 0x3FFE - l,
                                    UINT64_C(0xA2F9836E4E44152A)); /* INVTWOPI */
            twopi1 = packFloatx80(0, 0x3FFF + l, UINT64_C(0xC90FDAA200000000));
            twopi2 = packFloatx80(0, 0x3FDD + l, UINT64_C(0x85A308D300000000));

            /* SIGN(INARG)*2^63 IN SGL */
            twoto63 = packFloat32(xSign, 0xBE, 0);

            fp2 = floatx80_mul(fp0, invtwopi, status);
            fp2 = floatx80_add(fp2, float32_to_floatx80(twoto63, status),
                               status); /* THE FRACT PART OF FP2 IS ROUNDED */
            fp2 = floatx80_sub(fp2, float32_to_floatx80(twoto63, status),
                               status); /* FP2 is N */
            fp4 = floatx80_mul(twopi1, fp2, status); /* W = N*P1 */
            fp5 = floatx80_mul(twopi2, fp2, status); /* w = N*P2 */
            fp3 = floatx80_add(fp4, fp5, status); /* FP3 is P */
            fp4 = floatx80_sub(fp4, fp3, status); /* W-P */
            fp0 = floatx80_sub(fp0, fp3, status); /* FP0 is A := R - P */
            fp4 = floatx80_add(fp4, fp5, status); /* FP4 is p = (W-P)+w */
            fp3 = fp0; /* FP3 is A */
            fp1 = floatx80_sub(fp1, fp4, status); /* FP1 is a := r - p */
            fp0 = floatx80_add(fp0, fp1, status); /* FP0 is R := A+a */

            if (endflag) {
                n = floatx80_to_int32(fp2, status);
                goto sincont;
            }
            fp3 = floatx80_sub(fp3, fp0, status); /* A-R */
            fp1 = floatx80_add(fp1, fp3, status); /* FP1 is r := (A-R)+a */
            goto loop;
        } else {
            /* SINSM */
            fp0 = float32_to_floatx80(make_float32(0x3F800000),
                                      status); /* 1 */

            status->float_rounding_mode = user_rnd_mode;
            status->floatx80_rounding_precision = user_rnd_prec;

            /* SINTINY */
            a = floatx80_move(a, status);
            float_raise(float_flag_inexact, status);

            return a;
        }
    } else {
        fp1 = floatx80_mul(fp0, float64_to_floatx80(
                           make_float64(0x3FE45F306DC9C883), status),
                           status); /* X*2/PI */

        n = floatx80_to_int32(fp1, status);
        j = 32 + n;

        fp0 = floatx80_sub(fp0, pi_tbl[j], status); /* X-Y1 */
        fp0 = floatx80_sub(fp0, float32_to_floatx80(pi_tbl2[j], status),
                           status); /* FP0 IS R = (X-Y1)-Y2 */

    sincont:
        if (n & 1) {
            /* COSPOLY */
            fp0 = floatx80_mul(fp0, fp0, status); /* FP0 IS S */
            fp1 = floatx80_mul(fp0, fp0, status); /* FP1 IS T */
            fp2 = float64_to_floatx80(make_float64(0x3D2AC4D0D6011EE3),
                                      status); /* B8 */
            fp3 = float64_to_floatx80(make_float64(0xBDA9396F9F45AC19),
                                      status); /* B7 */

            xSign = extractFloatx80Sign(fp0); /* X IS S */
            xExp = extractFloatx80Exp(fp0);
            xSig = extractFloatx80Frac(fp0);

            if ((n >> 1) & 1) {
                xSign ^= 1;
                posneg1 = make_float32(0xBF800000); /* -1 */
            } else {
                xSign ^= 0;
                posneg1 = make_float32(0x3F800000); /* 1 */
            } /* X IS NOW R'= SGN*R */

            fp2 = floatx80_mul(fp2, fp1, status); /* TB8 */
            fp3 = floatx80_mul(fp3, fp1, status); /* TB7 */
            fp2 = floatx80_add(fp2, float64_to_floatx80(
                               make_float64(0x3E21EED90612C972), status),
                               status); /* B6+TB8 */
            fp3 = floatx80_add(fp3, float64_to_floatx80(
                               make_float64(0xBE927E4FB79D9FCF), status),
                               status); /* B5+TB7 */
            fp2 = floatx80_mul(fp2, fp1, status); /* T(B6+TB8) */
            fp3 = floatx80_mul(fp3, fp1, status); /* T(B5+TB7) */
            fp2 = floatx80_add(fp2, float64_to_floatx80(
                               make_float64(0x3EFA01A01A01D423), status),
                               status); /* B4+T(B6+TB8) */
            fp4 = packFloatx80(1, 0x3FF5, UINT64_C(0xB60B60B60B61D438));
            fp3 = floatx80_add(fp3, fp4, status); /* B3+T(B5+TB7) */
            fp2 = floatx80_mul(fp2, fp1, status); /* T(B4+T(B6+TB8)) */
            fp1 = floatx80_mul(fp1, fp3, status); /* T(B3+T(B5+TB7)) */
            fp4 = packFloatx80(0, 0x3FFA, UINT64_C(0xAAAAAAAAAAAAAB5E));
            fp2 = floatx80_add(fp2, fp4, status); /* B2+T(B4+T(B6+TB8)) */
            fp1 = floatx80_add(fp1, float32_to_floatx80(
                               make_float32(0xBF000000), status),
                               status); /* B1+T(B3+T(B5+TB7)) */
            fp0 = floatx80_mul(fp0, fp2, status); /* S(B2+T(B4+T(B6+TB8))) */
            fp0 = floatx80_add(fp0, fp1, status); /* [B1+T(B3+T(B5+TB7))]+
                                                   * [S(B2+T(B4+T(B6+TB8)))]
                                                   */

            x = packFloatx80(xSign, xExp, xSig);
            fp0 = floatx80_mul(fp0, x, status);

            status->float_rounding_mode = user_rnd_mode;
            status->floatx80_rounding_precision = user_rnd_prec;

            a = floatx80_add(fp0, float32_to_floatx80(posneg1, status), status);

            float_raise(float_flag_inexact, status);

            return a;
        } else {
            /* SINPOLY */
            xSign = extractFloatx80Sign(fp0); /* X IS R */
            xExp = extractFloatx80Exp(fp0);
            xSig = extractFloatx80Frac(fp0);

            xSign ^= (n >> 1) & 1; /* X IS NOW R'= SGN*R */

            fp0 = floatx80_mul(fp0, fp0, status); /* FP0 IS S */
            fp1 = floatx80_mul(fp0, fp0, status); /* FP1 IS T */
            fp3 = float64_to_floatx80(make_float64(0xBD6AAA77CCC994F5),
                                      status); /* A7 */
            fp2 = float64_to_floatx80(make_float64(0x3DE612097AAE8DA1),
                                      status); /* A6 */
            fp3 = floatx80_mul(fp3, fp1, status); /* T*A7 */
            fp2 = floatx80_mul(fp2, fp1, status); /* T*A6 */
            fp3 = floatx80_add(fp3, float64_to_floatx80(
                               make_float64(0xBE5AE6452A118AE4), status),
                               status); /* A5+T*A7 */
            fp2 = floatx80_add(fp2, float64_to_floatx80(
                               make_float64(0x3EC71DE3A5341531), status),
                               status); /* A4+T*A6 */
            fp3 = floatx80_mul(fp3, fp1, status); /* T(A5+TA7) */
            fp2 = floatx80_mul(fp2, fp1, status); /* T(A4+TA6) */
            fp3 = floatx80_add(fp3, float64_to_floatx80(
                               make_float64(0xBF2A01A01A018B59), status),
                               status); /* A3+T(A5+TA7) */
            fp4 = packFloatx80(0, 0x3FF8, UINT64_C(0x88888888888859AF));
            fp2 = floatx80_add(fp2, fp4, status); /* A2+T(A4+TA6) */
            fp1 = floatx80_mul(fp1, fp3, status); /* T(A3+T(A5+TA7)) */
            fp2 = floatx80_mul(fp2, fp0, status); /* S(A2+T(A4+TA6)) */
            fp4 = packFloatx80(1, 0x3FFC, UINT64_C(0xAAAAAAAAAAAAAA99));
            fp1 = floatx80_add(fp1, fp4, status); /* A1+T(A3+T(A5+TA7)) */
            fp1 = floatx80_add(fp1, fp2,
                               status); /* [A1+T(A3+T(A5+TA7))]+
                                         * [S(A2+T(A4+TA6))]
                                         */

            x = packFloatx80(xSign, xExp, xSig);
            fp0 = floatx80_mul(fp0, x, status); /* R'*S */
            fp0 = floatx80_mul(fp0, fp1, status); /* SIN(R')-R' */

            status->float_rounding_mode = user_rnd_mode;
            status->floatx80_rounding_precision = user_rnd_prec;

            a = floatx80_add(fp0, x, status);

            float_raise(float_flag_inexact, status);

            return a;
        }
    }
}

/*
 * Cosine
 */

floatx80 floatx80_cos(floatx80 a, float_status *status)
{
    bool aSign, xSign;
    int32_t aExp, xExp;
    uint64_t aSig, xSig;

    FloatRoundMode user_rnd_mode;
    FloatX80RoundPrec user_rnd_prec;

    int32_t compact, l, n, j;
    floatx80 fp0, fp1, fp2, fp3, fp4, fp5, x, invtwopi, twopi1, twopi2;
    float32 posneg1, twoto63;
    bool endflag;

    aSig = extractFloatx80Frac(a);
    aExp = extractFloatx80Exp(a);
    aSign = extractFloatx80Sign(a);

    if (aExp == 0x7FFF) {
        if ((uint64_t) (aSig << 1)) {
            return propagateFloatx80NaNOneArg(a, status);
        }
        float_raise(float_flag_invalid, status);
        return floatx80_default_nan(status);
    }

    if (aExp == 0 && aSig == 0) {
        return packFloatx80(0, one_exp, one_sig);
    }

    user_rnd_mode = status->float_rounding_mode;
    user_rnd_prec = status->floatx80_rounding_precision;
    status->float_rounding_mode = float_round_nearest_even;
    status->floatx80_rounding_precision = floatx80_precision_x;

    compact = floatx80_make_compact(aExp, aSig);

    fp0 = a;

    if (compact < 0x3FD78000 || compact > 0x4004BC7E) {
        /* 2^(-40) > |X| > 15 PI */
        if (compact > 0x3FFF8000) { /* |X| >= 15 PI */
            /* REDUCEX */
            fp1 = packFloatx80(0, 0, 0);
            if (compact == 0x7FFEFFFF) {
                twopi1 = packFloatx80(aSign ^ 1, 0x7FFE,
                                      UINT64_C(0xC90FDAA200000000));
                twopi2 = packFloatx80(aSign ^ 1, 0x7FDC,
                                      UINT64_C(0x85A308D300000000));
                fp0 = floatx80_add(fp0, twopi1, status);
                fp1 = fp0;
                fp0 = floatx80_add(fp0, twopi2, status);
                fp1 = floatx80_sub(fp1, fp0, status);
                fp1 = floatx80_add(fp1, twopi2, status);
            }
        loop:
            xSign = extractFloatx80Sign(fp0);
            xExp = extractFloatx80Exp(fp0);
            xExp -= 0x3FFF;
            if (xExp <= 28) {
                l = 0;
                endflag = true;
            } else {
                l = xExp - 27;
                endflag = false;
            }
            invtwopi = packFloatx80(0, 0x3FFE - l,
                                    UINT64_C(0xA2F9836E4E44152A)); /* INVTWOPI */
            twopi1 = packFloatx80(0, 0x3FFF + l, UINT64_C(0xC90FDAA200000000));
            twopi2 = packFloatx80(0, 0x3FDD + l, UINT64_C(0x85A308D300000000));

            /* SIGN(INARG)*2^63 IN SGL */
            twoto63 = packFloat32(xSign, 0xBE, 0);

            fp2 = floatx80_mul(fp0, invtwopi, status);
            fp2 = floatx80_add(fp2, float32_to_floatx80(twoto63, status),
                               status); /* THE FRACT PART OF FP2 IS ROUNDED */
            fp2 = floatx80_sub(fp2, float32_to_floatx80(twoto63, status),
                               status); /* FP2 is N */
            fp4 = floatx80_mul(twopi1, fp2, status); /* W = N*P1 */
            fp5 = floatx80_mul(twopi2, fp2, status); /* w = N*P2 */
            fp3 = floatx80_add(fp4, fp5, status); /* FP3 is P */
            fp4 = floatx80_sub(fp4, fp3, status); /* W-P */
            fp0 = floatx80_sub(fp0, fp3, status); /* FP0 is A := R - P */
            fp4 = floatx80_add(fp4, fp5, status); /* FP4 is p = (W-P)+w */
            fp3 = fp0; /* FP3 is A */
            fp1 = floatx80_sub(fp1, fp4, status); /* FP1 is a := r - p */
            fp0 = floatx80_add(fp0, fp1, status); /* FP0 is R := A+a */

            if (endflag) {
                n = floatx80_to_int32(fp2, status);
                goto sincont;
            }
            fp3 = floatx80_sub(fp3, fp0, status); /* A-R */
            fp1 = floatx80_add(fp1, fp3, status); /* FP1 is r := (A-R)+a */
            goto loop;
        } else {
            /* SINSM */
            fp0 = float32_to_floatx80(make_float32(0x3F800000), status); /* 1 */

            status->float_rounding_mode = user_rnd_mode;
            status->floatx80_rounding_precision = user_rnd_prec;

            /* COSTINY */
            a = floatx80_sub(fp0, float32_to_floatx80(
                             make_float32(0x00800000), status),
                             status);
            float_raise(float_flag_inexact, status);

            return a;
        }
    } else {
        fp1 = floatx80_mul(fp0, float64_to_floatx80(
                           make_float64(0x3FE45F306DC9C883), status),
                           status); /* X*2/PI */

        n = floatx80_to_int32(fp1, status);
        j = 32 + n;

        fp0 = floatx80_sub(fp0, pi_tbl[j], status); /* X-Y1 */
        fp0 = floatx80_sub(fp0, float32_to_floatx80(pi_tbl2[j], status),
                           status); /* FP0 IS R = (X-Y1)-Y2 */

    sincont:
        if ((n + 1) & 1) {
            /* COSPOLY */
            fp0 = floatx80_mul(fp0, fp0, status); /* FP0 IS S */
            fp1 = floatx80_mul(fp0, fp0, status); /* FP1 IS T */
            fp2 = float64_to_floatx80(make_float64(0x3D2AC4D0D6011EE3),
                                      status); /* B8 */
            fp3 = float64_to_floatx80(make_float64(0xBDA9396F9F45AC19),
                                      status); /* B7 */

            xSign = extractFloatx80Sign(fp0); /* X IS S */
            xExp = extractFloatx80Exp(fp0);
            xSig = extractFloatx80Frac(fp0);

            if (((n + 1) >> 1) & 1) {
                xSign ^= 1;
                posneg1 = make_float32(0xBF800000); /* -1 */
            } else {
                xSign ^= 0;
                posneg1 = make_float32(0x3F800000); /* 1 */
            } /* X IS NOW R'= SGN*R */

            fp2 = floatx80_mul(fp2, fp1, status); /* TB8 */
            fp3 = floatx80_mul(fp3, fp1, status); /* TB7 */
            fp2 = floatx80_add(fp2, float64_to_floatx80(
                               make_float64(0x3E21EED90612C972), status),
                               status); /* B6+TB8 */
            fp3 = floatx80_add(fp3, float64_to_floatx80(
                               make_float64(0xBE927E4FB79D9FCF), status),
                               status); /* B5+TB7 */
            fp2 = floatx80_mul(fp2, fp1, status); /* T(B6+TB8) */
            fp3 = floatx80_mul(fp3, fp1, status); /* T(B5+TB7) */
            fp2 = floatx80_add(fp2, float64_to_floatx80(
                               make_float64(0x3EFA01A01A01D423), status),
                               status); /* B4+T(B6+TB8) */
            fp4 = packFloatx80(1, 0x3FF5, UINT64_C(0xB60B60B60B61D438));
            fp3 = floatx80_add(fp3, fp4, status); /* B3+T(B5+TB7) */
            fp2 = floatx80_mul(fp2, fp1, status); /* T(B4+T(B6+TB8)) */
            fp1 = floatx80_mul(fp1, fp3, status); /* T(B3+T(B5+TB7)) */
            fp4 = packFloatx80(0, 0x3FFA, UINT64_C(0xAAAAAAAAAAAAAB5E));
            fp2 = floatx80_add(fp2, fp4, status); /* B2+T(B4+T(B6+TB8)) */
            fp1 = floatx80_add(fp1, float32_to_floatx80(
                               make_float32(0xBF000000), status),
                               status); /* B1+T(B3+T(B5+TB7)) */
            fp0 = floatx80_mul(fp0, fp2, status); /* S(B2+T(B4+T(B6+TB8))) */
            fp0 = floatx80_add(fp0, fp1, status);
                              /* [B1+T(B3+T(B5+TB7))]+[S(B2+T(B4+T(B6+TB8)))] */

            x = packFloatx80(xSign, xExp, xSig);
            fp0 = floatx80_mul(fp0, x, status);

            status->float_rounding_mode = user_rnd_mode;
            status->floatx80_rounding_precision = user_rnd_prec;

            a = floatx80_add(fp0, float32_to_floatx80(posneg1, status), status);

            float_raise(float_flag_inexact, status);

            return a;
        } else {
            /* SINPOLY */
            xSign = extractFloatx80Sign(fp0); /* X IS R */
            xExp = extractFloatx80Exp(fp0);
            xSig = extractFloatx80Frac(fp0);

            xSign ^= ((n + 1) >> 1) & 1; /* X IS NOW R'= SGN*R */

            fp0 = floatx80_mul(fp0, fp0, status); /* FP0 IS S */
            fp1 = floatx80_mul(fp0, fp0, status); /* FP1 IS T */
            fp3 = float64_to_floatx80(make_float64(0xBD6AAA77CCC994F5),
                                      status); /* A7 */
            fp2 = float64_to_floatx80(make_float64(0x3DE612097AAE8DA1),
                                      status); /* A6 */
            fp3 = floatx80_mul(fp3, fp1, status); /* T*A7 */
            fp2 = floatx80_mul(fp2, fp1, status); /* T*A6 */
            fp3 = floatx80_add(fp3, float64_to_floatx80(
                               make_float64(0xBE5AE6452A118AE4), status),
                               status); /* A5+T*A7 */
            fp2 = floatx80_add(fp2, float64_to_floatx80(
                               make_float64(0x3EC71DE3A5341531), status),
                               status); /* A4+T*A6 */
            fp3 = floatx80_mul(fp3, fp1, status); /* T(A5+TA7) */
            fp2 = floatx80_mul(fp2, fp1, status); /* T(A4+TA6) */
            fp3 = floatx80_add(fp3, float64_to_floatx80(
                               make_float64(0xBF2A01A01A018B59), status),
                               status); /* A3+T(A5+TA7) */
            fp4 = packFloatx80(0, 0x3FF8, UINT64_C(0x88888888888859AF));
            fp2 = floatx80_add(fp2, fp4, status); /* A2+T(A4+TA6) */
            fp1 = floatx80_mul(fp1, fp3, status); /* T(A3+T(A5+TA7)) */
            fp2 = floatx80_mul(fp2, fp0, status); /* S(A2+T(A4+TA6)) */
            fp4 = packFloatx80(1, 0x3FFC, UINT64_C(0xAAAAAAAAAAAAAA99));
            fp1 = floatx80_add(fp1, fp4, status); /* A1+T(A3+T(A5+TA7)) */
            fp1 = floatx80_add(fp1, fp2, status);
                                    /* [A1+T(A3+T(A5+TA7))]+[S(A2+T(A4+TA6))] */

            x = packFloatx80(xSign, xExp, xSig);
            fp0 = floatx80_mul(fp0, x, status); /* R'*S */
            fp0 = floatx80_mul(fp0, fp1, status); /* SIN(R')-R' */

            status->float_rounding_mode = user_rnd_mode;
            status->floatx80_rounding_precision = user_rnd_prec;

            a = floatx80_add(fp0, x, status);

            float_raise(float_flag_inexact, status);

            return a;
        }
    }
}

/*
 * Arc tangent
 */

floatx80 floatx80_atan(floatx80 a, float_status *status)
{
    bool aSign;
    int32_t aExp;
    uint64_t aSig;

    FloatRoundMode user_rnd_mode;
    FloatX80RoundPrec user_rnd_prec;

    int32_t compact, tbl_index;
    floatx80 fp0, fp1, fp2, fp3, xsave;

    aSig = extractFloatx80Frac(a);
    aExp = extractFloatx80Exp(a);
    aSign = extractFloatx80Sign(a);

    if (aExp == 0x7FFF) {
        if ((uint64_t) (aSig << 1)) {
            return propagateFloatx80NaNOneArg(a, status);
        }
        a = packFloatx80(aSign, piby2_exp, pi_sig);
        float_raise(float_flag_inexact, status);
        return floatx80_move(a, status);
    }

    if (aExp == 0 && aSig == 0) {
        return packFloatx80(aSign, 0, 0);
    }

    compact = floatx80_make_compact(aExp, aSig);

    user_rnd_mode = status->float_rounding_mode;
    user_rnd_prec = status->floatx80_rounding_precision;
    status->float_rounding_mode = float_round_nearest_even;
    status->floatx80_rounding_precision = floatx80_precision_x;

    if (compact < 0x3FFB8000 || compact > 0x4002FFFF) {
        /* |X| >= 16 or |X| < 1/16 */
        if (compact > 0x3FFF8000) { /* |X| >= 16 */
            if (compact > 0x40638000) { /* |X| > 2^(100) */
                fp0 = packFloatx80(aSign, piby2_exp, pi_sig);
                fp1 = packFloatx80(aSign, 0x0001, one_sig);

                status->float_rounding_mode = user_rnd_mode;
                status->floatx80_rounding_precision = user_rnd_prec;

                a = floatx80_sub(fp0, fp1, status);

                float_raise(float_flag_inexact, status);

                return a;
            } else {
                fp0 = a;
                fp1 = packFloatx80(1, one_exp, one_sig); /* -1 */
                fp1 = floatx80_div(fp1, fp0, status); /* X' = -1/X */
                xsave = fp1;
                fp0 = floatx80_mul(fp1, fp1, status); /* Y = X'*X' */
                fp1 = floatx80_mul(fp0, fp0, status); /* Z = Y*Y */
                fp3 = float64_to_floatx80(make_float64(0xBFB70BF398539E6A),
                                          status); /* C5 */
                fp2 = float64_to_floatx80(make_float64(0x3FBC7187962D1D7D),
                                          status); /* C4 */
                fp3 = floatx80_mul(fp3, fp1, status); /* Z*C5 */
                fp2 = floatx80_mul(fp2, fp1, status); /* Z*C4 */
                fp3 = floatx80_add(fp3, float64_to_floatx80(
                                   make_float64(0xBFC24924827107B8), status),
                                   status); /* C3+Z*C5 */
                fp2 = floatx80_add(fp2, float64_to_floatx80(
                                   make_float64(0x3FC999999996263E), status),
                                   status); /* C2+Z*C4 */
                fp1 = floatx80_mul(fp1, fp3, status); /* Z*(C3+Z*C5) */
                fp2 = floatx80_mul(fp2, fp0, status); /* Y*(C2+Z*C4) */
                fp1 = floatx80_add(fp1, float64_to_floatx80(
                                   make_float64(0xBFD5555555555536), status),
                                   status); /* C1+Z*(C3+Z*C5) */
                fp0 = floatx80_mul(fp0, xsave, status); /* X'*Y */
                /* [Y*(C2+Z*C4)]+[C1+Z*(C3+Z*C5)] */
                fp1 = floatx80_add(fp1, fp2, status);
                /* X'*Y*([B1+Z*(B3+Z*B5)]+[Y*(B2+Z*(B4+Z*B6))]) ?? */
                fp0 = floatx80_mul(fp0, fp1, status);
                fp0 = floatx80_add(fp0, xsave, status);
                fp1 = packFloatx80(aSign, piby2_exp, pi_sig);

                status->float_rounding_mode = user_rnd_mode;
                status->floatx80_rounding_precision = user_rnd_prec;

                a = floatx80_add(fp0, fp1, status);

                float_raise(float_flag_inexact, status);

                return a;
            }
        } else { /* |X| < 1/16 */
            if (compact < 0x3FD78000) { /* |X| < 2^(-40) */
                status->float_rounding_mode = user_rnd_mode;
                status->floatx80_rounding_precision = user_rnd_prec;

                a = floatx80_move(a, status);

                float_raise(float_flag_inexact, status);

                return a;
            } else {
                fp0 = a;
                xsave = a;
                fp0 = floatx80_mul(fp0, fp0, status); /* Y = X*X */
                fp1 = floatx80_mul(fp0, fp0, status); /* Z = Y*Y */
                fp2 = float64_to_floatx80(make_float64(0x3FB344447F876989),
                                          status); /* B6 */
                fp3 = float64_to_floatx80(make_float64(0xBFB744EE7FAF45DB),
                                          status); /* B5 */
                fp2 = floatx80_mul(fp2, fp1, status); /* Z*B6 */
                fp3 = floatx80_mul(fp3, fp1, status); /* Z*B5 */
                fp2 = floatx80_add(fp2, float64_to_floatx80(
                                   make_float64(0x3FBC71C646940220), status),
                                   status); /* B4+Z*B6 */
                fp3 = floatx80_add(fp3, float64_to_floatx80(
                                   make_float64(0xBFC24924921872F9),
                                   status), status); /* B3+Z*B5 */
                fp2 = floatx80_mul(fp2, fp1, status); /* Z*(B4+Z*B6) */
                fp1 = floatx80_mul(fp1, fp3, status); /* Z*(B3+Z*B5) */
                fp2 = floatx80_add(fp2, float64_to_floatx80(
                                   make_float64(0x3FC9999999998FA9), status),
                                   status); /* B2+Z*(B4+Z*B6) */
                fp1 = floatx80_add(fp1, float64_to_floatx80(
                                   make_float64(0xBFD5555555555555), status),
                                   status); /* B1+Z*(B3+Z*B5) */
                fp2 = floatx80_mul(fp2, fp0, status); /* Y*(B2+Z*(B4+Z*B6)) */
                fp0 = floatx80_mul(fp0, xsave, status); /* X*Y */
                /* [B1+Z*(B3+Z*B5)]+[Y*(B2+Z*(B4+Z*B6))] */
                fp1 = floatx80_add(fp1, fp2, status);
                /* X*Y*([B1+Z*(B3+Z*B5)]+[Y*(B2+Z*(B4+Z*B6))]) */
                fp0 = floatx80_mul(fp0, fp1, status);

                status->float_rounding_mode = user_rnd_mode;
                status->floatx80_rounding_precision = user_rnd_prec;

                a = floatx80_add(fp0, xsave, status);

                float_raise(float_flag_inexact, status);

                return a;
            }
        }
    } else {
        aSig &= UINT64_C(0xF800000000000000);
        aSig |= UINT64_C(0x0400000000000000);
        xsave = packFloatx80(aSign, aExp, aSig); /* F */
        fp0 = a;
        fp1 = a; /* X */
        fp2 = packFloatx80(0, one_exp, one_sig); /* 1 */
        fp1 = floatx80_mul(fp1, xsave, status); /* X*F */
        fp0 = floatx80_sub(fp0, xsave, status); /* X-F */
        fp1 = floatx80_add(fp1, fp2, status); /* 1 + X*F */
        fp0 = floatx80_div(fp0, fp1, status); /* U = (X-F)/(1+X*F) */

        tbl_index = compact;

        tbl_index &= 0x7FFF0000;
        tbl_index -= 0x3FFB0000;
        tbl_index >>= 1;
        tbl_index += compact & 0x00007800;
        tbl_index >>= 11;

        fp3 = atan_tbl[tbl_index];

        fp3.high |= aSign ? 0x8000 : 0; /* ATAN(F) */

        fp1 = floatx80_mul(fp0, fp0, status); /* V = U*U */
        fp2 = float64_to_floatx80(make_float64(0xBFF6687E314987D8),
                                  status); /* A3 */
        fp2 = floatx80_add(fp2, fp1, status); /* A3+V */
        fp2 = floatx80_mul(fp2, fp1, status); /* V*(A3+V) */
        fp1 = floatx80_mul(fp1, fp0, status); /* U*V */
        fp2 = floatx80_add(fp2, float64_to_floatx80(
                           make_float64(0x4002AC6934A26DB3), status),
                           status); /* A2+V*(A3+V) */
        fp1 = floatx80_mul(fp1, float64_to_floatx80(
                           make_float64(0xBFC2476F4E1DA28E), status),
                           status); /* A1+U*V */
        fp1 = floatx80_mul(fp1, fp2, status); /* A1*U*V*(A2+V*(A3+V)) */
        fp0 = floatx80_add(fp0, fp1, status); /* ATAN(U) */

        status->float_rounding_mode = user_rnd_mode;
        status->floatx80_rounding_precision = user_rnd_prec;

        a = floatx80_add(fp0, fp3, status); /* ATAN(X) */

        float_raise(float_flag_inexact, status);

        return a;
    }
}

/*
 * Arc sine
 */

floatx80 floatx80_asin(floatx80 a, float_status *status)
{
    bool aSign;
    int32_t aExp;
    uint64_t aSig;

    FloatRoundMode user_rnd_mode;
    FloatX80RoundPrec user_rnd_prec;

    int32_t compact;
    floatx80 fp0, fp1, fp2, one;

    aSig = extractFloatx80Frac(a);
    aExp = extractFloatx80Exp(a);
    aSign = extractFloatx80Sign(a);

    if (aExp == 0x7FFF && (uint64_t) (aSig << 1)) {
        return propagateFloatx80NaNOneArg(a, status);
    }

    if (aExp == 0 && aSig == 0) {
        return packFloatx80(aSign, 0, 0);
    }

    compact = floatx80_make_compact(aExp, aSig);

    if (compact >= 0x3FFF8000) { /* |X| >= 1 */
        if (aExp == one_exp && aSig == one_sig) { /* |X| == 1 */
            float_raise(float_flag_inexact, status);
            a = packFloatx80(aSign, piby2_exp, pi_sig);
            return floatx80_move(a, status);
        } else { /* |X| > 1 */
            float_raise(float_flag_invalid, status);
            return floatx80_default_nan(status);
        }

    } /* |X| < 1 */

    user_rnd_mode = status->float_rounding_mode;
    user_rnd_prec = status->floatx80_rounding_precision;
    status->float_rounding_mode = float_round_nearest_even;
    status->floatx80_rounding_precision = floatx80_precision_x;

    one = packFloatx80(0, one_exp, one_sig);
    fp0 = a;

    fp1 = floatx80_sub(one, fp0, status);   /* 1 - X */
    fp2 = floatx80_add(one, fp0, status);   /* 1 + X */
    fp1 = floatx80_mul(fp2, fp1, status);   /* (1+X)*(1-X) */
    fp1 = floatx80_sqrt(fp1, status);       /* SQRT((1+X)*(1-X)) */
    fp0 = floatx80_div(fp0, fp1, status);   /* X/SQRT((1+X)*(1-X)) */

    status->float_rounding_mode = user_rnd_mode;
    status->floatx80_rounding_precision = user_rnd_prec;

    a = floatx80_atan(fp0, status);         /* ATAN(X/SQRT((1+X)*(1-X))) */

    float_raise(float_flag_inexact, status);

    return a;
}

/*
 * Arc cosine
 */

floatx80 floatx80_acos(floatx80 a, float_status *status)
{
    bool aSign;
    int32_t aExp;
    uint64_t aSig;

    FloatRoundMode user_rnd_mode;
    FloatX80RoundPrec user_rnd_prec;

    int32_t compact;
    floatx80 fp0, fp1, one;

    aSig = extractFloatx80Frac(a);
    aExp = extractFloatx80Exp(a);
    aSign = extractFloatx80Sign(a);

    if (aExp == 0x7FFF && (uint64_t) (aSig << 1)) {
        return propagateFloatx80NaNOneArg(a, status);
    }
    if (aExp == 0 && aSig == 0) {
        float_raise(float_flag_inexact, status);
        return roundAndPackFloatx80(status->floatx80_rounding_precision, 0,
                                    piby2_exp, pi_sig, 0, status);
    }

    compact = floatx80_make_compact(aExp, aSig);

    if (compact >= 0x3FFF8000) { /* |X| >= 1 */
        if (aExp == one_exp && aSig == one_sig) { /* |X| == 1 */
            if (aSign) { /* X == -1 */
                a = packFloatx80(0, pi_exp, pi_sig);
                float_raise(float_flag_inexact, status);
                return floatx80_move(a, status);
            } else { /* X == +1 */
                return packFloatx80(0, 0, 0);
            }
        } else { /* |X| > 1 */
            float_raise(float_flag_invalid, status);
            return floatx80_default_nan(status);
        }
    } /* |X| < 1 */

    user_rnd_mode = status->float_rounding_mode;
    user_rnd_prec = status->floatx80_rounding_precision;
    status->float_rounding_mode = float_round_nearest_even;
    status->floatx80_rounding_precision = floatx80_precision_x;

    one = packFloatx80(0, one_exp, one_sig);
    fp0 = a;

    fp1 = floatx80_add(one, fp0, status);   /* 1 + X */
    fp0 = floatx80_sub(one, fp0, status);   /* 1 - X */
    fp0 = floatx80_div(fp0, fp1, status);   /* (1-X)/(1+X) */
    fp0 = floatx80_sqrt(fp0, status);       /* SQRT((1-X)/(1+X)) */
    fp0 = floatx80_atan(fp0, status);       /* ATAN(SQRT((1-X)/(1+X))) */

    status->float_rounding_mode = user_rnd_mode;
    status->floatx80_rounding_precision = user_rnd_prec;

    a = floatx80_add(fp0, fp0, status);     /* 2 * ATAN(SQRT((1-X)/(1+X))) */

    float_raise(float_flag_inexact, status);

    return a;
}

/*
 * Hyperbolic arc tangent
 */

floatx80 floatx80_atanh(floatx80 a, float_status *status)
{
    bool aSign;
    int32_t aExp;
    uint64_t aSig;

    FloatRoundMode user_rnd_mode;
    FloatX80RoundPrec user_rnd_prec;

    int32_t compact;
    floatx80 fp0, fp1, fp2, one;

    aSig = extractFloatx80Frac(a);
    aExp = extractFloatx80Exp(a);
    aSign = extractFloatx80Sign(a);

    if (aExp == 0x7FFF && (uint64_t) (aSig << 1)) {
        return propagateFloatx80NaNOneArg(a, status);
    }

    if (aExp == 0 && aSig == 0) {
        return packFloatx80(aSign, 0, 0);
    }

    compact = floatx80_make_compact(aExp, aSig);

    if (compact >= 0x3FFF8000) { /* |X| >= 1 */
        if (aExp == one_exp && aSig == one_sig) { /* |X| == 1 */
            float_raise(float_flag_divbyzero, status);
            return packFloatx80(aSign, floatx80_infinity.high,
                                floatx80_infinity.low);
        } else { /* |X| > 1 */
            float_raise(float_flag_invalid, status);
            return floatx80_default_nan(status);
        }
    } /* |X| < 1 */

    user_rnd_mode = status->float_rounding_mode;
    user_rnd_prec = status->floatx80_rounding_precision;
    status->float_rounding_mode = float_round_nearest_even;
    status->floatx80_rounding_precision = floatx80_precision_x;

    one = packFloatx80(0, one_exp, one_sig);
    fp2 = packFloatx80(aSign, 0x3FFE, one_sig); /* SIGN(X) * (1/2) */
    fp0 = packFloatx80(0, aExp, aSig); /* Y = |X| */
    fp1 = packFloatx80(1, aExp, aSig); /* -Y */
    fp0 = floatx80_add(fp0, fp0, status); /* 2Y */
    fp1 = floatx80_add(fp1, one, status); /* 1-Y */
    fp0 = floatx80_div(fp0, fp1, status); /* Z = 2Y/(1-Y) */
    fp0 = floatx80_lognp1(fp0, status); /* LOG1P(Z) */

    status->float_rounding_mode = user_rnd_mode;
    status->floatx80_rounding_precision = user_rnd_prec;

    a = floatx80_mul(fp0, fp2,
                     status); /* ATANH(X) = SIGN(X) * (1/2) * LOG1P(Z) */

    float_raise(float_flag_inexact, status);

    return a;
}

/*
 * e to x minus 1
 */

floatx80 floatx80_etoxm1(floatx80 a, float_status *status)
{
    bool aSign;
    int32_t aExp;
    uint64_t aSig;

    FloatRoundMode user_rnd_mode;
    FloatX80RoundPrec user_rnd_prec;

    int32_t compact, n, j, m, m1;
    floatx80 fp0, fp1, fp2, fp3, l2, sc, onebysc;

    aSig = extractFloatx80Frac(a);
    aExp = extractFloatx80Exp(a);
    aSign = extractFloatx80Sign(a);

    if (aExp == 0x7FFF) {
        if ((uint64_t) (aSig << 1)) {
            return propagateFloatx80NaNOneArg(a, status);
        }
        if (aSign) {
            return packFloatx80(aSign, one_exp, one_sig);
        }
        return packFloatx80(0, floatx80_infinity.high,
                            floatx80_infinity.low);
    }

    if (aExp == 0 && aSig == 0) {
        return packFloatx80(aSign, 0, 0);
    }

    user_rnd_mode = status->float_rounding_mode;
    user_rnd_prec = status->floatx80_rounding_precision;
    status->float_rounding_mode = float_round_nearest_even;
    status->floatx80_rounding_precision = floatx80_precision_x;

    if (aExp >= 0x3FFD) { /* |X| >= 1/4 */
        compact = floatx80_make_compact(aExp, aSig);

        if (compact <= 0x4004C215) { /* |X| <= 70 log2 */
            fp0 = a;
            fp1 = a;
            fp0 = floatx80_mul(fp0, float32_to_floatx80(
                               make_float32(0x42B8AA3B), status),
                               status); /* 64/log2 * X */
            n = floatx80_to_int32(fp0, status); /* int(64/log2*X) */
            fp0 = int32_to_floatx80(n, status);

            j = n & 0x3F; /* J = N mod 64 */
            m = n / 64; /* NOTE: this is really arithmetic right shift by 6 */
            if (n < 0 && j) {
                /*
                 * arithmetic right shift is division and
                 * round towards minus infinity
                 */
                m--;
            }
            m1 = -m;
            /*m += 0x3FFF; // biased exponent of 2^(M) */
            /*m1 += 0x3FFF; // biased exponent of -2^(-M) */

            fp2 = fp0; /* N */
            fp0 = floatx80_mul(fp0, float32_to_floatx80(
                               make_float32(0xBC317218), status),
                               status); /* N * L1, L1 = lead(-log2/64) */
            l2 = packFloatx80(0, 0x3FDC, UINT64_C(0x82E308654361C4C6));
            fp2 = floatx80_mul(fp2, l2, status); /* N * L2, L1+L2 = -log2/64 */
            fp0 = floatx80_add(fp0, fp1, status); /* X + N*L1 */
            fp0 = floatx80_add(fp0, fp2, status); /* R */

            fp1 = floatx80_mul(fp0, fp0, status); /* S = R*R */
            fp2 = float32_to_floatx80(make_float32(0x3950097B),
                                      status); /* A6 */
            fp2 = floatx80_mul(fp2, fp1, status); /* fp2 is S*A6 */
            fp3 = floatx80_mul(float32_to_floatx80(make_float32(0x3AB60B6A),
                               status), fp1, status); /* fp3 is S*A5 */
            fp2 = floatx80_add(fp2, float64_to_floatx80(
                               make_float64(0x3F81111111174385), status),
                               status); /* fp2 IS A4+S*A6 */
            fp3 = floatx80_add(fp3, float64_to_floatx80(
                               make_float64(0x3FA5555555554F5A), status),
                               status); /* fp3 is A3+S*A5 */
            fp2 = floatx80_mul(fp2, fp1, status); /* fp2 IS S*(A4+S*A6) */
            fp3 = floatx80_mul(fp3, fp1, status); /* fp3 IS S*(A3+S*A5) */
            fp2 = floatx80_add(fp2, float64_to_floatx80(
                               make_float64(0x3FC5555555555555), status),
                               status); /* fp2 IS A2+S*(A4+S*A6) */
            fp3 = floatx80_add(fp3, float32_to_floatx80(
                               make_float32(0x3F000000), status),
                               status); /* fp3 IS A1+S*(A3+S*A5) */
            fp2 = floatx80_mul(fp2, fp1,
                               status); /* fp2 IS S*(A2+S*(A4+S*A6)) */
            fp1 = floatx80_mul(fp1, fp3,
                               status); /* fp1 IS S*(A1+S*(A3+S*A5)) */
            fp2 = floatx80_mul(fp2, fp0,
                               status); /* fp2 IS R*S*(A2+S*(A4+S*A6)) */
            fp0 = floatx80_add(fp0, fp1,
                               status); /* fp0 IS R+S*(A1+S*(A3+S*A5)) */
            fp0 = floatx80_add(fp0, fp2, status); /* fp0 IS EXP(R) - 1 */

            fp0 = floatx80_mul(fp0, exp_tbl[j],
                               status); /* 2^(J/64)*(Exp(R)-1) */

            if (m >= 64) {
                fp1 = float32_to_floatx80(exp_tbl2[j], status);
                onebysc = packFloatx80(1, m1 + 0x3FFF, one_sig); /* -2^(-M) */
                fp1 = floatx80_add(fp1, onebysc, status);
                fp0 = floatx80_add(fp0, fp1, status);
                fp0 = floatx80_add(fp0, exp_tbl[j], status);
            } else if (m < -3) {
                fp0 = floatx80_add(fp0, float32_to_floatx80(exp_tbl2[j],
                                   status), status);
                fp0 = floatx80_add(fp0, exp_tbl[j], status);
                onebysc = packFloatx80(1, m1 + 0x3FFF, one_sig); /* -2^(-M) */
                fp0 = floatx80_add(fp0, onebysc, status);
            } else { /* -3 <= m <= 63 */
                fp1 = exp_tbl[j];
                fp0 = floatx80_add(fp0, float32_to_floatx80(exp_tbl2[j],
                                   status), status);
                onebysc = packFloatx80(1, m1 + 0x3FFF, one_sig); /* -2^(-M) */
                fp1 = floatx80_add(fp1, onebysc, status);
                fp0 = floatx80_add(fp0, fp1, status);
            }

            sc = packFloatx80(0, m + 0x3FFF, one_sig);

            status->float_rounding_mode = user_rnd_mode;
            status->floatx80_rounding_precision = user_rnd_prec;

            a = floatx80_mul(fp0, sc, status);

            float_raise(float_flag_inexact, status);

            return a;
        } else { /* |X| > 70 log2 */
            if (aSign) {
                fp0 = float32_to_floatx80(make_float32(0xBF800000),
                      status); /* -1 */

                status->float_rounding_mode = user_rnd_mode;
                status->floatx80_rounding_precision = user_rnd_prec;

                a = floatx80_add(fp0, float32_to_floatx80(
                                 make_float32(0x00800000), status),
                                 status); /* -1 + 2^(-126) */

                float_raise(float_flag_inexact, status);

                return a;
            } else {
                status->float_rounding_mode = user_rnd_mode;
                status->floatx80_rounding_precision = user_rnd_prec;

                return floatx80_etox(a, status);
            }
        }
    } else { /* |X| < 1/4 */
        if (aExp >= 0x3FBE) {
            fp0 = a;
            fp0 = floatx80_mul(fp0, fp0, status); /* S = X*X */
            fp1 = float32_to_floatx80(make_float32(0x2F30CAA8),
                                      status); /* B12 */
            fp1 = floatx80_mul(fp1, fp0, status); /* S * B12 */
            fp2 = float32_to_floatx80(make_float32(0x310F8290),
                                      status); /* B11 */
            fp1 = floatx80_add(fp1, float32_to_floatx80(
                               make_float32(0x32D73220), status),
                               status); /* B10 */
            fp2 = floatx80_mul(fp2, fp0, status);
            fp1 = floatx80_mul(fp1, fp0, status);
            fp2 = floatx80_add(fp2, float32_to_floatx80(
                               make_float32(0x3493F281), status),
                               status); /* B9 */
            fp1 = floatx80_add(fp1, float64_to_floatx80(
                               make_float64(0x3EC71DE3A5774682), status),
                               status); /* B8 */
            fp2 = floatx80_mul(fp2, fp0, status);
            fp1 = floatx80_mul(fp1, fp0, status);
            fp2 = floatx80_add(fp2, float64_to_floatx80(
                               make_float64(0x3EFA01A019D7CB68), status),
                               status); /* B7 */
            fp1 = floatx80_add(fp1, float64_to_floatx80(
                               make_float64(0x3F2A01A01A019DF3), status),
                               status); /* B6 */
            fp2 = floatx80_mul(fp2, fp0, status);
            fp1 = floatx80_mul(fp1, fp0, status);
            fp2 = floatx80_add(fp2, float64_to_floatx80(
                               make_float64(0x3F56C16C16C170E2), status),
                               status); /* B5 */
            fp1 = floatx80_add(fp1, float64_to_floatx80(
                               make_float64(0x3F81111111111111), status),
                               status); /* B4 */
            fp2 = floatx80_mul(fp2, fp0, status);
            fp1 = floatx80_mul(fp1, fp0, status);
            fp2 = floatx80_add(fp2, float64_to_floatx80(
                               make_float64(0x3FA5555555555555), status),
                               status); /* B3 */
            fp3 = packFloatx80(0, 0x3FFC, UINT64_C(0xAAAAAAAAAAAAAAAB));
            fp1 = floatx80_add(fp1, fp3, status); /* B2 */
            fp2 = floatx80_mul(fp2, fp0, status);
            fp1 = floatx80_mul(fp1, fp0, status);

            fp2 = floatx80_mul(fp2, fp0, status);
            fp1 = floatx80_mul(fp1, a, status);

            fp0 = floatx80_mul(fp0, float32_to_floatx80(
                               make_float32(0x3F000000), status),
                               status); /* S*B1 */
            fp1 = floatx80_add(fp1, fp2, status); /* Q */
            fp0 = floatx80_add(fp0, fp1, status); /* S*B1+Q */

            status->float_rounding_mode = user_rnd_mode;
            status->floatx80_rounding_precision = user_rnd_prec;

            a = floatx80_add(fp0, a, status);

            float_raise(float_flag_inexact, status);

            return a;
        } else { /* |X| < 2^(-65) */
            sc = packFloatx80(1, 1, one_sig);
            fp0 = a;

            if (aExp < 0x0033) { /* |X| < 2^(-16382) */
                fp0 = floatx80_mul(fp0, float64_to_floatx80(
                                   make_float64(0x48B0000000000000), status),
                                   status);
                fp0 = floatx80_add(fp0, sc, status);

                status->float_rounding_mode = user_rnd_mode;
                status->floatx80_rounding_precision = user_rnd_prec;

                a = floatx80_mul(fp0, float64_to_floatx80(
                                 make_float64(0x3730000000000000), status),
                                 status);
            } else {
                status->float_rounding_mode = user_rnd_mode;
                status->floatx80_rounding_precision = user_rnd_prec;

                a = floatx80_add(fp0, sc, status);
            }

            float_raise(float_flag_inexact, status);

            return a;
        }
    }
}

/*
 * Hyperbolic tangent
 */

floatx80 floatx80_tanh(floatx80 a, float_status *status)
{
    bool aSign, vSign;
    int32_t aExp, vExp;
    uint64_t aSig, vSig;

    FloatRoundMode user_rnd_mode;
    FloatX80RoundPrec user_rnd_prec;

    int32_t compact;
    floatx80 fp0, fp1;
    uint32_t sign;

    aSig = extractFloatx80Frac(a);
    aExp = extractFloatx80Exp(a);
    aSign = extractFloatx80Sign(a);

    if (aExp == 0x7FFF) {
        if ((uint64_t) (aSig << 1)) {
            return propagateFloatx80NaNOneArg(a, status);
        }
        return packFloatx80(aSign, one_exp, one_sig);
    }

    if (aExp == 0 && aSig == 0) {
        return packFloatx80(aSign, 0, 0);
    }

    user_rnd_mode = status->float_rounding_mode;
    user_rnd_prec = status->floatx80_rounding_precision;
    status->float_rounding_mode = float_round_nearest_even;
    status->floatx80_rounding_precision = floatx80_precision_x;

    compact = floatx80_make_compact(aExp, aSig);

    if (compact < 0x3FD78000 || compact > 0x3FFFDDCE) {
        /* TANHBORS */
        if (compact < 0x3FFF8000) {
            /* TANHSM */
            status->float_rounding_mode = user_rnd_mode;
            status->floatx80_rounding_precision = user_rnd_prec;

            a = floatx80_move(a, status);

            float_raise(float_flag_inexact, status);

            return a;
        } else {
            if (compact > 0x40048AA1) {
                /* TANHHUGE */
                sign = 0x3F800000;
                sign |= aSign ? 0x80000000 : 0x00000000;
                fp0 = float32_to_floatx80(make_float32(sign), status);
                sign &= 0x80000000;
                sign ^= 0x80800000; /* -SIGN(X)*EPS */

                status->float_rounding_mode = user_rnd_mode;
                status->floatx80_rounding_precision = user_rnd_prec;

                a = floatx80_add(fp0, float32_to_floatx80(make_float32(sign),
                                 status), status);

                float_raise(float_flag_inexact, status);

                return a;
            } else {
                fp0 = packFloatx80(0, aExp + 1, aSig); /* Y = 2|X| */
                fp0 = floatx80_etox(fp0, status); /* FP0 IS EXP(Y) */
                fp0 = floatx80_add(fp0, float32_to_floatx80(
                                   make_float32(0x3F800000),
                                   status), status); /* EXP(Y)+1 */
                sign = aSign ? 0x80000000 : 0x00000000;
                fp1 = floatx80_div(float32_to_floatx80(make_float32(
                                   sign ^ 0xC0000000), status), fp0,
                                   status); /* -SIGN(X)*2 / [EXP(Y)+1] */
                fp0 = float32_to_floatx80(make_float32(sign | 0x3F800000),
                                          status); /* SIGN */

                status->float_rounding_mode = user_rnd_mode;
                status->floatx80_rounding_precision = user_rnd_prec;

                a = floatx80_add(fp1, fp0, status);

                float_raise(float_flag_inexact, status);

                return a;
            }
        }
    } else { /* 2**(-40) < |X| < (5/2)LOG2 */
        fp0 = packFloatx80(0, aExp + 1, aSig); /* Y = 2|X| */
        fp0 = floatx80_etoxm1(fp0, status); /* FP0 IS Z = EXPM1(Y) */
        fp1 = floatx80_add(fp0, float32_to_floatx80(make_float32(0x40000000),
                           status),
                           status); /* Z+2 */

        vSign = extractFloatx80Sign(fp1);
        vExp = extractFloatx80Exp(fp1);
        vSig = extractFloatx80Frac(fp1);

        fp1 = packFloatx80(vSign ^ aSign, vExp, vSig);

        status->float_rounding_mode = user_rnd_mode;
        status->floatx80_rounding_precision = user_rnd_prec;

        a = floatx80_div(fp0, fp1, status);

        float_raise(float_flag_inexact, status);

        return a;
    }
}

/*
 * Hyperbolic sine
 */

floatx80 floatx80_sinh(floatx80 a, float_status *status)
{
    bool aSign;
    int32_t aExp;
    uint64_t aSig;

    FloatRoundMode user_rnd_mode;
    FloatX80RoundPrec user_rnd_prec;

    int32_t compact;
    floatx80 fp0, fp1, fp2;
    float32 fact;

    aSig = extractFloatx80Frac(a);
    aExp = extractFloatx80Exp(a);
    aSign = extractFloatx80Sign(a);

    if (aExp == 0x7FFF) {
        if ((uint64_t) (aSig << 1)) {
            return propagateFloatx80NaNOneArg(a, status);
        }
        return packFloatx80(aSign, floatx80_infinity.high,
                            floatx80_infinity.low);
    }

    if (aExp == 0 && aSig == 0) {
        return packFloatx80(aSign, 0, 0);
    }

    user_rnd_mode = status->float_rounding_mode;
    user_rnd_prec = status->floatx80_rounding_precision;
    status->float_rounding_mode = float_round_nearest_even;
    status->floatx80_rounding_precision = floatx80_precision_x;

    compact = floatx80_make_compact(aExp, aSig);

    if (compact > 0x400CB167) {
        /* SINHBIG */
        if (compact > 0x400CB2B3) {
            status->float_rounding_mode = user_rnd_mode;
            status->floatx80_rounding_precision = user_rnd_prec;

            return roundAndPackFloatx80(status->floatx80_rounding_precision,
                                        aSign, 0x8000, aSig, 0, status);
        } else {
            fp0 = floatx80_abs(a); /* Y = |X| */
            fp0 = floatx80_sub(fp0, float64_to_floatx80(
                               make_float64(0x40C62D38D3D64634), status),
                               status); /* (|X|-16381LOG2_LEAD) */
            fp0 = floatx80_sub(fp0, float64_to_floatx80(
                               make_float64(0x3D6F90AEB1E75CC7), status),
                               status); /* |X| - 16381 LOG2, ACCURATE */
            fp0 = floatx80_etox(fp0, status);
            fp2 = packFloatx80(aSign, 0x7FFB, one_sig);

            status->float_rounding_mode = user_rnd_mode;
            status->floatx80_rounding_precision = user_rnd_prec;

            a = floatx80_mul(fp0, fp2, status);

            float_raise(float_flag_inexact, status);

            return a;
        }
    } else { /* |X| < 16380 LOG2 */
        fp0 = floatx80_abs(a); /* Y = |X| */
        fp0 = floatx80_etoxm1(fp0, status); /* FP0 IS Z = EXPM1(Y) */
        fp1 = floatx80_add(fp0, float32_to_floatx80(make_float32(0x3F800000),
                           status), status); /* 1+Z */
        fp2 = fp0;
        fp0 = floatx80_div(fp0, fp1, status); /* Z/(1+Z) */
        fp0 = floatx80_add(fp0, fp2, status);

        fact = packFloat32(aSign, 0x7E, 0);

        status->float_rounding_mode = user_rnd_mode;
        status->floatx80_rounding_precision = user_rnd_prec;

        a = floatx80_mul(fp0, float32_to_floatx80(fact, status), status);

        float_raise(float_flag_inexact, status);

        return a;
    }
}

/*
 * Hyperbolic cosine
 */

floatx80 floatx80_cosh(floatx80 a, float_status *status)
{
    int32_t aExp;
    uint64_t aSig;

    FloatRoundMode user_rnd_mode;
    FloatX80RoundPrec user_rnd_prec;

    int32_t compact;
    floatx80 fp0, fp1;

    aSig = extractFloatx80Frac(a);
    aExp = extractFloatx80Exp(a);

    if (aExp == 0x7FFF) {
        if ((uint64_t) (aSig << 1)) {
            return propagateFloatx80NaNOneArg(a, status);
        }
        return packFloatx80(0, floatx80_infinity.high,
                            floatx80_infinity.low);
    }

    if (aExp == 0 && aSig == 0) {
        return packFloatx80(0, one_exp, one_sig);
    }

    user_rnd_mode = status->float_rounding_mode;
    user_rnd_prec = status->floatx80_rounding_precision;
    status->float_rounding_mode = float_round_nearest_even;
    status->floatx80_rounding_precision = floatx80_precision_x;

    compact = floatx80_make_compact(aExp, aSig);

    if (compact > 0x400CB167) {
        if (compact > 0x400CB2B3) {
            status->float_rounding_mode = user_rnd_mode;
            status->floatx80_rounding_precision = user_rnd_prec;
            return roundAndPackFloatx80(status->floatx80_rounding_precision, 0,
                                        0x8000, one_sig, 0, status);
        } else {
            fp0 = packFloatx80(0, aExp, aSig);
            fp0 = floatx80_sub(fp0, float64_to_floatx80(
                               make_float64(0x40C62D38D3D64634), status),
                               status);
            fp0 = floatx80_sub(fp0, float64_to_floatx80(
                               make_float64(0x3D6F90AEB1E75CC7), status),
                               status);
            fp0 = floatx80_etox(fp0, status);
            fp1 = packFloatx80(0, 0x7FFB, one_sig);

            status->float_rounding_mode = user_rnd_mode;
            status->floatx80_rounding_precision = user_rnd_prec;

            a = floatx80_mul(fp0, fp1, status);

            float_raise(float_flag_inexact, status);

            return a;
        }
    }

    fp0 = packFloatx80(0, aExp, aSig); /* |X| */
    fp0 = floatx80_etox(fp0, status); /* EXP(|X|) */
    fp0 = floatx80_mul(fp0, float32_to_floatx80(make_float32(0x3F000000),
                       status), status); /* (1/2)*EXP(|X|) */
    fp1 = float32_to_floatx80(make_float32(0x3E800000), status); /* 1/4 */
    fp1 = floatx80_div(fp1, fp0, status); /* 1/(2*EXP(|X|)) */

    status->float_rounding_mode = user_rnd_mode;
    status->floatx80_rounding_precision = user_rnd_prec;

    a = floatx80_add(fp0, fp1, status);

    float_raise(float_flag_inexact, status);

    return a;
}