target/i386: reimplement fpatan using floatx80 operations
The x87 fpatan emulation is currently based around conversion to double. This is inherently unsuitable for a good emulation of any floatx80 operation. Reimplement using the soft-float operations, as for other such instructions. Signed-off-by: Joseph Myers <joseph@codesourcery.com> Message-Id: <alpine.DEB.2.21.2006230000340.24721@digraph.polyomino.org.uk> Signed-off-by: Paolo Bonzini <pbonzini@redhat.com>
This commit is contained in:
Joseph Myers
Paolo Bonzini
parent
1f18a1e6ab
commit
ff57bb7b63
@ -1239,14 +1239,493 @@ void helper_fptan(CPUX86State *env)
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}
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}
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/* Values of pi/4, pi/2, 3pi/4 and pi, with 128-bit precision. */
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#define pi_4_exp 0x3ffe
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#define pi_4_sig_high 0xc90fdaa22168c234ULL
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#define pi_4_sig_low 0xc4c6628b80dc1cd1ULL
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#define pi_2_exp 0x3fff
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#define pi_2_sig_high 0xc90fdaa22168c234ULL
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#define pi_2_sig_low 0xc4c6628b80dc1cd1ULL
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#define pi_34_exp 0x4000
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#define pi_34_sig_high 0x96cbe3f9990e91a7ULL
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#define pi_34_sig_low 0x9394c9e8a0a5159dULL
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#define pi_exp 0x4000
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#define pi_sig_high 0xc90fdaa22168c234ULL
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#define pi_sig_low 0xc4c6628b80dc1cd1ULL
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/*
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* Polynomial coefficients for an approximation to atan(x), with only
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* odd powers of x used, for x in the interval [-1/16, 1/16]. (Unlike
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* for some other approximations, no low part is needed for the first
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* coefficient here to achieve a sufficiently accurate result, because
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* the coefficient in this minimax approximation is very close to
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* exactly 1.)
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*/
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#define fpatan_coeff_0 make_floatx80(0x3fff, 0x8000000000000000ULL)
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#define fpatan_coeff_1 make_floatx80(0xbffd, 0xaaaaaaaaaaaaaa43ULL)
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#define fpatan_coeff_2 make_floatx80(0x3ffc, 0xccccccccccbfe4f8ULL)
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#define fpatan_coeff_3 make_floatx80(0xbffc, 0x92492491fbab2e66ULL)
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#define fpatan_coeff_4 make_floatx80(0x3ffb, 0xe38e372881ea1e0bULL)
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#define fpatan_coeff_5 make_floatx80(0xbffb, 0xba2c0104bbdd0615ULL)
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#define fpatan_coeff_6 make_floatx80(0x3ffb, 0x9baf7ebf898b42efULL)
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struct fpatan_data {
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/* High and low parts of atan(x). */
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floatx80 atan_high, atan_low;
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};
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static const struct fpatan_data fpatan_table[9] = {
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{ floatx80_zero,
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floatx80_zero },
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{ make_floatx80(0x3ffb, 0xfeadd4d5617b6e33ULL),
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make_floatx80(0xbfb9, 0xdda19d8305ddc420ULL) },
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{ make_floatx80(0x3ffc, 0xfadbafc96406eb15ULL),
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make_floatx80(0x3fbb, 0xdb8f3debef442fccULL) },
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{ make_floatx80(0x3ffd, 0xb7b0ca0f26f78474ULL),
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make_floatx80(0xbfbc, 0xeab9bdba460376faULL) },
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{ make_floatx80(0x3ffd, 0xed63382b0dda7b45ULL),
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make_floatx80(0x3fbc, 0xdfc88bd978751a06ULL) },
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{ make_floatx80(0x3ffe, 0x8f005d5ef7f59f9bULL),
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make_floatx80(0x3fbd, 0xb906bc2ccb886e90ULL) },
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{ make_floatx80(0x3ffe, 0xa4bc7d1934f70924ULL),
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make_floatx80(0x3fbb, 0xcd43f9522bed64f8ULL) },
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{ make_floatx80(0x3ffe, 0xb8053e2bc2319e74ULL),
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make_floatx80(0xbfbc, 0xd3496ab7bd6eef0cULL) },
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{ make_floatx80(0x3ffe, 0xc90fdaa22168c235ULL),
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make_floatx80(0xbfbc, 0xece675d1fc8f8cbcULL) },
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};
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void helper_fpatan(CPUX86State *env)
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{
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double fptemp, fpsrcop;
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uint8_t old_flags = save_exception_flags(env);
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uint64_t arg0_sig = extractFloatx80Frac(ST0);
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int32_t arg0_exp = extractFloatx80Exp(ST0);
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bool arg0_sign = extractFloatx80Sign(ST0);
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uint64_t arg1_sig = extractFloatx80Frac(ST1);
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int32_t arg1_exp = extractFloatx80Exp(ST1);
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bool arg1_sign = extractFloatx80Sign(ST1);
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if (floatx80_is_signaling_nan(ST0, &env->fp_status)) {
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float_raise(float_flag_invalid, &env->fp_status);
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ST1 = floatx80_silence_nan(ST0, &env->fp_status);
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} else if (floatx80_is_signaling_nan(ST1, &env->fp_status)) {
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float_raise(float_flag_invalid, &env->fp_status);
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ST1 = floatx80_silence_nan(ST1, &env->fp_status);
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} else if (floatx80_invalid_encoding(ST0) ||
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floatx80_invalid_encoding(ST1)) {
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float_raise(float_flag_invalid, &env->fp_status);
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ST1 = floatx80_default_nan(&env->fp_status);
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} else if (floatx80_is_any_nan(ST0)) {
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ST1 = ST0;
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} else if (floatx80_is_any_nan(ST1)) {
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/* Pass this NaN through. */
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} else if (floatx80_is_zero(ST1) && !arg0_sign) {
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/* Pass this zero through. */
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} else if (((floatx80_is_infinity(ST0) && !floatx80_is_infinity(ST1)) ||
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arg0_exp - arg1_exp >= 80) &&
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!arg0_sign) {
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/*
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* Dividing ST1 by ST0 gives the correct result up to
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* rounding, and avoids spurious underflow exceptions that
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* might result from passing some small values through the
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* polynomial approximation, but if a finite nonzero result of
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* division is exact, the result of fpatan is still inexact
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* (and underflowing where appropriate).
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*/
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signed char save_prec = env->fp_status.floatx80_rounding_precision;
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env->fp_status.floatx80_rounding_precision = 80;
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ST1 = floatx80_div(ST1, ST0, &env->fp_status);
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env->fp_status.floatx80_rounding_precision = save_prec;
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if (!floatx80_is_zero(ST1) &&
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!(get_float_exception_flags(&env->fp_status) &
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float_flag_inexact)) {
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/*
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* The mathematical result is very slightly closer to zero
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* than this exact result. Round a value with the
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* significand adjusted accordingly to get the correct
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* exceptions, and possibly an adjusted result depending
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* on the rounding mode.
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*/
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uint64_t sig = extractFloatx80Frac(ST1);
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int32_t exp = extractFloatx80Exp(ST1);
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bool sign = extractFloatx80Sign(ST1);
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if (exp == 0) {
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normalizeFloatx80Subnormal(sig, &exp, &sig);
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}
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ST1 = normalizeRoundAndPackFloatx80(80, sign, exp, sig - 1,
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-1, &env->fp_status);
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}
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} else {
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/* The result is inexact. */
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bool rsign = arg1_sign;
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int32_t rexp;
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uint64_t rsig0, rsig1;
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if (floatx80_is_zero(ST1)) {
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/*
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* ST0 is negative. The result is pi with the sign of
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* ST1.
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*/
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rexp = pi_exp;
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rsig0 = pi_sig_high;
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rsig1 = pi_sig_low;
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} else if (floatx80_is_infinity(ST1)) {
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if (floatx80_is_infinity(ST0)) {
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if (arg0_sign) {
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rexp = pi_34_exp;
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rsig0 = pi_34_sig_high;
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rsig1 = pi_34_sig_low;
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} else {
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rexp = pi_4_exp;
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rsig0 = pi_4_sig_high;
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rsig1 = pi_4_sig_low;
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}
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} else {
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rexp = pi_2_exp;
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rsig0 = pi_2_sig_high;
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rsig1 = pi_2_sig_low;
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}
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} else if (floatx80_is_zero(ST0) || arg1_exp - arg0_exp >= 80) {
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rexp = pi_2_exp;
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rsig0 = pi_2_sig_high;
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rsig1 = pi_2_sig_low;
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} else if (floatx80_is_infinity(ST0) || arg0_exp - arg1_exp >= 80) {
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/* ST0 is negative. */
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rexp = pi_exp;
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rsig0 = pi_sig_high;
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rsig1 = pi_sig_low;
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} else {
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/*
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* ST0 and ST1 are finite, nonzero and with exponents not
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* too far apart.
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*/
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int32_t adj_exp, num_exp, den_exp, xexp, yexp, n, texp, zexp, aexp;
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int32_t azexp, axexp;
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bool adj_sub, ysign, zsign;
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uint64_t adj_sig0, adj_sig1, num_sig, den_sig, xsig0, xsig1;
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uint64_t msig0, msig1, msig2, remsig0, remsig1, remsig2;
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uint64_t ysig0, ysig1, tsig, zsig0, zsig1, asig0, asig1;
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uint64_t azsig0, azsig1;
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uint64_t azsig2, azsig3, axsig0, axsig1;
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floatx80 x8;
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FloatRoundMode save_mode = env->fp_status.float_rounding_mode;
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signed char save_prec = env->fp_status.floatx80_rounding_precision;
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env->fp_status.float_rounding_mode = float_round_nearest_even;
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env->fp_status.floatx80_rounding_precision = 80;
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if (arg0_exp == 0) {
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normalizeFloatx80Subnormal(arg0_sig, &arg0_exp, &arg0_sig);
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}
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if (arg1_exp == 0) {
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normalizeFloatx80Subnormal(arg1_sig, &arg1_exp, &arg1_sig);
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}
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if (arg0_exp > arg1_exp ||
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(arg0_exp == arg1_exp && arg0_sig >= arg1_sig)) {
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/* Work with abs(ST1) / abs(ST0). */
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num_exp = arg1_exp;
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num_sig = arg1_sig;
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den_exp = arg0_exp;
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den_sig = arg0_sig;
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if (arg0_sign) {
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/* The result is subtracted from pi. */
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adj_exp = pi_exp;
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adj_sig0 = pi_sig_high;
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adj_sig1 = pi_sig_low;
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adj_sub = true;
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} else {
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/* The result is used as-is. */
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adj_exp = 0;
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adj_sig0 = 0;
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adj_sig1 = 0;
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adj_sub = false;
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}
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} else {
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/* Work with abs(ST0) / abs(ST1). */
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num_exp = arg0_exp;
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num_sig = arg0_sig;
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den_exp = arg1_exp;
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den_sig = arg1_sig;
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/* The result is added to or subtracted from pi/2. */
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adj_exp = pi_2_exp;
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adj_sig0 = pi_2_sig_high;
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adj_sig1 = pi_2_sig_low;
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adj_sub = !arg0_sign;
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}
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/*
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* Compute x = num/den, where 0 < x <= 1 and x is not too
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* small.
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*/
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xexp = num_exp - den_exp + 0x3ffe;
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remsig0 = num_sig;
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remsig1 = 0;
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if (den_sig <= remsig0) {
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shift128Right(remsig0, remsig1, 1, &remsig0, &remsig1);
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++xexp;
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}
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xsig0 = estimateDiv128To64(remsig0, remsig1, den_sig);
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mul64To128(den_sig, xsig0, &msig0, &msig1);
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sub128(remsig0, remsig1, msig0, msig1, &remsig0, &remsig1);
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while ((int64_t) remsig0 < 0) {
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--xsig0;
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add128(remsig0, remsig1, 0, den_sig, &remsig0, &remsig1);
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}
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xsig1 = estimateDiv128To64(remsig1, 0, den_sig);
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/*
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* No need to correct any estimation error in xsig1; even
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* with such error, it is accurate enough.
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*/
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/*
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* Split x as x = t + y, where t = n/8 is the nearest
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* multiple of 1/8 to x.
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*/
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x8 = normalizeRoundAndPackFloatx80(80, false, xexp + 3, xsig0,
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xsig1, &env->fp_status);
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n = floatx80_to_int32(x8, &env->fp_status);
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if (n == 0) {
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ysign = false;
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yexp = xexp;
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ysig0 = xsig0;
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ysig1 = xsig1;
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texp = 0;
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tsig = 0;
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} else {
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int shift = clz32(n) + 32;
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texp = 0x403b - shift;
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tsig = n;
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tsig <<= shift;
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if (texp == xexp) {
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sub128(xsig0, xsig1, tsig, 0, &ysig0, &ysig1);
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if ((int64_t) ysig0 >= 0) {
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ysign = false;
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if (ysig0 == 0) {
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if (ysig1 == 0) {
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yexp = 0;
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} else {
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shift = clz64(ysig1) + 64;
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yexp = xexp - shift;
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shift128Left(ysig0, ysig1, shift,
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&ysig0, &ysig1);
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}
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} else {
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shift = clz64(ysig0);
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yexp = xexp - shift;
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shift128Left(ysig0, ysig1, shift, &ysig0, &ysig1);
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}
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} else {
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ysign = true;
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sub128(0, 0, ysig0, ysig1, &ysig0, &ysig1);
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if (ysig0 == 0) {
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shift = clz64(ysig1) + 64;
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} else {
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shift = clz64(ysig0);
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}
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yexp = xexp - shift;
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shift128Left(ysig0, ysig1, shift, &ysig0, &ysig1);
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}
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} else {
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/*
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* t's exponent must be greater than x's because t
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* is positive and the nearest multiple of 1/8 to
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* x, and if x has a greater exponent, the power
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* of 2 with that exponent is also a multiple of
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* 1/8.
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*/
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uint64_t usig0, usig1;
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shift128RightJamming(xsig0, xsig1, texp - xexp,
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&usig0, &usig1);
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ysign = true;
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sub128(tsig, 0, usig0, usig1, &ysig0, &ysig1);
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if (ysig0 == 0) {
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shift = clz64(ysig1) + 64;
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} else {
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shift = clz64(ysig0);
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}
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yexp = texp - shift;
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shift128Left(ysig0, ysig1, shift, &ysig0, &ysig1);
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}
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}
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/*
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* Compute z = y/(1+tx), so arctan(x) = arctan(t) +
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* arctan(z).
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*/
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zsign = ysign;
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if (texp == 0 || yexp == 0) {
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zexp = yexp;
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zsig0 = ysig0;
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zsig1 = ysig1;
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} else {
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/*
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* t <= 1, x <= 1 and if both are 1 then y is 0, so tx < 1.
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*/
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int32_t dexp = texp + xexp - 0x3ffe;
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uint64_t dsig0, dsig1, dsig2;
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mul128By64To192(xsig0, xsig1, tsig, &dsig0, &dsig1, &dsig2);
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/*
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* dexp <= 0x3fff (and if equal, dsig0 has a leading 0
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* bit). Add 1 to produce the denominator 1+tx.
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*/
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shift128RightJamming(dsig0, dsig1, 0x3fff - dexp,
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&dsig0, &dsig1);
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dsig0 |= 0x8000000000000000ULL;
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zexp = yexp - 1;
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remsig0 = ysig0;
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remsig1 = ysig1;
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remsig2 = 0;
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if (dsig0 <= remsig0) {
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shift128Right(remsig0, remsig1, 1, &remsig0, &remsig1);
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++zexp;
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}
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zsig0 = estimateDiv128To64(remsig0, remsig1, dsig0);
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mul128By64To192(dsig0, dsig1, zsig0, &msig0, &msig1, &msig2);
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sub192(remsig0, remsig1, remsig2, msig0, msig1, msig2,
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&remsig0, &remsig1, &remsig2);
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while ((int64_t) remsig0 < 0) {
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--zsig0;
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add192(remsig0, remsig1, remsig2, 0, dsig0, dsig1,
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&remsig0, &remsig1, &remsig2);
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}
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zsig1 = estimateDiv128To64(remsig1, remsig2, dsig0);
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/* No need to correct any estimation error in zsig1. */
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}
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if (zexp == 0) {
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azexp = 0;
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azsig0 = 0;
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azsig1 = 0;
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} else {
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floatx80 z2, accum;
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uint64_t z2sig0, z2sig1, z2sig2, z2sig3;
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/* Compute z^2. */
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mul128To256(zsig0, zsig1, zsig0, zsig1,
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&z2sig0, &z2sig1, &z2sig2, &z2sig3);
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z2 = normalizeRoundAndPackFloatx80(80, false,
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zexp + zexp - 0x3ffe,
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z2sig0, z2sig1,
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&env->fp_status);
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/* Compute the lower parts of the polynomial expansion. */
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accum = floatx80_mul(fpatan_coeff_6, z2, &env->fp_status);
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accum = floatx80_add(fpatan_coeff_5, accum, &env->fp_status);
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accum = floatx80_mul(accum, z2, &env->fp_status);
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accum = floatx80_add(fpatan_coeff_4, accum, &env->fp_status);
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accum = floatx80_mul(accum, z2, &env->fp_status);
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accum = floatx80_add(fpatan_coeff_3, accum, &env->fp_status);
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accum = floatx80_mul(accum, z2, &env->fp_status);
|
||||
accum = floatx80_add(fpatan_coeff_2, accum, &env->fp_status);
|
||||
accum = floatx80_mul(accum, z2, &env->fp_status);
|
||||
accum = floatx80_add(fpatan_coeff_1, accum, &env->fp_status);
|
||||
accum = floatx80_mul(accum, z2, &env->fp_status);
|
||||
|
||||
/*
|
||||
* The full polynomial expansion is z*(fpatan_coeff_0 + accum).
|
||||
* fpatan_coeff_0 is 1, and accum is negative and much smaller.
|
||||
*/
|
||||
aexp = extractFloatx80Exp(fpatan_coeff_0);
|
||||
shift128RightJamming(extractFloatx80Frac(accum), 0,
|
||||
aexp - extractFloatx80Exp(accum),
|
||||
&asig0, &asig1);
|
||||
sub128(extractFloatx80Frac(fpatan_coeff_0), 0, asig0, asig1,
|
||||
&asig0, &asig1);
|
||||
/* Multiply by z to compute arctan(z). */
|
||||
azexp = aexp + zexp - 0x3ffe;
|
||||
mul128To256(asig0, asig1, zsig0, zsig1, &azsig0, &azsig1,
|
||||
&azsig2, &azsig3);
|
||||
}
|
||||
|
||||
/* Add arctan(t) (positive or zero) and arctan(z) (sign zsign). */
|
||||
if (texp == 0) {
|
||||
/* z is positive. */
|
||||
axexp = azexp;
|
||||
axsig0 = azsig0;
|
||||
axsig1 = azsig1;
|
||||
} else {
|
||||
bool low_sign = extractFloatx80Sign(fpatan_table[n].atan_low);
|
||||
int32_t low_exp = extractFloatx80Exp(fpatan_table[n].atan_low);
|
||||
uint64_t low_sig0 =
|
||||
extractFloatx80Frac(fpatan_table[n].atan_low);
|
||||
uint64_t low_sig1 = 0;
|
||||
axexp = extractFloatx80Exp(fpatan_table[n].atan_high);
|
||||
axsig0 = extractFloatx80Frac(fpatan_table[n].atan_high);
|
||||
axsig1 = 0;
|
||||
shift128RightJamming(low_sig0, low_sig1, axexp - low_exp,
|
||||
&low_sig0, &low_sig1);
|
||||
if (low_sign) {
|
||||
sub128(axsig0, axsig1, low_sig0, low_sig1,
|
||||
&axsig0, &axsig1);
|
||||
} else {
|
||||
add128(axsig0, axsig1, low_sig0, low_sig1,
|
||||
&axsig0, &axsig1);
|
||||
}
|
||||
if (azexp >= axexp) {
|
||||
shift128RightJamming(axsig0, axsig1, azexp - axexp + 1,
|
||||
&axsig0, &axsig1);
|
||||
axexp = azexp + 1;
|
||||
shift128RightJamming(azsig0, azsig1, 1,
|
||||
&azsig0, &azsig1);
|
||||
} else {
|
||||
shift128RightJamming(axsig0, axsig1, 1,
|
||||
&axsig0, &axsig1);
|
||||
shift128RightJamming(azsig0, azsig1, axexp - azexp + 1,
|
||||
&azsig0, &azsig1);
|
||||
++axexp;
|
||||
}
|
||||
if (zsign) {
|
||||
sub128(axsig0, axsig1, azsig0, azsig1,
|
||||
&axsig0, &axsig1);
|
||||
} else {
|
||||
add128(axsig0, axsig1, azsig0, azsig1,
|
||||
&axsig0, &axsig1);
|
||||
}
|
||||
}
|
||||
|
||||
if (adj_exp == 0) {
|
||||
rexp = axexp;
|
||||
rsig0 = axsig0;
|
||||
rsig1 = axsig1;
|
||||
} else {
|
||||
/*
|
||||
* Add or subtract arctan(x) (exponent axexp,
|
||||
* significand axsig0 and axsig1, positive, not
|
||||
* necessarily normalized) to the number given by
|
||||
* adj_exp, adj_sig0 and adj_sig1, according to
|
||||
* adj_sub.
|
||||
*/
|
||||
if (adj_exp >= axexp) {
|
||||
shift128RightJamming(axsig0, axsig1, adj_exp - axexp + 1,
|
||||
&axsig0, &axsig1);
|
||||
rexp = adj_exp + 1;
|
||||
shift128RightJamming(adj_sig0, adj_sig1, 1,
|
||||
&adj_sig0, &adj_sig1);
|
||||
} else {
|
||||
shift128RightJamming(axsig0, axsig1, 1,
|
||||
&axsig0, &axsig1);
|
||||
shift128RightJamming(adj_sig0, adj_sig1,
|
||||
axexp - adj_exp + 1,
|
||||
&adj_sig0, &adj_sig1);
|
||||
rexp = axexp + 1;
|
||||
}
|
||||
if (adj_sub) {
|
||||
sub128(adj_sig0, adj_sig1, axsig0, axsig1,
|
||||
&rsig0, &rsig1);
|
||||
} else {
|
||||
add128(adj_sig0, adj_sig1, axsig0, axsig1,
|
||||
&rsig0, &rsig1);
|
||||
}
|
||||
}
|
||||
|
||||
env->fp_status.float_rounding_mode = save_mode;
|
||||
env->fp_status.floatx80_rounding_precision = save_prec;
|
||||
}
|
||||
/* This result is inexact. */
|
||||
rsig1 |= 1;
|
||||
ST1 = normalizeRoundAndPackFloatx80(80, rsign, rexp,
|
||||
rsig0, rsig1, &env->fp_status);
|
||||
}
|
||||
|
||||
fpsrcop = floatx80_to_double(env, ST1);
|
||||
fptemp = floatx80_to_double(env, ST0);
|
||||
ST1 = double_to_floatx80(env, atan2(fpsrcop, fptemp));
|
||||
fpop(env);
|
||||
merge_exception_flags(env, old_flags);
|
||||
}
|
||||
|
||||
void helper_fxtract(CPUX86State *env)
|
||||
|
||||
1071
tests/tcg/i386/test-i386-fpatan.c
Normal file
1071
tests/tcg/i386/test-i386-fpatan.c
Normal file
File diff suppressed because it is too large
Load Diff
Loading…
Reference in New Issue
Block a user