target/i386: reimplement fyl2x using floatx80 operations
The x87 fyl2x 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, building on top of the reimplementation of fyl2xp1 and factoring out code to be shared between the two instructions. The included test assumes that the result in round-to-nearest mode should always be one of the two closest floating-point numbers to the mathematically exact result (including that it should be exact, in the exact cases which cover more cases than for fyl2xp1). Signed-off-by: Joseph Myers <joseph@codesourcery.com> Message-Id: <alpine.DEB.2.21.2006172321530.20587@digraph.polyomino.org.uk> Signed-off-by: Paolo Bonzini <pbonzini@redhat.com>
This commit is contained in:
Joseph Myers
Paolo Bonzini
parent
5eebc49d2d
commit
1f18a1e6ab
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@ -1223,21 +1223,6 @@ void helper_f2xm1(CPUX86State *env)
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merge_exception_flags(env, old_flags);
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}
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void helper_fyl2x(CPUX86State *env)
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{
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double fptemp = floatx80_to_double(env, ST0);
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if (fptemp > 0.0) {
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fptemp = log(fptemp) / log(2.0); /* log2(ST) */
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fptemp *= floatx80_to_double(env, ST1);
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ST1 = double_to_floatx80(env, fptemp);
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fpop(env);
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} else {
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env->fpus &= ~0x4700;
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env->fpus |= 0x400;
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}
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}
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void helper_fptan(CPUX86State *env)
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{
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double fptemp = floatx80_to_double(env, ST0);
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@ -1395,6 +1380,118 @@ void helper_fprem(CPUX86State *env)
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#define fyl2x_coeff_8 make_floatx80(0x3ffc, 0xac5cf50cc57d6372ULL)
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#define fyl2x_coeff_9 make_floatx80(0x3ffc, 0xb1ed0066d971a103ULL)
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/*
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* Compute an approximation of log2(1+arg), where 1+arg is in the
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* interval [sqrt(2)/2, sqrt(2)]. It is assumed that when this
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* function is called, rounding precision is set to 80 and the
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* round-to-nearest mode is in effect. arg must not be exactly zero,
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* and must not be so close to zero that underflow might occur.
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*/
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static void helper_fyl2x_common(CPUX86State *env, floatx80 arg, int32_t *exp,
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uint64_t *sig0, uint64_t *sig1)
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{
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uint64_t arg0_sig = extractFloatx80Frac(arg);
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int32_t arg0_exp = extractFloatx80Exp(arg);
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bool arg0_sign = extractFloatx80Sign(arg);
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bool asign;
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int32_t dexp, texp, aexp;
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uint64_t dsig0, dsig1, tsig0, tsig1, rsig0, rsig1, rsig2;
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uint64_t msig0, msig1, msig2, t2sig0, t2sig1, t2sig2, t2sig3;
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uint64_t asig0, asig1, asig2, asig3, bsig0, bsig1;
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floatx80 t2, accum;
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/*
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* Compute an approximation of arg/(2+arg), with extra precision,
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* as the argument to a polynomial approximation. The extra
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* precision is only needed for the first term of the
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* approximation, with subsequent terms being significantly
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* smaller; the approximation only uses odd exponents, and the
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* square of arg/(2+arg) is at most 17-12*sqrt(2) = 0.029....
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*/
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if (arg0_sign) {
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dexp = 0x3fff;
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shift128RightJamming(arg0_sig, 0, dexp - arg0_exp, &dsig0, &dsig1);
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sub128(0, 0, dsig0, dsig1, &dsig0, &dsig1);
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} else {
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dexp = 0x4000;
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shift128RightJamming(arg0_sig, 0, dexp - arg0_exp, &dsig0, &dsig1);
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dsig0 |= 0x8000000000000000ULL;
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}
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texp = arg0_exp - dexp + 0x3ffe;
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rsig0 = arg0_sig;
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rsig1 = 0;
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rsig2 = 0;
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if (dsig0 <= rsig0) {
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shift128Right(rsig0, rsig1, 1, &rsig0, &rsig1);
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++texp;
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}
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tsig0 = estimateDiv128To64(rsig0, rsig1, dsig0);
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mul128By64To192(dsig0, dsig1, tsig0, &msig0, &msig1, &msig2);
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sub192(rsig0, rsig1, rsig2, msig0, msig1, msig2,
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&rsig0, &rsig1, &rsig2);
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while ((int64_t) rsig0 < 0) {
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--tsig0;
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add192(rsig0, rsig1, rsig2, 0, dsig0, dsig1,
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&rsig0, &rsig1, &rsig2);
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}
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tsig1 = estimateDiv128To64(rsig1, rsig2, dsig0);
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/*
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* No need to correct any estimation error in tsig1; even with
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* such error, it is accurate enough. Now compute the square of
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* that approximation.
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*/
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mul128To256(tsig0, tsig1, tsig0, tsig1,
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&t2sig0, &t2sig1, &t2sig2, &t2sig3);
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t2 = normalizeRoundAndPackFloatx80(80, false, texp + texp - 0x3ffe,
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t2sig0, t2sig1, &env->fp_status);
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/* Compute the lower parts of the polynomial expansion. */
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accum = floatx80_mul(fyl2x_coeff_9, t2, &env->fp_status);
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accum = floatx80_add(fyl2x_coeff_8, accum, &env->fp_status);
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accum = floatx80_mul(accum, t2, &env->fp_status);
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accum = floatx80_add(fyl2x_coeff_7, accum, &env->fp_status);
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accum = floatx80_mul(accum, t2, &env->fp_status);
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accum = floatx80_add(fyl2x_coeff_6, accum, &env->fp_status);
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accum = floatx80_mul(accum, t2, &env->fp_status);
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accum = floatx80_add(fyl2x_coeff_5, accum, &env->fp_status);
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accum = floatx80_mul(accum, t2, &env->fp_status);
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accum = floatx80_add(fyl2x_coeff_4, accum, &env->fp_status);
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accum = floatx80_mul(accum, t2, &env->fp_status);
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accum = floatx80_add(fyl2x_coeff_3, accum, &env->fp_status);
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accum = floatx80_mul(accum, t2, &env->fp_status);
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accum = floatx80_add(fyl2x_coeff_2, accum, &env->fp_status);
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accum = floatx80_mul(accum, t2, &env->fp_status);
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accum = floatx80_add(fyl2x_coeff_1, accum, &env->fp_status);
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accum = floatx80_mul(accum, t2, &env->fp_status);
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accum = floatx80_add(fyl2x_coeff_0_low, accum, &env->fp_status);
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/*
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* The full polynomial expansion is fyl2x_coeff_0 + accum (where
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* accum has much lower magnitude, and so, in particular, carry
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* out of the addition is not possible), multiplied by t. (This
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* expansion is only accurate to about 70 bits, not 128 bits.)
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*/
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aexp = extractFloatx80Exp(fyl2x_coeff_0);
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asign = extractFloatx80Sign(fyl2x_coeff_0);
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shift128RightJamming(extractFloatx80Frac(accum), 0,
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aexp - extractFloatx80Exp(accum),
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&asig0, &asig1);
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bsig0 = extractFloatx80Frac(fyl2x_coeff_0);
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bsig1 = 0;
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if (asign == extractFloatx80Sign(accum)) {
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add128(bsig0, bsig1, asig0, asig1, &asig0, &asig1);
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} else {
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sub128(bsig0, bsig1, asig0, asig1, &asig0, &asig1);
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}
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/* Multiply by t to compute the required result. */
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mul128To256(asig0, asig1, tsig0, tsig1,
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&asig0, &asig1, &asig2, &asig3);
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aexp += texp - 0x3ffe;
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*exp = aexp;
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*sig0 = asig0;
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*sig1 = asig1;
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}
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void helper_fyl2xp1(CPUX86State *env)
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{
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uint8_t old_flags = save_exception_flags(env);
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@ -1462,109 +1559,18 @@ void helper_fyl2xp1(CPUX86State *env)
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ST1 = normalizeRoundAndPackFloatx80(80, arg0_sign ^ arg1_sign, exp,
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sig0, sig1, &env->fp_status);
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} else {
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bool asign;
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uint32_t dexp, texp, aexp;
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uint64_t dsig0, dsig1, tsig0, tsig1, rsig0, rsig1, rsig2;
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uint64_t msig0, msig1, msig2, t2sig0, t2sig1, t2sig2, t2sig3;
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uint64_t asig0, asig1, asig2, asig3, bsig0, bsig1;
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floatx80 t2, accum;
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int32_t aexp;
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uint64_t asig0, asig1, asig2;
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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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helper_fyl2x_common(env, ST0, &aexp, &asig0, &asig1);
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/*
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* Compute an approximation of ST0/(2+ST0), with extra
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* precision, as the argument to a polynomial approximation.
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* The extra precision is only needed for the first term of
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* the approximation, with subsequent terms being
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* significantly smaller; the approximation only uses odd
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* exponents, and the square of ST0/(2+ST0) is at most
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* 17-12*sqrt(2) = 0.029....
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* Multiply by the second argument to compute the required
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* result.
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*/
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if (arg0_sign) {
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dexp = 0x3fff;
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shift128RightJamming(arg0_sig, 0, dexp - arg0_exp, &dsig0, &dsig1);
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sub128(0, 0, dsig0, dsig1, &dsig0, &dsig1);
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} else {
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dexp = 0x4000;
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shift128RightJamming(arg0_sig, 0, dexp - arg0_exp, &dsig0, &dsig1);
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dsig0 |= 0x8000000000000000ULL;
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}
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texp = arg0_exp - dexp + 0x3ffe;
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rsig0 = arg0_sig;
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rsig1 = 0;
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rsig2 = 0;
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if (dsig0 <= rsig0) {
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shift128Right(rsig0, rsig1, 1, &rsig0, &rsig1);
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++texp;
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}
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tsig0 = estimateDiv128To64(rsig0, rsig1, dsig0);
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mul128By64To192(dsig0, dsig1, tsig0, &msig0, &msig1, &msig2);
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sub192(rsig0, rsig1, rsig2, msig0, msig1, msig2,
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&rsig0, &rsig1, &rsig2);
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while ((int64_t) rsig0 < 0) {
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--tsig0;
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add192(rsig0, rsig1, rsig2, 0, dsig0, dsig1,
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&rsig0, &rsig1, &rsig2);
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}
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tsig1 = estimateDiv128To64(rsig1, rsig2, dsig0);
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/*
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* No need to correct any estimation error in tsig1; even with
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* such error, it is accurate enough. Now compute the square
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* of that approximation.
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*/
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mul128To256(tsig0, tsig1, tsig0, tsig1,
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&t2sig0, &t2sig1, &t2sig2, &t2sig3);
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t2 = normalizeRoundAndPackFloatx80(80, false, texp + texp - 0x3ffe,
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t2sig0, t2sig1, &env->fp_status);
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/* Compute the lower parts of the polynomial expansion. */
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accum = floatx80_mul(fyl2x_coeff_9, t2, &env->fp_status);
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accum = floatx80_add(fyl2x_coeff_8, accum, &env->fp_status);
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accum = floatx80_mul(accum, t2, &env->fp_status);
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accum = floatx80_add(fyl2x_coeff_7, accum, &env->fp_status);
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accum = floatx80_mul(accum, t2, &env->fp_status);
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accum = floatx80_add(fyl2x_coeff_6, accum, &env->fp_status);
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accum = floatx80_mul(accum, t2, &env->fp_status);
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accum = floatx80_add(fyl2x_coeff_5, accum, &env->fp_status);
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accum = floatx80_mul(accum, t2, &env->fp_status);
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accum = floatx80_add(fyl2x_coeff_4, accum, &env->fp_status);
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accum = floatx80_mul(accum, t2, &env->fp_status);
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accum = floatx80_add(fyl2x_coeff_3, accum, &env->fp_status);
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accum = floatx80_mul(accum, t2, &env->fp_status);
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accum = floatx80_add(fyl2x_coeff_2, accum, &env->fp_status);
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accum = floatx80_mul(accum, t2, &env->fp_status);
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accum = floatx80_add(fyl2x_coeff_1, accum, &env->fp_status);
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accum = floatx80_mul(accum, t2, &env->fp_status);
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accum = floatx80_add(fyl2x_coeff_0_low, accum, &env->fp_status);
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/*
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* The full polynomial expansion is fyl2x_coeff_0 + accum
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* (where accum has much lower magnitude, and so, in
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* particular, carry out of the addition is not possible),
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* multiplied by t. (This expansion is only accurate to about
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* 70 bits, not 128 bits.)
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*/
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aexp = extractFloatx80Exp(fyl2x_coeff_0);
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asign = extractFloatx80Sign(fyl2x_coeff_0);
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shift128RightJamming(extractFloatx80Frac(accum), 0,
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aexp - extractFloatx80Exp(accum),
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&asig0, &asig1);
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bsig0 = extractFloatx80Frac(fyl2x_coeff_0);
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bsig1 = 0;
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if (asign == extractFloatx80Sign(accum)) {
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add128(bsig0, bsig1, asig0, asig1, &asig0, &asig1);
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} else {
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sub128(bsig0, bsig1, asig0, asig1, &asig0, &asig1);
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}
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/*
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* Multiply by t and by the second argument to compute the
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* required result.
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*/
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mul128To256(asig0, asig1, tsig0, tsig1,
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&asig0, &asig1, &asig2, &asig3);
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aexp += texp - 0x3ffe;
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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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@ -1581,6 +1587,151 @@ void helper_fyl2xp1(CPUX86State *env)
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merge_exception_flags(env, old_flags);
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}
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void helper_fyl2x(CPUX86State *env)
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{
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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 (arg0_sign && !floatx80_is_zero(ST0)) {
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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_infinity(ST1)) {
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FloatRelation cmp = floatx80_compare(ST0, floatx80_one,
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&env->fp_status);
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switch (cmp) {
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case float_relation_less:
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ST1 = floatx80_chs(ST1);
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break;
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case float_relation_greater:
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/* Result is infinity of the same sign as ST1. */
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break;
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default:
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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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break;
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}
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} else if (floatx80_is_infinity(ST0)) {
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if (floatx80_is_zero(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 (arg1_sign) {
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ST1 = floatx80_chs(ST0);
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} else {
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ST1 = ST0;
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}
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} else if (floatx80_is_zero(ST0)) {
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if (floatx80_is_zero(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 {
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/* Result is infinity with opposite sign to ST1. */
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float_raise(float_flag_divbyzero, &env->fp_status);
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ST1 = make_floatx80(arg1_sign ? 0x7fff : 0xffff,
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0x8000000000000000ULL);
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}
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} else if (floatx80_is_zero(ST1)) {
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if (floatx80_lt(ST0, floatx80_one, &env->fp_status)) {
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ST1 = floatx80_chs(ST1);
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}
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/* Otherwise, ST1 is already the correct result. */
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} else if (floatx80_eq(ST0, floatx80_one, &env->fp_status)) {
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if (arg1_sign) {
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ST1 = floatx80_chs(floatx80_zero);
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} else {
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ST1 = floatx80_zero;
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}
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} else {
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int32_t int_exp;
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floatx80 arg0_m1;
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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);
|
||||
}
|
||||
int_exp = arg0_exp - 0x3fff;
|
||||
if (arg0_sig > 0xb504f333f9de6484ULL) {
|
||||
++int_exp;
|
||||
}
|
||||
arg0_m1 = floatx80_sub(floatx80_scalbn(ST0, -int_exp,
|
||||
&env->fp_status),
|
||||
floatx80_one, &env->fp_status);
|
||||
if (floatx80_is_zero(arg0_m1)) {
|
||||
/* Exact power of 2; multiply by ST1. */
|
||||
env->fp_status.float_rounding_mode = save_mode;
|
||||
ST1 = floatx80_mul(int32_to_floatx80(int_exp, &env->fp_status),
|
||||
ST1, &env->fp_status);
|
||||
} else {
|
||||
bool asign = extractFloatx80Sign(arg0_m1);
|
||||
int32_t aexp;
|
||||
uint64_t asig0, asig1, asig2;
|
||||
helper_fyl2x_common(env, arg0_m1, &aexp, &asig0, &asig1);
|
||||
if (int_exp != 0) {
|
||||
bool isign = (int_exp < 0);
|
||||
int32_t iexp;
|
||||
uint64_t isig;
|
||||
int shift;
|
||||
int_exp = isign ? -int_exp : int_exp;
|
||||
shift = clz32(int_exp) + 32;
|
||||
isig = int_exp;
|
||||
isig <<= shift;
|
||||
iexp = 0x403e - shift;
|
||||
shift128RightJamming(asig0, asig1, iexp - aexp,
|
||||
&asig0, &asig1);
|
||||
if (asign == isign) {
|
||||
add128(isig, 0, asig0, asig1, &asig0, &asig1);
|
||||
} else {
|
||||
sub128(isig, 0, asig0, asig1, &asig0, &asig1);
|
||||
}
|
||||
aexp = iexp;
|
||||
asign = isign;
|
||||
}
|
||||
/*
|
||||
* Multiply by the second argument to compute the required
|
||||
* result.
|
||||
*/
|
||||
if (arg1_exp == 0) {
|
||||
normalizeFloatx80Subnormal(arg1_sig, &arg1_exp, &arg1_sig);
|
||||
}
|
||||
mul128By64To192(asig0, asig1, arg1_sig, &asig0, &asig1, &asig2);
|
||||
aexp += arg1_exp - 0x3ffe;
|
||||
/* This result is inexact. */
|
||||
asig1 |= 1;
|
||||
env->fp_status.float_rounding_mode = save_mode;
|
||||
ST1 = normalizeRoundAndPackFloatx80(80, asign ^ arg1_sign, aexp,
|
||||
asig0, asig1, &env->fp_status);
|
||||
}
|
||||
|
||||
env->fp_status.floatx80_rounding_precision = save_prec;
|
||||
}
|
||||
fpop(env);
|
||||
merge_exception_flags(env, old_flags);
|
||||
}
|
||||
|
||||
void helper_fsqrt(CPUX86State *env)
|
||||
{
|
||||
uint8_t old_flags = save_exception_flags(env);
|
||||
|
|
|
|||
File diff suppressed because it is too large
Load Diff
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Reference in New Issue