diff mbox series

target/i386: reimplement f2xm1 using floatx80 operations

Message ID alpine.DEB.2.21.2006112341010.18393@digraph.polyomino.org.uk
State New
Headers show
Series target/i386: reimplement f2xm1 using floatx80 operations | expand

Commit Message

Joseph Myers June 11, 2020, 11:45 p.m. UTC 
The x87 f2xm1 emulation is currently based around conversion to
double.  This is inherently unsuitable for a good emulation of any
floatx80 operation, even before considering that it is a particularly
naive implementation using double (computing with pow and then
subtracting 1 rather than attempting a better emulation using expm1).

Reimplement using the soft-float operations, including additions and
multiplications with higher precision where appropriate to limit
accumulation of errors.  I considered reusing some of the m68k code
for transcendental operations, but the instructions don't generally
correspond exactly to x87 operations (for example, m68k has 2^x and
e^x - 1, but not 2^x - 1); to avoid possible accumulation of errors
from applying multiple such operations each rounding to floatx80
precision, I wrote a direct implementation of 2^x - 1 instead.  It
would be possible in principle to make the implementation more
efficient by doing the intermediate operations directly with
significands, signs and exponents and not packing / unpacking floatx80
format for each operation, but that would make it significantly more
complicated and it's not clear that's worthwhile; the m68k emulation
doesn't try to do that.

A test is included with many randomly generated inputs.  The
assumption of the test is that the result in round-to-nearest mode
should always be one of the two closest floating-point numbers to the
mathematical value of 2^x - 1; the implementation aims to do somewhat
better than that (about 70 correct bits before rounding).  I haven't
investigated how accurate hardware is.

Signed-off-by: Joseph Myers <joseph@codesourcery.com>

---

This patch depends on at least some of my previous x87 emulation fixes
being present (probably only the ones in the recent pull request; I
don't think it depends on any of the most recent series fixing fprem
and fprem1).  I expect to make similar fixes for fyl2xp1, fyl2x and
fpatan.  (The other transcendental instructions (fcos, fptan, fsin,
fsincos) may follow, but as a lower priority, as I'm aiming at getting
reasonable glibc test results under QEMU and those trigonometric
instructions - with their documented semantics that they are defined
to do range reduction using a specific 66-bit approximation to pi -
aren't used in glibc.)

checkpatch.pl has its usual false-positive complaints about hex
floating-point constants in the testcase.  It also complains about
lines over 80 columns in that test; I can reformat the test if
desired, but it's not clear line length matters for such a randomly
generated table of test inputs and expected results.

---
 target/i386/fpu_helper.c         |  385 +++++++++-
 tests/tcg/i386/test-i386-f2xm1.c | 1140 ++++++++++++++++++++++++++++++
 2 files changed, 1522 insertions(+), 3 deletions(-)
 create mode 100644 tests/tcg/i386/test-i386-f2xm1.c
diff mbox series

Patch

diff --git a/target/i386/fpu_helper.c b/target/i386/fpu_helper.c
index 0e531e3821..8f34ea9776 100644
--- a/target/i386/fpu_helper.c
+++ b/target/i386/fpu_helper.c
@@ -25,6 +25,7 @@ 
 #include "exec/exec-all.h"
 #include "exec/cpu_ldst.h"
 #include "fpu/softfloat.h"
+#include "fpu/softfloat-macros.h"
 
 #ifdef CONFIG_SOFTMMU
 #include "hw/irq.h"
@@ -836,12 +837,390 @@  void helper_fbst_ST0(CPUX86State *env, target_ulong ptr)
     merge_exception_flags(env, old_flags);
 }
 
+/* 128-bit significand of log(2).  */
+#define ln2_sig_high 0xb17217f7d1cf79abULL
+#define ln2_sig_low 0xc9e3b39803f2f6afULL
+
+/*
+ * Polynomial coefficients for an approximation to (2^x - 1) / x, on
+ * the interval [-1/64, 1/64].
+ */
+#define f2xm1_coeff_0 make_floatx80(0x3ffe, 0xb17217f7d1cf79acULL)
+#define f2xm1_coeff_0_low make_floatx80(0xbfbc, 0xd87edabf495b3762ULL)
+#define f2xm1_coeff_1 make_floatx80(0x3ffc, 0xf5fdeffc162c7543ULL)
+#define f2xm1_coeff_2 make_floatx80(0x3ffa, 0xe35846b82505fcc7ULL)
+#define f2xm1_coeff_3 make_floatx80(0x3ff8, 0x9d955b7dd273b899ULL)
+#define f2xm1_coeff_4 make_floatx80(0x3ff5, 0xaec3ff3c4ef4ac0cULL)
+#define f2xm1_coeff_5 make_floatx80(0x3ff2, 0xa184897c3a7f0de9ULL)
+#define f2xm1_coeff_6 make_floatx80(0x3fee, 0xffe634d0ec30d504ULL)
+#define f2xm1_coeff_7 make_floatx80(0x3feb, 0xb160111d2db515e4ULL)
+
+struct f2xm1_data {
+    /*
+     * A value very close to a multiple of 1/32, such that 2^t and 2^t - 1
+     * are very close to exact floatx80 values.
+     */
+    floatx80 t;
+    /* The value of 2^t.  */
+    floatx80 exp2;
+    /* The value of 2^t - 1.  */
+    floatx80 exp2m1;
+};
+
+static const struct f2xm1_data f2xm1_table[65] = {
+    { make_floatx80(0xbfff, 0x8000000000000000ULL),
+      make_floatx80(0x3ffe, 0x8000000000000000ULL),
+      make_floatx80(0xbffe, 0x8000000000000000ULL) },
+    { make_floatx80(0xbffe, 0xf800000000002e7eULL),
+      make_floatx80(0x3ffe, 0x82cd8698ac2b9160ULL),
+      make_floatx80(0xbffd, 0xfa64f2cea7a8dd40ULL) },
+    { make_floatx80(0xbffe, 0xefffffffffffe960ULL),
+      make_floatx80(0x3ffe, 0x85aac367cc488345ULL),
+      make_floatx80(0xbffd, 0xf4aa7930676ef976ULL) },
+    { make_floatx80(0xbffe, 0xe800000000006f10ULL),
+      make_floatx80(0x3ffe, 0x88980e8092da5c14ULL),
+      make_floatx80(0xbffd, 0xeecfe2feda4b47d8ULL) },
+    { make_floatx80(0xbffe, 0xe000000000008a45ULL),
+      make_floatx80(0x3ffe, 0x8b95c1e3ea8ba2a5ULL),
+      make_floatx80(0xbffd, 0xe8d47c382ae8bab6ULL) },
+    { make_floatx80(0xbffe, 0xd7ffffffffff8a9eULL),
+      make_floatx80(0x3ffe, 0x8ea4398b45cd8116ULL),
+      make_floatx80(0xbffd, 0xe2b78ce97464fdd4ULL) },
+    { make_floatx80(0xbffe, 0xd0000000000019a0ULL),
+      make_floatx80(0x3ffe, 0x91c3d373ab11b919ULL),
+      make_floatx80(0xbffd, 0xdc785918a9dc8dceULL) },
+    { make_floatx80(0xbffe, 0xc7ffffffffff14dfULL),
+      make_floatx80(0x3ffe, 0x94f4efa8fef76836ULL),
+      make_floatx80(0xbffd, 0xd61620ae02112f94ULL) },
+    { make_floatx80(0xbffe, 0xc000000000006530ULL),
+      make_floatx80(0x3ffe, 0x9837f0518db87fbbULL),
+      make_floatx80(0xbffd, 0xcf901f5ce48f008aULL) },
+    { make_floatx80(0xbffe, 0xb7ffffffffff1723ULL),
+      make_floatx80(0x3ffe, 0x9b8d39b9d54eb74cULL),
+      make_floatx80(0xbffd, 0xc8e58c8c55629168ULL) },
+    { make_floatx80(0xbffe, 0xb00000000000b5e1ULL),
+      make_floatx80(0x3ffe, 0x9ef5326091a0c366ULL),
+      make_floatx80(0xbffd, 0xc2159b3edcbe7934ULL) },
+    { make_floatx80(0xbffe, 0xa800000000006f8aULL),
+      make_floatx80(0x3ffe, 0xa27043030c49370aULL),
+      make_floatx80(0xbffd, 0xbb1f79f9e76d91ecULL) },
+    { make_floatx80(0xbffe, 0x9fffffffffff816aULL),
+      make_floatx80(0x3ffe, 0xa5fed6a9b15171cfULL),
+      make_floatx80(0xbffd, 0xb40252ac9d5d1c62ULL) },
+    { make_floatx80(0xbffe, 0x97ffffffffffb621ULL),
+      make_floatx80(0x3ffe, 0xa9a15ab4ea7c30e6ULL),
+      make_floatx80(0xbffd, 0xacbd4a962b079e34ULL) },
+    { make_floatx80(0xbffe, 0x8fffffffffff162bULL),
+      make_floatx80(0x3ffe, 0xad583eea42a1b886ULL),
+      make_floatx80(0xbffd, 0xa54f822b7abc8ef4ULL) },
+    { make_floatx80(0xbffe, 0x87ffffffffff4d34ULL),
+      make_floatx80(0x3ffe, 0xb123f581d2ac7b51ULL),
+      make_floatx80(0xbffd, 0x9db814fc5aa7095eULL) },
+    { make_floatx80(0xbffe, 0x800000000000227dULL),
+      make_floatx80(0x3ffe, 0xb504f333f9de539dULL),
+      make_floatx80(0xbffd, 0x95f619980c4358c6ULL) },
+    { make_floatx80(0xbffd, 0xefffffffffff3978ULL),
+      make_floatx80(0x3ffe, 0xb8fbaf4762fbd0a1ULL),
+      make_floatx80(0xbffd, 0x8e08a1713a085ebeULL) },
+    { make_floatx80(0xbffd, 0xe00000000000df81ULL),
+      make_floatx80(0x3ffe, 0xbd08a39f580bfd8cULL),
+      make_floatx80(0xbffd, 0x85eeb8c14fe804e8ULL) },
+    { make_floatx80(0xbffd, 0xd00000000000bccfULL),
+      make_floatx80(0x3ffe, 0xc12c4cca667062f6ULL),
+      make_floatx80(0xbffc, 0xfb4eccd6663e7428ULL) },
+    { make_floatx80(0xbffd, 0xc00000000000eff0ULL),
+      make_floatx80(0x3ffe, 0xc5672a1155069abeULL),
+      make_floatx80(0xbffc, 0xea6357baabe59508ULL) },
+    { make_floatx80(0xbffd, 0xb000000000000fe6ULL),
+      make_floatx80(0x3ffe, 0xc9b9bd866e2f234bULL),
+      make_floatx80(0xbffc, 0xd91909e6474372d4ULL) },
+    { make_floatx80(0xbffd, 0x9fffffffffff2172ULL),
+      make_floatx80(0x3ffe, 0xce248c151f84bf00ULL),
+      make_floatx80(0xbffc, 0xc76dcfab81ed0400ULL) },
+    { make_floatx80(0xbffd, 0x8fffffffffffafffULL),
+      make_floatx80(0x3ffe, 0xd2a81d91f12afb2bULL),
+      make_floatx80(0xbffc, 0xb55f89b83b541354ULL) },
+    { make_floatx80(0xbffc, 0xffffffffffff81a3ULL),
+      make_floatx80(0x3ffe, 0xd744fccad69d7d5eULL),
+      make_floatx80(0xbffc, 0xa2ec0cd4a58a0a88ULL) },
+    { make_floatx80(0xbffc, 0xdfffffffffff1568ULL),
+      make_floatx80(0x3ffe, 0xdbfbb797daf25a44ULL),
+      make_floatx80(0xbffc, 0x901121a0943696f0ULL) },
+    { make_floatx80(0xbffc, 0xbfffffffffff68daULL),
+      make_floatx80(0x3ffe, 0xe0ccdeec2a94f811ULL),
+      make_floatx80(0xbffb, 0xf999089eab583f78ULL) },
+    { make_floatx80(0xbffc, 0x9fffffffffff4690ULL),
+      make_floatx80(0x3ffe, 0xe5b906e77c83657eULL),
+      make_floatx80(0xbffb, 0xd237c8c41be4d410ULL) },
+    { make_floatx80(0xbffb, 0xffffffffffff8aeeULL),
+      make_floatx80(0x3ffe, 0xeac0c6e7dd24427cULL),
+      make_floatx80(0xbffb, 0xa9f9c8c116ddec20ULL) },
+    { make_floatx80(0xbffb, 0xbfffffffffff2d18ULL),
+      make_floatx80(0x3ffe, 0xefe4b99bdcdb06ebULL),
+      make_floatx80(0xbffb, 0x80da33211927c8a8ULL) },
+    { make_floatx80(0xbffa, 0xffffffffffff8ccbULL),
+      make_floatx80(0x3ffe, 0xf5257d152486d0f4ULL),
+      make_floatx80(0xbffa, 0xada82eadb792f0c0ULL) },
+    { make_floatx80(0xbff9, 0xffffffffffff11feULL),
+      make_floatx80(0x3ffe, 0xfa83b2db722a0846ULL),
+      make_floatx80(0xbff9, 0xaf89a491babef740ULL) },
+    { floatx80_zero,
+      make_floatx80(0x3fff, 0x8000000000000000ULL),
+      floatx80_zero },
+    { make_floatx80(0x3ff9, 0xffffffffffff2680ULL),
+      make_floatx80(0x3fff, 0x82cd8698ac2b9f6fULL),
+      make_floatx80(0x3ff9, 0xb361a62b0ae7dbc0ULL) },
+    { make_floatx80(0x3ffb, 0x800000000000b500ULL),
+      make_floatx80(0x3fff, 0x85aac367cc488345ULL),
+      make_floatx80(0x3ffa, 0xb5586cf9891068a0ULL) },
+    { make_floatx80(0x3ffb, 0xbfffffffffff4b67ULL),
+      make_floatx80(0x3fff, 0x88980e8092da7cceULL),
+      make_floatx80(0x3ffb, 0x8980e8092da7cce0ULL) },
+    { make_floatx80(0x3ffb, 0xffffffffffffff57ULL),
+      make_floatx80(0x3fff, 0x8b95c1e3ea8bd6dfULL),
+      make_floatx80(0x3ffb, 0xb95c1e3ea8bd6df0ULL) },
+    { make_floatx80(0x3ffc, 0x9fffffffffff811fULL),
+      make_floatx80(0x3fff, 0x8ea4398b45cd4780ULL),
+      make_floatx80(0x3ffb, 0xea4398b45cd47800ULL) },
+    { make_floatx80(0x3ffc, 0xbfffffffffff9980ULL),
+      make_floatx80(0x3fff, 0x91c3d373ab11b919ULL),
+      make_floatx80(0x3ffc, 0x8e1e9b9d588dc8c8ULL) },
+    { make_floatx80(0x3ffc, 0xdffffffffffff631ULL),
+      make_floatx80(0x3fff, 0x94f4efa8fef70864ULL),
+      make_floatx80(0x3ffc, 0xa7a77d47f7b84320ULL) },
+    { make_floatx80(0x3ffc, 0xffffffffffff2499ULL),
+      make_floatx80(0x3fff, 0x9837f0518db892d4ULL),
+      make_floatx80(0x3ffc, 0xc1bf828c6dc496a0ULL) },
+    { make_floatx80(0x3ffd, 0x8fffffffffff80fbULL),
+      make_floatx80(0x3fff, 0x9b8d39b9d54e3a79ULL),
+      make_floatx80(0x3ffc, 0xdc69cdceaa71d3c8ULL) },
+    { make_floatx80(0x3ffd, 0x9fffffffffffbc23ULL),
+      make_floatx80(0x3fff, 0x9ef5326091a10313ULL),
+      make_floatx80(0x3ffc, 0xf7a993048d081898ULL) },
+    { make_floatx80(0x3ffd, 0xafffffffffff20ecULL),
+      make_floatx80(0x3fff, 0xa27043030c49370aULL),
+      make_floatx80(0x3ffd, 0x89c10c0c3124dc28ULL) },
+    { make_floatx80(0x3ffd, 0xc00000000000fd2cULL),
+      make_floatx80(0x3fff, 0xa5fed6a9b15171cfULL),
+      make_floatx80(0x3ffd, 0x97fb5aa6c545c73cULL) },
+    { make_floatx80(0x3ffd, 0xd0000000000093beULL),
+      make_floatx80(0x3fff, 0xa9a15ab4ea7c30e6ULL),
+      make_floatx80(0x3ffd, 0xa6856ad3a9f0c398ULL) },
+    { make_floatx80(0x3ffd, 0xe00000000000c2aeULL),
+      make_floatx80(0x3fff, 0xad583eea42a17876ULL),
+      make_floatx80(0x3ffd, 0xb560fba90a85e1d8ULL) },
+    { make_floatx80(0x3ffd, 0xefffffffffff1e3fULL),
+      make_floatx80(0x3fff, 0xb123f581d2abef6cULL),
+      make_floatx80(0x3ffd, 0xc48fd6074aafbdb0ULL) },
+    { make_floatx80(0x3ffd, 0xffffffffffff1c23ULL),
+      make_floatx80(0x3fff, 0xb504f333f9de2cadULL),
+      make_floatx80(0x3ffd, 0xd413cccfe778b2b4ULL) },
+    { make_floatx80(0x3ffe, 0x8800000000006344ULL),
+      make_floatx80(0x3fff, 0xb8fbaf4762fbd0a1ULL),
+      make_floatx80(0x3ffd, 0xe3eebd1d8bef4284ULL) },
+    { make_floatx80(0x3ffe, 0x9000000000005d67ULL),
+      make_floatx80(0x3fff, 0xbd08a39f580c668dULL),
+      make_floatx80(0x3ffd, 0xf4228e7d60319a34ULL) },
+    { make_floatx80(0x3ffe, 0x9800000000009127ULL),
+      make_floatx80(0x3fff, 0xc12c4cca6670e042ULL),
+      make_floatx80(0x3ffe, 0x82589994cce1c084ULL) },
+    { make_floatx80(0x3ffe, 0x9fffffffffff06f9ULL),
+      make_floatx80(0x3fff, 0xc5672a11550655c3ULL),
+      make_floatx80(0x3ffe, 0x8ace5422aa0cab86ULL) },
+    { make_floatx80(0x3ffe, 0xa7fffffffffff80dULL),
+      make_floatx80(0x3fff, 0xc9b9bd866e2f234bULL),
+      make_floatx80(0x3ffe, 0x93737b0cdc5e4696ULL) },
+    { make_floatx80(0x3ffe, 0xafffffffffff1470ULL),
+      make_floatx80(0x3fff, 0xce248c151f83fd69ULL),
+      make_floatx80(0x3ffe, 0x9c49182a3f07fad2ULL) },
+    { make_floatx80(0x3ffe, 0xb800000000000e0aULL),
+      make_floatx80(0x3fff, 0xd2a81d91f12aec5cULL),
+      make_floatx80(0x3ffe, 0xa5503b23e255d8b8ULL) },
+    { make_floatx80(0x3ffe, 0xc00000000000b7faULL),
+      make_floatx80(0x3fff, 0xd744fccad69dd630ULL),
+      make_floatx80(0x3ffe, 0xae89f995ad3bac60ULL) },
+    { make_floatx80(0x3ffe, 0xc800000000003aa6ULL),
+      make_floatx80(0x3fff, 0xdbfbb797daf25a44ULL),
+      make_floatx80(0x3ffe, 0xb7f76f2fb5e4b488ULL) },
+    { make_floatx80(0x3ffe, 0xd00000000000a6aeULL),
+      make_floatx80(0x3fff, 0xe0ccdeec2a954685ULL),
+      make_floatx80(0x3ffe, 0xc199bdd8552a8d0aULL) },
+    { make_floatx80(0x3ffe, 0xd800000000004165ULL),
+      make_floatx80(0x3fff, 0xe5b906e77c837155ULL),
+      make_floatx80(0x3ffe, 0xcb720dcef906e2aaULL) },
+    { make_floatx80(0x3ffe, 0xe00000000000582cULL),
+      make_floatx80(0x3fff, 0xeac0c6e7dd24713aULL),
+      make_floatx80(0x3ffe, 0xd5818dcfba48e274ULL) },
+    { make_floatx80(0x3ffe, 0xe800000000001a5dULL),
+      make_floatx80(0x3fff, 0xefe4b99bdcdb06ebULL),
+      make_floatx80(0x3ffe, 0xdfc97337b9b60dd6ULL) },
+    { make_floatx80(0x3ffe, 0xefffffffffffc1efULL),
+      make_floatx80(0x3fff, 0xf5257d152486a2faULL),
+      make_floatx80(0x3ffe, 0xea4afa2a490d45f4ULL) },
+    { make_floatx80(0x3ffe, 0xf800000000001069ULL),
+      make_floatx80(0x3fff, 0xfa83b2db722a0e5cULL),
+      make_floatx80(0x3ffe, 0xf50765b6e4541cb8ULL) },
+    { make_floatx80(0x3fff, 0x8000000000000000ULL),
+      make_floatx80(0x4000, 0x8000000000000000ULL),
+      make_floatx80(0x3fff, 0x8000000000000000ULL) },
+};
+
 void helper_f2xm1(CPUX86State *env)
 {
-    double val = floatx80_to_double(env, ST0);
+    uint8_t old_flags = save_exception_flags(env);
+    uint64_t sig = extractFloatx80Frac(ST0);
+    int32_t exp = extractFloatx80Exp(ST0);
+    bool sign = extractFloatx80Sign(ST0);
+
+    if (floatx80_invalid_encoding(ST0)) {
+        float_raise(float_flag_invalid, &env->fp_status);
+        ST0 = floatx80_default_nan(&env->fp_status);
+    } else if (floatx80_is_any_nan(ST0)) {
+        if (floatx80_is_signaling_nan(ST0, &env->fp_status)) {
+            float_raise(float_flag_invalid, &env->fp_status);
+            ST0 = floatx80_silence_nan(ST0, &env->fp_status);
+        }
+    } else if (exp > 0x3fff ||
+               (exp == 0x3fff && sig != (0x8000000000000000ULL))) {
+        /* Out of range for the instruction, treat as invalid.  */
+        float_raise(float_flag_invalid, &env->fp_status);
+        ST0 = floatx80_default_nan(&env->fp_status);
+    } else if (exp == 0x3fff) {
+        /* Argument 1 or -1, exact result 1 or -0.5.  */
+        if (sign) {
+            ST0 = make_floatx80(0xbffe, 0x8000000000000000ULL);
+        }
+    } else if (exp < 0x3fb0) {
+        if (!floatx80_is_zero(ST0)) {
+            /*
+             * Multiplying the argument by an extra-precision version
+             * of log(2) is sufficiently precise.  Zero arguments are
+             * returned unchanged.
+             */
+            uint64_t sig0, sig1, sig2;
+            if (exp == 0) {
+                normalizeFloatx80Subnormal(sig, &exp, &sig);
+            }
+            mul128By64To192(ln2_sig_high, ln2_sig_low, sig, &sig0, &sig1,
+                            &sig2);
+            /* This result is inexact.  */
+            sig1 |= 1;
+            ST0 = normalizeRoundAndPackFloatx80(80, sign, exp, sig0, sig1,
+                                                &env->fp_status);
+        }
+    } else {
+        floatx80 tmp, y, accum;
+        bool asign, bsign;
+        int32_t n, aexp, bexp;
+        uint64_t asig0, asig1, asig2, bsig0, bsig1;
+        FloatRoundMode save_mode = env->fp_status.float_rounding_mode;
+        signed char save_prec = env->fp_status.floatx80_rounding_precision;
+        env->fp_status.float_rounding_mode = float_round_nearest_even;
+        env->fp_status.floatx80_rounding_precision = 80;
+
+        /* Find the nearest multiple of 1/32 to the argument.  */
+        tmp = floatx80_scalbn(ST0, 5, &env->fp_status);
+        n = 32 + floatx80_to_int32(tmp, &env->fp_status);
+        y = floatx80_sub(ST0, f2xm1_table[n].t, &env->fp_status);
+
+        if (floatx80_is_zero(y)) {
+            /*
+             * Use the value of 2^t - 1 from the table, to avoid
+             * needing to special-case zero as a result of
+             * multiplication below.
+             */
+            ST0 = f2xm1_table[n].t;
+            set_float_exception_flags(float_flag_inexact, &env->fp_status);
+            env->fp_status.float_rounding_mode = save_mode;
+        } else {
+            /*
+             * Compute the lower parts of a polynomial expansion for
+             * (2^y - 1) / y.
+             */
+            accum = floatx80_mul(f2xm1_coeff_7, y, &env->fp_status);
+            accum = floatx80_add(f2xm1_coeff_6, accum, &env->fp_status);
+            accum = floatx80_mul(accum, y, &env->fp_status);
+            accum = floatx80_add(f2xm1_coeff_5, accum, &env->fp_status);
+            accum = floatx80_mul(accum, y, &env->fp_status);
+            accum = floatx80_add(f2xm1_coeff_4, accum, &env->fp_status);
+            accum = floatx80_mul(accum, y, &env->fp_status);
+            accum = floatx80_add(f2xm1_coeff_3, accum, &env->fp_status);
+            accum = floatx80_mul(accum, y, &env->fp_status);
+            accum = floatx80_add(f2xm1_coeff_2, accum, &env->fp_status);
+            accum = floatx80_mul(accum, y, &env->fp_status);
+            accum = floatx80_add(f2xm1_coeff_1, accum, &env->fp_status);
+            accum = floatx80_mul(accum, y, &env->fp_status);
+            accum = floatx80_add(f2xm1_coeff_0_low, accum, &env->fp_status);
+
+            /*
+             * The full polynomial expansion is f2xm1_coeff_0 + accum
+             * (where accum has much lower magnitude, and so, in
+             * particular, carry out of the addition is not possible).
+             * (This expansion is only accurate to about 70 bits, not
+             * 128 bits.)
+             */
+            aexp = extractFloatx80Exp(f2xm1_coeff_0);
+            asign = extractFloatx80Sign(f2xm1_coeff_0);
+            shift128RightJamming(extractFloatx80Frac(accum), 0,
+                                 aexp - extractFloatx80Exp(accum),
+                                 &asig0, &asig1);
+            bsig0 = extractFloatx80Frac(f2xm1_coeff_0);
+            bsig1 = 0;
+            if (asign == extractFloatx80Sign(accum)) {
+                add128(bsig0, bsig1, asig0, asig1, &asig0, &asig1);
+            } else {
+                sub128(bsig0, bsig1, asig0, asig1, &asig0, &asig1);
+            }
+            /* And thus compute an approximation to 2^y - 1.  */
+            mul128By64To192(asig0, asig1, extractFloatx80Frac(y),
+                            &asig0, &asig1, &asig2);
+            aexp += extractFloatx80Exp(y) - 0x3ffe;
+            asign ^= extractFloatx80Sign(y);
+            if (n != 32) {
+                /*
+                 * Multiply this by the precomputed value of 2^t and
+                 * add that of 2^t - 1.
+                 */
+                mul128By64To192(asig0, asig1,
+                                extractFloatx80Frac(f2xm1_table[n].exp2),
+                                &asig0, &asig1, &asig2);
+                aexp += extractFloatx80Exp(f2xm1_table[n].exp2) - 0x3ffe;
+                bexp = extractFloatx80Exp(f2xm1_table[n].exp2m1);
+                bsig0 = extractFloatx80Frac(f2xm1_table[n].exp2m1);
+                bsig1 = 0;
+                if (bexp < aexp) {
+                    shift128RightJamming(bsig0, bsig1, aexp - bexp,
+                                         &bsig0, &bsig1);
+                } else if (aexp < bexp) {
+                    shift128RightJamming(asig0, asig1, bexp - aexp,
+                                         &asig0, &asig1);
+                    aexp = bexp;
+                }
+                /* The sign of 2^t - 1 is always that of the result.  */
+                bsign = extractFloatx80Sign(f2xm1_table[n].exp2m1);
+                if (asign == bsign) {
+                    /* Avoid possible carry out of the addition.  */
+                    shift128RightJamming(asig0, asig1, 1,
+                                         &asig0, &asig1);
+                    shift128RightJamming(bsig0, bsig1, 1,
+                                         &bsig0, &bsig1);
+                    ++aexp;
+                    add128(asig0, asig1, bsig0, bsig1, &asig0, &asig1);
+                } else {
+                    sub128(bsig0, bsig1, asig0, asig1, &asig0, &asig1);
+                    asign = bsign;
+                }
+            }
+            env->fp_status.float_rounding_mode = save_mode;
+            /* This result is inexact.  */
+            asig1 |= 1;
+            ST0 = normalizeRoundAndPackFloatx80(80, asign, aexp, asig0, asig1,
+                                                &env->fp_status);
+        }
 
-    val = pow(2.0, val) - 1.0;
-    ST0 = double_to_floatx80(env, val);
+        env->fp_status.floatx80_rounding_precision = save_prec;
+    }
+    merge_exception_flags(env, old_flags);
 }
 
 void helper_fyl2x(CPUX86State *env)
diff --git a/tests/tcg/i386/test-i386-f2xm1.c b/tests/tcg/i386/test-i386-f2xm1.c
new file mode 100644
index 0000000000..4513ed8cc1
--- /dev/null
+++ b/tests/tcg/i386/test-i386-f2xm1.c
@@ -0,0 +1,1140 @@ 
+/* Test f2xm1 instruction.  */
+
+#include <stdio.h>
+
+struct test {
+    long double arg, down, up;
+};
+
+const struct test tests[] = {
+    { -1.0L, -0.5L, -0.5L },
+    { -0.0L, -0.0L, -0.0L },
+    { 0.0L, 0.0L, 0.0L },
+    /* Randomly generated tests.  */
+    { 0x4.1481697ac693aa6p-4L, 0x3.17ec9f8454896518p-4L, 0x3.17ec9f845489651cp-4L },
+    { -0xd.84a873b14b9c0e2p-4L, -0x7.1788c46ac260d948p-4L, -0x7.1788c46ac260d94p-4L },
+    { 0xa.a3dc18b1eff7e8ap-188L, 0x7.6009241b9e21523p-188L, 0x7.6009241b9e215238p-188L },
+    { -0xe.846aeb6f58174d5p-92L, -0xa.1006405817acc33p-92L, -0xa.1006405817acc32p-92L },
+    { 0x5.4459f2ac77bb0978p-4L, 0x4.19d3ce7fd5b90ac8p-4L, 0x4.19d3ce7fd5b90adp-4L },
+    { -0xb.79bece734a62216p-4L, -0x6.4489a7fc150c0fp-4L, -0x6.4489a7fc150c0ef8p-4L },
+    { 0xa.ab48f9ef732f5c4p-4L, 0x9.66acd7d4b7cf015p-4L, 0x9.66acd7d4b7cf016p-4L },
+    { -0xb.8204e63359a46e6p-4L, -0x6.48060f0a504e3488p-4L, -0x6.48060f0a504e348p-4L },
+    { 0xd.c732865701ae935p-4L, 0xd.103bc1a15cd9f71p-4L, 0xd.103bc1a15cd9f72p-4L },
+    { -0x1.6296e8ff499827a2p-4L, -0xe.e8dc973f0bce9d1p-8L, -0xe.e8dc973f0bce9dp-8L },
+    { 0x8.3e49377820195c8p-4L, 0x6.ddff7e8caa601a08p-4L, 0x6.ddff7e8caa601a1p-4L },
+    { -0x7.ece8699d62a9f76p-4L, -0x4.a6516088a15ab01p-4L, -0x4.a6516088a15ab008p-4L },
+    { 0x4.b875c0342c9f86b8p-4L, 0x3.a1709cfaecf11ce8p-4L, 0x3.a1709cfaecf11cecp-4L },
+    { -0xe.a37e0fa859e499cp-4L, -0x7.83956f7028853738p-4L, -0x7.83956f702885373p-4L },
+    { 0x7.23210d9474f0715p-4L, 0x5.cc1ac556913b5258p-4L, 0x5.cc1ac556913b526p-4L },
+    { -0xb.755e74862e61e2bp-4L, -0x6.42b11ec6fd4c00dp-4L, -0x6.42b11ec6fd4c00c8p-4L },
+    { 0x3.48cc248e266ab90cp-4L, 0x2.724bd1b7f02d354cp-4L, 0x2.724bd1b7f02d355p-4L },
+    { -0xa.9a331b76f8ece94p-4L, -0x5.e47b32e80b1f837p-4L, -0x5.e47b32e80b1f8368p-4L },
+    { 0x5.8312ebb25c93d22p-4L, 0x4.50bcc3442a6e832p-4L, 0x4.50bcc3442a6e8328p-4L },
+    { -0xa.d41581f0036d233p-4L, -0x5.fdb41cec4e2c108p-4L, -0x5.fdb41cec4e2c1078p-4L },
+    { 0x4.84a87d8107c5f408p-4L, 0x3.759419ac694e8798p-4L, 0x3.759419ac694e879cp-4L },
+    { -0x1.1a592590e007fap-4L, -0xb.f1b5fdf338edbc1p-8L, -0xb.f1b5fdf338edbcp-8L },
+    { 0x2.72f96b27827d2054p-4L, 0x1.ca7a491c0c9ae094p-4L, 0x1.ca7a491c0c9ae096p-4L },
+    { -0x8.34634eae18e60c5p-4L, -0x4.c941052638a95e6p-4L, -0x4.c941052638a95e58p-4L },
+    { 0x2.f6cff94cffe53048p-180L, 0x2.0df7fb06812da41p-180L, 0x2.0df7fb06812da414p-180L },
+    { -0x3.e0779bd58963da5p-120L, -0x2.afed04ed88e2c16cp-120L, -0x2.afed04ed88e2c168p-120L },
+    { 0xc.1c72a98f7733051p-4L, 0xb.09ddaf3c3330ff9p-4L, 0xb.09ddaf3c3330ffap-4L },
+    { -0x9.6eacf3012c77e7p-4L, -0x5.5df25bc91430e81p-4L, -0x5.5df25bc91430e808p-4L },
+    { 0x4.962ce97c4afbc1f8p-4L, 0x3.845e1e9659d35364p-4L, 0x3.845e1e9659d35368p-4L },
+    { -0xa.a7735b993f17f55p-4L, -0x5.ea46e99ae5f6dce8p-4L, -0x5.ea46e99ae5f6dcep-4L },
+    { 0x5.155f76560f08fccp-4L, 0x3.f1149b22956dff34p-4L, 0x3.f1149b22956dff38p-4L },
+    { -0xd.32a453289bd47b3p-4L, -0x6.f7a99ad68a5d961p-4L, -0x6.f7a99ad68a5d9608p-4L },
+    { 0xa.9942e7418052b4bp-4L, 0x9.52df2bbafc3218bp-4L, 0x9.52df2bbafc3218cp-4L },
+    { -0x5.4f4efad2aff4f76p-4L, -0x3.49afb77e7a12385p-4L, -0x3.49afb77e7a12384cp-4L },
+    { 0x3.c9e289d962998608p-4L, 0x2.da96d228ab6c8fd8p-4L, 0x2.da96d228ab6c8fdcp-4L },
+    { -0x7.cc295689678770bp-4L, -0x4.962bd983de0367b8p-4L, -0x4.962bd983de0367bp-4L },
+    { 0xa.8fc7c1f2a46626cp-4L, 0x9.487a90c858224c9p-4L, 0x9.487a90c858224cap-4L },
+    { -0x8.a1d9201d5f09ad6p-4L, -0x4.fdf0ccee86f8d98p-4L, -0x4.fdf0ccee86f8d978p-4L },
+    { 0x7.5b8ee6778ad1d64p-4L, 0x6.01a5419abf1cb4f8p-4L, 0x6.01a5419abf1cb5p-4L },
+    { -0x9.d20d0f7fc98548p-4L, -0x5.8b571e52bd288448p-4L, -0x5.8b571e52bd28844p-4L },
+    { 0x5.f135e81ee2608d4p-4L, 0x4.b293c42ca99fd6e8p-4L, 0x4.b293c42ca99fd6fp-4L },
+    { -0x5.d981a42b6b7a36fp-4L, -0x3.94e920725edbe7d4p-4L, -0x3.94e920725edbe7dp-4L },
+    { 0xa.edffe301db8be0bp-4L, 0x9.b08144d0a85602p-4L, 0x9.b08144d0a856021p-4L },
+    { -0x4.5a026d37f55f1d18p-4L, -0x2.bfc10df32554a28cp-4L, -0x2.bfc10df32554a288p-4L },
+    { 0x7.82c193b48128193p-4L, 0x6.2723ac59ee5faf68p-4L, 0x6.2723ac59ee5faf7p-4L },
+    { -0xd.2d0fe1cd05a87f4p-4L, -0x6.f57a61e00a5f24bp-4L, -0x6.f57a61e00a5f24a8p-4L },
+    { 0x5.e1494f95151c64fp-196L, 0x4.13628f9a498f05d8p-196L, 0x4.13628f9a498f05ep-196L },
+    { -0x4.51babb72810e518p-140L, -0x2.fe6ee847d0741a5cp-140L, -0x2.fe6ee847d0741a58p-140L },
+    { 0xb.638d8454a685474p-4L, 0xa.34a429815e10dc1p-4L, 0xa.34a429815e10dc2p-4L },
+    { -0xb.9ec4e9f266dce49p-4L, -0x6.54194f84395ed2b8p-4L, -0x6.54194f84395ed2bp-4L },
+    { 0xe.4b7a4c83290855cp-4L, 0xd.b8a9a282646fa0cp-4L, 0xd.b8a9a282646fa0dp-4L },
+    { -0xf.13ec97b6c4f17a7p-4L, -0x7.ac86ac65cc0a8878p-4L, -0x7.ac86ac65cc0a887p-4L },
+    { 0x3.8ded178a72c15bcp-4L, 0x2.a9dd11713298de98p-4L, 0x2.a9dd11713298de9cp-4L },
+    { -0xd.36a9965916287d1p-4L, -0x6.f93c3981d5369078p-4L, -0x6.f93c3981d536907p-4L },
+    { 0x6.b3a10f94dcd70e1p-4L, 0x5.63cd831188f697c8p-4L, 0x5.63cd831188f697dp-4L },
+    { -0xc.8517674f15bbcbfp-4L, -0x6.b2be7a8ee34bfc8p-4L, -0x6.b2be7a8ee34bfc78p-4L },
+    { 0xb.204e5335e697f73p-4L, 0x9.e8bb034ff53dc6p-4L, 0x9.e8bb034ff53dc61p-4L },
+    { -0x8.913a951884085ddp-4L, -0x4.f60101f7884f4f6p-4L, -0x4.f60101f7884f4f58p-4L },
+    { 0x4.5861903e9a2c5178p-4L, 0x3.50645bac48af734cp-4L, 0x3.50645bac48af735p-4L },
+    { -0x5.24585590086993p-4L, -0x3.31f08d8ca7e0c6e4p-4L, -0x3.31f08d8ca7e0c6ep-4L },
+    { 0xf.2ba8f23d35f13f9p-4L, 0xe.dedc34179a9e3acp-4L, 0xe.dedc34179a9e3adp-4L },
+    { -0xa.3ecdb386b33fbe5p-4L, -0x5.bc2672b634fa598p-4L, -0x5.bc2672b634fa5978p-4L },
+    { 0x9.9b8e544f05c6de4p-8L, 0x6.bf33cd9ab91f6d28p-8L, 0x6.bf33cd9ab91f6d3p-8L },
+    { -0x7.abd5585035c4696p-4L, -0x4.862497557f052a6p-4L, -0x4.862497557f052a58p-4L },
+    { 0xa.e654e5ca1c1d1fbp-4L, 0x9.a7fa0d5fa5d62cbp-4L, 0x9.a7fa0d5fa5d62ccp-4L },
+    { -0x7.8b963b5c9698ae88p-8L, -0x5.2d4a519ba339886p-8L, -0x5.2d4a519ba3398858p-8L },
+    { 0xb.ea47beace8589dep-4L, 0xa.cf59bd897bb1319p-4L, 0xa.cf59bd897bb131ap-4L },
+    { -0x3.8f66d5a2d60e1fc8p-4L, -0x2.496dee34a71055ap-4L, -0x2.496dee34a710559cp-4L },
+    { 0x3.1a53eaa26d0157p-188L, 0x2.269608f745c0b83p-188L, 0x2.269608f745c0b834p-188L },
+    { -0x8.6659e1a891ccbd3p-96L, -0x5.d282825fc03c7ca8p-96L, -0x5.d282825fc03c7cap-96L },
+    { 0x9.4ae3410622cd598p-4L, 0x7.ee3a22f81622643p-4L, 0x7.ee3a22f816226438p-4L },
+    { -0x9.b8fe7ab721fb04cp-4L, -0x5.7ff768a6654000e8p-4L, -0x5.7ff768a6654000ep-4L },
+    { 0x4.ee554b54200eeb18p-4L, 0x3.cf77028b579146a8p-4L, 0x3.cf77028b579146acp-4L },
+    { -0x1.e1d0727b5f12c23cp-8L, -0x1.4d1e625247cef1dap-8L, -0x1.4d1e625247cef1d8p-8L },
+    { 0x8.f3637cea7b9b0b8p-4L, 0x7.942f15c8b77d89c8p-4L, 0x7.942f15c8b77d89dp-4L },
+    { -0x2.f3202c602060bd7cp-4L, -0x1.eb59cec0fd5e5b22p-4L, -0x1.eb59cec0fd5e5b2p-4L },
+    { 0xc.cdb9d9e3a3a5b61p-4L, 0xb.dcaaf5c009c0684p-4L, 0xb.dcaaf5c009c0685p-4L },
+    { -0x5.7ddc79efb147e828p-4L, -0x3.63390bf8b99265d4p-4L, -0x3.63390bf8b99265dp-4L },
+    { 0x6.7236b6f8976437ap-4L, 0x5.27852c069a4fd5ep-4L, 0x5.27852c069a4fd5e8p-4L },
+    { -0x5.e1ad137b44bc3ad8p-4L, -0x3.994d814216774764p-4L, -0x3.994d81421677476p-4L },
+    { 0xb.f5ec1a26fcc9d7ep-4L, 0xa.dce2b2a69a74106p-4L, 0xa.dce2b2a69a74107p-4L },
+    { -0xd.dcb826624975b1ep-4L, -0x7.394429db03b0d5e8p-4L, -0x7.394429db03b0d5ep-4L },
+    { 0x1.a983e64980e6104p-4L, 0x1.31d2cb35db04030ep-4L, 0x1.31d2cb35db04031p-4L },
+    { -0xa.14ebef82079ff92p-4L, -0x5.a9758de717320278p-4L, -0x5.a9758de71732027p-4L },
+    { 0x1.e4fcc97f32b404d8p-4L, 0x1.5e5913e4b0dadd5ep-4L, 0x1.5e5913e4b0dadd6p-4L },
+    { -0xe.9391126d81ddf25p-4L, -0x7.7db899379b97afep-4L, -0x7.7db899379b97afd8p-4L },
+    { 0xb.83be497f42b1776p-8L, 0x8.1b67845064d833ap-8L, 0x8.1b67845064d833bp-8L },
+    { -0xb.6c13349b9671c7bp-4L, -0x6.3ec4737bebffb8f8p-4L, -0x6.3ec4737bebffb8fp-4L },
+    { 0xd.00d476fab7a907dp-4L, 0xc.1a9e868d759da06p-4L, 0xc.1a9e868d759da07p-4L },
+    { -0x3.bf394566ed3e5a44p-4L, -0x2.65b989f46e7a2458p-4L, -0x2.65b989f46e7a2454p-4L },
+    { 0x7.4a72aacaec9cd52p-52L, 0x5.0db91de577a1e5c8p-52L, 0x5.0db91de577a1e5dp-52L },
+    { -0x4.3354d8429f36037p-24L, -0x2.e95ce5bede67faap-24L, -0x2.e95ce5bede67fa9cp-24L },
+    { 0x5.431e650334b97d18p-4L, 0x4.18c10ccaa716c258p-4L, 0x4.18c10ccaa716c26p-4L },
+    { -0xf.1eb2c535e06fba3p-4L, -0x7.b068a3edafc6822p-4L, -0x7.b068a3edafc68218p-4L },
+    { 0x8.54a857fb1034b62p-4L, 0x6.f433cc318f296fep-4L, 0x6.f433cc318f296fe8p-4L },
+    { -0xa.d3c15d582c446d9p-4L, -0x5.fd8fa08a9be23ac8p-4L, -0x5.fd8fa08a9be23acp-4L },
+    { 0xc.cb73edcbfcb307fp-4L, 0xb.d9ecb2c64e8df6bp-4L, 0xb.d9ecb2c64e8df6cp-4L },
+    { -0x3.fb61f1b2cf35f60cp-4L, -0x2.88fef3c7864d396cp-4L, -0x2.88fef3c7864d3968p-4L },
+    { 0x9.d7eb5c50bc8c632p-4L, 0x8.8231f68c5c65f6cp-4L, 0x8.8231f68c5c65f6dp-4L },
+    { -0x4.d312891f5f4e786p-4L, -0x3.048b329391356fc8p-4L, -0x3.048b329391356fc4p-4L },
+    { 0xe.ae0633b99b178edp-4L, 0xe.389ce9e10301401p-4L, 0xe.389ce9e10301402p-4L },
+    { -0x1.39568b7ef55672cp-4L, -0xd.38818f18029f0edp-8L, -0xd.38818f18029f0ecp-8L },
+    { 0x4.cf293b1353f539bp-4L, 0x3.b4c86315977b5c7cp-4L, 0x3.b4c86315977b5c8p-4L },
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+    { 0xf.05da5fd59fc565bp-4L, 0xe.ac75be21fa0a721p-4L, 0xe.ac75be21fa0a722p-4L },
+    { -0xd.dd9a1c0c442c4c6p-4L, -0x7.399a1163598e674p-4L, -0x7.399a1163598e6738p-4L },
+    { 0x4.61b51c01df55d6d8p-4L, 0x3.5833a282f0757d38p-4L, 0x3.5833a282f0757d3cp-4L },
+    { -0xb.dce6fd9bad9f495p-4L, -0x6.6dfecf316daaa2b8p-4L, -0x6.6dfecf316daaa2bp-4L },
+    { 0xa.b6f22a1b9f2939fp-4L, 0x9.73850a513137669p-4L, 0x9.73850a51313766ap-4L },
+    { -0x3.4bb35afb05788e3p-4L, -0x2.20fa7ab319293c2cp-4L, -0x2.20fa7ab319293c28p-4L },
+    { 0xd.0db3afda3c5f8cp-4L, 0xc.2a4edf1f8e608e3p-4L, 0xc.2a4edf1f8e608e4p-4L },
+    { -0x2.1ce57b45214ebd74p-4L, -0x1.6646119faf2579e4p-4L, -0x1.6646119faf2579e2p-4L },
+    { 0x5.067f9f48fc5b234p-8L, 0x3.81d3c5994dfa29ep-8L, 0x3.81d3c5994dfa29e4p-8L },
+    { -0xb.a04244a598be88fp-4L, -0x6.54b9128406b6e57p-4L, -0x6.54b9128406b6e568p-4L },
+    { 0xf.d97f1711de15f9cp-4L, 0xf.cacbd7b24bfa344p-4L, 0xf.cacbd7b24bfa345p-4L },
+    { -0xf.493b2b477feaaf9p-4L, -0x7.bfaad9fbab559b1p-4L, -0x7.bfaad9fbab559b08p-4L },
+    { 0xc.deaf7691740cdefp-8L, 0x9.13f529a0032aecap-8L, 0x9.13f529a0032aecbp-8L },
+    { -0xa.59b5d478c821a2ep-4L, -0x5.c816a0d158b46128p-4L, -0x5.c816a0d158b4612p-4L },
+    { 0xd.1b186c2e3417901p-4L, 0xc.3aab3f3a165b5b1p-4L, 0xc.3aab3f3a165b5b2p-4L },
+    { -0xf.14939428966efa8p-4L, -0x7.acc2e6e3a1c40bfp-4L, -0x7.acc2e6e3a1c40be8p-4L },
+    { 0xa.548931dd5b08516p-4L, 0x9.07e9820c45dc918p-4L, 0x9.07e9820c45dc919p-4L },
+    { -0x1.86c3057b9088fe1cp-4L, -0x1.06181e6e8d7c4ee6p-4L, -0x1.06181e6e8d7c4ee4p-4L },
+    { 0x8.de5082bfa47b272p-8L, 0x6.38b52f74fd4fac9p-8L, 0x6.38b52f74fd4fac98p-8L },
+    { -0x6.381df51cf6ba1e58p-4L, -0x3.c7677b23d838f2c4p-4L, -0x3.c7677b23d838f2cp-4L },
+    { 0x2.f43f9bb64395d398p-28L, 0x2.0c3105ebb2d3ec1p-28L, 0x2.0c3105ebb2d3ec14p-28L },
+    { -0x1.7d1826b58589517p-188L, -0x1.08278b32d446a3dap-188L, -0x1.08278b32d446a3d8p-188L },
+    { 0x3.24bd5453a5d96c38p-4L, 0x2.5591a327002dbbfp-4L, 0x2.5591a327002dbbf4p-4L },
+    { -0xd.ac66274a591f9a9p-4L, -0x7.26d1c15c81b1be3p-4L, -0x7.26d1c15c81b1be28p-4L },
+    { 0x7.4bbb894be77050dp-4L, 0x5.f29408389bbe66ep-4L, 0x5.f29408389bbe66e8p-4L },
+    { -0xa.eacc82e14c1610fp-4L, -0x6.0788b0f7dc794f7p-4L, -0x6.0788b0f7dc794f68p-4L },
+    { 0x2.a982ac56625aefc4p-4L, 0x1.f4b47ebd7795a254p-4L, 0x1.f4b47ebd7795a256p-4L },
+    { -0x8.056940c538fa279p-4L, -0x4.b257711af2be1e78p-4L, -0x4.b257711af2be1e7p-4L },
+    { 0x1.66b64b9c9f79a1dep-4L, 0x1.00578a1c0c673a1p-4L, 0x1.00578a1c0c673a12p-4L },
+    { -0x3.26b75fa52c7ce30cp-4L, -0x2.0aaf1c1238c99944p-4L, -0x2.0aaf1c1238c9994p-4L },
+    { 0x9.da5604fb75e8d87p-4L, 0x8.84c2f5daaacf75ep-4L, 0x8.84c2f5daaacf75fp-4L },
+    { -0x8.f39b1339c38973dp-4L, -0x5.24a94b90f03e7ed8p-4L, -0x5.24a94b90f03e7edp-4L },
+    { 0x7.677b36d2e1d48358p-4L, 0x6.0d06229c56a97f4p-4L, 0x6.0d06229c56a97f48p-4L },
+    { -0xa.996804efaa5460cp-4L, -0x5.e4224415b8782278p-4L, -0x5.e4224415b878227p-4L },
+    { 0x6.b6c06e4a29c88afp-4L, 0x5.66b27094b245b1ep-4L, 0x5.66b27094b245b1e8p-4L },
+    { -0x5.a5149fe9b18171c8p-4L, -0x3.7894bad1006fb798p-4L, -0x3.7894bad1006fb794p-4L },
+    { 0x5.375a31264862647p-4L, 0x4.0e852a933247c008p-4L, 0x4.0e852a933247c01p-4L },
+    { -0xc.55651fd1cbee3d4p-4L, -0x6.9f72345b02eab28p-4L, -0x6.9f72345b02eab278p-4L },
+    { 0xe.006deb92f93d672p-4L, 0xd.58a49a5d8de28c4p-4L, 0xd.58a49a5d8de28c5p-4L },
+    { -0xa.6871090121d471bp-4L, -0x5.ce99fb28aafa5bb8p-4L, -0x5.ce99fb28aafa5bbp-4L },
+    { 0xc.8ed445e1ea26da6p-4L, 0xb.9126f62f86bcb47p-4L, 0xb.9126f62f86bcb48p-4L },
+    { -0x3.70640030d409ab74p-4L, -0x2.36f53ff3b132cba8p-4L, -0x2.36f53ff3b132cba4p-4L },
+    { 0x2.219473696b04364cp-96L, 0x1.7a2acafbc3adc14ep-96L, 0x1.7a2acafbc3adc15p-96L },
+    { -0xd.bdc3902e400dcddp-144L, -0x9.865401201b95f7ap-144L, -0x9.865401201b95f79p-144L },
+    { 0xb.b53f28201a854efp-4L, 0xa.9207b77bb750cf7p-4L, 0xa.9207b77bb750cf8p-4L },
+    { -0x4.28b1a78cc7055bd8p-4L, -0x2.a3536d42907d291p-4L, -0x2.a3536d42907d290cp-4L },
+    { 0xd.e2cee7a54e7c7dfp-4L, 0xd.331435f3041bf4fp-4L, 0xd.331435f3041bf5p-4L },
+    { -0x9.3f6896a8070ab3ep-4L, -0x5.4816171c316ed77p-4L, -0x5.4816171c316ed768p-4L },
+    { 0x1.a1524a334652c37cp-4L, 0x1.2bb95dd5b9658e26p-4L, 0x1.2bb95dd5b9658e28p-4L },
+    { -0x1.9b7f6344a4875e14p-4L, -0x1.13861edcadba3e08p-4L, -0x1.13861edcadba3e06p-4L },
+    { 0xb.4660bc20f1141f9p-4L, 0xa.1399f4f27c33975p-4L, 0xa.1399f4f27c33976p-4L },
+    { -0xd.9888197bcafba2ap-4L, -0x7.1f30db722ee63d78p-4L, -0x7.1f30db722ee63d7p-4L },
+    { 0xf.3adad3101e81209p-4L, 0xe.f33515340a557e4p-4L, 0xe.f33515340a557e5p-4L },
+    { -0xa.79ea74b25ad8a16p-4L, -0x5.d64e6bad7c9fffc8p-4L, -0x5.d64e6bad7c9fffcp-4L },
+    { 0xd.4d87683a39ac568p-4L, 0xc.789c1f6e5dcac31p-4L, 0xc.789c1f6e5dcac32p-4L },
+    { -0xd.0f2848388d6bd4fp-4L, -0x6.e9bc44c0f7734168p-4L, -0x6.e9bc44c0f773416p-4L },
+    { 0x5.d9fb99a27648b5d8p-4L, 0x4.9dca7407214af058p-4L, 0x4.9dca7407214af06p-4L },
+    { -0x1.705dc2d9924977d6p-4L, -0xf.7895af9cd8410b4p-8L, -0xf.7895af9cd8410b3p-8L },
+    { 0xe.de1ad3b0df8a929p-4L, 0xe.77d17cd52544381p-4L, 0xe.77d17cd52544382p-4L },
+    { -0xe.4bc9f399afa1199p-4L, -0x7.6319db0e3314bc98p-4L, -0x7.6319db0e3314bc9p-4L },
+    { 0x9.4bc88b56990e957p-4L, 0x7.ef27dce522664078p-4L, 0x7.ef27dce52266408p-4L },
+    { -0xe.2a8337406c02664p-4L, -0x7.56a65648e9cbee38p-4L, -0x7.56a65648e9cbee3p-4L },
+};
+
+int check_equal(long double res, long double expected)
+{
+    if (res != expected) {
+        return 0;
+    }
+    return (__builtin_copysignl(1.0L, res) ==
+            __builtin_copysignl(1.0L, expected));
+}
+
+int main(void)
+{
+    int ret = 0;
+    int i;
+    for (i = 0; i < sizeof(tests) / sizeof(tests[0]); i++) {
+        long double ld_res;
+        __asm__ volatile ("f2xm1" : "=t" (ld_res) : "0" (tests[i].arg));
+        if (!check_equal(ld_res, tests[i].down) &&
+            !check_equal(ld_res, tests[i].up)) {
+            printf("FAIL: f2xm1 %La, expected %La or %La, got %La\n",
+                   tests[i].arg, tests[i].down, tests[i].up, ld_res);
+            ret = 1;
+        }
+    }
+    return ret;
+}