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glibc/math/gen-fromfp-tests-inputs
Joseph Myers 423c2b9d08 Add fromfp functions. 
TS 18661-1 defines fromfp functions (fromfp, fromfpx, ufromfp,
ufromfpx, and float and long double variants) to convert from
floating-point to an integer type with any signedness and any given
width up to that of intmax_t, in any of the five IEEE rounding modes
(the usual four for binary floating point, plus rounding to nearest
with ties rounding away from zero), with control of whether in-range
non-integer values should result in the "inexact" exception being
raised.  This patch implements these functions for glibc.

These implementations are (apart from raising exceptions) pure integer
implementations; it's entirely possible optimized versions could be
devised for some architectures.  A common math/fromfp.h header
provides various common helper code that can readily be shared between
the implementations for different types.  For each type, the bulk of
the implementation is also shared between the four functions, with
wrappers that define UNSIGNED and INEXACT macros appropriately before
including the main implementation.

As the functions return intmax_t and uintmax_t without math.h being
allowed to expose those typedef names, they are declared using
__intmax_t and __uintmax_t as obtained from <bits/types.h>.

The FP_INT_* rounding direction macros are defined as ascending
integers in the order the names are listed in the TS; I see no
significant value in allowing architectures to vary the values of
them.

The libm-test machinery is duly adapted to handle unsigned int
arguments, and intmax_t and uintmax_t results.  Because each test
input is generally tested for four functions, five rounding modes and
several different widths, the libm-test.inc additions are very large.
Thus, the diffs in the body of this message exclude the libm-test.inc
changes, with the full patch being attached gzipped.  The bulk of the
new tests were generated (expanded from a test input plus rounding
results and information about where it lies in the relevant interval
between integers, to libm-test tests for all relevant combinations of
function, rounding direction and width) by a script that's included in
the patch as math/gen-fromfp-tests.py (input data
math/gen-fromfp-tests-inputs); as an ad hoc script that's not really
expected to be rerun, it's not very polished, but it's at least
plausibly useful for adding any further tests for these functions in
future.  I may split the libm-test tests up by function in future (so
both libm-test.inc and auto-libm-test-out are split into separate
files, and the tests for each function are also built and run
separately), but not for 2.25.

For no obvious reason, adding tgmath tests for the new functions
resulted in -Wuninitialized errors from test-tgmath.c about the
variable i being used uninitialized.  Those errors were correct - the
variable is read by the frexp version in test-tgmath.c (where real
frexp would write through that pointer instead of reading it) - but I
don't know why this patch would result in the pre-existing issue being
newly detected.  The patch initializes the variable to avoid those
errors.

With these changes, glibc 2.25 should have all the library features
from TS 18661-1 other than the functions that round result to narrower
type (and constant rounding directions, but I'm considering those
mainly a compiler feature not a library one).

Tested for x86_64, x86, mips64 and powerpc.

	* math/bits/mathcalls.h [__GLIBC_USE (IEC_60559_BFP_EXT)]
	(fromfp): New declaration.
	[__GLIBC_USE (IEC_60559_BFP_EXT)] (fromfpx): Likewise.
	[__GLIBC_USE (IEC_60559_BFP_EXT)] (ufromfp): Likewise.
	[__GLIBC_USE (IEC_60559_BFP_EXT)] (ufromfpx): Likewise.
	* math/tgmath.h (__TGMATH_TERNARY_FIRST_REAL_RET_ONLY): New macro.
	[__GLIBC_USE (IEC_60559_BFP_EXT)] (fromfp): Likewise.
	[__GLIBC_USE (IEC_60559_BFP_EXT)] (ufromfp): Likewise.
	[__GLIBC_USE (IEC_60559_BFP_EXT)] (fromfpx): Likewise.
	[__GLIBC_USE (IEC_60559_BFP_EXT)] (ufromfpx): Likewise.
	* math/math.h: Include <bits/types.h>.
	[__GLIBC_USE (IEC_60559_BFP_EXT)] (FP_INT_UPWARD): New enum
	constant and macro.
	(FP_INT_DOWNWARD): Likewise.
	(FP_INT_TOWARDZERO): Likewise.
	(FP_INT_TONEARESTFROMZERO): Likewise.
	(FP_INT_TONEAREST): Likewise.
	* math/Versions (fromfp): New libm symbol at version GLIBC_2.25.
	(fromfpf): Likewise.
	(fromfpl): Likewise.
	(ufromfp): Likewise.
	(ufromfpf): Likewise.
	(ufromfpl): Likewise.
	(fromfpx): Likewise.
	(fromfpxf): Likewise.
	(fromfpxl): Likewise.
	(ufromfpx): Likewise.
	(ufromfpxf): Likewise.
	(ufromfpxl): Likewise.
	* math/Makefile (libm-calls): Add s_fromfpF, s_ufromfpF,
	s_fromfpxF and s_ufromfpxF.
	* math/gen-fromfp-tests.py: New file.
	* math/gen-fromfp-tests-inputs: Likewise.
	* math/libm-test.inc: Include <stdint.h>
	(check_intmax_t): New function.
	(check_uintmax_t): Likewise.
	(struct test_fiu_M_data): New type.
	(struct test_fiu_U_data): Likewise.
	(RUN_TEST_fiu_M): New macro.
	(RUN_TEST_LOOP_fiu_M): Likewise.
	(RUN_TEST_fiu_U): Likewise.
	(RUN_TEST_LOOP_fiu_U): Likewise.
	(fromfp_test_data): New array.
	(fromfp_test): New function.
	(fromfpx_test_data): New array.
	(fromfpx_test): New function.
	(ufromfp_test_data): New array.
	(ufromfp_test): New function.
	(ufromfpx_test_data): New array.
	(ufromfpx_test): New function.
	(main): Call fromfp_test, fromfpx_test, ufromfp_test and
	ufromfpx_test.
	* math/gen-libm-test.pl (parse_args): Handle u, M and U descriptor
	characters.
	* math/test-tgmath-ret.c: Include <stdint.h>.
	(rm): New variable.
	(width): Likewise.
	(CHECK_RET_CONST_TYPE): Take extra arguments and pass them to
	called function.
	(CHECK_RET_CONST_FLOAT): Take extra arguments and pass them to
	CHECK_RET_CONST_TYPE.
	(CHECK_RET_CONST_DOUBLE): Likewise.
	(CHECK_RET_CONST_LDOUBLE): Likewise.
	(CHECK_RET_CONST): Take extra arguments and pass them to calls
	macros.
	(fromfp): New CHECK_RET_CONST call.
	(ufromfp): Likewise.
	(fromfpx): Likewise.
	(ufromfpx): Likewise.
	(do_test): Call check_return_fromfp, check_return_ufromfp,
	check_return_fromfpx and check_return_ufromfpx.
	* math/test-tgmath.c: Include <stdint.h>
	(NCALLS): Increase to 138.
	(F(compile_test)): Initialize i.  Call fromfp functions.
	(F(fromfp)): New function.
	(F(fromfpx)): Likewise.
	(F(ufromfp)): Likewise.
	(F(ufromfpx)): Likewise.
	* manual/arith.texi (Rounding Functions): Document FP_INT_UPWARD,
	FP_INT_DOWNWARD, FP_INT_TOWARDZERO, FP_INT_TONEARESTFROMZERO,
	FP_INT_TONEAREST, fromfp, fromfpf, fromfpl, ufromfp, ufromfpf,
	ufromfpl, fromfpx, fromfpxf, fromfpxl, ufromfpx, ufromfpxf and
	ufromfpxl.
	* manual/libm-err-tab.pl (@all_functions): Add fromfp, fromfpx,
	ufromfp and ufromfpx.
	* math/fromfp.h: New file.
	* sysdeps/ieee754/dbl-64/s_fromfp.c: Likewise.
	* sysdeps/ieee754/dbl-64/s_fromfp_main.c: Likewise.
	* sysdeps/ieee754/dbl-64/s_fromfpx.c: Likewise.
	* sysdeps/ieee754/dbl-64/s_ufromfp.c: Likewise.
	* sysdeps/ieee754/dbl-64/s_ufromfpx.c: Likewise.
	* sysdeps/ieee754/flt-32/s_fromfpf.c: Likewise.
	* sysdeps/ieee754/flt-32/s_fromfpf_main.c: Likewise.
	* sysdeps/ieee754/flt-32/s_fromfpxf.c: Likewise.
	* sysdeps/ieee754/flt-32/s_ufromfpf.c: Likewise.
	* sysdeps/ieee754/flt-32/s_ufromfpxf.c: Likewise.
	* sysdeps/ieee754/ldbl-128/s_fromfpl.c: Likewise.
	* sysdeps/ieee754/ldbl-128/s_fromfpl_main.c: Likewise.
	* sysdeps/ieee754/ldbl-128/s_fromfpxl.c: Likewise.
	* sysdeps/ieee754/ldbl-128/s_ufromfpl.c: Likewise.
	* sysdeps/ieee754/ldbl-128/s_ufromfpxl.c: Likewise.
	* sysdeps/ieee754/ldbl-128ibm/s_fromfpl.c: Likewise.
	* sysdeps/ieee754/ldbl-128ibm/s_fromfpl_main.c: Likewise.
	* sysdeps/ieee754/ldbl-128ibm/s_fromfpxl.c: Likewise.
	* sysdeps/ieee754/ldbl-128ibm/s_ufromfpl.c: Likewise.
	* sysdeps/ieee754/ldbl-128ibm/s_ufromfpxl.c: Likewise.
	* sysdeps/ieee754/ldbl-96/s_fromfpl.c: Likewise.
	* sysdeps/ieee754/ldbl-96/s_fromfpl_main.c: Likewise.
	* sysdeps/ieee754/ldbl-96/s_fromfpxl.c: Likewise.
	* sysdeps/ieee754/ldbl-96/s_ufromfpl.c: Likewise.
	* sysdeps/ieee754/ldbl-96/s_ufromfpxl.c: Likewise.
	* sysdeps/ieee754/ldbl-opt/Makefile (libnldbl-calls): Add fromfp,
	ufromfp, fromfpx and ufromfpx.
	(CFLAGS-nldbl-fromfp.c): New variable.
	(CFLAGS-nldbl-fromfpx.c): Likewise.
	(CFLAGS-nldbl-ufromfp.c): Likewise.
	(CFLAGS-nldbl-ufromfpx.c): Likewise.
	* sysdeps/ieee754/ldbl-opt/nldbl-compat.h: Include <stdint.h>.
	* sysdeps/ieee754/ldbl-opt/nldbl-fromfp.c: New file.
	* sysdeps/ieee754/ldbl-opt/nldbl-fromfpx.c: Likewise.
	* sysdeps/ieee754/ldbl-opt/nldbl-ufromfp.c: Likewise.
	* sysdeps/ieee754/ldbl-opt/nldbl-ufromfpx.c: Likewise.
	* sysdeps/nacl/libm.abilist: Update.
	* sysdeps/unix/sysv/linux/aarch64/libm.abilist: Likewise.
	* sysdeps/unix/sysv/linux/alpha/libm.abilist: Likewise.
	* sysdeps/unix/sysv/linux/arm/libm.abilist: Likewise.
	* sysdeps/unix/sysv/linux/hppa/libm.abilist: Likewise.
	* sysdeps/unix/sysv/linux/i386/libm.abilist: Likewise.
	* sysdeps/unix/sysv/linux/ia64/libm.abilist: Likewise.
	* sysdeps/unix/sysv/linux/m68k/coldfire/libm.abilist: Likewise.
	* sysdeps/unix/sysv/linux/m68k/m680x0/libm.abilist: Likewise.
	* sysdeps/unix/sysv/linux/microblaze/libm.abilist: Likewise.
	* sysdeps/unix/sysv/linux/mips/mips32/libm.abilist: Likewise.
	* sysdeps/unix/sysv/linux/mips/mips64/libm.abilist: Likewise.
	* sysdeps/unix/sysv/linux/nios2/libm.abilist: Likewise.
	* sysdeps/unix/sysv/linux/powerpc/powerpc32/fpu/libm.abilist:
	Likewise.
	* sysdeps/unix/sysv/linux/powerpc/powerpc32/nofpu/libm.abilist:
	Likewise.
	* sysdeps/unix/sysv/linux/powerpc/powerpc64/libm-le.abilist:
	Likewise.
	* sysdeps/unix/sysv/linux/powerpc/powerpc64/libm.abilist:
	Likewise.
	* sysdeps/unix/sysv/linux/s390/s390-32/libm.abilist: Likewise.
	* sysdeps/unix/sysv/linux/s390/s390-64/libm.abilist: Likewise.
	* sysdeps/unix/sysv/linux/sh/libm.abilist: Likewise.
	* sysdeps/unix/sysv/linux/sparc/sparc32/libm.abilist: Likewise.
	* sysdeps/unix/sysv/linux/sparc/sparc64/libm.abilist: Likewise.
	* sysdeps/unix/sysv/linux/tile/tilegx/tilegx32/libm.abilist:
	Likewise.
	* sysdeps/unix/sysv/linux/tile/tilegx/tilegx64/libm.abilist:
	Likewise.
	* sysdeps/unix/sysv/linux/tile/tilepro/libm.abilist: Likewise.
	* sysdeps/unix/sysv/linux/x86_64/64/libm.abilist: Likewise.
	* sysdeps/unix/sysv/linux/x86_64/x32/libm.abilist: Likewise.
2016-12-31 00:40:59 +00:00

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/* Integer inputs within range of uintmax_t. */
i 1:1
i -1:1
i 2:2
i -2:2
i 3:2
i -3:3
i 4:3
i -4:3
i 5:3
i -5:4
i 6:3
i -6:4
i 7:3
i -7:4
i 8:4
i -8:4
i 9:4
i -9:5
i 15:4
i -15:5
i 16:5
i -16:5
i 17:5
i -17:6
i 0x3fffff:22
i -0x3fffff:23
i 0x400000:23
i -0x400000:23
i 0x400001:23
i -0x400001:24
i 0x7fffff:23
i -0x7fffff:24
i 0x800000:24
i -0x800000:24
i 0x800001:24
i -0x800001:25
i 0xffffff:24
i -0xffffff:25
i 0x1000000:25
i -0x1000000:25
#if MANT_DIG >= 53
i 0x1000001:25
i -0x1000001:26
i 0x7ffffffffffffLL:51
i -0x7ffffffffffffLL:52
#endif
i 0x8000000000000LL:52
i -0x8000000000000LL:52
#if MANT_DIG >= 53
i 0x8000000000001LL:52
i -0x8000000000001LL:53
i 0xfffffffffffffLL:52
i -0xfffffffffffffLL:53
#endif
i 0x10000000000000LL:53
i -0x10000000000000LL:53
#if MANT_DIG >= 53
i 0x10000000000001LL:53
i -0x10000000000001LL:54
i 0x1fffffffffffffLL:53
i -0x1fffffffffffffLL:54
#endif
i 0x20000000000000LL:54
i -0x20000000000000LL:54
#if MANT_DIG >= 64
i 0x20000000000001LL:54
i -0x20000000000001LL:55
i 0x3fffffffffffffffLL:62
i -0x3fffffffffffffffLL:63
#endif
i 0x4000000000000000LL:63
i -0x4000000000000000LL:63
#if MANT_DIG >= 64
i 0x4000000000000001LL:63
i -0x4000000000000001LL:64
i 0x7fffffffffffffffLL:63
i -0x7fffffffffffffffLL:64
#endif
i 0x8000000000000000ULL:64
i -INT64_MAX-1:64
#if MANT_DIG >= 64
i 0x8000000000000001ULL:64
i 0xffffffffffffffffULL:64
#endif
i 0x7fffff8000000000LL:63
i -0x7fffff8000000000LL:64
i 0x8000010000000000ULL:64
i 0xffffff0000000000ULL:64
#if MANT_DIG >= 53
i 0x7ffffffffffffc00LL:63
i -0x7ffffffffffffc00LL:64
i 0x8000000000000800ULL:64
i 0xfffffffffffff800ULL:64
#endif
/* Inputs with absolute value between 0 and 1. */
t min_subnorm_value a 0:1 1:1
t -min_subnorm_value a 0:1 -1:1
t min_value a 0:1 1:1
t -min_value a 0:1 -1:1
t 0.1 a 0:1 1:1
t -0.1 a 0:1 -1:1
t 0.25 a 0:1 1:1
t -0.25 a 0:1 -1:1
t 0.499 a 0:1 1:1
t -0.499 a 0:1 -1:1
t 0x0.ffffffp-1 a 0:1 1:1
t -0x0.ffffffp-1 a 0:1 -1:1
#if MANT_DIG >= 53
t 0x0.fffffffffffff8p-1 a 0:1 1:1
t -0x0.fffffffffffff8p-1 a 0:1 -1:1
#endif
#if MANT_DIG >= 64
t 0x0.ffffffffffffffffp-1 a 0:1 1:1
t -0x0.ffffffffffffffffp-1 a 0:1 -1:1
#endif
#if MANT_DIG >= 106
t 0x0.ffffffffffffffffffffffffffcp-1 a 0:1 1:1
t -0x0.ffffffffffffffffffffffffffcp-1 a 0:1 -1:1
#endif
#if MANT_DIG >= 113
t 0x0.ffffffffffffffffffffffffffff8p-1 a 0:1 1:1
t -0x0.ffffffffffffffffffffffffffff8p-1 a 0:1 -1:1
#endif
t 0.5 be 0:1 1:1
t -0.5 be 0:1 -1:1
t 0x1.000002p-1 c 0:1 1:1
t -0x1.000002p-1 c 0:1 -1:1
#if MANT_DIG >= 53
t 0x1.0000000000001p-1 c 0:1 1:1
t -0x1.0000000000001p-1 c 0:1 -1:1
#endif
#if MANT_DIG >= 64
t 0x1.0000000000000002p-1 c 0:1 1:1
t -0x1.0000000000000002p-1 c 0:1 -1:1
#endif
#if MANT_DIG >= 106
t 0x1.000000000000000000000000008p-1 c 0:1 1:1
t -0x1.000000000000000000000000008p-1 c 0:1 -1:1
#endif
#if MANT_DIG >= 113
t 0x1.0000000000000000000000000001p-1 c 0:1 1:1
t -0x1.0000000000000000000000000001p-1 c 0:1 -1:1
#endif
t 0.501 c 0:1 1:1
t -0.501 c 0:1 -1:1
t 0.75 c 0:1 1:1
t -0.75 c 0:1 -1:1
t 0.9 c 0:1 1:1
t -0.9 c 0:1 -1:1
t 0x0.ffffffp0 c 0:1 1:1
t -0x0.ffffffp0 c 0:1 -1:1
#if MANT_DIG >= 53
t 0x0.fffffffffffff8p0 c 0:1 1:1
t -0x0.fffffffffffff8p0 c 0:1 -1:1
#endif
#if MANT_DIG >= 64
t 0x0.ffffffffffffffffp0 c 0:1 1:1
t -0x0.ffffffffffffffffp0 c 0:1 -1:1
#endif
#if MANT_DIG >= 106
t 0x0.ffffffffffffffffffffffffffcp0 c 0:1 1:1
t -0x0.ffffffffffffffffffffffffffcp0 c 0:1 -1:1
#endif
#if MANT_DIG >= 113
t 0x0.ffffffffffffffffffffffffffff8p0 c 0:1 1:1
t -0x0.ffffffffffffffffffffffffffff8p0 c 0:1 -1:1
#endif
/* Various non-integer inputs. */
t 1.25 a 1:1 2:2
t -1.25 a -1:1 -2:2
t 1.5 bo 1:1 2:2
t -1.5 bo -1:1 -2:2
t 1.75 c 1:1 2:2
t -1.75 c -1:1 -2:2
t 2.25 a 2:2 3:2
t -2.25 a -2:2 -3:3
t 2.5 be 2:2 3:2
t -2.5 be -2:2 -3:3
t 2.75 c 2:2 3:2
t -2.75 c -2:2 -3:3
t 3.25 a 3:2 4:3
t -3.25 a -3:3 -4:3
t 3.5 bo 3:2 4:3
t -3.5 bo -3:3 -4:3
t 3.75 c 3:2 4:3
t -3.75 c -3:3 -4:3
t 4.25 a 4:3 5:3
t -4.25 a -4:3 -5:4
t 4.5 be 4:3 5:3
t -4.5 be -4:3 -5:4
t 4.75 c 4:3 5:3
t -4.75 c -4:3 -5:4
t 5.25 a 5:3 6:3
t -5.25 a -5:4 -6:4
t 5.5 bo 5:3 6:3
t -5.5 bo -5:4 -6:4
t 5.75 c 5:3 6:3
t -5.75 c -5:4 -6:4
/* 1, 1.5, 2, 2.5, 3, 3.5 +/- 1ulp. */
t 0x1.000002p0 a 1:1 2:2
t -0x1.000002p0 a -1:1 -2:2
t 0x2.fffffcp-1 a 1:1 2:2
t -0x2.fffffcp-1 a -1:1 -2:2
t 0x3.000004p-1 c 1:1 2:2
t -0x3.000004p-1 c -1:1 -2:2
t 0x0.ffffffp1 c 1:1 2:2
t -0x0.ffffffp1 c -1:1 -2:2
t 0x1.000002p1 a 2:2 3:2
t -0x1.000002p1 a -2:2 -3:3
t 0x4.fffff8p-1 a 2:2 3:2
t -0x4.fffff8p-1 a -2:2 -3:3
t 0x5.000008p-1 c 2:2 3:2
t -0x5.000008p-1 c -2:2 -3:3
t 0x2.fffffcp0 c 2:2 3:2
t -0x2.fffffcp0 c -2:2 -3:3
t 0x3.000004p0 a 3:2 4:3
t -0x3.000004p0 a -3:3 -4:3
t 0x6.fffff8p-1 a 3:2 4:3
t -0x6.fffff8p-1 a -3:3 -4:3
t 0x7.000008p-1 c 3:2 4:3
t -0x7.000008p-1 c -3:3 -4:3
#if MANT_DIG >= 53
t 0x1.0000000000001p0 a 1:1 2:2
t -0x1.0000000000001p0 a -1:1 -2:2
t 0x2.ffffffffffffep-1 a 1:1 2:2
t -0x2.ffffffffffffep-1 a -1:1 -2:2
t 0x3.0000000000002p-1 c 1:1 2:2
t -0x3.0000000000002p-1 c -1:1 -2:2
t 0x0.fffffffffffff8p1 c 1:1 2:2
t -0x0.fffffffffffff8p1 c -1:1 -2:2
t 0x1.0000000000001p1 a 2:2 3:2
t -0x1.0000000000001p1 a -2:2 -3:3
t 0x4.ffffffffffffcp-1 a 2:2 3:2
t -0x4.ffffffffffffcp-1 a -2:2 -3:3
t 0x5.0000000000004p-1 c 2:2 3:2
t -0x5.0000000000004p-1 c -2:2 -3:3
t 0x2.ffffffffffffep0 c 2:2 3:2
t -0x2.ffffffffffffep0 c -2:2 -3:3
t 0x3.0000000000002p0 a 3:2 4:3
t -0x3.0000000000002p0 a -3:3 -4:3
t 0x6.ffffffffffffcp-1 a 3:2 4:3
t -0x6.ffffffffffffcp-1 a -3:3 -4:3
t 0x7.0000000000004p-1 c 3:2 4:3
t -0x7.0000000000004p-1 c -3:3 -4:3
#endif
#if MANT_DIG >= 64
t 0x1.0000000000000002p0 a 1:1 2:2
t -0x1.0000000000000002p0 a -1:1 -2:2
t 0x2.fffffffffffffffcp-1 a 1:1 2:2
t -0x2.fffffffffffffffcp-1 a -1:1 -2:2
t 0x3.0000000000000004p-1 c 1:1 2:2
t -0x3.0000000000000004p-1 c -1:1 -2:2
t 0x0.ffffffffffffffffp1 c 1:1 2:2
t -0x0.ffffffffffffffffp1 c -1:1 -2:2
t 0x1.0000000000000002p1 a 2:2 3:2
t -0x1.0000000000000002p1 a -2:2 -3:3
t 0x4.fffffffffffffff8p-1 a 2:2 3:2
t -0x4.fffffffffffffff8p-1 a -2:2 -3:3
t 0x5.0000000000000008p-1 c 2:2 3:2
t -0x5.0000000000000008p-1 c -2:2 -3:3
t 0x2.fffffffffffffffcp0 c 2:2 3:2
t -0x2.fffffffffffffffcp0 c -2:2 -3:3
t 0x3.0000000000000004p0 a 3:2 4:3
t -0x3.0000000000000004p0 a -3:3 -4:3
t 0x6.fffffffffffffff8p-1 a 3:2 4:3
t -0x6.fffffffffffffff8p-1 a -3:3 -4:3
t 0x7.0000000000000008p-1 c 3:2 4:3
t -0x7.0000000000000008p-1 c -3:3 -4:3
#endif
#if MANT_DIG >= 106
t 0x1.000000000000000000000000008p0 a 1:1 2:2
t -0x1.000000000000000000000000008p0 a -1:1 -2:2
t 0x2.ffffffffffffffffffffffffffp-1 a 1:1 2:2
t -0x2.ffffffffffffffffffffffffffp-1 a -1:1 -2:2
t 0x3.00000000000000000000000001p-1 c 1:1 2:2
t -0x3.00000000000000000000000001p-1 c -1:1 -2:2
t 0x0.ffffffffffffffffffffffffffcp1 c 1:1 2:2
t -0x0.ffffffffffffffffffffffffffcp1 c -1:1 -2:2
t 0x1.000000000000000000000000008p1 a 2:2 3:2
t -0x1.000000000000000000000000008p1 a -2:2 -3:3
t 0x4.fffffffffffffffffffffffffep-1 a 2:2 3:2
t -0x4.fffffffffffffffffffffffffep-1 a -2:2 -3:3
t 0x5.00000000000000000000000002p-1 c 2:2 3:2
t -0x5.00000000000000000000000002p-1 c -2:2 -3:3
t 0x2.ffffffffffffffffffffffffffp0 c 2:2 3:2
t -0x2.ffffffffffffffffffffffffffp0 c -2:2 -3:3
t 0x3.00000000000000000000000001p0 a 3:2 4:3
t -0x3.00000000000000000000000001p0 a -3:3 -4:3
t 0x6.fffffffffffffffffffffffffep-1 a 3:2 4:3
t -0x6.fffffffffffffffffffffffffep-1 a -3:3 -4:3
t 0x7.00000000000000000000000002p-1 c 3:2 4:3
t -0x7.00000000000000000000000002p-1 c -3:3 -4:3
#endif
#if MANT_DIG >= 113
t 0x1.0000000000000000000000000001p0 a 1:1 2:2
t -0x1.0000000000000000000000000001p0 a -1:1 -2:2
t 0x2.fffffffffffffffffffffffffffep-1 a 1:1 2:2
t -0x2.fffffffffffffffffffffffffffep-1 a -1:1 -2:2
t 0x3.0000000000000000000000000002p-1 c 1:1 2:2
t -0x3.0000000000000000000000000002p-1 c -1:1 -2:2
t 0x0.ffffffffffffffffffffffffffff8p1 c 1:1 2:2
t -0x0.ffffffffffffffffffffffffffff8p1 c -1:1 -2:2
t 0x1.0000000000000000000000000001p1 a 2:2 3:2
t -0x1.0000000000000000000000000001p1 a -2:2 -3:3
t 0x4.fffffffffffffffffffffffffffcp-1 a 2:2 3:2
t -0x4.fffffffffffffffffffffffffffcp-1 a -2:2 -3:3
t 0x5.0000000000000000000000000004p-1 c 2:2 3:2
t -0x5.0000000000000000000000000004p-1 c -2:2 -3:3
t 0x2.fffffffffffffffffffffffffffep0 c 2:2 3:2
t -0x2.fffffffffffffffffffffffffffep0 c -2:2 -3:3
t 0x3.0000000000000000000000000002p0 a 3:2 4:3
t -0x3.0000000000000000000000000002p0 a -3:3 -4:3
t 0x6.fffffffffffffffffffffffffffcp-1 a 3:2 4:3
t -0x6.fffffffffffffffffffffffffffcp-1 a -3:3 -4:3
t 0x7.0000000000000000000000000004p-1 c 3:2 4:3
t -0x7.0000000000000000000000000004p-1 c -3:3 -4:3
#endif
/* 31, 32, 33 fractional bits. */
#if MANT_DIG >= 53
t 0x200000.7ffffffep0 a 0x200000:22 0x200001:22
t -0x200000.7ffffffep0 a -0x200000:22 -0x200001:23
t 0x200000.8p0 be 0x200000:22 0x200001:22
t -0x200000.8p0 be -0x200000:22 -0x200001:23
t 0x200000.80000002p0 c 0x200000:22 0x200001:22
t -0x200000.80000002p0 c -0x200000:22 -0x200001:23
t 0x200001.7ffffffep0 a 0x200001:22 0x200002:22
t -0x200001.7ffffffep0 a -0x200001:23 -0x200002:23
t 0x200001.8p0 bo 0x200001:22 0x200002:22
t -0x200001.8p0 bo -0x200001:23 -0x200002:23
t 0x200001.80000002p0 c 0x200001:22 0x200002:22
t -0x200001.80000002p0 c -0x200001:23 -0x200002:23
t 0x3fffff.fffffffep0 c 0x3fffff:22 0x400000:23
t -0x3fffff.fffffffep0 c -0x3fffff:23 -0x400000:23
t 0x100000.7fffffffp0 a 0x100000:21 0x100001:21
t -0x100000.7fffffffp0 a -0x100000:21 -0x100001:22
t 0x100000.8p0 be 0x100000:21 0x100001:21
t -0x100000.8p0 be -0x100000:21 -0x100001:22
t 0x100000.80000001p0 c 0x100000:21 0x100001:21
t -0x100000.80000001p0 c -0x100000:21 -0x100001:22
t 0x100001.7fffffffp0 a 0x100001:21 0x100002:21
t -0x100001.7fffffffp0 a -0x100001:22 -0x100002:22
t 0x100001.8p0 bo 0x100001:21 0x100002:21
t -0x100001.8p0 bo -0x100001:22 -0x100002:22
t 0x100001.80000001p0 c 0x100001:21 0x100002:21
t -0x100001.80000001p0 c -0x100001:22 -0x100002:22
t 0x1fffff.ffffffffp0 c 0x1fffff:21 0x200000:22
t -0x1fffff.ffffffffp0 c -0x1fffff:22 -0x200000:22
t 0x80000.7fffffff8p0 a 0x80000:20 0x80001:20
t -0x80000.7fffffff8p0 a -0x80000:20 -0x80001:21
t 0x80000.8p0 be 0x80000:20 0x80001:20
t -0x80000.8p0 be -0x80000:20 -0x80001:21
t 0x80000.800000008p0 c 0x80000:20 0x80001:20
t -0x80000.800000008p0 c -0x80000:20 -0x80001:21
t 0x80001.7fffffff8p0 a 0x80001:20 0x80002:20
t -0x80001.7fffffff8p0 a -0x80001:21 -0x80002:21
t 0x80001.8p0 bo 0x80001:20 0x80002:20
t -0x80001.8p0 bo -0x80001:21 -0x80002:21
t 0x80001.800000008p0 c 0x80001:20 0x80002:20
t -0x80001.800000008p0 c -0x80001:21 -0x80002:21
t 0xfffff.ffffffff8p0 c 0xfffff:20 0x100000:21
t -0xfffff.ffffffff8p0 c -0xfffff:21 -0x100000:21
#endif
#if MANT_DIG >= 64
t 0x100000000.7ffffffep0 a 0x100000000LL:33 0x100000001LL:33
t -0x100000000.7ffffffep0 a -0x100000000LL:33 -0x100000001LL:34
t 0x100000000.8p0 be 0x100000000LL:33 0x100000001LL:33
t -0x100000000.8p0 be -0x100000000LL:33 -0x100000001LL:34
t 0x100000000.80000002p0 c 0x100000000LL:33 0x100000001LL:33
t -0x100000000.80000002p0 c -0x100000000LL:33 -0x100000001LL:34
t 0x100000001.7ffffffep0 a 0x100000001LL:33 0x100000002LL:33
t -0x100000001.7ffffffep0 a -0x100000001LL:34 -0x100000002LL:34
t 0x100000001.8p0 bo 0x100000001LL:33 0x100000002LL:33
t -0x100000001.8p0 bo -0x100000001LL:34 -0x100000002LL:34
t 0x100000001.80000002p0 c 0x100000001LL:33 0x100000002LL:33
t -0x100000001.80000002p0 c -0x100000001LL:34 -0x100000002LL:34
t 0x1ffffffff.fffffffep0 c 0x1ffffffffLL:33 0x200000000LL:34
t -0x1ffffffff.fffffffep0 c -0x1ffffffffLL:34 -0x200000000LL:34
t 0x80000000.7fffffffp0 a 0x80000000LL:32 0x80000001LL:32
t -0x80000000.7fffffffp0 a -0x80000000LL:32 -0x80000001LL:33
t 0x80000000.8p0 be 0x80000000LL:32 0x80000001LL:32
t -0x80000000.8p0 be -0x80000000LL:32 -0x80000001LL:33
t 0x80000000.80000001p0 c 0x80000000LL:32 0x80000001LL:32
t -0x80000000.80000001p0 c -0x80000000LL:32 -0x80000001LL:33
t 0x80000001.7fffffffp0 a 0x80000001LL:32 0x80000002LL:32
t -0x80000001.7fffffffp0 a -0x80000001LL:33 -0x80000002LL:33
t 0x80000001.8p0 bo 0x80000001LL:32 0x80000002LL:32
t -0x80000001.8p0 bo -0x80000001LL:33 -0x80000002LL:33
t 0x80000001.80000001p0 c 0x80000001LL:32 0x80000002LL:32
t -0x80000001.80000001p0 c -0x80000001LL:33 -0x80000002LL:33
t 0xffffffff.ffffffffp0 c 0xffffffffLL:32 0x100000000LL:33
t -0xffffffff.ffffffffp0 c -0xffffffffLL:33 -0x100000000LL:33
t 0x40000000.7fffffff8p0 a 0x40000000LL:31 0x40000001LL:31
t -0x40000000.7fffffff8p0 a -0x40000000LL:31 -0x40000001LL:32
t 0x40000000.8p0 be 0x40000000LL:31 0x40000001LL:31
t -0x40000000.8p0 be -0x40000000LL:31 -0x40000001LL:32
t 0x40000000.800000008p0 c 0x40000000LL:31 0x40000001LL:31
t -0x40000000.800000008p0 c -0x40000000LL:31 -0x40000001LL:32
t 0x40000001.7fffffff8p0 a 0x40000001LL:31 0x40000002LL:31
t -0x40000001.7fffffff8p0 a -0x40000001LL:32 -0x40000002LL:32
t 0x40000001.8p0 bo 0x40000001LL:31 0x40000002LL:31
t -0x40000001.8p0 bo -0x40000001LL:32 -0x40000002LL:32
t 0x40000001.800000008p0 c 0x40000001LL:31 0x40000002LL:31
t -0x40000001.800000008p0 c -0x40000001LL:32 -0x40000002LL:32
t 0x7fffffff.ffffffff8p0 c 0x7fffffffLL:31 0x80000000LL:32
t -0x7fffffff.ffffffff8p0 c -0x7fffffffLL:32 -0x80000000LL:32
#endif
/* Tests where overflow depends on the rounding mode. */
#if MANT_DIG >= 64
t 0x7fffffffffffffff.8p0 bo 0x7fffffffffffffffLL:63 0x8000000000000000ULL:64
#endif
#if MANT_DIG >= 72
t 0x7fffffffffffffff.7fp0 a 0x7fffffffffffffffLL:63 0x8000000000000000ULL:64
t 0x7fffffffffffffff.81p0 c 0x7fffffffffffffffLL:63 0x8000000000000000ULL:64
t 0xffffffffffffffff.7fp0 a 0xffffffffffffffffULL:64 0x10000000000000000ULL:65
t 0xffffffffffffffff.8p0 bo 0xffffffffffffffffULL:64 0x10000000000000000ULL:65
t 0xffffffffffffffff.81p0 c 0xffffffffffffffffULL:64 0x10000000000000000ULL:65
t -0x8000000000000000.7fp0 a -INT64_MAX-1:64 -0x8000000000000001LL:65
t -0x8000000000000000.8p0 be -INT64_MAX-1:64 -0x8000000000000001LL:65
t -0x8000000000000000.81p0 c -INT64_MAX-1:64 -0x8000000000000001LL:65
#endif
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