Fix ldbl-128 j1l spurious underflows (bug 18612).

The ldbl-128 implementation of j1l produces spurious underflow
exceptions for some small arguments, as a result of squaring the
argument.  This patch fixes it just to use a linear approximation for
sufficiently small arguments, and then to force an underflow exception
only in the cases where it is required.

Tested for mips64.

	[BZ #18612]
	* sysdeps/ieee754/ldbl-128/e_j1l.c (__ieee754_j1l): For small
	arguments, just return 0.5 times the argument, with underflow
	forced as needed.
	* math/auto-libm-test-in: Add more tests of j1.
	* math/auto-libm-test-out: Regenerated.

2 files changed, 178 insertions, 0 deletions

diff --git a/math/auto-libm-test-in b/math/auto-libm-test-in
index 34b02c91f7..f4313a2b99 100644
--- a/math/auto-libm-test-in
+++ b/math/auto-libm-test-in
@@ -1812,6 +1812,9 @@ j1 0x1.ff00000000002p+840
 j1 0x1p1023
 j1 0x1p16382
 j1 0x1p16383
+j1 0x1p-100
+j1 0x1p-600
+j1 0x1p-10000
 # Bug 18611: errno setting may be missing.
 j1 min missing-errno
 j1 -min missing-errno
diff --git a/math/auto-libm-test-out b/math/auto-libm-test-out
index 8ae005d081..b71429b4ac 100644
--- a/math/auto-libm-test-out
+++ b/math/auto-libm-test-out
@@ -142437,6 +142437,181 @@ j1 0x1p16383
 = j1 tonearest ldbl-128ibm 0xf.ffffffffffffbffffffffffffcp+1020L : -0x5.34b8be56c9cb044a0ef191b026p-516L : inexact-ok
 = j1 towardzero ldbl-128ibm 0xf.ffffffffffffbffffffffffffcp+1020L : -0x5.34b8be56c9cb044a0ef191b024p-516L : inexact-ok
 = j1 upward ldbl-128ibm 0xf.ffffffffffffbffffffffffffcp+1020L : -0x5.34b8be56c9cb044a0ef191b024p-516L : inexact-ok
+j1 0x1p-100
+= j1 downward flt-32 0x1p-100f : 0x7.fffff8p-104f : inexact-ok
+= j1 tonearest flt-32 0x1p-100f : 0x8p-104f : inexact-ok
+= j1 towardzero flt-32 0x1p-100f : 0x7.fffff8p-104f : inexact-ok
+= j1 upward flt-32 0x1p-100f : 0x8p-104f : inexact-ok
+= j1 downward dbl-64 0x1p-100 : 0x7.ffffffffffffcp-104 : inexact-ok
+= j1 tonearest dbl-64 0x1p-100 : 0x8p-104 : inexact-ok
+= j1 towardzero dbl-64 0x1p-100 : 0x7.ffffffffffffcp-104 : inexact-ok
+= j1 upward dbl-64 0x1p-100 : 0x8p-104 : inexact-ok
+= j1 downward ldbl-96-intel 0x1p-100L : 0x7.fffffffffffffff8p-104L : inexact-ok
+= j1 tonearest ldbl-96-intel 0x1p-100L : 0x8p-104L : inexact-ok
+= j1 towardzero ldbl-96-intel 0x1p-100L : 0x7.fffffffffffffff8p-104L : inexact-ok
+= j1 upward ldbl-96-intel 0x1p-100L : 0x8p-104L : inexact-ok
+= j1 downward ldbl-96-m68k 0x1p-100L : 0x7.fffffffffffffff8p-104L : inexact-ok
+= j1 tonearest ldbl-96-m68k 0x1p-100L : 0x8p-104L : inexact-ok
+= j1 towardzero ldbl-96-m68k 0x1p-100L : 0x7.fffffffffffffff8p-104L : inexact-ok
+= j1 upward ldbl-96-m68k 0x1p-100L : 0x8p-104L : inexact-ok
+= j1 downward ldbl-128 0x1p-100L : 0x7.fffffffffffffffffffffffffffcp-104L : inexact-ok
+= j1 tonearest ldbl-128 0x1p-100L : 0x8p-104L : inexact-ok
+= j1 towardzero ldbl-128 0x1p-100L : 0x7.fffffffffffffffffffffffffffcp-104L : inexact-ok
+= j1 upward ldbl-128 0x1p-100L : 0x8p-104L : inexact-ok
+= j1 downward ldbl-128ibm 0x1p-100L : 0x7.fffffffffffffffffffffffffep-104L : inexact-ok
+= j1 tonearest ldbl-128ibm 0x1p-100L : 0x8p-104L : inexact-ok
+= j1 towardzero ldbl-128ibm 0x1p-100L : 0x7.fffffffffffffffffffffffffep-104L : inexact-ok
+= j1 upward ldbl-128ibm 0x1p-100L : 0x8p-104L : inexact-ok
+j1 0x1p-600
+= j1 downward flt-32 0x8p-152f : 0x0p+0f : inexact-ok underflow errno-erange
+= j1 tonearest flt-32 0x8p-152f : 0x0p+0f : inexact-ok underflow errno-erange
+= j1 towardzero flt-32 0x8p-152f : 0x0p+0f : inexact-ok underflow errno-erange
+= j1 upward flt-32 0x8p-152f : 0x8p-152f : inexact-ok underflow errno-erange-ok
+= j1 downward dbl-64 0x8p-152 : 0x3.ffffffffffffep-152 : inexact-ok
+= j1 tonearest dbl-64 0x8p-152 : 0x4p-152 : inexact-ok
+= j1 towardzero dbl-64 0x8p-152 : 0x3.ffffffffffffep-152 : inexact-ok
+= j1 upward dbl-64 0x8p-152 : 0x4p-152 : inexact-ok
+= j1 downward ldbl-96-intel 0x8p-152L : 0x3.fffffffffffffffcp-152L : inexact-ok
+= j1 tonearest ldbl-96-intel 0x8p-152L : 0x4p-152L : inexact-ok
+= j1 towardzero ldbl-96-intel 0x8p-152L : 0x3.fffffffffffffffcp-152L : inexact-ok
+= j1 upward ldbl-96-intel 0x8p-152L : 0x4p-152L : inexact-ok
+= j1 downward ldbl-96-m68k 0x8p-152L : 0x3.fffffffffffffffcp-152L : inexact-ok
+= j1 tonearest ldbl-96-m68k 0x8p-152L : 0x4p-152L : inexact-ok
+= j1 towardzero ldbl-96-m68k 0x8p-152L : 0x3.fffffffffffffffcp-152L : inexact-ok
+= j1 upward ldbl-96-m68k 0x8p-152L : 0x4p-152L : inexact-ok
+= j1 downward ldbl-128 0x8p-152L : 0x3.fffffffffffffffffffffffffffep-152L : inexact-ok
+= j1 tonearest ldbl-128 0x8p-152L : 0x4p-152L : inexact-ok
+= j1 towardzero ldbl-128 0x8p-152L : 0x3.fffffffffffffffffffffffffffep-152L : inexact-ok
+= j1 upward ldbl-128 0x8p-152L : 0x4p-152L : inexact-ok
+= j1 downward ldbl-128ibm 0x8p-152L : 0x3.ffffffffffffffffffffffffffp-152L : inexact-ok
+= j1 tonearest ldbl-128ibm 0x8p-152L : 0x4p-152L : inexact-ok
+= j1 towardzero ldbl-128ibm 0x8p-152L : 0x3.ffffffffffffffffffffffffffp-152L : inexact-ok
+= j1 upward ldbl-128ibm 0x8p-152L : 0x4p-152L : inexact-ok
+= j1 downward flt-32 0x0p+0f : 0x0p+0f : inexact-ok
+= j1 tonearest flt-32 0x0p+0f : 0x0p+0f : inexact-ok
+= j1 towardzero flt-32 0x0p+0f : 0x0p+0f : inexact-ok
+= j1 upward flt-32 0x0p+0f : 0x0p+0f : inexact-ok
+= j1 downward dbl-64 0x0p+0 : 0x0p+0 : inexact-ok
+= j1 tonearest dbl-64 0x0p+0 : 0x0p+0 : inexact-ok
+= j1 towardzero dbl-64 0x0p+0 : 0x0p+0 : inexact-ok
+= j1 upward dbl-64 0x0p+0 : 0x0p+0 : inexact-ok
+= j1 downward ldbl-96-intel 0x0p+0L : 0x0p+0L : inexact-ok
+= j1 tonearest ldbl-96-intel 0x0p+0L : 0x0p+0L : inexact-ok
+= j1 towardzero ldbl-96-intel 0x0p+0L : 0x0p+0L : inexact-ok
+= j1 upward ldbl-96-intel 0x0p+0L : 0x0p+0L : inexact-ok
+= j1 downward ldbl-96-m68k 0x0p+0L : 0x0p+0L : inexact-ok
+= j1 tonearest ldbl-96-m68k 0x0p+0L : 0x0p+0L : inexact-ok
+= j1 towardzero ldbl-96-m68k 0x0p+0L : 0x0p+0L : inexact-ok
+= j1 upward ldbl-96-m68k 0x0p+0L : 0x0p+0L : inexact-ok
+= j1 downward ldbl-128 0x0p+0L : 0x0p+0L : inexact-ok
+= j1 tonearest ldbl-128 0x0p+0L : 0x0p+0L : inexact-ok
+= j1 towardzero ldbl-128 0x0p+0L : 0x0p+0L : inexact-ok
+= j1 upward ldbl-128 0x0p+0L : 0x0p+0L : inexact-ok
+= j1 downward ldbl-128ibm 0x0p+0L : 0x0p+0L : inexact-ok
+= j1 tonearest ldbl-128ibm 0x0p+0L : 0x0p+0L : inexact-ok
+= j1 towardzero ldbl-128ibm 0x0p+0L : 0x0p+0L : inexact-ok
+= j1 upward ldbl-128ibm 0x0p+0L : 0x0p+0L : inexact-ok
+= j1 downward dbl-64 0x1p-600 : 0x7.ffffffffffffcp-604 : inexact-ok
+= j1 tonearest dbl-64 0x1p-600 : 0x8p-604 : inexact-ok
+= j1 towardzero dbl-64 0x1p-600 : 0x7.ffffffffffffcp-604 : inexact-ok
+= j1 upward dbl-64 0x1p-600 : 0x8p-604 : inexact-ok
+= j1 downward ldbl-96-intel 0x1p-600L : 0x7.fffffffffffffff8p-604L : inexact-ok
+= j1 tonearest ldbl-96-intel 0x1p-600L : 0x8p-604L : inexact-ok
+= j1 towardzero ldbl-96-intel 0x1p-600L : 0x7.fffffffffffffff8p-604L : inexact-ok
+= j1 upward ldbl-96-intel 0x1p-600L : 0x8p-604L : inexact-ok
+= j1 downward ldbl-96-m68k 0x1p-600L : 0x7.fffffffffffffff8p-604L : inexact-ok
+= j1 tonearest ldbl-96-m68k 0x1p-600L : 0x8p-604L : inexact-ok
+= j1 towardzero ldbl-96-m68k 0x1p-600L : 0x7.fffffffffffffff8p-604L : inexact-ok
+= j1 upward ldbl-96-m68k 0x1p-600L : 0x8p-604L : inexact-ok
+= j1 downward ldbl-128 0x1p-600L : 0x7.fffffffffffffffffffffffffffcp-604L : inexact-ok
+= j1 tonearest ldbl-128 0x1p-600L : 0x8p-604L : inexact-ok
+= j1 towardzero ldbl-128 0x1p-600L : 0x7.fffffffffffffffffffffffffffcp-604L : inexact-ok
+= j1 upward ldbl-128 0x1p-600L : 0x8p-604L : inexact-ok
+= j1 downward ldbl-128ibm 0x1p-600L : 0x7.fffffffffffffffffffffffffep-604L : inexact-ok
+= j1 tonearest ldbl-128ibm 0x1p-600L : 0x8p-604L : inexact-ok
+= j1 towardzero ldbl-128ibm 0x1p-600L : 0x7.fffffffffffffffffffffffffep-604L : inexact-ok
+= j1 upward ldbl-128ibm 0x1p-600L : 0x8p-604L : inexact-ok
+j1 0x1p-10000
+= j1 downward flt-32 0x8p-152f : 0x0p+0f : inexact-ok underflow errno-erange
+= j1 tonearest flt-32 0x8p-152f : 0x0p+0f : inexact-ok underflow errno-erange
+= j1 towardzero flt-32 0x8p-152f : 0x0p+0f : inexact-ok underflow errno-erange
+= j1 upward flt-32 0x8p-152f : 0x8p-152f : inexact-ok underflow errno-erange-ok
+= j1 downward dbl-64 0x8p-152 : 0x3.ffffffffffffep-152 : inexact-ok
+= j1 tonearest dbl-64 0x8p-152 : 0x4p-152 : inexact-ok
+= j1 towardzero dbl-64 0x8p-152 : 0x3.ffffffffffffep-152 : inexact-ok
+= j1 upward dbl-64 0x8p-152 : 0x4p-152 : inexact-ok
+= j1 downward ldbl-96-intel 0x8p-152L : 0x3.fffffffffffffffcp-152L : inexact-ok
+= j1 tonearest ldbl-96-intel 0x8p-152L : 0x4p-152L : inexact-ok
+= j1 towardzero ldbl-96-intel 0x8p-152L : 0x3.fffffffffffffffcp-152L : inexact-ok
+= j1 upward ldbl-96-intel 0x8p-152L : 0x4p-152L : inexact-ok
+= j1 downward ldbl-96-m68k 0x8p-152L : 0x3.fffffffffffffffcp-152L : inexact-ok
+= j1 tonearest ldbl-96-m68k 0x8p-152L : 0x4p-152L : inexact-ok
+= j1 towardzero ldbl-96-m68k 0x8p-152L : 0x3.fffffffffffffffcp-152L : inexact-ok
+= j1 upward ldbl-96-m68k 0x8p-152L : 0x4p-152L : inexact-ok
+= j1 downward ldbl-128 0x8p-152L : 0x3.fffffffffffffffffffffffffffep-152L : inexact-ok
+= j1 tonearest ldbl-128 0x8p-152L : 0x4p-152L : inexact-ok
+= j1 towardzero ldbl-128 0x8p-152L : 0x3.fffffffffffffffffffffffffffep-152L : inexact-ok
+= j1 upward ldbl-128 0x8p-152L : 0x4p-152L : inexact-ok
+= j1 downward ldbl-128ibm 0x8p-152L : 0x3.ffffffffffffffffffffffffffp-152L : inexact-ok
+= j1 tonearest ldbl-128ibm 0x8p-152L : 0x4p-152L : inexact-ok
+= j1 towardzero ldbl-128ibm 0x8p-152L : 0x3.ffffffffffffffffffffffffffp-152L : inexact-ok
+= j1 upward ldbl-128ibm 0x8p-152L : 0x4p-152L : inexact-ok
+= j1 downward flt-32 0x0p+0f : 0x0p+0f : inexact-ok
+= j1 tonearest flt-32 0x0p+0f : 0x0p+0f : inexact-ok
+= j1 towardzero flt-32 0x0p+0f : 0x0p+0f : inexact-ok
+= j1 upward flt-32 0x0p+0f : 0x0p+0f : inexact-ok
+= j1 downward dbl-64 0x0p+0 : 0x0p+0 : inexact-ok
+= j1 tonearest dbl-64 0x0p+0 : 0x0p+0 : inexact-ok
+= j1 towardzero dbl-64 0x0p+0 : 0x0p+0 : inexact-ok
+= j1 upward dbl-64 0x0p+0 : 0x0p+0 : inexact-ok
+= j1 downward ldbl-96-intel 0x0p+0L : 0x0p+0L : inexact-ok
+= j1 tonearest ldbl-96-intel 0x0p+0L : 0x0p+0L : inexact-ok
+= j1 towardzero ldbl-96-intel 0x0p+0L : 0x0p+0L : inexact-ok
+= j1 upward ldbl-96-intel 0x0p+0L : 0x0p+0L : inexact-ok
+= j1 downward ldbl-96-m68k 0x0p+0L : 0x0p+0L : inexact-ok
+= j1 tonearest ldbl-96-m68k 0x0p+0L : 0x0p+0L : inexact-ok
+= j1 towardzero ldbl-96-m68k 0x0p+0L : 0x0p+0L : inexact-ok
+= j1 upward ldbl-96-m68k 0x0p+0L : 0x0p+0L : inexact-ok
+= j1 downward ldbl-128 0x0p+0L : 0x0p+0L : inexact-ok
+= j1 tonearest ldbl-128 0x0p+0L : 0x0p+0L : inexact-ok
+= j1 towardzero ldbl-128 0x0p+0L : 0x0p+0L : inexact-ok
+= j1 upward ldbl-128 0x0p+0L : 0x0p+0L : inexact-ok
+= j1 downward ldbl-128ibm 0x0p+0L : 0x0p+0L : inexact-ok
+= j1 tonearest ldbl-128ibm 0x0p+0L : 0x0p+0L : inexact-ok
+= j1 towardzero ldbl-128ibm 0x0p+0L : 0x0p+0L : inexact-ok
+= j1 upward ldbl-128ibm 0x0p+0L : 0x0p+0L : inexact-ok
+= j1 downward dbl-64 0x4p-1076 : 0x0p+0 : inexact-ok underflow errno-erange
+= j1 tonearest dbl-64 0x4p-1076 : 0x0p+0 : inexact-ok underflow errno-erange
+= j1 towardzero dbl-64 0x4p-1076 : 0x0p+0 : inexact-ok underflow errno-erange
+= j1 upward dbl-64 0x4p-1076 : 0x4p-1076 : inexact-ok underflow errno-erange-ok
+= j1 downward ldbl-96-intel 0x4p-1076L : 0x1.fffffffffffffffep-1076L : inexact-ok
+= j1 tonearest ldbl-96-intel 0x4p-1076L : 0x2p-1076L : inexact-ok
+= j1 towardzero ldbl-96-intel 0x4p-1076L : 0x1.fffffffffffffffep-1076L : inexact-ok
+= j1 upward ldbl-96-intel 0x4p-1076L : 0x2p-1076L : inexact-ok
+= j1 downward ldbl-96-m68k 0x4p-1076L : 0x1.fffffffffffffffep-1076L : inexact-ok
+= j1 tonearest ldbl-96-m68k 0x4p-1076L : 0x2p-1076L : inexact-ok
+= j1 towardzero ldbl-96-m68k 0x4p-1076L : 0x1.fffffffffffffffep-1076L : inexact-ok
+= j1 upward ldbl-96-m68k 0x4p-1076L : 0x2p-1076L : inexact-ok
+= j1 downward ldbl-128 0x4p-1076L : 0x1.ffffffffffffffffffffffffffffp-1076L : inexact-ok
+= j1 tonearest ldbl-128 0x4p-1076L : 0x2p-1076L : inexact-ok
+= j1 towardzero ldbl-128 0x4p-1076L : 0x1.ffffffffffffffffffffffffffffp-1076L : inexact-ok
+= j1 upward ldbl-128 0x4p-1076L : 0x2p-1076L : inexact-ok
+= j1 downward ldbl-128ibm 0x4p-1076L : 0x0p+0L : inexact-ok underflow errno-erange
+= j1 tonearest ldbl-128ibm 0x4p-1076L : 0x0p+0L : inexact-ok underflow errno-erange
+= j1 towardzero ldbl-128ibm 0x4p-1076L : 0x0p+0L : inexact-ok underflow errno-erange
+= j1 upward ldbl-128ibm 0x4p-1076L : 0x4p-1076L : inexact-ok underflow errno-erange-ok
+= j1 downward ldbl-96-intel 0x1p-10000L : 0x7.fffffffffffffff8p-10004L : inexact-ok
+= j1 tonearest ldbl-96-intel 0x1p-10000L : 0x8p-10004L : inexact-ok
+= j1 towardzero ldbl-96-intel 0x1p-10000L : 0x7.fffffffffffffff8p-10004L : inexact-ok
+= j1 upward ldbl-96-intel 0x1p-10000L : 0x8p-10004L : inexact-ok
+= j1 downward ldbl-96-m68k 0x1p-10000L : 0x7.fffffffffffffff8p-10004L : inexact-ok
+= j1 tonearest ldbl-96-m68k 0x1p-10000L : 0x8p-10004L : inexact-ok
+= j1 towardzero ldbl-96-m68k 0x1p-10000L : 0x7.fffffffffffffff8p-10004L : inexact-ok
+= j1 upward ldbl-96-m68k 0x1p-10000L : 0x8p-10004L : inexact-ok
+= j1 downward ldbl-128 0x1p-10000L : 0x7.fffffffffffffffffffffffffffcp-10004L : inexact-ok
+= j1 tonearest ldbl-128 0x1p-10000L : 0x8p-10004L : inexact-ok
+= j1 towardzero ldbl-128 0x1p-10000L : 0x7.fffffffffffffffffffffffffffcp-10004L : inexact-ok
+= j1 upward ldbl-128 0x1p-10000L : 0x8p-10004L : inexact-ok
 j1 min missing-errno
 = j1 downward flt-32 0x4p-128f : 0x1.fffff8p-128f : inexact-ok underflow errno-erange-ok
 = j1 tonearest flt-32 0x4p-128f : 0x2p-128f : inexact-ok underflow errno-erange-ok