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Fix x86/x86_64 expm1l inaccuracy and exceptions (bugs 13885, 13923).
This commit is contained in:
Joseph Myers
parent
6693d69429
commit
495fd99f3a
23
ChangeLog
23
ChangeLog
@ -1,3 +1,26 @@
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2012-05-07 Joseph Myers <joseph@codesourcery.com>
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[BZ #13885]
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[BZ #13923]
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* sysdeps/i386/fpu/e_expl.S (IEEE754_EXPL): Define conditional on
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USE_AS_EXPM1L.
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(EXPL_FINITE): Likewise.
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(FLDLOG): Likewise.
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(IEEE754_EXPL) [USE_AS_EXPM1L]: Support use as expm1l.
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* sysdeps/i386/fpu/s_expm1l.S: Define USE_AS_EXPM1L and include
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e_expl.S.
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* sysdeps/x86_64/fpu/e_expl.S (IEEE754_EXPL): Define conditional on
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USE_AS_EXPM1L.
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(EXPL_FINITE): Likewise.
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(FLDLOG): Likewise.
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(IEEE754_EXPL) [USE_AS_EXPM1L]: Support use as expm1l.
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* sysdeps/x86_64/fpu/s_expm1l.S: Define USE_AS_EXPM1L and include
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e_expl.S.
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* math/libm-test.inc (expm1_test): Add more tests. Do not disable
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test of -max_value argument for long double.
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* sysdeps/i386/fpu/libm-test-ulps: Update.
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* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
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2012-05-06 David S. Miller <davem@davemloft.net>
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* scripts/data/localplt-sparc-linux-gnu.data: Add '?' markers to
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10
NEWS
10
NEWS
@ -20,11 +20,11 @@ Version 2.16
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13583, 13592, 13618, 13637, 13656, 13658, 13673, 13691, 13695, 13704,
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13705, 13706, 13726, 13738, 13739, 13758, 13760, 13761, 13775, 13786,
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13787, 13792, 13806, 13824, 13840, 13841, 13844, 13846, 13851, 13852,
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13854, 13871, 13872, 13873, 13879, 13883, 13884, 13886, 13892, 13895,
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13908, 13910, 13911, 13912, 13913, 13914, 13915, 13916, 13917, 13918,
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13919, 13920, 13921, 13922, 13924, 13926, 13927, 13928, 13938, 13941,
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13942, 13963, 13967, 13970, 13973, 14027, 14033, 14034, 14040, 14049,
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14055, 14064
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13854, 13871, 13872, 13873, 13879, 13883, 13884, 13885, 13886, 13892,
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13895, 13908, 13910, 13911, 13912, 13913, 13914, 13915, 13916, 13917,
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13918, 13919, 13920, 13921, 13922, 13923, 13924, 13926, 13927, 13928,
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13938, 13941, 13942, 13963, 13967, 13970, 13973, 14027, 14033, 14034,
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14040, 14049, 14055, 14064
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* ISO C11 support:
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@ -3551,6 +3551,13 @@ expm1_test (void)
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TEST_f_f (expm1, 1, M_El - 1.0);
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TEST_f_f (expm1, 0.75L, 1.11700001661267466854536981983709561L);
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TEST_f_f (expm1, 50.0L, 5.1847055285870724640864533229334853848275e+21L);
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#ifndef TEST_FLOAT
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TEST_f_f (expm1, 127.0L, 1.4302079958348104463583671072905261080748e+55L);
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TEST_f_f (expm1, 500.0L, 1.4035922178528374107397703328409120821806e+217L);
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#endif
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#if defined TEST_LDOUBLE && LDBL_MAX_EXP >= 16384
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TEST_f_f (expm1, 11356.25L, 9.05128237311923300051376115753226014206e+4931L);
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#endif
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@ -3559,9 +3566,7 @@ expm1_test (void)
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TEST_f_f (expm1, 100000.0, plus_infty, OVERFLOW_EXCEPTION);
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check_int ("errno for expm1(large) == ERANGE", errno, ERANGE, 0, 0, 0);
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TEST_f_f (expm1, max_value, plus_infty, OVERFLOW_EXCEPTION);
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#ifndef TEST_LDOUBLE /* Bug 13923. */
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TEST_f_f (expm1, -max_value, -1);
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#endif
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END (expm1);
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}
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@ -28,6 +28,10 @@
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# define IEEE754_EXPL __ieee754_exp10l
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# define EXPL_FINITE __exp10l_finite
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# define FLDLOG fldl2t
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#elif defined USE_AS_EXPM1L
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# define IEEE754_EXPL __expm1l
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# undef EXPL_FINITE
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# define FLDLOG fldl2e
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#else
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# define IEEE754_EXPL __ieee754_expl
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# define EXPL_FINITE __expl_finite
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@ -69,6 +73,12 @@ csat: .byte 0, 0, 0, 0, 0, 0, 0, 0x80, 0x0e, 0x40
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.text
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ENTRY(IEEE754_EXPL)
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#ifdef USE_AS_EXPM1L
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movzwl 4+8(%esp), %eax
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xorb $0x80, %ah // invert sign bit (now 1 is "positive")
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cmpl $0xc006, %eax // is num positive and exp >= 6 (number is >= 128.0)?
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jae HIDDEN_JUMPTARGET (__expl) // (if num is denormal, it is at least >= 64.0)
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#endif
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fldt 4(%esp)
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/* I added the following ugly construct because expl(+-Inf) resulted
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in NaN. The ugliness results from the bright minds at Intel.
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@ -78,7 +88,9 @@ ENTRY(IEEE754_EXPL)
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#ifdef PIC
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LOAD_PIC_REG (cx)
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#endif
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#ifndef USE_AS_EXPM1L
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movzwl 4+8(%esp), %eax
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#endif
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andl $0x7fff, %eax
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cmpl $0x400d, %eax
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jle 3f
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@ -96,7 +108,16 @@ ENTRY(IEEE754_EXPL)
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andb $2, %ah
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jz 3f
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fchs
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3: FLDLOG /* 1 log2(base) */
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3:
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#ifdef USE_AS_EXPM1L
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/* Test for +-0 as argument. */
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fstsw %ax
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movb $0x45, %dh
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andb %ah, %dh
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cmpb $0x40, %dh
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je 2f
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#endif
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FLDLOG /* 1 log2(base) */
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fmul %st(1), %st /* 1 x log2(base) */
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frndint /* 1 i */
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fld %st(1) /* 2 x */
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@ -114,17 +135,39 @@ ENTRY(IEEE754_EXPL)
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fmul %st(4), %st /* 4 c1 * x */
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faddp %st, %st(1) /* 3 f = f + c1 * x */
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f2xm1 /* 3 2^(fract(x * log2(base))) - 1 */
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#ifdef USE_AS_EXPM1L
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fstp %st(1) /* 2 */
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fscale /* 2 scale factor is st(1); base^x - 2^i */
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fxch /* 2 i */
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fld1 /* 3 1.0 */
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fscale /* 3 2^i */
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fld1 /* 4 1.0 */
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fsubrp %st, %st(1) /* 3 2^i - 1.0 */
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fstp %st(1) /* 2 */
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faddp %st, %st(1) /* 1 base^x - 1.0 */
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#else
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fld1 /* 4 1.0 */
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faddp /* 3 2^(fract(x * log2(base))) */
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fstp %st(1) /* 2 */
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fscale /* 2 scale factor is st(1); base^x */
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fstp %st(1) /* 1 */
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#endif
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fstp %st(1) /* 0 */
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jmp 2f
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1: testl $0x200, %eax /* Test sign. */
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jz 2f /* If positive, jump. */
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fstp %st
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#ifdef USE_AS_EXPM1L
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fld1
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fchs
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#else
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fldz /* Set result to 0. */
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#endif
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2: ret
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END(IEEE754_EXPL)
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#ifdef USE_AS_EXPM1L
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libm_hidden_def (__expm1l)
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weak_alias (__expm1l, expm1l)
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#else
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strong_alias (IEEE754_EXPL, EXPL_FINITE)
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#endif
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@ -1008,10 +1008,6 @@ Test "cos_upward (9) == -0.9111302618846769883682947111811653112463":
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ildouble: 1
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ldouble: 1
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# cosh
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Test "cosh (0.75) == 1.29468328467684468784170818539018176":
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ildouble: 1
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# cosh_downward
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Test "cosh_downward (22) == 1792456423.065795780980053377632656584997":
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double: 1
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@ -1899,29 +1895,20 @@ double: 1
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float: 1
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idouble: 1
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ifloat: 1
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ildouble: 4
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ldouble: 4
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ildouble: 2
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ldouble: 2
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Test "sinh_downward (23) == 4872401723.124451299966006944252978187305":
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double: 1
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float: 1
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idouble: 1
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ifloat: 1
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ildouble: 2
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ldouble: 2
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Test "sinh_downward (24) == 13244561064.92173614705070540368454568168":
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float: 1
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ifloat: 1
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ildouble: 5
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ldouble: 5
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# sinh_tonearest
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Test "sinh_tonearest (22) == 1792456423.065795780701106568345764104225":
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ildouble: 3
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ldouble: 3
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Test "sinh_tonearest (23) == 4872401723.124451299966006944252978187305":
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ildouble: 1
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ldouble: 1
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Test "sinh_tonearest (24) == 13244561064.92173614705070540368454568168":
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ildouble: 6
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ldouble: 6
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ildouble: 2
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ldouble: 2
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# sinh_towardzero
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Test "sinh_towardzero (22) == 1792456423.065795780701106568345764104225":
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@ -1929,31 +1916,31 @@ double: 1
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float: 1
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idouble: 1
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ifloat: 1
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ildouble: 4
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ldouble: 4
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ildouble: 2
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ldouble: 2
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Test "sinh_towardzero (23) == 4872401723.124451299966006944252978187305":
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double: 1
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float: 1
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idouble: 1
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ifloat: 1
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ildouble: 2
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ldouble: 2
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Test "sinh_towardzero (24) == 13244561064.92173614705070540368454568168":
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float: 1
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ifloat: 1
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ildouble: 5
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ldouble: 5
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ildouble: 2
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ldouble: 2
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# sinh_upward
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Test "sinh_upward (22) == 1792456423.065795780701106568345764104225":
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ildouble: 16
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ldouble: 16
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ildouble: 1
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ldouble: 1
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Test "sinh_upward (23) == 4872401723.124451299966006944252978187305":
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ildouble: 27
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ldouble: 27
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ildouble: 1
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ldouble: 1
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Test "sinh_upward (24) == 13244561064.92173614705070540368454568168":
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double: 1
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idouble: 1
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ildouble: 7
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ldouble: 7
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# tan
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Test "tan (0x1p16383) == 0.422722393732022337800504160054440141575":
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@ -2587,9 +2574,6 @@ ifloat: 1
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ildouble: 1
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ldouble: 1
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Function: "cosh":
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ildouble: 1
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Function: "cosh_downward":
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double: 1
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float: 1
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@ -2862,26 +2846,22 @@ double: 1
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float: 1
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idouble: 1
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ifloat: 1
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ildouble: 5
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ldouble: 5
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Function: "sinh_tonearest":
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ildouble: 6
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ldouble: 6
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ildouble: 2
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ldouble: 2
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Function: "sinh_towardzero":
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double: 1
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float: 1
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idouble: 1
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ifloat: 1
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ildouble: 5
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ldouble: 5
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ildouble: 2
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ldouble: 2
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Function: "sinh_upward":
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double: 1
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idouble: 1
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ildouble: 27
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ldouble: 27
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ildouble: 1
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ldouble: 1
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Function: "tan":
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double: 1
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@ -1,89 +1,2 @@
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/* ix87 specific implementation of exp(x)-1.
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Copyright (C) 1996-1997, 2002, 2005, 2008, 2012 Free Software Foundation, Inc.
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This file is part of the GNU C Library.
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Contributed by Ulrich Drepper <drepper@cygnus.com>, 1996.
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Based on code by John C. Bowman <bowman@ipp-garching.mpg.de>.
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Corrections by H.J. Lu (hjl@gnu.ai.mit.edu), 1997.
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The GNU C Library is free software; you can redistribute it and/or
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modify it under the terms of the GNU Lesser General Public
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License as published by the Free Software Foundation; either
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version 2.1 of the License, or (at your option) any later version.
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The GNU C Library is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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Lesser General Public License for more details.
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You should have received a copy of the GNU Lesser General Public
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License along with the GNU C Library; if not, see
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<http://www.gnu.org/licenses/>. */
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/* Using: e^x - 1 = 2^(x * log2(e)) - 1 */
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#include <sysdep.h>
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#include <machine/asm.h>
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.section .rodata
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.align ALIGNARG(4)
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ASM_TYPE_DIRECTIVE(minus1,@object)
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minus1: .double -1.0
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ASM_SIZE_DIRECTIVE(minus1)
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ASM_TYPE_DIRECTIVE(one,@object)
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one: .double 1.0
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ASM_SIZE_DIRECTIVE(one)
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ASM_TYPE_DIRECTIVE(l2e,@object)
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l2e: .tfloat 1.442695040888963407359924681002
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ASM_SIZE_DIRECTIVE(l2e)
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#ifdef PIC
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#define MO(op) op##@GOTOFF(%edx)
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#else
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#define MO(op) op
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#endif
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.text
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ENTRY(__expm1l)
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movzwl 4+8(%esp), %eax // load sign bit and 15-bit exponent
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xorb $0x80, %ah // invert sign bit (now 1 is "positive")
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cmpl $0xc006, %eax // is num positive and exp >= 6 (number is >= 128.0)?
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jae HIDDEN_JUMPTARGET (__expl) // (if num is denormal, it is at least >= 64.0)
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fldt 4(%esp) // x
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fxam // Is NaN or +-Inf?
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fstsw %ax
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movb $0x45, %ch
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andb %ah, %ch
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cmpb $0x40, %ch
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je 3f // If +-0, jump.
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#ifdef PIC
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LOAD_PIC_REG (dx)
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#endif
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cmpb $0x05, %ch
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je 2f // If +-Inf, jump.
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fldt MO(l2e) // log2(e) : x
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fmulp // log2(e)*x
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fld %st // log2(e)*x : log2(e)*x
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frndint // int(log2(e)*x) : log2(e)*x
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fsubr %st, %st(1) // int(log2(e)*x) : fract(log2(e)*x)
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fxch // fract(log2(e)*x) : int(log2(e)*x)
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f2xm1 // 2^fract(log2(e)*x)-1 : int(log2(e)*x)
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fscale // 2^(log2(e)*x)-2^int(log2(e)*x) : int(log2(e)*x)
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fxch // int(log2(e)*x) : 2^(log2(e)*x)-2^int(log2(e)*x)
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fldl MO(one) // 1 : int(log2(e)*x) : 2^(log2(e)*x)-2^int(log2(e)*x)
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fscale // 2^int(log2(e)*x) : int(log2(e)*x) : 2^(log2(e)*x)-2^int(log2(e)*x)
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fsubrl MO(one) // 1-2^int(log2(e)*x) : int(log2(e)*x) : 2^(log2(e)*x)-2^int(log2(e)*x)
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fstp %st(1) // 1-2^int(log2(e)*x) : 2^(log2(e)*x)-2^int(log2(e)*x)
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fsubrp %st, %st(1) // 2^(log2(e)*x)
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ret
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2: testl $0x200, %eax // Test sign.
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jz 3f // If positive, jump.
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fstp %st
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fldl MO(minus1) // Set result to -1.0.
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3: ret
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END(__expm1l)
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libm_hidden_def (__expm1l)
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weak_alias (__expm1l, expm1l)
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#define USE_AS_EXPM1L
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#include <e_expl.S>
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@ -28,6 +28,10 @@
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# define IEEE754_EXPL __ieee754_exp10l
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# define EXPL_FINITE __exp10l_finite
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# define FLDLOG fldl2t
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#elif defined USE_AS_EXPM1L
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# define IEEE754_EXPL __expm1l
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# undef EXPL_FINITE
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# define FLDLOG fldl2e
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#else
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# define IEEE754_EXPL __ieee754_expl
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# define EXPL_FINITE __expl_finite
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@ -69,13 +73,21 @@ csat: .byte 0, 0, 0, 0, 0, 0, 0, 0x80, 0x0e, 0x40
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.text
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ENTRY(IEEE754_EXPL)
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#ifdef USE_AS_EXPM1L
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movzwl 8+8(%rsp), %eax
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xorb $0x80, %ah // invert sign bit (now 1 is "positive")
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cmpl $0xc006, %eax // is num positive and exp >= 6 (number is >= 128.0)?
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jae HIDDEN_JUMPTARGET (__expl) // (if num is denormal, it is at least >= 64.0)
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#endif
|
||||
fldt 8(%rsp)
|
||||
/* I added the following ugly construct because expl(+-Inf) resulted
|
||||
in NaN. The ugliness results from the bright minds at Intel.
|
||||
For the i686 the code can be written better.
|
||||
-- drepper@cygnus.com. */
|
||||
fxam /* Is NaN or +-Inf? */
|
||||
#ifndef USE_AS_EXPM1L
|
||||
movzwl 8+8(%rsp), %eax
|
||||
#endif
|
||||
andl $0x7fff, %eax
|
||||
cmpl $0x400d, %eax
|
||||
jle 3f
|
||||
@ -93,7 +105,16 @@ ENTRY(IEEE754_EXPL)
|
||||
andb $2, %ah
|
||||
jz 3f
|
||||
fchs
|
||||
3: FLDLOG /* 1 log2(base) */
|
||||
3:
|
||||
#ifdef USE_AS_EXPM1L
|
||||
/* Test for +-0 as argument. */
|
||||
fstsw %ax
|
||||
movb $0x45, %dh
|
||||
andb %ah, %dh
|
||||
cmpb $0x40, %dh
|
||||
je 2f
|
||||
#endif
|
||||
FLDLOG /* 1 log2(base) */
|
||||
fmul %st(1), %st /* 1 x log2(base) */
|
||||
frndint /* 1 i */
|
||||
fld %st(1) /* 2 x */
|
||||
@ -111,17 +132,39 @@ ENTRY(IEEE754_EXPL)
|
||||
fmul %st(4), %st /* 4 c1 * x */
|
||||
faddp %st, %st(1) /* 3 f = f + c1 * x */
|
||||
f2xm1 /* 3 2^(fract(x * log2(base))) - 1 */
|
||||
#ifdef USE_AS_EXPM1L
|
||||
fstp %st(1) /* 2 */
|
||||
fscale /* 2 scale factor is st(1); base^x - 2^i */
|
||||
fxch /* 2 i */
|
||||
fld1 /* 3 1.0 */
|
||||
fscale /* 3 2^i */
|
||||
fld1 /* 4 1.0 */
|
||||
fsubrp %st, %st(1) /* 3 2^i - 1.0 */
|
||||
fstp %st(1) /* 2 */
|
||||
faddp %st, %st(1) /* 1 base^x - 1.0 */
|
||||
#else
|
||||
fld1 /* 4 1.0 */
|
||||
faddp /* 3 2^(fract(x * log2(base))) */
|
||||
fstp %st(1) /* 2 */
|
||||
fscale /* 2 scale factor is st(1); base^x */
|
||||
fstp %st(1) /* 1 */
|
||||
#endif
|
||||
fstp %st(1) /* 0 */
|
||||
jmp 2f
|
||||
1: testl $0x200, %eax /* Test sign. */
|
||||
jz 2f /* If positive, jump. */
|
||||
fstp %st
|
||||
#ifdef USE_AS_EXPM1L
|
||||
fld1
|
||||
fchs
|
||||
#else
|
||||
fldz /* Set result to 0. */
|
||||
#endif
|
||||
2: ret
|
||||
END(IEEE754_EXPL)
|
||||
#ifdef USE_AS_EXPM1L
|
||||
libm_hidden_def (__expm1l)
|
||||
weak_alias (__expm1l, expm1l)
|
||||
#else
|
||||
strong_alias (IEEE754_EXPL, EXPL_FINITE)
|
||||
#endif
|
||||
|
||||
@ -1358,6 +1358,9 @@ ifloat: 1
|
||||
Test "expm1 (11356.25) == 9.05128237311923300051376115753226014206e+4931":
|
||||
ildouble: 1
|
||||
ldouble: 1
|
||||
Test "expm1 (500.0) == 1.4035922178528374107397703328409120821806e+217":
|
||||
double: 1
|
||||
idouble: 1
|
||||
|
||||
# gamma
|
||||
Test "gamma (-0.5) == log(2*sqrt(pi))":
|
||||
@ -1831,62 +1834,47 @@ Test "sincos (pi/6, &sin_res, &cos_res) puts 0.866025403784438646763723170752936
|
||||
float: 1
|
||||
ifloat: 1
|
||||
|
||||
# sinh
|
||||
Test "sinh (0x8p-32) == 1.86264514923095703232705808926175479e-9":
|
||||
ildouble: 1
|
||||
ldouble: 1
|
||||
|
||||
# sinh_downward
|
||||
Test "sinh_downward (22) == 1792456423.065795780701106568345764104225":
|
||||
float: 1
|
||||
ifloat: 1
|
||||
ildouble: 4
|
||||
ldouble: 4
|
||||
ildouble: 2
|
||||
ldouble: 2
|
||||
Test "sinh_downward (23) == 4872401723.124451299966006944252978187305":
|
||||
float: 1
|
||||
ifloat: 1
|
||||
ildouble: 2
|
||||
ldouble: 2
|
||||
Test "sinh_downward (24) == 13244561064.92173614705070540368454568168":
|
||||
float: 1
|
||||
ifloat: 1
|
||||
ildouble: 5
|
||||
ldouble: 5
|
||||
|
||||
# sinh_tonearest
|
||||
Test "sinh_tonearest (22) == 1792456423.065795780701106568345764104225":
|
||||
ildouble: 3
|
||||
ldouble: 3
|
||||
Test "sinh_tonearest (23) == 4872401723.124451299966006944252978187305":
|
||||
ildouble: 1
|
||||
ldouble: 1
|
||||
Test "sinh_tonearest (24) == 13244561064.92173614705070540368454568168":
|
||||
ildouble: 6
|
||||
ldouble: 6
|
||||
ildouble: 2
|
||||
ldouble: 2
|
||||
|
||||
# sinh_towardzero
|
||||
Test "sinh_towardzero (22) == 1792456423.065795780701106568345764104225":
|
||||
float: 1
|
||||
ifloat: 1
|
||||
ildouble: 4
|
||||
ldouble: 4
|
||||
ildouble: 2
|
||||
ldouble: 2
|
||||
Test "sinh_towardzero (23) == 4872401723.124451299966006944252978187305":
|
||||
float: 1
|
||||
ifloat: 1
|
||||
ildouble: 2
|
||||
ldouble: 2
|
||||
Test "sinh_towardzero (24) == 13244561064.92173614705070540368454568168":
|
||||
float: 1
|
||||
ifloat: 1
|
||||
ildouble: 5
|
||||
ldouble: 5
|
||||
ildouble: 2
|
||||
ldouble: 2
|
||||
|
||||
# sinh_upward
|
||||
Test "sinh_upward (22) == 1792456423.065795780701106568345764104225":
|
||||
ildouble: 16
|
||||
ldouble: 16
|
||||
ildouble: 1
|
||||
ldouble: 1
|
||||
Test "sinh_upward (23) == 4872401723.124451299966006944252978187305":
|
||||
ildouble: 27
|
||||
ldouble: 27
|
||||
Test "sinh_upward (24) == 13244561064.92173614705070540368454568168":
|
||||
ildouble: 7
|
||||
ldouble: 7
|
||||
ildouble: 1
|
||||
ldouble: 1
|
||||
|
||||
# tan
|
||||
Test "tan (0x1p16383) == 0.422722393732022337800504160054440141575":
|
||||
@ -2733,29 +2721,21 @@ ifloat: 1
|
||||
ildouble: 1
|
||||
ldouble: 1
|
||||
|
||||
Function: "sinh":
|
||||
ildouble: 1
|
||||
ldouble: 1
|
||||
|
||||
Function: "sinh_downward":
|
||||
float: 1
|
||||
ifloat: 1
|
||||
ildouble: 5
|
||||
ldouble: 5
|
||||
|
||||
Function: "sinh_tonearest":
|
||||
ildouble: 6
|
||||
ldouble: 6
|
||||
ildouble: 2
|
||||
ldouble: 2
|
||||
|
||||
Function: "sinh_towardzero":
|
||||
float: 1
|
||||
ifloat: 1
|
||||
ildouble: 5
|
||||
ldouble: 5
|
||||
ildouble: 2
|
||||
ldouble: 2
|
||||
|
||||
Function: "sinh_upward":
|
||||
ildouble: 27
|
||||
ldouble: 27
|
||||
ildouble: 1
|
||||
ldouble: 1
|
||||
|
||||
Function: "tan":
|
||||
double: 1
|
||||
|
||||
@ -1,85 +1,2 @@
|
||||
/* ix87 specific implementation of exp(x)-1.
|
||||
Copyright (C) 1996,1997,2001,2002,2008,2009,2012 Free Software Foundation, Inc.
|
||||
This file is part of the GNU C Library.
|
||||
Contributed by Ulrich Drepper <drepper@cygnus.com>, 1996.
|
||||
Based on code by John C. Bowman <bowman@ipp-garching.mpg.de>.
|
||||
Corrections by H.J. Lu (hjl@gnu.ai.mit.edu), 1997.
|
||||
|
||||
The GNU C Library is free software; you can redistribute it and/or
|
||||
modify it under the terms of the GNU Lesser General Public
|
||||
License as published by the Free Software Foundation; either
|
||||
version 2.1 of the License, or (at your option) any later version.
|
||||
|
||||
The GNU C Library is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
|
||||
Lesser General Public License for more details.
|
||||
|
||||
You should have received a copy of the GNU Lesser General Public
|
||||
License along with the GNU C Library; if not, see
|
||||
<http://www.gnu.org/licenses/>. */
|
||||
|
||||
/* Using: e^x - 1 = 2^(x * log2(e)) - 1 */
|
||||
|
||||
#include <machine/asm.h>
|
||||
|
||||
.section .rodata
|
||||
|
||||
.align ALIGNARG(4)
|
||||
ASM_TYPE_DIRECTIVE(minus1,@object)
|
||||
minus1: .double -1.0
|
||||
ASM_SIZE_DIRECTIVE(minus1)
|
||||
ASM_TYPE_DIRECTIVE(one,@object)
|
||||
one: .double 1.0
|
||||
ASM_SIZE_DIRECTIVE(one)
|
||||
ASM_TYPE_DIRECTIVE(l2e,@object)
|
||||
l2e: .tfloat 1.442695040888963407359924681002
|
||||
ASM_SIZE_DIRECTIVE(l2e)
|
||||
|
||||
#ifdef PIC
|
||||
#define MO(op) op##(%rip)
|
||||
#else
|
||||
#define MO(op) op
|
||||
#endif
|
||||
|
||||
.text
|
||||
ENTRY(__expm1l)
|
||||
movzwl 8+8(%rsp), %eax // load sign bit and 15-bit exponent
|
||||
xorb $0x80, %ah // invert sign bit (now 1 is "positive")
|
||||
cmpl $0xc006, %eax // is num positive and exp >= 6 (number is >= 128.0)?
|
||||
jae __expl // (if num is denormal, it is at least >= 64.0)
|
||||
|
||||
fldt 8(%rsp) // x
|
||||
fxam // Is NaN or +-Inf?
|
||||
fstsw %ax
|
||||
movb $0x45, %ch
|
||||
andb %ah, %ch
|
||||
cmpb $0x40, %ch
|
||||
je 3f // If +-0, jump.
|
||||
cmpb $0x05, %ch
|
||||
je 2f // If +-Inf, jump.
|
||||
|
||||
fldt MO(l2e) // log2(e) : x
|
||||
fmulp // log2(e)*x
|
||||
fld %st // log2(e)*x : log2(e)*x
|
||||
frndint // int(log2(e)*x) : log2(e)*x
|
||||
fsubr %st, %st(1) // int(log2(e)*x) : fract(log2(e)*x)
|
||||
fxch // fract(log2(e)*x) : int(log2(e)*x)
|
||||
f2xm1 // 2^fract(log2(e)*x)-1 : int(log2(e)*x)
|
||||
fscale // 2^(log2(e)*x)-2^int(log2(e)*x) : int(log2(e)*x)
|
||||
fxch // int(log2(e)*x) : 2^(log2(e)*x)-2^int(log2(e)*x)
|
||||
fldl MO(one) // 1 : int(log2(e)*x) : 2^(log2(e)*x)-2^int(log2(e)*x)
|
||||
fscale // 2^int(log2(e)*x) : int(log2(e)*x) : 2^(log2(e)*x)-2^int(log2(e)*x)
|
||||
fsubrl MO(one) // 1-2^int(log2(e)*x) : int(log2(e)*x) : 2^(log2(e)*x)-2^int(log2(e)*x)
|
||||
fstp %st(1) // 1-2^int(log2(e)*x) : 2^(log2(e)*x)-2^int(log2(e)*x)
|
||||
fsubrp %st, %st(1) // 2^(log2(e)*x)-1
|
||||
ret
|
||||
|
||||
2: testl $0x200, %eax // Test sign.
|
||||
jz 3f // If positive, jump.
|
||||
fstp %st
|
||||
fldl MO(minus1) // Set result to -1.0.
|
||||
3: ret
|
||||
END(__expm1l)
|
||||
libm_hidden_def (__expm1l)
|
||||
weak_alias (__expm1l, expm1l)
|
||||
#define USE_AS_EXPM1L
|
||||
#include <e_expl.S>
|
||||
|
||||
Loading…
Reference in New Issue
Block a user