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5b0626b9c5
This patch fixes bug 16356, bad results from x86 / x86_64 expl / exp10l in directed rounding modes, the most serious of the bugs shown up by my patch expanding libm test coverage. When I fixed bug 16293, I thought it was only necessary to set round-to-nearest when using frndint in expm1 functions, because in other cases the cancellation error from having the resulting fractional part close to 1 or -1 would not be significant. However, in expl and exp10l, the way the final fractional part gets computed (something more complicated than a simple subtraction, because more precision is needed than you'd get that way) can result in a value outside the range [-1, 1] when the argument to frndint was very close to an integer and was rounded the "wrong" way because of the rounding mode - and the f2xm1 instruction has undefined results if its argument is outside [-1, 1], so resulting in the large errors seen. So this patch removes the USE_AS_EXPM1L conditionals on the round-to-nearest settings, so all of expl, expm1l and exp10l now get round-to-nearest used for frndint (meaning the final fractional part can at most be slightly above 0.5 in magnitude). Associated tests of exp and exp10 are added and testing of exp10 in directed rounding modes enabled. Tested x86_64 and x86 and ulps updated accordingly. * sysdeps/i386/fpu/e_expl.S (IEEE754_EXPL): Also set round-to-nearest for [!USE_AS_EXPM1L]. * sysdeps/x86_64/fpu/e_expl.S (IEEE754_EXPL): Likewise. * math/auto-libm-test-in: Do not expect cosh tests to fail. Add more tests of exp and exp10. Expect some exp10 tests to miss exceptions or fail in directed rounding modes. * math/auto-libm-test-out: Regenerated. * math/libm-test.inc (exp10_tonearest_test_data): New array. (exp10_test_tonearest): New function. (exp10_towardzero_test_data): New array. (exp10_test_towardzero): New function. (exp10_downward_test_data): New array. (exp10_test_downward): New function. (exp10_upward_test_data): New array. (exp10_test_upward): New function. (main): Call the new functions. * sysdeps/i386/fpu/libm-test-ulps: Update. * sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
199 lines
5.1 KiB
ArmAsm
199 lines
5.1 KiB
ArmAsm
/*
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* Written by J.T. Conklin <jtc@netbsd.org>.
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* Public domain.
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*
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* Adapted for `long double' by Ulrich Drepper <drepper@cygnus.com>.
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*/
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/*
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* The 8087 method for the exponential function is to calculate
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* exp(x) = 2^(x log2(e))
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* after separating integer and fractional parts
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* x log2(e) = i + f, |f| <= .5
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* 2^i is immediate but f needs to be precise for long double accuracy.
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* Suppress range reduction error in computing f by the following.
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* Separate x into integer and fractional parts
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* x = xi + xf, |xf| <= .5
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* Separate log2(e) into the sum of an exact number c0 and small part c1.
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* c0 + c1 = log2(e) to extra precision
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* Then
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* f = (c0 xi - i) + c0 xf + c1 x
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* where c0 xi is exact and so also is (c0 xi - i).
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* -- moshier@na-net.ornl.gov
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*/
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#include <machine/asm.h>
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#ifdef USE_AS_EXP10L
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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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# define FLDLOG fldl2e
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#endif
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.section .rodata.cst16,"aM",@progbits,16
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.p2align 4
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#ifdef USE_AS_EXP10L
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.type c0,@object
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c0: .byte 0, 0, 0, 0, 0, 0, 0x9a, 0xd4, 0x00, 0x40
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.byte 0, 0, 0, 0, 0, 0
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ASM_SIZE_DIRECTIVE(c0)
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.type c1,@object
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c1: .byte 0x58, 0x92, 0xfc, 0x15, 0x37, 0x9a, 0x97, 0xf0, 0xef, 0x3f
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.byte 0, 0, 0, 0, 0, 0
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ASM_SIZE_DIRECTIVE(c1)
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#else
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.type c0,@object
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c0: .byte 0, 0, 0, 0, 0, 0, 0xaa, 0xb8, 0xff, 0x3f
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.byte 0, 0, 0, 0, 0, 0
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ASM_SIZE_DIRECTIVE(c0)
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.type c1,@object
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c1: .byte 0x20, 0xfa, 0xee, 0xc2, 0x5f, 0x70, 0xa5, 0xec, 0xed, 0x3f
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.byte 0, 0, 0, 0, 0, 0
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ASM_SIZE_DIRECTIVE(c1)
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#endif
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#ifndef USE_AS_EXPM1L
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.type csat,@object
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csat: .byte 0, 0, 0, 0, 0, 0, 0, 0x80, 0x0e, 0x40
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.byte 0, 0, 0, 0, 0, 0
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ASM_SIZE_DIRECTIVE(csat)
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#endif
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#ifdef PIC
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# define MO(op) op##@GOTOFF(%ecx)
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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(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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For the i686 the code can be written better.
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-- drepper@cygnus.com. */
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fxam /* Is NaN or +-Inf? */
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#ifdef PIC
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LOAD_PIC_REG (cx)
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#endif
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#ifdef USE_AS_EXPM1L
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xorb $0x80, %ah
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cmpl $0xc006, %eax
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fstsw %ax
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movb $0x45, %dh
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jb 4f
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/* Below -64.0 (may be -NaN or -Inf). */
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andb %ah, %dh
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cmpb $0x01, %dh
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je 2f /* Is +-NaN, jump. */
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jmp 1f /* -large, possibly -Inf. */
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4: /* In range -64.0 to 64.0 (may be +-0 but not NaN or +-Inf). */
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/* Test for +-0 as argument. */
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andb %ah, %dh
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cmpb $0x40, %dh
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je 2f
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#else
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movzwl 4+8(%esp), %eax
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andl $0x7fff, %eax
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cmpl $0x400d, %eax
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jle 3f
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/* Overflow, underflow or infinity or NaN 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 $0x05, %dh
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je 1f /* Is +-Inf, jump. */
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cmpb $0x01, %dh
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je 2f /* Is +-NaN, jump. */
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/* Overflow or underflow; saturate. */
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fstp %st
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fldt MO(csat)
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andb $2, %ah
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jz 3f
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fchs
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#endif
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3: FLDLOG /* 1 log2(base) */
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fmul %st(1), %st /* 1 x log2(base) */
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/* Set round-to-nearest temporarily. */
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subl $8, %esp
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cfi_adjust_cfa_offset (8)
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fstcw 4(%esp)
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movl $0xf3ff, %edx
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andl 4(%esp), %edx
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movl %edx, (%esp)
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fldcw (%esp)
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frndint /* 1 i */
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fld %st(1) /* 2 x */
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frndint /* 2 xi */
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fldcw 4(%esp)
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addl $8, %esp
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cfi_adjust_cfa_offset (-8)
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fld %st(1) /* 3 i */
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fldt MO(c0) /* 4 c0 */
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fld %st(2) /* 5 xi */
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fmul %st(1), %st /* 5 c0 xi */
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fsubp %st, %st(2) /* 4 f = c0 xi - i */
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fld %st(4) /* 5 x */
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fsub %st(3), %st /* 5 xf = x - xi */
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fmulp %st, %st(1) /* 4 c0 xf */
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faddp %st, %st(1) /* 3 f = f + c0 xf */
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fldt MO(c1) /* 4 */
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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:
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#ifdef USE_AS_EXPM1L
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/* For expm1l, only negative sign gets here. */
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fstp %st
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fld1
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fchs
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#else
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testl $0x200, %eax /* Test sign. */
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jz 2f /* If positive, jump. */
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fstp %st
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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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