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9bd3ef8e19
The i386 and x86_64 implementations of expl, exp10l and expm1l (code shared between the functions) return sNaN for sNaN input. This patch fixes them to add NaN inputs to themselves so that qNaN is returned in this case. Tested for x86_64 and x86. [BZ #20226] * sysdeps/i386/fpu/e_expl.S (IEEE754_EXPL): Add NaN argument to itself. * sysdeps/x86_64/fpu/e_expl.S (IEEE754_EXPL): Likewise. * math/libm-test.inc (exp_test_data): Add sNaN tests. (exp10_test_data): Likewise. (expm1_test_data): Likewise.
220 lines
5.6 KiB
ArmAsm
220 lines
5.6 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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#include <x86_64-math-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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DEFINE_LDBL_MIN
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#endif
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#ifdef PIC
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# define MO(op) op##(%rip)
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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 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
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fldt 8(%rsp)
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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 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 6f /* 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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/* Test for arguments that are small but not subnormal. */
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movzwl 8+8(%rsp), %eax
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andl $0x7fff, %eax
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cmpl $0x3fbf, %eax
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jge 3f
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/* Argument's exponent below -64; avoid spurious underflow if
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normal. */
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cmpl $0x0001, %eax
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jge 2f
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/* Force underflow and return the argument, to avoid wrong signs
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of zero results from the code below in some rounding modes. */
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fld %st
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fmul %st
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fstp %st
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jmp 2f
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#else
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movzwl 8+8(%rsp), %eax
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andl $0x7fff, %eax
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cmpl $0x400d, %eax
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jg 5f
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cmpl $0x3fbc, %eax
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jge 3f
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/* Argument's exponent below -67, result rounds to 1. */
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fld1
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faddp
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jmp 2f
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5: /* 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 6f /* 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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fstcw -4(%rsp)
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movl $0xf3ff, %edx
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andl -4(%rsp), %edx
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movl %edx, -8(%rsp)
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fldcw -8(%rsp)
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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(%rsp)
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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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LDBL_CHECK_FORCE_UFLOW_NONNEG
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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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6: /* NaN argument. */
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fadd %st
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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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