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cb0937b299
In the x86 / x86_64 implementations of expm1l, when expm1l's result should underflow to 0 (argument minus the least subnormal, in some rounding modes), it can be a zero of the wrong sign. This patch fixes this by returning the argument with underflow forced in that case (this is a 1ulp error relative to the correctly rounded result of -0, which is OK in terms of the documented accuracy goals, whereas a result with the wrong sign never is). Tested for x86_64 and x86. [BZ #18569] * sysdeps/i386/fpu/e_expl.S (IEEE754_EXPL) [USE_AS_EXPM1L]: Force underflow and return argument in case of subnormal argument. * sysdeps/x86_64/fpu/e_expl.S (IEEE754_EXPL) [USE_AS_EXPM1L]: Likewise. * math/auto-libm-test-in: Add more tests of expm1. * math/auto-libm-test-out: Regenerated.
227 lines
5.8 KiB
ArmAsm
227 lines
5.8 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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.type cmin,@object
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cmin: .byte 0, 0, 0, 0, 0, 0, 0, 0x80, 0x1, 0
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.byte 0, 0, 0, 0, 0, 0
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ASM_SIZE_DIRECTIVE(cmin)
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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 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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/* 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 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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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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/* Ensure underflow for tiny result. */
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fldt MO(cmin) /* 2 cmin */
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fld %st(1) /* 3 */
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fcomip %st(1), %st /* 2 */
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fstp %st /* 1 */
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jnc 6f
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fld %st
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fmul %st
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fstp %st
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#endif
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6: 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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