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f88acd39da
Bug 16293 is inaccuracy of x86/x86_64 versions of expm1, near 0 in directed rounding modes, that arises from frndint rounding the exponent to 1 or -1 instead of 0, resulting in large cancellation error. This inaccuracy in turn affects other functions such as sinh that use expm1. This patch fixes the problem by setting round-to-nearest mode temporarily around the affected calls to frndint. I don't think this is needed for other uses of frndint, such as in exp itself, as only for expm1 is the cancellation error significant. Tested x86_64 and x86 and ulps updated accordingly. * sysdeps/i386/fpu/e_expl.S (IEEE754_EXPL) [USE_AS_EXPM1L]: Set round-to-nearest mode when using frndint. * sysdeps/i386/fpu/s_expm1.S (__expm1): Likewise. * sysdeps/i386/fpu/s_expm1f.S (__expm1f): Likewise. * sysdeps/x86_64/fpu/e_expl.S (IEEE754_EXPL) [USE_AS_EXPM1L]: Likewise. * math/auto-libm-test-in: Add more tests of expm1. Do not expect sinh test to fail. * math/auto-libm-test-out: Regenerated. * math/libm-test.inc (TEST_COND_x86_64): Remove macro. (TEST_COND_x86): Likewise. (expm1_tonearest_test_data): New array. (expm1_test_tonearest): New function. (expm1_towardzero_test_data): New array. (expm1_test_towardzero): New function. (expm1_downward_test_data): New array. (expm1_test_downward): New function. (expm1_upward_test_data): New array. (expm1_test_upward): New function. (main): Run the new test functions. * sysdeps/i386/fpu/libm-test-ulps: Update. * sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
110 lines
3.1 KiB
ArmAsm
110 lines
3.1 KiB
ArmAsm
/* ix87 specific implementation of exp(x)-1.
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Copyright (C) 1996-2013 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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.type minus1,@object
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minus1: .double -1.0
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ASM_SIZE_DIRECTIVE(minus1)
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.type one,@object
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one: .double 1.0
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ASM_SIZE_DIRECTIVE(one)
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.type 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(__expm1)
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movzwl 4+6(%esp), %eax
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xorb $0x80, %ah // invert sign bit (now 1 is "positive")
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cmpl $0xc086, %eax // is num >= 704?
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jae HIDDEN_JUMPTARGET (__exp)
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fldl 4(%esp) // x
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fxam // Is NaN, +-Inf or +-0?
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xorb $0x80, %ah
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cmpl $0xc043, %eax // is num <= -38.0?
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fstsw %ax
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movb $0x45, %ch
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jb 4f
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// Below -38.0 (may be -NaN or -Inf).
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andb %ah, %ch
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#ifdef PIC
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LOAD_PIC_REG (dx)
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#endif
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cmpb $0x01, %ch
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je 5f // If -NaN, jump.
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jmp 2f // -large, possibly -Inf.
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4: // In range -38.0 to 704.0 (may be +-0 but not NaN or +-Inf).
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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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5: 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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// 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, %ecx
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andl 4(%esp), %ecx
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movl %ecx, (%esp)
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fldcw (%esp)
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frndint // int(log2(e)*x) : log2(e)*x
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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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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: 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(__expm1)
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weak_alias (__expm1, expm1)
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