| 1 | /* ix87 specific implementation of pow function.
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| 2 | Copyright (C) 1996, 1997, 1998, 1999, 2001, 2004 Free Software Foundation
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| 3 | This file is part of the GNU C Library.
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| 4 | Contributed by Ulrich Drepper <drepper@cygnus.com>, 1996.
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| 5 |
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| 6 | The GNU C Library is free software; you can redistribute it and/or
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| 7 | modify it under the terms of the GNU Lesser General Public
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| 8 | License as published by the Free Software Foundation; either
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| 9 | version 2.1 of the License, or (at your option) any later version.
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| 10 |
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| 11 | The GNU C Library is distributed in the hope that it will be useful,
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| 12 | but WITHOUT ANY WARRANTY; without even the implied warranty of
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| 13 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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| 14 | Lesser General Public License for more details.
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| 15 |
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| 16 | You should have received a copy of the GNU Lesser General Public
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| 17 | License along with the GNU C Library; if not, write to the Free
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| 18 | Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
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| 19 | 02111-1307 USA. */
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| 20 |
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| 21 | /*
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| 22 | * Oracle LGPL Disclaimer: For the avoidance of doubt, except that if any license choice
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| 23 | * other than GPL or LGPL is available it will apply instead, Oracle elects to use only
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| 24 | * the Lesser General Public License version 2.1 (LGPLv2) at this time for any software where
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| 25 | * a choice of LGPL license versions is made available with the language indicating
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| 26 | * that LGPLv2 or any later version may be used, or where a choice of which version
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| 27 | * of the LGPL is applied is otherwise unspecified.
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| 28 | */
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| 29 |
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| 30 | /*#include <machine/asm.h>*/
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| 31 | #include <iprt/cdefs.h>
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| 32 |
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| 33 | #define ALIGNARG(log2) 1<<log2
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| 34 | #define ASM_TYPE_DIRECTIVE(name,typearg) .type name,typearg;
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| 35 | #define ASM_SIZE_DIRECTIVE(name) .size name,.-name;
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| 36 | #define ASM_GLOBAL_DIRECTIVE .global
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| 37 |
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| 38 | #define C_LABEL(name) name:
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| 39 | #define C_SYMBOL_NAME(name) name
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| 40 |
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| 41 | #define ENTRY(name) \
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| 42 | ASM_GLOBAL_DIRECTIVE C_SYMBOL_NAME(name); \
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| 43 | ASM_TYPE_DIRECTIVE (C_SYMBOL_NAME(name),@function) \
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| 44 | .align ALIGNARG(4); \
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| 45 | C_LABEL(name)
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| 46 |
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| 47 | #undef END
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| 48 | #define END(name) \
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| 49 | ASM_SIZE_DIRECTIVE(name)
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| 50 |
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| 51 |
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| 52 | #ifdef __ELF__
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| 53 | .section .rodata
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| 54 | #else
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| 55 | .text
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| 56 | #endif
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| 57 |
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| 58 | .align ALIGNARG(4)
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| 59 | ASM_TYPE_DIRECTIVE(infinity,@object)
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| 60 | inf_zero:
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| 61 | infinity:
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| 62 | .byte 0, 0, 0, 0, 0, 0, 0xf0, 0x7f
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| 63 | ASM_SIZE_DIRECTIVE(infinity)
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| 64 | ASM_TYPE_DIRECTIVE(zero,@object)
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| 65 | zero: .double 0.0
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| 66 | ASM_SIZE_DIRECTIVE(zero)
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| 67 | ASM_TYPE_DIRECTIVE(minf_mzero,@object)
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| 68 | minf_mzero:
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| 69 | minfinity:
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| 70 | .byte 0, 0, 0, 0, 0, 0, 0xf0, 0xff
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| 71 | mzero:
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| 72 | .byte 0, 0, 0, 0, 0, 0, 0, 0x80
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| 73 | ASM_SIZE_DIRECTIVE(minf_mzero)
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| 74 | ASM_TYPE_DIRECTIVE(one,@object)
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| 75 | one: .double 1.0
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| 76 | ASM_SIZE_DIRECTIVE(one)
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| 77 | ASM_TYPE_DIRECTIVE(limit,@object)
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| 78 | limit: .double 0.29
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| 79 | ASM_SIZE_DIRECTIVE(limit)
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| 80 | ASM_TYPE_DIRECTIVE(p63,@object)
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| 81 | p63:
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| 82 | .byte 0, 0, 0, 0, 0, 0, 0xe0, 0x43
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| 83 | ASM_SIZE_DIRECTIVE(p63)
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| 84 |
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| 85 | //#ifdef PIC
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| 86 | //#define MO(op) op##(%rip)
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| 87 | //#else
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| 88 | #define MO(op) op
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| 89 | //#endif
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| 90 |
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| 91 | .text
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| 92 | /*ENTRY(__ieee754_powl)*/
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| 93 | ENTRY(RT_NOCRT(powl))
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| 94 |
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| 95 | fldt 24(%rsp) // y
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| 96 | fxam
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| 97 |
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| 98 |
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| 99 | fnstsw
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| 100 | movb %ah, %dl
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| 101 | andb $0x45, %ah
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| 102 | cmpb $0x40, %ah // is y == 0 ?
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| 103 | je 11f
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| 104 |
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| 105 | cmpb $0x05, %ah // is y == ±inf ?
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| 106 | je 12f
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| 107 |
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| 108 | cmpb $0x01, %ah // is y == NaN ?
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| 109 | je 30f
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| 110 |
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| 111 | fldt 8(%rsp) // x : y
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| 112 |
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| 113 | fxam
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| 114 | fnstsw
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| 115 | movb %ah, %dh
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| 116 | andb $0x45, %ah
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| 117 | cmpb $0x40, %ah
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| 118 | je 20f // x is ±0
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| 119 |
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| 120 | cmpb $0x05, %ah
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| 121 | je 15f // x is ±inf
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| 122 |
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| 123 | fxch // y : x
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| 124 |
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| 125 | /* fistpll raises invalid exception for |y| >= 1L<<63. */
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| 126 | fldl MO(p63) // 1L<<63 : y : x
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| 127 | fld %st(1) // y : 1L<<63 : y : x
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| 128 | fabs // |y| : 1L<<63 : y : x
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| 129 | fcomip %st(1), %st // 1L<<63 : y : x
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| 130 | fstp %st(0) // y : x
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| 131 | jnc 2f
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| 132 |
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| 133 | /* First see whether `y' is a natural number. In this case we
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| 134 | can use a more precise algorithm. */
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| 135 | fld %st // y : y : x
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| 136 | fistpll -8(%rsp) // y : x
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| 137 | fildll -8(%rsp) // int(y) : y : x
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| 138 | fucomip %st(1),%st // y : x
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| 139 | jne 2f
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| 140 |
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| 141 | /* OK, we have an integer value for y. */
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| 142 | mov -8(%rsp),%eax
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| 143 | mov -4(%rsp),%edx
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| 144 | orl $0, %edx
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| 145 | fstp %st(0) // x
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| 146 | jns 4f // y >= 0, jump
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| 147 | fdivrl MO(one) // 1/x (now referred to as x)
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| 148 | negl %eax
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| 149 | adcl $0, %edx
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| 150 | negl %edx
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| 151 | 4: fldl MO(one) // 1 : x
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| 152 | fxch
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| 153 |
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| 154 | 6: shrdl $1, %edx, %eax
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| 155 | jnc 5f
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| 156 | fxch
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| 157 | fmul %st(1) // x : ST*x
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| 158 | fxch
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| 159 | 5: fmul %st(0), %st // x*x : ST*x
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| 160 | shrl $1, %edx
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| 161 | movl %eax, %ecx
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| 162 | orl %edx, %ecx
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| 163 | jnz 6b
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| 164 | fstp %st(0) // ST*x
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| 165 | ret
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| 166 |
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| 167 | /* y is ±NAN */
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| 168 | 30: fldt 8(%rsp) // x : y
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| 169 | fldl MO(one) // 1.0 : x : y
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| 170 | fucomip %st(1),%st // x : y
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| 171 | je 31f
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| 172 | fxch // y : x
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| 173 | 31: fstp %st(1)
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| 174 | ret
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| 175 |
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| 176 | .align ALIGNARG(4)
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| 177 | 2: /* y is a real number. */
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| 178 | fxch // x : y
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| 179 | fldl MO(one) // 1.0 : x : y
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| 180 | fld %st(1) // x : 1.0 : x : y
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| 181 | fsub %st(1) // x-1 : 1.0 : x : y
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| 182 | fabs // |x-1| : 1.0 : x : y
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| 183 | fcompl MO(limit) // 1.0 : x : y
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| 184 | fnstsw
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| 185 | fxch // x : 1.0 : y
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| 186 | test $4500,%eax
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| 187 | jz 7f
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| 188 | fsub %st(1) // x-1 : 1.0 : y
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| 189 | fyl2xp1 // log2(x) : y
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| 190 | jmp 8f
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| 191 |
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| 192 | 7: fyl2x // log2(x) : y
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| 193 | 8: fmul %st(1) // y*log2(x) : y
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| 194 | fxam
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| 195 | fnstsw
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| 196 | andb $0x45, %ah
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| 197 | cmpb $0x05, %ah // is y*log2(x) == ±inf ?
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| 198 | je 28f
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| 199 | fst %st(1) // y*log2(x) : y*log2(x)
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| 200 | frndint // int(y*log2(x)) : y*log2(x)
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| 201 | fsubr %st, %st(1) // int(y*log2(x)) : fract(y*log2(x))
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| 202 | fxch // fract(y*log2(x)) : int(y*log2(x))
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| 203 | f2xm1 // 2^fract(y*log2(x))-1 : int(y*log2(x))
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| 204 | faddl MO(one) // 2^fract(y*log2(x)) : int(y*log2(x))
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| 205 | fscale // 2^fract(y*log2(x))*2^int(y*log2(x)) : int(y*log2(x))
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| 206 | fstp %st(1) // 2^fract(y*log2(x))*2^int(y*log2(x))
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| 207 | ret
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| 208 |
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| 209 | 28: fstp %st(1) // y*log2(x)
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| 210 | fldl MO(one) // 1 : y*log2(x)
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| 211 | fscale // 2^(y*log2(x)) : y*log2(x)
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| 212 | fstp %st(1) // 2^(y*log2(x))
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| 213 | ret
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| 214 |
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| 215 | // pow(x,±0) = 1
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| 216 | .align ALIGNARG(4)
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| 217 | 11: fstp %st(0) // pop y
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| 218 | fldl MO(one)
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| 219 | ret
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| 220 |
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| 221 | // y == ±inf
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| 222 | .align ALIGNARG(4)
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| 223 | 12: fstp %st(0) // pop y
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| 224 | fldt 8(%rsp) // x
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| 225 | fabs
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| 226 | fcompl MO(one) // < 1, == 1, or > 1
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| 227 | fnstsw
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| 228 | andb $0x45, %ah
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| 229 | cmpb $0x45, %ah
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| 230 | je 13f // jump if x is NaN
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| 231 |
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| 232 | cmpb $0x40, %ah
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| 233 | je 14f // jump if |x| == 1
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| 234 |
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| 235 | shlb $1, %ah
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| 236 | xorb %ah, %dl
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| 237 | andl $2, %edx
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| 238 | #ifdef PIC
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| 239 | lea inf_zero(%rip),%rcx
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| 240 | fldl (%rcx, %rdx, 4)
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| 241 | #else
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| 242 | fldl inf_zero(,%rdx, 4)
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| 243 | #endif
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| 244 | ret
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| 245 |
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| 246 | .align ALIGNARG(4)
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| 247 | 14: fldl MO(one)
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| 248 | ret
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| 249 |
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| 250 | .align ALIGNARG(4)
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| 251 | 13: fldt 8(%rsp) // load x == NaN
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| 252 | ret
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| 253 |
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| 254 | .align ALIGNARG(4)
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| 255 | // x is ±inf
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| 256 | 15: fstp %st(0) // y
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| 257 | testb $2, %dh
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| 258 | jz 16f // jump if x == +inf
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| 259 |
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| 260 | // We must find out whether y is an odd integer.
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| 261 | fld %st // y : y
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| 262 | fistpll -8(%rsp) // y
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| 263 | fildll -8(%rsp) // int(y) : y
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| 264 | fucomip %st(1),%st
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| 265 | ffreep %st // <empty>
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| 266 | jne 17f
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| 267 |
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| 268 | // OK, the value is an integer, but is it odd?
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| 269 | mov -8(%rsp), %eax
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| 270 | mov -4(%rsp), %edx
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| 271 | andb $1, %al
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| 272 | jz 18f // jump if not odd
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| 273 | // It's an odd integer.
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| 274 | shrl $31, %edx
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| 275 | #ifdef PIC
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| 276 | lea minf_mzero(%rip),%rcx
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| 277 | fldl (%rcx, %rdx, 8)
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| 278 | #else
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| 279 | fldl minf_mzero(,%rdx, 8)
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| 280 | #endif
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| 281 | ret
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| 282 |
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| 283 | .align ALIGNARG(4)
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| 284 | 16: fcompl MO(zero)
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| 285 | fnstsw
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| 286 | shrl $5, %eax
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| 287 | andl $8, %eax
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| 288 | #ifdef PIC
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| 289 | lea inf_zero(%rip),%rcx
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| 290 | fldl (%rcx, %rax, 1)
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| 291 | #else
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| 292 | fldl inf_zero(,%rax, 1)
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| 293 | #endif
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| 294 | ret
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| 295 |
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| 296 | .align ALIGNARG(4)
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| 297 | 17: shll $30, %edx // sign bit for y in right position
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| 298 | 18: shrl $31, %edx
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| 299 | #ifdef PIC
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| 300 | lea inf_zero(%rip),%rcx
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| 301 | fldl (%rcx, %rdx, 8)
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| 302 | #else
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| 303 | fldl inf_zero(,%rdx, 8)
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| 304 | #endif
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| 305 | ret
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| 306 |
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| 307 | .align ALIGNARG(4)
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| 308 | // x is ±0
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| 309 | 20: fstp %st(0) // y
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| 310 | testb $2, %dl
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| 311 | jz 21f // y > 0
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| 312 |
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| 313 | // x is ±0 and y is < 0. We must find out whether y is an odd integer.
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| 314 | testb $2, %dh
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| 315 | jz 25f
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| 316 |
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| 317 | fld %st // y : y
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| 318 | fistpll -8(%rsp) // y
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| 319 | fildll -8(%rsp) // int(y) : y
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| 320 | fucomip %st(1),%st
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| 321 | ffreep %st // <empty>
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| 322 | jne 26f
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| 323 |
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| 324 | // OK, the value is an integer, but is it odd?
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| 325 | mov -8(%rsp),%eax
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| 326 | mov -4(%rsp),%edx
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| 327 | andb $1, %al
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| 328 | jz 27f // jump if not odd
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| 329 | // It's an odd integer.
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| 330 | // Raise divide-by-zero exception and get minus infinity value.
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| 331 | fldl MO(one)
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| 332 | fdivl MO(zero)
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| 333 | fchs
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| 334 | ret
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| 335 |
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| 336 | 25: fstp %st(0)
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| 337 | 26:
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| 338 | 27: // Raise divide-by-zero exception and get infinity value.
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| 339 | fldl MO(one)
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| 340 | fdivl MO(zero)
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| 341 | ret
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| 342 |
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| 343 | .align ALIGNARG(4)
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| 344 | // x is ±0 and y is > 0. We must find out whether y is an odd integer.
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| 345 | 21: testb $2, %dh
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| 346 | jz 22f
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| 347 |
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| 348 | fld %st // y : y
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| 349 | fistpll -8(%rsp) // y
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| 350 | fildll -8(%rsp) // int(y) : y
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| 351 | fucomip %st(1),%st
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| 352 | ffreep %st // <empty>
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| 353 | jne 23f
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| 354 |
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| 355 | // OK, the value is an integer, but is it odd?
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| 356 | mov -8(%rsp),%eax
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| 357 | mov -4(%rsp),%edx
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| 358 | andb $1, %al
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| 359 | jz 24f // jump if not odd
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| 360 | // It's an odd integer.
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| 361 | fldl MO(mzero)
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| 362 | ret
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| 363 |
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| 364 | 22: fstp %st(0)
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| 365 | 23:
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| 366 | 24: fldl MO(zero)
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| 367 | ret
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| 368 |
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| 369 | /*END(__ieee754_powl)*/
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| 370 | END(RT_NOCRT(powl))
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| 371 |
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