1 | /* ix87 specific implementation of exp(x)-1. |
2 | Copyright (C) 1996-2024 Free Software Foundation, Inc. |
3 | This file is part of the GNU C Library. |
4 | |
5 | The GNU C Library is free software; you can redistribute it and/or |
6 | modify it under the terms of the GNU Lesser General Public |
7 | License as published by the Free Software Foundation; either |
8 | version 2.1 of the License, or (at your option) any later version. |
9 | |
10 | The GNU C Library is distributed in the hope that it will be useful, |
11 | but WITHOUT ANY WARRANTY; without even the implied warranty of |
12 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
13 | Lesser General Public License for more details. |
14 | |
15 | You should have received a copy of the GNU Lesser General Public |
16 | License along with the GNU C Library; if not, see |
17 | <https://www.gnu.org/licenses/>. */ |
18 | |
19 | /* Using: e^x - 1 = 2^(x * log2(e)) - 1 */ |
20 | |
21 | #include <sysdep.h> |
22 | #include <machine/asm.h> |
23 | #include <i386-math-asm.h> |
24 | #include <libm-alias-double.h> |
25 | |
26 | .section .rodata |
27 | |
28 | .align ALIGNARG(4) |
29 | .type minus1,@object |
30 | minus1: .double -1.0 |
31 | ASM_SIZE_DIRECTIVE(minus1) |
32 | .type one,@object |
33 | one: .double 1.0 |
34 | ASM_SIZE_DIRECTIVE(one) |
35 | .type l2e,@object |
36 | l2e: .quad 0xb8aa3b295c17f0bc /* 1.442695040888963407359924681002 */ |
37 | .short 0x3fff |
38 | ASM_SIZE_DIRECTIVE(l2e) |
39 | |
40 | DEFINE_DBL_MIN |
41 | |
42 | #ifdef PIC |
43 | #define MO(op) op##@GOTOFF(%edx) |
44 | #else |
45 | #define MO(op) op |
46 | #endif |
47 | |
48 | .text |
49 | ENTRY(__expm1) |
50 | movzwl 4+6(%esp), %eax |
51 | xorb $0x80, %ah // invert sign bit (now 1 is "positive") |
52 | cmpl $0xc086, %eax // is num >= 704? |
53 | jae HIDDEN_JUMPTARGET (__exp) |
54 | |
55 | fldl 4(%esp) // x |
56 | fxam // Is NaN, +-Inf or +-0? |
57 | xorb $0x80, %ah |
58 | cmpl $0xc043, %eax // is num <= -38.0? |
59 | fstsw %ax |
60 | movb $0x45, %ch |
61 | jb 4f |
62 | |
63 | // Below -38.0 (may be -NaN or -Inf). |
64 | andb %ah, %ch |
65 | #ifdef PIC |
66 | LOAD_PIC_REG (dx) |
67 | #endif |
68 | cmpb $0x01, %ch |
69 | je 5f // If -NaN, jump. |
70 | jmp 2f // -large, possibly -Inf. |
71 | |
72 | 4: // In range -38.0 to 704.0 (may be +-0 but not NaN or +-Inf). |
73 | andb %ah, %ch |
74 | cmpb $0x40, %ch |
75 | je 3f // If +-0, jump. |
76 | #ifdef PIC |
77 | LOAD_PIC_REG (dx) |
78 | #endif |
79 | |
80 | 5: fldt MO(l2e) // log2(e) : x |
81 | fmulp // log2(e)*x |
82 | fld %st // log2(e)*x : log2(e)*x |
83 | // Set round-to-nearest temporarily. |
84 | subl $8, %esp |
85 | cfi_adjust_cfa_offset (8) |
86 | fstcw 4(%esp) |
87 | movl $0xf3ff, %ecx |
88 | andl 4(%esp), %ecx |
89 | movl %ecx, (%esp) |
90 | fldcw (%esp) |
91 | frndint // int(log2(e)*x) : log2(e)*x |
92 | fldcw 4(%esp) |
93 | addl $8, %esp |
94 | cfi_adjust_cfa_offset (-8) |
95 | fsubr %st, %st(1) // int(log2(e)*x) : fract(log2(e)*x) |
96 | fxch // fract(log2(e)*x) : int(log2(e)*x) |
97 | f2xm1 // 2^fract(log2(e)*x)-1 : int(log2(e)*x) |
98 | fscale // 2^(log2(e)*x)-2^int(log2(e)*x) : int(log2(e)*x) |
99 | fxch // int(log2(e)*x) : 2^(log2(e)*x)-2^int(log2(e)*x) |
100 | fldl MO(one) // 1 : int(log2(e)*x) : 2^(log2(e)*x)-2^int(log2(e)*x) |
101 | fscale // 2^int(log2(e)*x) : int(log2(e)*x) : 2^(log2(e)*x)-2^int(log2(e)*x) |
102 | fsubrl MO(one) // 1-2^int(log2(e)*x) : int(log2(e)*x) : 2^(log2(e)*x)-2^int(log2(e)*x) |
103 | fstp %st(1) // 1-2^int(log2(e)*x) : 2^(log2(e)*x)-2^int(log2(e)*x) |
104 | fsubrp %st, %st(1) // 2^(log2(e)*x) |
105 | DBL_CHECK_FORCE_UFLOW |
106 | ret |
107 | |
108 | 2: fstp %st |
109 | fldl MO(minus1) // Set result to -1.0. |
110 | 3: ret |
111 | END(__expm1) |
112 | libm_alias_double (__expm1, expm1) |
113 | |