| /* Compute cubic root of double value. |
| Copyright (C) 1997, 2005 Free Software Foundation, Inc. |
| This file is part of the GNU C Library. |
| Contributed by Dirk Alboth <dirka@uni-paderborn.de> and |
| Ulrich Drepper <drepper@cygnus.com>, 1997. |
| |
| The GNU C Library is free software; you can redistribute it and/or |
| modify it under the terms of the GNU Lesser General Public |
| License as published by the Free Software Foundation; either |
| version 2.1 of the License, or (at your option) any later version. |
| |
| The GNU C Library is distributed in the hope that it will be useful, |
| but WITHOUT ANY WARRANTY; without even the implied warranty of |
| MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
| Lesser General Public License for more details. |
| |
| You should have received a copy of the GNU Lesser General Public |
| License along with the GNU C Library; if not, write to the Free |
| Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA |
| 02111-1307 USA. */ |
| |
| #include <machine/asm.h> |
| |
| #ifdef __ELF__ |
| .section .rodata |
| #else |
| .text |
| #endif |
| |
| .align ALIGNARG(4) |
| ASM_TYPE_DIRECTIVE(f7,@object) |
| f7: .double -0.145263899385486377 |
| ASM_SIZE_DIRECTIVE(f7) |
| ASM_TYPE_DIRECTIVE(f6,@object) |
| f6: .double 0.784932344976639262 |
| ASM_SIZE_DIRECTIVE(f6) |
| ASM_TYPE_DIRECTIVE(f5,@object) |
| f5: .double -1.83469277483613086 |
| ASM_SIZE_DIRECTIVE(f5) |
| ASM_TYPE_DIRECTIVE(f4,@object) |
| f4: .double 2.44693122563534430 |
| ASM_SIZE_DIRECTIVE(f4) |
| ASM_TYPE_DIRECTIVE(f3,@object) |
| f3: .double -2.11499494167371287 |
| ASM_SIZE_DIRECTIVE(f3) |
| ASM_TYPE_DIRECTIVE(f2,@object) |
| f2: .double 1.50819193781584896 |
| ASM_SIZE_DIRECTIVE(f2) |
| ASM_TYPE_DIRECTIVE(f1,@object) |
| f1: .double 0.354895765043919860 |
| ASM_SIZE_DIRECTIVE(f1) |
| |
| #define CBRT2 1.2599210498948731648 |
| #define ONE_CBRT2 0.793700525984099737355196796584 |
| #define SQR_CBRT2 1.5874010519681994748 |
| #define ONE_SQR_CBRT2 0.629960524947436582364439673883 |
| |
| ASM_TYPE_DIRECTIVE(factor,@object) |
| factor: .double ONE_SQR_CBRT2 |
| .double ONE_CBRT2 |
| .double 1.0 |
| .double CBRT2 |
| .double SQR_CBRT2 |
| ASM_SIZE_DIRECTIVE(factor) |
| |
| ASM_TYPE_DIRECTIVE(two54,@object) |
| two54: .byte 0, 0, 0, 0, 0, 0, 0x50, 0x43 |
| ASM_SIZE_DIRECTIVE(two54) |
| |
| #ifdef PIC |
| #define MO(op) op##@GOTOFF(%ebx) |
| #define MOX(op,x) op##@GOTOFF(%ebx,x,1) |
| #else |
| #define MO(op) op |
| #define MOX(op,x) op(x) |
| #endif |
| |
| .text |
| ENTRY(__cbrt) |
| movl 4(%esp), %ecx |
| movl 8(%esp), %eax |
| movl %eax, %edx |
| andl $0x7fffffff, %eax |
| orl %eax, %ecx |
| jz 1f |
| xorl %ecx, %ecx |
| cmpl $0x7ff00000, %eax |
| jae 1f |
| |
| #ifdef PIC |
| pushl %ebx |
| cfi_adjust_cfa_offset (4) |
| cfi_rel_offset (ebx, 0) |
| LOAD_PIC_REG (bx) |
| #endif |
| |
| cmpl $0x00100000, %eax |
| jae 2f |
| |
| #ifdef PIC |
| fldl 8(%esp) |
| #else |
| fldl 4(%esp) |
| #endif |
| fmull MO(two54) |
| movl $-54, %ecx |
| #ifdef PIC |
| fstpl 8(%esp) |
| movl 12(%esp), %eax |
| #else |
| fstpl 4(%esp) |
| movl 8(%esp), %eax |
| #endif |
| movl %eax, %edx |
| andl $0x7fffffff, %eax |
| |
| 2: shrl $20, %eax |
| andl $0x800fffff, %edx |
| subl $1022, %eax |
| orl $0x3fe00000, %edx |
| addl %eax, %ecx |
| #ifdef PIC |
| movl %edx, 12(%esp) |
| |
| fldl 8(%esp) /* xm */ |
| #else |
| movl %edx, 8(%esp) |
| |
| fldl 4(%esp) /* xm */ |
| #endif |
| fabs |
| |
| /* The following code has two tracks: |
| a) compute the normalized cbrt value |
| b) compute xe/3 and xe%3 |
| The right track computes the value for b) and this is done |
| in an optimized way by avoiding division. |
| |
| But why two tracks at all? Very easy: efficiency. Some FP |
| instruction can overlap with a certain amount of integer (and |
| FP) instructions. So we get (except for the imull) all |
| instructions for free. */ |
| |
| fld %st(0) /* xm : xm */ |
| |
| fmull MO(f7) /* f7*xm : xm */ |
| movl $1431655766, %eax |
| faddl MO(f6) /* f6+f7*xm : xm */ |
| imull %ecx |
| fmul %st(1) /* (f6+f7*xm)*xm : xm */ |
| movl %ecx, %eax |
| faddl MO(f5) /* f5+(f6+f7*xm)*xm : xm */ |
| sarl $31, %eax |
| fmul %st(1) /* (f5+(f6+f7*xm)*xm)*xm : xm */ |
| subl %eax, %edx |
| faddl MO(f4) /* f4+(f5+(f6+f7*xm)*xm)*xm : xm */ |
| fmul %st(1) /* (f4+(f5+(f6+f7*xm)*xm)*xm)*xm : xm */ |
| faddl MO(f3) /* f3+(f4+(f5+(f6+f7*xm)*xm)*xm)*xm : xm */ |
| fmul %st(1) /* (f3+(f4+(f5+(f6+f7*xm)*xm)*xm)*xm)*xm : xm */ |
| faddl MO(f2) /* f2+(f3+(f4+(f5+(f6+f7*xm)*xm)*xm)*xm)*xm : xm */ |
| fmul %st(1) /* (f2+(f3+(f4+(f5+(f6+f7*xm)*xm)*xm)*xm)*xm)*xm : xm */ |
| faddl MO(f1) /* u:=f1+(f2+(f3+(f4+(f5+(f6+f7*xm)*xm)*xm)*xm)*xm)*xm : xm */ |
| |
| fld %st /* u : u : xm */ |
| fmul %st(1) /* u*u : u : xm */ |
| fld %st(2) /* xm : u*u : u : xm */ |
| fadd %st /* 2*xm : u*u : u : xm */ |
| fxch %st(1) /* u*u : 2*xm : u : xm */ |
| fmul %st(2) /* t2:=u*u*u : 2*xm : u : xm */ |
| movl %edx, %eax |
| fadd %st, %st(1) /* t2 : t2+2*xm : u : xm */ |
| leal (%edx,%edx,2),%edx |
| fadd %st(0) /* 2*t2 : t2+2*xm : u : xm */ |
| subl %edx, %ecx |
| faddp %st, %st(3) /* t2+2*xm : u : 2*t2+xm */ |
| shll $3, %ecx |
| fmulp /* u*(t2+2*xm) : 2*t2+xm */ |
| fdivp %st, %st(1) /* u*(t2+2*xm)/(2*t2+xm) */ |
| fmull MOX(16+factor,%ecx) /* u*(t2+2*xm)/(2*t2+xm)*FACT */ |
| pushl %eax |
| cfi_adjust_cfa_offset (4) |
| fildl (%esp) /* xe/3 : u*(t2+2*xm)/(2*t2+xm)*FACT */ |
| fxch /* u*(t2+2*xm)/(2*t2+xm)*FACT : xe/3 */ |
| fscale /* u*(t2+2*xm)/(2*t2+xm)*FACT*2^xe/3 */ |
| popl %edx |
| cfi_adjust_cfa_offset (-4) |
| #ifdef PIC |
| movl 12(%esp), %eax |
| popl %ebx |
| cfi_adjust_cfa_offset (-4) |
| cfi_restore (ebx) |
| #else |
| movl 8(%esp), %eax |
| #endif |
| testl %eax, %eax |
| fstp %st(1) |
| jns 4f |
| fchs |
| 4: ret |
| |
| /* Return the argument. */ |
| 1: fldl 4(%esp) |
| ret |
| END(__cbrt) |
| weak_alias (__cbrt, cbrt) |
