/* Compute cubic root of long double value. Copyright (C) 1997-2016 Free Software Foundation, Inc. This file is part of the GNU C Library. Contributed by Dirk Alboth and Ulrich Drepper , 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, see . */ #include .section .rodata .align ALIGNARG(4) .type f8,@object f8: .tfloat 0.161617097923756032 ASM_SIZE_DIRECTIVE(f8) .align ALIGNARG(4) .type f7,@object f7: .tfloat -0.988553671195413709 ASM_SIZE_DIRECTIVE(f7) .align ALIGNARG(4) .type f6,@object f6: .tfloat 2.65298938441952296 ASM_SIZE_DIRECTIVE(f6) .align ALIGNARG(4) .type f5,@object f5: .tfloat -4.11151425200350531 ASM_SIZE_DIRECTIVE(f5) .align ALIGNARG(4) .type f4,@object f4: .tfloat 4.09559907378707839 ASM_SIZE_DIRECTIVE(f4) .align ALIGNARG(4) .type f3,@object f3: .tfloat -2.82414939754975962 ASM_SIZE_DIRECTIVE(f3) .align ALIGNARG(4) .type f2,@object f2: .tfloat 1.67595307700780102 ASM_SIZE_DIRECTIVE(f2) .align ALIGNARG(4) .type f1,@object f1: .tfloat 0.338058687610520237 ASM_SIZE_DIRECTIVE(f1) #define CBRT2 1.2599210498948731648 #define ONE_CBRT2 0.793700525984099737355196796584 #define SQR_CBRT2 1.5874010519681994748 #define ONE_SQR_CBRT2 0.629960524947436582364439673883 /* We make the entries in the following table all 16 bytes wide to avoid having to implement a multiplication by 10. */ .type factor,@object .align ALIGNARG(4) factor: .tfloat ONE_SQR_CBRT2 .byte 0, 0, 0, 0, 0, 0 .tfloat ONE_CBRT2 .byte 0, 0, 0, 0, 0, 0 .tfloat 1.0 .byte 0, 0, 0, 0, 0, 0 .tfloat CBRT2 .byte 0, 0, 0, 0, 0, 0 .tfloat SQR_CBRT2 ASM_SIZE_DIRECTIVE(factor) .type two64,@object .align ALIGNARG(4) two64: .byte 0, 0, 0, 0, 0, 0, 0xf0, 0x43 ASM_SIZE_DIRECTIVE(two64) #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(__cbrtl) movl 4(%esp), %ecx movl 12(%esp), %eax orl 8(%esp), %ecx movl %eax, %edx andl $0x7fff, %eax orl %eax, %ecx jz 1f xorl %ecx, %ecx cmpl $0x7fff, %eax je 1f #ifdef PIC pushl %ebx cfi_adjust_cfa_offset (4) cfi_rel_offset (ebx, 0) LOAD_PIC_REG (bx) #endif cmpl $0, %eax jne 2f #ifdef PIC fldt 8(%esp) #else fldt 4(%esp) #endif fmull MO(two64) movl $-64, %ecx #ifdef PIC fstpt 8(%esp) movl 16(%esp), %eax #else fstpt 4(%esp) movl 12(%esp), %eax #endif movl %eax, %edx andl $0x7fff, %eax 2: andl $0x8000, %edx subl $16382, %eax orl $0x3ffe, %edx addl %eax, %ecx #ifdef PIC movl %edx, 16(%esp) fldt 8(%esp) /* xm */ #else movl %edx, 12(%esp) fldt 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. */ fldt MO(f8) /* f8 : xm */ fmul %st(1) /* f8*xm : xm */ fldt MO(f7) faddp /* f7+f8*xm : xm */ fmul %st(1) /* (f7+f8*xm)*xm : xm */ movl $1431655766, %eax fldt MO(f6) faddp /* f6+(f7+f8*xm)*xm : xm */ imull %ecx fmul %st(1) /* (f6+(f7+f8*xm)*xm)*xm : xm */ movl %ecx, %eax fldt MO(f5) faddp /* f5+(f6+(f7+f8*xm)*xm)*xm : xm */ sarl $31, %eax fmul %st(1) /* (f5+(f6+(f7+f8*xm)*xm)*xm)*xm : xm */ subl %eax, %edx fldt MO(f4) faddp /* f4+(f5+(f6+(f7+f8*xm)*xm)*xm)*xm : xm */ fmul %st(1) /* (f4+(f5+(f6+(f7+f8*xm)*xm)*xm)*xm)*xm : xm */ fldt MO(f3) faddp /* f3+(f4+(f5+(f6+(f7+f8*xm)*xm)*xm)*xm)*xm : xm */ fmul %st(1) /* (f3+(f4+(f5+(f6+(f7+f8*xm)*xm)*xm)*xm)*xm)*xm : xm */ fldt MO(f2) faddp /* f2+(f3+(f4+(f5+(f6+(f7+f8*xm)*xm)*xm)*xm)*xm)*xm : xm */ fmul %st(1) /* (f2+(f3+(f4+(f5+(f6+(f7+f8*xm)*xm)*xm)*xm)*xm)*xm)*xm : xm */ fldt MO(f1) faddp /* u:=f1+(f2+(f3+(f4+(f5+(f6+(f7+f8*xm)*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 $4, %ecx fmulp /* u*(t2+2*xm) : 2*t2+xm */ fdivp %st, %st(1) /* u*(t2+2*xm)/(2*t2+xm) */ fldt MOX(32+factor,%ecx) fmulp /* 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 16(%esp), %eax popl %ebx cfi_adjust_cfa_offset (-4) cfi_restore (ebx) #else movl 12(%esp), %eax #endif testl $0x8000, %eax fstp %st(1) jz 4f fchs 4: ret /* Return the argument. */ 1: fldt 4(%esp) ret END(__cbrtl) weak_alias (__cbrtl, cbrtl)