fpc/rtl/i386/math.inc

365 lines
9.9 KiB
PHP

{
This file is part of the Free Pascal run time library.
Copyright (c) 1999-2001 by the Free Pascal development team
Implementation of mathematical routines (for extended type)
See the file COPYING.FPC, included in this distribution,
for details about the copyright.
This program 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.
**********************************************************************}
{-------------------------------------------------------------------------
Using functions from AMath/DAMath libraries, which are covered by the
following license:
(C) Copyright 2009-2013 Wolfgang Ehrhardt
This software is provided 'as-is', without any express or implied warranty.
In no event will the authors be held liable for any damages arising from
the use of this software.
Permission is granted to anyone to use this software for any purpose,
including commercial applications, and to alter it and redistribute it
freely, subject to the following restrictions:
1. The origin of this software must not be misrepresented; you must not
claim that you wrote the original software. If you use this software in
a product, an acknowledgment in the product documentation would be
appreciated but is not required.
2. Altered source versions must be plainly marked as such, and must not be
misrepresented as being the original software.
3. This notice may not be removed or altered from any source distribution.
----------------------------------------------------------------------------}
{****************************************************************************
FPU Control word
****************************************************************************}
{$push}
{$codealign constmin=16}
const
FPC_ABSMASK_SINGLE: array[0..1] of qword=($7fffffff7fffffff,$7fffffff7fffffff); cvar; public;
FPC_ABSMASK_DOUBLE: array[0..1] of qword=($7fffffffffffffff,$7fffffffffffffff); cvar; public;
{$pop}
procedure Set8087CW(cw:word);
begin
{ pic-safe ; cw will not be a regvar because it's accessed from }
{ assembler }
default8087cw:=cw;
asm
fnclex
fldcw cw
end;
end;
function Get8087CW:word;assembler;
asm
pushl $0
fnstcw (%esp)
popl %eax
end;
procedure SetMXCSR(w : dword);
begin
defaultmxcsr:=w;
{$ifndef OLD_ASSEMBLER}
asm
ldmxcsr w
end;
{$else}
{ Use convoluted code to avoid relocation on
ldmxcsr opcode, and use .byte version }
asm
mov w,%eax
subl $4,%esp
mov %eax,(%esp)
//ldmxcsr (%esp)
.byte 0x0f,0xae,0x14,0x24
addl $4,%esp
end;
{$endif OLD_ASSEMBLER}
end;
function GetMXCSR : dword;
var
_w : dword;
begin
{$ifndef OLD_ASSEMBLER}
asm
stmxcsr _w
end;
{$else}
asm
{ Use convoluted code to avoid relocation on
ldmxcsr opcode, and use .byte version }
subl $4,%esp
//stmxcsr (%esp)
.byte 0x0f,0xae,0x14,0x24
mov (%esp),%eax
addl $4,%esp
mov %eax,_w
end;
{$endif OLD_ASSEMBLER}
result:=_w;
end;
function GetNativeFPUControlWord: TNativeFPUControlWord; {$if defined(SYSTEMINLINE)}inline;{$endif}
begin
result.cw8087:=Get8087CW;
if has_sse_support then
result.MXCSR:=GetMXCSR
else
result.MXCSR:=-1;
end;
procedure SetNativeFPUControlWord(const cw: TNativeFPUControlWord); {$if defined(SYSTEMINLINE)}inline;{$endif}
begin
Set8087CW(cw.cw8087);
if cw.MXCSR<>-1 then
SetMXCSR(cw.MXCSR);
end;
procedure SetSSECSR(w : dword);
begin
SetMXCSR(w);
end;
function GetSSECSR: dword;
begin
result:=GetMXCSR;
end;
{****************************************************************************
EXTENDED data type routines
****************************************************************************}
{$define FPC_SYSTEM_HAS_ABS}
function fpc_abs_real(d : ValReal) : ValReal;compilerproc;
begin
{ Function is handled internal in the compiler }
runerror(207);
result:=0;
end;
{$define FPC_SYSTEM_HAS_SQR}
function fpc_sqr_real(d : ValReal) : ValReal;compilerproc;
begin
{ Function is handled internal in the compiler }
runerror(207);
result:=0;
end;
{$define FPC_SYSTEM_HAS_SQRT}
function fpc_sqrt_real(d : ValReal) : ValReal;compilerproc;
begin
{ Function is handled internal in the compiler }
runerror(207);
result:=0;
end;
{$define FPC_SYSTEM_HAS_ARCTAN}
function fpc_arctan_real(d : ValReal) : ValReal;compilerproc;
begin
{ Function is handled internal in the compiler }
runerror(207);
result:=0;
end;
{$define FPC_SYSTEM_HAS_LN}
function fpc_ln_real(d : ValReal) : ValReal;compilerproc;
begin
{ Function is handled internal in the compiler }
runerror(207);
result:=0;
end;
{$define FPC_SYSTEM_HAS_SIN}
function fpc_sin_real(d : ValReal) : ValReal;compilerproc;
begin
{ Function is handled internal in the compiler }
runerror(207);
result:=0;
end;
{$define FPC_SYSTEM_HAS_COS}
function fpc_cos_real(d : ValReal) : ValReal;compilerproc;
begin
{ Function is handled internal in the compiler }
runerror(207);
result:=0;
end;
{$ifdef OLD_ASSEMBLER}
{$define DISABLE_PIC_IN_EXP_REAL}
{$endif}
{$define FPC_SYSTEM_HAS_EXP}
{ exp function adapted from AMath library (C) Copyright 2009-2013 Wolfgang Ehrhardt
* translated into AT&T syntax
+ PIC support
* return +Inf/0 for +Inf/-Inf input, instead of NaN }
function fpc_exp_real(d : ValReal) : ValReal;assembler;compilerproc;
const
ln2hi: double=6.9314718036912382E-001;
ln2lo: double=1.9082149292705877E-010;
large: single=24576.0;
two: single=2.0;
half: single=0.5;
asm
{$ifndef DISABLE_PIC_IN_EXP_REAL}
call .LPIC
.LPIC:
pop %ecx
{$endif not DISABLE_PIC_IN_EXP_REAL}
fldt d
fldl2e
fmul %st(1),%st { z = d * log2(e) }
frndint
{ Calculate frac(z) using modular arithmetic to avoid precision loss. }
{$ifndef DISABLE_PIC_IN_EXP_REAL}
fldl ln2hi-.LPIC(%ecx)
{$else}
fldl ln2hi
{$endif}
fmul %st(1),%st
fsubrp %st,%st(2)
{$ifndef DISABLE_PIC_IN_EXP_REAL}
fldl ln2lo-.LPIC(%ecx)
{$else}
fldl ln2lo
{$endif}
fmul %st(1),%st
fsubrp %st,%st(2)
fxch %st(1) { (d-int(z)*ln2_hi)-int(z)*ln2_lo }
fldl2e
fmulp %st,%st(1) { frac(z) }
{ The above code can result in |frac(z)|>1, particularly when rounding mode
is not "round to nearest". f2xm1 is undefined in this case, so a check
is necessary. Furthermore, frac(z) evaluates to NaN for d=+-Inf. }
fld %st
fabs
fld1
fcompp
fstsw %ax
sahf
jp .L3 { NaN }
jae .L1 { frac(z) <= 1 }
fld %st(1)
fabs
{$ifndef DISABLE_PIC_IN_EXP_REAL}
fcomps large-.LPIC(%ecx)
{$else}
fcomps large
{$endif}
fstsw %ax
sahf
jb .L0 { int(z) < 24576 }
.L3:
fstp %st { zero out frac(z), hard way because }
fldz { "fsub %st,%st" does not work for NaN }
jmp .L1
.L0:
{ Calculate 2**frac(z)-1 as N*(N+2), where N=2**(frac(z)/2)-1 }
{$ifndef DISABLE_PIC_IN_EXP_REAL}
fmuls half-.LPIC(%ecx)
{$else}
fmuls half
{$endif}
f2xm1
fld %st
{$ifndef DISABLE_PIC_IN_EXP_REAL}
fadds two-.LPIC(%ecx)
{$else}
fadds two
{$endif}
fmulp %st,%st(1)
jmp .L2
.L1:
f2xm1
.L2:
fld1
faddp %st,%st(1)
fscale
fstp %st(1)
end;
{$define FPC_SYSTEM_HAS_FRAC}
function fpc_frac_real(d : ValReal) : ValReal;assembler;compilerproc;
asm
subl $4,%esp
fnstcw (%esp)
fwait
movw (%esp),%cx
orw $0x0f00,(%esp)
fldcw (%esp)
fldt d
frndint
fldt d
fsub %st(1),%st
fstp %st(1)
movw %cx,(%esp)
fldcw (%esp)
end;
{$define FPC_SYSTEM_HAS_INT}
function fpc_int_real(d : ValReal) : ValReal;assembler;compilerproc;
asm
subl $4,%esp
fnstcw (%esp)
fwait
movw (%esp),%cx
orw $0x0f00,(%esp)
fldcw (%esp)
fwait
fldt d
frndint
fwait
movw %cx,(%esp)
fldcw (%esp)
end;
{$define FPC_SYSTEM_HAS_TRUNC}
function fpc_trunc_real(d : ValReal) : int64;assembler;compilerproc;
asm
subl $12,%esp
fldt d
fnstcw (%esp)
movw (%esp),%cx
orw $0x0f00,(%esp)
fldcw (%esp)
movw %cx,(%esp)
fistpq 4(%esp)
fldcw (%esp)
fwait
movl 4(%esp),%eax
movl 8(%esp),%edx
end;
{$define FPC_SYSTEM_HAS_ROUND}
{ keep for bootstrapping with 2.0.x }
function fpc_round_real(d : ValReal) : int64;compilerproc;assembler;
var
res : int64;
asm
fldt d
fistpq res
fwait
movl res,%eax
movl res+4,%edx
end;