浮点程序给出无效结果
Floating Point Program gives Invalid Result
最近编辑
我正尝试在 x86 MASM 上 运行 这个浮点二次方程程序。这段代码可以在 Kip Irvine x86 教科书中找到，我想看看它是如何在视觉上工作的。以下代码如下：
include irvine32.inc
.DATA
a REAL4 3.0
b REAL4 7.0
cc REAL4 2.0
posx REAL4 0.0
negx REAL4 0.0
.CODE
main proc
; Solve quadratic equation - no error checking
; The formula is: -b +/- squareroot(b2 - 4ac) / (2a)
fld1 ; Get constants 2 and 4
fadd st,st ; 2 at bottom
fld st ; Copy it
fmul a ; = 2a
fmul st(1),st ; = 4a
fxch ; Exchange
fmul cc ; = 4ac
fld b ; Load b
fmul st,st ; = b2
fsubr ; = b2 - 4ac
; Negative value here produces error
fsqrt ; = square root(b2 - 4ac)
fld b ; Load b
fchs ; Make it negative
fxch ; Exchange
fld st ; Copy square root
fadd st,st(2) ; Plus version = -b + root(b2 - 4ac)
fxch ; Exchange
fsubp st(2),st ; Minus version = -b - root(b2 - 4ac)
fdiv st,st(2) ; Divide plus version
fstp posx ; Store it
fdivr ; Divide minus version
fstp negx ; Store it
call writeint
exit
main endp
end main
所以我能够让我的程序编译、执行并完全工作。但是，每当我 运行 程序时，我都会得到这样的结果：
+1694175115
为什么结果这么大？我也尝试调用 writefloat，但它说此过程不在 Irvine32.inc 或 Macros.inc 库中。有人可以告诉我为什么它不起作用以及需要修复什么吗？谢谢。
感谢 Michael Petch
您的错误不在于计算本身，这在 MASM 中是正确的，而在于您打印结果。对于打印浮点数，writeint 是不正确的；您应该使用 WriteFloat，它有自己的调用约定。
WriteFloat 在 st(0) 中接受一个浮点数并将其打印到控制台 [1]。它不会从 x87 堆栈中弹出值。
因此，在您的 FPU 代码之后，您应该立即添加
fld posx
call WriteFloat
call Crlf
fld negx
call WriteFloat
call Crlf
emms
您还应该在开头包含正确的 MASM。类似于：
INCLUDE irvine32.inc
INCLUDE floatio.inc
INCLUDE macros.inc
INCLUDELIB kernel32.lib
INCLUDELIB user32.lib
INCLUDELIB Irvine32.lib
我的机器上缺少 MASM，我将您的程序重写为带有内联汇编的 GNU C 程序，并且除了每条指令之外，还对当时浮点堆栈的状态进行了注释。
#include <stdio.h>
int main(void){
asm(
".intel_syntax\n"
".data\n"
"a: .single 3.0\n"
"b: .single 7.0\n"
"cc: .single 2.0\n"
"posx: .single 0.0\n"
"negx: .single 0.0\n"
".text\n"
"fld1\n" // [1]
"fadd %st, %st\n" // [2]
"fld %st\n" // [2, 2]
"fmul dword ptr a\n" // [2a, 2]
"fmul %st(1), %st\n" // [2a, 4a]
"fxch\n" // [4a, 2a]
"fmul dword ptr cc\n" // [4ac, 2a]
"fld dword ptr b\n" // [b, 4ac, 2a]
"fmul %st, %st\n" // [b^2, 4ac, 2a]
"fsubrp\n" // [b^2-4ac, 2a]
"fsqrt\n" // [sqrt(b^2-4ac), 2a]
"fld dword ptr b\n" // [b, sqrt(b^2-4ac), 2a]
"fchs\n" // [-b, sqrt(b^2-4ac), 2a]
"fxch\n" // [sqrt(b^2-4ac), -b, 2a]
"fld %st\n" // [sqrt(b^2-4ac), sqrt(b^2-4ac), -b, 2a]
"fadd %st, %st(2)\n" // [-b+sqrt(b^2-4ac), sqrt(b^2-4ac), -b, 2a]
"fxch\n" // [ sqrt(b^2-4ac), -b+sqrt(b^2-4ac), -b, 2a]
"fsubp %st(2), %st\n" // [-b+sqrt(b^2-4ac), -b-sqrt(b^2-4ac), 2a]
"fdiv %st, %st(2)\n" // [(-b+sqrt(b^2-4ac))/2a, -b-sqrt(b^2-4ac), 2a]
"fstp dword ptr posx\n" // [ -b-sqrt(b^2-4ac), 2a]
"fdivrp\n" // [(-b-sqrt(b^2-4ac))/2a]
"fstp dword ptr negx\n" // []
".att_syntax\n"
);
extern float posx, negx;
printf("posx: %+0.17f\nnegx: %+0.17f\n", posx, negx);
return 0;
}
打印
posx: -0.33333334326744080
negx: -2.00000000000000000
正确的是：
- 3*(-1/3)^2 + 7*(-1/3) + 2 = 3/9 - 7/3 + 2 = 1/3-7/3+2 = -6/ 3+2 = -2+2 = 0
- 3*(-2)^2 + 7*(-2) + 2 = 3*4 -14 + 2 = 12-14+2 = -2+2 = 0
[1] § 12.2.7 读写浮点值
浮点数在特殊处理器（FPU）的特殊寄存器中处理并以特殊格式存储，不能被视为整数（WriteInt）。浮点数包含有关数字的更多信息，例如符号和指数。数字本身被更改为 1 到 2 之间的数字，并带有适当的指数，其中前导 1 通常被隐藏。在这里查看双精度格式：https://en.wikipedia.org/wiki/Double-precision_floating-point_format。这些数字不太可能准确。
至少从 11 年开始，Irvine32 库提供了函数 WriteFloat 以指数形式显示 FPU 寄存器 ST0 的值。它不会弹出或释放该寄存器。
改变
call writeint
到
fld posx ; Load floating point number into ST0
call WriteFloat ; Write ST0
ffree st[0] ; Free ST0 - don't forget it!
call Crlf ; New line
fld negx ; Load floating point number into ST0
call WriteFloat ; Write ST0
ffree st[0] ; Free ST0 - don't forget it!
call Crlf ; New line
如果您的图书馆没有 WriteFloat，我建议从 Irvine 的主页下载并安装最新的文件：http://www.kipirvine.com/asm/examples/index.htm (Example programs and link library source code for the Seventh Edition). You can also use another library, e.g. the C-runtime library (msvcrt.inc and msvcrt.lib) or Raymond Filiatreault's FPU library.
如果您不能使用提供浮点例程的库，您必须自己转换数字：
INCLUDE irvine32.inc
.DATA
a REAL4 3.0
b REAL4 7.0
cc REAL4 2.0
posx REAL4 0.0
negx REAL4 0.0
buf BYTE 1024 DUP (?)
.CODE
double2dec PROC C USES edi ; Args: ST(0): FPU-register to convert, EDI: pointer to string
LOCAL CONTROL_WORD:WORD, TEN:WORD, TEMP:WORD, DUMMY:QWORD
; modifying rounding mode
fstcw CONTROL_WORD
mov ax, CONTROL_WORD
or ah, 00001100b ; Set RC=11: truncating rounding mode
mov TEMP, ax
fldcw TEMP ; Load new rounding mode
; Check for negative
ftst ; ST0 negative?
fstsw ax
test ah, 001b
jz @F ; No: skip the next instructions
mov byte ptr [edi], '-' ; Negative sign
add edi, 1
@@:
FABS ; Abs (upper case to differ from C-library)
; Separate integer and fractional part & convert integer part into ASCII
fst st(1) ; Doubling ST(0) - ST(1)=ST(0)
frndint ; ST(0) to integer
fsub st(1), st(0) ; Integral part in ST(0), fractional part in ST(1)
; Move 10 to st(1)
mov TEN, 10
fild TEN
fxch
xor ecx, ecx ; Push/pop counter
@@: ; First loop
fst st(3) ; Preserve ST(0)
fprem ; ST(0) = remainder ST(0)/ST(1)
fistp word ptr TEMP ; ST(3) -> ST(2) !
push word ptr TEMP
inc ecx
fld st(2) ; Restore ST(0)
fdiv st(0), st(1)
frndint ; ST(0) to integer
fxam ; ST0 == 0.0?
fstsw ax
sahf
jnz @B ; No: loop
fxch st(2) ; ST(0) <-> ST(2) (fractional part)
ffree st(2)
ffree st(3)
@@: ; Second loop
pop ax
or al, '0'
mov [edi], al
inc edi
loop @B ; Loop ECX times
mov byte ptr [edi], '.' ; Decimal point
add edi, 1
; Isolate digits of fractional part and store ASCII
get_fractional:
fmul st(0), st(1) ; Multiply by 10 (shift one decimal digit into integer part)
fist word ptr TEMP ; Store digit
fisub word ptr TEMP ; Clear integer part
mov al, byte ptr TEMP ; Load digit
or al, 30h ; Convert digit to ASCII
mov byte ptr [edi], al ; Append it to string
add edi, 1 ; Increment pointer to string
fxam ; ST0 == 0.0?
fstsw ax
sahf
jnz get_fractional ; No: once more
mov byte ptr [edi], 0 ; Null-termination for ASCIIZ
; clean up FPU
ffree st(0) ; Empty ST(0)
ffree st(1) ; Empty ST(1)
fldcw CONTROL_WORD ; Restore old rounding mode
ret ; Return: EDI points to the null-terminated string
double2dec ENDP
main proc
; Solve quadratic equation - no error checking
; The formula is: -b +/- squareroot(b2 - 4ac) / (2a)
fld1 ; Get constants 2 and 4
fadd st,st ; 2 at bottom
fld st ; Copy it
fmul a ; = 2a
fmul st(1),st ; = 4a
fxch ; Exchange
fmul cc ; = 4ac
fld b ; Load b
fmul st,st ; = b2
fsubr ; = b2 - 4ac
; Negative value here produces error
fsqrt ; = square root(b2 - 4ac)
fld b ; Load b
fchs ; Make it negative
fxch ; Exchange
fld st ; Copy square root
fadd st,st(2) ; Plus version = -b + root(b2 - 4ac)
fxch ; Exchange
fsubp st(2),st ; Minus version = -b - root(b2 - 4ac)
fdiv st,st(2) ; Divide plus version
fstp posx ; Store it
fdivr ; Divide minus version
fstp negx ; Store it
; Write the results
fld posx ; Load floating point number into ST0
lea edi, buf ; EDI: pointer to a buffer for a string
call double2dec ; Convert ST0 to buf and pop
mov edx, edi ; EDX: pointer to a null-terminated string
call WriteString ; Irvine32
call Crlf ; Irvine32: New line
fld negx ; Load floating point number into ST0
lea edi, buf ; EDI: pointer to a buffer for a string
call double2dec ; Convert ST0 to buf and pop
mov edx, edi ; EDX: pointer to a null-terminated string
call WriteString ; Irvine32
call Crlf ; Irvine32: New line
exit ; Irvine32: ExitProcess
main ENDP
end main
最近编辑
我正尝试在 x86 MASM 上 运行 这个浮点二次方程程序。这段代码可以在 Kip Irvine x86 教科书中找到，我想看看它是如何在视觉上工作的。以下代码如下：
include irvine32.inc
.DATA
a REAL4 3.0
b REAL4 7.0
cc REAL4 2.0
posx REAL4 0.0
negx REAL4 0.0
.CODE
main proc
; Solve quadratic equation - no error checking
; The formula is: -b +/- squareroot(b2 - 4ac) / (2a)
fld1 ; Get constants 2 and 4
fadd st,st ; 2 at bottom
fld st ; Copy it
fmul a ; = 2a
fmul st(1),st ; = 4a
fxch ; Exchange
fmul cc ; = 4ac
fld b ; Load b
fmul st,st ; = b2
fsubr ; = b2 - 4ac
; Negative value here produces error
fsqrt ; = square root(b2 - 4ac)
fld b ; Load b
fchs ; Make it negative
fxch ; Exchange
fld st ; Copy square root
fadd st,st(2) ; Plus version = -b + root(b2 - 4ac)
fxch ; Exchange
fsubp st(2),st ; Minus version = -b - root(b2 - 4ac)
fdiv st,st(2) ; Divide plus version
fstp posx ; Store it
fdivr ; Divide minus version
fstp negx ; Store it
call writeint
exit
main endp
end main
所以我能够让我的程序编译、执行并完全工作。但是，每当我 运行 程序时，我都会得到这样的结果：
+1694175115
为什么结果这么大？我也尝试调用 writefloat，但它说此过程不在 Irvine32.inc 或 Macros.inc 库中。有人可以告诉我为什么它不起作用以及需要修复什么吗？谢谢。
感谢 Michael Petch
您的错误不在于计算本身，这在 MASM 中是正确的，而在于您打印结果。对于打印浮点数，writeint 是不正确的；您应该使用 WriteFloat，它有自己的调用约定。
WriteFloat 在 st(0) 中接受一个浮点数并将其打印到控制台 [1]。它不会从 x87 堆栈中弹出值。
因此，在您的 FPU 代码之后，您应该立即添加
fld posx
call WriteFloat
call Crlf
fld negx
call WriteFloat
call Crlf
emms
您还应该在开头包含正确的 MASM。类似于：
INCLUDE irvine32.inc
INCLUDE floatio.inc
INCLUDE macros.inc
INCLUDELIB kernel32.lib
INCLUDELIB user32.lib
INCLUDELIB Irvine32.lib
我的机器上缺少 MASM，我将您的程序重写为带有内联汇编的 GNU C 程序，并且除了每条指令之外，还对当时浮点堆栈的状态进行了注释。
#include <stdio.h>
int main(void){
asm(
".intel_syntax\n"
".data\n"
"a: .single 3.0\n"
"b: .single 7.0\n"
"cc: .single 2.0\n"
"posx: .single 0.0\n"
"negx: .single 0.0\n"
".text\n"
"fld1\n" // [1]
"fadd %st, %st\n" // [2]
"fld %st\n" // [2, 2]
"fmul dword ptr a\n" // [2a, 2]
"fmul %st(1), %st\n" // [2a, 4a]
"fxch\n" // [4a, 2a]
"fmul dword ptr cc\n" // [4ac, 2a]
"fld dword ptr b\n" // [b, 4ac, 2a]
"fmul %st, %st\n" // [b^2, 4ac, 2a]
"fsubrp\n" // [b^2-4ac, 2a]
"fsqrt\n" // [sqrt(b^2-4ac), 2a]
"fld dword ptr b\n" // [b, sqrt(b^2-4ac), 2a]
"fchs\n" // [-b, sqrt(b^2-4ac), 2a]
"fxch\n" // [sqrt(b^2-4ac), -b, 2a]
"fld %st\n" // [sqrt(b^2-4ac), sqrt(b^2-4ac), -b, 2a]
"fadd %st, %st(2)\n" // [-b+sqrt(b^2-4ac), sqrt(b^2-4ac), -b, 2a]
"fxch\n" // [ sqrt(b^2-4ac), -b+sqrt(b^2-4ac), -b, 2a]
"fsubp %st(2), %st\n" // [-b+sqrt(b^2-4ac), -b-sqrt(b^2-4ac), 2a]
"fdiv %st, %st(2)\n" // [(-b+sqrt(b^2-4ac))/2a, -b-sqrt(b^2-4ac), 2a]
"fstp dword ptr posx\n" // [ -b-sqrt(b^2-4ac), 2a]
"fdivrp\n" // [(-b-sqrt(b^2-4ac))/2a]
"fstp dword ptr negx\n" // []
".att_syntax\n"
);
extern float posx, negx;
printf("posx: %+0.17f\nnegx: %+0.17f\n", posx, negx);
return 0;
}
打印
posx: -0.33333334326744080
negx: -2.00000000000000000
正确的是：
- 3*(-1/3)^2 + 7*(-1/3) + 2 = 3/9 - 7/3 + 2 = 1/3-7/3+2 = -6/ 3+2 = -2+2 = 0
- 3*(-2)^2 + 7*(-2) + 2 = 3*4 -14 + 2 = 12-14+2 = -2+2 = 0
[1] § 12.2.7 读写浮点值
浮点数在特殊处理器（FPU）的特殊寄存器中处理并以特殊格式存储，不能被视为整数（WriteInt）。浮点数包含有关数字的更多信息，例如符号和指数。数字本身被更改为 1 到 2 之间的数字，并带有适当的指数，其中前导 1 通常被隐藏。在这里查看双精度格式：https://en.wikipedia.org/wiki/Double-precision_floating-point_format。这些数字不太可能准确。
至少从 11 年开始，Irvine32 库提供了函数 WriteFloat 以指数形式显示 FPU 寄存器 ST0 的值。它不会弹出或释放该寄存器。
改变
call writeint
到
fld posx ; Load floating point number into ST0
call WriteFloat ; Write ST0
ffree st[0] ; Free ST0 - don't forget it!
call Crlf ; New line
fld negx ; Load floating point number into ST0
call WriteFloat ; Write ST0
ffree st[0] ; Free ST0 - don't forget it!
call Crlf ; New line
如果您的图书馆没有 WriteFloat，我建议从 Irvine 的主页下载并安装最新的文件：http://www.kipirvine.com/asm/examples/index.htm (Example programs and link library source code for the Seventh Edition). You can also use another library, e.g. the C-runtime library (msvcrt.inc and msvcrt.lib) or Raymond Filiatreault's FPU library.
如果您不能使用提供浮点例程的库，您必须自己转换数字：
INCLUDE irvine32.inc
.DATA
a REAL4 3.0
b REAL4 7.0
cc REAL4 2.0
posx REAL4 0.0
negx REAL4 0.0
buf BYTE 1024 DUP (?)
.CODE
double2dec PROC C USES edi ; Args: ST(0): FPU-register to convert, EDI: pointer to string
LOCAL CONTROL_WORD:WORD, TEN:WORD, TEMP:WORD, DUMMY:QWORD
; modifying rounding mode
fstcw CONTROL_WORD
mov ax, CONTROL_WORD
or ah, 00001100b ; Set RC=11: truncating rounding mode
mov TEMP, ax
fldcw TEMP ; Load new rounding mode
; Check for negative
ftst ; ST0 negative?
fstsw ax
test ah, 001b
jz @F ; No: skip the next instructions
mov byte ptr [edi], '-' ; Negative sign
add edi, 1
@@:
FABS ; Abs (upper case to differ from C-library)
; Separate integer and fractional part & convert integer part into ASCII
fst st(1) ; Doubling ST(0) - ST(1)=ST(0)
frndint ; ST(0) to integer
fsub st(1), st(0) ; Integral part in ST(0), fractional part in ST(1)
; Move 10 to st(1)
mov TEN, 10
fild TEN
fxch
xor ecx, ecx ; Push/pop counter
@@: ; First loop
fst st(3) ; Preserve ST(0)
fprem ; ST(0) = remainder ST(0)/ST(1)
fistp word ptr TEMP ; ST(3) -> ST(2) !
push word ptr TEMP
inc ecx
fld st(2) ; Restore ST(0)
fdiv st(0), st(1)
frndint ; ST(0) to integer
fxam ; ST0 == 0.0?
fstsw ax
sahf
jnz @B ; No: loop
fxch st(2) ; ST(0) <-> ST(2) (fractional part)
ffree st(2)
ffree st(3)
@@: ; Second loop
pop ax
or al, '0'
mov [edi], al
inc edi
loop @B ; Loop ECX times
mov byte ptr [edi], '.' ; Decimal point
add edi, 1
; Isolate digits of fractional part and store ASCII
get_fractional:
fmul st(0), st(1) ; Multiply by 10 (shift one decimal digit into integer part)
fist word ptr TEMP ; Store digit
fisub word ptr TEMP ; Clear integer part
mov al, byte ptr TEMP ; Load digit
or al, 30h ; Convert digit to ASCII
mov byte ptr [edi], al ; Append it to string
add edi, 1 ; Increment pointer to string
fxam ; ST0 == 0.0?
fstsw ax
sahf
jnz get_fractional ; No: once more
mov byte ptr [edi], 0 ; Null-termination for ASCIIZ
; clean up FPU
ffree st(0) ; Empty ST(0)
ffree st(1) ; Empty ST(1)
fldcw CONTROL_WORD ; Restore old rounding mode
ret ; Return: EDI points to the null-terminated string
double2dec ENDP
main proc
; Solve quadratic equation - no error checking
; The formula is: -b +/- squareroot(b2 - 4ac) / (2a)
fld1 ; Get constants 2 and 4
fadd st,st ; 2 at bottom
fld st ; Copy it
fmul a ; = 2a
fmul st(1),st ; = 4a
fxch ; Exchange
fmul cc ; = 4ac
fld b ; Load b
fmul st,st ; = b2
fsubr ; = b2 - 4ac
; Negative value here produces error
fsqrt ; = square root(b2 - 4ac)
fld b ; Load b
fchs ; Make it negative
fxch ; Exchange
fld st ; Copy square root
fadd st,st(2) ; Plus version = -b + root(b2 - 4ac)
fxch ; Exchange
fsubp st(2),st ; Minus version = -b - root(b2 - 4ac)
fdiv st,st(2) ; Divide plus version
fstp posx ; Store it
fdivr ; Divide minus version
fstp negx ; Store it
; Write the results
fld posx ; Load floating point number into ST0
lea edi, buf ; EDI: pointer to a buffer for a string
call double2dec ; Convert ST0 to buf and pop
mov edx, edi ; EDX: pointer to a null-terminated string
call WriteString ; Irvine32
call Crlf ; Irvine32: New line
fld negx ; Load floating point number into ST0
lea edi, buf ; EDI: pointer to a buffer for a string
call double2dec ; Convert ST0 to buf and pop
mov edx, edi ; EDX: pointer to a null-terminated string
call WriteString ; Irvine32
call Crlf ; Irvine32: New line
exit ; Irvine32: ExitProcess
main ENDP
end main