i thought aout doing a short article on Euler, but then i found this video from the philoctetes Institute, with Dominic Balestra, Loren Graham, Edward Nelson, Rebecca Newberger Goldstein, and Max Tegmark.
I think that this video does a better job than i would, plus it is a wicked lecture on Euler, easy to digest even if you don't have a maths background.
We should keep in mind that not only he was one of the most prolific contributor to maths and other areas like physics, mechanics, fluid dynamics, optics, and astronomy., but also the one who has more terms named after him ( an overwhelming advantage, when compared to other big names in science if i might say).
In one of my previous posts, Euler's identity is mentioned, in order to achieve the sine wave generator!
http://en.wikipedia.org/wiki/Leonhard_Euler
Thursday, 29 August 2013
Tuesday, 27 August 2013
Mathematical curiosities: Gödel's ontological proof of the existence of God
As a curiosity, i had to share this !!
Famous logician, mathematician, and philosopher Kurt F. Gödel was considered with Aristotle and Frege to be one of the most significant logicians in human history, Gödel made an immense impact upon scientific and philosophical thinking in the 20 th century, a time when others were pioneering the use of logic and set theory to understand the foundations of mathematics.
Calling Godel interesting is an understatement. A man who was Einstein's only reason to go to the university, in his later years; just to have the privilege of walking back home with Godel !
He used Leibniz "positive and negative properties" concept to formulate an "ontological proof" for the existence of God
Definition 1: x is God-like if and only if x has as essential properties those and only those properties which are positive
Definition 2: A is an essence of x if and only if for every property B, x has B necessarily if and only if A entails B
Definition 3: x necessarily exists if and only if every essence of x is necessarily exemplified
Axiom 1: Any property entailed by—i.e., strictly implied by—a positive property is positive
Axiom 2: If a property is positive, then its negation is not positive
Axiom 3: The property of being God-like is positive
Axiom 4: If a property is positive, then it is necessarily positive
Axiom 5: Necessary existence is a positive property
Axiom 6: For any property P, if P is positive, then being necessarily P is positive
Axiom 1 assumes that it is possible to single out positive properties from among all properties. Gödel comments that "Positive means positive in the moral aesthetic sense (independently of the accidental structure of the world)... It may also mean pure attribution as opposed to privation (or containing privation)." (Gödel 1995). Axioms 2, 3 and 4 can be summarized by saying that positive properties form a principal ultrafilter.
From these axioms and definitions and a few other axioms from modal logic, the following theorems can be proved:
Theorem 1: If a property is positive, then it is consistent, i.e., possibly exemplified.
Corollary 1: The property of being God-like is consistent.
Theorem 2: If something is God-like, then the property of being God-like is an essence of that thing.
Theorem 3: Necessarily, the property of being God-like is exemplified.
Thursday, 8 August 2013
PIC32- Variable type defs
One of the main concerns about migrating/working with other type of uC’s ( 8 bits like AVR & PIC, or 16 like PIC24 or the DSC’s dsPIC family), was how the 32 bit architecture will influence any previous code i might have regarding variable type definitions.
As its based on the GCC compiler, it is prepared for both ANSI with CCI compliance. Ill keep with the basics out of type defs.
The ANSI C Standard does indicate minimum requirements for these
types, as specified in
* For more info on compiler compliance check the XC32 Compiler User guide in chapter “2.4.6 Sizes of Type
From researching the include files, one can get this info :
/* 7.18.1.1 Exact-width integer types */
typedef __signed char __int8_t;
typedef unsigned char __uint8_t;
typedef short int __int16_t;
typedef unsigned short int __uint16_t;
typedef int __int32_t;
typedef unsigned int __uint32_t;
#ifdef __COMPILER_INT64__
typedef __COMPILER_INT64__ __int64_t;
typedef __COMPILER_UINT64__ __uint64_t;
#elif defined(_LP64)
typedef long int __int64_t;
typedef unsigned long int __uint64_t;
#else
/* LONGLONG */
__extension__
typedef long long int __int64_t;
/* LONGLONG */
__extension__
typedef unsigned long long int __uint64_t;
#endif
#define __BIT_TYPES_DEFINED__
Which gives us :
// MPLAB C32 range of Signed values
char c; // -128 to 127
short s; // -32,768 to 32,767
int i; // -2,147,483,648 to 2,147,483,647
long l; // -2,147,483,648 to 2,147,483,647
Of course, we also have the unsigned attribute:
// MPLAB C32 range of Unsigned values
unsigned char c; // 0 to 255
unsigned short s; // 0 to 65,535
unsigned int i; // 0 to 4,294,967,295
unsigned long l; // 0 to 4,294,967,295
For int, 4 bytes in the physical RAM is used.
So, if we do not have to use int and long, we should use char.
To hold one char variable, C32 compiler will use only 8 bits.
Another possibility is short type, which will use 16 bits to hold one short variable
PIC32‘s ALU is performing all arithmetic operations in the same number of cycles for 32-bit, 16-bit or 8-bit integers, which turns the variable long into just a synonym of the basic integer type int.
It is ok from performance point of view, but it comes with a price.
The only limiting factor, preventing us from always using 32-bit integers , is the consideration of the internal resources , and in this case the RAM memory
* keep the size of your variables to the minimum necessary; operating on bytes versus word can make a big difference in terms of code compactness/efficiency.
If really a large range of values is needed, we can use 64-bit types
// C32 range of 64-bit type values
long long l; // ranges from -2 to the power of 63 to +2 to the power of 63-1
unsigned long long l; // ranges from 0 to +2 to the power of 64
// C32 range of Floating point type values
float f; // 32-bit floating point
double d; // 64-bit floating point
long double d; // 64-bit floating point, synonym of double
The long long integer type offers 64-bit support and requires 8 bytes of memory; So, we can expect a small performance decrease for using long long integers.
Ill leave several excerpts from the header files...
/* 7.18.1.1 Exact-width integer types */
typedef __signed char __int8_t;
typedef unsigned char __uint8_t;
typedef short int __int16_t;
typedef unsigned short int __uint16_t;
typedef int __int32_t;
typedef unsigned int __uint32_t;
#ifdef __COMPILER_INT64__
typedef __COMPILER_INT64__ __int64_t;
typedef __COMPILER_UINT64__ __uint64_t;
#elif defined(_LP64)
typedef long int __int64_t;
typedef unsigned long int __uint64_t;
#else
/* LONGLONG */
__extension__
typedef long long int __int64_t;
/* LONGLONG */
__extension__
typedef unsigned long long int __uint64_t;
#endif
#define __BIT_TYPES_DEFINED__
/* 7.18.1.4 Integer types capable of holding object pointers */
#ifdef _LP64
typedef long int __intptr_t;
typedef unsigned long int __uintptr_t;
#else
typedef int __intptr_t;
typedef unsigned int __uintptr_t;
#endif
#endif /* !_MIPS_INT_TYPES_H_ */
__extension__
typedef __signed char int_least8_t;
typedef unsigned char uint_least8_t;
typedef short int int_least16_t;
typedef unsigned short int uint_least16_t;
typedef int int_least24_t;
typedef unsigned int uint_least24_t;
typedef int int_least32_t;
typedef unsigned int uint_least32_t;
#ifdef __COMPILER_INT64__
typedef __COMPILER_INT64__ int_least64_t;
typedef __COMPILER_UINT64__ uint_least64_t;
#elif defined(_LP64)
typedef long int int_least64_t;
typedef unsigned long int uint_least64_t;
#else
/* LONGLONG */
__extension__
typedef long long int int_least64_t;
/* LONGLONG */
__extension__
typedef unsigned long long int uint_least64_t;
#endif
/* 7.18.1.3 Fastest minimum-width integer types */
typedef int int_fast8_t;
typedef unsigned int uint_fast8_t;
typedef int int_fast16_t;
typedef unsigned int uint_fast16_t;
typedef int int_fast24_t;
typedef unsigned int uint_fast24_t;
typedef int int_fast32_t;
typedef unsigned int uint_fast32_t;
#ifdef __COMPILER_INT64__
typedef __COMPILER_INT64__ int_fast64_t;
typedef __COMPILER_UINT64__ uint_fast64_t;
#elif defined(_LP64)
typedef long int int_fast64_t;
typedef unsigned long int uint_fast64_t;
#else
/* LONGLONG */
__extension__
typedef long long int int_fast64_t;
/* LONGLONG */
__extension__
typedef unsigned long long int uint_fast64_t;
#endif
/* 7.18.1.5 Greatest-width integer types */
#ifdef __COMPILER_INT64__
typedef __COMPILER_INT64__ intmax_t;
typedef unsigned __COMPILER_INT64__ uintmax_t;
#elif defined(_LP64)
typedef long int intmax_t;
typedef unsigned long int uintmax_t;
#else
/* LONGLONG */
__extension__
typedef long long int intmax_t;
/* LONGLONG */
__extension__
typedef unsigned long long int uintmax_t;
#endif
#endif /* !_MIPS_INT_MWGWTYPES_H_ */
/* $NetBSD: int_limits.h,v 1.3 2002/11/03 19:55:23 thorpej Exp $ */
/*-
* Copyright (c) 2001 The NetBSD Foundation, Inc.
* All rights reserved.
*/
...
/*
* 7.18.2 Limits of specified-width integer types
*/
/* 7.18.2.1 Limits of exact-width integer types */
/* minimum values of exact-width signed integer types */
#define INT8_MIN (-0x7f-1) /* int8_t */
#define INT16_MIN (-0x7fff-1) /* int16_t */
#define INT32_MIN (-0x7fffffff-1) /* int32_t */
#ifdef _LP64
#define INT64_MIN (-0x7fffffffffffffffL-1) /* int64_t */
#else
#define INT64_MIN (-0x7fffffffffffffffLL-1) /* int64_t */
#endif
/* maximum values of exact-width signed integer types */
#define INT8_MAX 0x7f /* int8_t */
#define INT16_MAX 0x7fff /* int16_t */
#define INT32_MAX 0x7fffffff /* int32_t */
#ifdef _LP64
#define INT64_MAX 0x7fffffffffffffffL /* int64_t */
#else
#define INT64_MAX 0x7fffffffffffffffLL /* int64_t */
#endif
/* maximum values of exact-width unsigned integer types */
#define UINT8_MAX 0xffU /* uint8_t */
#define UINT16_MAX 0xffffU /* uint16_t */
#define UINT32_MAX 0xffffffffU /* uint32_t */
#ifdef _LP64
#define UINT64_MAX 0xffffffffffffffffUL /* uint64_t */
#else
#define UINT64_MAX 0xffffffffffffffffULL /* uint64_t */
#endif
/* 7.18.2.2 Limits of minimum-width integer types */
/* minimum values of minimum-width signed integer types */
#define INT_LEAST8_MIN (-0x7f-1) /* int_least8_t */
#define INT_LEAST16_MIN (-0x7fff-1) /* int_least16_t */
#define INT_LEAST24_MIN (-0x7fffffff-1) /* int_least24_t */
#define INT_LEAST32_MIN (-0x7fffffff-1) /* int_least32_t */
#ifdef _LP64
#define INT_LEAST64_MIN (-0x7fffffffffffffffL-1) /* int_least64_t */
#else
#define INT_LEAST64_MIN (-0x7fffffffffffffffLL-1) /* int_least64_t */
#endif
/* maximum values of minimum-width signed integer types */
#define INT_LEAST8_MAX 0x7f /* int_least8_t */
#define INT_LEAST16_MAX 0x7fff /* int_least16_t */
#define INT_LEAST24_MAX 0x7fffffff /* int_least24_t */
#define INT_LEAST32_MAX 0x7fffffff /* int_least32_t */
#ifdef _LP64
#define INT_LEAST64_MAX 0x7fffffffffffffffL /* int_least64_t */
#else
#define INT_LEAST64_MAX 0x7fffffffffffffffLL /* int_least64_t */
#endif
/* maximum values of minimum-width unsigned integer types */
#define UINT_LEAST8_MAX 0xffU /* uint_least8_t */
#define UINT_LEAST16_MAX 0xffffU /* uint_least16_t */
#define UINT_LEAST24_MAX 0xffffffffU /* uint_least24_t */
#define UINT_LEAST32_MAX 0xffffffffU /* uint_least32_t */
#ifdef _LP64
#define UINT_LEAST64_MAX 0xffffffffffffffffUL /* uint_least64_t */
#else
#define UINT_LEAST64_MAX 0xffffffffffffffffULL /* uint_least64_t */
#endif
/* 7.18.2.3 Limits of fastest minimum-width integer types */
/* minimum values of fastest minimum-width signed integer types */
#define INT_FAST8_MIN (-0x7fffffff-1) /* int_fast8_t */
#define INT_FAST16_MIN (-0x7fffffff-1) /* int_fast16_t */
#define INT_FAST24_MIN (-0x7fffffff-1) /* int_fast24_t */
#define INT_FAST32_MIN (-0x7fffffff-1) /* int_fast32_t */
#ifdef _LP64
#define INT_FAST64_MIN (-0x7fffffffffffffffL-1) /* int_fast64_t */
#else
#define INT_FAST64_MIN (-0x7fffffffffffffffLL-1) /* int_fast64_t */
#endif
/* maximum values of fastest minimum-width signed integer types */
#define INT_FAST8_MAX 0x7fffffff /* int_fast8_t */
#define INT_FAST16_MAX 0x7fffffff /* int_fast16_t */
#define INT_FAST24_MAX 0x7fffffff /* int_fast24_t */
#define INT_FAST32_MAX 0x7fffffff /* int_fast32_t */
#ifdef _LP64
#define INT_FAST64_MAX 0x7fffffffffffffffL /* int_fast64_t */
#else
#define INT_FAST64_MAX 0x7fffffffffffffffLL /* int_fast64_t */
#endif
/* maximum values of fastest minimum-width unsigned integer types */
#define UINT_FAST8_MAX 0xffffffffU /* uint_fast8_t */
#define UINT_FAST16_MAX 0xffffffffU /* uint_fast16_t */
#define UINT_FAST24_MAX 0xffffffffU /* uint_fast24_t */
#define UINT_FAST32_MAX 0xffffffffU /* uint_fast32_t */
#ifdef _LP64
#define UINT_FAST64_MAX 0xffffffffffffffffUL /* uint_fast64_t */
#else
#define UINT_FAST64_MAX 0xffffffffffffffffULL /* uint_fast64_t */
#endif
/* 7.18.2.4 Limits of integer types capable of holding object pointers */
#ifdef _LP64
#define INTPTR_MIN (-0x7fffffffffffffffL-1) /* intptr_t */
#define INTPTR_MAX 0x7fffffffffffffffL /* intptr_t */
#define UINTPTR_MAX 0xffffffffffffffffUL /* uintptr_t */
#else
#define INTPTR_MIN (-0x7fffffff-1) /* intptr_t */
#define INTPTR_MAX 0x7fffffff /* intptr_t */
#define UINTPTR_MAX 0xffffffffU /* uintptr_t */
#endif
/* 7.18.2.5 Limits of greatest-width integer types */
#ifdef _LP64
#define INTMAX_MIN (-0x7fffffffffffffffL-1) /* intmax_t */
#define INTMAX_MAX 0x7fffffffffffffffL /* intmax_t */
#define UINTMAX_MAX 0xffffffffffffffffUL /* uintmax_t */
#else
#define INTMAX_MIN (-0x7fffffffffffffffLL-1) /* intmax_t */
#define INTMAX_MAX 0x7fffffffffffffffLL /* intmax_t */
#define UINTMAX_MAX 0xffffffffffffffffULL /* uintmax_t */
#endif
/*
* 7.18.3 Limits of other integer types
*/
/* limits of ptrdiff_t */
#ifdef _LP64
#define PTRDIFF_MIN (-0x7fffffffffffffffL-1) /* ptrdiff_t */
#define PTRDIFF_MAX 0x7fffffffffffffffL /* ptrdiff_t */
#else
#define PTRDIFF_MIN (-0x7fffffff-1) /* ptrdiff_t */
#define PTRDIFF_MAX 0x7fffffff /* ptrdiff_t */
#endif
/* limits of sig_atomic_t */
#define SIG_ATOMIC_MIN (-0x7fffffff-1) /* sig_atomic_t */
#define SIG_ATOMIC_MAX 0x7fffffff /* sig_atomic_t */
/* limit of size_t */
#ifdef _LP64
#define SIZE_MAX 0xffffffffffffffffUL /* size_t */
#else
#define SIZE_MAX 0xffffffffU /* size_t */
#endif
#ifndef WCHAR_MIN /* also possibly defined in */
/* limits of wchar_t */
#define WCHAR_MIN 0 /* wchar_t */
#define WCHAR_MAX 0xffff /* wchar_t */
/* limits of wint_t */
#define WINT_MIN (-0x7fffffff-1) /* wint_t */
#define WINT_MAX 0x7fffffff /* wint_t */
#endif
#endif /* !_MIPS_INT_LIMITS_H_ */
(1): http://ww1.microchip.com/downloads/en/DeviceDoc/51686F.pdf
(2): http://www.youtube.com/watch?v=6FNKJSWuaJE
As its based on the GCC compiler, it is prepared for both ANSI with CCI compliance. Ill keep with the basics out of type defs.
The ANSI C Standard does indicate minimum requirements for these
types, as specified in
* For more info on compiler compliance check the XC32 Compiler User guide in chapter “2.4.6 Sizes of Type
From researching the include files, one can get this info :
/* 7.18.1.1 Exact-width integer types */
typedef __signed char __int8_t;
typedef unsigned char __uint8_t;
typedef short int __int16_t;
typedef unsigned short int __uint16_t;
typedef int __int32_t;
typedef unsigned int __uint32_t;
#ifdef __COMPILER_INT64__
typedef __COMPILER_INT64__ __int64_t;
typedef __COMPILER_UINT64__ __uint64_t;
#elif defined(_LP64)
typedef long int __int64_t;
typedef unsigned long int __uint64_t;
#else
/* LONGLONG */
__extension__
typedef long long int __int64_t;
/* LONGLONG */
__extension__
typedef unsigned long long int __uint64_t;
#endif
#define __BIT_TYPES_DEFINED__
Which gives us :
// MPLAB C32 range of Signed values
char c; // -128 to 127
short s; // -32,768 to 32,767
int i; // -2,147,483,648 to 2,147,483,647
long l; // -2,147,483,648 to 2,147,483,647
Of course, we also have the unsigned attribute:
// MPLAB C32 range of Unsigned values
unsigned char c; // 0 to 255
unsigned short s; // 0 to 65,535
unsigned int i; // 0 to 4,294,967,295
unsigned long l; // 0 to 4,294,967,295
For int, 4 bytes in the physical RAM is used.
So, if we do not have to use int and long, we should use char.
To hold one char variable, C32 compiler will use only 8 bits.
Another possibility is short type, which will use 16 bits to hold one short variable
PIC32‘s ALU is performing all arithmetic operations in the same number of cycles for 32-bit, 16-bit or 8-bit integers, which turns the variable long into just a synonym of the basic integer type int.
It is ok from performance point of view, but it comes with a price.
The only limiting factor, preventing us from always using 32-bit integers , is the consideration of the internal resources , and in this case the RAM memory
* keep the size of your variables to the minimum necessary; operating on bytes versus word can make a big difference in terms of code compactness/efficiency.
If really a large range of values is needed, we can use 64-bit types
// C32 range of 64-bit type values
long long l; // ranges from -2 to the power of 63 to +2 to the power of 63-1
unsigned long long l; // ranges from 0 to +2 to the power of 64
// C32 range of Floating point type values
float f; // 32-bit floating point
double d; // 64-bit floating point
long double d; // 64-bit floating point, synonym of double
The long long integer type offers 64-bit support and requires 8 bytes of memory; So, we can expect a small performance decrease for using long long integers.
Ill leave several excerpts from the header files...
/* 7.18.1.1 Exact-width integer types */
typedef __signed char __int8_t;
typedef unsigned char __uint8_t;
typedef short int __int16_t;
typedef unsigned short int __uint16_t;
typedef int __int32_t;
typedef unsigned int __uint32_t;
#ifdef __COMPILER_INT64__
typedef __COMPILER_INT64__ __int64_t;
typedef __COMPILER_UINT64__ __uint64_t;
#elif defined(_LP64)
typedef long int __int64_t;
typedef unsigned long int __uint64_t;
#else
/* LONGLONG */
__extension__
typedef long long int __int64_t;
/* LONGLONG */
__extension__
typedef unsigned long long int __uint64_t;
#endif
#define __BIT_TYPES_DEFINED__
/* 7.18.1.4 Integer types capable of holding object pointers */
#ifdef _LP64
typedef long int __intptr_t;
typedef unsigned long int __uintptr_t;
#else
typedef int __intptr_t;
typedef unsigned int __uintptr_t;
#endif
#endif /* !_MIPS_INT_TYPES_H_ */
Also :
* 7.18.1.2 Minimum-width integer types */__extension__
typedef __signed char int_least8_t;
typedef unsigned char uint_least8_t;
typedef short int int_least16_t;
typedef unsigned short int uint_least16_t;
typedef int int_least24_t;
typedef unsigned int uint_least24_t;
typedef int int_least32_t;
typedef unsigned int uint_least32_t;
#ifdef __COMPILER_INT64__
typedef __COMPILER_INT64__ int_least64_t;
typedef __COMPILER_UINT64__ uint_least64_t;
#elif defined(_LP64)
typedef long int int_least64_t;
typedef unsigned long int uint_least64_t;
#else
/* LONGLONG */
__extension__
typedef long long int int_least64_t;
/* LONGLONG */
__extension__
typedef unsigned long long int uint_least64_t;
#endif
/* 7.18.1.3 Fastest minimum-width integer types */
typedef int int_fast8_t;
typedef unsigned int uint_fast8_t;
typedef int int_fast16_t;
typedef unsigned int uint_fast16_t;
typedef int int_fast24_t;
typedef unsigned int uint_fast24_t;
typedef int int_fast32_t;
typedef unsigned int uint_fast32_t;
#ifdef __COMPILER_INT64__
typedef __COMPILER_INT64__ int_fast64_t;
typedef __COMPILER_UINT64__ uint_fast64_t;
#elif defined(_LP64)
typedef long int int_fast64_t;
typedef unsigned long int uint_fast64_t;
#else
/* LONGLONG */
__extension__
typedef long long int int_fast64_t;
/* LONGLONG */
__extension__
typedef unsigned long long int uint_fast64_t;
#endif
/* 7.18.1.5 Greatest-width integer types */
#ifdef __COMPILER_INT64__
typedef __COMPILER_INT64__ intmax_t;
typedef unsigned __COMPILER_INT64__ uintmax_t;
#elif defined(_LP64)
typedef long int intmax_t;
typedef unsigned long int uintmax_t;
#else
/* LONGLONG */
__extension__
typedef long long int intmax_t;
/* LONGLONG */
__extension__
typedef unsigned long long int uintmax_t;
#endif
#endif /* !_MIPS_INT_MWGWTYPES_H_ */
Regarding the limits of each type def...
/* $NetBSD: int_limits.h,v 1.3 2002/11/03 19:55:23 thorpej Exp $ */
/*-
* Copyright (c) 2001 The NetBSD Foundation, Inc.
* All rights reserved.
*/
...
/*
* 7.18.2 Limits of specified-width integer types
*/
/* 7.18.2.1 Limits of exact-width integer types */
/* minimum values of exact-width signed integer types */
#define INT8_MIN (-0x7f-1) /* int8_t */
#define INT16_MIN (-0x7fff-1) /* int16_t */
#define INT32_MIN (-0x7fffffff-1) /* int32_t */
#ifdef _LP64
#define INT64_MIN (-0x7fffffffffffffffL-1) /* int64_t */
#else
#define INT64_MIN (-0x7fffffffffffffffLL-1) /* int64_t */
#endif
/* maximum values of exact-width signed integer types */
#define INT8_MAX 0x7f /* int8_t */
#define INT16_MAX 0x7fff /* int16_t */
#define INT32_MAX 0x7fffffff /* int32_t */
#ifdef _LP64
#define INT64_MAX 0x7fffffffffffffffL /* int64_t */
#else
#define INT64_MAX 0x7fffffffffffffffLL /* int64_t */
#endif
/* maximum values of exact-width unsigned integer types */
#define UINT8_MAX 0xffU /* uint8_t */
#define UINT16_MAX 0xffffU /* uint16_t */
#define UINT32_MAX 0xffffffffU /* uint32_t */
#ifdef _LP64
#define UINT64_MAX 0xffffffffffffffffUL /* uint64_t */
#else
#define UINT64_MAX 0xffffffffffffffffULL /* uint64_t */
#endif
/* 7.18.2.2 Limits of minimum-width integer types */
/* minimum values of minimum-width signed integer types */
#define INT_LEAST8_MIN (-0x7f-1) /* int_least8_t */
#define INT_LEAST16_MIN (-0x7fff-1) /* int_least16_t */
#define INT_LEAST24_MIN (-0x7fffffff-1) /* int_least24_t */
#define INT_LEAST32_MIN (-0x7fffffff-1) /* int_least32_t */
#ifdef _LP64
#define INT_LEAST64_MIN (-0x7fffffffffffffffL-1) /* int_least64_t */
#else
#define INT_LEAST64_MIN (-0x7fffffffffffffffLL-1) /* int_least64_t */
#endif
/* maximum values of minimum-width signed integer types */
#define INT_LEAST8_MAX 0x7f /* int_least8_t */
#define INT_LEAST16_MAX 0x7fff /* int_least16_t */
#define INT_LEAST24_MAX 0x7fffffff /* int_least24_t */
#define INT_LEAST32_MAX 0x7fffffff /* int_least32_t */
#ifdef _LP64
#define INT_LEAST64_MAX 0x7fffffffffffffffL /* int_least64_t */
#else
#define INT_LEAST64_MAX 0x7fffffffffffffffLL /* int_least64_t */
#endif
/* maximum values of minimum-width unsigned integer types */
#define UINT_LEAST8_MAX 0xffU /* uint_least8_t */
#define UINT_LEAST16_MAX 0xffffU /* uint_least16_t */
#define UINT_LEAST24_MAX 0xffffffffU /* uint_least24_t */
#define UINT_LEAST32_MAX 0xffffffffU /* uint_least32_t */
#ifdef _LP64
#define UINT_LEAST64_MAX 0xffffffffffffffffUL /* uint_least64_t */
#else
#define UINT_LEAST64_MAX 0xffffffffffffffffULL /* uint_least64_t */
#endif
/* 7.18.2.3 Limits of fastest minimum-width integer types */
/* minimum values of fastest minimum-width signed integer types */
#define INT_FAST8_MIN (-0x7fffffff-1) /* int_fast8_t */
#define INT_FAST16_MIN (-0x7fffffff-1) /* int_fast16_t */
#define INT_FAST24_MIN (-0x7fffffff-1) /* int_fast24_t */
#define INT_FAST32_MIN (-0x7fffffff-1) /* int_fast32_t */
#ifdef _LP64
#define INT_FAST64_MIN (-0x7fffffffffffffffL-1) /* int_fast64_t */
#else
#define INT_FAST64_MIN (-0x7fffffffffffffffLL-1) /* int_fast64_t */
#endif
/* maximum values of fastest minimum-width signed integer types */
#define INT_FAST8_MAX 0x7fffffff /* int_fast8_t */
#define INT_FAST16_MAX 0x7fffffff /* int_fast16_t */
#define INT_FAST24_MAX 0x7fffffff /* int_fast24_t */
#define INT_FAST32_MAX 0x7fffffff /* int_fast32_t */
#ifdef _LP64
#define INT_FAST64_MAX 0x7fffffffffffffffL /* int_fast64_t */
#else
#define INT_FAST64_MAX 0x7fffffffffffffffLL /* int_fast64_t */
#endif
/* maximum values of fastest minimum-width unsigned integer types */
#define UINT_FAST8_MAX 0xffffffffU /* uint_fast8_t */
#define UINT_FAST16_MAX 0xffffffffU /* uint_fast16_t */
#define UINT_FAST24_MAX 0xffffffffU /* uint_fast24_t */
#define UINT_FAST32_MAX 0xffffffffU /* uint_fast32_t */
#ifdef _LP64
#define UINT_FAST64_MAX 0xffffffffffffffffUL /* uint_fast64_t */
#else
#define UINT_FAST64_MAX 0xffffffffffffffffULL /* uint_fast64_t */
#endif
/* 7.18.2.4 Limits of integer types capable of holding object pointers */
#ifdef _LP64
#define INTPTR_MIN (-0x7fffffffffffffffL-1) /* intptr_t */
#define INTPTR_MAX 0x7fffffffffffffffL /* intptr_t */
#define UINTPTR_MAX 0xffffffffffffffffUL /* uintptr_t */
#else
#define INTPTR_MIN (-0x7fffffff-1) /* intptr_t */
#define INTPTR_MAX 0x7fffffff /* intptr_t */
#define UINTPTR_MAX 0xffffffffU /* uintptr_t */
#endif
/* 7.18.2.5 Limits of greatest-width integer types */
#ifdef _LP64
#define INTMAX_MIN (-0x7fffffffffffffffL-1) /* intmax_t */
#define INTMAX_MAX 0x7fffffffffffffffL /* intmax_t */
#define UINTMAX_MAX 0xffffffffffffffffUL /* uintmax_t */
#else
#define INTMAX_MIN (-0x7fffffffffffffffLL-1) /* intmax_t */
#define INTMAX_MAX 0x7fffffffffffffffLL /* intmax_t */
#define UINTMAX_MAX 0xffffffffffffffffULL /* uintmax_t */
#endif
/*
* 7.18.3 Limits of other integer types
*/
/* limits of ptrdiff_t */
#ifdef _LP64
#define PTRDIFF_MIN (-0x7fffffffffffffffL-1) /* ptrdiff_t */
#define PTRDIFF_MAX 0x7fffffffffffffffL /* ptrdiff_t */
#else
#define PTRDIFF_MIN (-0x7fffffff-1) /* ptrdiff_t */
#define PTRDIFF_MAX 0x7fffffff /* ptrdiff_t */
#endif
/* limits of sig_atomic_t */
#define SIG_ATOMIC_MIN (-0x7fffffff-1) /* sig_atomic_t */
#define SIG_ATOMIC_MAX 0x7fffffff /* sig_atomic_t */
/* limit of size_t */
#ifdef _LP64
#define SIZE_MAX 0xffffffffffffffffUL /* size_t */
#else
#define SIZE_MAX 0xffffffffU /* size_t */
#endif
#ifndef WCHAR_MIN /* also possibly defined in
/* limits of wchar_t */
#define WCHAR_MIN 0 /* wchar_t */
#define WCHAR_MAX 0xffff /* wchar_t */
/* limits of wint_t */
#define WINT_MIN (-0x7fffffff-1) /* wint_t */
#define WINT_MAX 0x7fffffff /* wint_t */
#endif
#endif /* !_MIPS_INT_LIMITS_H_ */
(1): http://ww1.microchip.com/downloads/en/DeviceDoc/51686F.pdf
(2): http://www.youtube.com/watch?v=6FNKJSWuaJE
Tuesday, 6 August 2013
PIC32's : Some basics
Among the many features available on a PIC32, to chose from, we should maybe start with the basic port operations...
On the Microchip datasheet (1), we can read the following, about some of the the key features of the I/O Ports module:
• Individual output pin open-drain enable/disable
• Individual input pin pull-up enable/disable
• Monitor select inputs and generate interrupt on mismatch condition
• Operate during CPU Sleep and Idle modes
• Fast bit manipulation using CLR, SET and INV registers ( mentioned previous article- see below).
Before reading and writing any I/O port, the correct registers of the desired pins should be properly configured .
Each I/O port has nine registers directly associated with the operation of the port and one control register. Each I/O port pin has a corresponding bit in these registers. Throughout this section, the letter ‘x’, refers to relevant port module ( TRISA, TRISB, TRISC, etc).
NOTE: Any bit and its associated data and control registers that is not valid for a particular device will be disabled and will read as zeros.
TRISx registers configure the data direction through port pins; in other words, it determines whether a port pin is an input or an output:
If data direction bit is ‘1’, the pin is an input; If data direction bit is ‘0’, the t pin is an output
A read from a TRISx register reads the last value written to the TRISx register
* to note that all I/O pins are defined as inputs after a Power-on Reset
A write to a PORTx register writes to the corresponding LATx register (PORTx data latch).
Those I/O port pin(s) configured as outputs are updated.
The datasheet refers to the fact that a write to a PORTx register is the effectively the same as a write to a LATx register; they also note that a read from a PORTx register reads the synchronized signal applied to the pins
LATx registers act as PORTx data latch, and hold the data written to port I/O pin(s):
A write to a LATx register latches data to corresponding port I/O pins. And only those port pins configured as outputs are updated.
A read from LATx register reads the data held in the PORTx data latch, not from the port
pins themselves.
You should check the file p32mx250f128b.h for a list of all definitions names of the Special-Function Registers (SFRs) of the device.
Inside, we can expect something like this( Port A basic registers as example):
__TRISAbits_t;
extern volatile __TRISAbits_t TRISAbits __asm__ ("TRISA") __attribute__((section("sfrs")));
extern volatile unsigned int TRISACLR __attribute__((section("sfrs")));
extern volatile unsigned int TRISASET __attribute__((section("sfrs")));
extern volatile unsigned int TRISAINV __attribute__((section("sfrs")));
extern volatile unsigned int PORTA __attribute__((section("sfrs")));
typedef union {
struct {
unsigned RA0:1;
unsigned RA1:1;
unsigned RA2:1;
unsigned RA3:1;
unsigned RA4:1;
};
struct {
unsigned w:32;
};
} __PORTAbits_t;
extern volatile __PORTAbits_t PORTAbits __asm__ ("PORTA") __attribute__((section("sfrs")));
extern volatile unsigned int PORTACLR __attribute__((section("sfrs")));
extern volatile unsigned int PORTASET __attribute__((section("sfrs")));
extern volatile unsigned int PORTAINV __attribute__((section("sfrs")));
extern volatile unsigned int LATA __attribute__((section("sfrs")));
typedef union {
struct {
unsigned LATA0:1;
unsigned LATA1:1;
unsigned LATA2:1;
unsigned LATA3:1;
unsigned LATA4:1;
};
struct {
unsigned w:32;
};
} __LATAbits_t;
extern volatile __LATAbits_t LATAbits __asm__ ("LATA") __attribute__((section("sfrs")));
extern volatile unsigned int LATACLR __attribute__((section("sfrs")));
extern volatile unsigned int LATASET __attribute__((section("sfrs")));
extern volatile unsigned int LATAINV __attribute__((section("sfrs")));
extern volatile unsigned int ODCA __attribute__((section("sfrs")));
typedef struct {
unsigned w:32;
}
So lets start with some basic code.
First, i would advise you with the priceless tool that is the Sim included in MPLab and MPLab X.
#include < p32xxxx.h >
/*
* We could include p32mx250f128b.h directly, but this way we make the code more
* portable.
*/
main()
{
int a;
#ifndef PIC32_STARTER_KIT
/*The JTAG is on by default on POR. A PIC32 Starter Kit uses the JTAG, but
for other debug tool use, like ICD 3 and Real ICE, the JTAG should be off
to free up the JTAG I/O */
DDPCONbits.JTAGEN = 0;
#endif
// init the needed registers:
TRISA = 0xff00; // PORTA pin 0..7 as output
// main loop:
while(1){
a=256; // Variable to waste time
while (a --){
// While variable a decrements, we keep pin 0 on, for debug purposes
PORTA = 0x0001; // turn pin 0 on
}
PORTA = 0; /* turn all pins off; notice that, without 0x prefix, the compiler assumes the default decimal radix */
}
}
From the previous article, we can remember the following :The PIC32 brings also a set of registers called SET, CLEAR, and INVERT.
When you write to any of these registers, the PIC32 performs the read-modify-write operation in a single clock, allowing the ability to quickly manipulate I/O ports and bits. This means that, you can toggle any general purpose I/O pin at the SYSCLK speed! This atomic bit manipulation capability means that the SET, CLR, and INV operations cannot be interrupted.
For example, the LATA SFR is followed by LATACLR, LATASET, and LATAINV. To clear a group of bits in the LATA register, you would write the corresponding mask values into the LATACLR register.
Similarly, a write to the SET register would set the corresponding bits and a write to INV register would toggle the bits..
This of course, makes basic port operations much easier, as we can see from the next example !
So lets put it into practice
/*
Example 2
*/
#include < p32xxxx.h >
main()
{
#ifndef PIC32_STARTER_KIT
/*The JTAG is on by default on POR. A PIC32 Starter Kit uses the JTAG, but
for other debug tool use, like ICD 3 and Real ICE, the JTAG should be off
to free up the JTAG I/O */
DDPCONbits.JTAGEN = 0;
#endif
/*The JTAG is on by default on POR. A PIC32 Starter Kit uses the JTAG, but
for other debug tool use, like ICD 3 and Real ICE, the JTAG should be off
to free up the JTAG I/O */
DDPCONbits.JTAGEN = 0;
#endif
LATACLR = 0x0001; // RA0 Off
TRISACLR = 0x0001; // RA0 as output
while(1)
{
LATAINV = 0x0001;// toggle RA0
Nop(); //Kill time.
}
Friday, 2 August 2013
hacker Barnaby Jack R.I.P.
Famed hacker dies... Whether or not in suspicious situation, will not be relevant now.!
May you stand tall, wherever you are !
http://www.reuters.com/article/2013/07/26/us-hacker-death-idUSBRE96P0K120130726
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