Hello. This is my implementation of the Floating point numbers for #1. I have implemented 32 point bit floating point numbers based on the IEEE 754 standard.
Idea:
I have stored single precision floating point numbers in the 64-bit integer by storing the mantissa m, the exponent e, and the sign s where the floating point number = (-1)^s * 2^(e - 127) + (1+m). The 64-bit integer will have the first 3 most-right bits and the next 5 most-right bits be 1 in order to represent its flag of being a float. Then, the next 23 most-right bits will represent the mantissa m in binary form without the decimal point, the next 8 most-right bits will represent the exponent e, and the next bit will represent the sign s that will be 0 for positive or 1 for negative. Then, the next 3 bits will represent how decimal places d to round the floating point up to when the bits get converted to a float and printed.
Currently, the number is only accurate up to 7 significant figures and therefore will only round up to 0 or n many decimals where n = 7 - significant figures.
The summary of the changes I made are:
types.rkt
imm -> bits: Adds the case for floats and calls the function float -> bits on v to convert it to a float
float -> bits : Figures out the sign s, figures out how many decimal places to round to by calling decimal_place and 'integer-size' to see how many decimals d the float would need to be rounded when it gets printed (standard described above), determines the exponent e using calc-exp, and using the data returned by calc-exp to get the mantissa m. Finally, it gets the mantissa m that gets converted to a binary integer without its decimal place using dec->binary. After that, all 4 of these variables get taken to float->bits_helper to make a 64 bit integer in the way described in the introduction.
integer-size : Given an integer number, figures out the tens place.
decimal_place : Given a decimal number, accumulator, and maximum, figures out and returns the minimum between the number's decimal places and the maximum.
calc-exp: Depending on the sign and operator given which shows if the absolute number of the number given less greater than 0 and less than one or not, it will recursively test which exponent e it is true that 1 <= abs(num)/2^(e -127) <2.
dec->binary: Gets the rounded binary number representation of the decimal mantissa without its decimal place.
float->bits_helper : Using the four parameters of decimal place d, binary representation of mantissa m without its decimal place, exponent e plus its bias of 127, and sign s to construct of 64-bit integer in the way described in the introduction.
bits->imm: Implements the case of a float, by extracting the four parameters of decimal place d, the decimal representation of binary representation of mantissa m using binary->decimal , exponent e, and sign s, returns a float using the formula (-1)^s * 2^(e - 127) + (1+m) to calculate the float number and using round_dec to round this number by d decimal places.
Implements the case of a float by using functions from the math library to do the same process as bits->imm.
Makefile, a86/interp.rkt
In order to make it so executables could compile, did the hacky way of adding -lm to the line in each file that compiles the executable. Open to suggestions on better ways to do this.
Steven tests to see that the compiler can compile 4.2, -4.2, 3.3333, 790.321, -8990.32, -9999999, and .9999999 correctly.
Possible things to add next:
A better way to make it possible for executables to run with the C Math Library
A way to throw errors if a number is bigger than 6 significant digits.
Float Operations (fl+, fl-, fl=)
Note about Tests:
The tests on github cannot currently run after I updated the test-runner.rkt and compile.rkt due to the billing issue, but they ran correctly on my local machine.
Hello. This is my implementation of the Floating point numbers for #1. I have implemented 32 point bit floating point numbers based on the IEEE 754 standard.
Idea:
I have stored single precision floating point numbers in the 64-bit integer by storing the mantissa m, the exponent e, and the sign s where the floating point number = (-1)^s * 2^(e - 127) + (1+m). The 64-bit integer will have the first 3 most-right bits and the next 5 most-right bits be 1 in order to represent its flag of being a float. Then, the next 23 most-right bits will represent the mantissa m in binary form without the decimal point, the next 8 most-right bits will represent the exponent e, and the next bit will represent the sign s that will be 0 for positive or 1 for negative. Then, the next 3 bits will represent how decimal places d to round the floating point up to when the bits get converted to a float and printed.
Currently, the number is only accurate up to 7 significant figures and therefore will only round up to 0 or n many decimals where n = 7 - significant figures.
The summary of the changes I made are:
types.rktimm -> bits: Adds the case for floats and calls the functionfloat -> bitson v to convert it to a floatfloat -> bits: Figures out the sign s, figures out how many decimal places to round to by callingdecimal_placeand 'integer-size' to see how many decimals d the float would need to be rounded when it gets printed (standard described above), determines the exponent e usingcalc-exp, and using the data returned bycalc-expto get the mantissa m. Finally, it gets the mantissa m that gets converted to a binary integer without its decimal place usingdec->binary. After that, all 4 of these variables get taken tofloat->bits_helperto make a 64 bit integer in the way described in the introduction.integer-size: Given an integer number, figures out the tens place.decimal_place: Given a decimal number, accumulator, and maximum, figures out and returns the minimum between the number's decimal places and the maximum.calc-exp: Depending on the sign and operator given which shows if the absolute number of the number given less greater than 0 and less than one or not, it will recursively test which exponent e it is true that 1 <= abs(num)/2^(e -127) <2.dec->binary: Gets the rounded binary number representation of the decimal mantissa without its decimal place.float->bits_helper: Using the four parameters of decimal place d, binary representation of mantissa m without its decimal place, exponent e plus its bias of 127, and sign s to construct of 64-bit integer in the way described in the introduction.bits->imm: Implements the case of a float, by extracting the four parameters of decimal place d, the decimal representation of binary representation of mantissa m usingbinary->decimal, exponent e, and sign s, returns a float using the formula (-1)^s * 2^(e - 127) + (1+m) to calculate the float number and usinground_decto round this number by d decimal places.binary->decimal,round_dec,float-bits?: Self explanatorymain.cbits->imm.Makefile,a86/interp.rkt-lmto the line in each file that compiles the executable. Open to suggestions on better ways to do this.ast.rkt,compile.rkt,interp.rkt,parse.rkt,types.htest-runner.rktPossible things to add next:
Note about Tests:
test-runner.rktandcompile.rktdue to the billing issue, but they ran correctly on my local machine.