DCPU-FP32

3rd Generation Floating Point library for DCPU

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Provides basic floating point arithmetic for DCPU. Floating point numbers are represented in proprietary format that provides 8 bit exponent and 32 bit mantissa (only 31 significant bits as msb is always 1).

Design Philosophy

- Easy API for integration into operating systems and applications - Small and simple codebase

Implementation Principles

- float parameters are passed in stack by pointer - int16 return value is passes in stack - parameters are pushed to stack in right to left order - caller is responsible for cleaning the stack (arguments and possible return value) - registers a, b, c, i, j, x, y and z are preserved - same pointer can be used as any or all arguments

SHORTCOMINGS

- Support only truncate rounding - No denormalized numbers - Both exponent's and significant's bit widths are hardcoded - Division uses slow long division algorithm

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Installation

Required files:

defs.dasm16

float.dasm16

Test files (not needed):

test_float.dasm16

dunit.dasm16

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API

int16 float_cmp(float *left, float *right)
void float_add(float *left, float *right, float *result)
void float_sub(float *left, float *right, float *result)
void float_mul(float *left, float *right, float *result)
void float_div(float *left, float *right, float *result)
uint16 float_to_uint16(float *src)
void float_from_uint16(uint16 value, float *dst)
void float_negate(float *src, float *dst)
void float_abs(float *src, float *dst)

Candidates for future development

float_from_str
float_to_str
sqrt
pow
sin, cos, tan

Example

; calculate (2 + 4) * 2

#include "defs.dasm16"

:f_result dat 0,0,0,0
:f_2      dat FLOAT_TYPE_PNUM, 0x8001, 0x8000, 0x0000
:f_4      dat FLOAT_TYPE_PNUM, 0x8002, 0x8000, 0x0000

; API calls
set push, f_result      ; push result address
set push, f_4           ; push 4.0 address
set push, f_2           ; push 2.0 address
jst float_add

add sp, 3               ; cleanup stack

set push, f_result      ; push result address
set push, f_2           ; push 2.0 address
set push, f_result      ; push (2 + 4) result address
                      ; same address can be used as multiple parameters
jsr float_mul

add sp, 3               ; cleanup stack

; f_result now contains 12.0

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Data Format

Each floating point number takes 4 words.

[0] FLOAT_TYPE:
    FLOAT_TYPE_NAN   0x8000
    FLOAT_TYPE_PINF  -3
    FLOAT_TYPE_PNUM  -2
    FLOAT_TYPE_PZERO -1
    FLOAT_TYPE_DBZ    0     (Divide By Zero error)
    FLOAT_TYPE_NZERO  1
    FLOAT_TYPE_NNUM   2
    FLOAT_TYPE_NINF   3
[1] FLOAT_EXP
    Exponent with 0x8000 bias (1.0 has exponent 0x8000)
    NA if FLOAT_TYPE is not NNUM or PNUM
[2-3] FLOAT_HIGH:FLOAT_LOW
    Normalized mantissa with msb always set
    NA if FLOAT_TYPE is not NNUM or PNUM