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Merge pull request #856 from boriel-basic/feat/fmath_lib
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feat: add fmath.bas library by @Britlion
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@boriel
boriel authored Nov 6, 2024
2 parents 1c61a23 + f99e68b commit 2b0d364
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140 changes: 140 additions & 0 deletions src/lib/arch/zx48k/stdlib/fmath.bas
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' ----------------------------------------------------------------
' This file is released under the MIT License
'
' Copyleft (k) 2024
' Contributed by Britlion
' ----------------------------------------------------------------

#pragma once

#pragma push(case_insensitive)
#pragma case_insensitive = True


FUNCTION fSin(num as FIXED) as FIXED
DIM quad as byte
DIM est1,dif as uByte

'This change made now that MOD works with FIXED types.
'This is much faster than the repeated subtraction method for large angles (much > 360)
'while having some tiny rounding errors that should not significantly affect our results.
'Note that the result may be positive or negative still, and for SIN(360) might come out
'fractionally above 360 (which would cause issued) so the below code still is required.

IF num >= 360 THEN
num = num MOD 360
ELSEIF num < 0 THEN
num = 360 - ABS(num) MOD 360
END IF

IF num>180 then
quad=-1
num=num-180
ELSE
quad=1
END IF

IF num>90 then num=180-num

num=num/2
dif=num : rem Cast to byte loses decimal
num=num-dif : rem so this is just the decimal bit


est1=PEEK (@sinetable+dif)
dif=PEEK (@sinetable+dif+1)-est1 : REM this is just the difference to the next up number.

num=est1+(num*dif): REM base +interpolate to the next value.

return (num/255)*quad


sinetable:
asm
DEFB 000,009,018,027,035,044,053,062
DEFB 070,079,087,096,104,112,120,127
DEFB 135,143,150,157,164,171,177,183
DEFB 190,195,201,206,211,216,221,225
DEFB 229,233,236,240,243,245,247,249
DEFB 251,253,254,254,255,255
end asm
END FUNCTION

FUNCTION fCos(num as FIXED) as FIXED
return fSin(90-num)
END FUNCTION

FUNCTION fTan(num as FIXED) as FIXED
return fSin(num)/fSin(90-num)
END FUNCTION

REM Fast floating Point Square Root Function
REM Adapted and modified for Boriel's ZX BASIC
REM By Britlion

FUNCTION FASTCALL fSqrt (radicand as FLOAT) as FLOAT
ASM
push namespace core

; FLOAT value arrives in A ED CB
; A is the exponent.
AND A ; Test for zero argument
RET Z ; Return with zero.

;Strictly we should test the number for being negative and quit if it is.
;But let's assume we like imaginary numbers, hmm?
; If you'd rather break it change to a jump to an error below.
;BIT 7,E ; Test the bit.
;JR NZ,REPORT ; back to REPORT_A
; 'Invalid argument'
RES 7,E ; Now it's a positive number, no matter what.

call __FPSTACK_PUSH ; Okay, We put it on the calc stack. Stack contains ABS(x)

; Halve the exponent to achieve a good guess.(accurate with .25 16 64 etc.)

; Remember, A is the exponent.
XOR $80 ; toggle sign of exponent
SRA A ; shift right, bit 7 unchanged.
INC A ;
JR Z,ASIS ; forward with say .25 -> .5
JP P,ASIS ; leave increment if value > .5
DEC A ; restore to shift only.

ASIS:
XOR $80 ; restore sign.
call __FPSTACK_PUSH ; Okay, NOW we put the guess on the stack
rst 28h ; ROM CALC ;;guess,x
DEFB $C3 ;;st-mem-3
DEFB $02 ;;delete

SQRLOOP:
DEFB $31 ;;duplicate
DEFB $E3 ;;get-mem-3
DEFB $C4 ;;st-mem-4
DEFB $05 ;;div
DEFB $E3 ;;get-mem-3
DEFB $0F ;;addition
DEFB $A2 ;;stk-half
DEFB $04 ;;multiply
DEFB $C3 ;;st-mem-3
DEFB $E4 ;;get-mem-4
DEFB $03 ;;subtract
DEFB $2A ;;abs
DEFB $37 ;;greater-0
DEFB $00 ;;jump-true

DEFB SQRLOOP - $ ;;to sqrloop

DEFB $02 ;;delete
DEFB $E3 ;;get-mem-3
DEFB $38 ;;end-calc sqr x.

jp __FPSTACK_POP

pop namespace

END ASM
END FUNCTION

#pragma pop(case_insensitive)
140 changes: 140 additions & 0 deletions src/lib/arch/zxnext/stdlib/fmath.bas
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Original file line number Diff line number Diff line change
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' ----------------------------------------------------------------
' This file is released under the MIT License
'
' Copyleft (k) 2024
' Contributed by Britlion
' ----------------------------------------------------------------

#pragma once

#pragma push(case_insensitive)
#pragma case_insensitive = True


FUNCTION fSin(num as FIXED) as FIXED
DIM quad as byte
DIM est1,dif as uByte

'This change made now that MOD works with FIXED types.
'This is much faster than the repeated subtraction method for large angles (much > 360)
'while having some tiny rounding errors that should not significantly affect our results.
'Note that the result may be positive or negative still, and for SIN(360) might come out
'fractionally above 360 (which would cause issued) so the below code still is required.

IF num >= 360 THEN
num = num MOD 360
ELSEIF num < 0 THEN
num = 360 - ABS(num) MOD 360
END IF

IF num>180 then
quad=-1
num=num-180
ELSE
quad=1
END IF

IF num>90 then num=180-num

num=num/2
dif=num : rem Cast to byte loses decimal
num=num-dif : rem so this is just the decimal bit


est1=PEEK (@sinetable+dif)
dif=PEEK (@sinetable+dif+1)-est1 : REM this is just the difference to the next up number.

num=est1+(num*dif): REM base +interpolate to the next value.

return (num/255)*quad


sinetable:
asm
DEFB 000,009,018,027,035,044,053,062
DEFB 070,079,087,096,104,112,120,127
DEFB 135,143,150,157,164,171,177,183
DEFB 190,195,201,206,211,216,221,225
DEFB 229,233,236,240,243,245,247,249
DEFB 251,253,254,254,255,255
end asm
END FUNCTION

FUNCTION fCos(num as FIXED) as FIXED
return fSin(90-num)
END FUNCTION

FUNCTION fTan(num as FIXED) as FIXED
return fSin(num)/fSin(90-num)
END FUNCTION

REM Fast floating Point Square Root Function
REM Adapted and modified for Boriel's ZX BASIC
REM By Britlion

FUNCTION FASTCALL fSqrt (radicand as FLOAT) as FLOAT
ASM
push namespace core

; FLOAT value arrives in A ED CB
; A is the exponent.
AND A ; Test for zero argument
RET Z ; Return with zero.

;Strictly we should test the number for being negative and quit if it is.
;But let's assume we like imaginary numbers, hmm?
; If you'd rather break it change to a jump to an error below.
;BIT 7,E ; Test the bit.
;JR NZ,REPORT ; back to REPORT_A
; 'Invalid argument'
RES 7,E ; Now it's a positive number, no matter what.

call __FPSTACK_PUSH ; Okay, We put it on the calc stack. Stack contains ABS(x)

; Halve the exponent to achieve a good guess.(accurate with .25 16 64 etc.)

; Remember, A is the exponent.
XOR $80 ; toggle sign of exponent
SRA A ; shift right, bit 7 unchanged.
INC A ;
JR Z,ASIS ; forward with say .25 -> .5
JP P,ASIS ; leave increment if value > .5
DEC A ; restore to shift only.

ASIS:
XOR $80 ; restore sign.
call __FPSTACK_PUSH ; Okay, NOW we put the guess on the stack
rst 28h ; ROM CALC ;;guess,x
DEFB $C3 ;;st-mem-3
DEFB $02 ;;delete

SQRLOOP:
DEFB $31 ;;duplicate
DEFB $E3 ;;get-mem-3
DEFB $C4 ;;st-mem-4
DEFB $05 ;;div
DEFB $E3 ;;get-mem-3
DEFB $0F ;;addition
DEFB $A2 ;;stk-half
DEFB $04 ;;multiply
DEFB $C3 ;;st-mem-3
DEFB $E4 ;;get-mem-4
DEFB $03 ;;subtract
DEFB $2A ;;abs
DEFB $37 ;;greater-0
DEFB $00 ;;jump-true

DEFB SQRLOOP - $ ;;to sqrloop

DEFB $02 ;;delete
DEFB $E3 ;;get-mem-3
DEFB $38 ;;end-calc sqr x.

jp __FPSTACK_POP

pop namespace

END ASM
END FUNCTION

#pragma pop(case_insensitive)

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