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;ACME 0.94.5
!ifdef lib_cbm_mflpt_a !eof
lib_cbm_mflpt_a = 1
; CAUTION! The Commodore BASIC interpreter uses two different formats for
; handling floating-point values, so do not confuse them:
; The "float registers" fac1 and fac2 (actually structures in zero page) use a
; six-byte format commonly known as "flpt" (floating point).
; When storing values in variables (or reading values from ROM), a compressed
; five-byte format is used, commonly known as "mflpt" (memory floating point).
; This file contains a macro for writing floating point numbers in the five-byte
; "mflpt" format, where the sign bit is packed into the mantissa.
; Several interpreter functions use this format (see <cbm/c64/float.a>).
; Use the macro like this:
; +mflpt 3.1415926 ; each use will take up five bytes of memory
; now for the technical stuff (stop reading right now if you value your sanity)
; five-byte layout in memory:
; eeeeeeee smmmmmmm mmmmmmmm mmmmmmmm mmmmmmmm ; eight bits exponent, 32 bits mantissa with sign bit overlay
; exponent byte:
; exponent has a bias of 128 (128 means the decimal point is right before the mantissa's leading digit)
; if exponent is zero, number value is considered to be zero, regardless of mantissa
; exponents 1..128 are for values < 1
; exponents 129..255 are for values >= 1
; mantissa:
; mantissa is stored big-endian(!)
; the mantissa's mandatory leading '1' is replaced by the sign bit
; so logically, this is equivalent to:
; + .1mmmmmmm mmmmmmmm mmmmmmmm mmmmmmmm * 2^(eeeeeeee - 128) if sign bit is 0
; - .1mmmmmmm mmmmmmmm mmmmmmmm mmmmmmmm * 2^(eeeeeeee - 128) if sign bit is 1
; this is ugly, but it gets the job done
; (if it's stupid, but it works, then it's not stupid)
!macro mflpt .value {
!set .float = float(.value) ; make sure to do passes until value is defined
!ifndef .float {
!by $ff, $ff, $ff, $ff, $ff ; five place holder bytes
} else {
; value is defined, so split up into sign and non-negative value
!if .float < 0 {
!set .sign = $80
!set .float = -.float
} else {
!set .sign = $00
}
!if .float = 0 {
!by 0, 0, 0, 0, 0 ; five zeroes (zero is represented by all bits zero)
} else {
; split up into exponent and mantissa
!set .exponent = 128 + 32 ; 128 is cbm's bias, 32 is this algo's bias
; if mantissa is too large, shift right and adjust exponent
!do while .float >= (2.0 ^ 32.0) {
!set .float = .float >> 1
!set .exponent = .exponent + 1
}
; if mantissa is too small, shift left and adjust exponent
!do while .float < (2.0 ^ 31.0) {
!set .float = .float << 1
!set .exponent = .exponent - 1
}
!if .exponent < 1 {
!warn "MFLPT underflow, using zero instead"
!set .float = 0
!set .exponent = 0
!set .sign = 0
}
!if .exponent > 255 {
!error "MFLPT overflow"
}
!by .exponent
!by (127 & int(.float >> 24)) | .sign
!by 255 & int(.float >> 16)
!by 255 & int(.float >> 8)
!by 255 & int(.float)
}
}
}
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