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;ACME 0.94.5
!ifdef lib_cbm_flpt_a !eof
lib_cbm_flpt_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 six-byte
; "flpt" format, where the sign bit occupies the sixth byte.
; There are no interpreter functions to use this format, so you will have to
; write your own functions for "copy-mem-to-fac1", "copy-fac2-to-mem" etc.
; Use the macro like this:
; +flpt 3.1415926 ; each use will take up six bytes of memory
; now for the technical stuff (stop reading right now if you value your sanity)
; six-byte layout in memory:
; eeeeeeee 1mmmmmmm mmmmmmmm mmmmmmmm mmmmmmmm sxxxxxxx ; eight bits exponent, 32 bits mantissa with leading '1', sign byte
; 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 leading digit is always '1' (unless the whole value represents zero)
; sign byte:
; most significant bit is sign: 0 means positive number, 1 means negative number
; the seven lower bits are unused
; 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 flpt .value {
!set .float = float(.value) ; make sure to do passes until value is defined
!ifndef .float {
!by $ff, $ff, $ff, $ff, $ff, $ff ; six 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, 0 ; six 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 "FLPT underflow, using zero instead"
!set .float = 0
!set .exponent = 0
!set .sign = 0
}
!if .exponent > 255 {
!error "FLPT overflow"
}
!by .exponent
!by 255 & int(.float >> 24)
!by 255 & int(.float >> 16)
!by 255 & int(.float >> 8)
!by 255 & int(.float)
!by .sign
}
}
}
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