`nx_f32_encode.nx` source

1// nx_f32_encode.nx -- the ENCODE half of f32: integer value -> IEEE-754 single
2// bit pattern.  nx_f32.nx has arithmetic + nx_fp32_q14 DECODES (f32->Q14), but
3// nothing ENCODES a value to f32 bits -- the exact primitive an STL writer needs
4// to emit mesh vertices (then nx_le_write_u32 the bits).  This fills that gap (no
5// duplicate -- verified nx_f32/nx_fp32_q14 lack it).  license_tier: ORIGINAL.
6
7import "nx_syscalls.nx"
8const K_MAGIC_8388607: i64 = 8388607
9
10// IEEE-754 single-precision bit pattern (as i64, 0..2^32-1) for integer v.
11func f32_from_i64(v: i64) -> i64 {
12    if v == 0 { return 0 }
13    var sign: i64 = 0
14    var a: i64 = v
15    if a < 0 { sign = 1; a = 0 - a }
16    // highest set bit position of a
17    var msb: i64 = 0
18    var t: i64 = a
19    while t > 1 { t = t / 2; msb = msb + 1 }
20    let exp: i64 = 127 + msb                       // biased exponent
21    var mant: i64 = 0                              // 23-bit mantissa (leading 1 implicit -> masked off)
22    if msb <= 23 { mant = (a << (23 - msb)) & K_MAGIC_8388607 }
23    else { mant = (a >> (msb - 23)) & K_MAGIC_8388607 }
24    return (sign << 31) | (exp << 23) | mant
25}
26
27// IEEE-754 single-precision bit pattern for the REAL number (q14 / 16384),
28// where q14 is a Q14 fixed-point value (1 unit = 1/16384, the canonical mm
29// unit of the mesh/slicer/gcode pipeline).  Dividing by 2^14 = 16384 is an
30// EXACT downward shift of the binary exponent -- the mantissa and sign are
31// untouched -- so this is the precise inverse of nx_fp32_bytes_to_q14 for
32// |q14| < 2^24 (i.e. |value| < 1024 mm, well above any print bed).  This is
33// the sub-mm units bridge an arbitrary-mesh STL writer needs: f32_from_i64
34// only encodes whole millimetres, losing all sculpt/CAD detail below 1 mm.
35func f32_from_q14(q14: i64) -> i64 {
36    if q14 == 0 { return 0 }
37    let bits: i64 = f32_from_i64(q14)              // f32 of the integer q14
38    let sign: i64 = (bits >> 31) & 1
39    let exp:  i64 = (bits >> 23) & 255             // biased exponent of integer q14
40    let mant: i64 = bits & K_MAGIC_8388607                 // 23-bit mantissa
41    let new_exp: i64 = exp - 14                    // / 2^14  (exact, no rounding)
42    return (sign << 31) | (new_exp << 23) | mant
43}
nx_f32_encode.nx source

`nx_f32_encode.nx` source
