`nx_f32_div.nx` source

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1// nx_f32_div.nx -- IEEE 754 binary32 division (standalone).
2//
3// Separated from runtime/nx_f32.nx because having division code in
4// the same file as nx_f32_mul triggers the nxc2 codegen quirk
5// tracked in Task #10 (negative-literal sign-extension regression
6// in earlier mul KAT after certain patterns added).  Isolating this
7// brick in its own file sidesteps the quirk while preserving the
8// L4 bits-up tower's contract.
9//
10// Composes:
11//   nx_f32.nx -- classify / sign / exp_field / mant_field / constants
12//
13// Algorithm:
14//   1. NaN/Inf/Zero special cases per IEEE 754.
15//   2. Build 24-bit significands.
16//   3. (a_sig << 24) / b_sig gives 24- or 25-bit quotient.
17//   4. Normalize to 24-bit mantissa, extract guard from dropped bit,
18//      sticky from remainder.
19//   5. Round-to-nearest-even.
20//   6. Overflow → inf, underflow → subnormal/zero.
21//
22// v1 limitations: subnormal input/output conservatively zero/inf.
23
24import "nx_syscalls.nx"
25import "nx_tier.nx"
26import "nx_f32.nx"
27
28func nx_f32_div(a: i64, b: i64) -> i64 {
29    let cls_a: nx_int = nx_f32_classify(a)
30    let cls_b: nx_int = nx_f32_classify(b)
31    let sign_out: i64 = nx_f32_sign(a) ^ nx_f32_sign(b)
32
33    if cls_a == NX_F32_CLS_NAN { return NX_F32_NAN_RAW }
34    if cls_b == NX_F32_CLS_NAN { return NX_F32_NAN_RAW }
35
36    if cls_b == NX_F32_CLS_ZERO {
37        if cls_a == NX_F32_CLS_ZERO { return NX_F32_NAN_RAW }
38        return (sign_out << 31) | NX_F32_INF_RAW
39    }
40    if cls_b == NX_F32_CLS_INF {
41        if cls_a == NX_F32_CLS_INF { return NX_F32_NAN_RAW }
42        return sign_out << 31
43    }
44
45    if cls_a == NX_F32_CLS_ZERO { return sign_out << 31 }
46    if cls_a == NX_F32_CLS_INF {
47        return (sign_out << 31) | NX_F32_INF_RAW
48    }
49
50    if cls_a == NX_F32_CLS_SUBNORMAL { return sign_out << 31 }
51    if cls_b == NX_F32_CLS_SUBNORMAL {
52        return (sign_out << 31) | NX_F32_INF_RAW
53    }
54
55    let mant_a: i64 = nx_f32_mant_field(a)
56    let exp_a:  i64 = nx_f32_exp_field(a)
57    let sig_a:  i64 = mant_a | NX_F32_IMPLICIT_1
58
59    let mant_b: i64 = nx_f32_mant_field(b)
60    let exp_b:  i64 = nx_f32_exp_field(b)
61    let sig_b:  i64 = mant_b | NX_F32_IMPLICIT_1
62
63    var exp_out: i64 = exp_a - exp_b + NX_F32_EXP_BIAS
64
65    // ONE EXTRA QUOTIENT BIT (root fix 2026-09-14): the v1 body computed only 24 quotient bits, so in Case B the
66    // guard bit was set to a CONSTANT 0 and every such division was TRUNCATED, never rounded to nearest even.
67    // nx_f32_bricks_hw_gate measured it against the hardware divide: 937 of 4096 random pairs off the IEEE result
68    // while add and mul matched bit for bit. With sig_a << 25 the guard is a real quotient bit in both cases.
69    let dividend: i64 = sig_a << 25
70    let q:        i64 = dividend / sig_b
71    let rem:      i64 = dividend - q * sig_b
72
73    // Case A (sig_a >= sig_b): q in [2^25, 2^26); mantissa = q >> 2, guard = bit 1, sticky = bit 0 or remainder,
74    //   exp_out UNCHANGED (real ratio in [1,2)).
75    // Case B (sig_a <  sig_b): q in [2^24, 2^25); mantissa = q >> 1, guard = bit 0, sticky = remainder, and the
76    //   real ratio is in [0.5,1) so DECREMENT exp_out by 1 to keep canonical implicit-1 form.
77    var mant_out:  i64 = 0
78    var guard_bit: i64 = 0
79    var sticky:    i64 = 0
80    if sig_a >= sig_b {
81        mant_out  = q >> 2
82        guard_bit = (q >> 1) & 1
83        if (q & 1) != 0 { sticky = 1 }
84        if rem != 0 { sticky = 1 }
85    } else {
86        mant_out  = q >> 1
87        guard_bit = q & 1
88        if rem != 0 { sticky = 1 }
89        exp_out = exp_out - 1
90    }
91
92    var round_up: i64 = 0
93    if guard_bit == 1 {
94        if sticky == 1 { round_up = 1 }
95        if sticky == 0 {
96            if (mant_out & 1) == 1 { round_up = 1 }
97        }
98    }
99    if round_up == 1 {
100        mant_out = mant_out + 1
101        if mant_out >= 0x01000000 {
102            mant_out = mant_out >> 1
103            exp_out = exp_out + 1
104        }
105    }
106
107    if exp_out >= 255 {
108        return (sign_out << 31) | NX_F32_INF_RAW
109    }
110    if exp_out <= 0 {
111        let shifts: i64 = 1 - exp_out
112        if shifts > 24 {
113            return sign_out << 31
114        }
115        mant_out = mant_out >> shifts
116        return (sign_out << 31) | (mant_out & NX_F32_MANT_MASK)
117    }
118
119    let mant_final: i64 = mant_out & NX_F32_MANT_MASK
120    return (sign_out << 31) | (exp_out << NX_F32_EXP_SHIFT) | mant_final
121}
nx_f32_div.nx source

`nx_f32_div.nx` source
