_f64_sinhcosh_gate_authored.nx source

1// _f64_sinhcosh_gate_authored.nx -- ME1 sinh/cosh gate: dd kernels 2// (_pe_f64sinhcosh) vs the LIVE sovereign bigfloat oracle. Pure Nishi. 3// Edges: Taylor/exp seam at 1, I-drop seam at 28, overflow boundary 4// (710.0 / ln(2^1025) / 710.5), tiny/subnormal; bands across (0,1), [1,28), 5// [28,710]. GREEN iff max ULP <= 1 on BOTH functions. 6// Markers: SHBAD/CHBAD x= exp= got= ulp= / SINH-ULP / COSH-ULP / verdict= 7 8import "nx_syscalls.nx" 9import "nx_f64.nx" 10import "nx_f64_div.nx" 11import "nx_f64_cvt.nx" 12import "nx_bigfloat120.nx" 13import "nx_bigfloat120_div.nx" 14import "nx_bigfloat120_exp.nx" 15import "nx_bigfloat120_ln.nx" 16import "nx_bigfloat120_pow.nx" 17import "nx_bigfloat120_sinh.nx" 18import "_pm_sinhcosh_spec.nx" 19import "_pe_f64sinhcosh.nx" 20 21func shg_puts(s: *u8) -> i64 { var n: i64 = 0; while s[n] != (0 as u8) { n = n + 1 } sys_write(1, s, n); return 0 } 22func shg_putn(v: i64) -> i64 { let bb: *u8 = sys_mmap(28); var m: i64 = v; if m < 0 { m = 0 - m; sys_write(1, "-" as *u8, 1) }; let t: *u8 = sys_mmap(28); var k: i64 = 0; if m == 0 { t[0] = 48; k = 1 }; while m > 0 { t[k] = 48 + (m % 10); m = m / 10; k = k + 1 }; var i: i64 = 0; while i < k { bb[i] = t[k-1-i]; i = i + 1 }; sys_write(1, bb, k); return 0 } 23func shg_puthex(v: i64) -> i64 { let bb: *u8 = sys_mmap(20); var i: i64 = 0; while i < 16 { let nib: i64 = (v >> ((15 - i) * 4)) & 15; if nib < 10 { bb[i] = 48 + nib } else { bb[i] = 55 + nib } i = i + 1 } sys_write(1, bb, 16); return 0 } 24 25func shg_rng(state: *i64) -> i64 { 26 var s: i64 = state[0] 27 s = s ^ ((s >> 12) & 0x000FFFFFFFFFFFFF) 28 s = s ^ (s << 25) 29 s = s ^ ((s >> 27) & 0x0000001FFFFFFFFF) 30 state[0] = s 31 return s * 2685821657736338717 32} 33 34func shg_ord(v: i64) -> i64 { 35 if v >= 0 { return v } 36 return (1 << 63) - v 37} 38 39func shg_ulp(got: i64, want: i64) -> i64 { 40 if got == want { return 0 } 41 var u: i64 = shg_ord(got) - shg_ord(want) 42 if u < 0 { u = 0 - u } 43 return u 44} 45 46func main() -> i64 { 47 let xs: *i64 = sys_mmap(8 * 512) as *i64 48 var n: i64 = 0 49 xs[n] = 0x7FF8000000000000; n = n + 1 50 xs[n] = 0x7FF0000000000000; n = n + 1 51 xs[n] = 0xFFF0000000000000; n = n + 1 52 xs[n] = 0; n = n + 1 53 xs[n] = 1 << 63; n = n + 1 54 xs[n] = 1; n = n + 1 // min subnormal 55 xs[n] = 0x000FFFFFFFFFFFFF; n = n + 1 56 xs[n] = 0x3E50000000000000; n = n + 1 // 2^-26 57 xs[n] = 0x3FEFFFFFFFFFFFFF; n = n + 1 // 1 - ulp (Taylor side) 58 xs[n] = 0x3FF0000000000000; n = n + 1 // 1.0 (exp side) 59 xs[n] = 0x3FF0000000000001; n = n + 1 60 xs[n] = 0x403BFFFFFFFFFFFF; n = n + 1 // 28 - ulp (I-branch) 61 xs[n] = 0x403C000000000000; n = n + 1 // 28 (E/2 branch) 62 xs[n] = 0x4086300000000000; n = n + 1 // 710.0 finite 63 xs[n] = 0x40862E42FEFA39EF; n = n + 1 // ln(2^1025): the brink 64 xs[n] = 0x4086340000000000; n = n + 1 // 710.5 inf 65 xs[n] = 0x4086380000000000; n = n + 1 // 711 inf 66 xs[n] = 0xC086300000000000; n = n + 1 // -710 (sinh sign) 67 xs[n] = 0xBFE0000000000000; n = n + 1 // -0.5 68 let st: *i64 = sys_mmap(16) as *i64 69 // LN40 (2026-09-03): this PRNG seed was written as a 20-digit decimal that does not fit 64 bits, so 70 // every build before today WRAPPED it silently. The value below is exactly what it wrapped to, so the 71 // sequence this gate has always exercised is unchanged -- the literal now says what the machine does. 72 st[0] = 8736074210880900737 73 var j: i64 = 0 74 while j < 320 { 75 var raw: i64 = shg_rng(st) 76 var efr: i64 = 0 77 let band: i64 = raw & 3 78 if band == 0 { efr = 1015 + (raw & 7) } // (2^-8, 2) Taylor zone 79 if band == 1 { efr = 1023 + (raw & 3) } // [1, 16) I-branch 80 if band == 2 { efr = 1027 + (raw & 3) } // [16, 256) seam + E/2 81 if band == 3 { efr = 990 + (raw & 63) } // tiny through mid 82 var rw: i64 = (efr << 52) | (shg_rng(st) & 0x000FFFFFFFFFFFFF) 83 if efr == 1032 { rw = (1032 << 52) | (shg_rng(st) & 0x0006FFFFFFFFFFFF) } // cap < ~700 84 if (shg_rng(st) & 1) == 1 { rw = rw | (1 << 63) } 85 xs[n] = rw 86 n = n + 1 87 j = j + 1 88 } 89 90 var s_exact: i64 = 0 91 var s_u1: i64 = 0 92 var s_worse: i64 = 0 93 var s_max: i64 = 0 94 var c_exact: i64 = 0 95 var c_u1: i64 = 0 96 var c_worse: i64 = 0 97 var c_max: i64 = 0 98 var i: i64 = 0 99 while i < n { 100 let x: i64 = xs[i] 101 let sw: i64 = bf_sinh_f64(x) 102 let sg: i64 = nx_f64_sinh(x) 103 let su: i64 = shg_ulp(sg, sw) 104 if su == 0 { s_exact = s_exact + 1 } 105 if su == 1 { s_u1 = s_u1 + 1 } 106 if su > 1 { 107 s_worse = s_worse + 1 108 if s_worse <= 20 { 109 shg_puts("SHBAD x=" as *u8); shg_puthex(x) 110 shg_puts(" exp=" as *u8); shg_puthex(sw) 111 shg_puts(" got=" as *u8); shg_puthex(sg) 112 shg_puts(" ulp=" as *u8); shg_putn(su) 113 shg_puts("\n" as *u8) 114 } 115 } 116 if su > s_max { s_max = su } 117 let cw: i64 = bf_cosh_f64(x) 118 let cg: i64 = nx_f64_cosh(x) 119 let cu: i64 = shg_ulp(cg, cw) 120 if cu == 0 { c_exact = c_exact + 1 } 121 if cu == 1 { c_u1 = c_u1 + 1 } 122 if cu > 1 { 123 c_worse = c_worse + 1 124 if c_worse <= 20 { 125 shg_puts("CHBAD x=" as *u8); shg_puthex(x) 126 shg_puts(" exp=" as *u8); shg_puthex(cw) 127 shg_puts(" got=" as *u8); shg_puthex(cg) 128 shg_puts(" ulp=" as *u8); shg_putn(cu) 129 shg_puts("\n" as *u8) 130 } 131 } 132 if cu > c_max { c_max = cu } 133 i = i + 1 134 } 135 136 shg_puts("SINH-ULP total=" as *u8); shg_putn(n) 137 shg_puts(" exact=" as *u8); shg_putn(s_exact) 138 shg_puts(" ulp1=" as *u8); shg_putn(s_u1) 139 shg_puts(" worse=" as *u8); shg_putn(s_worse) 140 shg_puts(" max=" as *u8); shg_putn(s_max) 141 shg_puts("\n" as *u8) 142 shg_puts("COSH-ULP total=" as *u8); shg_putn(n) 143 shg_puts(" exact=" as *u8); shg_putn(c_exact) 144 shg_puts(" ulp1=" as *u8); shg_putn(c_u1) 145 shg_puts(" worse=" as *u8); shg_putn(c_worse) 146 shg_puts(" max=" as *u8); shg_putn(c_max) 147 shg_puts("\n" as *u8) 148 if s_worse == 0 { 149 if c_worse == 0 { 150 shg_puts("SINHCOSH-GATE verdict=GREEN\n" as *u8) 151 return 0 152 } 153 } 154 shg_puts("SINHCOSH-GATE verdict=RED\n" as *u8) 155 var rc: i64 = s_worse + c_worse 156 if rc > 100 { rc = 100 } 157 return rc 158}