code wiki / _hdl_build / nx_intfp_rmsnorm_gradcheck_gate.nx

nx_intfp_rmsnorm_gradcheck_gate.nx

buildroot/runtime/_hdl_build/nx_intfp_rmsnorm_gradcheck_gate.nx

5338 B92 linesdepth 2pulls 2 transitivereach 0 importersview sourcekind gate/prooftopic intfp
docsdependenciesstructsconstsfunctions

about

nx_intfp_rmsnorm_gradcheck_gate.nx -- LAST transcendental for integer transformer training: RMSNorm needs 1/sqrt, exactly where the software-float tape uses f32_sqrtx. Here: integer isqrt (exact bit-by-bit) + RMSNorm forward + the full coupled Jacobian backward, gradchecked (integer finite-diff), NO float. fwd: ms=mean(x^2)+eps ; rms=sqrt(ms) ; y_i = (x_i/rms)*gamma_i bwd: dL/dx_j = gamma_j*g_j/rms - x_j*c/(D*rms^3), c=sum_i g_i*gamma_i*x_i, g_i=dL/dy_i Key Q16 trick: rms_q16 = isqrt(ms_q32) exactly (isqrt(ms*S^2)=sqrt(ms)*S=rms*S). Uses inv_rms to avoid rms^3 overflow. If this gradchecks, the last hard op is proven and the whole integer tape is assemblable. license_tier: ORIGINAL

dependencies 1 imports · 0 importers

nx_syscalls.nx nx_intfp_rmsnorm_gradcheck_gat

imports: nx_syscalls.nx

imported by: nobody (leaf or entry point)

call flow from main pre-order; caps 40 nodes / depth 6 declared; ↻ = already shown

main w sys_write wn sys_write ↻ sys_mmap isqrt sys_mmap ↻ rms_fwd isqrt ↻ iabs

structs

none

consts

14const S: i64 = 65536
15const D: i64 = 4

functions

10func w(s: *u8) -> i64 { var n: i64=0; while s[n]!=(0 as u8){n=n+1} sys_write(1,s,n); return 0 }
called by 1: main calls 1: sys_write
11func wn(v: i64) -> i64 { if v==0 { sys_write(1,"0" as *u8,1); return 0 } var m: i64=v; if m<0{sys_write(1,"-" as *u8,1);m=0-m} let t: *u8=sys_mmap(24); var k: i64=0; while m>0{t[k]=(48+(m%10)) as u8;m=m/10;k=k+1} let o: *u8=sys_mmap(24); var q: i64=k-1; var i: i64=0; while q>=0{o[i]=t[q];i=i+1;q=q-1} sys_write(1,o,i); return 0 }
called by 1: main calls 2: sys_writesys_mmap
12func iabs(v: i64) -> i64 { if v<0 { return 0-v } return v }
called by 1: main
18func isqrt(n: i64) -> i64
called by 2: rms_fwdmain
30func rms_fwd(x: *i64, gamma: *i64, y: *i64, rmsout: *i64) -> i64
called by 1: main calls 1: isqrt
42func main() -> i64