Fix NaN-safe mode

[devmotion]

Fixes #774. Fixes #745. Closes #386.

On this PR, ForwardDiff with NaN-safe mode gives for the example in #774

julia> using ForwardDiff

julia> log(ForwardDiff.Dual{:tag}(0.0, 0.0))
Dual{:tag}(-Inf,0.0)

julia> log(ForwardDiff.Dual{:tag}(0.0, 0.0, 1.0))
Dual{:tag}(-Inf,0.0,Inf)

julia> ForwardDiff.derivative(log ∘ zero, 1.0)
0.0

julia> f(x) = log(zero(x[1]) + x[2])
f (generic function with 1 method)

julia> ForwardDiff.gradient(f, [1.0, 0.0])
2-element Vector{Float64}:
  0.0
 Inf

and the example in #745:

julia> using ForwardDiff

julia> foo(a) = a[1] * exp(-a[2])
foo (generic function with 1 method)

julia> ForwardDiff.gradient(foo, [1., -1e3])
2-element Vector{Float64}:
  Inf
 -Inf

---

Based on #776, so NaN-safe mode can actually be tested in CI.

---

Edit: I just realized that @jrevels tried to address this issue in #386

---

The Rosenbrock benchmark

julia> using ForwardDiff, Chairmarks

julia> function rosenbrock(x::Vector)
           a = 1.0
           b = 100.0
           result = 0.0
           for i in 1:length(x)-1
               result += (a - x[i])^2 + b*(x[i+1] - x[i]^2)^2
           end
           return result
       end

julia> @be rand(1000) ForwardDiff.gradient($rosenbrock, _)

and the native code analysis in https://github.com/JuliaDiff/ForwardDiff.jl/issues/719#issuecomment-2484955066

julia> a = ForwardDiff.Dual(1.0,2.0,3.0,4.0,5.0)
Dual{Nothing}(1.0,2.0,3.0,4.0,5.0)

julia> @code_native debuginfo=:none ForwardDiff._mul_partials(a.partials, a.partials, 2.0, 1.0)

indicates that this PR does not impact performance when NaN-safe mode is disabled but actually can improve performance when NaN-safe mode is enabled:

master

NaN-safe mode disabled:

julia> @be rand(1000) ForwardDiff.gradient($rosenbrock, _)
Benchmark: 152 samples with 1 evaluation
 min    546.375 μs (7 allocs: 121.266 KiB)
 median 587.812 μs (7 allocs: 121.266 KiB)
 mean   627.082 μs (7 allocs: 121.266 KiB, 1.16% gc time)
 max    2.580 ms (7 allocs: 121.266 KiB, 71.90% gc time)

julia> @code_native debuginfo=:none ForwardDiff._mul_partials(a.partials, a.partials, 2.0, 1.0)
        .section        __TEXT,__text,regular,pure_instructions
        .build_version macos, 16, 0
        .globl  _julia__mul_partials_12796      ; -- Begin function julia__mul_partials_12796
        .p2align        2
_julia__mul_partials_12796:             ; @julia__mul_partials_12796
; Function Signature: _mul_partials(ForwardDiff.Partials{4, Float64}, ForwardDiff.Partials{4, Float64}, Float64, Float64)
; %bb.0:                                ; %top
        ;DEBUG_VALUE: _mul_partials:a <- [DW_OP_deref] [$x0+0]
        ;DEBUG_VALUE: _mul_partials:b <- [DW_OP_deref] [$x1+0]
        ;DEBUG_VALUE: _mul_partials:x_a <- $d0
        ;DEBUG_VALUE: _mul_partials:x_b <- $d1
                                        ; kill: def $d1 killed $d1 def $q1
        ;DEBUG_VALUE: _mul_partials:x_b <- $d1
                                        ; kill: def $d0 killed $d0 def $q0
        ;DEBUG_VALUE: _mul_partials:x_a <- $d0
        ;DEBUG_VALUE: _mul_partials:b <- [DW_OP_deref] [$x1+0]
        ;DEBUG_VALUE: _mul_partials:a <- [DW_OP_deref] [$x0+0]
        ldp     q2, q3, [x0]
        fmul.2d v2, v2, v0[0]
        ldp     q4, q5, [x1]
        fmul.2d v4, v4, v1[0]
        fadd.2d v2, v2, v4
        fmul.2d v0, v3, v0[0]
        fmul.2d v1, v5, v1[0]
        fadd.2d v0, v0, v1
        stp     q2, q0, [x8]
        ret
                                        ; -- End function
        .section        __DATA,__const
        .p2align        3, 0x0                          ; @"+ForwardDiff.Partials#12798"
"l_+ForwardDiff.Partials#12798":
        .quad   "l_+ForwardDiff.Partials#12798.jit"

.set "l_+ForwardDiff.Partials#12798.jit", 5419293392
.subsections_via_symbols

NaN-safe mode enabled:

julia> @be rand(1000) ForwardDiff.gradient($rosenbrock, _)
Benchmark: 51 samples with 1 evaluation
 min    1.680 ms (7 allocs: 121.266 KiB)
 median 1.856 ms (7 allocs: 121.266 KiB)
 mean   1.985 ms (7 allocs: 121.266 KiB, 1.26% gc time)
 max    5.300 ms (7 allocs: 121.266 KiB, 64.43% gc time)

julia> @code_native debuginfo=:none ForwardDiff._mul_partials(a.partials, a.partials, 2.0, 1.0)
        .section        __TEXT,__text,regular,pure_instructions
        .build_version macos, 16, 0
        .globl  _julia__mul_partials_10411      ; -- Begin function julia__mul_partials_10411
        .p2align        2
_julia__mul_partials_10411:             ; @julia__mul_partials_10411
; Function Signature: _mul_partials(ForwardDiff.Partials{4, Float64}, ForwardDiff.Partials{4, Float64}, Float64, Float64)
; %bb.0:                                ; %top
        ;DEBUG_VALUE: _mul_partials:a <- [DW_OP_deref] [$x0+0]
        ;DEBUG_VALUE: _mul_partials:b <- [DW_OP_deref] [$x1+0]
        ;DEBUG_VALUE: _mul_partials:x_a <- $d0
        ;DEBUG_VALUE: _mul_partials:x_b <- $d1
                                        ; kill: def $d1 killed $d1 def $q1
        ;DEBUG_VALUE: _mul_partials:x_b <- $d1
        ;DEBUG_VALUE: _mul_partials:x_a <- $d0
        ;DEBUG_VALUE: _mul_partials:b <- [DW_OP_deref] [$x1+0]
        ;DEBUG_VALUE: _mul_partials:a <- [DW_OP_deref] [$x0+0]
        ldp     q4, q2, [x0]
        fsub    d5, d1, d1
        ldr     d3, [x1]
        fcmp    d5, d5
        b.vs    LBB0_3
; %bb.1:                                ; %top.L61_crit_edge
        ldr     d5, [x1, #8]
LBB0_2:                                 ; %L61
        fsub    d6, d0, d0
        fcmp    d6, d6
        cset    w9, vc
        fcmeq.2d        v6, v4, #0.0
        fcmeq.2d        v7, v2, #0.0
        uzp1.4s v6, v6, v7
        mvn.16b v6, v6
        xtn.4h  v6, v6
        umaxv.4h        h6, v6
        fmov    w10, s6
        orr     w9, w10, w9
        tst     w9, #0x1
        fmov    d6, #1.00000000
        fcsel   d0, d0, d6, ne
        fmul.2d v4, v4, v0[0]
        mov.d   v3[1], v5[0]
        fmul.2d v3, v3, v1[0]
        fadd.2d v3, v4, v3
        fmul.2d v0, v2, v0[0]
        ldr     q2, [x1, #16]
        fmul.2d v1, v2, v1[0]
        fadd.2d v0, v0, v1
        stp     q3, q0, [x8]
        ret
LBB0_3:                                 ; %L37
        ldr     d5, [x1, #8]
        fcmp    d3, #0.0
        b.ne    LBB0_2
; %bb.4:                                ; %L37
        fcmp    d5, #0.0
        b.ne    LBB0_2
; %bb.5:                                ; %L37
        ldr     d6, [x1, #16]
        fcmp    d6, #0.0
        b.ne    LBB0_2
; %bb.6:                                ; %L50
        ldr     d6, [x1, #24]
        fcmp    d6, #0.0
        fmov    d6, #1.00000000
        fcsel   d1, d1, d6, ne
        b       LBB0_2
                                        ; -- End function
        .section        __DATA,__const
        .p2align        3, 0x0                          ; @"+ForwardDiff.Partials#10413"
"l_+ForwardDiff.Partials#10413":
        .quad   "l_+ForwardDiff.Partials#10413.jit"

.set "l_+ForwardDiff.Partials#10413.jit", 4539581520
.subsections_via_symbols

this PR

NaN-safe mode disabled:

julia> @be rand(1000) ForwardDiff.gradient($rosenbrock, _)
Benchmark: 144 samples with 1 evaluation
 min    547.666 μs (7 allocs: 121.266 KiB)
 median 596.917 μs (7 allocs: 121.266 KiB)
 mean   664.194 μs (7 allocs: 121.266 KiB, 0.64% gc time)
 max    7.721 ms (7 allocs: 121.266 KiB, 92.06% gc time)

julia> @code_native debuginfo=:none ForwardDiff._mul_partials(a.partials, a.partials, 2.0, 1.0)
        .section        __TEXT,__text,regular,pure_instructions
        .build_version macos, 16, 0
        .globl  _julia__mul_partials_8061       ; -- Begin function julia__mul_partials_8061
        .p2align        2
_julia__mul_partials_8061:              ; @julia__mul_partials_8061
; Function Signature: _mul_partials(ForwardDiff.Partials{4, Float64}, ForwardDiff.Partials{4, Float64}, Float64, Float64)
; %bb.0:                                ; %top
        ;DEBUG_VALUE: _mul_partials:a <- [DW_OP_deref] [$x0+0]
        ;DEBUG_VALUE: _mul_partials:b <- [DW_OP_deref] [$x1+0]
        ;DEBUG_VALUE: _mul_partials:x_a <- $d0
        ;DEBUG_VALUE: _mul_partials:x_b <- $d1
                                        ; kill: def $d1 killed $d1 def $q1
        ;DEBUG_VALUE: _mul_partials:x_b <- $d1
                                        ; kill: def $d0 killed $d0 def $q0
        ;DEBUG_VALUE: _mul_partials:x_a <- $d0
        ;DEBUG_VALUE: _mul_partials:b <- [DW_OP_deref] [$x1+0]
        ;DEBUG_VALUE: _mul_partials:a <- [DW_OP_deref] [$x0+0]
        ldp     q2, q3, [x0]
        fmul.2d v2, v2, v0[0]
        ldp     q4, q5, [x1]
        fmul.2d v4, v4, v1[0]
        fadd.2d v2, v2, v4
        fmul.2d v0, v3, v0[0]
        fmul.2d v1, v5, v1[0]
        fadd.2d v0, v0, v1
        stp     q2, q0, [x8]
        ret
                                        ; -- End function
        .section        __DATA,__const
        .p2align        3, 0x0                          ; @"+ForwardDiff.Partials#8063"
"l_+ForwardDiff.Partials#8063":
        .quad   "l_+ForwardDiff.Partials#8063.jit"

.set "l_+ForwardDiff.Partials#8063.jit", 5182817040
.subsections_via_symbols

NaN-safe mode enabled:

julia> @be rand(1000) ForwardDiff.gradient($rosenbrock, _)
Benchmark: 111 samples with 1 evaluation
 min    789.709 μs (7 allocs: 121.266 KiB)
 median 853.167 μs (7 allocs: 121.266 KiB)
 mean   899.946 μs (7 allocs: 121.266 KiB, 0.60% gc time)
 max    2.531 ms (7 allocs: 121.266 KiB, 66.18% gc time)

julia> @code_native debuginfo=:none ForwardDiff._mul_partials(a.partials, a.partials, 2.0, 1.0)
        .section        __TEXT,__text,regular,pure_instructions
        .build_version macos, 16, 0
        .globl  _julia__mul_partials_15428      ; -- Begin function julia__mul_partials_15428
        .p2align        2
_julia__mul_partials_15428:             ; @julia__mul_partials_15428
; Function Signature: _mul_partials(ForwardDiff.Partials{4, Float64}, ForwardDiff.Partials{4, Float64}, Float64, Float64)
; %bb.0:                                ; %top
        ;DEBUG_VALUE: _mul_partials:a <- [DW_OP_deref] [$x0+0]
        ;DEBUG_VALUE: _mul_partials:b <- [DW_OP_deref] [$x1+0]
        ;DEBUG_VALUE: _mul_partials:x_a <- $d0
        ;DEBUG_VALUE: _mul_partials:x_b <- $d1
                                        ; kill: def $d1 killed $d1 def $q1
        ;DEBUG_VALUE: _mul_partials:x_b <- $d1
                                        ; kill: def $d0 killed $d0 def $q0
        ;DEBUG_VALUE: _mul_partials:x_a <- $d0
        ;DEBUG_VALUE: _mul_partials:b <- [DW_OP_deref] [$x1+0]
        ;DEBUG_VALUE: _mul_partials:a <- [DW_OP_deref] [$x0+0]
        ldp     q2, q3, [x0]
        fmul.2d v4, v2, v0[0]
        fcmeq.2d        v2, v2, #0.0
        bic.16b v2, v4, v2
        ldp     q4, q5, [x1]
        fmul.2d v6, v4, v1[0]
        fcmeq.2d        v4, v4, #0.0
        bic.16b v4, v6, v4
        fadd.2d v2, v2, v4
        fmul.2d v0, v3, v0[0]
        fcmeq.2d        v3, v3, #0.0
        bic.16b v0, v0, v3
        fmul.2d v1, v5, v1[0]
        fcmeq.2d        v3, v5, #0.0
        bic.16b v1, v1, v3
        fadd.2d v0, v0, v1
        stp     q2, q0, [x8]
        ret
                                        ; -- End function
        .section        __DATA,__const
        .p2align        3, 0x0                          ; @"+ForwardDiff.Partials#15430"
"l_+ForwardDiff.Partials#15430":
        .quad   "l_+ForwardDiff.Partials#15430.jit"

.set "l_+ForwardDiff.Partials#15430.jit", 5213265424
.subsections_via_symbols

julia> versioninfo()
Julia Version 1.11.7
Commit f2b3dbda30a (2025-09-08 12:10 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: macOS (arm64-apple-darwin24.0.0)
  CPU: 10 × Apple M2 Pro
  WORD_SIZE: 64
  LLVM: libLLVM-16.0.6 (ORCJIT, apple-m2)
Threads: 1 default, 0 interactive, 1 GC (on 6 virtual cores)
Environment:
  JULIA_PKG_USE_CLI_GIT = true
  JULIA_PKG_PRESERVE_TIERED_INSTALLED = true

[KristofferC]

More correctness and better performance. What's not to like? :)

[andreasnoack]

What is this buildkite check?

[devmotion]

There's no actual check since there's no buildkite configuration. Apparently Chris registered the package on buildkite as part of #761 but since there's no configuration it just errors.