`grad()`

Function in IR

Differentiate a function of a module with respect to one of its parameters, in forward mode, and add the derivative as a new function.

import { grad } from 'typeshade'

The signature, the description and the examples come from the compiler's own source at commit 26de7be8.

Syntax

function grad(m: ModuleDecl, fn: string, param: string, opts?: GradOptions): GradResult

Parameters

m ModuleDecl: the module holding fn.
fn string: the name of the function to differentiate. It must return f32, an f32 vector or an f32 matrix.
param string: the name of the parameter to differentiate with respect to: an f32, or an f32 vector with opts.direction.
optsoptional GradOptions: the generated name and, for a vector parameter, the direction.

Return value

GradResult

the module with the derivative added, and the derivative’s name.

Exceptions

SD0118: SD0118 when the function, the parameter or a construct the parameter reaches cannot be differentiated; the message names it.

Description

The new function takes the same parameters as fn and returns d fn / d param at them, with the type of fn’s result. It differentiates f32, float-vector and float-matrix arithmetic, the component-wise builtins (sin, exp, pow, mix, smoothstep, dot, length, normalize and the rest), if, switch and for, and calls to other functions of the module. floor, ceil, round, trunc, sign and step have a zero derivative. A construct with no derivative rule, a texture sample or a derivative builtin among them, is refused by name when the parameter reaches it, never given a zero derivative.

Examples

Example

import { compile, compileModule, grad } from 'typeshade'

const { module } = compile(`"use typeshade"
export function f(x: f32, k: f32): f32 {
  return sin(k * x) * k
}`)
const d = grad(module, 'f', 'k')
compileModule(d.module).fns[d.name]!(0.5, 2) // cos(1) * 0.5 * 2 + sin(1)

In the guide

The CPU oracle

Source

src/core/passes/grad.ts, line 93, at commit 26de7be8

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