Go Assembly by Example: Arcsin

The following example is the implementation of the Arcsin function (the inverse of sin) taken from the standard Go library.

package main
import (
    "fmt"
)
func Asin(x float64) float64
func main() {
    fmt.Println(Asin(1))
}

This #include is required to use Go Assembly’s constants like NOSPLIT. Otherwise their associated number can be used instead (NOSPLIT=4).

#include "textflag.h"

In this example, we use the TEXT instruction with 3 arguments instead of 2. The new argument NOSPLIT is an optimization to warn the compiler that no expansion of the stack will be needed. Indeed, the third argument indicates a stack of 0 bytes.

TEXT ·Asin(SB),NOSPLIT,$0-16

To implement the Arcsin function on a float64 argument, the FPU registers will be used. FMOVD sets F0 and F1 to the function’s input x.

  FMOVD   x+0(FP), F0
  FMOVD   F0, F1
  FMULD   F0, F0

FLD1 pushes +1.0 onto the FPU stack. This makes F0 = 1, F1 = F0 and F2 = F1.

  FLD1

FSUBRDP substracts F0 to F1 and stores it in F1. It then pops the FPU stack, this makes F0 = F1, F1 = F2 and F2 = NaN.
In other words: F0 = 1-x*x and F1 = x.

  FSUBRDP F0, F1

FSQRT computes the square root of F0 and stores it in F0.

  FSQRT

FPATAN computes arctan(F1/F0) and stores it in F1, then it pops the FPU stack placing the result in F0 and setting F1 to NaN.
This gives us arctan(x / sqrt(1 - x * x)) which is a way to compute the arcsin function on x.

  FPATAN

FMOVDP moves the result to the return address (the memory offset from FP after the argument of 64-bit) and pops the FPU stack, getting rid of the last FPU value F0.

  FMOVDP  F0, ret+8(FP)
  RET

Next example: Sync Atomic.