Merge pull request #503 from Gathros/euler_asm

Forward euler in x86_64

Author: Julian

contents/forward_euler_method/code/asm-x64/euler.s

@@ -0,0 +1,97 @@
+.intel_syntax noprefix
+
+.section .rodata
+  three:      .double -3.0
+  fabs_const:
+              .long   4294967295
+              .long   2147483647
+              .long   0
+              .long   0
+  inital_val: .double 1.0
+  threshold:  .double 0.01
+  timestep:   .double 0.01
+  error_fmt:  .string "%f    %f\n"
+  fmt:        .string "%d\n"
+
+.section .text
+  .global main
+  .extern printf
+  .extern exp
+
+# rdi  - array size
+# rsi  - array ptr
+# xmm0 - timestep
+solve_euler:
+  movsd  xmm1, inital_val
+  lea    rax, [rsi + 8 * rdi + 8]    # Set to end of the array
+solve_euler_loop:
+  movsd  xmm3, three                 # Set to -3.0
+  mulsd  xmm2, xmm1                  # xmm2 = -3.0 * array[i-1] * timestep
+  mulsd  xmm2, xmm0
+  subsd  xmm1, xmm2                  # xmm1 = xmm1 - xmm2
+  movsd  QWORD PTR [rsi], xmm1
+  add    rsi, 8
+  cmp    rsi, rax                    # Test if we have gone through the array
+  jne    solve_euler_loop
+solve_euler_return:
+  ret
+
+# rdi  - array size
+# rsi  - array ptr
+# xmm0 - timestep
+# xmm1 - threshold
+# RET rax - success code 0 if sucess else 1
+check_result:
+  push   r12
+  push   r13
+  xor    rax, rax                    # Return code is 0
+  xor    r12, r12                    # The index is set to 0
+  mov    r13, rdi                    # Moving array size to free rdi for printf
+  movsd  xmm2, xmm0                  # Moving timestep to free xmm0 for exp
+  jmp    loop_check
+results_loop:
+  cvtsi2sd xmm0, r12                 # Making int to a double
+  movsd  xmm3, three                 # Calculating exp(-3.0 * i * timestep)
+  mulsd  xmm0, xmm3
+  mulsd  xmm0, xmm2
+  call   exp
+  movsd  xmm3, QWORD PTR [rsi + r12 * 8] # Calculating abs(array[i] - xmm0)
+  subsd  xmm2, xmm3
+  movq   xmm3, fabs_const
+  andpd  xmm0, xmm3
+  comisd xmm0, xmm1                  # Check if abs(...) > threshold
+  jbe    if_false
+  mov    rdi, OFFSET error_fmt       # If true print out array[i] and solution
+  mov    rax, 1
+  call   printf
+  mov    rax, 1                      # and set sucess code to failed (rax = 1)
+if_false:
+  add    r12, 1
+loop_check:
+  cmp    r12, r13                    # Check if index is less the array size
+  jle    results_loop
+  pop    r13
+  pop    r12
+  ret
+
+main:
+  push   rbp
+  sub    rsp, 800                    # Making double array[100]
+  mov    rdi, 100
+  mov    rsi, rsp
+  movsd  xmm0, timestep
+  call   solve_euler                 # Calling solve_euler
+  mov    rdi, 100
+  mov    rsi, rsp
+  movsd  xmm0, timestep
+  movsd  xmm1, threshold
+  call   check_result                # Check if results are correct
+  mov    rdi, OFFSET fmt
+  mov    rsi, rax
+  xor    rax, rax
+  call   printf                      # Print out success code
+  add    rsp, 800                    # Deallocating array
+  pop    rbp
+  xor    rax, rax
+  ret
+

contents/forward_euler_method/forward_euler_method.md

@@ -126,6 +126,8 @@ Full code for the visualization follows:
 [import, lang:"fortran"](code/fortran/euler.f90)
 {% sample lang="go" %}
 [import, lang:"go"](code/golang/euler.go)
+{% sample lang="asm-x64" %}
+[import, lang:"asm-x64"](code/asm-x64/euler.s)
 {% endmethod %}
 
 <script>