complex: Fix expm1 formula computing exp(z-1) instead of exp(z)-1

The complex implementation of expm1(z) incorrectly computed e^(z-1)
instead of e^z - 1. Added tests for complex expm1 to prevent regression.

Author: duncanita

AUTHORS

@@ -16,6 +16,7 @@ This software was brought to you by the DB48X authors below
 - Ed van Gasteren <Ed@vanGasteren.net> (Bug fixes)
 - Jerome Ibanes <jibanes@gmail.com> (Dockerfile)
 - Jesus Cano <jcanovel@gmail.com>
+- Riccardo Lucatuorto <gnuduncan@gmail.com>
 
 Copyright (c) 2022-2025, the DB48X authors
 

doc/0-Overview.md

@@ -825,6 +825,7 @@ Additional contributors to the project include (in order of appearance):
 * Ed van Gasteren (Ed@vanGasteren.net) (Bug fixes)
 * Jerome Ibanes (jibanes@gmail.com) (Dockerfile)
 * Jesus Cano (jcanovel@gmail.com) (bug fixes)
+* Riccardo Lucatuorto (gnuduncan@gmail.com)
 
 The authors would like to acknowledge
 

help/db48x.md

@@ -767,6 +767,7 @@ Additional contributors to the project include (in order of appearance):
 * Ed van Gasteren (Ed@vanGasteren.net) (Bug fixes)
 * Jerome Ibanes (jibanes@gmail.com) (Dockerfile)
 * Jesus Cano (jcanovel@gmail.com) (bug fixes)
+* Riccardo Lucatuorto (gnuduncan@gmail.com)
 
 The authors would like to acknowledge
 

help/db50x.md

@@ -776,6 +776,7 @@ Additional contributors to the project include (in order of appearance):
 * Ed van Gasteren (Ed@vanGasteren.net) (Bug fixes)
 * Jerome Ibanes (jibanes@gmail.com) (Dockerfile)
 * Jesus Cano (jcanovel@gmail.com) (bug fixes)
+* Riccardo Lucatuorto (gnuduncan@gmail.com)
 
 The authors would like to acknowledge
 

src/complex.cc

@@ -1266,13 +1266,14 @@ COMPLEX_BODY(ln1p)
     return ln(one + z);
 }
 
+
 COMPLEX_BODY(expm1)
 // ----------------------------------------------------------------------------
 //   Complex implementation of expm1
 // ----------------------------------------------------------------------------
 {
     complex_g one = complex::make(1, 0);
-    return exp(z - one);
+    return exp(z) - one;
 }
 
 

src/tests.cc

@@ -5101,6 +5101,18 @@ void tests::complex_functions()
     test(ID_exp)
         .expect("18.43908 89145 85774 62∡0.86217 00546 67226 34884ʳ");
 
+    step("Complex exponential minus 1 (zero)");
+    test(CLEAR, "0+0ⅈ expm1", ENTER)
+        .expect("0+0ⅈ");  // expm1(0) = e^0 - 1 = 0
+
+    step("Complex exponential minus 1 (real)");
+    test(CLEAR, "1+0ⅈ expm1", ENTER)
+        .match("1\\.71828.*\\+0ⅈ");  // e - 1
+
+    step("Complex exponential minus 1 (imaginary)");
+    test(CLEAR, "0+3.14159265358979323846ⅈ expm1", ENTER)
+        .match("-2\\..*ⅈ");  // expm1(πi) ≈ -2 (with tiny floating point error)
+
     step("Power");
     test(CLEAR, "3+7ⅈ", ENTER, "2-3ⅈ", ID_pow)
         .expect("1 916.30979 15541 96293 8∡2.52432 98723 79583 8639ʳ");