math/aarch64/sve: more updates in exps.

Update comments and coefficient indices for consistency and
correctness. No change in codegen.
Fix copyright years in inline helper.

Author: blapie

math/aarch64/sve/exp.c

@@ -11,16 +11,15 @@
 
 static const struct data
 {
-  double poly_even[2];
+  double c0, c2;
   double c1, c3;
   double ln2_hi, ln2_lo, inv_ln2, shift, thres;
 
 } data = {
-  .poly_even = { /* ulp error: 0.53.  */
-	    0x1.fffffffffdbcdp-2,  0x1.555573c6a9f7dp-5,
-	   },
-      .c1 = 0x1.555555555444cp-3,
-      .c3 = 0x1.1111266d28935p-7,
+  .c0 = 0x1.fffffffffdbcdp-2,
+  .c1 = 0x1.555555555444cp-3,
+  .c2 = 0x1.555573c6a9f7dp-5,
+  .c3 = 0x1.1111266d28935p-7,
   .ln2_hi = 0x1.62e42fefa3800p-1,
   .ln2_lo = 0x1.ef35793c76730p-45,
   /* 1/ln2.  */
@@ -49,13 +48,13 @@ special_case (svbool_t pg, svfloat64_t s, svfloat64_t y, svfloat64_t n)
   svuint64_t b
       = svdup_u64_z (p_sign, SpecialOffset); /* Inactive lanes set to 0.  */
 
-  /* Set s1 to generate overflow depending on sign of exponent n.  */
-  svfloat64_t s1 = svreinterpret_f64 (
-      svsubr_x (pg, b, SpecialBias1)); /* 0x70...0 - b.  */
-  /* Offset s to avoid overflow in final result if n is below threshold.  */
+  /* Set s1 to generate overflow depending on sign of exponent n,
+     ie. s1 = 0x70...0 - b.  */
+  svfloat64_t s1 = svreinterpret_f64 (svsubr_x (pg, b, SpecialBias1));
+  /* Offset s to avoid overflow in final result if n is below threshold.
+     ie. s2 = as_u64 (s) - 0x3010...0 + b.  */
   svfloat64_t s2 = svreinterpret_f64 (
-      svadd_x (pg, svsub_x (pg, svreinterpret_u64 (s), SpecialBias2),
-	       b)); /* as_u64 (s) - 0x3010...0 + b.  */
+      svadd_x (pg, svsub_x (pg, svreinterpret_u64 (s), SpecialBias2), b));
 
   /* |n| > 1280 => 2^(n) overflows.  */
   svbool_t p_cmp = svacgt (pg, n, 1280.0);
@@ -104,8 +103,8 @@ svfloat64_t SV_NAME_D1 (exp) (svfloat64_t x, const svbool_t pg)
 
   /* y = exp(r) - 1 ~= r + C0 r^2 + C1 r^3 + C2 r^4 + C3 r^5.  */
   svfloat64_t r2 = svmul_x (svptrue_b64 (), r, r);
-  svfloat64_t p01 = svmla_lane (sv_f64 (d->poly_even[0]), r, c13, 0);
-  svfloat64_t p23 = svmla_lane (sv_f64 (d->poly_even[1]), r, c13, 1);
+  svfloat64_t p01 = svmla_lane (sv_f64 (d->c0), r, c13, 0);
+  svfloat64_t p23 = svmla_lane (sv_f64 (d->c2), r, c13, 1);
   svfloat64_t p04 = svmla_x (pg, p01, p23, r2);
   svfloat64_t y = svmla_x (pg, r, p04, r2);
 

math/aarch64/sve/exp10.c

@@ -13,19 +13,19 @@
 
 static const struct data
 {
-  double poly_even[2];
-  double c0, c2, c1, c3, c5;
+  double c1, c3, c2, c4, c0;
   double shift, log10_2, log2_10_hi, log2_10_lo, scale_thres, special_bound;
 } data = {
   /* Coefficients generated using Remez algorithm.
      rel error: 0x1.9fcb9b3p-60
      abs error: 0x1.a20d9598p-60 in [ -log10(2)/128, log10(2)/128 ]
      max ulp err 0.52 +0.5.  */
-  .poly_even = { 0x1.53524c73cd32ap1, 0x1.2bd77b1361ef6p0 },
+  .c0 = 0x1.26bb1bbb55516p1,
+  .c1 = 0x1.53524c73cd32ap1,
+  .c2 = 0x1.0470591daeafbp1,
+  .c3 = 0x1.2bd77b1361ef6p0,
+  .c4 = 0x1.142b5d54e9621p-1,
   /* 1.5*2^46+1023. This value is further explained below.  */
-  .c1 = 0x1.0470591daeafbp1,
-  .c3 = 0x1.142b5d54e9621p-1,
-  .c5 = 0x1.26bb1bbb55516p1,
   .shift = 0x1.800000000ffc0p+46,
   .log10_2 = 0x1.a934f0979a371p1,     /* 1/log2(10).  */
   .log2_10_hi = 0x1.34413509f79ffp-2, /* log2(10).  */
@@ -95,14 +95,14 @@ svfloat64_t SV_NAME_D1 (exp10) (svfloat64_t x, svbool_t pg)
      comes at significant performance cost.  */
   svuint64_t u = svreinterpret_u64 (z);
   svfloat64_t scale = svexpa (u);
-  svfloat64_t c13 = svld1rq (svptrue_b64 (), &d->c1);
+  svfloat64_t c24 = svld1rq (svptrue_b64 (), &d->c2);
   /* Approximate exp10(r) using polynomial.  */
   svfloat64_t r2 = svmul_x (svptrue_b64 (), r, r);
-  svfloat64_t p01 = svmla_lane (sv_f64 (d->poly_even[0]), r, c13, 0);
-  svfloat64_t p23 = svmla_lane (sv_f64 (d->poly_even[1]), r, c13, 1);
-  svfloat64_t p04 = svmla_x (pg, p01, p23, r2);
+  svfloat64_t p12 = svmla_lane (sv_f64 (d->c1), r, c24, 0);
+  svfloat64_t p34 = svmla_lane (sv_f64 (d->c3), r, c24, 1);
+  svfloat64_t p14 = svmla_x (pg, p12, p34, r2);
 
-  svfloat64_t y = svmla_x (pg, svmul_x (svptrue_b64 (), r, d->c5), r2, p04);
+  svfloat64_t y = svmla_x (pg, svmul_x (svptrue_b64 (), r, d->c0), r2, p14);
 
   /* Assemble result as exp10(x) = 2^n * exp10(r).  If |x| > SpecialBound
      multiplication may overflow, so use special case routine.  */

math/aarch64/sve/exp2.c

@@ -16,18 +16,15 @@
 
 static const struct data
 {
-  double poly_even[2];
+  double c0, c2;
   double c1, c3;
   double shift, big_bound, uoflow_bound;
 } data = {
   /* Coefficients are computed using Remez algorithm with
      minimisation of the absolute error.  */
-  .poly_even = { 0x1.62e42fefa3686p-1, 0x1.c6b09b16de99ap-5,
-	     },
-      .c1 =  0x1.ebfbdff82c241p-3,
-      .c3 = 0x1.3b2abf5571ad8p-7,
-  .shift = 0x1.8p52 / N,
-  .uoflow_bound = UOFlowBound,
+  .c0 = 0x1.62e42fefa3686p-1, .c1 = 0x1.ebfbdff82c241p-3,
+  .c2 = 0x1.c6b09b16de99ap-5, .c3 = 0x1.3b2abf5571ad8p-7,
+  .shift = 0x1.8p52 / N,      .uoflow_bound = UOFlowBound,
   .big_bound = BigBound,
 };
 
@@ -93,10 +90,10 @@ svfloat64_t SV_NAME_D1 (exp2) (svfloat64_t x, svbool_t pg)
 
   svfloat64_t c13 = svld1rq (svptrue_b64 (), &d->c1);
   /* Approximate exp2(r) using polynomial.  */
-  /* y = exp(r) - 1 ~= r + C0 r^2 + C1 r^3 + C2 r^4 + C3 r^5.  */
+  /* y = exp2(r) - 1 ~= C0 r + C1 r^2 + C2 r^3 + C3 r^4.  */
   svfloat64_t r2 = svmul_x (svptrue_b64 (), r, r);
-  svfloat64_t p01 = svmla_lane (sv_f64 (d->poly_even[0]), r, c13, 0);
-  svfloat64_t p23 = svmla_lane (sv_f64 (d->poly_even[1]), r, c13, 1);
+  svfloat64_t p01 = svmla_lane (sv_f64 (d->c0), r, c13, 0);
+  svfloat64_t p23 = svmla_lane (sv_f64 (d->c2), r, c13, 1);
   svfloat64_t p = svmla_x (pg, p01, p23, r2);
   svfloat64_t y = svmul_x (svptrue_b64 (), r, p);
   /* Assemble exp2(x) = exp2(r) * scale.  */

math/aarch64/sve/sv_expf_inline.h

@@ -2,7 +2,7 @@
  * SVE helper for single-precision routines which calculate exp(x) and do
  * not need special-case handling
  *
- * Copyright (c) 2023-2024, Arm Limited.
+ * Copyright (c) 2023-2025, Arm Limited.
  * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
  */