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PingTakPeterTangPingTakPeterTang
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added double-precision erf function
1 parent 8e54234 commit d57e6f0

9 files changed

+380
-4
lines changed

‎CMakeLists.txt

+2
Original file line numberDiff line numberDiff line change
@@ -35,6 +35,8 @@ set(PROJECT_SOURCES
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${CMAKE_CURRENT_SOURCE_DIR}/src/rvvlm_cbrtDI.c
3636
${CMAKE_CURRENT_SOURCE_DIR}/src/rvvlm_cdfnormD.c
3737
${CMAKE_CURRENT_SOURCE_DIR}/src/rvvlm_cdfnormDI.c
38+
${CMAKE_CURRENT_SOURCE_DIR}/src/rvvlm_erfD.c
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${CMAKE_CURRENT_SOURCE_DIR}/src/rvvlm_erfDI.c
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${CMAKE_CURRENT_SOURCE_DIR}/src/rvvlm_erfcD.c
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${CMAKE_CURRENT_SOURCE_DIR}/src/rvvlm_erfcDI.c
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${CMAKE_CURRENT_SOURCE_DIR}/src/rvvlm_expD_tbl.c

‎include/rvvlm.h

+11
Original file line numberDiff line numberDiff line change
@@ -250,6 +250,13 @@ union sui64_fp64 {
250250
#define RVVLM_CDFNORMDI_VSET_CONFIG "rvvlm_fp64m1.h"
251251
#define RVVLM_CDFNORMDI_STD rvvlm_cdfnormI
252252

253+
// FP64 erf function configuration
254+
#define RVVLM_ERFD_VSET_CONFIG "rvvlm_fp64m2.h"
255+
#define RVVLM_ERFD_STD rvvlm_erf
256+
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#define RVVLM_ERFDI_VSET_CONFIG "rvvlm_fp64m2.h"
258+
#define RVVLM_ERFDI_STD rvvlm_erfI
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253260
// FP64 erfc function configuration
254261
#define RVVLM_ERFCD_VSET_CONFIG "rvvlm_fp64m1.h"
255262
#define RVVLM_ERFCD_STD rvvlm_erfc
@@ -482,6 +489,10 @@ void RVVLM_CDFNORMD_STD(size_t x_len, const double *x, double *y);
482489
void RVVLM_CDFNORMDI_STD(size_t x_len, const double *x, size_t stride_x,
483490
double *y, size_t stride_y);
484491

492+
void RVVLM_ERFD_STD(size_t x_len, const double *x, double *y);
493+
void RVVLM_ERFDI_STD(size_t x_len, const double *x, size_t stride_x, double *y,
494+
size_t stride_y);
495+
485496
void RVVLM_ERFCD_STD(size_t x_len, const double *x, double *y);
486497
void RVVLM_ERFCDI_STD(size_t x_len, const double *x, size_t stride_x, double *y,
487498
size_t stride_y);

‎include/rvvlm_erfD.inc.h

+219
Original file line numberDiff line numberDiff line change
@@ -0,0 +1,219 @@
1+
// SPDX-FileCopyrightText: 2023 Rivos Inc.
2+
//
3+
// SPDX-License-Identifier: Apache-2.0
4+
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#if (STRIDE == UNIT_STRIDE)
6+
#define F_VER1 RVVLM_ERFD_STD
7+
#else
8+
#define F_VER1 RVVLM_ERFDI_STD
9+
#endif
10+
11+
#include <fenv.h>
12+
13+
// T is 2.0
14+
#define T 0x1.0p+1
15+
16+
// For x in [0, T] odd-polynomial
17+
// coefficients P_1 to P_17 are in fixed-point
18+
// scaled so that they have high precision
19+
#define P_1 0x120dd750429b6d0f // Q60
20+
#define P_3 -0x1812746b0379e00c // Q62
21+
#define P_5 0x1ce2f21a04292b5f // Q64
22+
#define P_7 -0x1b82ce31281b38e1 // Q66
23+
#define P_9 0x1565bcd0dd0bcd58 // Q68
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#define P_11 -0xe016d9f815a019d // Q70
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#define P_13 0x7e68c976c0ebcdc // Q72
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#define P_15 -0x3e9a49c76e6ee9a // Q74
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#define P_17 0x1b9e64a589f8da9 // Q76
28+
#define P_19 -0x1.5f70cd90f1878p-23
29+
#define P_21 0x1.fca2b5f17c85ap-27
30+
#define P_23 -0x1.514eafaeffc30p-30
31+
#define P_25 0x1.9b3583b6b826dp-34
32+
#define P_27 -0x1.c97ffcf4f4e22p-38
33+
#define P_29 0x1.c2f4a46d3297dp-42
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#define P_31 -0x1.6ef3c7000b58bp-46
35+
#define P_33 0x1.ac36453182837p-51
36+
#define P_35 -0x1.0482966738f0ep-56
37+
38+
// For x in (T, 6.0], general polynomial
39+
// Coefficients Q_0 through Q_8 are in fixed points
40+
#define Q_0 0xffff87b6641370f // Q60
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#define Q_1 -0x9062a79f9b29022 // Q62
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#define Q_2 -0x11dc7e40e4efb77d // Q64
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#define Q_3 -0x1dd1004e1f59ed4 // Q66
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#define Q_4 0x1980c051527d41e7 // Q68
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#define Q_5 0x902cddcb829790b // Q70
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#define Q_6 -0x33d6f572cdbfa228 // Q72
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#define Q_7 0x425f9974bef87221 // Q74
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#define Q_8 -0x5363e91dfca5d4df // Q76
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#define Q_9 0x1.b5eea4ad8cdbfp-16
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#define Q_10 -0x1.ded0a34468c8cp-18
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#define Q_11 0x1.af4968b4d634ap-20
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#define Q_12 -0x1.51de51c57f11ap-22
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#define Q_13 0x1.cbbf535e64b65p-25
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#define Q_14 -0x1.025a03d4fdf7bp-27
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#define Q_15 0x1.c735f1e16e8cdp-31
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#define Q_16 -0x1.2de00f5eeee49p-34
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#define Q_17 0x1.219bdcb68d070p-38
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#define Q_18 -0x1.7b5fc54357bcfp-43
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#define Q_19 0x1.301ac8caec6e3p-48
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#define Q_20 -0x1.c3232aa28d427p-55
61+
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// The error function erf is an odd function: erf(-x) = -erf(x)
63+
// and thus we compute erf(|x|) and restore the sign at the end.
64+
// For x >= 6, erf(x) rounds to 1.0
65+
// The algorithm uses two approximation methods on [0, T], and
66+
// (T, 6.]. For the first region, we approximate with an odd
67+
// polynomial. For the second region, the polynomial used actually
68+
// approximates (erfc(x))^(1/8). The desired result is 1 - (poly(x))^8
69+
// Some algorithm for erf approximates log(erfc(x)) for x large. But
70+
// this requires an evaluation of expm1(y) after the polynomial approximation.
71+
// We essentially replaced the the cost of expm1 with 3 multiplications.
72+
void F_VER1(API) {
73+
size_t vlen;
74+
VFLOAT vx, vx_orig, vy, vy_special;
75+
VBOOL special_args;
76+
77+
SET_ROUNDTONEAREST;
78+
// stripmining over input arguments
79+
for (; _inarg_n > 0; _inarg_n -= vlen) {
80+
vlen = VSET(_inarg_n);
81+
vx = VFLOAD_INARG1(vlen);
82+
vx_orig = vx;
83+
84+
// Handle Inf and NaN
85+
EXCEPTION_HANDLING_ERF(vx, special_args, vy_special, vlen);
86+
87+
// At this point, vx is 0 or >= 2^(-30). Can saturate vx at 6.0
88+
vx = __riscv_vfsgnj(vx, fp_posOne, vlen);
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vx = __riscv_vfmin(vx, 0x1.8p+2, vlen);
90+
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VBOOL x_gt_T = __riscv_vmfgt(vx, T, vlen);
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VFLOAT r, delta_r, xsq;
93+
xsq = __riscv_vfmul(vx, vx, vlen);
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r = __riscv_vmerge(xsq, vx, x_gt_T, vlen);
95+
delta_r = I_AS_F(__riscv_vxor(F_AS_I(delta_r), F_AS_I(delta_r), vlen));
96+
delta_r = __riscv_vmerge(__riscv_vfmsub(vx, vx, xsq, vlen), delta_r, x_gt_T,
97+
vlen);
98+
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// Compute polynomial in r.
100+
// For x in [0, T], r = x*x
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// the polynomial in r is x*(p_1 + p_3 r + p_5 r^2 ... + p_35 r^22)
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// For x in (T, 6], r = x
103+
// the polynomial in r is q_0 + q_1 r + q_2 r^2 + ... + q_20 r^20
104+
// The higher order of the polynomial is computed in floating point;
105+
// the lower order part (more significant) are then done in fixed point
106+
// Both lower parts have 17 coefficients and so can be done with the
107+
// exact instruction sequence using the corresponding coefficients
108+
109+
VFLOAT poly = PSTEP(Q_18, r, PSTEP(Q_19, Q_20, r, vlen), vlen);
110+
111+
VFLOAT poly_right;
112+
poly_right =
113+
I_AS_F(__riscv_vxor(F_AS_I(poly_right), F_AS_I(poly_right), vlen));
114+
poly_right = __riscv_vmerge(poly_right, poly, x_gt_T, vlen);
115+
116+
poly_right = PSTEP_ab(x_gt_T, Q_17, P_35, r, poly_right, vlen);
117+
poly_right = PSTEP_ab(x_gt_T, Q_16, P_33, r, poly_right, vlen);
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poly_right = PSTEP_ab(x_gt_T, Q_15, P_31, r, poly_right, vlen);
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poly_right = PSTEP_ab(x_gt_T, Q_14, P_29, r, poly_right, vlen);
120+
poly_right = PSTEP_ab(x_gt_T, Q_13, P_27, r, poly_right, vlen);
121+
122+
VFLOAT r4 = __riscv_vfmul(r, r, vlen);
123+
r4 = __riscv_vfmul(r4, r4, vlen);
124+
125+
VFLOAT poly_left = VFMV_VF(P_25, vlen);
126+
poly_left = __riscv_vfmerge(poly_left, Q_12, x_gt_T, vlen);
127+
poly_left = PSTEP_ab(x_gt_T, Q_11, P_23, r, poly_left, vlen);
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poly_left = PSTEP_ab(x_gt_T, Q_10, P_21, r, poly_left, vlen);
129+
poly_left = PSTEP_ab(x_gt_T, Q_9, P_19, r, poly_left, vlen);
130+
131+
poly = __riscv_vfmadd(poly_right, r4, poly_left, vlen);
132+
VINT POLY = __riscv_vfcvt_x(__riscv_vfmul(poly, 0x1.0p78, vlen), vlen);
133+
134+
VINT R = __riscv_vfcvt_x(__riscv_vfmul(r, 0x1.0p60, vlen), vlen);
135+
VINT D_R = __riscv_vfcvt_x(__riscv_vfmul(delta_r, 0x1.0p60, vlen), vlen);
136+
R = __riscv_vadd(R, D_R, vlen);
137+
// POLY is in Q78, R is in Q60
138+
139+
VINT COEFF = __riscv_vmerge(VMVI_VX(P_17, vlen), Q_8, x_gt_T, vlen);
140+
POLY = __riscv_vsll(__riscv_vsmul(R, POLY, 1, vlen), 1, vlen);
141+
POLY = __riscv_vadd(POLY, COEFF, vlen); // Q76
142+
143+
COEFF = __riscv_vmerge(VMVI_VX(P_15, vlen), Q_7, x_gt_T, vlen);
144+
POLY = __riscv_vsll(__riscv_vsmul(R, POLY, 1, vlen), 1, vlen);
145+
POLY = __riscv_vadd(POLY, COEFF, vlen); // Q74
146+
147+
COEFF = __riscv_vmerge(VMVI_VX(P_13, vlen), Q_6, x_gt_T, vlen);
148+
POLY = __riscv_vsll(__riscv_vsmul(R, POLY, 1, vlen), 1, vlen);
149+
POLY = __riscv_vadd(POLY, COEFF, vlen); // Q72
150+
151+
COEFF = __riscv_vmerge(VMVI_VX(P_11, vlen), Q_5, x_gt_T, vlen);
152+
POLY = __riscv_vsll(__riscv_vsmul(R, POLY, 1, vlen), 1, vlen);
153+
POLY = __riscv_vadd(POLY, COEFF, vlen); // Q70
154+
155+
COEFF = __riscv_vmerge(VMVI_VX(P_9, vlen), Q_4, x_gt_T, vlen);
156+
POLY = __riscv_vsll(__riscv_vsmul(R, POLY, 1, vlen), 1, vlen);
157+
POLY = __riscv_vadd(POLY, COEFF, vlen); // Q68
158+
159+
COEFF = __riscv_vmerge(VMVI_VX(P_7, vlen), Q_3, x_gt_T, vlen);
160+
POLY = __riscv_vsll(__riscv_vsmul(R, POLY, 1, vlen), 1, vlen);
161+
POLY = __riscv_vadd(POLY, COEFF, vlen); // Q66
162+
163+
COEFF = __riscv_vmerge(VMVI_VX(P_5, vlen), Q_2, x_gt_T, vlen);
164+
POLY = __riscv_vsll(__riscv_vsmul(R, POLY, 1, vlen), 1, vlen);
165+
POLY = __riscv_vadd(POLY, COEFF, vlen); // Q64
166+
167+
COEFF = __riscv_vmerge(VMVI_VX(P_3, vlen), Q_1, x_gt_T, vlen);
168+
POLY = __riscv_vsll(__riscv_vsmul(R, POLY, 1, vlen), 1, vlen);
169+
POLY = __riscv_vadd(POLY, COEFF, vlen); // Q62
170+
171+
COEFF = __riscv_vmerge(VMVI_VX(P_1, vlen), Q_0, x_gt_T, vlen);
172+
POLY = __riscv_vsll(__riscv_vsmul(R, POLY, 1, vlen), 1, vlen);
173+
POLY = __riscv_vadd(POLY, COEFF, vlen); // Q60
174+
175+
VINT POLY_RIGHT = __riscv_vsll(POLY, 3, vlen); // Q63
176+
POLY_RIGHT = __riscv_vsmul(POLY_RIGHT, POLY_RIGHT, 1, vlen);
177+
POLY_RIGHT = __riscv_vsmul(POLY_RIGHT, POLY_RIGHT, 1, vlen);
178+
POLY_RIGHT = __riscv_vsmul(POLY_RIGHT, POLY_RIGHT, 1, vlen);
179+
// POLY_RIGHT is POLY^8
180+
181+
// convert x to fixed-point Q62+m, 2^m <= x < 2^(m+1)
182+
VINT e = __riscv_vsra(F_AS_I(vx), MAN_LEN, vlen);
183+
e = __riscv_vmax(e, EXP_BIAS - 40, vlen);
184+
e = __riscv_vrsub(e, 2 * EXP_BIAS + 62, vlen);
185+
VFLOAT scale = I_AS_F(__riscv_vsll(e, MAN_LEN, vlen));
186+
// scale is 2^(62-m), X is x in Q_(62-m)
187+
VINT X = __riscv_vfcvt_x(__riscv_vfmul(vx, scale, vlen), vlen);
188+
POLY = __riscv_vsmul(X, POLY, 1, vlen);
189+
// X is Q_(62-m) POLY is now Q_(59-m)
190+
// x in [0, T], POLY is result in Q 59-m
191+
192+
// x in (T, 6], result is 1 - 2^(-63) POLY_RIGHT
193+
// that is, 2^(-62)(2^62 - (POLY_RIGHT>>1))
194+
INT one = (1LL << 62);
195+
POLY_RIGHT = __riscv_vsra(POLY_RIGHT, 1, vlen);
196+
POLY_RIGHT = __riscv_vrsub(POLY_RIGHT, one, vlen);
197+
198+
POLY = __riscv_vmerge(POLY, POLY_RIGHT, x_gt_T, vlen);
199+
// POLY contains the result in fixed point
200+
// scale is 59-m for x in [0, T] and 62 for x > T
201+
202+
e = __riscv_vrsub(e, 2 * EXP_BIAS + 3, vlen);
203+
// exponent field of 2^(-59+m)
204+
e = __riscv_vmerge(e, EXP_BIAS - 62, x_gt_T, vlen);
205+
scale = I_AS_F(__riscv_vsll(e, MAN_LEN, vlen));
206+
207+
vy = __riscv_vfcvt_f(POLY, vlen);
208+
vy = __riscv_vfmul(vy, scale, vlen);
209+
vy = __riscv_vfsgnj(vy, vx_orig, vlen);
210+
211+
vy = __riscv_vmerge(vy, vy_special, special_args, vlen);
212+
// copy vy into y and increment addr pointers
213+
VFSTORE_OUTARG1(vy, vlen);
214+
215+
INCREMENT_INARG1(vlen);
216+
INCREMENT_OUTARG1(vlen);
217+
}
218+
RESTORE_FRM;
219+
}

‎include/rvvlm_errorfuncsD.h

+31
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@@ -34,6 +34,37 @@ static_assert(false, "Must define COMPILE_FOR_{ERFC,ERF,CDFNORM}" __FILE__);
3434
} \
3535
} while (0)
3636

37+
// ALPHA is 2/sqrt(pi), erf'(0) derivative of erf(x) at x=0
38+
#define ALPHA_HI 0x1.20dd750429b6dp+0
39+
#define ALPHA_LO 0x1.1ae3a914fed80p-56
40+
41+
#define EXCEPTION_HANDLING_ERF(vx, special_args, vy_special, vlen) \
42+
do { \
43+
VUINT vclass = __riscv_vfclass((vx), (vlen)); \
44+
VUINT expo_x = __riscv_vsrl(F_AS_U((vx)), MAN_LEN, (vlen)); \
45+
expo_x = __riscv_vand(expo_x, 0x7FF, (vlen)); \
46+
IDENTIFY(vclass, class_NaN | class_Inf, (special_args), (vlen)); \
47+
VBOOL expo_small = __riscv_vmsltu(expo_x, EXP_BIAS - 30, (vlen)); \
48+
(special_args) = __riscv_vmor((special_args), expo_small, (vlen)); \
49+
UINT nb_special_args = __riscv_vcpop((special_args), (vlen)); \
50+
if (nb_special_args > 0) { \
51+
VBOOL id_mask; \
52+
IDENTIFY(vclass, class_NaN, id_mask, (vlen)); \
53+
(vy_special) = __riscv_vfadd(id_mask, (vx), (vx), (vlen)); \
54+
IDENTIFY(vclass, class_posInf, id_mask, (vlen)); \
55+
(vy_special) = \
56+
__riscv_vfmerge((vy_special), Y_AT_posINF, id_mask, (vlen)); \
57+
IDENTIFY(vclass, class_negInf, id_mask, (vlen)); \
58+
(vy_special) = \
59+
__riscv_vfmerge((vy_special), Y_AT_negINF, id_mask, (vlen)); \
60+
VFLOAT vy_small = __riscv_vfmul(expo_small, (vx), ALPHA_LO, (vlen)); \
61+
vy_small = __riscv_vfmacc(expo_small, vy_small, ALPHA_HI, (vx), (vlen)); \
62+
(vy_special) = \
63+
__riscv_vmerge((vy_special), vy_small, expo_small, (vlen)); \
64+
(vx) = __riscv_vfmerge((vx), fp_posZero, (special_args), (vlen)); \
65+
} \
66+
} while (0)
67+
3768
#define LOG2_HI 0x1.62e42fefa39efp-1
3869
#define LOG2_LO 0x1.abc9e3b39803fp-56
3970
#define NEG_LOG2_INV -0x1.71547652b82fep+0

‎src/rvvlm_erfD.c

+17
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@@ -0,0 +1,17 @@
1+
// SPDX-FileCopyrightText: 2023 Rivos Inc.
2+
//
3+
// SPDX-License-Identifier: Apache-2.0
4+
5+
#include <riscv_vector.h>
6+
#include <stdio.h>
7+
8+
#include "rvvlm.h"
9+
#define API_SIGNATURE API_SIGNATURE_11
10+
#define STRIDE UNIT_STRIDE
11+
12+
#include RVVLM_ERFD_VSET_CONFIG
13+
14+
#define COMPILE_FOR_ERF
15+
#include "rvvlm_errorfuncsD.h"
16+
17+
#include "rvvlm_erfD.inc.h"

‎src/rvvlm_erfDI.c

+17
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@@ -0,0 +1,17 @@
1+
// SPDX-FileCopyrightText: 2023 Rivos Inc.
2+
//
3+
// SPDX-License-Identifier: Apache-2.0
4+
5+
#include <riscv_vector.h>
6+
#include <stdio.h>
7+
8+
#include "rvvlm.h"
9+
#define API_SIGNATURE API_SIGNATURE_11
10+
#define STRIDE GENERAL_STRIDE
11+
12+
#include RVVLM_ERFDI_VSET_CONFIG
13+
14+
#define COMPILE_FOR_ERF
15+
#include "rvvlm_errorfuncsD.h"
16+
17+
#include "rvvlm_erfD.inc.h"

‎test/CMakeLists.txt

+6-4
Original file line numberDiff line numberDiff line change
@@ -78,10 +78,12 @@ set(TEST_SOURCES
7878
# ${CMAKE_CURRENT_SOURCE_DIR}/src/test_atanhI.cpp
7979
# ${CMAKE_CURRENT_SOURCE_DIR}/src/test_cbrt.cpp
8080
# ${CMAKE_CURRENT_SOURCE_DIR}/src/test_cbrtI.cpp
81-
${CMAKE_CURRENT_SOURCE_DIR}/src/test_cdfnorm.cpp
82-
${CMAKE_CURRENT_SOURCE_DIR}/src/test_cdfnormI.cpp
83-
${CMAKE_CURRENT_SOURCE_DIR}/src/test_erfc.cpp
84-
${CMAKE_CURRENT_SOURCE_DIR}/src/test_erfcI.cpp
81+
# ${CMAKE_CURRENT_SOURCE_DIR}/src/test_cdfnorm.cpp
82+
# ${CMAKE_CURRENT_SOURCE_DIR}/src/test_cdfnormI.cpp
83+
${CMAKE_CURRENT_SOURCE_DIR}/src/test_erf.cpp
84+
${CMAKE_CURRENT_SOURCE_DIR}/src/test_erfI.cpp
85+
# ${CMAKE_CURRENT_SOURCE_DIR}/src/test_erfc.cpp
86+
# ${CMAKE_CURRENT_SOURCE_DIR}/src/test_erfcI.cpp
8587
# ${CMAKE_CURRENT_SOURCE_DIR}/src/test_exp.cpp
8688
# ${CMAKE_CURRENT_SOURCE_DIR}/src/test_expI.cpp
8789
# ${CMAKE_CURRENT_SOURCE_DIR}/src/test_exp2.cpp

‎test/src/test_erf.cpp

+48
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@@ -0,0 +1,48 @@
1+
// SPDX-FileCopyrightText: 2023 Rivos Inc.
2+
//
3+
// SPDX-License-Identifier: Apache-2.0
4+
5+
#include <math.h>
6+
#include <stdio.h>
7+
8+
#include "rvvlm.h"
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#include "test_infra.h"
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#define COMMENT(comment) \
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{ printf("\n=====\t" comment "\n"); }
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int main() {
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unsigned long nb_tests;
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double x_start, x_end;
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COMMENT("erf: current chosen algorithm; reduced argument in FP64 only")
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// show_special_fp64(rvvlm_erf, "Special Value handling of this function");
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x_start = 0x1.0p-40;
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x_end = 0x1.0p-20;
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nb_tests = 40000;
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report_err_fp64(rvvlm_erf, erfl, x_start, x_end, nb_tests);
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x_start = 0x1.0p-20;
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x_end = 0x1.0p1;
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nb_tests = 40000;
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report_err_fp64(rvvlm_erf, erfl, x_start, x_end, nb_tests);
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x_start = 0x1.0p1;
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x_end = 0x1.0p2;
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nb_tests = 40000;
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report_err_fp64(rvvlm_erf, erfl, x_start, x_end, nb_tests);
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x_start = 0x1.0p2;
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x_end = 7.0;
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nb_tests = 40000;
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report_err_fp64(rvvlm_erf, erfl, x_start, x_end, nb_tests);
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x_start = -6.5;
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x_end = 6.5;
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nb_tests = 40000;
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report_err_fp64(rvvlm_erf, erfl, x_start, x_end, nb_tests);
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return 0;
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}

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